GRLWEAP 2010 Background

GRLWEAP 2010 Background Report Table of Contents 1. PREFACE ......................................... ............................................................. ......................................... .................................. ............. 1 1.1 History of the Wave W ave Equation Approach ....................................... ............................................ ..... 1 1.2 Program History...................................... .......................................................... ......................................... ....................... .. 1 1.3 What’s New in GRLWEAP GRLWEAP 2010................... 2010 ........................................ ..................................... ................ 3 1.4 The Wave W ave Equation Approach ....................................... ........................................................... .................... 5 2. BASIC CONSIDERATIONS AND APPLICATIONS OF THE WAVE WAV E EQUATION ......................................... ............................................................. ......................................... ..................................... ................ 7 2.1 Energy Transfer ...................................... .......................................................... ......................................... ....................... .. 7 2.2 Preparation for a Bearing Graph Analysis ............................ ....................................... ........... 12 2.3 Preparation for a Driveability Analysis ....................................... ............................................. ...... 13 2.4 Interpretation of Wave Equation Results .............................. ......................................... ........... 14 2.5 Checking Wave Equation Results ................................... ................................................... ................ 15 3. THE WEAP ANALYSIS MODELS ....................................... ......................................................... .................. 17 3.1 Introduction......................................... ............................................................. ......................................... ......................... .... 17 3.2 Hammer Details ...................................... .......................................................... ......................................... ..................... 17 3.2.1 Working Principle of Liquid Injection Diesel Hammers .............. 17 3.2.2 Working Principle of Atomized Injection Diesel Hammers ......... 20 3.2.3 Working Principle of External Combustion Hammers Hammers ............... 20 3.2.4 Working Principle of Closed End or Double Acting Hammers ... 22

3.2.4.1 Closed End Diesel Hammers ..................... ............................... .............. .... 22 3.2.4.2 Double Acting External Combustion Hammers ...... 22 3.2.5 Drop Hammers........................................ ............................................................ .................................. .............. 23 3.2.6 Vibratory Hammers ......................... .............................................. .......................................... ..................... 25

3.2.6.1 Working Principle ............. ........................ ....................... ...................... ............... ..... 25 3.2.6.2 Limitations of Vibratory Hammer Analysis ............ ............ 26 3.2.6.3 Preliminary Recommendations for Vibratory Vibratory Hammer Analyses ............................................................... 27 3.3 Basic Hammer Models...................................... Models.......................................................... ............................... ........... 28 3.3.1 External Combustion Hammers .......................................... ................................................ ...... 29

3.3.1.1 The Ram of EC Hammers..................... ................................. .................... ........ 29 Version 2010

GRLWEAP Procedures and Models

i

3.3.1.2 Assembly of EC Hammers..................... Hammers................................ .................. ....... 29 3.3.2 Diesel Hammers ............................................... .................................................................... ........................ ... 32 3.3.3 Thermodynamic Models Models of Diesel Hammers ............................ ............................ 32

3.3.3.1 Liquid Fuel Injection (Impact Atomization) Model. 32 3.3.3.2 The Atomized Fuel Injection Model ................ ....................... ....... 36 3.3.4 Closed End Hammers (Double Acting) .................................. ..................................... ... 38

3.3.4.1 Double, Differential or Compound ECH ............ ................. ..... 38 3.3.4.2 Closed End Diesel Hammers ..................... ............................... .............. .... 39 3.3.5 Vibratory Hammer Model .................................. ...................................................... ........................ .... 40 3.3.6 Hydroblok Hammers .............................. ................................................... ................................... .............. 41 3.3.7 Drop Hammers........................................ ............................................................ .................................. .............. 42 3.3.8 Hammer Energy Losses....................................... ........................................................... ...................... 42 3.3.9 Inclined Pile Driving......................... Driving.............................................. .......................................... ..................... 43 3.3.10 Driving at the the Pile Bottom Bottom or at an Intermediate Pile Pile Location 44 3.3.11 Static Soil Column Weight ......................................... ....................................................... .............. 45 3.4 Driving System Model....................................... ........................................................... ............................... ........... 46 3.5 Pile Model ........................................ ............................................................ ........................................ ............................ ........ 48 3.6 Splice/Slack Splice/Slack Model .................................................. ....................................................................... ........................ ... 50 3.7 Soil Model ........................................ ............................................................ ........................................ ............................ ........ 51 3.7.1 The Basic Smith Static Resistance Model................................. ................................. 51 3.7.2 Soil Damping....................................... ........................................................... ...................................... .................. 53

3.7.2.1 The Basic Smith Damping Model ............................ ............................ 53 3.7.2.2 Extensions to the Damping Model ..................... ......................... .... 54 3.7.2.3

Distribution of Shaft Damping................. Damping........................... ............ .. 55

3.7.2.4

Selection of Damping Factors .................... ............................. ......... 55

3.7.3 Soil Model Extensions ....................................... ........................................................... ........................ .... 56 3.8 Numerical Procedure and Integration ...................... ........................................... ........................ ... 57 3.8.1 Time Increment ..................... .......................................... ......................................... ............................... ........... 57 3.8.2 Analysis Steps ........................................... ............................................................... ............................... ........... 58

3.8.2.1 Prediction of Pile Variable at Time j ..................... ....................... .. 58 3.8.2.2 Forces at a Given Segment ..................... ................................ ................ ..... 60 ii

GRLWEAP Procedures and Models

Version 2010

3.8.2.3 Newton's Second Second Law for Acceleration Acceleration Calculation  ............................................................................................. 61 3.8.2.4 Corrector Integration .................... ............................... ...................... .............. ... 61 3.8.2.5 Further Iterations ............... .......................... ...................... ...................... .............. ... 62 3.9 Stop Criteria......................................... ............................................................. ......................................... ........................ ... 62 3.10 Blow Count Computation - Non Residual Stress Analysis ............. 64 3.11 Residual Stress Analyses (RSA) ....................... ............................................. ............................ ...... 64 3.11.1 Introduction ............................. ................................................. .......................................... ............................ ...... 64 3.11.2 Details of the GRLWEAP RSA Procedure ...................... .............................. ........ 66 3.11.3 Additional Comments about abou t RSA ......................................... ............................................ ... 68 3.11.4 RSA Restrictions ...................................... .......................................................... ............................... ........... 69 3.12 GRLWEAP Analysis Options ....................................... ......................................................... .................. 69 3.12.1 Bearing Graph....................................... ........................................................... .................................. .............. 69 3.12.2 Inspector’s Chart: Blow Count vs. Stroke  Stroke ................................ ............................... 69 3.12.3 Driveability Analysis ...................... ........................................... ......................................... ...................... 70

3.12.3.1 Gain/Loss Factors .................. ............................. ....................... .................... ........ 71 3.12.3.2 Variable Variabl e Set-Up .......................... ............ ........................... .......................... ............. 73 3.12.3.3 Notes and Hints Hints on the Variable Variable Set-Up Analysis 75 3.12.4 Second Pile Toe ....................................... ........................................................... ............................... ........... 77 3.12.5 Two-Pile Analysis........................................ ............................................................ ............................ ........ 77 3.13 Static Geotechnical Analysis ............................. ................................................. ............................ ........ 78 3.13.1 Introduction ............................. ................................................. .......................................... ............................ ...... 78 3.13.2 Soil Type Based Method (ST) ....................................... ................................................. .......... 78 3.13.3 SPT N-value Based Method (SA) ........................................ ........................................... ... 80 3.13.4 The CPT Method in GRLWEAP ........................................ .............................................. ...... 83

3.13.4.1 Introduction ..................... ................................ ...................... ..................... .............. .... 83 3.13.4.2 Data Import Import ............................ .............. ........................... ........................... ................. ... 83 3.13.4.3 Soil Classification ..................... ................................. ...................... ................. ....... 85 3.13.4.4 Resistance calculation ............ ...................... ...................... .................... ........ 87 3.13.5 The API Method in GRLWEAP (Offshore Wave Version) ....... 88 3.13.6 Comments on GRLWEAP’s static formula methods ............... 89 Version 2010

GRLWEAP Procedures and Models

iii

3.13.7 Consideration of Pile Inclination in Static Soil Analyses .......... 91 3.13.8 Static Bending Stress Calculation of Inclined Piles ................. 91 3.14 Program Flow ................................................................................ 94 3.14.1 Bearing Graph ......................................................................... 94 3.14.2 Driveability .............................................................................. 95 3.14.3 Inspector’s Chart..................................................................... 97 3.14.4 Diesel Analysis Procedure ...................................................... 98 3.14.5 Vibratory Analysis Procedure .................................................. 99 4. INPUT INFORMATION ..................................................................... 101 4.1 Hammer Data ................................................................................ 101 4.2 Driving System Data ...................................................................... 101 4.3 Pile Data ........................................................................................ 102 4.4 Soil ................................................................................................ 105 4.5 Options .......................................................................................... 106 5. OUTPUT AND HELP INFORMATION ............................................. 111 5.1 Numerical Output........................................................................... 111 5.2 Bearing Graph ............................................................................... 112 5.3 Driveability ..................................................................................... 112 5.4 Variables vs. Time ......................................................................... 112 5.5 Stress Maxima Range Ouput for Fatigue Studies .......................... 113 5.6 Help ............................................................................................... 114 6. CONCLUSIONS AND RECOMMENDATIONS ................................ 117  APPENDIX A: CORRELATIONS ............................................................ 119  APPENDIX B: HAMMER MODEL DETAILS ........................................... 121 B1 Diesel Hammer Studies.................................................................. 121 B2 2002 Method for Diesel Hammer Pmax Calculation ......................... 121 B3 Measured Hammer Performance ................................................... 122  APPENDIX C: GRLWEAP FIRST STEPS .............................................. 125 Starting the Program ............................................................................ 125 Data Input ............................................................................................. 125 The Main Input Form ............................................................................ 126 Drop Down Menus ................................................................................ 126 EXAMPLE............................................................................................. 130  Appendix D: The GRLWEAP Friction Fatigue Approach.......................... 137

iv

GRLWEAP Procedures and Models

Version 2010

 APPENDIX E: REFERENCES ................................................................ 146

Version 2010

GRLWEAP Procedures and Models

v

vi

GRLWEAP Procedures and Models

Version 2010

1. PREFACE 1.1 History of the Wave Equation Approach Since the early 1950's, when E.A.L. Smith introduced the wave equation concept, this method of dynamic pile analysis has become increasingly popular and its use widespread. Computer programs were prepared by many private corporations as well as by the U.S. Department of Transportation Federal Highway Administration (FHWA). The FHWA supported work when both the Texas Transportation Institute (TTI) and the WEAP programs were published (Hirsch, et al. (1976) and Goble, et al. (1976)) and when the WEAP program was first updated (Goble, et al. (1981)). Throughout the development of this software package, PDI has strived to keep the help files updated with the most recent hammer and driving system information. This data has been submitted by hammer manufacturers and equipment sales organizations. Preparation of this data is a time-consuming effort and PDI gratefully acknowledges the effort made by all contributors. 1.2 Program History GRLWEAP developed out of the WEAP program of 1976. The original WEAP had been written by GRL in cooperation with engineers of the FHWA and the New York Department of Transportation. The software was updated in 1981, and in 1986 a major rewriting was done which resulted in WEAP86. WEAP86 also included the residual stress analysis of Hery (1983) and was applicable to both mainframe and personal computers. WEAP86 was further updated in 1987, resulting in a program nearly identical with WEAP86. However, a new hammer data file, HAMMER.ALT, was included in the package as part of an extensive study on diesel hammer performance. WEAP87 was developed, tested and documented under the sponsorship of the Federal Highway Administration. Their contribution is gratefully acknowledged. However, WEAP87 had to conform to certain limitations making further developments difficult. For this reason, further program developments, necessitated by industry developments, were made in the GRLWEAP version. The GRLWEAP package prior to 1993 consisted of several executable files that had to be invoked by the user from the DOS prompt. The 1993 release incorporated a shell program that provided a menu driven graphics interface. This menu allowed for selection of input preparation, modification, analysis, graphing, and program execution. The 1998 Windows Version and the present version of GRLWEAP basically follow the 1993 concept in that they divide the program into four distinctly Version 2010

GRLWEAP Procedures and Models

1

different sections: Input, Analysis, Output and Hammer File Maintenance. However, the program documentation was now contained in a single Report Volume. The actual “User’s Manual” exists in the form of help files that are released together with the program software. The novice may prefer to generate a hard copy of these help files for ease of use. The 2003-2005 versions included among others the following modifications: 

Two static analysis methods were added to simplify the input of resistance distribution for bearing graph analyses and the shaft resistance and end bearing input for Driveablity analyses. The soil type based ST method allows for a simple analysis where only basic soil information is available. Another method, the SA static geotechnical analysis, uses SPT N –value input of soil resistance for the Driveability analysis.



Copy and paste features were added to Depth/Modifier Input Form (D) and the Resistance Distribution Input Forms (S1 and S2) to share information between GRLWEAP and other applications, such as Excel.



The hammer information was now organized in two separate hammer database files: the PDI generated hammer file and a user generated hammer file. This will prevent the user hammer information from getting overwritten when PDI updates its hammer files. Additionally, new hammer information was added to the hammer database and to the drive system help. The hammer efficiencies were also adjusted.



 Assembly Weight input was added to Hammer Override Dialog box to allow easy override of assembly weight for external combustion hammers. This is helpful, for example, when a hammer model is available with different guides or sleeves which add substantial weight to the hammer assembly and, therefore, the static force of the hammer exerted on the soil. Gravitational acceleration input for pile and hammer allow for modification of the hammer and pile static weights to account, for example, for batter and/or buoyancy.

 Rated and maximum diesel hammer stroke are distinguished. Diesel

iterations always start with the same initial stroke, rather than the stroke from the previous analysis. Diesel hammer combustion pressures were modified. For diesel hammers with very low soil resistance values, the hammer may not run and such conditions are now more clearly identified in the output.  In the output programs the “Copy to Clipboard” command was added

to the “View” menu and variable times numerical output was modified so that it can be saved to file and processed in other programs. 2

GRLWEAP Procedures and Models

Version 2010

1.3 What’s New in GRLWEAP 2010 This section lists the significant features that have been added recently to the GRLWEAP program along with program enhancements. In addition to these changes, PDI has been continuously updating the hammer data file which along with update files can be downloaded from our website (www.pile.com). GRLWEAP’s 2010 program version comes in two modules, the standard program and the “Offshore Wave”. Standard program features now include: For static geotechnical analysis in addition to the ST and SA methods: (a) a CPT method for which the data has to be provided in the form of a three column text file and (b) a method based on API requirements. For static geotechnical analysis, the SA method was modified as follows: 

In lieu of entering an SPT-N value, allow for an input of qu, the unconfined compressive strength  for clay and other cohesive soils and allow for input of φ, the internal friction angle, for sand and other cohesionless soils.

 

The SPT-N value input is now completed in the main SA window with automatic interpolation for each soil layer. Also the SPT-N values for a certain layer will not be changed when a soil layer depth is changed. A manually modified SPT-N value for a soil layer will be maintained for a certain depth regardless of layer



The graphics of the SA and ST input windows have been modified now allowing for expansion by scrolling.

For the analysis of inclined (battered) pile driving: 

The program now allows entering the inclination degree or ratio. The user then can accept/modify the suggested reduction factors for hammer and pile weight, stroke reduction and efficiency.



The graphics of the main input form shows the pile batter.

The Area Calculator   now offers for pipe pile input of either outside diameter and wall thickness or outside diameter and inside diameter. Improvements related to Driveability analysis include:

Version 2010

GRLWEAP Procedures and Models

3



Most importantly: the end bearing input for driveability analyses now has to be made as a unit resistance in the S1 form. It is very important to remember this change when entering the soil resistance data.



Also very important, in the S1 input form, a new column, Toe Area, was added. This allows for a simplified data entry in cases of soil plugging in certain layers.



 An automatic feature was added for generating an improved Depth/Modifier   table; this feature initializes the D-table based on both the penetration entered in the main input form and the soil layer information of the S1 table.



The reset button in D-table input form has been improved to allow users to reset depths considering both depth increment and soil layers.



 After the S1-table has been complete, Gain/Loss factors  are initialized using the inverse of the maximum setup factor unless they had been manually set before.



The final penetration depth now can be modified in the main input form (before it was inactive and showed the last depth entered in the D-table). This penetration is now used to initialize the D-table.

For Inspector Chart  analysis, the stroke increments were rounded off to either 0.5 ft or 1 ft or 0.25 m or 0.5 m depending on the starting stroke value. In the Numerical Output, the format for SI output has been changed for 2 steel piles with a cross sectional area ≥ 1 m so that certain outputs will now be shown in MN and MN/mm rather than kN and kN/mm. The bearing graph output now includes additional information such as pressure (diesel), coefficient of restitution of pile cushions (concrete piles) or hammer cushions (steel piles), and capacity (Inspector’s Charts);  Allow to copy hammer/pile/soil model plot to other applications such as MS Word. The physical property table for pile, hammer cushion and pile cushion material has been combined and updated.  A copy/paste feature has been added to the pile profile form (P1) to allow creation/modification of pile input from other programs. Changed pile strength/yield input to a critical section index for a simple input of 0 for non-critical and 1 for critical sections.

4

GRLWEAP Procedures and Models

Version 2010

Features available in the Offshore Wave Version: 











A Pipe Pile Builder   for simplified input of complex pipe pile sections and add-ons allowing for consideration of cut-off and stabbing guide. In this case the graphical representation of the model shows the stabbing guides instead of the solid area plot. Alternate hammer location  at any point along the pile. The related inputs are hammer location, hammer cushion stiffness and helmet stiffness. Static bending analysis for inclined pile driving; related additional input included: center of hammer gravity, hammer total weight,  jacket height and water depth; the latter two inputs are also shown on the model plot. The output replaces the tension stresses with the combined static bending and dynamic compression stresses. Fatigue Analysis tables are now an output based on a so-called single blow approach. The tables include for each segment maximum compressive and tensile stresses multiplied with the number of their occurrences (from average blow count). Consideration of the Soil Column Weight in the static equilibrium analysis which considers the help that the soil weight can add to pile driveability. Friction Fatigue  resistance distribution; this calculation is based on the assumption that the shaft resistance near the pile does not immediately lose resistance while the resistance some distance above the toe reaches fully reduced values. .

1.4 The Wave Equation Approach GRL's Wave Equation Analysis of Pile Driving is a program which simulates motions and forces in a foundation pile when driven by either an impact hammer or a vibratory hammer. The program computes the following: 

The blow count (number of hammer blows/unit length of permanent set) of a pile under one or more assumed ultimate resistance values and other dynamic soil resistance parameters, given a hammer and driving system (helmet, hammer cushion, pile cushion). For vibratory hammers the equivalent result is the time required for a unit penetration.



The axial stresses in a pile, both tension and compression, averaged over the cross section for a certain pile penetration and associated ultimate capacity values. In the offshore version certain bending stresses are also considered.



The energy transferred by the hammer to the pile for certain pile penetration and associated capacity values.



The pile velocity and displacements along the pile for certain pile penetration and associated capacity values.

Version 2010

GRLWEAP Procedures and Models

5



The residual stresses remaining in the pile between hammer blows.

Based on these results the following can be indirectly determined: 

The pile's bearing capacity at the time of driving or restriking, given its observed penetration resistance (blow count).



The stresses during pile driving, given an observed blow count.



The expected blow count if the static bearing capacity of the pile is known (e.g., from a static soil analysis).

Of course, by varying the hammer type, driving system parameters (cushions, helmet) and pile properties for a number of simulations, an optimal system can be selected. The present report does not replace previously published literature. Certain basic features of wave equation programs will not be discussed. On the other hand, this volume will elaborate on those details which experience has shown to be the most difficult to comprehend. Among references useful to the engineer involved in the analysis of impact pile driving are Smith (1951 and 1960), describing the early wave equation approach, Samson et al. (1963), Forehand and Reese (1964), Lowery et al. (1967) and Coyle et al. (1973), as representative publications of the work performed at the TTI. It should be pointed out that the thorough checking of the original 1976 WEAP code would not have been possible without the research work performed at Case Institute of Technology (now known as the Case School of Engineering at Case Western Reserve University) as reported by Goble, et al. (1975). Additional developmental work conducted by the private practice of the authors, as well as studies done by others, e.g.  Blendy, (1979), supplied the necessary correlation data. In addition, results from an FHWA-sponsored study, "The Performance of Pile Driving Systems" by Rausche, et al. (1985) were used in the development of WEAP. Other relevant papers are referenced throughout this text and are listed in  Appendix E. Program performance has been evaluated by Thendean, et al. (1996) and Rausche et al. (2004).

6

GRLWEAP Procedures and Models

Version 2010

2. BASIC CONSIDERATIONS AND APPLICATIONS OF THE WAVE EQUATION 2.1 Energy Transfer The pile driving process readily provides information regarding the soil resistance: the smaller the permanent set, s, of a pile under a hammer blow with kinetic energy, E k, the greater the soil resistance, R u, which opposes the pile penetration. This concept has been used for well over one hundred years in the so-called dynamic or energy formulas, (the most commonly used one in the U.S. is the Engineering News Formula). Note that E k is the kinetic energy of the ram immediately preceding ram impact and that R u is the ultimate pile capacity,  i.e., the maximum load that the pile can bear before it experiences large settlement due to soil failure. Although GRLWEAP does not directly work with an energy approach, these basic principles still apply and should be discussed. The concept of the dynamic formula is as follows: Es = Ru s

(2.1)

where Es  is the energy available to do work on the soil and s l represents losses in the soil, e.g. due to damping. The energy value, Es, is not simply obtained from Ek. In general, the following energy balance is applicable: Es = Ek - Eds - Epl - Esl 

(2.2)

In this equation E ds, Epl  and Esl are quantities of energy lost in the driving system, pile and soil, respectively. However, even E k is not readily known. Generally, for modern hammers a "rated energy", E r , is given by the manufacturer. Exceptions are hammers with internal impact velocity measurement device which display on a control panel the energy of the ram shortly before impact. Using the hammer efficiency, eh, one computes: Ek = eh Er  

(2.3)

The hammer efficiency is a number between 0 and 1. Modern hammers have an attachment called a helmet at the bottom of the hammer, and one or two cushions. These and other devices make up the components of the driving system. Energy, Eds, is lost in the driving system and may be modeled with another loss factor called e d (see Figure 2.1). Then the kinetic energy available at the top of the pile is: Ek - Eds = ed eh Er  

(2.4)

and the energy formula may be written as: ed eh Er  - Epl - Esl = Ru s

Version 2010

GRLWEAP Procedures and Models

(2.5)

7

Figure 2.1: Terminology and Energy Balance in the Hammer-Pile-Soil System  Assuming Er  to be known, an estimate of e d, eh, Epl, and Esl would yield the permanent set, s, given R u  or vice versa R u  given s. The set, s, may be computed from Ru before a pile is driven. The blow count, Bc, is the inverse of s. Plotting the ultimate capacity vs. the blow count leads to the so-called Bearing Graph. An example of two bearing graphs from different energy formulas are shown in Figure 2.2. Unfortunately, estimating the energy lost in pile and soil and estimating the efficiencies of driving system and hammer are not easy tasks. The wave equation approach differs from the energy formula primarily in the evaluation of ed, Epl, and Esl. These losses are now computed by mathematically modeling the driving system, pile, and soil. However, for 8

GRLWEAP Procedures and Models

Version 2010

hammer losses, a hammer efficiency, e h, again is estimated based on hammer type, hammer mode of operation and pile inclination (batter). This estimate has been complicated by different hammer types and energy definition. For example, the diesel hammer model calculates the energy losses due to the precompression process, but uses an e h value (typically 0.8) to estimate all other losses (mainly friction) while hammers with internal energy instrumentation are rated by the measured ram energy available j ust before impact (eh is then often 0.95).

4500 4000    N3500    k   n 3000    i   y 2500    t    i   c 2000   a   p 1500   a    C1000

500 0 0

5

10

15

20

Blows /25 mm

Figure 2.2: Bearing graphs from two different dynamic formulas For calculating the ed  (losses in the driving system) effect, the wave equation requires that stiffness values and coefficients of restitution of the cushions and the weight of the helmet are known. For calculating E pl  the elastic modulus, length, specific weight of the pile and a coefficient of restitution of the pile top are considered. The soil losses, E sl, are computed by considering both a soil stiffness and a soil damping factor. The computational procedure established by Smith again leads to a Bearing Graph by calculation of the set s for an assumed or calculated ultimate capacity value. In addition, tension and compression stress maxima can be plotted vs. blow count. The engineer may require that the pile be driven to a minimum blow count taken from the Bearing Graph to assure that the corresponding minimum ultimate capacity, R u  has been obtained. In this way, the wave equation result is used to establish a driving criterion. On the other hand, during pile driving the blow count, B c, may be observed and R u computed. This process may be considered a dynamic pile test. However, it is not a very thorough test because many analysis parameters have been estimated. However, once a dynamic pile test has been conducted and the estimated quantities have been verified, the resulting analysis is called a Refined Wave Equation und its results are then more reliable.

Version 2010

GRLWEAP Procedures and Models

9

For the inspector who in the field has to ascertain that the piles are driven to the correct blow count, the task is complicated if the hammer cannot or should not work at a constant stroke. For example, a hydraulic hammer can and sometimes should be operated at different energy levels for reasons of safety or expediency. In that case, for a desired end-of-drive ultimate capacity, the pile should be driven to blow counts which are higher for lo wer hammer energies and lower for higher energies. This relationship can be readily prepared by GRLWEAP in the so-called Inspector’s Chart (Figure 2.3).  A third situation is also common. The engineer performs as accurate a static soil analysis as is possible, and plots the ultimate soil capacity as a function of depth. The wave equation is then used to calculate the blow count for certain depth values and the input bearing capacity. In this way, the blow count vs.  depth curve is obtained. This process is called a driveability analysis, as it indicates the limits of an economical or safe pile installation. Both Bearing Graph and Driveability analysis are very helpful for optimal driving system selection. 1.50

Stroke in m

1.20

0.90

0.60

0.30

0.00 0

20

40

60

80

100

120

Blow Count Figure 2.3: Inspector’s Chart from GRLWEAP

10

GRLWEAP Procedures and Models

Version 2010

Figure 2.4: GRLWEAP Driveability Result (Capacity and Blow Count vs Depth) In summary, the computational process in a wave equation is elaborately compared to the simple dynamic formula, yet the wave equation still requires assumptions and estimates of soil behavior, hammer efficiency, and certain driving system parameters. Finally, a word about the term "wave equation", this term refers to a partial differential equation. Fortunately, it is unnecessary for the piling engineer to solve this equation; this is done in an approximate manner by means of Smith’s lumped mass model. However, the important contribution of Smith was not solving the wave equation, but devising a complete analysis procedure including recommendations for hammer, driving system, and pile and soil parameters. GRLWEAP has been expanded to include not only the basic wave equation analysis but additional tools such static soils analyses and even a static pile bending analysis for offshore piles. It is important to remember, however, that these additional routines are only accessories to a dynamic analysis. GRLWEAP has not been devised to design a pile. Its main task is to calculate blow count and dynamic stresses given an assumed or calculated ultimate bearing capacity value.

Version 2010

GRLWEAP Procedures and Models

11

2.2 Preparation for a Bearing Graph Analysis Before doing an analysis, prepare yourself by reading the relevant information in Chapter 4 and in the on-line help section of the program (print it out for convenience). Analyze the example cases. Submit to the contractor and/or geotechnical engineer Form 1 of Chapter 4 (may be printed for that purpose) for data collection. The following steps are required for a standard analysis. 

Obtain a soil profile, including approximate soil strength values such as standard penetration values, N. At least soil types and densities or consistencies should be known.



Establish a design (working) load, Qd, and a factor of safety (FS). The factor of safety should reflect how well one knows the loads, the soil properties, and the sensitivity of the structure to settlements; also, the factor of safety should be greater the less effort is made to determine the pile's bearing capacity. In general, FS = 2 is only acceptable if more than just a wave equation is done to ascertain pile bearing capacity. A Load Resistance Factor Design (LRFD) approach (e.g. PDCA 2001) is preferable to the allowable stress design procedure as LRFD considers of a variety of uncertainties in the design and construction of driven piles.



Compute the required ultimate pile capacity Rur  = Qd FS

 Alternatively, for the LRFD approach, proceed as follows: 

Combine the various load components, Qi, multiplied by their associated load factors, f i, to obtain the Factored Load.



Determine the resistance factor, φ,  as appropriate for the agreed upon testing method and testing effort.



Divide the Factored load by the resistance factor to determine the required nominal load (which will be referred to as required ultimate capacity in this document), R ur . Rur  = (1 / φ) Σf i Qi Decide on a pile type.



12

From static geotechnical analysis, establish the depth at which the pile will most likely reach R ur   and calculate the percentage and distribution of the skin friction. If the soil strength changes due to pile driving effects are known, determine the estimated amount of skin friction and end bearing for both the end of driving and GRLWEAP Procedures and Models

Version 2010

restrike (after set-up) situations. It may be possible to drive the pile only to Rur  / f s, with f s  being an overall setup factor which covers capacity changes of both end bearing and shaft resistance. If the soil loses strength during driving and then regains it after driving, f s is greater than one. On the other hand, f s may be less than one in the case of relaxation. Relaxation is a phenomenon which causes the pile to lose strength after installation. In the troublesome case of relaxation, the pile must be driven to a capacity in excess of R ur . 

Dynamic soil resistance parameters, damping, and quake may be taken from the GRLWEAP help files for the given soil and pile parameters, or they may be known from dynamic tests conducted under similar circumstances.



Select a hammer and driving system based on local availability.



Submit all of this data for a wave equation analysis. Run the analysis using Rur   as well as other R u values so that a curve can be plotted with Ru being a function of the calculated blow count.



Also plot the maximum tensile and compressive stresses, which may occur at any location along the pile, as a function of blow count.

2.3 Preparation for a Driveability Analysis The following steps are required for a very basic driveability analysis. 

It is assumed that a geotechnical analysis has been performed which established a required pile tip penetration. In that cases, both unit shaft resistance and end bearing may be readily available for input. If not, obtain reliable soil strength information as an input to GRLWEAP and use SA, ST, API or CPT routines.



For the soil types of the various layers, determine the appropriate soil setup factors, f s  (i.e., the factor with which the end of driving capacity has to multiplied to find the long term pile capacity).



In GRLWEAP enter the hammer, driving system and pile information.



In GRLWEAP enter the given unit shaft resistance and end bearing directly into the S1 input form or choose from the four different static analysis methods ST, SA, CPT or API to calculate the unit soil resistance for all layers.



In GRLWEAP decide on the Gain/Loss factors; usually one chooses as the first shaft G/L factor the inverse of the highest setup factor (Static Resistance to Driving, SRD) and as a second

Version 2010

GRLWEAP Procedures and Models

13

one a factor 1.0 (representing the long term capacity). The G/L values for the toe are normally left at 1.0. 

Complete the input and perform the analysis for various pile penetrations.



Two capacity vs depth relationships will be established (a) the low resistance result which pertains to the continuous driving and thus end-of-driving situation and (b) the high resistance analysis based on the long term capacity which would be expected if major driving interruptions occurred, e.g. after a waiting period during the beginning of restrike testing.

2.4 Interpretation of Wave Equation Results 

Check the maximum pile stresses to see whether a safe pile installation is possible.



If the predicted blow count at Rur   is excessive (e.g., greater than 100 blows/ft (330 blows/m or less than 3 mm set per blow) for friction piles or 240 blows/ft (800 blows/m or less than 1.25 mm set per blow) for end bearing piles, re-analyze with a more powerful hammer. This more powerful hammer may have to be one with more ram weight rather than drop height if stresses are high.



If the predicted blow count at Rur   is very low (e.g., less than 24 blows/ft (80 blows/m or greater than 12 mm set per blow), construction control with a blow count driving criterion may be inaccurate, and it is recommended to re-analyze with a reduced hammer energy or a less powerful hammer.



