Geotechnical Engineering Design Criteria

GEOTECHNICAL SUMMARIES General We will be using the term foundation to describe the structural elements that connect a structure to the ground. These elements are made of concrete, steel, wood, or perhaps other materials. We will divide foundations into two broad categories : 1. Shallow foundations Shallow foundations transmit the structural loads to the near-surface soils. 2. Deep foundations Deep foundations transmit somes or all of the loads to deeper soils. Classification of foundations are ilustrated in this figure belows :

Figure 3.

Types of foundation

Common types of piles are as follows :  Batter pile A pile driven in at an angle inclined to the vertical to provide high resistance to lateral loads. 

End-bearing pile A pile whose support capacity is derived principally from the resistance of the foundation material on whinch the pile tip rests. End-bearing piles are often used when a soft upper layer is underlain by a dense or hard strata. If the upper soft layer should settle, the pile could be subjected to down-drag forces, and the pile must be designed to resist these soil-induced forces.

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Friction pile A pile whose support capacity is derived principally from the resitance of the soil friction and/or adhesion mobilized along the side of the pile. Friction piles are often used in soft clays where the end-bearing resistance is small because of punching shear at the pile tip.

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Combined end-bearing and friction pile A pile that derives its support capacity from combined end-bearing resistance developed at the pile tip and friction and/or adhesion resistance ont pile perimeter.

Once the design loads have been defined, we need to develop foundation designs that satisfy several performance requirements. The first category is strength requirements, which are intended to avoid catastrophic failures. There are two types :  Geotechnical strength requirements

Geotechnical strength requirements are those that address the ability of the soil or rock to accept the loads imparted by the foundation without failing. The strength of soil is governed by its capacity to sustain shear stresses, so we satisfy geotechnical strength requirements by comparing shear stresses with shear strengths and designing accordingly. Geotechnical strength analysis are almost always performed using allowable stress design (ASD) methods. 

Structural strength requirements Structural strength requirements address the foundation’s structural integrity and its ability to safely carry the applied loads.

Corrosion of Steel Under certain conditions, steel can be the object of extensive corrosion. This can be easily monitored when the steel is above ground, and routine maintenance, such as painting, will usually keep corrosion under control. However, it is impossible to inspect underground steel visually, so it is appropriate to be concerned about its potential for corrosion and long-term integrity. For corrosion assessment, steel foundations can be divided into two categories: those in marine environments and those in land environments. Both are shown in Figure below :

Figure 4.

(a) Marine environments include piers, docks, drilling platforms, and other similar structures where a portion of the foundation is exposed to open water. (b) Land environments include buildings and other structures that are built directly on the ground and the entire foundation is buried.

Safety Factor of Foundation Bearing Capacity Most building codes do not specify design factors of safety. Therefore, engineers must use their own discretion and proffesional judgment when selecting F. Items to consider when selecting a design factor of safety include the following :  Soil type Shear stregth in clays is less reliable than that in sands, and more failures have occured in clays than in sands. Therefore, use higher factors of safety in clays. 

Site characterization data Projects with minimal subsurface exploration and laboratory or in-situ tests have more uncertainty in the design soil parameters, and thus require higher factor of safety. However, when extensive site characterization data is available, thier is less uncertainty so lower factors of safety may be used.

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Importance of the structure and the consequences of a failure Important projects, suc as hospitals, where foundation failure would be more catstrophic may use higher factors of safety than less important projects, suc as agricultural storage buildings, where cost of construction is more important. Likewise, permanent sturctures justify higher factors of safety than temporary sturctures, such as construction falsework. Structures with large height-to-width ratio, such as chimneys or towers, could experience more catastrophic failure, and thus should be designed using higher factors of safety.

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The likelihood of the design load ever actually occuring Some structures, such as grain silos, are much more likely to actually experience their design loads, and thus might be designed using a higher factor of safety. Conversly, office buildings are much likely to experience the design load, and might use a slightly lower factor of safety.

The true factor of safety is probably much greater than the design factor of safety, because of the following :  The shear strength data are normally interpreted conservatively, so the design values of c and  implicitly contain another factor of safety.  The service loads are probably less than the design loads.  Settlement, not bearing capacity, often controls the final design, so the footing will likely be larger than that required to satisty bearing capacity criteria.  Spread footings are commonly built somewhat larger than the plan dimensions.

Safety Factor for Bearing Capacity of Single Pile Refers to Engineering Manual (EM 1110-2-2906) :

Safety Factors for Bearing Capacity of Pile Foundation

Table 1.

Method of Determining

Load Condition

Capacity Theoretical of empirical

Minimum Factor of Safety Compression Tensile

Usual

2,0

2,0

prediction to be verified by

Unusual

1,5

1,5

pile load test Theoretical or empirical

Extreme Usual

1,15 2,5

1,15 3,0

prediction to be verified by

Unusual

1,9

2,25

pile driving analyzer Theoretical or empirical

Extreme Usual

1,4 3,0

1,7 3,0

prediction not verified by

Unusual

2,25

2,25

load test

Extreme

1,7

1,7

Loading conditions :  Usual. These conditions include normal operating and frequent flood conditions. Basic allowable stresses and safety factors should be used for this type of loading condition.  Unusual. Higher allowable stresses and lower safety factors may be used for unusual loading conditions such as maintenance, infrequent floods, barge impact, construction, or hurricanes. For these conditions allowable stresses may be increased up to 33 percent. Lower safety factors for pile capacity may be used, as described in Table above.  Extreme. High allowable stresses and low safety factors are used for extreme loading conditions such as accidental or natural disasters that have a very remote probability of occurrence and that involve emergency maintenance conditions after such disasters. For these conditions allowable stresses may be increased up to 75 percent. Low safety factors for pile capacity may be used as described in Table above. An iterative (nonlinear) analysis of the pile group should be performed to determine that a state of ductile, stable equilibrium is attainable even if individual piles will be loaded to their peak, or beyond to their residual capacities. Special provisions (such as field instrumentation, frequent or continuous field monitoring or performance, engineering studies and analyses, constraints on operational or rehabilitation activities, etc.) are required to ensure that the structure will not catastrophically fail during or after extreme loading condition.