If blow count is acceptable but compressive stresses are unacceptably high, re-analyze with either a smaller hammer, decreased stroke or ram fall height (if hammer is adjustable), a heavier hammer with less stroke or an increased cushion thickness or a softer cushion material.



If blow count is low, but tension stresses are too high for concrete piles, either increase the pile cushion thickness, decrease the stroke or use a hammer with a heavier ram and then re-analyze.



If blow count is high and tension stresses are also too high for concrete piles it may be necessary to choose a hammer with greater ram weight and then re-analyze.



If both blow count and stresses are excessive, increase pile cross sectional area if possible or use a higher strength pile material and then re-analyze.

14

GRLWEAP Procedures and Models

Version 2010

2.5 Checking Wave Equation Results There are many potential error sources. It is the engineer's duty to assure that simulation and actual field conditions are in agreement. 

The first check must be on the actual pile size, length and material.



Cushions and helmet must be checked in the field for size, material type and condition. In particular, the pile cushion thickness of concrete piles may vary.



The hammer type must be checked and even though the data is taken from the GRLWEAP hammer data file, the numerical output must be checked to assure that the hammer data analyzed corresponds to the system specified. Also, during driving it must be confirmed that the hammer runs according to both the analysis parameters and the manufacturer's specifications.



In most cases, and always for high capacity piles or whenever unusual driving conditions exist, dynamic measurements should be taken during initial drive or restrike. Under certain circumstances, a static load test may also be necessary.

1.

If dynamic or static measurements have been taken under comparable soil and pile conditions, re-analyze the situation to learn about dynamic soil properties and use this information for a refined wave equation analysis.

2.

If dynamic measurements are available and have indicated a hammer performance either better or not as favorable as suggested by the “canned” GRLWEAP hammer models, be sure to modify the input parameters (primarily the hammer efficiency) accordingly. The hammer data file parameters represent average hammer properties over all makes of the same hammer type. These parameters do not represent the performance of a particular product and cannot possibly reflect a certain state of maintenance.

3.

The engineer must expect that the bearing capacity predictions obtained from correlation between wave equation analyses and actual pile driving blow counts will differ from static load test results. In general, the finer the grain of the soil material, the larger these differences can become. Correlation of wave equation results with blow counts from restrike tests may reduce the potential for inaccurate results. However, less than a 10 percent difference can never be expected, since even measurements and interpretations of static load tests are subject to errors or differences of such magnitude.

Version 2010

GRLWEAP Procedures and Models

15

16

GRLWEAP Procedures and Models

Version 2010

3. THE WEAP ANALYSIS MODELS 3.1 Introduction  After a short description of the construction and operation of commonly encountered impact hammers, this chapter describes how GRLWEAP represents the hammer components which are significant for the force, momentum and energy transfer to the piles. The models of the driving system, pile and soil also will be described. 3.2 Hammer Details Impact pile driving hammers may be classified as follows:    

Diesel hammers with liquid injection Diesel hammers with atomized injection Open end diesel hammers Closed end diesel hammers

    

Single acting air/steam/hydraulic hammers Double acting air/steam/hydraulic hammers Hydraulic drop hammers Hydraulic power assisted drop hammers Hydraulic hammers with internal energy measurements

 

Drop hammers - free fall Drop hammers - brake released



Vibratory hammers

 All except the diesel and vibratory hammers are called external combustion hammers. Their basic models are practically identical, however, their efficiencies vary. Diesel hammers are Internal Combustion Hammers. Normally hammers are thought to act at the pile top, however, certain external combustion hammers can also drive a pile at an intermediate pile point or at the bottom. The offshore version of GRLWEAP provides such a feature as an option.

 3.2.1 Working Principle of Liquid Injection D ies el Hammers Diesel hammers operate on a two stroke engine cycle. Figure 3.2.1 illustrates the working principle of a liquid injection open end diesel. The hammer is started by raising the ram with a lifting mechanism. At a certain fall height, the lifting mechanism is tripped (Figure 3.2.1a), the ram is released, and it descends under the action of gravity. When the ram bottom passes the exhaust ports, a certain volume of air, V i, is trapped in the cylinder, compressed, and therefore heated.

Version 2010

GRLWEAP Procedures and Models

17

Figure 3.2.1: Working Principle of a Liquid Injection Open End Diesel Hammer

18

GRLWEAP Procedures and Models

Version 2010



Sometime before impact, a certain amount of fuel is squirted into the cylinder under relatively low pressure (Figure 3.2.1b).



When the ram collides with the impact block (Figure 3.2.1c), the trapped air is compressed to a final volume, V f , which is usually equivalent to the volume of the hammer's combustion chamber. The fuel is splattered by the impact into this combustion chamber, and combusts after a short delay (Figure 3.2.1d).



The so-called combustion delay is due to the time required for the fuel to mix with the hot air and to ignite. More volatile fuels might have a shorter combustion delay than heavier ones. Combustion occurring before impact is called preignition (it can be modeled in GRLWEAP with a negative combustion delay) and can be caused by the wrong fuel type or an overheated hammer. In hard driving, severe preignition is usually undesirable, as it may reduce the velocity of the ram (and thus the ram’s energy) prior to and cushioning the impact.



After the fuel has begun to combust, it will be causing a quick increase in the pressure of the chamber until, after the so-called combustion duration, the maximum pressure, P max, is reached. The maximum pressure is an important quantity because it governs the achieved stroke height. The Pmax-value may be measured on the hammer, however, the pressure values in the GRLWEAP program have been back calculated in such a way that the calculated stroke reaches the rated stroke under refusal conditions (Appendix B2).



During impact, the impact block, hammer cushion and pile top are rapidly driven downward leaving the cylinder with no support and letting it descend by gravity.



Pile rebound and combustion pressure push the ram upwards. When the exhaust ports are cleared, some of the combustion products are exhausted leaving in the cylinder a volume, V i, of burned gases at ambient pressure (Figure 3.2.1e). As the ram continues to travel upwards, fresh air, drawn in through the exhaust ports, mixes with the remaining burned gases (Figure 3.2.1f).



Depending on the reaction of the pile and the energy provided by combustion, the ram will rise to some height (stroke). It then descends again under the action of gravity to start a new cycle. While the ram moves upward or downward with the exhaust ports open, the chamber is scavenged, and fresh air replaces the burned gas.

Version 2010

GRLWEAP Procedures and Models

19

 3.2.2 Working Principle of A tomized Injection Dies el Hammers This hammer type is started in a manner identical to the L.I. (Liquid Injection) type. However, for the Atomized Injection (A.I.) hammer, the ram descends to within a small distance of the impact block and only then is fuel injected at high pressure. The high pressure injection causes the fuel to be immediately atomized and mixed with the hot compressed air. Thus, combustion starts shortly after injection, independent of impact. Injection lasts until, some time after impact, the ram has traveled a certain distance from the impact block. Note that since distances and thus volumes (or sometimes associated pressures) govern the process, combustion start and stop volumes can be identified. Furthermore, the time duration from the start of combustion to its end depends on the speed of the ram. The higher the ram speed, the shorter the time periods between ignition and impact and between impact and the end of ignition and combustion. During the time of combustion the pressure is assumed to be maintained at a constant maximum value p max  which again is back calculated for the GRLWEAP hammer data file based on the energy rating of the hammer (Appendix B).

 3.2.3 Working Principle of E xternal C ombus tion Hammers Diesel hammers carry their own source of energy in a fuel tank attached directly to the hammer. All other hammers utilize an external engine or device to create mechanical energy. This energy is then transferred to the hammer either by means of hoses carrying steam (steam hammer), compressed air (air hammer), pressurized hydraulic fluid (hydraulic hammer) or a hoist and rope (drop hammer). For analysis purposes, it is only important to realize that immediately prior to impact, the ram is descending at a certain speed. In some cases, the action of the motive fluid may slow this descent and have a self cushioning effect. This will occur if the fluid causes a lifting force on the ram before impact. Generally, this pre-admission is an abnormal condition and occurs only in hammers with incorrect valve settings. The situation cannot be detected by simple inspection methods and, due to the large variety of hammer designs, it cannot be simulated in GRLWEAP. The equivalent to the diesel hammer's cylinder is the assembly of ECH (External Combustion Hammers). The assembly is simply the entire hammer, except for the ram and the attached piston rod and piston. Typically, the assembly consists of a hammer base, ram guides, cylinder and other hammer components of significant weight. Initially, the assembly is supported by the helmet, and therefore, by the pile which in turn precompresses the soil. As the ram impacts against the striker plate, hammer cushion, helmet and pile, the assembly is momentarily unsupported and starts to fall due to gravity. When the assembly reaches the helmet again, a so-called assembly impact occurs which may create significant forces in the pile, particularly if the pile and helmet sharply rebound from the initial impact of the ram. Thus, because of the soil precompression and because of the assembly impact forces, the assembly should also be included in the 20

GRLWEAP Procedures and Models

Version 2010

hammer model. Figure 3.2.3 shows the working principle of a single acting air/steam hammer as an illustration. In recent years, several different types of hydraulic hammers have come into use. Some of these units have stepless adjustable ram fall heights or energy settings. Several hammer types are designed with true free falls; others are double acting, but with internal ram speed monitoring. In general, these hammers avoid by design the problem of preadmission.

Figure 3.2.3: Working Principle of a Single Acting Air/Steam Hammer

Version 2010

GRLWEAP Procedures and Models

21

For most types of ECHs, the hammer potential energy is based on ram stroke times ram weight plus a contribution from the downward pressure. Impact velocity is then calculated from this energy rating under consideration of the hammer efficiency which covers energy losses occurring during the descent of the ram. As mentioned, several modern hydraulic hammers have a built-in energy monitoring device that can determine the kinetic energy just before impact. In this case, it is unnecessary to calculate the impact velocity from potential ram energy and an estimate of energy losses. The rating, in this case, reflects the impact energy, and the hammer efficiency is therefore near unity. Note: it is possible to equip practically all hammers with an impact measuring device, a highly recommended measure if construction control relies on blow count.

 3.2.4 Working Principle of Clos ed End or Double A cting Hammers Closed end or double acting hammers operate at a higher blow rate than open or single acting units. The higher frequency of impacts is accomplished by the exertion of a downward force on the ram during its descent. For closed end diesels, this force is passively created by air trapped between the top of the ram and the closed cylinder top. For ECH the ram stroke may be limited by either active (motive fluid) or passive pressure.

 3.2.4.1 C los ed End Dies el Hammers Closed end diesel hammers are very similar to open end diesels, except for the addition of a Bounce Chamber at the top of the cylinder. The bounce chamber has ports which, when open, allow the pressure inside the chamber to equalize with atmospheric pressure. As the ram moves toward the cylinder top, it passes these ports and closes them. Once these ports are closed, the pressure in the bounce chamber increases rapidly, slows the ram’s upward motion, and prevents a metal to metal impact between ram and cylinder top. The bounce chamber pressure can only increase until it is in balance with the weight of the cylinder, called the Reaction Weight. If the ram still has an upwards velocity, uplift of the entire cylinder will result. In the field, this uplifting cannot be tolerated as it can lead both to an unstable driving condition and to the destruction of the hammer. For this reason the fuel amount, and hence maximum combustion chamber pressure, has to be reduced such that there is only a very slight "lift off" or none at all. Figure 3.2.4.1 shows one particular type of closed end diesel hammer in various phases of operation. In order to modify the ram deceleration and acceleration over time, some closed end diesel models have a compression tank added to the upper cylinder; the portion of the cylinder between the tank ports and cylinder top is then referred to as a Safety Chamber.

 3.2.4.2 Double Acting E xternal C ombus tion Hammers The analysis of the ECH double acting hammer type does not significantly differ from single acting units. In fact, for ECH, GRLWEAP works with an

22

GRLWEAP Procedures and Models

Version 2010

equivalent stroke which is rated hammer energy divided by ram weight. It is , therefore, immaterial in the analysis of a double acting ECH whether or not the energy or impact velocity was attained by a downward pressure, free fall, or other means. Prior to 1998 GRLWEAP modeled double acting ECH with a rated pressure and the effective area over which this pressure works. This option has been removed and the data file simplified to reduce the possibility of errors due to confusion or lack of information. For ECH the downward force on the ram is often created by active pressure. In that case, under hard driving conditions, the hammer assembly tends to uplift which leads to unstable driving conditions. The operator will then reduce the pressure which in turn leads to a reduced impact energy. This is the main reason why double acting air/steam/hydraulic hammers have lower GRLWEAP efficiencies than their single acting counterparts. For modern power assisted ECH with passive pressures above the ram (similar to the compressed air above the piston of a closed-ended diesel hammer), uplift is normally avoided and such hammers can therefore be analyzed with higher efficiencies. Traditional double acting air/steam hammers are designed with either the truly double acting mechanism which maintains full active pressure throughout the downstroke. The other system, the differential hammer, is designed such that the initially full pressure expands and reduces during the downstroke. The differential hammer uses less motive fluid; however, either system achieves high blow rates such as 120 impacts per minute, Rausche, et al., (1985). Obviously, for these hammers, exact valve timing becomes even more important for full energy development than for single acting hammers which run at half this rate. Modern hydraulic hammers have been designed with a variety of other power assisting mechanisms during the downstroke. For example, the IHC hammers work with an adjustable downward directed nitrogen gas pressure which can be used to adjust the hammer impact velocity and blow rate. Other hydraulic hammers may use only a low pressure force that balances other potential energy losses.

 3.2.5 Drop Hammers The classic drop hammer is lifted with a hoist and rope and then released. If the ram is freely released (which is rarely the case), one can speak of a free fall hammer. If, however, the ram is released by releasing the brake of the hoist and letting the winch unspool, then significant losses of energy must be expected due to rope friction and winch inertia and possible early engaging of the brake by an operator who does not want to risk that the ram falls off the pile after impact.

Version 2010

GRLWEAP Procedures and Models

23

24

GRLWEAP Procedures and Models

Version 2010

 3.2.6 Vibratory Hammers  3.2.6.1 Working Principle Figure 3.2.6.1 shows a sketch of a vibratory hammer. These hammers may be powered either electrically or hydraulically, and both hoses and cables are usually elastically connected to the hammer's bias weight (vibration isolator or upper mass). Vibration is generated by pairs of rotating eccentric masses which rotate in opposite direction such that their horizontal forces cancel while their vertical forces superimpose. The drivers for these eccentric masses are located in the oscillator part (motor or lower mass) of the hammer, which is connected to the bias weight by means of springs and/or shock absorbers. Typically, low frequency hammers rotate at speeds of 10 to 40 revolutions per second (Hz). So-called resonance hammers rotate at higher speeds. Of course, the number of revolutions per second is equal to the hammer's vibratory frequency. The rotation of the eccentric masses produces centrifugal forces which are transferred to the pile through a "clamp", which is often remotely operated with hydraulic power. It is necessary to make this hammer-pile connection rigid to avoid destruction of the pile top. The maximum compressive or tensile forces which the eccentric masses, m e, with eccentric radius, r e, produce at a given frequency, f V, (in cycles per second or Hz) are given by: 2

FVX = me r e (2π f V)  

(3.1)

Therefore, the variation of the vibratory force, F V, over time, t, has the form: FV = FVX sin(2π f V t)

(3.2)

Figure 3.2.6.1: Sketch of a Vibratory Hammer

Version 2010

GRLWEAP Procedures and Models

25

The product mer e is referred to as the eccentric moment of the hammer. This moment is not necessarily constant for a particular hammer if the hammer model allows for a variation of the mass by insertion or removal of mass units. Furthermore, so-called resonance free hammers can vary the eccentric moment during operation. This allows for starting the hammer at low or zero eccentric moment until a high enough frequency is reached at which soil resonance does not occur. The eccentric moment is then increased as desirable. Vibrohammer manufacturers often specify the eccentric moment, maximum frequency, and rated power or the required power of the associated power pack. Also, a vibratory amplitude is often specified. When only the eccentric moment is known then for sufficient accuracy a reasonable eccentric radius can be assumed and the corresponding mass calculated by dividing moment with radius. In order to gain an understanding of the power transfer from hammer to pile, it is helpful to consider two extreme situations. In the first, the pile is light and has practically no soil resistance. The oscillator of the hammer then vibrates freely at an amplitude which is governed by the mass of the oscillator and frequency. Energy dissipation in this case occurs primarily in the connection between bias weight and oscillator. In other words, the hammer will run with very low power, practically transferring very little power to the pile, while it penetrates into the ground. In the second extreme (and physically impossible) case, the pile is held rigidly by the surrounding soil. Then there is no motion associated with the vibratory forces which means that no energy transfer occurs, and again the hammer cannot deliver any power to the pile. It is therefore reasonable to expect that the power requirements first increase and then decrease as soil resistance increases.

 3.2.6.2 Limitations of Vibratory Hammer A nalys is It is well recognized by the profession (see also Holeyman, 2002) that the analysis of vibratory pile driving is difficult at best. The main reason is the strong effect that vibratory pile motion has on the effective soil stresses and thus the soil resistance. As a result, piles in cohesionless soils, in particular those that are submerged, may lose up to 95% of their shaft resistance and 50% of their end bearing. On the other hand, for cohesive soils there may be no resistance losses at all during vibratory driving. Unfortunately, there are only few dynamic test results available that can quantify these soil resistance changes and for that reason, GRLWEAP does not include a method that calculates the resistance losses automatically. In fact, the few pile tests that were conducted first under a vibratory hammer and immediately thereafter under an impact hammer did not indicate soil resistance values of a significantly different magnitude under these two hammer types. Other effects also must be considered. For example, to a greater degree than impact hammering will vibratory pile driving densify loose coarse grained soils, yet reductions of soil density must be expected in very dense 26

GRLWEAP Procedures and Models

Version 2010

soils. Calculation of the long term pile capacity based on pre -installation soil parameters is therefore highly unreliable for vibratory driven piles. Even the rate of penetration of the pile at the end of vibratory installation seems to bear little relationship to pile capacity. For that reason, a final restrike test with an impact hammer is often required when bearing piles are installed with a vibratory hammer. Interlock friction of sheet piles is an important resistance force which is difficult or impossible to predict. It may depend on alignment of the two adjoining sheet piles, the roughness of the lock, and whether or not the lock is damaged or obstructed with sand. The hammer model allows for the specification of a start-up time. It may be assumed that during this time the hammer frequency increases linearly with time from zero to the specified value. As a consequence, the vibratory force increases quadratically (see Eq. 3.1) during that time. Note, however, that the feared start-up, low frequency resonance in the soil (which may cause damage to nearby structures) cannot be observed in the results of the wave equation calculation since the soil is treated as for the standard Smith analysis, i.e. without mass. The hammer is normally suspended from a crane and it is sometimes advantageous to maintain some Line Force, i.e. to keep some tension on the hammer. On the other hand, a negative line force would be a so-called crowd force and it could help push the hammer down which could be very effective when the end bearing is high. Note:  Shaft resistance does not necessarily slow down penetration, but may actually improve driveability by keeping a downward pressure on the pile bottom during the upward motion of the vibration cycle. The user should therefore not be surprised if penetration times decrease for higher capacities under certain circumstances.

 3.2.6.3 Preliminary R ecommendations for Vibratory Hammer A nalys es PDI's experience of predicting bearing capacity or driveability from vibratory hammer driving is limited. A good reference for the state of the art is Holeyman et al., 2002. The following recommendations were developed from theoretical considerations and a limited number of test cases. a. Display forces or penetrations during the analysis and check for consistency of traces; inconsistent (abrupt changes not repeated from cycle to cycle) traces may indicate a numerical stability problem. In that case analysis with a greater number of segments is suggested. b. Use the Smith-Viscous soil damping option. Since velocity and displacement variations are sometimes very small, standard Smith damping may be ineffective.

Version 2010

GRLWEAP Procedures and Models

27

c. It appears that damping factors should be chosen higher than for impact driving. It may be wise to double the damping factors normally recommended for impact driving, because velocities during vibratory driving are lower than for impact driven piles and soil damping is known to be non-linear with relatively high forces for low velocities. d. For cohesive soils it appears reasonable to double the quakes that are normally recommended for impact driven piles. e. Soil setup factors may be quite different for impact and vibratory driving. In cohesionless soils the shaft resistance may lose a substantial amount of resistance and, for example, a setup factor of 5 would be reasonable in a submerged sand (typically 1 or 1.2 for impact driving). On the other hand, for highly plastic cohesive soils, not much resistance may be lost and the setup factor may be as low as 1.0 for vibratory driving (often set to 2 for impact driving). On the other hand soft clays or any material which tends to behave in a thixotropic manner, may lose as much resistance as for impact driving and should be considered with a higher setup factor. f. Do not  specify waiting times to model the effect of driving interruptions, since soil setup times and/or limit distance values are even less known for vibratory driving than for impact driving. g. Interlock friction should be modeled with additional shaft soil damping or with an increased static end bearing. The latter model seems more reasonable where sheet alignment problems exist. Obviously, no quantitative recommendations can be given because of the large variety of possible conditions. 3.3 Basic Hammer Models  An understanding of the dynamics of hammer, pile and soil is important for performing a meaningful wave equation analysis and proper result interpretation. It is therefore most important that the analyst understands the working principals of pile driving hammers and their operation and performance as described in the previous chapter and in the literature (e.g., Hannigan et al., 2006) and it is strongly recommended that the GRLWEAP users familiarize themselves with that literature before attempting to perform the dynamic analysis pile driving. The following is a summary of important GRLWEAP hammer model details for the three basic hammer types ECH, Diesel and Vibratory. Basic schematics and associated model components of a typical single acting ECH, an open ended diesel hammer and a vibratory hammer with bias weight are, respectively, shown in Figures 3.3.1, 3.3.2 and 3.3.5.

28

GRLWEAP Procedures and Models

Version 2010

 3.3.1 E xternal C ombus tion Hammers  3.3.1.1 The R am of E C Hammers The ram is the simplest and most important hammer component. For small hammers a single mass element is often sufficient as its model. For slender rams as encountered for example in modern hydraulic units, more than one ram segment are necessary for a realistic simulation. Ram segments should be less than 3 ft or 1 m long; if they are very short numerical problems may be created because the critical time increment would become very small. With m being the number of ram segments, each segment, i, has a weight: W ri = γi Ai ΔLi 

(3.3)

where γi, Ai and ΔLi are the specific weight, cross sectional area and length of each ram segment I.  A ram spring is attached under each segment mass having stiffness: kri = Ei Ai / ΔLi 

(3.4)

where Ei is the elastic modulus of the ram. Note that γi, Ai, and Ei  may need to be averaged over length ΔLi. The bottom spring has an infinite slack, i.e. it is not possible to take any tension. This bottom spring is combined with the hammer cushion spring (note that a striker plate is not separately modeled; rather its mass has to be considered in the helmet mass. The combined model of the bottom (m-th) ram spring and the spring below it must allow for separations and deformation caused by impact. For that reason, a slack, d st (distance which spring extends at zero tension force), a "round out" deformation, dsc, and a coefficient of restitution, c s, are used to describe its behavior. A description of the characteristics of springs with slacks is given in Section 3.6.

 3.3.1.2 A s s embly of EC Hammers The assembly is only considered for EC hammers. As shown in Figure 3.3.1, their model usually consists of two assembly segment masses and springs. The bottom spring has an unlimited slack, i.e. it cannot take any tension. In most cases, their weights and stiffness values are calculated in an approximate manner since there is no need for great accuracy. Only the total assembly weight is important and since it is approximately equal to the total hammer weight minus the ram weight, it is readily available. Unless better information is provided by the manufacturer it is sufficiently accurate to make two assembly weights of ½ (Hammer weight - Ram weight).

Version 2010

GRLWEAP Procedures and Models

29

For hammers with columns linking base to top, the total assembly stiffness may be approximated by the combined stiffness of the columns. See also GRLWEAP Helps “External Combustion Hammer” and “Hydraulic Hammer (Steel-to-Steel Impact) and Assembly Modeling”. If no accurate information about the stiffness of the assembly is available, it is satisfactory to assign a relatively soft spring which corresponds to a total compression deformation of 0.005 mm (0.0002 inch) under the total weight of the assembly (kN or kips) which is estimated to be total hammer weight W H  (without helmet) minus ram weight, W R. Since we are making two assembly springs, each spring stiffness may be calculated from k1,a = k2,a = (WH  – W R) * kWA where kWA is either 400 (1/mm) or 10,000 (1/inch), yielding, respectively the assembly stiffness values in kN/mm or kips/inch.

30

GRLWEAP Procedures and Models

Version 2010

Figure 3.3.1: Schematic and Model of a Typical ECH hammer

Version 2010

GRLWEAP Procedures and Models

31

 3.3.2 Dies el Hammers The diesel hammer’s ram is usually relatively slender and, therefore, is modeled with several segments. Again, typical ram segments should have a length less than 3 ft (1 m). The diesel ram is subject to pressures during pre-compression, combustion and expansion which either slows it down during descent or accelerates it upwards during its rebound. These pressures are calculated as described in Section 3.3.3. Even though gas pressures act between the ram and the impact block, the ram also impacts against the impact block. The impact forces are transferred through the ram bottom spring which is combined with the impact block spring. The impact block mass contacts the hammer cushion spring. If no hammer cushion is present then the impact block spring replaces then the ram bottom spring and the impact block spring ram remain separate and act on top and bottom of the impact block, respectively.

 3.3.3 Thermodynamic Models of Dies el Hammers  3.3.3.1 Liquid Fuel Injection (Impact A tomization) Model Liquid Fuel Injection is the most common design principle for diesel hammers. The process is as follows (see Figures 3.3.3.1a and 3.3.3.1b): 

The ram descends and closes the exhaust ports.



The pressure and temperature of the air trapped inside the hammer cylinder between the ram and the impact block increase.



Shortly after the ports are closed, fuel is injected into the chamber under low pressure, i.e.  in liquid form. The liquid fuel collects on top of the impact block.



The ram strikes the impact block, thereby causing the fuel to be atomized. Pressure remains constant while the ram is in contact with the impact block and before ignition starts.



The atomized fuel starts to combust within a few milliseconds of impact. The time lag between impact and combustion is the combustion delay, td.



The combustion process is finished within the combustion duration tcd, i.e., within a few milliseconds of the start of combustion and after the gases inside the chamber have reached their maximum pressure.



During combustion, the ram usually starts to separate from the impact block. The corresponding increase in chamber volume causes a reduction of the pressure inside the chamber.

32

GRLWEAP Procedures and Models

Version 2010



The ram reaches the ports, and chamber pressure drops to atmospheric pressure.

Figure 3.3.2: Schematic and Model of a Typical Open Ended Diesel Hammer

Version 2010

GRLWEAP Procedures and Models

33

The foregoing stages of compression, combustion and expansion are all considered in the GRLWEAP Liquid Fuel Injection (impact atomization) model; the computational steps are shown below. Computed pressures are expressed in terms of gage pressure. Step A: At the beginning of compression, the chamber volume is equal to Vi, the initial volume. It can be computed from the combustion chamber volume, Vf , the cylinder area, A c, and the compressive stroke, hc: Vi = Vf  + Ac hc 

(3.5)

The position of the ram, u r , is: ur  = -hc 

(3.6)

With h being the hammer stroke, the ram velocity is: 1/2

vr  = [(h -hc) 2g]  

34

GRLWEAP Procedures and Models

(3.7)

Version 2010

The impact block position, uib, is zero at the time of port closure. Step B:  The ram has descended below the ports and the volume of the chamber is: Vc = Vf  + Ac (uib - ur )

(3.8)

The corresponding gage pressure, Pc, according to the Gas Law is: Pc = Pa ((Vi / Vc)cp - 1)

(3.9)

Where Pa is the atmospheric pressure (14.7 psi or 101 kPa) and cp is the exponent for adiabatic compression (1.4 for air, but 1.35 in GRLWEAP owing to some compression losses). Step C: No particular computation is necessary to reflect the injection process. However, throughout the compression cycle, a check is made on the (negative) time until impact occurs (t=0): ti = (uib - ur ) / (vib - vr )

(3.10)

where vr and vib are the ram and impact block velocity, respectively. Actually, the time ti is not exactly equal to the time until impact, primarily because vr changes under the effect of both gravity and gas pressure. However, for cases of preignition, where combustion starts before impact, this prediction is more accurate than other available information. For preignition, the combustion delay, td, is negative and combustion will start when ti ≤ td. Normally, the combustion delay is positive and between 0.5 and 2 ms. Step D: Immediately preceding impact, the ram velocity is reduced by the hammer efficiency leading to the reduced velocity vrr = vr (eh)½. Step E: After combustion has started (the combustion delay has occurred), two pressures are calculated. The first is the compression pressure, Pc, as in Step B with volume Vi and Pa as the r eference; the second is the expansion pressure: Pe = Pmax (Vc / Vi)ce - Pa 

(3.11)

with the maximum specified pressure, Pmax, and the initial volume, Vi, as a reference. The exponent, ce, is the expansion coefficient (ce = 1.25 for most L.I. hammers in GRLWEAP). With tcd being the combustion duration and td < tc < td + tcd where tc is the time of start of combustion, the final combustion pressure is calculated from Pe and Pc by linear interpolation. Normally, the combustion duration is between 0.5 and 2 ms. Version 2010

GRLWEAP Procedures and Models

35

Step F:  Expansion takes place and pressure is computed according to Equation 3.11. Step G:  The ports are reached, the gage pressure returns to zero. In summary, for liquid fuel injection the following nine quantities are used to compute the diesel hammer pressures. Vf   Ac hc cp ce Pmax td tcd Pa

the combustion chamber volume the inside cylinder area the compressive stroke the Gas Law compression coefficient the Gas Law expansion coefficient the maximum combustion pressure the combustion delay the combustion duration the atmospheric pressure

The coefficients c p  and ce  are not easily calculated from measurement. They may vary for a given hammer depending on its temperature, however, based on observed strokes, reasonable average values have been estimated. Thus, with atmospheric pressure known only six parameters need be obtained from the hammer manufacturer. The first three geometric values are usually well known. The timing quantities t d  and tcd  vary only slightly for normally performing hammers and are equal to 0.5 to 2 ms. The most important parameter is the maximum pressure, P max. Ideally, this value would be determined by measurement. However, as discussed, Pmax varies depending on a variety of conditions such as ambient temperature, altitude, fuel type, soil resistance, driving system properties, pile flexibility, hammer state of maintenance, etc. In addition, high frequency pressure waves in the chamber superimposed to the average pressure value make interpretation of pressure measurements difficult. Furthermore, testing all diesel hammers under controlled conditions would be prohibitively complicated and expensive. Therefore, instead of measurements, the P max values are iteratively computed such that the rated stroke is achieved by the hammer model under test conditions. The computational procedure followed for many of the hammers contained in the 2002 and later hammer data file is described in Appendix B2.

 3.3.3.2 The Atomized Fuel Injec tion Model  Atomized fuel injection is commonly used in diesel engines. The process requires that the fuel is injected into the chamber beginning and ending at certain piston positions or corresponding chamber pressures. The injection pressure may be 1000 psi (7000 kPa) or higher. Such pressures produce a finely distributed fuel spray. As soon as the fuel atomized in such a manner is mixed with hot air, it combusts. The following phases are distinguished (see Figure 3.3.3.2a and 3.3.3.2b). 

36

The ram descends and closes the exhaust ports. GRLWEAP Procedures and Models

Version 2010



The air trapped inside the hammer cylinder between the ram and the impact block is compressed and its temperature increases.



When the ram is at a certain, small distance from the impact block, atomized fuel is injected into the chamber. This ram position can be computed from the "initial combustion volume", V ci. The fuel starts to burn and reaches a maximum pressure level at the time of impact (smallest volume or “chamber volume”).



 After impact, the ram rises and combustion ends, when the ram has reached a certain distance from the impact block. Until the corresponding final combustion volume, V ce, is reached the pressure stays constant at P max.



The ram rises further allowing the gases to expand and pressures to decrease until it clears the exhaust ports and the pressure in the chamber returns to the atmospheric level.