Safety Factor of Pullout Capacity Table below gives typical design factors of safety based on these assessments. Consider them to be guides, not absolute dictates, so do not hesitate to modify them as necessary. Safety Factor of Pullout Capacity Design Factor of Safety, F Acceptable Probability Good Normal Poor Very Poor of Failure Control Control Control Control 10-5 2,3 3,0 3,5 4,0 10-4 2,0 2,5 2,8 3,4 10-3 1,4 2,0 2,3 2,8

Table 2.

Classification of Structure Monumental Permanent Temporary

Safety factor of pullout capacity will be equal of 3,00 Safety Factor of Lateral Resistance The definition of failure load should therefore be related to the acceptable or tolerate lateral deformation of the structure. Where no such criteria are available, 0.25 in. (6.25 mm) is considered as the criterion on which failure load is established. It should be realized that actual instability at which the load could not be held when the pile head had deformed about 1 in. (25 mm). (refers to “Pile Foundations In Engineering Practice”, Shamsher Prakash and Hari D. Sharma) For lateral resistance design of pile foundation, we use some boundary : Maximum Design for Lateral Deflection of Pile Foundation Table 3. Load Maximum Lateral Defflection Service Load without earthquake load 0,625 cm (0,25”) Service Load with earthquake load 1,25 cm (0,50”) Ultimate Load 2,50 cm (1,00”)

Allowable Settlement The amount of settlement that a foundation can tolerate is called the allowable settlement, the magnitude of this settlement depends upon it mode. A structure that has undergone uniform settlement is one where all points within the structure have moved vertically the same amount (Figure a). This type of settlement does not result in structural damage if it is constant across whole structure. However, there will be problems with appurtenances such as with pipes, entrance-ways, etc. Another possibility is settlement that varies linearly across the structure as shown in (Figure b). This causes the structure to tilt. Finally, (Figure c) shows a structure with irregular settlements. This mode distorts the structure and typically is the greatest source of problems.

Figure 5.

Modes of settlement; (a) Uniform; (b) Tilting with no distortion; (c) Distortion

Figure 6.

Types of foundation settlement

Table below presents typical design values for the allowable settlement, a. The design meets total settlement requirements if the following condition is met :   a

Where :  = total settlement of foundation a = allowable settlement

Type of Movement

Total Settlement

Tilting

Differential Movement

Allowable Settlement (Sowers, 1962) Table 4. Limiting Factor Limiting Factor Drainage 15-30 cm (6-12 in.) Access 30-60 cm (12-24 in.) Probability of non-uniform settlement : - Masonry walled structure 2,5-5 cm (1-2 in.) - Framed structures 5-10 cm (2-4 in.) - Smokestacks, silos, mats 8-30 cm (3-12 in.) Stability against overturning Depends on H and W Tilting of smokestacks, towers 0,004L Rolling of trucks, etc. 0,01L Stacking of goods 0,01L Machine operation – cotton loom 0,003L Machine operation – turbogenerator 0,0002L Crane rails 0,003L Drainage of floors 0,01-0,02L High continuous brick walls 0,0005-0,001L One-story brick mill building, wall cracking 0,001-0,002L Plaster cracking (gypsum) 0,001L Reinforced-concrete-building frame 0,0025-0,004L Reinforced-concrete-building curtain walls 0,003L Steel frame, continuous 0,002L Simple steel frame 0,005L

Note : L = distance between adjacent columns that settle diffrent amounts H = height of structure W = width of structure - Higher values are for regular settlements and more tolerant structures. - Lower values for irregular settlement and critical structures.

Table below also presents typical design values for the allowable total settlement, a. These values already include a factor of safety, and thus may be compared directly to the predicted settlement. Typical Allowable Total Settlements for Foundation Design Typical Allowable Total Settlement,  a Type of Structure (in) (mm) Office buildings 0,5-2,0 (1,0 is the most 12-50 (25 is the most common value) common value) Heavy industrial buildings 1,0-3,0 25-75 Bridges 2,0 50 Table 5.

Diffrential Settlement Engineer normally design the foundations for a structure such that all of them have the same computed total settlement. Thus, in theory, the structure will settle uniformly. Unfortunately, the actual performance of the foundations will usually not be exactly as predicted, with some of them settling more than expected and other less. This discrepancy between predicted behavior and actual behavior has many causes, including the following :  The soil profile may not be uniform across the site. This is nearly always true, no matter how uniform it might appear to be.  The ratio between the actual load and the design load may be different for each column. Thus, the column with the lower ratio will settle less than that with the higher ratio.

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

The ratio of dead load to live load may be different for each column. Settlement computations are usually based on dead-plus-live load, and the foundations are sized accordingly. However, in many structures much of the live load will rarely, if ever, occur, so foundations that have a large ratio of design live load to design dead load will probably settle less than those carrying predominantly dead loads. The as-built foundation dimensions may differ from the plan dimensions. This will cause the actual settlements to be correspondingly different.

The differential settlement, Da, is the difference in total settlement between two foundations or between two points on a single foundation. Differential settlements are generally more troublesome than total settlements because they distort the structure. This causes cracking in walls and other members, jamming in doors and windows, poor aesthetics, and other problems. If allowed to progress to an extreme, differential settlements could threaten the integrity of the structure. Therefore, we define a maximum allowable differential settlement, Da, and design the foundation so that :  D   Da

Table below presents a synthesis of these studies, expressed in terms of the allowable angular distortion, Da. These values already include a factor safety of at least 1.5, which is why they are called “allowable”. We use them to compute Da as follows :  Da   a .L

Where: Da = allowable differential settlement θa = allowable angular distortion (from table below) L = distance between adjacent columns that settle different amounts Allowable Angular Distortion, θa (Wahls, 1994; AASTHO, 1996; and Other Sources) Type of Structure θa Steel tanks 1/25 Bridges with simply-supported spans 1/125 Bridges with continous spans 1/250 Buildings that are very tolerant of differential settlements, such as industrial buildings with corrugated steel siding and no sensitive 1/250 interior finishes Typical commercial and residential buildings 1/500 Overhead traveling crane rails 1/500 Buildings that are especially intolerant of differential settlement, such 1/1000 as those with sensitive wall or floor finishes Machinery 1/1500 Buildings with unreinforced masonry load-bearing walls Length/height ≤ 3 1/2500 Length/height  5 1/1250

Table 6.

Site Investigation

The site investigation phase of the exploration program consists of planning, making test boreholes, and collecting soil samples at desired intervals for subsequent observation and laboratory tests. The approximate required minimum depth of the borings should be predetermined. The depth can be changed during the drilling operation, depending on the subsoil encountered. To determine the approximate minimum depth of boring, engineers may use the rules established by the American Society of Civil Engineers (1972):  Determine the net increase in the effective stress, ’, under a foundation with depth as shown in figure.  Estimate the variation of the vertical effective stress, ’0, with depth.  Determine the depth, D = D1, at which the effective stress increase ’ is equal to 0,1q (q = estimated net stress on the foundation).  Determine the depth, D = D2, at which ’/’0 = 0,05.  Choose the smaller of the two depths, D1 and D2, just determined as the approximate minimum depth of boring required, unless bedrock is encountered.

Figure 7.

Determination of the minimum depth of boring

If the preceding rules are used, the depths of boring for a building with a width of 30 m (100ft) will be approximately the following, according to Sowers and Sowers (1970): Boring depth for building Table 7. No. of stories Boring depth 1 3,5 m (11 ft) 2 6 m (20 ft) 3 10 m (33 ft) 4 16 m (53 ft) 5 24 m (79 ft)

To determine the boring depth for hospitals and office buildings, Sowers and Sowers also use the rule

Db  3.S 0,7

(for light steel or narrow concrete buildings)

And Db  6.S 0,7

(for heavy steel or wide concrete buildings)

Where: Db = depth of boring, in meters S = number of stories When deep excavations are anticipated, the depth of boring should be at least 1,5 times the depth of excavation. Sometimes, subsoil conditions require that the foundation load be transmitted to bedrock. The minimum depth of core boring into the bedrock is about 3 m. If the bedrock is irregular or weathered, the core borings may have to be deeper. There are no hard-and-fast rules for borehole spacing. Table below gives some general guidelines. Spacing can be increased or decreased, depending on the condition of the subsoil. If various soil strata are more or less uniform and predictable, fewer boreholes are needed than in non-homogeneous soil strata. Approximate spacing of boreholes Table 8. Type of project Spacing Multistory building 10-30 m (30-100 ft) One-story building 20-60 m (60-200 ft) Highways 250-500 m (800-1600 ft) Residential subdivision 250-500 m (800-1600 ft) Dams and dikes 40-80 m (130-260 ft)

The engineer should also take into account the ultimate cost of the structure when making decisions regarding the extent of field exploration. The exploration cost generally should be 0,1– 0,5% of the cost of the structure. Soil borings can be made by several methods, including auger boring, wash boring, percussion drilling, and rotary drilling. Auger boring is the simplest method of making exploratory boreholes. There are two types of hand auger: the posthole auger and the helical auger. Hand augers cannot be used for advancing holes to depths exceeding 3-5 m. However, the can be used for soil exploration work on some highways and small structures. Portable power-driven helical augers (76 mm to 305 mm in diameter) are available for making deeper boreholes. The soil samples obtained from such borings are highly disturbed. In some non-cohesive soils or soils having low cohesion, the walls of the boreholes will not stand unsupported. In such circumstances, a metal pipe is used as a casing to prevent the soil from caving in. When power is available, continuous-flight augers are probably the most common method used for advancing a borehole. The power for drilling is delivered by truck-or tractor-mounted drilling rigs. Boreholes up to about 60-70 m can easily be made by this method. Wash boring is another method of advancing boreholes. In this method, a casing about 2-3 m long is driven into the ground. The soil inside the casing is then removed by means of a chopping bit attached to a drilling rod. Water is forced through the drilling rod and exits at a very high velocity through the holes at the bottom of the chopping bit. The water and the chopped soil

particles rise in the drill hole and overflow at the top of the casing through a T connection. The washwater is collected in a container. The casing can be extended with additional pieces as the borehole progresses; however, that is not required if the borehole will stay open and not cave in. Wash borings are rarely used now in the United States and other developed countries. Rotary drilling is a procedure by which rapidly rotating drilling bits attached to the bottom of drilling rods cut and grind the soil and advance the borehole. There are several types of drilling bit. Rotary drilling can be used in sand, clay, and rocks (unless they are badly fissured). Water of drilling mud is forced down the drilling rods to the bits, and the return flow forces the cuttings to the surface. Boreholes with diameters of 50-203 mm (2-8 in.) can easily be made by this technique. The drilling mud is a slurry of water and bentonite. Generally, it is used when the soil that is encountered is likely to cave in. When soil samples are needed, the drilling rod is raised and the drilling bit is replaced by a sampler. With the environmental drilling applications, rotary drilling with air is becoming more common. Percussion drilling is an alternative method of advancing a borehole, particularly through hard soil and rock. A heavy drilling bit is raised and lowered to chop the hard soil. The chopped soil particles are brought up by the circulation of water. Percussion drilling may require casing. Procedures for Sampling Soil Two types of soil samples can be obtained during subsurface exploration: disturbed and undisturbed. Disturbed, but respresentative, samples can generally be used for the following types of laboratory test:  Grain-size analysis  Determination of liquid and plastic limits  Specific gravity of soil solids  Determination of organic content  Classification of soil Disturbed soil samples, however, cannot be used for consolidation, hydraulic conductivity, or shear strength tests. Undisturbed soil samples must be obtained for these types of laboratory tests. The degree of disturbance for a soil sample is usually expressed as: AR  % 

Do2  Di2 .100  Di2

Where: AR = area ratio (ratio of disturbed area to total area of soil) Do = outside diameter of the sampling tube Di = inside diameter of the sampling tube When the area ratio is 10% or less, the sample generally is considered to be undisturbed.

Split-Spoon Sampling (SPT) Split-spoon samplers can be used in the field to obtain soil samples that are generally disturbed, but still representative. A section of a standard split-spoon sample is shown in figure.

Figure 8.