Version 2010

GRLWEAP Procedures and Models

37

Differences between the atomized and liquid fuel injection models only occur shortly before and after impact, i.e. Steps C and E. Most of the compression and expansion periods are identically modeled for both types of fuel systems. An exception is an expansioin coefficient which is typically ce  = 1.35 in the GRLWEAP models. For the atomized injection, the GRLWEAP representation may be expressed as follows. Step C:  The gas pressure starts to increase from the precombustion pressure, Pci, defined by the volume V ci  (volume at which combustion begins). It reaches the maximum combustion pressure, Pmax, at impact (volume equal to V f ). In GRLWEAP this phase was modeled by a quadratic interpolation between P ci, Vci and Pmax, Vf . Step E: The pressure stays constant at Pmax until the volume V ce has been exceeded. At that point, both reference pressure and volume are set to Pmax and Vce, respectively. In summary, again nine quantities are needed to compute pressure for atomized fuel injection. For atomized injection, the two volumes, Vci and Vce take the place of the liquid injection parameters t cd  and td. However, in contrast to the rather insensitive liquid injection timing parameters, the two combustion volumes have a very significant effect on the hammer performance.

 3.3.4 C los ed E nd Hammers (Double Acting )  3.3.4.1 Double, Differential or C ompound E C H  As the ram descends, a closed end hammer not only falls under gravity but also experiences a downward pressure. For a double, differential or compound acting ECH, GRLWEAP does not differentiate as to how the ram has obtained its impact velocity and it is not necessary to deal with the active downward pressure. Instead of working with the actual stroke, it is therefore necessary to calculate an equivalent stroke: he = Er /Wr  

(3.12)

where Er  is the hammer's rated energy and W r  is the weight of the ram. With eh being the hammer efficiency, the impact velocity is then: ½

Vri = (2g he eh)  

(3.13)

If a double acting ECH is run at a pressure less than rated, then the energy provided by the pressure is proportionally lower. Given the portion of the energy that is provided by the pressure, f ep, and the ratio of actual to rated pressure, r ap, the reduced equivalent stroke becomes: her  = he [1 - f ep(1 - r ap)] 38

GRLWEAP Procedures and Models

(3.13a) Version 2010

For example, if the pressure provided energy component were 40% of the rated energy, then ram weight times fall height would be 60% of the rated energy. If the hammer were run at 70% pressure (r ap  = 0.7), then the equivalent stroke would be: her  = he[1 - 0.4(1 - 0.7)] = 0.88 he

(3.13b)

For inclined pile driving the same stroke reduction consideration has to be made as for single acting hammers.

 3.3.4.2 Clos ed End Dies el Hammers For double acting diesels, the force on the ram top is computed to determine (a) the hammer blow rate, (b) the hammer-pile-soil behavior during the precompression phase, and (c) the necessary fuel reduction to avoid uplift. GRLWEAP calculates gage pressure on the ram top based on an expansion coefficient, cbp, (which is usually 1.4). Thus, the bounce chamber pressure, Pb, may be calculated from: Pb = Pa (Vbi/Vb)cbp - Pa 

(3.14a)

where Vbi is the initial volume in the bounce chamber: Vbi = hb Art + Vct 

(3.14b)

with hb  being the "compressive stroke" of the bounce chamber, i.e., the distance from the bounce chamber ports to the top of the cylinder. Art is the cross sectional area of the ram top and V ct is the compression tank volume. The maximum stroke at which uplift is imminent is determined from the reaction (cylinder) weight of the hammer, W c, yielding the uplift pressure: Pu = Wc/Art 

(3.15)

and by substituting P u  into Eq. (3.14a) for P b, the volume and therefore position of the ram at uplift is easily calculated from Eq. (3.15). Note that the closed end diesel hammer has a reduced effective stroke when used on an inclined pile. The user therefore should not only reduce the reaction weight (Options/Hammer parameters), the hammer gravitational acceleration, the hammer efficiency (see Help Table), but also the pressure such that the maximum calculated stroke does not exceed the maximum geometric stroke times the cosine of the inclination angle.

Version 2010

GRLWEAP Procedures and Models

39

 3.3.5 Vibratory Hammer Model The GRLWEAP hammer model consists of 2 masses which are connected by a linear spring and by a linear dashpot (Figure 3.3.5) has to be redone. There may be hammers with more than two or only one mass, however, the GRLWEAP model currently does not represent these relatively rare cases. The bias (upper) mass serves as a vibration isolator and adds downward force to the driving system. It is also subjected to an upward directed force, called the crane line force, F L, which may represent the crane line pull (usually it may be assumed that the hammer's weight is fully supported by the pile and then F L  = 0). Downward directed (a negative value), it would represent a crowd force, which would help the pile to penetrate more quickly. Upwards directed (positive), it could cause an extraction, if it is greater than the weight of the hammer plus the weight of the pile. Note, however, that the program will not calculate an upward extraction rate of movement. GRLWEAP applies the sinusoidally varying vibratory force, F V, to the hammer's oscillator (lower) mass (which contains the eccentric masses). The power provided through this force is monitored and held to at most the rated power value. The vibratory force may also be modified (reduced) by an efficiency value which, in general, is left at unity (no efficiency reduction). The vibratory force is not affected by pile batter. Thus, ignoring the inertia of the eccentric mass (which is generally not accurately known) due to the motion of the bottom (oscillator) mass: 2

FV = me [ω  r e (sin(ωt)]

(3.16)

with me = the sum of all eccentric masses, r e = the radius of the center of gravity of the eccentric masses from their center of rotation The hammer model also considers a spring constant for the connecting spring between upper and lower mass. A dashpot constant can be specified for a dashpot in parallel with the connecting spring impact (as for the hammer cushion discussed in Section 3.4, Eq. 3.17). A clamp (sometimes also called jaws) weight, specified in the data input, is added to the weight of the oscillator. During the start-up time period the frequency of the hammer is linearly increased with time in GRLWEAP. As a result the vibratory force increases during that time period quadratically. In general, the start up time period analysis has little effect on the final results. It may be used for special studies. It cannot, however, be expected that the realistic resonance effects can be detected with a variable frequency analysis, because of the simplified soil resistance analysis according to Smith. The upper mass of a vibratory hammer is subjected to the upward directed crane line force. It can be input negatively to simulate a crowd force. 40

GRLWEAP Procedures and Models

Version 2010

Figure 3.3.5: Schematic and Model of a Vibratory Hammer The user can modify the frequency for vibratory hammers in the same way in which the stroke can be modified for impact hammers. Note, that although the highest (rated) frequency provides for the highest forces, the pile may actually penetrate easier at lower frequencies and it is, therefore, recommended to check the penetration times for a variety of frequencies. However, it may not be wise to reduce the frequency to values less than 10 Hz where it is known to cause undesirable resonance. Also, for very low frequencies it may be necessary to increase the analysis time (in General Options/Numerical) so that sufficiently many vibration cycles are analyzed.  A check of the graphical variable vs time output may be helpful in assuring proper convergence.

 3.3.6 Hydroblok H ammers Since 2002, GRLWEAP does not include a working model of the Hydroblok. For further information, please contact PDI.

Version 2010

GRLWEAP Procedures and Models

41

 3.3.7 Drop Hammers Drop hammers are not very easily standardized because of their many possible configurations. There are two main categories, (a) the drop hammer which is freely released and (b) the drop hammer which has to unspool a winch. Obviously in the latter case higher energy losses must be expected not only because of the inertia of the winch but also because the operator then tends to catch the ram just before impact so as to maintain stability. In both cases the hammer stroke is probably not very well known. These uncertainties have to be covered by the hammer efficiency. The remaining model is simply that of an external combustion hammer.

 3.3.8 Hammer E nerg y Los s es The wave equation analysis of an impact hammer requires the calculation of ram impact velocity, v ri. During the fall of an ECH ram, the pile does not experience dynamic forces. However, the weights of assembly and helmet create a static force in pile and soil. Thus, the dynamic analysis only has to cover the time period during and after impact. For the diesel hammer, appreciable forces are exerted onto the pile before impact due to air compression in the cylinder. In general, the pile already has a noticeable velocity prior to ram impact and soil resistance is activated. Therefore it is necessary to start the analysis of diesel hammers at the time of port closure. It has been stated earlier that energy losses in the hammer are easily considered using the hammer efficiency, e h, and certain rules of assigning efficiency values have been set up. For hammers with impact velocity monitoring, reasonable results are achieved with an efficiency e h = 0.95 if the monitored energy is the basis for the analysis. Obviously, most losses, such as friction, have been considered for these hammers by the impact velocity measurement. Only losses occurring during the impact event itself (e.g. due to hammer-pile misalignment) have to be considered. For vibratory hammers, the efficiency concept is not strictly applicable. However, in order to allow for some reduction of the output force, relative to the theoretical value, an efficiency multiplier (less than or equal to 1.0) may be applied to the calculated centrifugal force. The following efficiency values have been included in the hammer models in the GRLWEAP hammer data file. It is recommended that the analyzing engineer carefully review and modify these efficiency values, if measurements so indicate. Furthermore, because of the uncertainty of actual hammer behavior it is recommended to analyze (a) conservatively for stresses at a somewhat higher efficiency than normal or (b) conservatively for bearing capacities and/or blow counts with a slighlty lower efficiency). A ± 0.1 variation would be reasonable (even for a 0.95 efficiency, since values above 1.0 have occasionally been observed, maybe due to overstroking. The following recommendations for drop hammer efficiencies are just that

42

GRLWEAP Procedures and Models

Version 2010

and like all efficiency values should be backed up by individual measurements. eh = 0.67 for single acting air/steam hammers and for drop hammers with free release eh = 0.50 for double acting air/steam/hydraulic hammers and drop hammers with spooling winch eh = 0.80 for all types of diesel hammers eh = 0.80 for hydraulic hammers, single acting or power assisted but not double acting and without impact velocity measurement eh = 0.95 for hammers whose rating is based on measured impact velocity eh = 1.0 for vibratory hammers  Again, these recommendations represent an average hammer behavior and efficiency values may be required to match measurements. Note also that eh normally covers losses occurring both during ram descent and impact. The efficiencies in the GRLWEAP hammer data file have been chosen with no consideration of hammer manufacturer. Hammer performance differences should be individually accounted for by the user. For hydraulic hammers, a more uniform rating has been adopted by combining the freefall hydraulic hammer category of pre-2002 versions with the category of other modern hydraulic hammers without impact velocity measurements. Hammers which optionally can be equipped with impact velocity monitoring sensors, have been given a 0.8 efficiency as though they are not equipped with that feature. In that case, the user is responsible for modifying the efficiency. In fact, under all circumstances, it is the user’s responsibility to check all hammer data of the GRLWEAP hammer data file prior to using it.

 3.3.9 Inclined Pile Driving Since 2010 GRLWEAP does provide for an input of the pile inclination (Options/ Pile Parameters/ Batter-Inclination), and gives the analyst immediate recommendations which are also given in the On-line Help. However, in any case, depending on the hammer type, the user has to be aware of and consider one or more of the following energy losses and model adjustments: Hammer Friction:  a reduction of the hammer efficiency should be considered according to the help table for all except vibratory hammers. Reduced Stroke: all hammers whose effective, vertical stroke is limited by the hammer inclination should be analyzed either with a reduced stroke or an efficiency reduction. Exceptions are open ended diesel hammers, Version 2010

GRLWEAP Procedures and Models

43

hammers whose rating is based on impact velocity monitoring and vibratory hammers. Note: reducing the gravitational acceleration of the hammer does not affect the ram’s mass or impact velocity, however, it does reduce the static assembly and helmet weight resting on pile and soil prior to impact. Reduced Reaction Weight: as stated earlier the reaction weight of closed ended diesel hammers must also be reduced to model the reduced maximum bounce chamber pressure. The input of a reduced hammer gravitational acceleration does not affect the reaction weight.

 3.3.10 Drivi ng at the Pile B ottom or at an Intermediate Pile Location This is an Offshore Wave option. It may be desired to locate a hammer not at the pile top but at an intermediate location along the or at the bottom (Figure 3.3.10.1). Actually, bottom pile driving is not an unusual technology, in fact, it is frequently done even on land.

Figure 3.3.10.1: Schematic of bottom and intermediate pile driving

44

GRLWEAP Procedures and Models

Version 2010

Only EC hammers can be used in this analysis. It is assumed that the ram of the hammer strikes a hammer cushion and that the hammer cushion is supported by a plate (the helmet in the input). This plate must be somehow supported by the pile. It is assumed that this pile support combined with the helmet have a certain stiffness which is an additional input (Figure 3.3.10.2). A further additional input is the hammer location which can have length values between 0 and the pile length. If it is zero then the hammer drives at the pile top. If it is equal to the pile length, then it drives at the bottom. It is interesting to view the stresses along the pile (extrema tables) when the pile is driven at an intermediate location.

Figure 3.3.10.2: Schematic of bottom and intermediate pile driving

 3.3.11 S tatic S oil C olumn Weig ht  This is an Offshore Wave option This option may be useful when analyzing an intermediate hammer position or a bottom plate inside the pile some distance above the pile toe. However, even a normal open ended pipe pile which drives in the coring (nonplugging) mode has a soil column acting as a static weight on the soil. While it may be assumed that this soil mass has negligible stiffness compared to the pile it potentially adds a large additional weight on the soil at the bottom of the pile. This GRLWEAP feature allows for consideration of the internal soil weight to be considered in the static equilibrium analysis which occurs prior to the dynamic analysis. Note: the static soil resistance in a driveability analysis should be equal to the weights of soil column and pile plus the load that can be supported by the pile. This option may be Version 2010

GRLWEAP Procedures and Models

45

helpful when comparing driveability of a coring pile with one driven at its bottom (empty pile). If it is desired to consider the mass effect of this plug in the dynamic analysis, then that must be accomplished by an increased specific weight in the pile model (P1 input form); this would assume that the stiffness of the soil mass can be ignored. The input of the static soil column weight requires the following input (Figure 3.3.11.1).   

Effective Soil Column Area, A S; Buoyant Soil Specific Weight, γ S; Maximum Soil Column Length, LS.

Figure 3.3.11.1: Soil column weight model In the calculation, the total plug soil weight is evenly distributed among the pile segments which are located between segments No. i and N when performing the static equilibrium analysis prior to the dynamic analysis. In this notation, i is the segment where the soil column begins and N is the bottom segment number. The soil column, L C, is assumed to begin at either LS or Lp (pile penetration), whichever is smaller. The total plug weight is WP = AS γS LC . 3.4 Driving System Model The driving system consists of a striker plate, hammer cushion, helmet, helmet insert and, for concrete piles, a pile cushion. This system is represented by two nonlinear springs and a mass. For the ECH the spring for the hammer cushion is modeled in series with the ram spring (Figure 3.4). For all impact hammers, the pile cushion spring is modeled in series with the pile top spring. For diesel hammers, if no hammer cushion is present, then GRLWEAP splits the impact block spring and places one spring on top of the impact block and the second one on top of the helmet. For ECH without hammer cushion, the bottom ram spring acts on top of the helmet. 46

GRLWEAP Procedures and Models

Version 2010

Figure 3.4: Schematic and Model of the Driving System For systems without helmet mass, the ram’s bottom spring acts directly on the pile top spring for ECH. For diesel hammers, the pile top spring is combined in series with the hammer cushion spring (if any) and/or the impact block spring. Note that earlier versions of GRLWEAP required a helmet mass for diesel hammers. Since 2002 this requirement has been removed, because diesel hammers have now been introduced (e.g., “Direct Drive” hammers) whose impact block strikes the pile directly. The mass between hammer and pile is called “Helmet” in GRLWEAP terminology, although it is also often called the “Cap”. In any event, the weight of devices like the striker plate, hammer and pile cushion, pile adapters or inserts, etc. should all be included in the "helmet mass", since it is really the total mass separating hammer components from pile top. The driving system model also contains a dashpot in parallel with the hammer cushion spring. Its damping constant is computed from: ½

cdh = 1/50 cdhi (kr ma)  

(3.17)

where cdhi is a non-dimensionalized input value, k r   is the hammer cushion stiffness, and m a is either the impact block (diesel) or helmet (ECH) mass. The default value of c dhi  is 1. The user can remove this dahpot whose function is to suppress spurious vibrations by entering certain multipliers (see General Options/Damping and On-Line Help: Damping Options /Hammer).

Version 2010

GRLWEAP Procedures and Models

47

3.5 Pile Model The pile model consists of springs, masses, and dashpots (see Figure 3.5). The pile is divided into N segments whose lengths are given by: Li = αiL

(3.18)

The program chooses the number N such that approximately 1 m long pile segments result. (It is sometimes reasonable to a user larger N number for increased accuracy of calculation. For example, for uncushioned hammers, an N producing 0.1 m segment lengths has already been successfully tried where measured records had to be matched.) In Eq. 3.18 L is the total pile length and α i is a multiplier which is normalized such that: ∑ (αi) = 1.0, i = 1,2,...,N

(3.19)

Ordinarily, the αi values are all assumed to be equal to 1/N by the program, however, the user may modify these values (Options/ Pile Segment Input). Weights of pile masses and their stiffness values are calculated as for rams (Eq. 3.3 and 3.4). In pre-2002 versions of GRLWEAP, the pile's static weight was not considered in the Bearing Graph analysis. Thus, it was tacitly assumed that the soil supports the pile weight before the ram impacted. The GRLWEAP capacity calculated from the bearing graph and observed blow count would then be the limit load which can be placed on the pile top. This also implied that the ultimate pile capacity would really be the GRLWEAP capacity plus the pile weight. The pile weight, however, was considered in residual stress analysis, in the vibratory analysis, and by s ubtraction of a “dead load”, in the driveability analysis option. This created a confusing situation when Bearing Graphs were compared with driveability results. GRLWEAP now allows the user to enter two gravity values, one for the pile, g p, and one for the hammer, gh. Since the basic input for the mass of pile, helmet and hammer is done in the form of their weight, the program first converts these 2 2 values to mass by division with g = 9.81 m/s   (32.17 ft/s ). The effective static weights, however, are then backcalculated by multiplication with gp and gh. Normally, g p = gh = g, however, the user may modify g p and gh to account, for example, for buoyancy or pile batter. The gravity values are used in an equilibrium analysis, which precedes the dynamic analysis to calculate initial soil and pile deformations and forces. For the hammer, the ram is not included in this analysis since it is expected that the ram is not supported by the pile prior to impact. Note that a reduction of pile and/or hammer gravity should be considered for battered and underwater pile driving.

48

GRLWEAP Procedures and Models

Version 2010

 A third parameter, the pile damping value, can be specified by the user. Since little is known about the correct structural damping model, and since this type of damping produces relatively small energy losses compared to soil damping, an elaborate model does not seem justified. Thus, viscous damping was assumed as follows: cdp = (1/50) cdpi (EA/c)

(3.20)

with cdpi  being a non-dimensionalized input number and EA/c being the impedance of the pile top; c dp is the same for all pile segments regardless of segment length or impedance. For piles with greatly varying cross sectional or material properties, it is suggested that comparison runs be made with different cdpi  values to test the sensitivity of the solution to pile damping. (The input can be made in General Options / Damping).

Figure 3.5: Wave Equation Models for Various Hammer TypesThe pile data input also contains additional parameters which are not used for the generation of the pile model. These values include: 



Perimeter, which is needed in driveability analyses and static geotechnical analyses (ST, SA, CPT, API) for the calculation of shaft resistance forces from unit resistance values. (Note: it is sometimes convenient to consider inside friction in an open ended pipe by an increased perimeter). Toe Area, which is needed in driveability analyses and static geotechnical analyses (ST, SA, CPT and API) for the calculation of end bearing. (Note: in the S1 table the Toe Area can be varied

Version 2010

GRLWEAP Procedures and Models

49

such that, for example, the plugging can be considered in certain soil layers and not in others by entering, respectively, the full pipe area and the toe steel cross sectional area. 

Pile size and Pile type, both of which are used for the assignment of pile toe quakes and for finding finding in the data base the appropriate manufacturer’s manufacturer’s   recommended driving system (which is a function of hammer model, pile type and pile size).



For non-uniform piles only, a Critical Section Index which allows for selection of that portion of the pile model that is considered important for the output of “maximum” stresses. This index is either 1 or 0. The user should set it to 1 for those sections of the non-uniform pile model whose maximum stresses should be considered for final output. The CSI is only reasonable when two or more pile materials are analyzed. For example, a system consisting of a steel follower driving a concrete pile will have numerically highest compression stresses in the steel, however, the concrete stresses will most likely be of more interest and the CSI should, therefore, be zero for all steel sections while the CSI of the concrete portions of the pile profile should be set to 1.

3.6 Splice/Slack Model GRLWEAP uses a splice/slack model which has also been incorporated into the models models for the cushions, impact impact block/helmet, block/helmet, and pile top. This model contains three parameters: a tension slack, d st, a coefficient of restitution, ca, and a round-out deformation or compressive slack, dsc. The general shape of the resulting force-deformation curve is shown in Figure 3.6.

50

GRLWEAP Procedures and Models

Version 2010

During compression of the splice model, force increases quadratically (stiffness increases linearly) with respect to deformation until the round-out deformation, dsc, is reached. The corresponding force at this point is Flim. Beyond this point, force increases linearly, with the slope given by the spring stiffness, stiffness, k. During the subsequent expansion, force decreases 2 linearly with respect to deformation, but this time the slope is k/c a . Note, however, that the deformation, over which round out occurs, is smaller during unloading than during loading for c a values less than 1. For the extension of the spring, GRLWEAP applies the same rounding procedure. However, the spring stiffness begins to increase from zero only after the spring has extended beyond the slack distance, d sl. Within this separation distance, the spring force is always zero. For springs, which should not take any tension at all, the user should set d sl to an arbitrarily large value such as 9 ft or 99 mm. For all other interface springs, experience shows that a 0.01 ft or 3 mm (default) value is adequate. Attempts to match measurement results have shown that only very soft materials, such as a plywood cushion, require a larger than the default round-out value. In this way, cushion, pile top, and splice forces can be calculated with the same algorithm. algorithm. Because of the rounding feature, numerical stability of the analysis of splice piling is assured. Note that this this rounded-out splice model is always always used in GRLWEAP, when d sl > 0. The splice model is only needed for those splices which allow for some forceless deformation (slack). For example, mechanical splices of concrete piles fall in this category while welded splices of steel piles do not. Also a can splice (has no tension connection at all) could be modeled with the splice model. As an example, the can splice, which usually includes a thin plywood sheet, could be modeled with  dsc = 3 mm (0.01 ft), default dsl = 99 mm (9 ft), an arbitrarily large number for an  unlimited extension, and ca = 0.5 (for wood)  3.7 Soil Model

 3.7.1  3.7 .1 The Th e B asi as i c S mith S tatic tatic R es i s tanc tance e Model GRLWEAP’s soil model is basically a Smith approach, appro ach, i.e. it i.e. it consists of a spring and dashpot (Figure 3.5). The elastic spring yields at a pile segment displacement equal to qi  (quake). Beyond that point, there is no further increase in static resistance, R si, with increased displacement, u i. Thus, as long as the pile segment’s velocity is positive (downward), i.e., during the initial loading phase, Rsi = (ui/qi) Rui for ui < qi 

(3.21a)

and

Version 2010

GRLWEAP Procedures and Models

51

Rsi = Rui for ui > qi (3.21b) where Rui  is the the ultimate static resistance at segment i. During unloading, i.e.  i.e.  when the pile segment has an upward (negative) velocity, the spring rate is equal to that used in the loading path.The most negative shaft resistance value is  –R  –Rui. The lowest toe resistance value is equal to zero. For shaft resistance elements, the soil resistance can be come negative; however, it cannot be less than -Rui. At the toe, the static static soil resistance cannot be less than zero. The static shaft resistance and end bearing values, Rui, added together make up the ultimate capacity of the pile, R ult. For the bearing graph analysis it is customary to choose 10 different R ult  values, one of them usually equal to the expected or required R ult. Thus, in a bearing graph analysis, the static geotechnical analysis only serves to determine how many percent of R ult are expected to act along the shaft and how the shaft resistance is distributed along the pile. Also, the end bearing percentage is found in that manner since it is the difference between shaft resistance and total resistance. Of course, it is wise to make a reasonably accurate static geotechnical analysis prior to the dynamic analysis, not only to find a meaningful resistance distribution, but also to determine the most likely penetration where the required capacity will be obtained. Please note that these static formula methods (such as ST, SA, CPT and  and  API)  API)  generally calculate a long term resistance while at the end of driving both a different resistance distribution and total capacity must be expected due to the dynamic effects on the resistance (the reverse effects of setup and relaxation). This long term capacity would correspond to a restrike situation. To be strictly correct, therefore, a so-called SRD (Static Resistance to Driving) analysis would have to be performed as it is usually done for a Driveability analysis. While the Rui values are practically assumed to construct a bearing graph (which then serves to find a capacity given an observed blow count), the driveability requires that an accurate static analysis is performed for each depth where an analysis is to be performed. This process is discussed in detail in Section 3.12.2. Shaft quakes have been found to vary little and clear relationships between soil type and shaft quake or pile size and shaft quake have not been established. A 2.5 mm (0.1 inch) shaft quake is reasonable reasonable and generally accepted. Toe quakes, on the other hand, can vary widely. In general, hard soils or rock are stiffer and the toe quake (the inverse of the toe resistance stiffness) stiffness) is is therefore smaller smaller than in softer soils. soils. Furthermore, displacement piles such as a concrete or closed ended pipe piles require much larger displacements to activate the ultimate toe resistance than nondisplacements piles. The reason is that activating the ultimate capacity then requires a much larger pile toe penetration, often leading to pile size dependent failure criteria (e.g., D/30 or D/10). The GRLWEAP GRLWEAP toe quake recommendation similarly expresses its magnitude in terms of a function of pile diameter (size), D. For very dense or hard soils the recommendation recommendation is 52

GRLWEAP Procedures and Models

Version 2010

D/120; for softer materials it is D/60. Please note, that much larger toe quake values have also been observed and that toe quakes are often quite different when driving, restriking or statically loading the same pile. Large toe quakes can cause tension stresses even when resistance values are high. Large toe quakes also produce high blow counts and can, therefore, make driving of displacement piles very difficult. For bearing graphs, a more detailed though rarely used input mode is also available allowing for specification of different shaft quakes for each pile segment. See Options/ Soil Parameters/ Soil Segment Damping/ Quake/ Individual Damping Input for Each Segment. Activating the shaft quake input in this window, however, requires that first the static resistance distribution is entered individually for each segment, after choosing “Detailed Resistance Distribution” in the resistance distribution drop down menu. For residual stress analyses or vibratory analyses, both of which calculate pile motions and forces under consecutive loadings, the possibility exists that the pile toe is pushed upwards a certain distance above the maximum penetration achieved under the previous blow or compressive cycle. GRLWEAP static toe resistance model has therefore been modified for these two types of analyses such that the static toe resistance will remain zero until the pile toe has moved through the cavity developed under the previous impact or compressive cycle.

 3.7.2 S oil Damping  3.7.2.1 The B asic S mith Damping Model GRLWEAP’s standard damping model is identical to original Smith model. Other models can be chosen in Options/ General Options/ Damping. Rdi = jsi |Rsi|vi 

(3.22)

where Rdi is the damping resistance force and j si, vi  and Rsi are the Smith damping factor, the pile segment velocity, and the static resistance force, all at segment i, respectively. Smith's damping factor has units of time over length. Even though more than half a century has passed since Smith developed this model, today we are still recommending the same basic factors for damping along the shaft, i.e., 0.15 s/m (0.05 s/ft) for sands and 0.65 s/m (0.2 s/ft) for clays. Different values are used where measurements have been made or in mixed soils. Only for toe damping recommendation changed to 0.5 s/m (0.15 s/ft) for all soil types (see also 3.7.2.3). The second choice is called Smith viscous damping and it replaces the term |Rsi| in Eq. 3.22 by R ui, i.e the ultimate capacity value which, like j si, is a constant. Thus Eq. 3.23 expresses a linear viscous damping model. Rdi = jsi |Rui|vi 

Version 2010

(3.23)

GRLWEAP Procedures and Models

53

This approach is recommended for RSA, because, in agreement with measurements, the Smith-viscous model produces dampened pile motions after pile rebound when Rsi  values are small. Also for vibratory hammers, the Smith viscous approach appears to be preferable because of the relatively small velocities of vibratory driven piles. (Please note, however, that viscous damping for vibratory hammers works in both directions, upwards and downwards; the damping effect is, therefore, not necessarily one that reduces driveability. Also for lack of correlation data, there is no proof that the GRLWEAP model is reasonably accurate for vibratory analyses).

 3.7.2.2 E xtens ions to the Damping Model Note: The following three extensions of the damping model are usually reserved for research and require matching with measurements for successful implementation; they can be chosen in Options/ General Options/ Damping. The third damping choice is a non-dimensionalized viscous damping. ½

Rdi = jci vi (kpimpi)  

(3.24)

Here jci is the Case (Institute of Technology) damping factor. Note that the bracketed expression on the right hand side of Eq. 3.24, i.e. the square root of the product of segment stiffness and mass, is equivalent to the impedance of the pile segment (Young's Modulus, E, times the cross sectional area, A, divided by wave speed, c). This approach produces the ½ same linear damping as the Smith-viscous one if jci = jsi Rui / (kpimpi) .  A fourth expression allows for damping calculations according to Coyle, et al., (1970), i.e. with an exponential approach: n

Rdi = Rsi jgi vi  

(3.25)

where jgi is the Gibson damping factor with units of time over length to the 1/n power where n is an exponent, typically 0.2. Because of numerical problems with this approach, another damping equation was proposed by Rausche, et al., (1994): n

Rdi = Rai jRi vi  (vi/ vxi)

(3.26)

where jRi is the Rausche damping (also with units of time over length to the 1/n power), vxi  is the maximum pile velocity and R ai  is the maximum activated static resistance value of segment i. Both vxi and Rai are values that have occurred prior to or at the time of calculation of damping. After vxi and Rai have reached their maxima, Rdi is essentially linearly viscous.

54

GRLWEAP Procedures and Models

Version 2010

 3.7.2.3 Dis tribution of S haft Damping Smith’s approach varies damping forces along the shaft in two ways: it allows for different damping factors for different soil layers with cohesive materials getting a higher and granular soils a lower damping factor. Secondly, by making the damping force also a function of static resistance, a higher static resistance will also produce higher damping given the same damping factor and velocity. In standard bearing graph analyses which are normally done with either Smith or Smith-Viscous damping factors, we are usually a bit careless merely choosing a constant damping factor for the shaft. This shaft damping factor should be a weighted average over the shaft of the pile, weighted with respect to static soil resistance magnitudes. The static geotechnical analysis options (SA, ST, CPT and API) automatically perform this averaging. For bearing graphs, a more detailed though rarely used input mode is also available allowing for specification of different damping factors for each pile segment. See Options/ Soil Parameters/ Soil Segment Damping/ Quake/ Individual Damping Input for Each Segment. In non-research applications, either Smith or Smith-Viscous damping should be used. For these two damping approaches, damping factors are practically identical, with the Smith-Viscous approach yielding somewhat higher blow count results. In a driveability analysis, the damping factors are chosen for each layer according to their soil type. The static geotechnical analysis options ( SA, ST, CPT and API) help select these values and automatically enter them in the resistance distribution table (S1). For Case Damping the standard input also consists of one shaft and one toe damping factor. After multiplication with the impedance (conversion of a non-dimensional to a viscous damping factor), the total skin damping factor is distributed among the pile segments in proportion to the static resistance.  Again, the three non-Smith type damping models (Case, Coyle-Gibson, Rausche) are not recommended for non-research applications.

 3.7.2.4 S election of Damping Factors Damping factors would be quite different for any other type of damping approach; in other words, changing the damping definition must be accompanied by appropriate changes in damping factors. Generally, applicable damping factor recommendations are only available for Smith damping. Normally, for Bearing Graph analyses, GRLWEAP users input a constant damping factor even where the soil is layered. For conservatism of capacity Version 2010

GRLWEAP Procedures and Models

55

results, such average values may be somewhat biased towards the higher clay values. When choosing an average shaft damping value for a multilayer soil, the user should remember that damping according to Smith is greater in the layers with higher static resistance. Accordingly, the average damping factor should be a weighted average with respect to the static resistance components (see also 3.7.2.3). For mixed soils or silts an average value also has to be chosen. For example, the shaft damping factor for a soil consisting of clayey silt, a value of 0.5 s/m (0.15 s/ft) may be chosen which is somewhere between sand (normally js = 0.15 s/m) and clay (normally j s 0.65 s/m). For a non-cohesive silt, the damping factor chosen may be closer to sand, e.g. 0.33 s/m (0.1 s/ft). Toe damping input is generally rather simple, requiring only one factor for all soil and pile types. Note, however, that the 0.5 s/m (0.15 s/ft) recommendation is an average over potentially widely varying values. One exception should be made for this simple approach and that is when driving a pile to hard rock is considered. In that case the standard toe damping option may be too high and a lower factor such as 0.15 s/m (0.05 s/ft) may be more appropriate. Shales, soft or moderately hard limestones, weathered rock among other intermediate geotechnical materials probably behave dynamically more like their underlying soil components and their damping factors should reflect that (also as far as shaft damping is concerned).

 3.7.3 S oil Model Extens ions So-called research extensions of the soil model, described in Rausche et al. (1994), include the Plug, Toe Gap, Hyperbolic Toe Quake factor and Radiation Damping Models for Toe and Shaft. These extensions should only be used for research, e.g .  for correlation purposes with measured data. The Plug would be entered either with a plug toe area, which the program uses to calculate a plug mass, or directly as a plug mass. This plug only exerts compressive inertia resistance forces onto the pile bottom for a brief time period.  A Toe Gap is a short distance between pile bottom and a hard soil layer, as it may occur when a pile with little skin friction separates from rock during rebound. This feature makes blow count calculations uncertain, but is sometimes essential to explain large quakes and is generally only important in signal matching (CAPWAP) and not in wave equation analyses. The Hyperbolic Toe Quake Factor allows for a rounded-out toe resistance vs. toe displacement behavior. This factor multiplied with the toe quake (which defines the slope of the hyperbole at the origin) indicates at which pile toe displacement the ultimate resistance value is reached. Again, blow count calculations are more erratic when using this model. 56

GRLWEAP Procedures and Models

Version 2010

The Radiation Damping Models include a mass and a dashpot underneath the mass which represent the soil surrounding the pile soil interface represented by the Smith soil model. Recommendations for these model parameters are not available. 3.8 Numerical Procedure and Integration

 3.8.1 Ti me Increment Smith’s lumped mass model is mathematically stable only if the computational time increment is chosen shorter than the shortest (critical) wave travel time of any segment I. The critical time increment is the time that it takes the stress wave to travel through the pile segment: tcri = Li/ci 

(3.27)

or for a lumped mass element: tcri = (mi/ki)

½

(3.28)

where mi, ki, Li  and ci  are the segment mass, stiffness, length, and wave speed in segment I, respectively. The wave speed of the segment is: 1/2

ci = (Ei /ρi)  

(3.29)

with ρi  being unit mass of the segment. Where pile properties change within a segment length, all segment properties are averaged. In order to avoid instability, the computational time increment, t, is chosen as: t = min(tcri)/ 

(3.30)

where min(tcri) stands for the minimum critical time increment of all hammer and pile segments, and  is a number greater than 1. The program defaults to   = 1.6 (since input is in percent it would be input as 160). However, if numerical instability is indicated in the Numerical Output the user has the responsibility to choose a larger value (e.g. 300) in Options/ General Options/ Numeric/ Time Increment Ratio. While the critical time of the hammer-driving system-pile model is normally determined from the stiffest segment in hammer or driving system, the program also checks the pile segments, considering the effects of soil resistance on the stiffness of the pile segments. As a consequence, GRLWEAP may select the computational time increment with smaller values for high capacities than for low capacities.

Version 2010

GRLWEAP Procedures and Models

57

 3.8.2 A nalys is S teps  3.8.2.1 Prediction of Pile Variable at Ti me j The computation starts with a pre-integration (see block diagram in Figure 3.8.2.1a). Velocity values, vij, at segment, i, and time step, j, are calculated in a simple Euler integration from accelerations, aij. Displacements, uij, are predicted from vij-1  and uij-1,  i.e.  from their value at the previous time increment. For example, the ram of an ECH may be a simple mass, mr , that has an initial velocity equal to the ram impact velocity, v ri. Furthermore, at the beginning of the computations (j = 1) the first ram segment (i = 1) acceleration becomes a11 = gH 

(3.31)

with gH being the gravitational acceleration of the hammer. In this case the pre-integration produces: v12 = vri + a11 t

(3.32a)

u12 = u11 + vri t

(3.32b)

and

This process is repeated for all hammer, driving system and pile segments.

58

GRLWEAP Procedures and Models

Version 2010

Figure 3.8.2.1a: Block Diagram of Predictor-Corrector Analysis

Version 2010

GRLWEAP Procedures and Models

59

 3.8.2.2 Forces at a G iven S eg ment The force of the top spring on a segment is calculated from spring stiffness and spring compression, i.e.  the difference between the displacements of neighboring segments (see Figure 3.8.2.1b). t

Fsij = ki (ui-1 - ui)

(3.33)

The stiffness k i  is that of any hammer, driving system, or pile segment, subject to modification if there is a positive slack d st at spring i. The force of the top dashpot is calculated from the pile damping factor and the difference in the velocities of the neighboring segments. t

Fdij = cp (vi-1 - vi)

(3.34)

The force of the bottom spring is: b

F sij = ki+1 (ui - ui+1)

(3.35)

The force of the bottom dashpot is: b

F dij = cp (vi - vi+1)

(3.36)

Figure 3.8.2.1b: Schematic of Model of Segment i (left) and Free -Body Diagram (right)

60

GRLWEAP Procedures and Models

Version 2010

 3.8.2.3 Newton's S econd Law for A cceleration C alculation Using the external resistance forces, R sij and Rdij, calculated at the end of a previous time step, and the gravitational acceleration of the segment, g, it is now possible to compute the acceleration of a pile segment, i, during the current time step, j (see free body diagram in Figure 3.8.2.1b). t

t

b

b

aij = g + (Fsij - Fdij + Fsij - Fdij - Rsij - Rdij) / mi 

(3.37)

Of course, for a hammer or driving system segment, a similar equation would result, except that no resistance forces would be present. Note that g = g P for pile segment calculations and g = g H for hammer or driving system segments. For the bottom ram segment and impact block of a diesel hammer, the hammer’s pressure force would be a decelerating and accelerating force, respectively.  As mentioned earlier, since version 2002, GRLWEAP allows for an input of gravitational acceleration values, gH  and gP, for hammer and pile. This allows the user to modify the effect of weight, for example due to buoyancy or pile batter. The mass effect of the ram, pile or any other system component is not affected by the input of a gravitational acceleration different from the standard value. Note that the effect of batter on the impact velocity has to be considered primarily through modified inputs of stroke and efficiency. Since 2010 GRLWEAP provides automatic suggestions. As for the pile, if it is desired to construct a bearing graph that does not contain the weight effect of the pile, then g P should be set to zero. Except for long piles or those with a significant portion of their length extending above grade, it is expected that the pile weight has an insignificant effect on the results. Note that variation of g P  along the pile length is not possible. However, the offshore version allows for adding a soil plug mass effect for a user defined plug length.

 3.8.2.4 C orrector Integ ration  After the acceleration value has been calculated for a segment, its velocity and displacement values are corrected by integration under the assumption of a linearly varying acceleration: vij = vij-1 + (aij + aij-1) t/2

(3.38a)

and 2

uij = uij-1 + vij-1 t + (2aij-1 + aij) t /6

(3.38b)

Since the displacements are now more accurately known than after the t b initial prediction, the spring forces F sij  and F sij  are recalculated. The t b changes of dashpot forces F dij and F dij are also recalculated. Thus, for the calculation of the spring forces on the next lower segment, i+1, updated force values are available.

Version 2010

GRLWEAP Procedures and Models

61

 3.8.2.5 Further Iterations The process of calculation of forces, accelerations, and then displacements can be repeated for the same time increment, with the newly computed a ij, vij, and uij  values taking the place of the previous prediction. Repeat calculations would not be done if either the number of required iteration steps had been exceeded (the maximum number of iterations is an input in Options/ General Options/ Numeric) or if convergence of the velocities of the top and bottom pile elements had been achieved. After convergence of the pile variables, the resistance forces are calculated for the next interval according to Section 3.7. In general, additional iteration steps do not lead to a noticeable improvement of program performance and, since they have not been used in correlation calculations, they are therefore not encouraged. Experience has shown that smaller pile segments and/or smaller time increments are more successful in improving the numerical performance of the program than additional iterations. 3.9 Stop Criteria It is not possible to predict the required analysis duration (or for how many time steps an analysis has to be carried out) to assure accurate computation for the permanent set. If the analysis runs longer than necessary, undue computational effort is expended and round-off errors may increase. If it is stopped too early, the computed permanent set may be inaccurate (in easy driving too small). The stop criteria had to be different between ECH and diesels because of the diesel's particular requirements, primarily the need to analyze over a sufficient time period for an accurate stroke calculation. For vibratory hammers, a convergence of pile variables from cycle to cycle has to be considered. For ECH, the following stop criteria are used (this is not applicable for RSA): A1: The analysis is run until the user-specified (Options/ General Options/ Numeric) elapsed time, t max, has been covered. Of course, a short user specified t max may cause erroneous results. Therefore, tmax should be specified cautiously, and comparative analyses should be run. A2: If the user did not specify an analysis time t max, the analysis will cover an analysis time after impact of at least 3L/c (three times pile length divided by wave speed) plus 5 ms or at least 50 ms. The analysis is then stopped only when one or more of the following additional criteria are met: A2.1: The absolute value of the rebound (upward) velocity exceeds 20 percent of the maximum pile top velocity and 4L/c has been exceeded. A2.2: The pile toe displacement has exceeded 100 mm (4 in). Since this presents rather easy driving, not much can be learned from a

62

GRLWEAP Procedures and Models

Version 2010

longer analysis, however, this means that the minimum calculated blow count is 10 blows/m (3 blows/ft). A2.3:  The pile toe has rebounded to 80 percent of the maximum pile toe displacement. (Such a rebound is sufficient to assure that the pile will not penetrate deeper). A2.4:  No pile segment speed is greater than 20 percent of the maximum pile top velocity and the pile toe has rebounded to 98 percent of the maximum pile toe displacement. For 2-pile analysis, rebound checks are made on both piles. For diesel hammers, elapsed time is counted starting 2 ms before either impact or ignition, whichever occurs earlier. The analysis stops when either: B1:  The user-specified elapsed time, t max, has been covered. (See also  A1).Note that a very long analysis duration specified by the user may last into a new downward cycle and produce erroneous results, which may cause the message “Ram has downward velocity at end of blow”. B2:  If the user did not specify a time, t max, the analysis will cover an elapsed time of 3L/c + 5 ms or 50 ms, whichever is longer. The analysis then stops only if at least one of the following two conditions occurs: B2.1: No pile segment speed exceeds 20 percent of the maximum pile top velocity and B2.1.1: The pile toe has rebounded to 80 percent of the maximum pile toe displacement and the ram has reached a distance of at least 10 percent of the compressive stroke from the impact block. B2.1.2: The pile toe has rebounded to 98 percent of the maximum pile toe displacement and the ram has reached a distance of at least 20% of the compressive stroke from the impact block. For vibratory hammers, the user specified t max is analyzed. Alternatively, after the greater of 200 ms or 2L/c + 5 ms + 5 cycles have been analyzed, the segment displacements of consecutive cycles are compared. Once they converge or after at most 10,000 ms have passed, the analysis is finished. Obviously, this implies that for very low hammer frequencies, only a few cycles would be analyzed; for a 1 Hz vibratory frequency (60 cycles per minute, representing an almost static condition), this would correspond to at most 10 cycles. For the Smith algorithm, this is an extremely long analysis. For an analysis with a good chance of convergence to a steady state pile penetration, the hammer frequency should probably be at least 5 Hz.

Version 2010

GRLWEAP Procedures and Models

63

3.10 Blow Count Computation - Non Residual Stress Analysis For blow count calculations, the difference between the maximum toe displacement, umt, and the average quake is calculated. The average quake is: qav = ∑ [Rui(qi)]/Rut 

(3.39)

where Rui  and qi are the individual ultimate resistance values and quakes, respectively, and Rut  is the total ultimate capacity. A summation is made over all elements from i = 1 to N+1 (N is the number of pile segments). Resistance number N+1 represents the end bearing. The predicted permanent pile set is then: s = umt - qav 

(3.40)

and the blow count is: Bct = 1/s

(3.41)

It should be noted that for strongly variable quakes a residual stress analysis may be a more accurate method of blow count computation. For 2-pile analyses, umt  is the lesser of the two pile toe maximum displacements. However, this does not guarantee that the blow count is calculated accurately for a 2-pile analysis. For this analysis option, the user must carefully review the relative motions of both piles. For two pile toe resistance values, only the primary pile toe is considered, however, qav considers the resistance effect of the second pile toe. For vibratory analysis the average pile penetration per unit time corresponds to set per blow for impact hammers. The inverse of this value is the penetration time per unit time (e.g. per second) and this is a value that is often recorded for construction control. 3.11 Residual Stress Analyses (RSA)

 3.11.1 Introduction Primarily for reasons of computational economy, the Smith approach to wave equation analyses makes two important simplifications. 

64

In the beginning of the analyses, it is assumed that the forces in the pile and the soil are zero. GRLWEAP corrects this assumption only to the extent that the helmet-hammer assembly and pile weight are balanced by the static soil resistance. Since 2002, GRLWEAP performs an accurate equilibrium check prior to dynamic analysis. Earlier versions of the program only performed a simplified analysis. GRLWEAP Procedures and Models

Version 2010



At the end of the analysis, the pile starts to rebound. However, the full rebound is not analyzed, and the final permanent set is "predicted" by subtracting the average quake from the maximum toe displacement. This approach assumes that the pile rebounds to a stressless state and is therefore consistent with Smith's simplifications.

There are many cases for which Smith’s simplified approach is satisfactory. For example, if the soil exhibits little or no skin friction forces, the conventional assumptions are justified. Another example is a pile which is relatively rigid such that its elastic compression is small compared to the soil quakes. Hery (1983) and Holloway et al. (1978) describe reasons for, and calculation methods of, residual stress assessment. In general, however, a pile does not completely rebound after the hammer blow is finished. Often the toe quake is larger than the skin quake and therefore, the toe tends to push the pile back up a relatively long distance.  As the shaft elements of the pile move upward during rebound, their resistance first decreases to zero and then becomes negative until an equilibrium exists between the upward directed (positive) resistance forces at the lower portion of the pile and the downward directed (negative) shaft resistance values of the upper pile. The pile is then at rest and compressive forces are locked into pile and soil.  A large toe quake is not the only condition necessary for residual stresses to occur in pile and soil at the end of a blow. Consider a very flexible pile with a high percentage of shaft resistance. During the first hammer blow, the pile's upper portion will move deeply downward due to the pile's high flexibility. The shaft resistance will prevent a large pile toe penetration.  After the hammer ceases to load the pile head, the upper pile portion attempts to elastically rebound a large distance, the toe only a short one. The upper friction forces will turn negative and the pile will remain compressed. The next blow will be able to drive the upper pile portion deeper because the pile is pre-compressed and the downward upper resistance forces help move the pile. At the end of the second blow, the precompression in the pile may be greater than for the first blow and extend deeper along the pile. Eventually, all pile segments will achieve the same set, and pile compression will no longer increase from blow to blow. (For very long and flexible piles, it may take groups of blows to produce a converging compression pattern.) Also, it is possible that pile sets per blow converge towards zero (refusal) after initial blows produced a pile top set (but probably no pile toe set). It is also conceivable that in very long piles both tensile and compressive stresses remain after a blow is finished. It is likely that the major portion of compressive soil resistance acts along the shaft of the pile near its bottom. End bearing need not be present for residual stresses to be locked in pile and soil. Version 2010

GRLWEAP Procedures and Models

65

For very long and flexible piles it may be difficult to decide whether or not convergence has occurred in an analysis. For that reason, since 2002 GRLWEAP has allowed a user to input the number of trial analyses with the default increased from 10 to 100. Also, the RSA blow count calculation now relies on the trends of sets that groups of blows develop rather than the difference of the sets of two consecutive blows. In this way, nonconvergence of RSA analyses is generally avoided.

 3.11.2 Details of the G R LWE A P R S A Procedure GRLWEAP undertakes the following computational steps in an RSA: 

After the first standard dynamic analysis is finished for one R ut value, and displacement and static resistance values together with the quakes are subjected to static analysis, the pile and soil displacements and forces in static equilibrium (all velocities are zero) result.



A second dynamic analysis (which may be thought of as a simulation of a second blow) is done with the displacements and forces from the static analysis as initial values.



Again a static analysis is performed after the dynamic analysis is finished.



After at least 3 repeat analyses, pile sets are computed as the static pile top displacement of the present repeat analysis (or a group of analyses if sufficient analyses have been performed) and compared to the set from the previous analysis (or group of analyses). If these set values compare within 0.1% the analysis is finished. The analysis is also finished if the sets are very small and tend to go towards zero (refusal) or if the maximum number of trial analyses (input value) has been exceeded. Calculated set values are included in the numerical output and the user is urged to assure that the rather complex convergence analysis has performed satisfactorily by reviewing this list of sets .

Further details of possible interest to the GRLWEAP user are: 

66

The computed static displacement vector is always normalized such that the pile top displacement is always zero at the beginning of an analysis. The subtracted value can be considered the pile set if the analysis has converged, i.e. if the displacement pattern and therefore the residual forces are the same from blow to blow. Subtraction of the same pile top set from all segment displacements is acceptable, because pile segment displacements are relative values only. Pile and soil forces and the relative pile displacements are not affected by this normalization. This

GRLWEAP Procedures and Models

Version 2010

explains, however, why sometimes negative displacement values appear near the bottom of the pile. 

The output includes the final displacement pattern, normalized such that the top displacement equals the computed final pile set. The maximum stresses listed in the extrema table and the final summary table include residual stresses. The stresses remaining in the pile after the impact event is finished are listed in the RSA table following the extrema table.

The basic concept of RSA is to find the displacements and static soil resistance values when the pile has completely come to rest, or in other words, when a static equilibrium of the system is achieved. Theoretically, in a dynamic analysis, the pile never comes co mes to rest. It is therefore necessary to interrupt the dynamic analysis once it has been ascertained that the pile will not achieve additional penetration.  At the end of the dynamic analysis, for all N pile segments and N+1 resistance values, the final pile segment displacements and static resistance values are saved. ufi, i = 1,2,...,N

(3.42)

Rsfi, i = 1, 2,...,N+1

(3.43)

and

The unknowns are the pile segment displacement, u si, and static soil resistance values, R ssi, for which static equilibrium exists. For the static equilibrium analysis, the pile-soil model is the same as in the dynamic analysis, except that now the inertia forces and the forces in pile and soil dashpots do not exist. exist. The soil springs are still elasto-plastic elasto-plastic and at the end of the dynamic phase, a soil spring may be in any one of the following situations. 

the spring did not go plastic and therefore loading and unloading will occur on the same path (Figure 3.11.2a).



the spring did go plastic and the soil resistance is the ultimate resistance. The unloading will start from the point D and will follow a path parallel to the loading line (Figure 3.11.2b)



the spring did go plastic but started to unload. Further unloading will occur occur on the the same slope. If the ultimate soil resistance resistance in tension is reached, unloading will follow the plastic path (Figure 3.11.2c).

Version 2010

GRLWEAP Procedures and Models

67

Figure 3.11.2: Resistance vs. Displacement Diagrams Showing End of Dynamic (D) and Static (S) Analyses 

the spring did go plastic in compression, then in tension. Thus,unloading will occur along the plastic line (Figure 3.11.2d).

 A priori, it is not known which springs will become plastic and whether there will be loading or unloading of the soil springs. The best formulation, linking displacements and soil resistance values is Rsi = Rsfi - (Rui/qi)(ufi - ui)

(3.44)

with Rsi  being subjected to the same ultimate limits as discussed earlier. The mathematical solution of the problem involves a set of linear equations subject to the conditions of elasto-plastic springs.

 3.11.3  3.1 1.3 A ddition ddi tional al C omments about abou t R S A There is no doubt that the RSA better approximates actual piling behavior than the traditional approach which ignores the initial conditions of pile and soil. A drawback of using the approach is the fact that many correlation studies have been done without RSA. The magnitude of quake and/or soil damping values, obtained from such studies, may need adjustment when using RSA. For high resistance values, the accuracy of the RSA approach depends heavily on the accuracy of the soil model. For example, the relative magnitude of shaft resistance and end bearing and the relative magnitudes of quakes may significantly affect stress and blow b low count results. Even Smith’s simplifying assumption that loading and unloading quakes are equal or that the static resistance is elastic-ideal plastic may cause significant errors in RSA. Thus, before accepting potentially nonconservative RSA results, it may be wise to perform comparative analyses or use measurements to back up the calculations. calculations. At this time, time, the need for 68

GRLWEAP Procedures and Models

Version 2010

RSA has only been proven for Monotube™ piles, but not for regular p ipe piles, H-piles or concrete piles. For very long offshore offshore pipe piles, indications are that RSA results are more realistic than non-RSA results.

 3.11.4  3.1 1.4 R S A R es tri c tions tion s RSA cannot be run in conjunction with    

Two-pile analysis Two pile toe analysis Vibratory analysis (it practically does consider residual stresses) Piles involving slacks

In order to assure a well dampened behavior of the calculated pile motion (measurements do indicate a well dampened behavior) it is recommended to use the Smith-viscous damping approach rather than the standard method (Options/ General Options/ Damping). 3.12 GRLWEAP GRLWEAP Analysis Options

 3.12.1  3.1 2.1 B earing eari ng G r aph The most commonly used GRLWEAP analysis is the bearing graph calculation. A total ultimate capacity capacity is assumed and distributed on shaft and toe toe as per input. The blow count is is then then calculated. calculated. A higher total ultimate capacity value is chosen next and shaft and toe resistance are proportionally increased to match the capacity; this is followed by the dynamic analysis. analysis. Up to ten capacity values are analyzed in this way and an d then capacity is plotted vs calculated blow count. GRLWEAP also allows for an increase in either shaft resistance or end bearing with the other resistance component held constant for the ten capacities analyzed. These are then called constant end bearing or constant shaft resistance bearing graph analyses, respectively. 3.12.2 Inspector’s Chart: Blow Count vs. S troke troke

For diesel hammers, it is often required to adjust the driving criterion according to the apparent stroke. Stroke of open end diesel hammers can TM easily be monitored using a Saximeter  . Thus, it may be required to run individual analyses with several fixed strokes in order to provide the field inspector with a driving criterion for each apparent stroke. For simplification, an inspection graph option was built into GRLWEAP which automatically produces ten analyses with strokes increasing from a user specified minimum value to the hammer’s rated stroke. The Inpector’s Chart (IC) Chart (IC) provides a relationship between stroke (equivalent energy) applied and blow count required to achieve one ultimate capacity value. This option is often done in conjunction with a Bearing Graph analysis or a Refined Wave Equation Analysis. The IC analysis option Version 2010

GRLWEAP Procedures and Models

69

would not be meaningful for traditional mechanical hammers which are only capable of operation with a single fixed stroke. However, modern hydraulic hammers and diesel hammers can and/or should be operated at different stroke or energy levels in order to control stresses. The option is particularly useful for hammers which are difficult to control which means that a certain stroke or energy level cannot be required and the inspector has to select that blow count criterion that matches the actual stroke. For example diesel hammers may respond to certain conditions, among them ambient temperature, altitude, state of maintenance, fuel type and soil stiffness with different stroke levels. Note that it is important that the actual hammer stroke or energy level is known for a meaningful use of the IC. For example, hydraulic hammers without internal kinetic energy monitoring or without visible ram movement cannot be judged as to their energy output. Such hammers should be equipped with the appropriate measurement device (e.g., with the Energy Saximeter). For diesel hammers caution is advised, because a high stroke is sometimes an indication of preignition which increases the stroke while self cushioning the ram impact and thus transferring less energy than a normally performing hammer with lower stroke. Furthermore, high diesel hammer strokes for a relatively low capacity may not be achievable and the IC would show unusually high transferred energies if the combustion pressure, p max, were unreasonably increased to produce such a high stroke. For that reason, the IC analysis option for diesel hammers works most reasonably with a single hammer impact without adjustment of p max. However, the experienced analyst may want to review the two stroke options available for diesels: “Convergence of pressure with fixed stroke”  and “Single analysis with fixed stroke and fixed pressure” (see Options/ General Options/ Stroke which is only accessible for diesel hammers.) In the IC analysis mode, the former option will only reduce the pressure for low strokes and not increase the pressure for high strokes for conservatism. Please note, since the IC analysis options calculates blow counts for 10 different strokes, it is performing fixed stroke analyses and the hammer setting (p max level) has no effect when pressures are adjusted for convergence. However, p max  has some effect in the single drop case, because higher pressures add to the energy transfer.

 3.12.3 Driveability A nalys is This option calculates blow count, stresses and transferred energy vs pile penetration without running separate bearing graph analyses for each depth. In other words, the driveability analysis performs numerous bearing graph analyses automatically for user specified pile tip penetrations. Input consists of unit shaft resistance and end bearing values (since 2010 unit end bearing plus toe area) obtained by static soil analysis along with soil layer specific quake and damping values. In addition, so-called gain/loss factors modifying the unit shaft resistance or unit end bearing values, can be specified. These factors allow the user to model complete or partial loss of soil setup, relaxation effects or the long term soil resistance. Up to five gain/loss factors can be entered and analyzed, in effect providing for up to 70

GRLWEAP Procedures and Models

Version 2010

five capacity values at every analyzed depth. Note that in order to differentiate between the specific resistance losses of different soil layers a soil setup factor will also be considered in the driveability analysis as explained below. At the end of the analysis, the driving time can then be estimated from calculated blow count and hammer blow rate for each gain/loss factor.  An accurate static geotechnical analysis must be performed prior to calculating blow count vs depth. Since 2002 several static analysis routines were added to GRLWEAP and it is tempting to merely use these methods for the calculation of shaft resistance and end bearing. However, the analyst should be carefully reviewing the static analysis results. Details of these static calculations are discussed in Section 3.13.

 3.12.3.1 G ain/Los s Factors Prior to performing a dynamic analysis, the static resistance has to be estimated by geotechnical analysis of the soil. The result of this analysis is the Long Term Static Resistance (LTSR). However, during pile driving the soil properties change and the pile encounters the Static Resistance to Driving (SRD). The conversion of LTSR to SRD is accomplished in GRLWEAP by means of Gain/Loss Factors, f R, and Setup Factors, f S. While the Gain/Loss factors control the absolute change of static soil resistance, the Setup Factor controls the relative change of soil resistance among the various soil layers. There are two different approaches which allow for the calculation of SRD from LTSR. The standard GRLWEAP approach will be discussed in this section. A second approach referred to as Friction Fatigue is an Offshore Wave feature and is described in Appendix E. For a particular soil type LTSR = f S SRD

(3.45)

if SRD is soil resistance occurring after the pile has been driven a certain distance, called limit distance, L L, In theory, driving the pile a distance equal to LL  assures that SRD has been achieved. The LTSR will be occurring some time after driving which is called the setup time, t S. The GRLWEAP gain/loss and setup factor concept will be explained by example. The simplest example would be a single soil layer, e.g.  a clay, with setup factor f S  = 2.5. The reduction factor during driving would therefore be f RD = (1.0/2.5) = 0.4, if we would want to reduce the LTSR to the SRD to represent full resistance loss. If we would want to analyze the restrike situation with full setup, f RD = 1.0 would be appropriate. For incomplete setup we could also analyze f RD = 0.7. For each depth analyzed, with the three gain/loss factors f GL = 0.4, 0.7 and 1.0 specified as an input, a bearing graph would be calculated by the driveability analysis with three ultimate capacity values, one bearing graph for each depth analyzed. For each of these analyses, an appropriate end bearing gain/loss factor could also be considered in the input. Version 2010

GRLWEAP Procedures and Models

71

Let us now assume that two soil layers exist, with different setup factors like a clay layer and a sand layer with setup factor f S = 1.25. We would expect that full loss of setup resistance would reduce the sand LTSR to an SRD of 1/1.25 or to 80% of its long term capacity. We would therefore want to use f RD = 0.8 for the sand and f RD  = 0.4 for the clay. This is a dilemma which GRLWEAP solves by considering the gain/loss factor, f GL, specified by the user to be consistent with the most sensitive layer. For less sensitive layers the reductions of resistance would be proportionate to the ratio of setup factors. Therefore, if we again analyze a gain/loss factor f GL = 0.4 (to cover the set-up factor 2.5 of the most sensitive layer) and a gain/loss factor 0.7 (half loss of resistance of the most sensitive layer) and a gain/loss factor 1 for full setup (no loss of driving resistance) then the sand’s corresponding reduction factors would be f RD = 0.8, 0.9 and 1.0 while for the clay we would have f RD = f GL = 0.4, 0.7 and 1.0. Mathematically, the capacity multipliers for the individual layers, f RD, are calculated by GRLWEAP as follows. First, a relative soil/pile sensitivity, f S*, is calculated from the set-up factors, f S. f s* = (1-1/f s)/(1-1/f sx)

(3.46a)

For the sand with f S = 1.25, f s* = (1 - 1/1.25)/(1 - 1/2.5) = 0.333 (the sand is only a third as sensitive as the clay because it loses 20% when the clay loses 60%) where f sx  is the maximum set-up factor of all soil layers analyzed (i.e. the setup factor of the clay, f S  = 2.5, in our example). Next, the friction reduction factor during driving is calculated from the gain/loss factor, f GL, and relative soil/pile sensitivity. f RD = (1-f s* + f s*f GL)

(3.46b)

f RD  = 1 - 0.333 + 0.333(0.7) = 0.9. Thus, when the clay is analyzed with 70% of its long term strength, the sand has 90% of its full capacity. This capacity reduction factor is subject to variation as described under Section 3.12.2.2 below if setup time, t S, and limit distance, L L, are specified. So far we have only considered shaft resistance setup. However, it should be possible to vary the end bearing as the shaft resistance is varied at a particular analysis depth. For example, the pile is driven through clay into a silty sand. Since the silty sand layer is very dense, it has the potential to build up negative pore water pressures and therefore high end bearing values during driving, say 50% higher than the long term value. When driving is over, the pore water pressures dissipate and then the toe capacity goes back to the value which is known from static calculations. For example, if the pile is driven through clay (set-up factor 2.5 in our example) into a very dense, fine sand and silt, it may be reasonable to perform an analysis with shaft gain/loss factors of 0.4 and 1.0 and respective toe gain/loss factors of 1.5 and 1.0. The resulting two analyses at each depth would consider the temporary dynamic (expected) and the long-term static (restrike or worst-case driveability) situation, respectively. 72

GRLWEAP Procedures and Models

Version 2010

The above examples are reasonable for impact driven piles. For vibratory pile driving, sands and clays often behave very differently with sands losing a very high and clays losing a very low percentage of their LTSR. Suggestions are given in the “Table of Soil Set-Up Factors” (GRLWEAP On-line Help).