Standard split-spoon sampler

The tool consists of a steel driving shoe, a steel tube that is split longitudinally in half, and a coupling at the top. The coupling connects the sampler to the drill rod. The standard split tube 3 in.) and an outside diameter of 50,8 mm (2 in.); 8 1 however, samplers having inside and outside diameters up to 63,5 mm ( 2 in.) and 76,2 mm (3 2

has an inside diameter of 34,93 mm ( 1

in.), respectively, are also available. When a borehole is extended to a predetermined depth, the drill tools are removed and the sampler is lowered to the bottom of the hole. The sampler is driven into the soil by hammer blows to the top of the drill rod. The standard weight of the hammer is 622,72 N (140 lb), and for each blow, the hammer drops a distance of 0,762 m (30 in.). The number of blows required for a spoon penetration of three 152,4 mm (6 in.) intervals are recorded. The number of blows required for the last two intervals are added to give the standard penetration number, N, at that depth. This number is generally referred to as the N value (American Society for Testing and Materials, 2001, Designation D-1586-99). The sampler is then withdrawn, and the shoe and coupling are removed. Finally, the soil sample recovered from the tube is placed in a glass bottle and transported to the laboratory. This field test is called the standard penetration test (SPT). The boring log shows refusal and the test is halted if :  50 blows are required for any 150-mm increment.  100 blows are obtained (to drive the required 300 mm).  10 successive blows produce no advance. For a standard split-spoon sampler, AR  % 

 50,8  2   34,93 2 .100   111,5%  34,93  2

When the area ratio is 10% or less, the sample generally is considered to be undisturbed. Hence, these samples are highly disturbed. Split-spoon samples generally are taken at intervals of about

1,53 m (5 ft). When the material encoutered in the field is sand (particularly fine sand below the water table), recovery of the sample by a split-spoon sampler may be difficult. In that case, a device such as a spring core catcher may have to be placed inside the split spoon.

Figure 9.

Spring core catcher

At this juncture, it is important to point out that several factors contribute to the variation of the standard penetration number N at a given depth for similar soil profiles. Among these factors are the SPT hammer effeciency, borehole diameter, sampling method, and rod length factor (Skempton, 1986; Seed et al., 1985). The two most common types of SPT hammers used in the field are the safety hammer and donut hammer. They are commonly dropped by a rope with two wraps around a pulley.

Figure 10.

(a) Safety hammer; (b) Donut hammer (after Seed et. Al., 1985)

Figure 11.

The SPT sampler in place in the boring with hammer, rope and cathead (Kovacs, et al. 1981)

Soil density or consistency description based on SPT blowcount values can be seen below (after AASHTO, 1988) : Soil density/consistency based on SPT blowcount values Cohesionless Soils Cohesive Soils N-SPT values N-SPT values Relative Density Consistency (blows/300 mm) (blows/300 mm) Very soft 0–1 Very loose 0–4 Soft 2–4 Loose 5 – 10 Medium stiff 5–8 Medium dense 11 – 24 Stiff 9 – 15 Dense 25 – 50 Very stiff 16 – 30 Very dense > 51 Hard 31 – 60 Very hard > 61 Table 9.

Cone Penetration Test (CPT) The cone penetration test (CPT), originally known as the Dutch cone penetration test, is a versatile sounding method that can be used to determine the materials in a soil profile and estimate their engineering properties. The test is also called the static penetration test, and no borehole is necessary to perform it. In the original version, a 60 cone with a base area of 10 cm2 was pushed into the ground at a steady rate of about 20 mm/sec, and the resistance to penetration (called the point resistance) was measured.

The cone penetrometers in use at present measure (a) the cone resistance (qc) to penetration developed by the cone, which is equal to the vertical force applied to the cone, divided by its horizontally projected area; and (b) the frictional resistance (fc), which is the resistance measured by a sleeve located above the cone with the local soil surrounding it. The frictional resistance is equal to the vertical force applied to the sleeve, divided by its surface area – actually, the sum of friction and adhesion. The original mechanical cone test is illustrated in Figure below with the step sequence as follows :  The cone system is stationary at position 1.  The cone is advanced by pushing an inner rod to extrude the cone tip and a short length of cone shaft. This action measures the tip resistance qc.  The outer shaft is now advanced to the cone base, and skin resistance is measured as the force necessary to advance the shaft fc.  Now the cone and sleeve are advanced in combination to obtain position 4 and to obtain a qtotal, which should be approximately the sum of the q c + fc just measured. The cone is now positioned for a new position 1.

Figure 12.

Mechanical (or Dutch) cone, operations sequence, and tip resistance data

Luas proyeksi ujung = 10 cm2 (ASTM D3411) Luas selimut = 150 cm2 (ASTM D3411) atau ada juga 100 cm2 Luas piston = 10 cm2 (ASTM D3411) Berikut adalah penelusuran perhitungan bacaan pada sondir : 1. Bacaan I = tahanan ujung → (R1) qc x Aproyeksi = R1 x Apiston (qc, R1 = kg/cm2) qc = R1 x (Apiston / Aproyeksi) 2. Bacaan II = (tahanan ujung + tahanan selimut) → (R2) (qc x Aproyeksi) + (fs x Aselimut) = R2 x Apiston (qc, fs, R2 = kg/cm2) fs = {( R2 x Apiston)-( qc x Aproyeksi)}/ Aselimut fs = (R2- qc) x (Apiston or Aproyeksi / Aselimut) dimana = (Apiston or Aproyeksi / Aselimut) → faktor koreksi alat

Several correlations that are useful in estimating the properties of soils encountered during an exploration program have been developed for the point resistance (qc) and the friction ratio (Fr) obtained from the cone penetration tests. The friction ratio is defined as : f Fr  c qc

Where: fc = frictional resistance qc = cone resistance Fr = friction ratio It may also be used to give an estimate of the soil sensitivity, St with the correlation being approximately : St 

10 Fr

Where: St = sensitivity Fr = friction ratio (in percent) Clays may be classified as follows :

Shear Strength The shear strength of a soil, defined in terms of effective stress, is   c ' '. tan( ' )