 3.12.3.2 Variable S et-Up The above relationships are valid for a complete gain or loss of set-up as shown in Figure 3.12.1. If the set-up period is interrupted by renewed driving or if the loss of capacity due to driving is interrupted by a new set-up period, then capacity losses or gains commence from an intermediate level. GRLWEAP calculates for these situations, respectively, equivalent relative dissipation energies or set-up times (Figure 3.12.2). For driveability analyses which consider the variations of soil resistance as the pile penetrates into the ground, it is also desirable to include soil set-up effects that might occur during driving interruptions. When pile driving resumes, the soil strength is lost depending on the energy dissipated in the soil. To model this behavior, two relationships were developed: (a) the capacity reduction factor due to the wait, f RW, as a function of set-up time, tS; and (b) the capacity reduction as a function of the distance of driving (which is related to energy expended on the soil remolding or pore water pressure generation). The capacity reduction factor varies between the inverse of the set-up factor and 1.0. When it is equal to the inverse of the set-up factor, all of the set-up capacity of the soil has disappeared due to the action of the dynamic energy of the striking hammer. When it is 1.0, set up has completely reappeared during the time following pile driving and the capacity is then at its full long term level. For example, assume again a clay with a set-up factor of 2.5. The capacity of an element embedded in clay can therefore be as little as 0.4 times the full long term capacity. The reduction factor can in this case vary between 0.4 and 1.0. The capacity reduction factor due to the wait is defined as: f RW = RUR / RUF 

(3.47)

where RUR is the capacity (of a pile/soil segment) reduced by the action of the dynamic energy. RUF is the full ultimate capacity (achieved after full setup time) at the same segment. Skov and Denver, (1988), suggested that the reduction factor is a function of set-up time, t S, and follows a log 10 function: f RW = 1/f S + A log10 (t / tB)

(3.48)

 A = (1 - 1/f S) / log10 (tS / tB)

(3.49)

with

Version 2010

GRLWEAP Procedures and Models

73

Remember that f S  is the soil's set-up factor for the shaft resistance. Also, the time, t, elapsed since driving was halted, has to be greater than the reference time tB. This reference time has been set to 0.01 hours in GRLWEAP, even though Skov et al . (1988) recommend a larger period such as a day for a stable prediction of set-up strength. However, it is reasonable to assume this set-up behavior occurs in short interruptions in driving as well as during long wait periods as considered by the authors. A one-day base time period would be outside of the time considered for such driving interruptions. For Any Segment I

Rui

Rui

During Driving - Full Loss

RUF

During Waiting - Full Gain

Resume Driving

Stop Driving

RUR Penetration Limit Distance after Wait

Setup Time

Time

Figure 3.12.1: Capacity vs Energy/Time for Complete Gain/Loss

Figure 3.12.2: Capacity vs Penetration or Time for Incomplete Gain/Loss For the loss of resistance due to pile driving, a simple linear relationship has been adopted, between distance driven and SRD. If the pile has penetrated a particular soil layer a limiting distance, L L, it is assumed that all setup has been lost. The limiting driving distance has been called a relative energy in the past, because in its simplest form driving energy is resistance force times the distance that the pile has been driven. Normalizing by division 74

GRLWEAP Procedures and Models

Version 2010

with the average resistance leads to the limit distance. The limit distance, LL, is a constant and may be considered a soil property (it is entered by the user in the soil resistance profile). It has the dimension of length, i.e. m or ft. Of course, the reduction factor can never be less than the inverse of the set-up factor nor can it be greater than 1. Important: variable setup works only for the first gain/loss factor, i.e., for the first analysis of each depth. This calculation is not performed for the other four gain/loss factors.

 3.12.3.3 Notes and Hints on the Variable Set-Up Analys is Entering the limit distance and setup time numbers in the S1 input screen, the soil properties for the variable setup analysis are available. However, a variable setup analysis will only then be performed when at least one waiting time has been specified greater than 0.01 hours (base time for setup calculations). Thus, when no driving interruption is specified in the D screen, energy limit and setup time are ignored.  A variable setup analysis considers the remolding energy expended on the soil. For each depth analyzed this energy is calculated as the distance driven since the last waiting time. For example, it is assumed that at the very bottom of the pile the soil has not been remolded while, at grade, it has been remolded by the pile moving the full driven distance through the soil since the most recent waiting time. The unchanged soil element at the bottom of the pile will break down from full static resistance to the reduced resistance as the pile is driven past the element. Only when the pile has moved a distance equal to the limit distance will the former bottom soil element be at its reduced static resistance.  A pile will therefore never experience complete resistance loss near the toe for a variable setup analysis. This fact will be clearly apparent for a pile with a high concentration of shaft resistance near the toe. To display the effect of variable setup results, the same gain/loss factor can be used in the second analysis that was analyzed in the first one.  A word of caution: The program always analyzes all depth values specified in the D  screen. The analysis results may indicate that, where a waiting time was specified, the pile would refuse. Yet some distance below the point with the waiting time, the pile may actually have a non-refusal blow count. In reality, it would not be possible to drive the pile to this deeper penetration because of the refusal, unless some jetting or other driving aids were employed. Thus, casual inspection of the calculated blow counts vs. depth, which misses the one depth result with refusal due to setup, may suggest that the pile can be driven. In reality, it would only reach the depth where the driving interruption and refusal blow counts occur.

Version 2010

GRLWEAP Procedures and Models

75

 Additional suggestions: a. Variable setup analysis is only done for the first Gain/loss factor. b. Variable setup analysis cannot be performed for Friction Fatigue analyses (Offshore Wave Option). c. GRLWEAP does not consider a variation of toe bearing with driving energy or set-up time; the end bearing is either fully increased or fully reduced as specified by the toe gain/loss factor. No variation of this factor with soil layer properties is possible. d.If no set-up time or relative energy is known (and the corresponding inputs are left zero or blank), then the "variable set-up" analysis cannot be performed. However, a constant loss or gain analysis is still possible. Probably, the constant loss/gain analysis is as reasonable or more reasonable than the variable one, because of the uncertainty of limit distance, set-up time, and their variation with time. e. If no set-up factors are specified, GRLWEAP assumes set-up factors of 1 for all layers. Gain/loss factors then produce uniform capacity gains or losses in all soil layers along the pile. f. There is no point in specifying set-up time if the limit distance is not known or vice-versa. Entering one parameter and not specifying the other leads to curious results. g. GRLWEAP does not allow for a meaningful vibratory analysis with variable set-up. h. In a first effort, GRLWEAP users should attempt to perform hindsight analyses matching the blow count behavior of known projects with well documented hammer and soil data. Only after having gathered enough experience should class A predictions be attempted of variable set-up behavior of a hammer-pile-soil system. i. As an aid in preparing input for a first trial analysis, the relative energy may be estimated as 2 m (7 ft). This would mean for the GRLWEAP approach that the soil would lose its set-up capacity after the pile has been driven for approximately 2 m or 7 ft. k. Set-up time may be as long as 6 weeks in some clays and as little as a few minutes in sands. GRLWEAP assumes that the full set-up capacity has been regained after a driving interruption greater than or equal to the set-up time. l. For reasonably accurate analysis results and driving time estimates sufficiently many depths must be analyzed. This is particularly true when modeling variable set-up and where soil layer changes or waiting times are specified. However, even in uniform soil/driving conditions 76

GRLWEAP Procedures and Models

Version 2010

increments of depths analyzed should not exceed 3 m (10 ft). On the other hand, the maximum number of depths that can be analyzed is 98. m.Variable set-up analysis is only performed on the analysis of the first gain/loss factor. For all other gain/loss factors, no wait times or energies are considered.

 3.12.4 S econd Pile Toe  Assume that a composite pile has to be analyzed. It consists of a large concrete pile which at its toe is fitted with an H-beam tip of considerable length. During driving, this pile experiences end bearing both at its concrete bottom and at the H-pile tip. In order to facilitate the analysis of such a situation both end bearing values can be specified. The sum of both end bearing forces is the total toe resistance. Individual quakes and damping factors can be specified for both toe resistance forces. For example, a larger quake would be reasonable for the concrete toe, while a smaller quake would be reasonable for the H pile tip. The second toe can be specified when a Non-Uniform Pile is chosen in the P1 form. Nothing needs to be done if the second toe resistance is to remain equal to zero.  As in a standard analysis, the set and blow count calculation for the Two Pile Toe analysis uses the maximum first toe displacement (bottom of pile) minus the average quake. The average quake, however, is calculated under consideration of the second pile toe resistance and quake.  An RSA cannot be combined with a Two Pile Toe analysis.

 3.12.5 Two-P ile A nalys is Possible applications of this option include a helmet with a long sleeve, a mandrel and shell configuration, or a non-bonded, two-material pile. In short, two piles should be analyzed where the stress wave is split into parallel branches. The Two-Pile analysis cannot be combined with RSA or driveability analyses. The GRLWEAP Two-Pile option is flexible enough to accommodate the following configurations.  The second pile is directly driven by the helmet and is not attached

to the first pile either at its top or at any other segment. 

The second pile can be attached to any segment of the first pile.

 Attachment of the two piles onto each other is accomplished by a spring with slack, round-out and coefficient of restitution. The Users Manual contains two examples. Resistance distribution can be accomplished along both piles. Their relative distribution numbers automatically assign different magnitudes of shaft Version 2010

GRLWEAP Procedures and Models

77

resistance to the two piles. For end bearing, the two-toe capability is utilized in the P1 form.  Analyzing two piles is not complicated except that the blow count computation becomes highly questionable. It is not simple to decide from which toe displacement the set should be calculated. Currently, GRLWEAP uses the smaller of the maxima of the two toe displacements. The user is advised to carefully review the output, experiment with analysis durations (Options/ General Options/ Numeric), and check the blow count calculation to assure that the results are reasonable. 3.13 Static Geotechnical Analysis

 3.13.1 Introduction To simplify the soil model input process, two simple static analyses are included in the GRLWEAP code. These analyses only yield an estimate of static soil resistance. The user is urged to also try other methods (e.g. computerized methods such as UNIPILE, DRIVEN and SPT97, the former described by Fellenius, 1996 and the latter two made available by the FHWA and the Florida DOT, respectively). Local experience may indicate which methods of static pile analysis work and which do not work in a particular geology. GRLWEAP’s analysis may or may not work well. One of the reasons is that there are a large number of error sources in the soil strength information obtained from borings and/or insitu test methods such as SPT or CPT. Thus, it is virtually impossible to predict the accuracy and/or precision of GRLWEAP’s static analysis methods compared with static load tests. Basically, however, it should be assumed that any static analysis predicts the long term pile bearing capacity. It has to be modified to yield the static resistance to driving (SRD). In addition to the static resistance values, the GRLWEAP static geotechnical analysis methods also provide a help for dynamic parameters, shaft damping and toe quake (toe damping and shaft quake are always considered independent of soil or pile type). For the driveability analysis, also rough estimates of the soil parameters pertaining to the soil resistance’s gain/loss behavior are provided (setup factor, relative energy and setup time). Please review the method descriptions and application notes (Sections 313.2 through 3.13.4) before accepting the results of these static geotechnical analyses.

 3.13.2 S oil Type B as ed Method (S T) This method is intended as an aid in the input process for both bearing graph and driveability analyses. For bearing graph analysis, it calculates the percentage of shaft resistance and the shaft resistance distribution, for which it selects reasonable dynamic soil parameters based on a very basic soil description and classification. As with all of such approximate 78

GRLWEAP Procedures and Models

Version 2010

calculation or estimation methods, the user should become familiar with the basic concept of static soil analysis and its limitations and perform comparison analyses using other methods to avoid serious errors. With simplifying assumptions, the method uses information from Bowles and Fellenius contained in Hannigan et al. (2006). For Non-Cohesive soils: The program applies the β-Method (Effective Stress Method). With this method, the unit shaft resistance is: qS = β pO 

(3.50)

with β= The Bjerrum-Burland beta coefficient (earth pressure coefficient times the tangent of the friction angle between pile and soil ) and po = Average effective overburden pressure along the pile shaft. The unit toe resistance is: qt = Nt Pt 

(3.51)

where: Nt = Toe bearing capacity coefficient. Pt = Effective overburden pressure at the pile toe. The method  converts the soil classifications of Tables 3.12.2a to soil unit weight, β-value, and Nt-value,  calculates the overburden pressure (under consideration of buoyancy, thus the water table depth must be provided in the input),  with the β and Nt values of the table finds the unit shaft resistance and end bearing and  subjects these values to the limits in Table 3.12.2a.

Version 2010

GRLWEAP Procedures and Models

79

Table 3.12.2a: ST Analysis Parameters for Non-Cohesive Soils Soil Type

Very Loose Loose Medium Dense Very Dense

SPT N

2

Friction  Angle deg. 25 – 30

7 20 40 50+

Unit Weight kN/m 13.5

27 – 32 30 – 35 35 – 40 38 – 43

β

Nt

Limit (kPa) qs

0.203

16.0 18.5 19.5 22.0

0.242 0.313 0.483 0.627

12.1 18.1 33.2 86.0 147.0

qt

24

2400

48 72 96 192

4800 7200 9600 19000

The user can also use the SPT N-values (corrected for the effect of overburden pressure) given in the following table to find the corresponding soil classification. (However, if the N-value is known then the more detailed SA method may be used instead of ST.) For Cohesive Soils: For cohesive soils, the ST method applies a modified α-method (total stress method). The calculation steps are 

From Table 3.12.3b and the given soil classification find the unit weight, unit shaft resistance and unit end bearing.



From unit weight and depth of water table (input) find the overburden pressure (in case there are lower non-cohesive layers for which the β method needs to be applied. Table 3.12.2b: ST Analysis Parameters for Cohesive Soils Soil SPT Unit qu qs qt Type N Weight kPa kN/m kPa kPa

Very Soft

1

12

17.5

3.5

54

Soft

3

36

17.5

10.5

162

Medium

6

72

18.5

19

324

Stiff

12

144

20.5

38.5

648

Very Stiff

24

288

20.5

63.5

1296

Hard

32+

384+

19 - 22

77

1728

 3.13.3 S P T N-value B ased Method (S A ) The method is based on SPT N –value and soil type and only available in conjunction with the Variable Resistance Distribution option, however, for 80

GRLWEAP Procedures and Models

Version 2010

either Bearing Graph or Driveability Analysis. Since Version 2010 friction angle and/or unconfined compressive strength can also be entered in the SA window. Direct input of unit shaft resistance and end bearing is also possible if a soil type “Other” is to be specified. This mode of input can also be helpful to enter resistance values for rock. The SPT N-value based method presented here does not use corrected N – values as per FHWA recommendations (Hannigan et. al., 2006); however, it limits N to at most 60. On the other hand, it is strongly recommended that energy measurements be taken during SPT testing and that the N-value be adjusted to the N60 value. In effect, this is a normalization which increases the N-value for hammers with high transfer efficiency (greater than 60%) and lowers them for poorly performing hammers (those with transfer efficiencies less than 60%). The SPT Analyzer measures the transfer efficiency of SPT hammers. The method does not make recommendations for rock. As mentioned for “Other” soil types, the user must input unit shaft resistance and end bearing values. The user can also input the depth of the water table relative to grade and an overburden causing a non-zero effective stress at grade.  As a basis for the calculation of several of the following quantities, the vertical effective stress is calculated first, as follows: Step 1: Find the soil’s unit weight (γ) based on Bowles (1977). Step 2: Find the vertical effective stress, σ v’, in the layer based on the overburden on the layer, layer thickness, γ from Step 1, and the water table depth.  A: Shaft resistance for sands and gravels Step A1: Find relative density, Dr , from Kulhawy (1989 and 1991). Step A2: Find friction angle, φ’, based on Schmertmann (1975 and 1978). Step A3: Assume the pile-soil friction angle as δ = φ’. Step A4: Find the earth pressure coefficient at rest, k o, based on Dr , according to Robertson and Campanella (1983) with (1 - sinφ’)/(1 + sinφ’) < k o < (1 + sinφ’)/(1 - sinφ’) Step A5: Calculate friction: q s = ko tan δ σv’ with q s ≤ 250 kPa Notes: (a) Depending on the grading of a sand and its coarseness, the calculations may be slightly modified. (b) If friction angle is entered in lieu of N-value, skip steps A1 and A2.

Version 2010

GRLWEAP Procedures and Models

81

B: Shaft resistance for clays Step B1: Find the friction angle from φ’= 17 + 0.5N with φ’ ≤ 43 degrees. Step B2: Define the pile-soil friction angle as δ = φ’. Step B3: Find the overconsolidation ratio (OCR) from N and σ v’ [kPa] OCR = 18N/σv’. Step B4: Find the normally consolidated and earth pressure coefficient according to Jaky (1944) knc = 1 - sin φ’ Step B5: Find the earth pressure coefficient at rest as ½ ko = knc (OCR) with (1 - sinφ’)/(1 + sinφ’) ≤ k o ≤ (1 + sinφ’)/(1 - sinφ’) Step B6: Calculate the unit shaft resistance from qs = ko tanδ σv’ with qs ≤75 [kPa] Note: if the unconfined compressive stress q u  is entered in lieu of the Nvalue, the program will calculate adhesion values according to Tomlinson (see Hannigan, 2006). C: Shaft resistance for silts Step C1: Use the friction angle φ’ from Step A2 if it is non -cohesive or from Step B1 if it is cohesive. Step C2: Find the Bjerrum-Borland β coefficient according to Fellenius (1996) by linear interpolation. β = (φ’ - 28)(0.23/6) + 0.27 with 0.27 ≤ β ≤ 0.5 Step C3: Calculate q s = β σv’, with qs ≤ 75 kPa (cohesive), q s ≤ 250 kPa (non-cohesive). Note: if the unconfined compressive stress q u  is entered in lieu of the Nvalue, the program will calculate adhesion values according to Tomlinson (see Hannigan, 2006). D: Unit end bearing for sands and gravels Step D1: Calculate the unit end bearing based on the uncorrected SPT Nvalue from qtoe = 200 N [kPa], with qtoe ≤12,000 kPa.

82

GRLWEAP Procedures and Models

Version 2010

If friction angle has been directly entered, find corresponding N-value from Bowles in Hannigan, 2006 and then calculate as shown. E: Unit end bearing for clays Step E1: Calculate the unit end bearing based on the uncorrected SPT Nvalue from qtoe = 54 N [kPa] with qtoe ≤ 3240 [kPa]. If qu has been directly entered calculate unit end bearing as 4.5 q u F: Unit end bearing for silts Step F1: Find friction angle φ’ from Step A2 if it is non -cohesive or from Step B1 if it is cohesive. (or use directly entered friction angle). Step F2: Find the toe capacity coefficient, N t, according to Fellenius (1996) by interpolation. Nt = (φ’ - 28)/0.3 + 20 with 20 ≤ N t ≤ 40 Step F3: qtoe = Nt σv’ with 20 ≤ N t ≤ 40 and qtoe ≤ 6,000 kPa.

 3.13.4 The C PT Method in G R LWE A P  3.13.4.1 Introduction Cone penetration tests are semistatic and resemble, though at a much smaller scale, a pile. A variety of penetrometers such as mechanical and electrical ones have been developed and there are penetrometers in use which are not of standard size. The preferred Dutch Cone configuration has 2 a cone tip area of 10 cm and a cone angle of 60 degrees. GRLWEAP’s method for calculating pile unit friction, f s, and unit end bearing, q t, programmed in GRLWEAP assumes that the cone tip resistance, q c, and the cone’s sleeve friction, q s, have been measured with such a standard cone. The soil type determination is based on Robertson et al (1986) and the resistance calculation is as proposed by Schmertmann, 1978.

 3.13.4.2 Data Import CPT data can only be imported into GRLWEAP from a text file. The file format must meet following requirements (see also example in Table 3.13.4.1). a. Titles or comments should be placed at the beginining of the file and the number of title and/or comment rows is an input to the program; The program skips that many lines before beginning to read the numerical data. Version 2010

GRLWEAP Procedures and Models

83

b. CPT data must consist of at least 3 number columns, containing in order: depth, tip resistance, q c, and sleeve friction, q s. c. Additonal columns of data such as pore water pressure are ignored; d. The following combination of units will be recognized if as such defined in the column headers.  SI: Depth in m, both tip and sleeve resistance in MPa;  SI: Depth in m, q c in MPa and qs in kPa;  English: Depth in ft, both tip and sleeve resistance in tsf.  An additional input is penetrometer type (Electronic or Mechanical), which serves to select the appropriate design curves. Note: Since the CPT based resistance computation requires averaging the data over certain ranges, smaller cone data depth increments are highly recommended for better accuracy. Also at least five input depths (rows of data) are required. The program checks and modifies if necessary the depth increments using the following procedur  First the average depth increment is found based on the imported CPT

data:  Average depth increment = Maximum depth / number of rows of data;  If the average depth Increment is larger than 0.8 ft (0.25 m), the program

prompts a warning and increases the number of data points by interpolation of the CPT data at a depth increment of (0.3 ft) 0.1 m; Note:  It is recommended that the user manually inserts as many rows of data as are needed to make the depth increment 0.8 ft (0.25 m) before importing the data.

Table 3.13.4,1: Example of the top portion of a CPT text file with 3 comment lines and MPa units for both resistance values.

84

GRLWEAP Procedures and Models

Version 2010

 3.13.4.3 S oil C las s ification The first step in the resistance calculation is based on the paper by Robertson et al., (1986) with some modifications. This classification is a necessary step in the procedure to calculate the resistance values and determine recommended soil parameters such as quakes, damping factors and soil setup related parameters. The friction ratio is calculated from q s / qc. (sleeve friction divided by cone resistance).

Figure 3.13.4.1: Soil Classification Chart of Robertson et al, (1986)

Version 2010

GRLWEAP Procedures and Models

85

Table 3.13.4.2: Soil Classifications Soil Description corresponding to Hannigan et al. (2006) Zone

to SA Method

Soil Behavior Type

1)

sensitive fine grained

Poorly graded fine sand

2)

organic material

Peat

3)

Clay

Clay

4)

silty clay to clay

Clay

5)

clayey silt to silty clay

6)

sandy silt to clayey silt

Cohesive silt Split between and 7)

7)

silty sand to sandy silt

Cohesionless silt

8)

sand to silty sand

Sand

9)

Sand

Sand

10)

gravelly sand to sand

11)

very stiff fine grained

Well graded sand Poorly graded fine sand

12)

sand to clayey sand

Sand

86

GRLWEAP Procedures and Models

Version 2010

5)

 3.13.4.4 R es is tance calculation (Distribution of friction and toe bearing) is based on Schmertmann, 1978,  An additional assumption is a uniform pile. This simplification has been proposed by Schmertmann and since unit resistance is the result of this calculation procedure and since the pile surface area will be as per user input, the error is considered immaterial. Additonal inputs affecting the results include:    

Pile material: steel, concrete and timber; Pile average diameter or width, B, for average depth D to B ratio; Pile toe size is used to determine the averaging range for toe resistance calculation; Unit resistance limit based on a maximum q c of 15 MPa.

Unit shaft resistance for cohesive soils: f s = α qs where: α = ratio of pile to sleeve friction in cohesive soil; a function of q s and pile material (Schmertmann 1978). qs = unit sleeve friction Unit shaft resistance for cohesionless soils: f s = kr  K qs where: K = Ratio of unit pile shaft resistance to unit cone sleeve friction (Schmertmann, 1978) as a function of depth, Z, penetrometer type and pile material. qs = unit sleeve friction. kr  = Z/8B for Z = 0 to 8B. kr  = 1 for Z ≥ 8B. B = Pile width or diameter. Note: In GRLWEAP’s CPT routine,  Schmertmann’s  curves for steel pipe piles are used for all steel piles and those for square concrete piles are used for all concrete piles. f s ≤ f s, lim the unit shaft resistance limit entered by the user (default is 150 kPa) Unit toe resistance for all soil types: qt = ½ (qc1 + qc2) where: qc1  and qc2 are averages of unit cone tip resistance below and above pile toe as per Schmertmann, 1978. qt ≤ qt,lim the unit toe resistance limit entered by user (default is 15 MPa).

Version 2010

GRLWEAP Procedures and Models

87

 3.13.5 The A PI Method in G R LWE A P (Offs hor e Wave Vers ion) The method is based on API (1993). Note that this is an approximate method and that API recommends instead using high quality soil strength information where available. Also, this method is specifically applicable to pipe piles. Soil strength input for GRLWEAP’s routine is undrained shear strength for cohesive soils and a general density classification for cohesionless soils. Unit Shaft Resistance for cohesive soils: f s = α c where: α = a dimensionless factor ; it can be computed from: -0.5 α = 0.5 ψ for ψ ≤ 1.0 -0.25 α = 0.5 ψ for ψ > 1.0 α ≤ 1.0. ψ = c/p o’ po’ = effective overburden pressure c = undrained shear strength of the soil, which is an input Unit shaft resistance for cohesionless soils: f s = K po’ tan δ where (see also Table 3.13.5.1): K = dimensionless coefficient of lateral earth pressure (ratio of horizontal to vertical normal effective stress). K = 0.8 for unplugged. K = 1.0 for plugged. User can indicate if it is plugged in the program. For fully displacement piles, user should indicate plugged to use K = 1.0. δ = friction angle between the soil and pile wall. f s ≤ f s, lim the unit shaft resistance limit. Unit toe resistance for cohesive soil types: qt = 9 c with the c being the undrained shear strength. Unit toe resistance for cohesionless soil types: qt = po’ Nq where (see also Table 3.13.5.1): Nq = is a bearing capacity factor. qt ≤ qt,lim the unit toe resistance limit.

88

GRLWEAP Procedures and Models

Version 2010

Table 3.13.5.1: Design Parameters for Cohesionless Soils (API, 1993, p67,

Reproduced courtesy of the American Petroleum Institute)

 3.13.6 C omments on GRLWEAP’s s tatic formula methods Static formulas for pile capacity determination are generally inaccurate for a variety of reasons. For example, soil strength from N –value and soil type is always only an estimate because SPT N –values are inherently inaccurate and soil type information is subjective and the pile driving process itself changes the properties of the soils and, therefore, affects both long term soil resistance and SRD. Moreover, different physical, chemical or geological conditions will produce different relationships between in -situ test results and unit resistance values. Program users are, therefore, strongly advised to always check the friction and end bearing values that the program calculates both by comparing with other methods and using any additional information, most notably local experience, that might be available. Not only pile driving changes the soil properties. Pile material has an effect on the shaft resistance and effects like predrilling or jetting, an oversized toe plate, driving of nearby piles causing heave and densification, group effects, time effects like setup and relaxation, variable water table e levation, excavations or refilling around and in the neighborhood of the pile, and many other phenomena have a significant effect on shaft resistance and end bearing. GRLWEAP’s static geotechnical analysis methods should merely be seen as an aid for the program user in estimating very basic soil resistance input parameters. When performing the soil layer input, the p rogram also displays the calculated capacity and the shaft resistance. This additional information may be used as a check on how reasonable the basic assumptions are and whether or not the intended pile capacity can indeed be achieved. Again, this capacity value should not serve for design purposes.

Version 2010

GRLWEAP Procedures and Models

89

The total capacity of the pile is unit shaft resistance times shaft area plus unit end bearing times toe area. The shaft area is based on the perimeter values that the user inputs. Normally for H-piles, perimeter is computed by the 4 sides of the piles. An argument could be made for using 6 sides, but that assumption is highly uncommon. For the open ended pipes, the question of internal friction is difficult to answer. It would be expected that an unplugged pile (the soil remains at its location, i.e., it does fill the pile and does not move with the pile  –  the cookie cutter effect) has some internal soil resistance. However, unless diameter to embedment is relatively large, the effective stresses will be relatively low inside the pipe and the driving process will reduce the internal friction. Thus for most unplugged analyses only partial internal friction is normally considered (it can be modeled in GRLWEAP by increasing the perimeter value over that length of the pile where internal friction is expected (e.g. on an internal driving shoe which is an increased pipe wall thickness at constant outside diameter). A case could be made for internal friction acting over 10 pile diameters if the pipe wall thickness is uniform (please also note that API makes recommendation regarding friction calculations in the plugged and unplugged cases). For the toe area, the user must determine whether or not plugging can occur for open profiles. In very dense sands or during restrike testing after a long waiting time, plugging may be expected unless the pile diameter is very large (say greater than 900 mm or 30 inches) or the penetration into the bearing layer is very shallow (say less than 3 diameters). Since H-piles are normally relatively small (typically less than 350 mm or 14 inch) square, the fully plugged area is usually assumed for end bearing calculations. In general, the GRLWEAP’s default value for the pile toe area is that of the closed end condition. It is therefore extremely important that the users carefully review and possibly correct the pile toe area input. In addition, it is also strongly recommended to perform optimistic (unplugged) and pessimistic (plugged) driveability analyses to establish lower and upper bound driving resistance values. Due to the simplicity of GRLWEAP’s static geotechnical calculation methods, effects of pile size, pile non-uniformity (such as a tapered pile which may have a relatively high shaft resistance), influence of upper lubricating soils on lower soil layers, the effect of pile material on the friction, and many other influences normally affecting friction and/or end bearing values were not necessarily considered in detail. Users should therefore adjust the result based on the recommendations in the literature or their own experience and judgment when these methods are used. The user must also consider that the soil resistance values, calculated by the static analysis, represent a long term pile capacity. For both bearing graph and driveability analyses, if they are to represent the pile installation conditions, both setup and relaxation effects must be considered.

90

GRLWEAP Procedures and Models

Version 2010

 3.13.7 C ons ideration of Pile Inclination in S tatic S oil A nalys es  An inclined pile driven through a certain soil layer is in contact with a larger surface area than a vertical pile. On the other hand the unit resistance is most likely somewhat lower. In general it can be assumed that the total shaft resistance acting on an inclined pile in a certain layer is the same whether the pile is inclined or not. However, an inclined pile of the same length as a vertical pile will not penetrate as deeply as the vertical one. Thus, for a given pile length the pile inclination reduces the total vertical pile penetration (Figure 3.13.6.1.) If the pile inclination has been entered then these length and associated resistance factors have been considered in the static soil analysis tools (ST, SA, CPT  and API). As a consequence, whenever the pile inclination is changed, the users must repeat the soil resistance calculation by reentering the particular analysis method chosen. Of course, the same is true if pile penetration (for bearing graph analyses), pile type or pile profile are changed.

Layer 1: Soft Clay

Layer 2: Medium Dense Sand

Layer 3: Stiff Clayer 

Layer 4: Dense Sand

Figure 3.13.6.1 Vertical and Inclined Piles of the Same Length Note that although the static soil analysis methods consider the actual inclined vs. vertical penetration depth, the calculation of resistance at the same vertical depth is identical for vertical and inclined pile.

 3.13.8 S tatic B ending S tres s C alculation of Inclined Piles This option is only available in the Offshore Wave version.