Where: ’ = effective normal stress on plane of shearing c’ = cohesion, or apparent cohesion ’ = effective stress angle of friction The equation above is referred to as the Mohr-Coulomb failure criterion. The value of c’ for sands and normally concolidated clays is equal to zero. For overconsolidated clays, c’ > 0. For most day-to-day work, the shear strength parameters of a soil (i.e., c’ and ’) are determined by two standard laboratory tests: the direct shear test and the triaxial test. Direct Shear Test

Dry sand can be conveniently tested by direct shear tests. The sand is placed in a shear box that is split into two halves. First a normal load is applied to specimen. Then a shear force is applied to the top half of the shear box to cause failure in the sand. The normal and shear stresses at failure are: '  

N A

and

R A

Where: A = area of the failure plan in soil - that is, the cross-sectional area of shear box R = applied shear force Several tests of this type can be conducted by varying the normal load. The angle of friction of the sand can be determined by plotting a graph of  against ’ (=  for dry sand), as shown in figure below, or :      '

 '  tan 1 

For sands, the angle of friction usually ranges from 26 to 45, increasing with the relative density of compaction. The approximate range of the relative density of compaction and the corresponding range of the angle of friction for various coarse-grained soils is shown in figure below:

Figure 13.

Direct shear test in sand ; (a) schematic diagram of test equipment; (b) plot of test results to obtain the friction angle ’

A thin soil sample is placed in a shear box consisting of two parallel blocks. The lower block is fixed while the upper block is moved parallel to it in a horizontal direction. The soil fails by shearing along a plane assumed to be horizontal. This test is relatively easy to perform. Consolidated-drained tests can be performed on soils of low permeability in a short period of time as compared to the triaxial test. However, the stress,

strain, and drainage conditions during shear are not as accurately understood or controlled as in the triaxial test.

Triaxial Test Two fundamentally different approaches to the solution of stability problems in geotechnical engineering : 1. The total stress approach In the total stress approach, we allow no drainage to take place during the shear test, and we make the assumption, admittedly a big one, that the pore water pressure and therefore the effective stresses in the test specimen are identical to those in the field. The method of stability analysis is called the total stress analysis, and it utilizes the total or the undrained shear strength f, of the soil. The undrained strength can be determined by either laboratory or field tests. If field tests such as the vane shear, Dutch cone penetrometer, or pressuremeter test are used, then they must be conducted rapidly enough so that undrained conditions prevail in situ. 2. The effective stress approach The second approach to calculate the stability of foundations, embankments, slopes, etc., uses the shear strength in terms of effective stresses. In this approach, we have to measure or estimate the excess hydrostatic pressure, both in the laboratory and in the field. Then, if we know or can estimate the initial and applied total stresses, we may calculate the effective stresses acting in the soil. Since we believe that shear strength and stress-deformation behavior of soils is really controlled or determined by the effective stresses, this second approach is philisophically more satisfying. But, it does have its practical problems. For example, estimating or measuring the pore pressures, especially in the field, is not easy to do. The method of stability is called the effective stress analysis, and it utilizes the drained shear strength or the shear strength in terms of effective stresses. The drained shear strength is ordinarily only determined by laboratory tests. Triaxial tests can be conducted on sands and clays. Essentially, the test consists of placing a soil specimen confined by a rubber membrane into a lucite chamber and then applying an all-arround confining pressure (3) to the specimen by means of the chamber fluid (generally, water or glycerin). An added stress () can also be applied to the specimen in the axial direction to cause failure ( = f at failure). Drainage from the specimen can be allowed or stopped, depending on the condition being tested. For clays, three main types of tests can be conducted with triaxial equipment:

1.

Figure 14.

Schematic diagram of triaxial test equipment

Figure 15.

Sequence of stress application in triaxial test

Consolidated – Drained test (CD test) Step 1. Apply chamber pressure 3. Allow complete drainage, so that the pore water pressure (u = u0) developed is zero. Step 2. Apply deviator stess  slowly. Allow drainage, so that the pore water pressure (u = ud) developed through the application of  is zero. At failure,  = f ; the total pore water pressure uf = u0 + ud = 0.

Figure 16.

Stress conditions in the consolidated-drained (CD) axial compression triaxial test

So for consolidated-drained tests, at failure, Major principal effective stress = 3 + f = 1 = 1‘ Minor principal effective stress = 3 = 3‘ Changing 3 allows several tests of this type to be conducted on various clay specimens. The shear strength parameters (c’ and ‘) can now be determined by plotting Mohr’s circle at failure, and drawing a common tangent to the Mohr’s circles. This is the Mohr-Coulomb failure envelope. (Note: For normally consolidated clay, c’ ≈ 0 ; For overconsolidated clay, c’ > 0) At failure, '  '     1 '   3 '. tan 2  45    2.c '. tan 45   2 2  

Figure 17.

Consolidated-drained test

The envelope for a normally consolidated clay is shown below. Even though only one Mohr circle (representing the stress conditions at failure) is shown, the results of three or more CD tests on identical specimens at different consolidation pressures would ordinarily be required to plot the complete Mohr failure envelope. If the consolidation stress range is large or the specimens do not have exactly the same initial water content, density, and stress history, then the three failure circles will not exactly define a straight line, and an average best-fit line by eye is drawn. The slope of the line determines the Mohr-Coulomb strength parameter ’, of course, in terms of effective stresses. When the failure envelope is extrapolated to the shear axis, it will show a surprisingly small intercept. Thus it is usually assumed that the c’ parameter for normally consolidated non-cemented clays is essentially zero for all practical purposes.

Figure 18.

Mohr failure envelope for a normally consolidated clay in drained shear

For overconsolidated clays the c’ parameter is greater than zero, as indicated by figures below. The overconsolidated portion of the strength envelope (DEC) lies above the normally consolidated envelope (ABCF). This portion (DEC) of the Mohr failure envelope is called the preconsolidated hump. The explanation for this behavior is shown in the e versus ’ curve of figure below. Let us assume that we begin consolidation of a sedimentary clay at a very high water content and high void ratio. As we continue to increase the vertical stress we reach point A on the virgin compression curve and conduct a CD triaxial test. The strength of the sample consolidated to point A on the virgin curve would correspond to point A on the normally consolidated Mohr failure envelope in figure below. If we consolidate and test another otherwise identical specimen which is loaded to point B, then we would obtain the

strength, again normally consolidated, at point B on the failure envelope in figure below. If we repeat the process to point C (’p, the preconsolidation stress), then rebound the specimen to point D, then reload it to point E and shear, we would obtain the strength shown at point E is greater than specimen B, even though they are tested at exactly the same effective consolidation stresses. The reason for the greater strength of E than B is suggested by the fact that E is at a lower water content, has a lower void ratio, and thus is denser than B, as shown in figure below. If another specimen were loaded to C, rebounded to D, reloaded back past E and C and on to F, it would have the strength as shown in figure at point F. Note that it is now back on the virgin compression curve and the normally consolidated failure envelope. The effects of the rebounding and reconsolidation have been in effect erased by the increased loading to point F. Once the soil has been loaded well past the preconsolidation pressure ’p, it no longer “remembers” its stress history.

Figure 19.

(a) Compression curve; (b) Mohr failure envelope (DEC) for an overconsolidated clay

In the CD test, complete consolidation of the test specimen is permitted under the confining pressure and drainage is permitted during shear. The rate of strain is controlled to prevent the build-up of pore pressure in the specimen. A minimum of three tests are required for c’ and ’ determination. CD tests are generally performed on well draining soils. For slow draining soils, several weeks may be required to perform a CD test.

Typical stress-strain curves and volume change versus strain curves for a remolded or compacted clay are shown below. Even though the two samples were tested at the same confining pressure, the overconsolidated specimen has a greater strength than the normally consolidated clay. Note also that it has a higher modulus and that failure [the maximum , which for the triaxial test is equal to (1 - 3)f] occurs at a much lower strain that for the normally consolidated specimen. The overconsolidated clay expands during shear while the normally consolidated clay compresses or consolidates during shear.

Figure 20.

Typical stress-strain and volume change versus strain curves for CD axial compression tests at the same effective confining stress

Average values of ’ for undisturbed clays range from around 20° for normally consolidated highly plastic up to 30° or more for silty and sandy clays. The value of ’ for compacted clays is typically 25 or 30° and occasionally as high as 35°. The value of c’ for normally consolidated non-cemented clays is very small and can be neglected for practical work. If the soil is overconsolidated, then ’ would be less, and the c’ intercept greater than for the normally consolidated part of the failure envelope. According to Ladd (1971b), for natural overconsolidated non-cemented clays with a preconsolidation stress of less than 500 to 1000 kPa, c’ will probably be less than 5 to 10 kPa at low stresses. For compacted clays at low stresses, c’ will be much greater due to the prestress caused by compaction. For stability analyses, the Mohr-Coulomb effective stress parameters ’ and c’ are determined over the range of effective normal stresses likely to be encountered in the field.

Empirical correlations between ’ and the plasticity index for normally consolidated clays are shown below:

Figure 21.

Emperical correlation between ’ and PI from triaxial compression tests on normally consolidated undisturbed clays (after U.S. Navy, 1971, and Ladd, et al., 1977)

Where do we use the strengths determined from the CD test? As mentioned previously, the limiting drainage conditions modeled in the triaxial test refer to real field situations. CD conditions are the most critical for the long-term steady seepage case for embankment dams and the long-term stability of excavations or slopes in both soft and stiff clays. The examples of CD analysis can be seen below:

Figure 22.

2.

Some examples of CD analyses for clays (after Ladd, 1971b)

Consolidated – Undrained test (CU test) Step 1. Apply chamber pressure 3. Allow complete drainage, so that the pore water pressure (u = u0) developed is zero. Step 2. Apply a deviator stress . Do not allow drainage, so that the pore water pressure u = ud ≠ 0. At failure,  = f ; the pore water pressure uf = u0 + ud = 0 + u d(f). Note that the excess pore water pressure u developed during shear can either be positive (that is, increase) or negative (that is, decrease). This happens because the sample tries to either contract or expand during shear. Remember, we are not allowing any volume change (an undrained test) and therefore no water can flow in or out of the specimen during shear. Because volume changes are prevanted, the tendency towards volume change induces a pressure in the pore water. If the specimen tends to contract or consolidate during shear, then the induced pore water pressure is positive. It wants to contract and squeeze water out of the pores, but cannot; thus the induced pore water pressure is positive. Positive pore pressures occur in normally consolidated clays. If the specimen tends to expand or swell during shear, the induced pore water pressure is negative. It wants to expand and

draw water into the pores, but cannot; thus the pore water pressure decreases and may even go negative (that is, below zero gage pressure). Negative pore pressures occur in overconsolidated clays. Hence, at failure, Major principal total stress = 3 + f = 1 Minor principal total stress = 3 Major principal effective stress = (3 + f) – uf = 1‘ Minor principal effective stress = 3 – uf = 3‘

Figure 23.

Conditions in specimen during a consolidated-undrained axial compression (CU) test

Changing 3 permits multiple tests of this type to be conducted on several soil specimens. The total stress Mohr’s circles at failure can now be plotted, and then a common tangent can be drawn to define the failure envelope. This total stress failure envelope is defined by the equation

  c   . tan( )

Where c and  are the consolidated-undrained cohesion and angle of friction, respectively (Note: c ≈ 0 for normally consolidated clays) Similarly, effective stress Mohr’s circles at failure can be drawn to determine the effective stress failure envelope, which satisfy the relation   c ' '. tan( ' ) .

Figure 24.