Version 2010

GRLWEAP Procedures and Models

91

When pile is inclined, supported by a jacket or template and the hammer is guided by an offshore lead which, in turn, is guided by the pile, then it is necessary to consider the bending stresses caused by the hammer weight plus the pile section extending above the pile support. Because this option is only available for GRLWEP’s offshore version, it is assumed that the pile is a pile of constant outside diameter. The cross sectional area, A, wall thickness, t, diameter, D, and specific weight, γ, of the pipe pile are, therefore, know from the pile profile. This then allows for a calculation of the bending moment due to pile weight, the moment of inertia and section modulus. However, the following additional input is required (see also Figure 3.13.7.1). Wh Total hammer weight (Sum of all weights acting on pile top including helmet weight and potentially a portion of the lead weight) hCG Center of hammer/helmet gravity (The distance from pile top to the Center of the Gravity of hammer while the hammer sits on top of the pile) β Pile inclination angle (the angle between the axis of pile and vertical direction)

Figure 3.13.7.1: Definition of static bending analysis parameters Note: The following calculation assumes that the highest bending stresses occur at the support point; bending stresses below that point are not considered. The static bending moment acting at a cross section at a distance y from the pile top (without consideration of deflection) can be computed as follows; first the shear force distribution at any point y from top is: 92

GRLWEAP Procedures and Models

Version 2010

() = (ℎ + ∫  ) ×sin()  And the bending moment is:

M = W ×hCG ×sin() + ∫z V(y) dy Bending caused by additional normal stresses require that deflections are known. To compute the deflection, it is assumed that pile at the support point is fixed and the angle of the pile axis at the support point is β. The total deflection at top can be calculated from:

     =   where: Lb is the pile length from support point to pile top. Using the segments of the dynamic model, a numerical procedure is then used to calculate shear, bending due to hammer and pile weight and deflections due to bending including the static axial forces. Dynamic forces are neglected owing to the shortness of the stress wave (both as far as time and length). Since deflections increase due to the normal forces, iterations are performed until convergence is assured. Convergence means that the system is stable. The following convergence criterion has been included.

| − | General Options->Output) and, as far as bending is concerned, Version 2010

GRLWEAP Procedures and Models

93

from the difference between compressive dynamic and bending plus dynamic stresses. stresses. The Stress Maxima Range Range tables (see Section 5.5) for for fatigue analysis do contain the tension stresses. Questions arose whether or not the normal forces due to the hammer-leaddriving system weight were included in the stress calculation. The answer is “No” and there are two reasons for not adding the sta tic hammer-lead driving system weight to the dynamic and bending stresses. First, as long as the gravitational acceleration of hammer and pile are properly input, the dynamic analysis already includes the weight effect of hammer (ram plus assembly), helmet and pile. Considering them again would double that effect. Secondly, while the free riding leads may add bending due to its weight component perpendicular to the pile axial direction, it is expected that most of the lead weight would be supported by the crane. And even if the weight of the leads were instead fully supported by the pile, during the impact the pile would be rapidly moving away from the leads and only later, during rebound, would it again be supported by the pile. At that time, however, the critical situation of maximum compression at the support point would have passed. Note that the axial weight effect of the leads is the same as the effect of the assembly. Note also that neglecting the lead’s axial weight effect on the soil prior to impact is conservative as far as blow counts are concerned. 3.14 Program Flow

 3.14.1  3.1 4.1 B earing eari ng G r aph 

After accepting hammer, driving system, pile and soil input (and potentially calculating static resistance values in the static geotechnical analyses), GRLWEAP sets up a lumped mass model for hammer, driving system, and pile and distributes the skin friction of the first ultimate capacity capacity value. value. A description description of the the complete model is then printed.



Next the analysis time increment is computed, followed by an equilibrium analysis which determines whether or not there is enough resistance to balance the dead loads (hammer assembly, helmet, pile weight). If there is not enough resistance, the analysis is skipped and a 0 blow count is output. o utput.



Next the actual wave equation analysis is performed for the first capacity or depth value. For diesel hammers, the the rated hammer hammer stroke is assumed if the standard stroke option has been selected.



At the end of the analysis, for RSA an equilibrium equilibrium analysis is performed and the analysis is repeated until RSA pile sets have converged. For diesels, the calculated calculated up stroke is compared with the down stroke. If they are not equal within the selected stroke convergence criterion, the analysis is repeated with the calculated up stroke as a down stroke (except for iteration on pressure for

94

GRLWEAP Procedures and Models

Version 2010

which the combustion pressure Pmax  is adjusted. For further details, see the section on “Diesel Analysis Procedure”). 

At the end of an analysis, and after diesel stroke and/or RSA convergence have occurred, GRLWEAP saves on disk extrema tables and variables vs. time vs. time tables, depending on the user chosen output option. On the monitor screen, a line of results is displayed.



The next ultimate capacity value is now distributed along the pile and at the pile toe and a nd then a new analysis cycle is performed.



If for one analysis a refusal blow count is calculated, calculated, the bearing graph calculation is finished. (For this reason, the user should enter capacity values in increasing order). An exception is the situation in which the previously analyzed capacity was relatively low. Then an additional a dditional capacity is interpolated and analyzed.



When all ultimate capacity values have been analyzed, the calculated stress extrema, transferred energies, and blow counts are saved in the the summary table table file. The analysis process is then then finished, and the user should now click on the output icon and check the numerical output. Be sure there are no messages in the numerical output that would indicate an unusual program performance (e.g. performance (e.g. numerical instability, or hammer did not run) . If satisfactory input and output have been ascertained, the user should choose to print and plot the bearing graph, print all or portions of the numerical output, and if desired, generate plots of hammer and/or pile variables versus time.

 3.14.2  3.1 4.2 D r i v eabi eability lity 

Driveability involves first of all a static soil analysis, which may be done either manually, using commercial software, or using the GRLWEAP static analysis options (ST, SA, CPT or API). If the static geotechnical analysis is not done with the GRLWEAP routines, then the depth, unit shaft resistance and unit end bearing values can be imported into the S1 soil resistance form using Window’s copy and paste features (Edit/ Paste Special).



In a first step, for the depth to be analyzed, the program program determines the temporary pile length (it may be less than the final pile length as per the Depth Table, i.e. the D input form). Then the lumped mass soil model is set up. From the D-table also the waiting time is checked and from it a determination of the status of soil setup is determined. Also hammer and cushion properties are checked based on the D-tables modifiers.



The dynamic analysis initiates with a calculation of the long term ultimate pile capacity and its resistance distribution for the first depth.

Version 2010

GRLWEAP Procedures and Models

95

In addition to unit shaft resistance and unit end bearing, based on the depth of penetration analyzed the following additional parameters are calculated as follows:





The shaft quake and damping values are averaged over the individual segment length (in case a soil layer change happens at a segment interface) to determine for each segment the appropriate value;



The soil setup factors, limit distance and setup time are determined for each segment;



The toe area which is then multiplied by toe unit resistance and toe gain/loss factor to yield the end bearing



Toe damping interpolation.



For the first gain/loss factor the SRD is calculated considering the variable setup based on the waiting time and driving distance since the last waiting time. For all other gain/loss factors, the shaft resistance is calculated based on setup factor and gain/loss factor only.

and

quake quake

values values

are

determined

by



A wave equation analysis is then performed subject to diesel hammer and RSA convergence, if applicable. A single output line is displayed for this first set of shaft and toe gain/loss factors. For the remaining gain/loss factors shaft resistance and end bearing are then calculated and analyzed.



After all gain/loss factors have been analyzed for the same depth, the program repeats the process of calculating temporary pile length, ultimate capacity and other resistance values for the next depth starting with the first gain/loss factor. Again a single output line is displayed for this first gain/loss factor at the new depth analyzed.



All depths specified in the D-form have been analyzed, GRLWEAP organizes the bearing graph results and generates a final result table of blow counts, stress extrema, transferred energy and stroke (equivalent to hammer energy) for each set of shaft and toe gain/loss factors. These results are then saved on disk.



As a next step, the user should inspect the numerical output and print all or portions of it. The “vs “vs depth” table can then be output in printed or plotted form. This is the driveability result.



If extrema table output is desired then the output option (Options/ General Options/ Output) should be set to normal (it is

96

GRLWEAP Procedures and Models

Version 2010

automatically set to minimum because of the potentially large volume of data) and repeat the analysis. If Variables vs time (e.g. a plot of pile top force and velocity) is needed, then it should be noted that GRLWEAP will only save the Variable vs Time data for the last depth analysis. Thus, the D-table should be shortened to allow for calculation of the desired depth in the last analysis. 3.14.3 Inspector’s Chart  

The first analysis is begun like the bearing graph analysis, with the ultimate capacity distributed in the same manner. For the first analysis, the stroke is either the user specified input value or an automatically selected value. For diesel hammers, the program then iterates with pressure adjustment or competes the single impact stroke option (see note below).



After the first analysis is finished, the program repeats the wave equation for second and later stroke values always with the same capacity and resistance distribution until 10 strokes (or energy levels, or frequencies) have been analyzed. The user proceeds with checking the input data in the numerical output and producing a stroke versus blow count output in numerical or graphical form.

Note for Inspector’s Chart analysis for diesel hammers: For diesel hammers, the hammer stroke analyzed generally is different from the hammer stroke normally calculated for the capacity analyzed and the combustion pressure of the hammer data file. Let us call this stroke the “normal” stroke. The reasons why the actual stroke in the field is different is not always clear. A low stroke generally can be attributed to a low combustion pressure. A high stroke, however, may either be due to very good hammer performance or, in the case of preignition, very poor hammer performance. High strokes, therefore, pose a dilemma for the wave equation analyst. For the Inspector’s Chart calculations, GRLWEAP offers the user two different stroke options that are conservative when analyzing high strokes. (A) The default option is identical to the Single Stroke Option (Options, General Options, Stroke). It only applies one impact, and no iterations will be performed on combustion pressure. As a result, for analyzed strokes less than the normal stroke, the rebound stroke will be higher than the analysis stroke. For analysis strokes above the “normal” one, the rebound stroke will be lower than the analyzed stroke (as for the default option). (B) If the Fixed Stroke, Variable Pressure Adjustment Option (Options, General Options, Stroke) is selected for analyzed strokes less than the “normal” one, a pressure reduction is applied until a stroke convergence is achieved. If however the rebound stroke is lower than the analyzed stroke, the single stroke option is used, i.e. no upward adjustment of pressure is applied. Version 2010

GRLWEAP Procedures and Models

97

Earlier program versions did make an upward pressure adjustment for diesel hammers if the pressure adjustment option was chosen. However, the results for high strokes showed unrealistically high transferred energies and therefore were potentially nonconservative.

 3.14.4 Dies el A nalys is Procedure  A flow chart for diesel analysis is shown in Figure 3.14.1. Under all stroke options, the program calculates the ram velocity at the exhaust ports based on either the rated stroke or the user selected down stroke. Then the wave equation analysis process begins with the diesel pressure calculation performed for the three phases of the process: Compression, Combustion and Expansion. Immediately prior to the impact, the ram velocity is reduced according to the hammer efficiency value. After impact, both due to ram rebound and diesel pressure, the ram begins to move upwards. After the ram position has reached the ports during the upwards ram motion, the program either continues with the wave equation until the stop criteria are satisfied or calculates the upward stroke from the upward ram velocity. The analysis proceeds depending on the stroke option: (a) Single analysis with fixed stroke and pressure: the wave equation diesel analysis is finished after the program has calculated the upstroke. (b) Convergence of stroke with fixed pressure: this is the commonly employed option under which the analysis is repeated with the downstroke equal to the calculated upstroke until stroke convergence has been achieved. (c) Convergence of pressure with fixed stroke: the analysis is repeated with the same down stroke and a P max  value that is proportionally adjusted to the difference between down stroke and up stroke. An exception is the Inspector’s Chart option for which only   pressure reductions will be made. For stroke options b and c, when the calculated upstroke exceeds the maximum hammer stroke (or when the closed end diesel uplifts), the analysis is repeated with a reduced ultimate pressure (fuel reduction) until the upstroke is less than the maximum stroke. (Note that the maximum stroke is sometimes greater than the rated stroke.) The starting stroke automatically chosen by the program is equal to the rated stroke of the hammer. This starting value may not be the best choice when a low resistance is analyzed. Then the available energy may be so large that the pile penetrates so much under the hammer blow and

98

GRLWEAP Procedures and Models

Version 2010

practically no upwards stroke can be calculated. In this case the program attempts a second analysis with a much lower stroke. For hammers deemed large relative to the soil resistance, energy may still be too high and the ram will not rebound. Then a “Hammer will not run” message may generate and no output will be made for that capacity or depth. The user may try other starting stroke values to overcome this problem; however, a better remedy would be the selection of a smaller hammer.

Figure 3.14.1: Diesel analysis flow chart

 3.14.5 Vibratory A nalys is Procedure The computational procedure is very similar to that for impact hammers. All three analysis options can be performed with frequency taking the place of stroke as the independent variable. Also, instead of blow count, the time required for unit pile penetration is calculated (seconds per foot or per meter).

Version 2010

GRLWEAP Procedures and Models

99



The analysis is begun by calculating the vibratory force which, as long as it is directed downward, compresses the pile top spring and extends the spring connecting the two vibratory hammer masses.



The vibratory force is subject to three potential reductions: start-up time reduced frequency, user specified "efficiency", and engine power limit. The latter is applied when the power per cycle exceeds the power rating of the hammer.



From cycle to cycle the program monitors the pile top penetration time. Once the penetration time has converged, or after the maximum analysis time has been exceeded, the analysis is finished and the program proceeds with analyzing the next capacity value, depth value, or frequency depending on the analysis option.

100

GRLWEAP Procedures and Models

Version 2010

4. INPUT INFORMATION The range of the required input data varies strongly, depending on the complexity of the problem to be solved. For example, the input for a simple bearing graph analysis can be entered on the Main Input Screen while a driveability with static analysis of a non-uniform, spliced pile may require data in at least 6 different screens. However, it has been attempted to make the input procedure as simple as possible. For this reason, the program calculates pile model details like springs and masses and distributes the shaft resistance to the various pile segments. For further simplification of the input preparation, the program database includes the models of hammer and driving systems. However, very basic soil and pile information must be supplied by the user. Prior to data input, pertinent information should be collected with the aid of Form 1, reproduced below, which was taken from Hannigan et al. (2006). This form can be downloaded from PDI’s website: http://www.pile.com/Specifications/Sample/histrain.rtf . For the beginner it is strongly recommended to perform the example problems. Then after they have been understood, the input process should be begun by clicking on the “New Document” icon. The analyst will then be guided through the necessary input sections. 4.1 Hammer Data The hammer manufacturer name and model No. is usually sufficient, since the hammer data file contains all necessary information for commonly used hammers. Further help files are available during program execution by clicking on Help or by pressing function key F3 after placing the cursor on the data field for which help is needed. For hammers whose data have not been entered into the file, hammer data should be requested from the manufacturer using Form 1. The necessary information depends upon the hammer type. If the hammer manufacturer is not familiar with the data required by GRLWEAP, PDI should be contacted for further help. For estimated efficiency values, refer to Section 3.3.8. For battered piles, additional efficiency reductions should be made as explained earlier and in the Help section. 4.2 Driving System Data The driving system input data, consisting of the hammer cushion properties, helmet weight (including striker plate, inserts, adapters, etc.), and pile cushion properties (in the case of concrete piles). All of this data can be entered in the Main Input Screen. Only if the actual field data is not known should the help file data of GRLWEAP be used. The GRLWEAP stored data can be retrieved using the F3 function key while the cursor is placed on a driving system data entry field.

Version 2010

GRLWEAP Procedures and Models

101

Cushions can be specified either by their area, elastic modulus, and thickness or by their stiffness. The stiffness value will override the other three inputs. In addition, a coefficient of restitution must be entered as specified by the material’s manufacturer . The round-out deformation is usually left unchanged at its default value (0.01 ft or 3 mm). Helmet weight is the weight of all components between hammer and pile top. The GRLWEAP supplied data may not include the weight of all of these components. Pile cushion area is usually equal to the pile top area, and the program would take that as a default. It would also defaults to an elastic modulus for relatively new plywood. Only the thickness of the cushion needs to be entered. The user should be aware, however, that softwood cushions generally compress during pile driving. A study described by Rausche et al. (2004) suggests that the elastic modulus of plywood for end-of-driving analyses should be chosen roughly 2.5 times higher than for early driving situations with new plywood (75 ksi instead of 30 ksi or 500 MPa instead of 200 MPa). The 2.5 times increase of modulus automatically accounts for reduced thickness effects and therefore can be used in conjunction with the nominal cushion thickness. 4.3 Pile Data Required pile data consists of total length, cross sectional area, elastic modulus, and specific weight, all as a function of depth. This is the socalled pile profile. For non-uniform piles, these values must be entered as a function of depth in the P1 input form. An alternative input form allows for the entry of a number of uniform segments (in the non-uniform pile window, the section input icon is active). The offshore version also offers an optional input mode which considers add-ons with cut-off and stabbing guides. For Two-pile analyses, the second pile profile, whether uniform or not, must be input in P2. This may only be occasionally necessary, if two piles are driven in parallel. This type of analysis is possible; however, it is complex and potentially inaccurate. If both piles are under the same cap and have the same length and resistance distribution, they could be considered as a single pile with a cross sectional areas equal to the sum of the two pile areas. Also, if one pile was driven with its toe against the top of a second pile, again a single, nonuniform pile analysis would be more reasonable a nd accurate than the Two-pile analysis. (The analysis of a follower on top of a pile is a typical example for a non-uniform single-pile analysis.)

102

GRLWEAP Procedures and Models

Version 2010

Version 2010

GRLWEAP Procedures and Models

103

 A Two Pile Toe analysis is recommended when a pile has a size reduction along its length, which causes soil displacement and, therefore, a second pile toe effect. The total end bearing can be distributed between the two pile toes and damping and quake can be specified for both.  A Pile Splice analysis must be performed if the pile, somewhere along its length, allows for extension with zero tension force. The distance of forceless extension is called a “slack”. This occurs, for example, when a pile is mechanically spliced. Obviously, the follower on top of a pile has an unlimited extension at its bottom and therefore a practically unlimited tension slack. This situation is also modeled with a splice input which has a large slack. A crack in a pile exhibits a reduced compression force while the crack closes under compression. This would again be modeled with a splice, where the tension slack could be made very small (but it must exist) and the compressive slack is modeled by the round-out input. To enter a splice click on Options/ Pile Parameters/ Splices; then enter the number of pile splices to be modeled, click “Update” and then enter the depth, tension slack, compression slack and coefficient of restitution data. Note: if a very soft material with low coefficient of restitution (like a softwood cushion) is modeled between two stiffer elements, then it is important that the segment with the low stiffness also has the low coefficient of restitution or the energy losses will be incorrectly calculated in the analysis. For that reason (and really under all circumstances), the Numerical Output, showing the pile model, must be very carefully reviewed and corrections to the input made if necessary. Input pile properties also include the Critical Index which is either 0 or 1. This input is only useful for the analysis of a pile consisting of more than one pile material. The sections which are marked as critical will be the ones checked for maximum stresses (see also output description). The pile perimeter is needed for converting unit shaft resistance to total shaft resistance. As mentioned earlier (Section 3.13.6) the perimeter is easily assessed for a solid pile; however, for H-piles and pipes sometimes questions exist. For H-piles, one usually chooses the box surrounding the pile cross section. For open ended piles, over a certain distance the perimeter may be increased or even doubled to consider friction over the inside of the pile. However, no clear guidelines or correlations can be referenced for this situation. For a static analysis, the pile’s effective Toe Area must also be entered (on the Main Input Screen and since 2010 in the S1 Screen). The Toe Area is closely related to the soil resistance; this input allow the user for certain soil layers to model the plugged, unplugged or partially plugged situation by, respectively, entering steel annulus area, pipe gross area or a value in between. As discussed in Section 3.13.6, this question is even more difficult to answer than the perimeter question for open profiles. In general, it may be assumed that H-piles plug during driving, and therefore the fully plugged area may be used. For pipe piles, plugging depends on pile diameter, soil density and depth of penetration into the dense material. Probably for 104

GRLWEAP Procedures and Models

Version 2010

diameters of 20 inches (500 mm) or less plugging occurs in competent soils. For pipes with diameters greater than 30 inches (900 mm) plugging during driving is usually not expected. Under all circumstances, plugging depends on the soil type, soil strength and penetration into the competent soil layer. As mentioned earlier it is recommended to analyze both the plugged and the unplugged situations to establish upper and lower bound results. Since 2010 a more realistic driveability analysis is possible, because the end bearing can now be calculated with variable Toe Area values vs. depth (in the S1 Screen). For example, if a soft clay layer is underlain by a very dense sand, and if it is expected that the pile “cores” in the clay but plugs in the sand, then the Toe Area should be, respectively in the clay and sand layers, the pile toe steel cross sectional area and the total plugged toe area. 4.4 Soil Static soil resistance calculations may be required before GRLWEAP analyses. For bearing graph analyses, when wave equation results are to be used in conjunction with an observed blow count, the soil resistance calculations can be done in a more casual manner than for a driveability analysis. The ST analysis, based on an assessment of soil density or consistency, may be sufficient for a bearing graph analysis where only a relative shaft resistance distribution and the percentage of shaft resistance are needed as an input. In a bearing graph analysis, it is common practice to allow the pile's depth of penetration and (relative) soil resistance distribution to remain constant throughout a series of analyses, even though the pile's ultimate capacity is made to vary. In other words, it is usually unnecessary to recompute the skin friction distribution, end bearing, quake, and damping for each ultimate capacity. Instead one uses the soil resistance distribution that has been calculated based on the soil investigation. The resulting resistance distribution is really associated with long term pile resistance and strictly applicable only to a redrive situation. The loss of resistance during driving adds another inaccuracy to the approach if it is not properly accounted for by means of setup factors. When it is desired to calculate the blow count and stresses more accurately for various depth values as the pile penetrates into the ground, the driveability analysis must be chosen. In this case, the static soil resistance should be input as accurately as possible. Static soil analysis provided by GRLWEAP is based on a general soil type information (ST), SPT N –values (SA), Cone Penetrometer values (CPT) and sand density and clay undrained shear strength (API). Hopefully, the more detailed and accurate the input is, the more realistic the results that can be expected. But as mentioned earlier, static geotechnical analyses are inherently inaccurate and should be complemented by local experience and dynamic testing. It is the users responsibility to make all necessary corrections in the S1 screen necessitated by the limitations of GRLWEAP’s static geotechnical analyses. Version 2010

GRLWEAP Procedures and Models

105

 Although the pile can be specified as “Nonuniform” as far as its cross sectional properties and perimeter, are concerned, special pile features like a taper may require additional consideration for the different unit resistance expected. Also second toes cannot be handled by GRLWEAP’s soil analyses and must be handled by separate user calculations and input. While, shaft quakes and toe damping are usually left constant with depth, the toe quake generally varies with the type of pile and the density of the soil and therefore with depth. Also the shaft damping values must usually be varied for the different soil layers. The soil analyses routines help in that regard, but the user is urged to carefully review what is automatically generated. 4.5 Options  A variety of input, output, and analysis options are available in GRLWEAP. Depending on the purpose of the analysis, these options might be extremely helpful. In the program, most of these options can be accessed through the toolbars, the icons, or the menu bar. Also, extensive help files were built into the program that describe the options and explain their use. The following are some of the major options available to the user. Hammer options (automatically invoked by choosing the associated hammer) • Open end diesels • Closed ended diesels • External combustion hammers, i.e. air, steam, hydraulic or drop hammers • Vibratory hammers Hammer parameter options  (Options/ Hammer Parameters  –  except Hammer Weight) • Modification of Stroke •  Efficiency • Combustion Pressure (diesels) • Reaction Weight (closed end diesels) • Combustion Delay to model pre-ignition (liquid injection diesels) • Ignition Volume (atomized fuel diesels) • Gas Expansion Coefficient • Vibratory Frequency (vibratory hammers) • Vibratory Delay (vibratory hammers) • Line Force (vibratory hammers) • Assembly Weight (external combustion hammers) • Hammer Weight (options/ General Options/ Numeric) Hammer file options • Modification of a model in the hammer data file (View/ Edit Hammer Database or double click on an ID number in the hammer window of the main screen) 106

GRLWEAP Procedures and Models

Version 2010

• User supplied new hammer model (View/ Edit Hammer Database) Stroke options for diesel hammers (see Options/ General Options/ Stroke) •  Convergence of (or iteration on) stroke with fixed combustion pressure; this is the normal mode of analysis. •  Convergence of (or iteration on) combustion pressure with fixed stroke; this option is used when the stroke is known (say from observation on site) but the associated pressure is uncertain. Note:  Allowing for a significantly increased pressure to match an unusually high stroke can lead to non-conservative capacity results. In Inspector’s Chart analysis option, the pressure is not  increased above the file specified pressure for conservative considerations. • Single analysis with fixed stroke and pressure; this option is ideal when analyzing a high stroke on a low soil resistance as it may occur when the pile suddenly breaks through a hard layer Driving system options • With helmet (cap) by entering a number greater than zero • Without helmet (cap) by entering a zero helmet weight • With hammer cushion by entering either area, elastic modulus and hickness, or a stiffness value • Without hammer cushion by leaving at least stiffness and thickness at zero •  With pile cushion by entering at least a nonzero thickness or a stiffness (concrete piles only) • Without pile cushion by leaving stiffness and thickness at zero  Analysis options (analysis option drop down menu in tool bar) •  Bearing graph, proportional is the standard result where shaft resistance and end bearing are equally uncertain •  Bearing graph, constant shaft resistance; applicable when shaft resistance is fairly well known and, for example, driving a short distance into a bearing layer is modeled. • Bearing graph, constant end bearing; applicable for situations when end bearing is well known or insignificant. • Inspector’s Chart; calculates the required blow count and associated stress maxima for a single ultimate capacity value. • Driveability; calculates blow count and stresses vs depth based on user supplied shaft resistance and end bearing vs depth data Driveability options • Gain/loss factor for both shaft resistance and end bearing increase/reduction to SRD (static resistance to driving); requires appropriate soil setup factors in the soil resistance vs depth input (S1 Window) • Variable setup for driving interruptions specified as “Waiting Time” in the D Window; requires also input of relative energy and setup time in the soil resistance input (S1 Window) • Variable pile length; specify length for each depth to be analyzed in the D Window Version 2010

GRLWEAP Procedures and Models

107

• Hammer, driving system modifiers; including fuel setting, efficiency, cushion COR, and cushion stiffness input (D Window) Static geotechnical analysis options • Static analyses; accessible from Main Input Form (S1) and from the S1 soil resistance window (ST, SA, CPT, API) Pile options • Variable pile weight (by specifying gravitational acceleration, Options/ General options/ Numeric) • Non-uniform piles (specify through the pile drop down menu) • Single pile with two pile toes; not for driveability or RSA analysis • Two-piles in parallel; not for driveability or RSA analysis • Splices and slacks (specify in Options/ Pile parameters) Pile input options (Options/ Pile Parameters/ Pile Segment Option) • Automatic number of segments and segment properties (standard) The following are not for driveability analyses • Input of number of segments with automatic segment properties • Input of number of segments and relative segment length with auto segment stiffnesses and masses • Input of number of segments, relative segment length, and segment stiffnesses and masses Splice input  (Pile Parameters/ Splices) • Splice modeling with slacks and coefficient of restitution • Slack representation • Crack representation Soil shaft resistance distribution options (automatically generated for each segment) • Simple distribution on main screen; not for driveability analysis • Variable distribution for situations that require more than a triangular or trapezoidal distribution Soil segment input options • Automatic soil damping, quakes, and ultimate resistance values • Input of segment soil damping with automatic quakes and ultimate resistance values (Options/ Soil Parameters/ Soil Segment Damping/Quake); not for driveability analysis • Input of segment soil damping, quakes and ultimate resistance values; (first choose “Detailed Resistance Distribution” in distribution Drop Down Menu and enter for each segment the ultimate resistance values; then click General Options/ Soil Parameters / Soil Segment Damping/Quake); not for driveability analysis Damping options (Options/ General options/ Damping) • Case soil damping; only in conjunction with measurements • Smith soil damping; recommended for all but RSA and vibratory hammer analyses 108

GRLWEAP Procedures and Models

Version 2010

• Smith viscous soil damping; recommended for RSA and vibratory hammer analyses • Gibson (Coyle) soil exponential damping; for research only • Rausche exponential soil damping; for research only • Hammer damping variation; for research only • Pile damping variation; for research only Numerical analysis options (Options/ General options/ Numeric) • Residual Stress Analysis, which is applicable to flexible piles with significant shaft resistance. It is recommended to always try this analysis in addition to the standard analysis as it provides for more realistic stresses and blow counts. For tapered pipe piles (e.g. Monotube), RSA is always recommended. An entry of “1" is recommended as it allows the program to perform up to 100 trial analyses to reach convergence. Other choices would numbers between 1 and 100 which would set the maximum number of trial analyses allowed. • Gravitational acceleration values may need adjustment if battered piling or underwater pile driving is analyzed. In the former case, adjustments must be made to include only the axial pile and hammer weight components, in the latter case to consider the buoyancy of the pile and hammer weight. For example, if a concrete pile is subject to buoyancy then its effective weight is roughly 60% of its weight above water. In that case, reducing the pile gravitational acceleration to 6 m/s2 (19 ft/s2) would reduce the static weight component of the pile. It would not reduce its mass. •  A larger “Phi” value (Time increment ratio) for the reduction of the computational time increment; may be necessary when the analysis becomes unstable (erratic results, non-proportionality between force and velocity, and other “noisy” calculated pile variables vs time are clear indications of instability; see variable vs time output). A number 300 would reduce the time increment by a factor 3 while default is 160 (1.6 reduction). •  An increased number of predictor-corrector iterations beyond the default of 1 is not recommended. • The maximum analysis time occasionally may need to be increased if there is evidence that either blow counts or stresses have not peaked within the analyzed time period. Examples where this may be needed are analyses with very low resistance or vibratory hammer analyses with low frequencies. Experimenting with this number may help determine if this is a necessary adjustment. • Hammer Cushion round-out values are usually not modified although for steel on steel impacts a reduction to 1 mm may be reasonable. In order to better match measured records, Pile Cushion round-out values sometimes are increased to significantly higher values than the 3 mm (0.01 ft) default. Output options (Options/ General Options/ Output) • Normal numerical output includes extrema tables; see the numerical output files; it is important that this listing is carefully reviewed prior Version 2010

GRLWEAP Procedures and Models

109

to accepting the results. • Minimum numerical output is automatically chosen for the driveability analysis to reduce the amount of output. It does not include extrema tables. However, particularly for complex situations, including multimaterial piles, it is strongly recommended to also check the Numerical Output (*.GWO file) for an indication of the location of maximum pile stresses along the pile and the various maxima in the different materials. •  Debug numerical output; only useful for those familiar with the program code. This option may generate extremely large files when driveability analyses are perfomed. • Bearing graph plot - single result; standard output. • Bearing graph plot - two results; convenient when bearing graphs from two different cases are to be compared. (Read Second File in the File Menu). • Driveability (vs depth) plot - result from current gain/loss factor or from more two gain/loss factors (View/ Ranges/ Selections). • Variable vs Time plots; helpful to check stability of analysis, for comparison with measurements and to learn about wave propagation. Only last analysis of driveability analysis is accessible when in Normal Output mode. Select quantities in Options/ General Options/ Output: - Mixed quantities (vs time) plot - Acceleration (vs time) plot - Velocities (vs time) plot - Displacement (vs time) plot - Forces (vs time) plot - Stresses (vs time) plot • Output segment numbers of the output variables can be chosen in Options/ General Options/ Output •  Output time increment is the time interval at which individual quantities are saved for output. For increased resolution in the variable vs. time plot, choose a smaller value; for increased plot length, choose a larger value (Options/ General Options/ Output). • Output of frequency of stress maxima and stress ranges (Output in the Offhore Wave Option: Driveability/ Edit/ Copy Stress Extrema or Copy Blows vs. Stress Ranges.

110

GRLWEAP Procedures and Models

Version 2010

5. OUTPUT AND HELP INFORMATION 5.1 Numerical Output GRLWEAP produces output in a variety of forms, depending on the analysis and output options chosen. It is important that the user checks thoroughly the Numerical Output (*.GWO files). It contains: • a listing of the input data file which may be permanently saved and recalled. • the hammer and pile model with soil resistance parameters. • extrema tables (not for output option: “minimum output”) with maxima of force and stress each (both tension and compression), velocity, displacement, and transferred energy, for every pile segment and for every capacity value analyzed. • a summary of the results in the form of blow counts, stress maxima, stroke, and transferred energy for each capacity value analyzed. For multi-material piles see note below. • for the driveability analysis, the “vs depth” tables, i.e. major results listed for each gain/loss factor as a function of depth. •  for diesel hammers, the strokes analyzed and the associated combustion pressure The numerical output listing also includes certain warning messages or program performance indicators. For example, non-convergence of residual stresses may have occurred or an excessive diesel hammer stroke may have been calculated, and the program would warn of this condition (although it would adjust the combustion pressure automatically to account for that condition). Thus, review of the numerical output file is an absolute necessity. For the driveability analysis, the numerical output can be very long, particularly if many depths are analyzed with several gain/loss factors. For that reason, the default numerical output option is automatically set to “minimum” and extrema tables are subsequently not shown. It may therefore be advantageous to select the “normal” output option, even though the output may then get long. Note that for each analysis depth, the pile and/or soil model may be quite different, and therefore, careful checking is essential. Also, the end of the numerical output listing for driveability analysis includes a summary of the user-submitted soil resistance parameters. Since these parameters are subject to modification by set-up or driving induced capacity reduction, careful checking is advisable.