Consolidated-undrained test

In the CU test, complete consolidation of the test specimen is permitted under the confining pressure, but no drainage is permitted during shear. A minimum of three tests is required to define strength parameters c and , through four test specimens are preferable with one serving as a check. Specimens must as a general rule be completely saturated before application of the deviator stress. Full saturation is achieved by back pressure. When a back pressure is applied to a sample, the cell pressure must also be increased by an amount equal to the back pressure so that the effective consolidation stresses will remain the same. Since the effective stress in the specimen does not change, the strength of the specimen is not supposed to be changed by the use of back pressure. In practice this may not be exactly true,

but the advantage of having 100% saturation for accurate measurement of induced pore water pressures far outweighs any disadvantages if the use of back pressure. Typical stress-strain, u, and ’1/’3 curves for CU tests are shown below, for both normally and overconsolidated clays. Also shown for comparison is a stress-strain curve for an overconsolidated clay at low effective consolidation stress. Note the peak, then the drop-off of stress as strain increases (work-softening material). The pore pressure versus strain curves illustrate what happens to the pore pressures during shear. The normally consolidated specimen develops positive pore pressure. In the overconsolidated specimen, after a slight initial increase, the pore pressure goes “negative” – in this case, negative with respect to the back pressure u 0. Another quantity that is useful for analyzing test results is the principal (effective) stress ratio ’1/’3. Note how this ratio peaks early, just like the stress difference curve, for the overconsolidated clay. Similar test specimens having similar behavior on an effective stress basis will have similarly shaped ’1/’3 curves. They are simply a way of normalizing the stress behavior with repect to the effective minor principal stress during the test. Sometimes, too, the maximum of this ratio is used as a criterion of failure. However, in this text we will continue to assume failure occurs at the maximum principal stress difference (compressive strength).

Figure 25.

Typical -, u, and ’1/’3 curves for normally and overconsolidated clays in undrained shear (CU test)

Since we can get both the total and effective stress circles at failure for a CU test when we measure the induced pore water pressures, it is possible to define the Mohr failure envelopes in terms of both total and effective stresses from a series of triaxial tests conducted over a range of stresses, as illustrated in figure below for a normally consolidated clay.

Figure 26.

Mohr circles at failure and Mohr failure envelopes for total (T) and effective (E) stresses for a normally consolidated clay

Note that the effective stress circle is displaced to the left, towards the origin, for the normally consolidated case, because the specimens develop positive pore pressure during shear and ’ =  - u. Note that both circles have the same diameter because of our definition of failure at maximum (1 - 3) = (’1 - ’3). Once the two failure envelopes are drawn, the Mohr-Coulomb strength parameters are readily definable in terms of both total (c,  or sometimes cT, T) and effective stresses (c’, ’). Again, as with the CD test, the envelope for normally consolidated clay passes essentially through the origin, and thus for practical purposes c’ can be taken to be zero, which is also true for the total stress c parameter. Note that  T is less than ’, and often it is about one-half of ’. Things are different if the clay is overconsolidated. Since an overconsolidated specimen tends to expand during shear, the pore water pressure decreases or even goes negative, as shown in previous figure. Because ’3f = 3f – (-uf) or ’1f = 1f – (-uf), the effective stresses are greater than the total stresses, and the effective stress circle at failure is shifted to the right of the total stress circle as shown in figure below. The shift of the effective stress circle at failure to the right sometimes means that the ’ is less than  T. Typically, the complete Mohr failure envelopes are determined by tests on several specimens consolidated over the working stress range of the field problem.

Figure 27.

Mohr circles at failure and Mohr failure envelopes for total (T) and effective (E) stresses for an overconsolidated clay

Figure below shows the Mohr failure envelopes over a wide range of stresses spanning the preconsolidation stress. Thus some of the specimens are overconsolidated and others are normally consolidated. You should note that the “break” in the total stress envelope (point z) occurs roughly about twice the ’p for typical clays (Hirschfeld, 1963). The two sets of Mohr circles at failure shown in figure below correspond to the two tests for the “normally consolidated” specimen and the specimen “overconsolidated at low ’hc”.

Figure 28.

Mohr failure envelopes over a range of stresses spanning the preconsolidation stress ’p

Note : Pore water pressure is measured during the CU test, thus permitting determination of the effective stress parameters c’ and ’. In the absence of pore pressure measurements CU tests can provide only total stress values c and . 3.

Unconsolidated – Undrained test (UU test)

Step 1. Apply chamber pressure 3. Do not allow drainage, so that the pore water pressure (u = u0) developed through the application of 3 is not zero. Step 2. Apply a deviator stress . Do not allow drainage (u = u d ≠ 0). At failure,  = f ; the pore water pressure uf = u0 + ud(f) For unconsolidated-undrained triaxial tests, Major principal total stress = 3 + f = 1 Minor principal total stress = 3

Figure 29.

Conditions in the specimen during the unconsolidated-undrained (UU) axial compression test

The total stress Mohr’s circle at failure can now be drawn. For saturated clays, the value of 1 - 3 = f is a constant, irrespective of the chamber confining pressure 3. The tangent to these Mohr’s circles will be a horizontal line, called the  = 0 condition. The shear stress for this condition is

  cu 

 f 2

Where cu = undrained cohesion (or undrained shear strength)

Figure 30.

Unconsolidated-undrained test

The pore pressure developed in the soil specimen during the unconsolidated-undrained triaxial test is u  ua  ud

The pore pressure ua is the contribution of the hydrostatic chamber pressure 3. Hence, u a  B. 3

Where B = Skempton’s pore pressure parameter Similarly, the pore parameter ud is the result of the added axial stress , so u d  A.

Where A = Skempton’s pore pressure parameter However,    1   3

Combining the equations above gives

u  u a  u d  B. 3  A. 1   3  The pore water pressure parameter B in soft saturated soils is unity, so u   3  A.( 1   3 )

The value of the pore water pressure parameter A at failure will vary with the type of soil. Following is a general range of the values of A at failure for various types of clayey soil encountered in nature: Values of A at failure for various types of clayey soil Table 10. Type of Soil A at failure Sandy clays 0,5 – 0,7 Normally consolidated clays 0,5 – 1,0 Overconsolidated clays -0,5 – 0,0

Unconfined Compression Test The unconfined compression test is a special type of unconsolidated-undrained triaxial test in which the confining pressure 3 = 0. In this test, an axial stress  is applied to the specimen to cause failure (i.e.,  = f). The corresponding Mohr’s circle is shown in figure. Note that, for this case,

Figure 31.

Figure 32.