Version 2010

GRLWEAP Procedures and Models

111

5.2 Bearing Graph The second type of output is the Bearing Graph, both numerically and graphically displayed. This type of output is available for the Bearing Graph and the Inspector’s Chart analyses. A variety of scale options exists in View/ Ranges/ Selections. The bearing graph output can also be done for two analyses in the same plot. After displaying the bearing graph from the first analysis result, click on nd File/ Read 2  file and then browse to find the bearing graph data that you want to add to the first output. This output option also displays the numerical summary table. Both graphical and numerical data can be copied and pasted into other applications such as a word processor. Click on the graph or table and the on Edit/ Copy to clipboard and then proceed with the pasting in the other application. 5.3 Driveability  After a driveability analysis has been performed, instead of “Bearing Graph” a “Driveability” option will be available, It provides for numerical and graphical summaries for up to two Gain/Loss factors (View/ Ranges and Selections). Scales can be changed in the same window (choose the Graph Tabs) and copy/paste options are as for the Bearing Graph. 5.4 Variables vs. Time  Additionally, Variables vs Time can be plotted or listed. The variables include accelerations, velocities, displacements, forces and stresses, for every pile segment. In order to reduce disk space requirements, this output is only available for a reduced set of piles segments (as selected in Options/ General Options/ Output), and for driveability analyses only for the last analysis. Pile force and velocity can also be displayed at a proportional scale for both the top segment and one additional user selectable segment. Numerically, variables vs time can be transferred to other programs using the copy and paste features of the windows system. The output time increment (Options/ General Options/ Output, Edit Segment Numbers) sometimes must be made longer, e.g., 1 ms, to allow for plotting of the whole range of calculated time period in the variable vs time plots. This may be of particular interest when the analysis time has been increased or the length of pile segments (and because of the shorter critical time also the time increment) has been decreased. In addition to proportional force velocity output for the pile top, another segment can also be designated for force and proportional velocity output in Options, General Options, Output, Edit Segment Numbers. This is only meaningful for the Mixed Variables. Note that the pile variables can also be displayed in the 3 -D plot. Note about maximum stress results: The stress maxima are normally the numerically highest values occurring somewhere along the length of the pile. This is satisfactory for piles consisting of only one type of material. 112

GRLWEAP Procedures and Models

Version 2010

However, for multi-material piles, the critical stresses are of greater interest and should be included in the summary table. For example, in a concrete pile with steel tip, the stresses are numerically much higher in the steel than in the concrete, yet we are really interested in the maximum tension stresses in the concrete. For that reason, the Critical Index input has been provided in the P1  input form, which selects for the summary table only stress maxima which occur in the critical sections. However, in order to avoid missing potentially damaging stresses in sections which were not considered critical, the analyst should not trust these automatically selected values exclusively and additionally look at the extrema tables of the numerical output. These tables will also tell when and where these critical stresses occur along the pile. 5.5 Stress Maxima Range Ouput for Fatigue Studies This is an Offshore Wave option Fatigue studies are done in different ways, sometimes requiring the number of stress maxima and sometimes the number of certain stress ranges occurring during pile installation. Selecting that information from extrema tables and finding the associated number of blows for each pile segment is very time consuming at best. To simplify this process, GRLWEAP has added two types of summary tables one for stress maxima and one for stress extrema. These tables can be transferred to a spread sheet. GRLWEAP does not provide tools to display or otherwise manipulate them.  After performing a driveability analysis, GRLWEAP has saved the two files containing stress information. The contents of these two files can be copied in the Output Section of the program by clicking on Driveability and then Edit. Two options will be displayed: Copy Stress Extrema Data and Copy Blows vs. Stress Ranges. Tables 5.5.1 and 5.5.2 show small portions of the stress extrema and stress range tables, respectively. Both tables include listings for the gain/loss factors chosen under View/ ranges and Selections. The extrema data include pairs of columns for maximum compressive and tensile stresses for every depth analyzed. It also shows the number of blows needed to drive to that depth from the previous depth. The columns then list for each segment the maximum stress calculated for that depth calculation.

Version 2010

GRLWEAP Procedures and Models

113

Table 5.5.1: Summary Table of Stress Extrema Stress Extrema for Gain/Loss 1 at Shaft and Toe 0.833 / 1.000 Depth (m)

1.83

3.66

5.49

Blows

0

4

8

Pile

mxCstrss

mxTstrss

mxCstrss

mxTstrss

mxCstrss

Seg #

MPa

MPa

MPa

MPa

MPa

1

0.1

0

149.6

0

156.7

2

0.2

0

150.1

0

157.3

3

0.5

0

150.5

0

157.8

4

1

0

151.1

0

158.5

Table 5.5.2: Summary Table of Stress Ranges Blows vs. Stress Range for Gain/Loss 1 at Shaft and Toe 0.833 / 1.000

Stress Range

0

42

84

126

168

(MPa)

42

84

126

168

210

1

0

0

0

22

93

2

0

0

0

22

93

3

0

0

0

22

93

25

0

0

0

10

105

26

0

0

0

18

97

27

0

0

0

32

84

28

0

0

0

115

0

Seg #

Table 5.5.2 basically lists number of blows for select stress ranges (in 42 MPa increments in the example). The user has the option to refine the stress ranges by choosing for example 10 instead of the 5 ranges shown. Table 5.5.2 indicates that segment 28 was exposed to 115 blows with a stress range (maximum  – minimum compressive stress) between 126 and 168 MPa. 5.6 Help Further information on available output options is available in the program’s Help section which can be accessed by pressing function key F1 at any point in the data input. This type of Help is given in written form describing 114

GRLWEAP Procedures and Models

Version 2010

input parameters, option functions, and examples. For the novice, it may be worthwhile to print out these articles for convenient reference. The examples are also helpful as a demonstration of program capabilities.  Another form of Help is for direct data entry. For example, if the cursor is activated on an input field that requires an area input, pressing function key F3 will activate the “Area Calculator”. Other direct input helps are available for driving system parameters and/or general cushion properties and pile material properties. Finally, an easy way to get started with the input process is the Data Entry Wizard which is invoked after pressing the New Document icon (or New in File).

Version 2010

GRLWEAP Procedures and Models

115

116

GRLWEAP Procedures and Models

Version 2010

6. CONCLUSIONS AND RECOMMENDATIONS GRLWEAP is a wave equation program for the analysis of the pile driving process. It is based on Smith's original algorithm but offers a variety of enhancements and options. The program analyzes what happens under the dynamic load applied by either a ram impact or a vibratory hammer. The program is not intended to predict the bearing capacity of a pile at a certain depth from static geotechnical analysis. Instead, the four static analyses available are thought to provide an aid in performing the dynamic analysis. Basically, the program either predicts: • the bearing capacity of a pile based on an observed blow count or  • the blow count based on a calculated or estimated static and dynamic soil resistance.  A wave equation analysis can be run only if information about hammer, driving system, pile, and soil is either known or assumed. It can then calculate the motions and thus the penetration of the pile and its stresses due to a hammer blow. The more accurate the input, the more realistic the results. Regarding hammer data input, it is most complex for diesel hammers whose thermodynamic behavior is simulated in GRLWEAP. External combustion hammers powered by hydraulic pressure, compressed air, steam or cable are more simply represented. GRLWEAP also models, vibratory hammers in a relatively simple manner. The driving system is represented with bilinear springs and some nonlinearity (round-out). In this way, good agreement between measured and computed pile quantities is often achieved. The pile model considers the pile mass (segment masses), its elasticity (springs), its structural damping (dashpots), and any slacks from splices. A wide variety of pile systems exists, including those consisting of more than one material or driven by a mandrel. Most commonly employed systems can be fairly realistically represented and analyzed by GRLWEAP. However, since the pile model is strictly linear and one-dimensional and only axial motions, stresses and forces are calculated (see below) and any yielding is not considered. On the other hand, residual stresses in pile and soil can be estimated by performing repetitive (blow after blow) analyses. In general, RSA leads to greater calculated pile sets per blow and higher stresses than the standard Smith analysis which assumes that the pile stresses are zero prior to hammer impact. The dynamic soil model considers the soil's elasticity (quakes), strength (capacity), and dynamic behavior (damping factors). There are a number of extensions to the soil model for damping (viscous, exponential), plug

Version 2010

GRLWEAP Procedures and Models

117

representation, soil radiation damping (soil motion), etc. However, these extensions are experimental and only of interest to the researcher. The user of the wave equation approach should realize that the dynamic analysis represents the soil in its disturbed state. Estimates of soil setup or relaxation must be additionally considered. For example, if a pile is driven and its blow count is observed at the end of driving, the wave equation bearing graph will provide an estimate of the bearing capacity at the end of driving based on that blow count. Soil setup is likely to add additional soil strength along the pile shaft, while relaxation effects might reduce the end bearing. One day, one week, or one month later, the pile may have a capacity that differs significantly from the end of driving value. The user must estimate these effects, or better, perform restrike or static load tests for a more accurate capacity assessment. Output is provided by the program in both numerical and graphical form. Most importantly, the program calculates for a given bearing capacity value both blow count and stress extrema. Capacity or stress vs  blow count establishes a bearing graph. Listing or plotting the results as a function of depth result in the driveability result. For comparison with dynamic measurements conducted during pile driving, forces and/or motions may be plotted as a function of time. The GRLWEAP wave equation model is obviously a great simplification of the real world and certain unusual circumstances may only be crudely represented. Furthermore, the model parameters are often inaccurate. For example, they may not represent the hammer’s actual state of maintenance, the soil’s in-situ static and dynamic behavior, or situations like plugging. For high blow counts, when the pile motions are small, incomplete resistance activation may occur and non-linear soil resistance effects or radiation damping may introduce greater errors than for easier driving conditions. On the other hand, very easy driving conditions with permanent sets in excess of 15 or 20 mm may also produce uncertainty due to high dynamic soil resistance components. Thus, where experience lacks, measurements, both static and dynamic, are the only way to assure an accurate assessment of bearing capacity. It is for that reason that modern safety factor concepts distinguish between different methods of capacity determination. For wave equation analyses, the typical overall factor of safety is between 2.5 and 2.8.  As mentioned above, the GRLWEAP provides a one-dimensional analysis. Thus, stresses caused by bending, non-uniformities of soil resistance or non-symmetric pile shapes are not calculated. For the stress results, it is therefore important to realize that the calculated values are averaged over the cross section and can be easily exceeded if the hammer-pile alignment is poor, the pile experiences bending, or the toe resistance is subjected to a non-uniform rock surface.

118

GRLWEAP Procedures and Models

Version 2010

APPENDIX A: CORRELATIONS For traditional wave equation work, the most important correlation is that of capacity based on observed blow count. A very early study was was published by Blendy (1979). A comprehensive correlation study has also been reported by Thendean et al. (1996). It shows that the correlations correlations between predicted and measured bearing capacities are dependent on time effects; restrike tests and corresponding static load tests should therefore be performed at comparable waiting waiting times after time of pile installation. The study also shows that restrike test results produce greater scatter than endof drive results. This can be explained explained by the uncertainty of blow count count and energy in restrike situations: the set per blow changes from blow to blow while hammer performance generally improves. Also during a restrike, the capacity of the pile often changes as the pile loses setup soil resistance or regains relaxed toe resistance.  A comprehensive study on the prediction of blow counts based on wave equation and soil resistance calculated from static geotechnical analyses has not been made. made. Because of the the difficulty of predicting soil resistance resistance accurately from soil borings, there is much more volatility in these results than in capacity predictions which are based on observed blow count.  A more recent study on stress, diesel hammer stroke, and transferred energy was published by Rausche et al. (2004) showing that the greatest uncertainty is introduced by the relatively soft pile cushion when driving concrete piles. In fact, the study suggests that for end of driving situations, used cushion properties should be used. For example, plywood cushions should be analyzed with 66% of nominal thickness and with an elastic modulus roughly 50% higher than the normally recommended value (300 instead of 211 MPa or 43 instead of 30 ksi). Early driving situations can be analyzed with the nominal thickness and a modulus corresponding to a slightly used material.  Anecdotal evidence suggests that GRLWEAP predicts lower than actual diesel hammer strokes. Indeed, GRLWEAP occasionally underpredicts strokes; however, there is no real evidence that stress or energy results have a bias. Hammers vary vary in their performance characteristics not only after months of use and abuse but even during a day depending on ambient temperature or weather conditions, the amount and hardness of pile driving, and other factors. Therefore, differences between energy and stress stress results from analysis and measurements must be expected to be in the 10 to 20% range. Further information information on GRLWEAP’s performance can can be found in Rausche et al., 2004. That reference also suggests that diesel hammer stroke results are somewhat underpredicted (3% on the average) and because of this potential underprediction it is suggested that stroke results are used in the following manner:  Accept results if the observed stroke is within 0.9 and 1.2 times the calculated value. If stroke is severely underpredicted, repeat analysis only with higher combustion pressures if (a) the actual stroke exceeds the Version 2010

GRLWEAP Procedures and Models

119

calculated value by more than 20% and (b) it is assured that the high stroke is the the result of good good hammer hammer performance performance and not preignition. preignition. It is suggested to adjust the pressure only so far that the calculated stroke is still about 10% lower lower than measured. To adjust stroke by 10%, increase the maximum combustion pressure by 10%. If stroke stroke is more than 10% overpredicted, it may appear that the hammer is not in working order. Reduce the maximum combustion pressure to make the computed stroke match the observed one. It is always recommended to make conservative predictions; conservative predictions has different meanings for different tasks as follows: 

For capacity capacity from blow count, use a pessimistic pessimistic hammer performance value (lower efficiency). e fficiency).



For stress predictions during driving, use an optimistic hammer performance (higher efficiency).



For blow counts in a driveability analysis, make an optimistic high soil resistance assessment and a pessimistic hammer performance assumption.



For stresses in a driveability analysis for steel piles, make an optimistic (high) soil resistance assessment and an optimistic hammer performance assumption.



For stresses in a driveability analysis for concrete piles, use two different analyses, one with an optimistic (high) soil resistance assessment and hammer performance assumption and the other with a pessimistic (low) soil resistance assessment and an optimistic hammer assumption (for high compression stresses and high tension stresses, respectively).

120

GRLWEAP Procedures and Models

Version 2010

APPENDIX B: HAMMER MODEL DETAILS B1 Diesel Hammer Studies Throughout the development of the various WEAP program versions and the GRLWEAP software, emphasis has been placed on realistic hammer models. The complexity complexity of the diesel hammer, hammer, consisting consisting of a variety of different makes, requires comparative analyses to produce a realistic mathematical representation. The Background report of the previous GRLWEAP documentation summarized these studies and included correlations of measured and computed results. Included in these comparisons were quantities such as maximum pile top force, maximum transferred energy (ENTHRU) (ENTHRU) and diesel hammer stroke. The 1986 study and related hammer model improvements were based on 57 different test results. For the 1998 1998 and later GRLWEAP program versions, the original hammer studies, although still relevant, were not reprinted in this report. The diesel hammer model has undergone a variety of changes which were made necessary, for example, by hammers that produced higher and higher strokes. One of the necessary necessary change involved involved the determination of the maximum combustion pressure in a consistent manner for all diesel hammers; another one concerned a modification in which the pressure  – volume relationship was calculated, requiring a different adiabatic expansion coefficient. These changes helped calculate more reliably and realistically strokes while at the same time producing calculated pile top forces and transferred energy values that agreed reasonably well with measurements. B2 2002 Method for Diesel Hammer Pmax Calculation The maximum combustion pressure, P max, is the most important parameter in the diesel hammer hammer model for diesel hammer stroke calculations. calculations. A large Pmax  value not only makes for a large hammer stroke, but also adds substantial transferred energy (ENTHRU) (ENTHRU) even if the stroke is kept constant in either a single stroke analysis or one that allows for stroke convergence with fixed pressures. Analyses with fixed stroke and convergence of pressure are, naturally not dependent on the Pmax value in the hammer data file. Direct measurements of P max are complicated, expensive, and subject to a variety variety of influences and errors. Most importantly, importantly, on a test stand, hammer combustion pressures usually do not represent the typical working conditions and are therefore not representative. A procedure was therefore developed that produces a reasonable Pmax value based on the hammer’s rated energy. energy. Essentially, the procedure determines that pressure pressure value value that would produce the rated stroke in a refusal condition on a pile that is matched to the hammer hammer size. A check is also made for a reasonable transfer energy value in the theoretical test stand. The “test stand” is assumed to be a steel pile driven into rock; the pile properties are matched to the hammer size as follows:

Version 2010

GRLWEAP Procedures and Models

121

Pile Length, L pile (ft) = 50 ft + ¼ of rated energy of hammer in kip-ft Lpile is limited up to 200 ft to consider larger hammer. 2

Pile Area, Apile (in ) is based on a pile weight to ram weight (W ram in kips) ratio of 2. Thus, 2

3

 Apile (in ) = 2 x W ram(144) / [(0.492 kips/ft )(Lpile in feet)]  A driving system is also included with the following parameters: Helmet weight (kips) = 20% of ram weight Hammer cushion stiffness (kips/inch) = W ram/(0.0004 inches) = 2500 (Wram in kips). Hammer cushion coefficient of restitution = 0.8. For the soil resistance the following parameters are set: The automatic Rult  values of the GRLWEAP Version 2002 program are used in a standard bearing graph. However, the highest R ult  value must produce a blow count at or above 240 b/ft. Default damping (0.2/0.15 s/ft) and quakes (0.1 inches). Triangular resistance distribution with 10% shaft resistance. Several bearing graph analyses are then performed. The Pmax  value is adjusted until the stroke at refusal is equal to 95% of rated stroke and  until the transferred energy is less than or equal to 50% of rated. The latter cor responds to the 90% point in the rated energy histogram of GRL’s diesel on steel pile data collection. In other words, only 10% of all diesel hammers driving steel piles will transfer more than 50% of their rated energy at EOD to a steel pile. In general the transferred energy calculated by GRLWEAP is significantly less than 50% and more likely the mean value of 37% (see table). Note: The following method has been used to determine the maximum combustion pressure for all open end diesel hammers, except for the ICE Iseries hammers. Correlation studies for this series of hammers showed that hammer performance was better modeled by using 95% of the hammer pressure used in GRLWEAP 1998 than by using the standard algorithm. B3 Measured Hammer Performance

122

GRLWEAP Procedures and Models

Version 2010

GRL Engineers, Inc. (formerly Goble Rausche Likins and Associates, Inc.) has taken measurements on many different construction sites and on many different hammer-pile systems. For end-of-driving situations, these measurements, pile top force and velocity, were used to calculate transferred energy and from it, by division with the rated hammer energy, the so-called transferred efficiency or transfer ratio. GRLWEAP calculates the equivalent value named ENTHRU. These transferred efficiency values were organized by hammer and pile type. A statistical evaluation was then made and, in 2009 yielding the results of Table B1. Table B1: Measured Transfer Efficiencies (Energy in Pile Divided by Manufacturer’s Rated Energy (%) Hammer Type (GRLWEAP Hammer Efficiency)

Steel Piles

Concrete and Timber

No. Cases

Mean %

CoV %

No. Cases

Mean %

CoV %

 All Diesel Hammers (0.8)

1419

39

26

668

26

30

Single Acting  Air/Steam (0.67)

747

56

23

194

41

29

Double Acting  Air/Steam (0.50)

68

40

34

47

32

33

 All Hydraulic (0.80/0.95)

203

69

24

67

47

34

The All Diesel category includes both open end and closed ended diesel hammers and both atomized and liquid injection type hammers. The GRLWEAP standard efficiency is 80% while on steel piles the transfer efficiency averages 39%. That means that the pre-compression phase, the driving system and the impact event itself cause the difference loss of 41%. Indeed it can be expected that the compression costs about 25 to 33% of the rated energy and that leaves an estimated 8 to 16% of the losses to the energy transmission process through the driving system. The concrete piles receive only 26% of the rated energy; the 13% difference between the steel piles and concrete and timber piles is the energy lost in the cushioning or the wooden pile top. (The very top of a timber pile often brooms and, therefore, behaves like a softwood cushion). The second group of hammers are the traditional air pressure or steam powered hammers whose upward and downward motions are controlled by ram position. This can lead to problems like pre-admission which can self cushion a hammer. These hammers also lose 13% due to driving system and impact event and an additional 15% in the pile cushion on concrete piles.

Version 2010

GRLWEAP Procedures and Models

123

Double Acting Air/Steam hammers are either traditional double acting, differential acting or compound hammers. They may be powered by compressed air or steam. In hard driving, i.e., at the end of driving, these hammers often have to be run at reduced pressure to avoid uplift. That pressure reduction reduces their down ram acceleration and makes that hammer type somewhat less efficient and more erratically behaving. It appears that this hammer category loses 10% due to driving system and impact event and additional 8% in the pile cushion. The fourth category shown in the table includes measurement results from a variety of modern hydraulic hammers. They are given many names such as hydraulic free-fall hammers, hydraulic drop hammers, hydraulic-power assisted hammers, doubling acting etc. These results also include those from hammers with internal monitoring of the kinetic energy. Obviously, these hammers are very different in design, rating, and relative performance and that may explain why their COV (coefficient of variation) is surprisingly high even though each individual hammer make performs with much greater reliability than the other hammer types. However, not enough data has been collected to make statistical summaries of the various hammer makes meaningful. For the hydraulic hammers the difference between steel and concrete performance is a surprisingly high 22%. This may be explained by the rather high impact velocities of at least some of these hammers which then requires relatively thick cushion stacks. In summary, the statistical results suggest that concrete piles receive between 8 and 22% less energy of the rated energy than the steel piles. Estimated losses in the driving system and the impact event itself vary between 8 and 16%.

124

GRLWEAP Procedures and Models

Version 2010

APPENDIX C: GRLWEAP FIRST STEPS Whether or not you are a seasoned wave equation analyst, GRLWEAP may present challenges, and you may benefit by reading the following section for basic help with the program's options and capabilities and hints for solving a basic problem. In additon, however, you should refer to the „Help“ offered in on line while performing the program. Starting the Program Instructions for installation are provided separately as an insert with your GRLWEAP Manual. With the proper installation accomplished, you may start the program by clicking on the GRLWEAP icon or by selecting the program GRLWEAP  application using the Windows Explorer. Please be aware that a license, i.e. a key, either a software key or hardware key, is required for the program to run. If you have problems using the program, please refer to GRLWEAP FAQ section on our website (www.pile.com), and if you don’t find the solution there, contact the software department of Pile Dynamics, Inc.  After starting the program, it is wise to check and set your desired unit system (SI or English). The program will remember this unit system after it has been set during subsequent program runs. Before Executing the Program Prior to doing actual calculations, you should be able to answer the following questions: • Why do I need this dynamic pile analysis and what results do I need? • What are the basic parameters to be analyzed (Pile properties, hammer and driving system, soil details, design load, ultimate capacity or nominal resistance)? • How will I assure that the results are realistic? What field testing will be done. What factors of safety will be used? • In what form do I want to present the results?  Answering these questions should provide the basic data needed for the program input. Data Input It is strongly recommended to start each new data analysis by clicking on the New  icon or on New under File. While assuring that no hidden data from previous program runs are present, New  will guide the user through title and file name entry and many (though not necessarily all) other parameters needed for a basic analysis. These are the same data entries Version 2010

GRLWEAP Procedures and Models

125

that are described in the following section on the Main Input Form. After the user has completed the data entry, GRLWEAP presents the data in the Main Input Form. The Main Input Form The Main Input Form consists of tool bar (top), Data Entry Fields (left side) and a graphic display area as a partial help for checking the data submitted (right side). The various data entry fields accept inputs of: • • • • • •

•

•

Job Information Hammer Information or data file ID, or direct hammer selection Pile material selection Cushion Information for hammer and pile, and helmet information Pile Information Ultimate Capacities or Resistance Gain/Loss Factors  - Bearing capacities to be analyzed in Bearing Graph or Inspector's Chart Options or Gain/Loss Factors (to be applied to long term static resistance values) for the Driveability Analysis Dynamic Soil Parameters - Averages for shaft damping and quake, toe quake and damping for bearing graphs, and default damping and quake values for driveability analyses Shaft Resistance percentage and resistance distribution parameter for the simplest cases in a bearing graph

For a bearing graph analysis of a uniform pile with simple resistance distribution, the Main Input Form generally suffices for data input. For more involved situations, one or more additional Input Forms  must be filled in. They are accessible through the View  menu or corresponding icons and under menu entry Options. The Main Input Form displays most of the selected options at appropriate locations. However, it does not allow for direct modification of these options. The user can choose major options from the following four option menus: •  The Unit Option, allowing for choice of SI or English units •  The Soil Resistance Distribution Option, to choose between simple resistance distribution, variable resistance distribution, and detailed resistance distribution input (segmental input) •  The Pile Option, to choose between uniform pile, non uniform pile and two pile analyses •  The Analysis Option, to choose Bearing graph (assuming proportional or constant shaft resistance or constant end bearing), or Inspector's Chart or Driveability analyses Drop Down Menus View  - Depending on the selections made for Pile, Soil, and Analysis Options, the following Input Forms are accessible:

126

GRLWEAP Procedures and Models

Version 2010

• •

•

Main Input Form Pile 1 Input Form, accepts input of cross-sectional properties if Pile 1 is non-uniform, if 2 piles are analyzed in parallel, or if 2nd pile toe is to be analyzed; access through View or P1 icon Accessible from the Pile 1 input form is the Pile Section Input  (click Options/ Pile Parameters/ Pile Profile Section Input); it allows for somewhat simpler input than the Pile 1 input form, if the pile consists of several uniform sections (not to be confused with the input of individual segment parameters, stiffness and weight). nd Also the 2  Pile Toe can be accessed from the P1 Pile 1 input  form. Pile 2 Input Form, (to analyze 2 piles; serves for the input of the 2nd pile’s profile  and the connection between the piles (pile attachment)); access through View or P2 icon

•

Resistance Distr., Pile 1 Input Form, for the bearing graph, if the Simple Resistance Distr. is not sufficiently detailed and ST, SA, CPT or API  cannot be used; or for the Driveability Analysis; or for 2-Pile  Analyses; access through View/ Resistance Distr./ Pile 1 Input Form or use S1 icon.

•

Resistance Distr., Pile 2 Input Form, (always necessary for 2-pile analysis); access through View/ Resistance Distr./ Pile 2 Input Form or use S2 icon. Two-pile analysis has to be selected first in the Uniform Pile Drop Down Menu.

•

Depths, Modifiers Input Form, to select those depths at which a driveability analysis is to be performed; click View/ Depths/ Modifiers Input Form or use D icon. Driveability analysis must be selected first in the analysis drop down menu initially at Bearing Graph.

•

Soil Type Static Analysis Input Form, generally useful for calculating a reasonable resistance distribution for bearing graph analyses or for driveability analyses after choosing the Variable Resistance Distribution; access through View or ST icon.

•

SPT N-value based Static Analysis Input Form, may be used as a help in preparation for bearing graph or driveability analyses; after choosing driveability, access through View/ Static Analysis Input Form or SA from the S1 input form.

•

CPT (Cone Penetration) based Static Analysis Input Form, may be used as a help in preparation for bearing graph or driveability analyses; after choosing driveability, access through View/ CPT Input or CPTfrom the S1 input form.

•

API conforming Static Analysis Input Form, may be used as a help in preparation for bearing graph or driveability analyses; after choosing driveability, access through View/ API Static Analysis or API from the Version 2010

GRLWEAP Procedures and Models

127

S1 input form. For Offshore Wave Version only. •

Edit Hammer Database,  to enter a new hammer or modify existing hammer data; click View, Edit Hammer Database or double click on any one of the hammer names shown. Once the hammer data base is opened, double clicking on an individual data entry opens a hammer data input form which then can be modified.

•

Output  after an analysis has been performed; starts output program; accessible through View/ Output or click on OU.

•

View Input File shows the numerical data contained in an input file which can be saved and reanalyzed at any time; accessible through View/ S1 input form.

Options  - The following options can be accessed through the Options menu. • Check Status  causes program to check whether or not input is complete. • Job information can be used to enter Problem Title and/or File name and location. • General Options, Damping tab  Soil damping option (Options/ General Options/ Damping) - Case damping (for research or when measured) - Smith (default) - Smith viscous (for Residual Stress Analysis) - Coyle and Gibson (for research) - Rausche (for research)  Hammer damping option, normally used at default (Options, General Options, Damping)  Pile damping option, normally preset based on pile top material selection (Options, General Options, Damping) • General Options/ Output  controls plotted output type and numerical output quantity  for Variable vs Time output, choose between - Mixed (default) - Aceleration - Velocity - Displacement - Forces - Stresses  For all except the mixed quantities: - Choose Output segments, pile segments for which forces, etc. can later be plotted and numerically displayed. - Output Time Interval, to cover longer output time intervals at the expense of a better resolution.  For the mixed quantities choose an additional FV Segment for which force and velocity will be saved for later plotting at a proportional scale.  For the Numerical Output, choose between 128

GRLWEAP Procedures and Models

Version 2010

- Minimum, preferred and default for long driveability analyses - Normal,preferred for input and result check, for all except long driveability analyses - Debug  (not recommended), see output description for further details • General Options/ Numeric;  except for the Residual Stress Analysis, these options are infrequently used:  Residual Stress Analysis  is invoked if a positive value is entered which limits the number of trials. An entry of „1“  allows for the maximum of 100 trial analyses (often more realistic for slender, elastic piles than normal analyses); a value between 1 and 100 specifies the maximum number of trial analyses.  Hammer gravity modifies static weight of assembly and helmet; it is normally set to the full gravitational value unless consideration is given to bouyancy or pile inclination.  Pile gravity normally set to the full gravitational value; may be set to zero which is the traditional option for bearing graphs or to a reduced value if the pile is subject to buoyancy or inclination.  Time Increment Ratio  in percent; may be reduced if there is a possibility of numerical instability; use a value greater than 160, e.g. 300.  Number of Iterations;  see description of numerical procedure. Normally not modified.  Round Out  deformations for hammer and pile cushions; rarely modified.  Analysis Duration, though generally set automatically, may sometimes be of interest for durations chosen longer than standard analysis. • General Options/ Stroke pertains only to diesel hammers;  Convergence of stroke with fixed pressure  Convergence of pressure with fixed stroke  Single analysis with fixed stroke and pressure  Stroke Convergence Criterion  Fuel Setting • Pile Parameters, to override certain hammer file data ( Options, Hammer Parameters)  Pile Segment Option, for direct input of the segment length, stiffness, and weight of the pile model; generally, this is a somewhat laborious procedure and it is easier to let the computer calculate these numbers.  Splices, accepts input of the number of splices, their depth, slack distance, round-out deformation, and coefficient of re stitution.  Additional Input - Coefficient of restitution for the pile top spring; - Round Out for the pile top spring;  Pile Profile Section Input (see P1 input form) • Soil Parameters  Soil Segment Damping/Quake for entering relative static resistance values and quakes for each segment; click first on Simple Resistance Distr. and then Detailed Resistance Distribution. Version 2010

GRLWEAP Procedures and Models

129

- No Individual soil segment input (default) - Individual damping input for each segment  Extended Soil Model - Toe Model (for research only) - Radiation Damping Model (for research only) • Hammer Parameters  to override certain hammer file data (Options, Hammer Parameters)  Stroke can also be changed on Main Screen  Efficiency can also be changed on Main Screen  Reaction Weight for closed ended diesel hammers,  Diesel hammer combustion parameters: - Combustion Pressure can also be changed on Main Screen - Combustion Delay for liquid fuel injection hammers negative to model preignition - Ignition Volume for atomized injection hammers  Vibratory hammer parameters: - Vibratory Frequency can also be changed on Main Screen - Vibratory Delay, time over which hammer is allowed to reach full frequency - Line force, positive if it reduces the weight effect of the hammer; negative if it pushes down (creates a crowd force).  Assembly Weight for external combustion hammers (these hammers are sometimes equipped with special guides or sleeves which increases the total assembly weight supported by pile and soil prior to impact.  Offshore  opens up the offshore input window; for Offshore Wave Version only.  - Pipe Pile Add-on Input for offshore pipe piles considering add-on properties (Elastic modulus, Specific weight, Critical section index, Length, Cut-off ). Also includes an option for generation an Stabbing Guide model.  - Inclination, allows for the input of the batter (inclination) angle input and calculates and then allows for input of gravity reduction, stroke reduction and efficiency reduction. The angle of inclination input is also necessary for the static bending analysis.  - Hammer , allows for modifying the point on the pile where hammer drives the pile: top, intermediate or bottom location.  - Jacket Template accepts the input necessary (Water Depth and Height of Pile support point of Template/Jacket) for above the mudline for the static pile bending analysis. EXAMPLE This example demonstrates a step-by-step solution for a basic case using only the Main Input Form for input including: Simple shaft resistance distribution, Uniform pile, Bearing graph or Inspector's Chart analysis, and Hammer information contained in the hammer data file. 130

GRLWEAP Procedures and Models

Version 2010

I. Data input Collect all relevant information using the Pile and Driving Equipment Form (Form 1 in Chapter 4). You may have to find driving system and pile material properties in the appropriate help files (performed during program execution). 1. Click on New Icon and enter the project title and file name with directory path. Click Next. 2. To select a hammer either enter the Hammer ID No.  –  if known  – or search the hammer list until the desired hammer is found. You may organize the listing by clicking on the heading to be sorted (e.g. view alphabetic order of hammer manufacturers by clicking on Name). Click on the desired hammer line or select the hammer manufacturer’s name for an abbreviated listing of the associated hammers. Click Next. 3. Select the analysis type, in our case, the bearing graph analysis option. Let us assume that the uncertainty for end bearing and shaft resistance is equal. Then we can choose the default bearing graph option with proportionally increasing shaft resistance and end bearing. For most bearing graph analyses, the proportionally increasing skin friction/end bearing option is satisfactory. (If the shaft resistance were well known, like when a pile is driven to a hard layer, the constant shaft resistance method may be more appropriate and if the end bearing were better known than the shaft resistance, then the constant end bearing analysis should be chosen). Click Next. 4. Select the pile top material (note that a concrete pile driven with a steel follower would require the Steel selection). If Concrete is chosen, the pile cushion properties must also be specified in this box. Pressing the F3 function key with the cursor on the pile cushion elastic modulus will bring up a table with cushion material properties. If the cursor is on the cushion area field, selecting F3 will bring up the area calculator. The program will also require entry of pile toe area and pile perimeter; these values are needed for use with the static geotechnical analyses (ST, SA, CPT or API). For displacement piles (concrete; closed ended pipes), the toe area is easily determined; for H-piles and for open end pipe piles with diameters 20 inches (500 mm) or less, it may be assumed that the piles behave like plugged displacement piles, and the toe area is therefore the full gross area. For larger open ended pipe piles (say greater than 30 inches in diameter), the assumption may be made that the piles are coring (not plugging). In that case, the toe area is that of the steel cross section. Please note that even though dynamically the large diameter pipes may not plug, it is often assumed that they plug under static loads. Plugging is a complex problem as it depends on the pile penetration, the soil type, the soil density, pile penetration into dense layers and other factors and cannot be dealt with Version 2010

GRLWEAP Procedures and Models

131

in a simple example demonstration such as this (see also Section 3.13.6). The input of a pile penetration is also required. This value may already be known from a previously performed static soil analysis or it will be established during the subsequent analysis. In the latter case an initial guess (maybe 2 ft or.0.5 m less than the total pile l ength) is satisfactory. Click Next. 5. Enter hammer cushion and helmet weight information. This may be done directly or after clicking on function key F3 and making selections from the PDI data collection. If no driving system data is available for the chosen hammer make, the data of a similar hammer can be chosen in a first analysis attempt. Obviously though, it would be best to obtain the correct information from either the hammer supplier or the contractor. Click Next. 6. The next step allow for a very simple soil input for a granular or cohesive input. If a more detailed analysis is desired, that can be done after the input wizard is finished. Click Next. 7. The program displays the resistance distribution and dynamic soil resistance parameters. The user should review and if necessary make corrections. Click Next. 8. The program displays 10 ultimate capacity values. They were selceted based on the pile impedance (size and material properties). These may be changed, but they are probably OK for a first analysis attempt. Clieck Next. 9.  After reading the input wizard’s comments, Click Finish. 10.The completed main input form displays the data submitted. Review the important hammer performance parameters shown below the hammer selection screen. In particular, check whether the efficiency  and/or hammer stroke  or energy setting are appropriate (for battered/inclined piles go to Options, Pile Parameters, Pile Batter/Inclination. Stroke may be important if the hammer is used with a reduced energy setting and Pressure  is an important parameter for diesel hammer analyses, particularly if the hammer is to be operated with a reduced fuel setting. 11. Review pile data such as length and cross sectional area and change (as explained earlier), if necessary. Also check the standard pile material parameters (e.g. the elastic modulus and/or the specific weight) assigned when the pile material was chosen. For example, a high strength concrete may have a higher modulus than the default value (the Help offers a pile mateial table).

132

GRLWEAP Procedures and Models

Version 2010

12. Find out the required design load (usually information is provided in the Pile and Driving Equipment Form) and the required factor of safety. The factor of safety depends among other things on the manner in which the pile bearing capacity is verified (static, dynamic testing, etc.), the quality of the pile installation method, the variability of the soil, the type of structure for which the foundation is built, and other important considerations. In general, if capacity determination is based on wave equation analysis alone, i.e. without other test results or measurements, factors of safety may vary between 2.5 and 3.0. A standard recommendation cannot be given here. More on this important subject may be found in Hannigan et al. (2006). Multiply the design load by the factor of safety to obtain the required Ultimate Capacity.  Be sure that the 10 Ultimate Capacity values chosen by the program include the values that are important for the present project. For a useful Bearing Graph, it is recommended to include enough points in the calculation both below and above the required ultimate capacity such that a smooth bearing graph can be plotted. You may click on Reset, enter a capacity increment and then click on the first capacity input field to fill all ten values or click on Action  and then Automatic to fill the array with reasonable values. For concrete piles, be sure to include small ultimate capacity values to find critical tension stresses. High capacity values allow for a check of compression stresses and the driveability limit of the hammer-pile-soil system. II. Check status Before submitting the data set for analysis, it should be checked for completeness. After clicking Options, Check Status, a message will be display which either indicates satisfactory or incomplete input data preparation. III. Save input data Click on the Save Input data icon. (Be sure that the file name and path are satisfactory – Save Input File As under File may also be used.) IV. Perform analysis Click on the A (for analysis) icon. Preliminary output will be displayed. This screen should be closed as soon as it is no longer needed, i.e.  after an initial result check. V. Inspect numerical output Click on the O (for output) icon to enter the output selection screen. View the calculated results in the *.GWO file by clicking on Numerical Output. Particular attention should be given to the hammer model, driving system Version 2010

GRLWEAP Procedures and Models

133

parameters, and pile model. The complete output should also be checked for any program performance messages. They may indicate a problem with the calculated output. Should there be a problem indicated, make changes to the input data by exiting the Numerical Display and by clicking on the Main Screen Icon. The Numerical output is often printed and included in reports. R ead and be aware of the dis claimer.   When finished with this inspection, exit the numerical display and return to the output selection screen. VI. Generate output In addition to the numerical output, you may want to generate a gr aphical or numerical summary output. For our simple example, this means, in general, plotting of the Bearing Graph and a tabulation of the numerical bearing graph results. Click on Bearing Graph in the Output Selection Screen. Both a graph and a numerical result table will be displayed. Enlarge one or the other (upper right hand corner). Return to both displays by selecting dual display (upper right hand corner). Changes to scales can be done in View, Ranges. The bearing graph can be interpreted as to the required blow count for a desired bearing capacity, or it can be interpreted for the capacity corresponding to an observed blow count. Associated with the capacity is, for the same blow count, a maximum compression stress and, important for concrete piles, a maximum tensile stress. The stress maxima may occur anywhere along the pile.  After inspecting and possibly printing (or after View, Copy to Clipboard pasting in a report document) the bearing graph output, exit the bearing graph program. If you are curious about certain calculated output variables, click on Variables in the Output Selection Screen. Certain curves and display modes may be selected in View, Ranges and Selections. This program is self-explanatory. Note that you may have to change your variables in Options, General Options, Output to get the desired results. You may return to the main screen and run a second example and then plot two results in the same bearing graph. (The second bearing graph can be nd chosen after clicking on File, Read 2  file.) This ends the demonstration of a simple bearing graph example. VII. More frequently used options For Non-uniform piles: Click on th the Pile Option  drop down menu and click on Non Uniform Pile  and then enter the pile properties (Cross sectional area, Elastic modulus, Specific weight, Pile Perimeter, Critical Stress Index) at all depth values where changes occur in the so-called P1 input form.

134

GRLWEAP Procedures and Models

Version 2010

Soil Resistance Distribution: The Simple Resistance Distribution is probably an exception and, unless the ST, SA, CPY, or API  static soil analyses have been performed, it is often necessary to enter a Variable Resistance Distribution. For bearing graph analyses, only relative magnitudes must be entered because the total capacity and the percentage shaft resistance are addtional inputs. Thus, the relative resistance distribution values will be multiplied by the shaft resistance percentage and the analyzed ultimate capacity to yield the shaft resistance. The remainder is the end bearing. In contrast, the  Detailed Resistance Distribution requires input of relative capacity values for every segment of the pile model. This is a rarely used option. Bearing Graph options: Instead of doing a bearing graph analysis with proportionally changing friction and end bearing components, the analysis options Constant Friction or Constant End Bearing  options may be selected. In the former case, the friction percentage will be applied to the first capacity analyzed and then only the end bearing will be increased. In the latter case, the end bearing will be the same for all analyses (see also Section 4.5, Options, Analysis Options.  Additional Analysis Options: The Inspector's Chart  option analyzes only one capacity for up to 10 different stroke (energy) values. Be sure to specify a reasonable stroke in the appropriate field below the hammer selection screen, as a low starting value. Depending on the numerical value of the starting stroke either full stroke or ½ m stroke increments will be used, or the program interpolates nine strokes between this minimum and maximum values of the hammer data file. If a diesel hammer is analyzed, it may also be of interest to review the hammer stroke option (see Options, General Options, Stroke). Pile Options: Splices in piles, if they allow for some forceless deformation, are input through Options, Pile Parameters, Splices. Numerical analysis: The Residual Stress Analysis  is (or has to be ) frequently performed when the pile is realtively flexible. The option is activated after selecting Options, General Options, Numerical  and then entering a number between 1 and 100. Enter "1" to perform a residual stress analysis with up to 100 trials for convergence. Enter a number greater than 1 to limit the maximum number of trial analyses. VIII. Less frequently used input options Pile Segment Input Option is for the input of individual values for mass, stiffness, and relative segment length for each segment of the pile model (Options, Pile Parameters, Pile Segment Option). Note that the corresponding pile profile input is necessary for non-uniform piles. Soil Segment Input is for the input of individual quakes, damping factors (Options, Soil Parameters, Soil Segment Damping/Quake), and ultimate resistance values at each segment (Detailed Resistance Distribution Version 2010

GRLWEAP Procedures and Models

135

from the Soil Resistance Distribution drop-down menu). Quakes can only be individually entered together with the static resistance distribution after choosing Detailed Resistance Distribution  in the resistance distribuion drop down menu. Damping input is not dependent on that option. The Soil, Pile, and Hammer Damping Options  are accessible through Options, General Options, Damping. Usually these options are of little help, except the soil damping option which should be set to Smith viscous for Residual Stress Analyses and for Vibratory Hammer analyses.  Any one of the Numerical options (Options, General Options, Numerical), except the Residual Stress Analysis, is rarely used. Not used in practice is the Extended Soil Model for the activation and use of non-standard soil models; this is only recommended for research (Options, Soil Parameters, Extended Soil Model). IX. About Help for GRLWEAP Click on Help and Help Topics and an index will open that links the user to all available help files. These files make up the complete Users Manual of GRLWEAP. For example, tables of hammers, efficiency reductions, setup factors, driving system parameters, etc. are included. Also, there are many links between these files to aid in navigation. In addition, the Help Section provides many example problems including descriptions of input preparation and output interpretation. Numerical results of these examples can be viewed by opening the *.GWO file. Please take some time to study the various documents within the help (and maybe print them out for your printed manual) prior to using the program.  As previously explained, direct help, i.e., direct entry of data in certain input fields is also available. Once the cursor is on such an input field, press F3 to activate the Help feature.

136

GRLWEAP Procedures and Models

Version 2010

 Appendix D: The GRLWEAP Friction Fatigue Approach  An Offshore Wave Option GRLWEAP 2010-6 Offshore Wave offers two means of calculating SRD: (a) the standard which is a uniform reduction of resistance in each soil layer based on setup factor(s) and Gain/Loss factors and (b) an exponentially varying approach which is related to Heerema, (1980) and, for example,  Alm and Hamre (2001). In the following we refer to “Friction Fatigue”   and it should be absolutely clear that it has nothing to do with the fatigue damage that may occur in the pile material due to pile driving. The uniform (standard) GRLWEAP approach calculates the static resistance to driving (SRD) as: SRDi = LTSRi/f si

(D1)

where LTSR is the long term static resistance as calculated by a static approach and i refers to a particular pile segment. Within this uniform setup method, GRLWEAP also offers a time/distance variable resistance setup and resistance loss approach which considers soil setup during a driving interruption to increase logarithmically with time and a related loss of resistance developing linearly with driving depth following the driving interruption. All segments along the pile are affected proportionally to their setup potential in this approach using a so-called limit distance, L li, which can be different for each segment i. Thus the setup resistance is assumed to have vanished and the soil resistance being again at the SRD level when the pile has been driven a distance Lli. This approach works fairly well for short distances, but it does not work well when losses of resistances occur over a greater distance of driving which would require that L li  is much greater than the length of one or two pile segments. The second method, developed at the end of 2013, combines features of the basic GRLWEAP setup factor approach with those proposed by, for example, Alm and Hamre (2001).This friction fatigue approach assumes that pile driving causes little loss of shaft soil resistance near the toe but a much higher resistance loss closer to the seabed where the pile shaft has already done much more work on the soil and between the pile toe and a certain distance (we use again the term Limit Length) above the toe the shaft resistance decreases exponentially. For the Modified Friction Fatigue approach, let us introduce a friction reduction factor, f fi, and designate as z the distance of the center point of a segment measured from the pile toe. We calculate the resistance on the shaft of a pile segment as SRDi = LTSRi * f fi

(D2)

where Version 2010

GRLWEAP Procedures and Models

137

f fi = 1/f si for z ≥ (1 + f L) Lli

(D3)

i.e., fully reduced resistance for pile segments above Limit Length plus bottom section f fi = 1

for z ≤ f L Lli 

(D4)

i.e., full resistance over a distance f L Lli above the pile toe and f fi = 1/f s - f o + x1 e

(αi z*)

for f L Lli ≤ z ≤ (1 + f L) Lli

(D5)

i.e., exponentially varying in between. The coordinate z* is zero at a distance f L Lli above the pile toe and therefore z* = z - f L Lli

(D6)

x1 = 1 – [(1/f s) - f o]

(D7)

αi = ln[f o/x1] / Lli

(D8)

 Also,

and

The factor f o defines the shape of the exponential function (see Figure 1). The factor f L allows for an unreduced resistance over a distance above the bottom (the “bottom section”) which is equal to f L Lli. Both f o and f L are the same for all soil layers. However, L li and f si can be chosen differently for the various soil layers. GRLWEAP applies the following limits f o ≤ 0.9(1/f si )

(D9)

f o ≥ 0.001 

(D10)

and

also the setup factor of any soil layer i has to be greater than 1 (GRLWEAP would replace a value less than 1 with 1 without warning): f si ≥ 1

(D11)

The user should be aware of the following : 



Only one G/L factor < 1 can be analyzed with this approach and it must be the first shaft G/L factor. Also the first shaft G/L should be the inverse of the largest setup factor f si  for a meaningful calculation. If it were 1.0 then the LTSR would be analyzed (no friction fatigue) and that may be conveniently be done with the second analysis and associated nd 2  shaft G/L factor. Using the same setup factors, the total SRD calculated with this method is lower than the SRD of the standard method; equivalent setup factors are discussed below. 138

GRLWEAP Procedures and Models

Version 2010



Both wait time and the soil setup time inputs are ignored in this analysis.

80 fL 0.1 fo 0.1

70

   m    o 60    t    t    o    B50    m    o 40    r     f    e30    c    n    a    t 20    s    i    D

fL 0.05 fo 0.001

10 0 0

0.5

1

1.5

Friction Fatigue Multiplier Figure 1: Exp. Multiplier for fs=5, Limit Dist=50m, Pile L=75m; fo=0.1 and 0.001 and fL=0.1 and 0.05 Potentially, the restriction of Equation (9) makes the f o  factor different for different soil layers. To explain, consider a clay with f s = 5 and a sand layer with f s = 1.2. The restriction is then f o ≤ 0.18 for the clay and f o ≤ 0.84 for the sand. However in general much lower fo values are used anyhow. The user can choose both f o and f L. Examples In the first example let us consider a single uniform soil layer where the LTSR of each 1 m long pile segment is 500 kN (10 m circumference and 50 kPa unit shaft resistance). Figure 2 shows how in Options/Offshore the “Friction Fatigue” option was activated with f o set to 0.01 and with a bottom section factor f L = 0.0 (which means over a distance of 0*Lli above the pile toe the friction is constant and equal to LTSR). Figure 3 shows the calculated resistance distribution for pile toe depths of 25, 50 and 75 m (equivalent ot ½ L li, Lli and 1.5 Lli since a limit length of L li = 50 m had been input in the S1 soil resistance table). The shaft G/L was set to 0.2 corresponding to a setup factor of 5; the fully reduced segment resistance is, therefore, 100 kN. The pile length was 100 Version 2010

GRLWEAP Procedures and Models

139

m. The results plotted in Figure 3 show for the 1 m depth below mudline a small resistance above the SRD, because the L li  is greater than the penetration. For the deeper penetration of 50 and 75 m the resistance at 1 m is at the fully reduced value. Note that the bottom segment resistance is never exactly equal to the full LTSR (in this case of f L = 0), because of the finite pile segment length of 1 m (at 1 m above the bottom the resistance is already reduced).

Figure 2: Friction Fatigue Option in the Offshore Wave Version of GRLWEAP

140

GRLWEAP Procedures and Models

Version 2010

Resistance per1 m segment in kN

0

100

200

300

400

500

0 10 20    m    n    i    e    n    i     l     d    u    m    w    o     l    e     b     h    t    p    e    D

30 40 50 60 70 80 25 m depth 90

50 m depth

75 m Depth

100

Figure 3: Uniform soil, 3 different depths, Lli=50m, f o=0.01 The next example is for a two layer situation. It was assumed that a 50 m sand layer with f s  = 1.25 overlies a clay layer with f s  = 5. The G/L was, therefore, set to 0.2. L li was set to 50 m for both layers. The LTSR for each sand segment was 250 kN; that of the clay again 500 kN. Figure 4 shows that at a depth of 50 m, the pile is still fully embedded in sand and experiences resistance values between slightly more than 200 kN and 250 kN (with f s=1.25 the fully reduced resistance is 250/1.25=200 kN). Note that once the pile reaches full depth, the sand resistance is practically completely reduced while the clay layer shows characteristics as per the first example. While Figure 4 shows the result with an f L = 0 (resistance loss begins at the very bottom), Figure 5 shows the results with a 5% unreduced bottom section.

Version 2010

GRLWEAP Procedures and Models

141

Segment Resistance in kN 0

100

200

300

400

500

600

0

20

   m 40    n    i    e    n    i     l     d    u    M60    w    o     l    e    B     h    t    p 80    e    D

Depth = 50m Depth = 75 m Depth = 100 m

100

120

Figure 4: 100 m pile; 50 m sand with f s=1.25; over 50 m clay with f s=5; Li=50m; f o =0.01; f L = 0.0

142

GRLWEAP Procedures and Models

Version 2010

Segment Resistance in kN

0

200

400

600

0

20    m    n    i 40    e    n    i     l     d    u    M60    w    o     l    e    B     h    t    p 80    e    D

Depth (m) 100 Depth (m) 75

100

120

Figure 5: 100 m pile; 50 m sand with f s=1.25; over 50 m clay with f s=5; Li=50m; f o =0.01; f L =0.05

Version 2010

GRLWEAP Procedures and Models

143

Relationship between standard and Friction Fatigue setup factors Define the Friction Fatigue setup factor f sFf   as the ratio of initial resistance (near the bottom) to fully reduced resistance (L l  above the bottom). Consider the following figure which is an example of a resistance distribution for a Friction Fatigue setup factor of 4. It shows the resistance distribution of over depth equal to the Limit Length. It can be shown that the total skin friction, which is equal to the area between the resistance distribution curve and the horizontal and vertical axes, is given by: Ll

FS-Ff  = x2 Ll +(x1/ α)(e - 1)

(D12)

where x2 = 1/fs – fo; x1 = 1 – x2; and α = ln(f o / x1) / Ll. The GRLWEAP shaft resistance over the same distance Ll is given by FS-GW = LTSR / SRD = (f initial / f s) Ll

(D13)

Ratio of residual/initial resistance 0

0.2

0.4

0.6

0.8

1

0 10     h    t    p    e     d    r    e    y    a     l     l    L     f    o    e    g    a    t    n    e    c    r    e    P

20 30 40 50 60 70 80 90 100

Figure 6: Example of the friction fatigue factor (reduced/initial resistance) vs. normalized depth assuming a Friction Fatigue setup factor f sFF=4. Using the above formulas, we can now calculate for different shape factors f o  the Friction Fatigue setup factors which would yield the same total Friction Fatigue shaft resistance as the standard GRLWEAP approach. They are shown below both numerically and graphically. The resulting setup factor conversions are shown in Figure 7 and Table 1. For example, if f o = 0.001 (the curve farthest to the right) then to get the same total friction in a layer (assuming the layer thickness and L l  are the same  –  which is usually not true and that is a severe limitation of these results) then a 144

GRLWEAP Procedures and Models

Version 2010

standard GRLWEAP setup factor of 3.14 corresponds to a Friction Fatigue setup factor of 5. Table 1: GW Standard Setup Factor vs Ff Setup Factors

Shape Factor (exponent), fo FfSetup F.

0.001

0.00 2

0.00 4

0.00 6

0.00 8

0.05

0.07 5

0.01

0.02

0.1

10.00

4.32

4.08

3.82

3.66

3.54

3.45

3.17

2.81

2.66

2.56

7.50

3.84

3.65

3.44

3.32

3.23

3.15

2.92

2.62

2.49

2.41

5.00

3.14

3.02

2.88

2.80

2.74

2.69

2.53

2.31

2.22

2.15

4.00

2.76

2.67

2.57

2.51

2.46

2.42

2.30

2.13

2.05

2.00

2.75

2.17

2.12

2.06

2.03

2.00

1.98

1.90

1.80

1.75

1.72

2.00

1.73

1.70

1.67

1.65

1.63

1.62

1.58

1.52

1.49

1.47

1.50

1.38

1.37

1.36

1.35

1.34

1.33

1.31

1.28

1.27

1.26

1.25

1.20

1.19

1.18

1.18

1.17

1.17

1.16

1.14

1.14

1.13

10.00 9.00 8.00    r    o    t    c    a    F    p    u    t    e    S     f    F

7.00 6.00 5.00 4.00 3.00 2.00 1.00 1.00

2.00

3.00

4.00

Standard GRLWEAP Setup Factor fo=0.001

0.002

0.004

0.006

0.008

0.01

0.02

0.05

0.075

0.1

Figure 7: Friction Fatigue setup factors which would give the same total shaft resistance as the standard setup factors for Ll = pile toe depth.

Version 2010

GRLWEAP Procedures and Models

145

APPENDIX E: REFERENCES  Alm, T. and Hamre, L., (2001). Soil model for pile drivability predictions th based on CPT interpretation. Proc. of the 15  Int. Conf. on Soil Mechanics and Geotechnical Engineering, 2, Istanbul, 1297-1302.  API, American Petroleum Institute, (1993). “Recommended Practice for Planning, Designing and Constructing Fixed Offshore Platforms – Load and Resistance Factor Design”, API Recommended Practice 2A-LRFD (RP 2ALRFD), First Edition, July 1, 1993. Reaffirmed 2003. Blendy, M.M., (1979), "Rational Approach to Pile Foundation," Symposium on Deep Foundations, ASCE National Convention. Bowles, J.E. (1977). Foundation Analysis and Design. Second Edition, McGraw-Hill Book Company, New York, 85-86. Coyle, H.M., Bartoskewitz, R.E., and Berger, W.J., (1973), "Bearing Capacity Prediction by Wave Equation Analysis - State of the Art," Texas Transportation Institute, Research Report 125-8. Fellenius, B.H. (1996). Basics of Foundation Design, a geotechnical textbook and background to the UniSoft programs, BiTech Publishers Ltd., Richmond, B.C., Canada. Forehand, P.W. and Reese, J.L., (1964), "Prediction of Pile Capacity by the Wave Equation," Journal of the Soil Mechanics and Foundations Division,  ASCE, Paper No. 3820, SM 2. Goble, G.G., Likins, G.E., and Rausche, F., (1975), "Bearing Capacity of Piles From Dynamic Measurements," Final Report, Department of Civil Engineering, Case Western Reserve University. Goble, G.G. and Rausche, F., (1976), "Wave Equation Analysis of Pile Driving-WEAP Program," Volumes 1 through 4, FHWA #IP-76-14.1 through #IP-76-14.4. Goble, G.G. and Rausche, F., (1981), "Wave Equation Analyses of Pile Driving-WEAP Program," Volumes 1 through 4, FHWA #IP-76-14.1 through #IP-76-14.4. Goble Rausche Likins and Associates, Inc. (1997), "Diesel Hammer Modeling for Wave Equation Analyses," from Background Report of the WEAP87 Program, Cleveland, Ohio. Hannigan, P.J., Goble, G.G., Likins, G.E.,and Rausche, F., (2006). "Design and Construction of Driven Pile Foundations". Vol. I and II; Nat. Highway Institute, Federal Highway Administration, US Department of Transportation, Report No. FHWA-NHI-05-042; NHI Courses No. 132021 and 132022, Washington, D.C. 146

GRLWEAP Procedures and Models

Version 2010

Heerema, E.P., (1980. Predicting pile drivability; Heather as an illustration of the friction fatigue theory. Ground Engineering, 13(3), 15 -37. Hery, P., (1983), "Residual Stress Analysis in WEAP," Master's Thesis, Department of Civil, Environmental, and Architectural Engineering, University of Colorado. Hirsch, T.J.Jr., Carr, L., and Lowery, L.L.Jr., (1976), "Pile Driving Analysis Wave Equation User's Manuals - TTI Program," Volumes 1 through 4, FHWA #IP-76-13.1 through #IP-76-13.4. Holeyman, A., Vanden Berghe, J.-F., and Charue, N. (eds.), 2002. Vibratory pile driving and deep soil compaction – TRANSVIB2002. Proc. of the Intern. Conference; A.A. Balkema, Lisse, Abingdon, Exton, Tokyo, ISBN 90 5809 5421 5. Holloway, D.M., Clough, G.W., and Vesic, A.S., (1978), "The Effect of Residual Driving Stresses on Pile Performance Under Axial Loads," OTC 3306. Jaky, J. (1944). “Coefficient of Earth Pressure at Rest”. J. Soc. Hungarian  Architects & Engineers: 355-358. Kulhawy, F.H., Jackson, C.S., & Mayne, P.W. (1989) “First-Order Estimation of K o in Sands and Clays”, Foundation Engineering: Current Principles and Practices, Vol. 1, Ed. F. H. Kulhawy, ASCE, New York, 121134. Kulhawy, F.H. & Mayne, P.W. (1991). “Relative Density, SPT & CPT Interrelationships”, Calibration Chamber Testing, Ed. A.  –B. Huang, Elsevier, New York, 197-211. Lowery, L.L., Hirsch, T.J.Jr., and Samson, C.H., (1967), "Pile Driving  Analysis - Simulation of Hammers, Cushions, Piles and Soils," Texas Transportation Institute, Research Report 33-9. PDCA (2001), “Recommended design specifications for driven bearing piles”, Third edition, Pile Driving Contractors Association, PO Box 1429, Glenwood Springs, CO 81602. Rausche, F., and Klesney, A., (2007). Hammer Types, Efficiencies and Models in GRLWEAP. Annual Int. Conf., PDCA, Nashville, TN, USA. Rausche, F., Likins, G.E., Goble, G.G., and Miner, R., (1985), "The Performance of Pile Driving Systems," Main Report, Volume 1 through 4, FHWA Contract # DTFH61-82-C-00059.

Version 2010

GRLWEAP Procedures and Models

147

Rausche, F., Liang, L., Allin, R., and Rancman, D., 2004. Applications and th Correlations of the Wave Equation Analysis Program GRLWEAP. 7   Int. Conf. on the Application of Stress Wave Theory to Piles, Kuala Lumpur. Rausche, F., Likins, G.E., and Goble, G.G., (1994), "A Rational and Usable Wave Equation Soil Model Based on Field Test Correlation," Proceedings, Design and Construction of Deep Foundations, Federal Highway  Administration, Washington, D.C. Rausche, F., Nagy, M., and Likins, G., (2008). “Mastering the Art of Pile Testing”. Keynote lecture, The Eighth Int. Conf. on the Appl. of Stress Wave Theory to Piles in Lisbon, Portugal. Rausche, F, Nagy, M., Webster, S., and Liang, L., (2009), “CAPWAP and Refined Wave Equation Analyses for Driveability and Capacity Assessment th of Offshore Pile Installations.”, Proc. of the ASME 28  Int. Conf. on Ocean, Offshore and Arctic Eng., May 31-June 5, Honolulu, HI, USA. Paper No. OMAE 2009-80163. Robertson, P.K. & Campanella, R.G. (1983). “Interpretation of Cone Penetration Tests: Sand”, Can. Geot. J., 20 (4), 718-733.

Robertson, P.K., Campanella, R.G., Gillespie, D. and Grieg, J. (1986). “Use of Piezometer Cone Data.” Proceedings of In -Situ’86, ASCE Specialty Conference, Use of In Situ Tests in Geotechnical Engineering, Special Publication No. 6, Blacksburg, 1263-1280. Samson, C.H., Hirsch, T.J.Jr., and Lowery, L.L., (1963), "Computer Study for Dynamic Behavior of Piling," Journal of the Structural Division, ASCE, Volume 89, No. ST4, Proc. Paper 3608. Schmertmann, J. H. (1975). “Measurement of In-Situ Shear Strength”, Proceedings of Conference on In Situ Measurement of Soil Properties,  ASCE, New York. Schmertmann, J. H. (1978). Guidelines for Cone Penetration Test: Performance and Design, FHWA-TS-78-209 (report), US Department of Transportation, 145. Skov, R. and Denver, H., (1988), "Time-Dependence of Bearing Capacity of Piles," Proc. of the Third International Conference on the Application of Stress-Wave Theory to Piles. Smith, E.A.L., (1951), "Pile Driving Impact," Proceedings, Industrial Computation Seminar, September 1950, International Business Machines Corp., New York, N.Y., p. 44. Smith, E.A.L., (1960), "Pile Driving Analysis by the Wave Equation," Journal of the Soil Mechanics and Foundations Division, ASCE, Volume 86.

148

GRLWEAP Procedures and Models

Version 2010