Soil specimen

Mohr’s circle for the unconfined compression test

Major principal total stress = f = qu Minor principal total stress = 0

The axial stress at failure, f = qu, is generally referred to as the unconfined compression strength. The shear strength of saturated clays under this condition ( = 0) is   cu 

qu 2

The unconfined compression strength can be used as an indicator of the consistency of clays. Unconfined compression tests are sometimes conducted on unsaturated soils. With the void ratio of soil specimen remaining constant, the unconfined compression strength rapidly decreases with the degree of saturation.

Figure 33.

Variation of qu with the degree of saturation

Sensitivity For many naturally deposited clay soils, the unconfined compression strength is much less when the soils are tested after remolding without any change in the moisture content. This property of clay soil is called sensitivity. The degree of sensitivity is the ratio of the unconfined compression strength in an undisturbed state to that in a remolded state, or St 

q u ( undisturbed ) q u ( remolded )

The sensitivity ratio of most clays from about 1 to 8; however, highly flocculent marine clay deposits may have sensitivity ratios ranging from about 10 to 80. Some clays turn to viscous liquids upon remolding, and these clays are referred to as “quick” clays. The loss of strength of clay soils from remolding is caused primarily by the destruction of the clay particle structure that was developed during the original process of sedimentation. Based on Holtz and Kovacs, 1981:  St ≤ 4 low sensitivity  4 < St ≤ 8 medium sensitivity  8 < St ≤ 16 high sensitivity  St > 16 quick sensitivity Note: when testing a remolded soil specimen, it is important to retain the same water content of the undisturb soil. If the soil specimen bleeds water during this process, then the sensitivity cannot be determined for the soil. An unsual feature of highly sensitive or quick clays is that the insitu water content is often greater than the liquid limit (liqudity index greater than one). Sensitive clays have unstable bonds between particles. As long as these unstable bonds are not broken, the clay can support a heavy load. But once remolded, the bonding is destroyed and the shear strength is substantially reduced.

Vane Shear Test The vane shear test (ASTM D-2573) may be used during the drilling operation to determine the in situ undrained shear strength (cu) of clay soils – particularly soft clays. The vane shear apparatus consists of four blades on the end of a rod, as shown in Figure below. The height, H, of the vane is twice the diameter, D. The vane can be either rectangular of tapered. The dimensions of vanes used in the field are given in Table below. The vanes of the apparatus are pushed into the soil at the bottom of a borehole without disturbing the soil appreciably. Torque is applied at the top of the rod to rotate the vanes at a standard rate of 0,1/sec (6/min). This rotation will induce failure in a soil of cylindrical shape surrounding the vanes. The maximum torque, T, applied to cause failure is measured. Note that T = f (cu, H, and D) or T K

cu 

Where: T = torque (N.m) cu = undrained shear strength (kN.m2) K = a constant with a magnitude depending on the dimension and shape of vane The constant  6  10 

K 

  D 2 .H    . 2   

D   . 1   3.H  

Where: D = diameter of vane (cm) H = measured height of vane (cm) K = a constant with a magnitude depending on the dimension and shape of vane

Geometry of Field Vane (after ASTM, 2001)

Figure 34.

Table 11.

Casing Size AX BX

Recommended Dimensions of Field Vanesa (After ASTM, 2001) Diamter, D Height, H Thickness of Blade Diameter of Rod mm (in.) mm (in.) mm (in.) mm (in.) 

1



2

50,8

 2

38,1

NX

63.5

4 in (101,6 mm)b

92,1

 1





1



2

 2





5



8

 3





76,2

 3

1,6 

101,6

 4

1,6 

127,0

 5

3,2 

184,1

 1



12,7 

1





16



1



4



12,7 



 2  1

12,7 

8



 2

 1

3,2 

 1

 





 2



 1



 7



1

 16 



 8

 1

12,7 



 2

a

The selection of a vane size is directly related to the consistency of the soil being tested; that is, the softer the soil, the larger the vane diameter should be. b Inside diameter.

Field vane shear tests are moderately rapid and economical and are used extensively in field soilexploration programs. The test gives good results in soft and medium-stiff clays and gives excellent results in determining the properties of sensitive clays. Sources of significant error in the field vane shear test are poor calibration of torque measurement and damaged vanes. Other errors may be introduced if the rate of rotation of the vane is not properly controlled.

For actual design purposes, the undrained shear strength values obtained from field vane shear tests [cu(VST)] are too high, and it is recommended that they be corrected according to the equation c u ( corrected )  .c u (VST )

Where: cu = undrained shear strength  = correction factor Several correlations have been given previously for the correction factor ; some more are as follows: Bjerrum (1972):   1,7  0,54. log PI  % 

Morris and Williams (1994):   1,18.e 0,08. PI   0,57   7,01.e 0,08. LL   0,57

(for PI > 5%) (LL in %)

Aas et al. (1986):  c u (VST ) 

 f 

 (see figure below)

 '0 

Figure 35.

Variation of  with cu(VST)/’0

Atterberg Limits When a clayey soil is mixed with an excessive amount of water, it may flow like a semiliquid. If the soil is gradually dried, it will behave like a plastic, semisolid, or solid material, depending on its moisture content. The moisture content, in percent, at which the soil changes from a liquid to a plastic state is defined as the liquid limit (LL). Similarly, the moisture content, in percent, at which the soil changes from a plastic to a semisolid state and from a semisolid to a solid state is defined as the plastic limit (PL) and the shrinkage limit (SL), repectively. These limits are referred to as Atterberg Limits:  The liquid limit of a soil is determined by Casagrande’s liquid device (ASTM Test Designation D-4318) and is defined as the moisture content at which a groove closure of 12.7 mm (1/2 in.) occurs at 25 blows.  The plastic limit is defined as the moisture content at which the soil crumbles when rolled into a thread of 3.18 mm (1/8 in.) in diameter (ASTM Test Designation D-4318).  The shrinkage limit is defined as the moisture content at which the soil does not undergo any further change in volume with loss of moisture (ASTM Test Designation D-4318). The difference between the liquid limit and the plastic limit of a soil is defined as the plasticity index (PI), or :

PI  LL  PL However, Atterberg limits for the different soils will vary considerably, depending on the origin of the soil and the nature and amount of clay minerals in it.

Figure 36.

Definition of Atterberg limits

The liquid and plastic limit values, together with wN (natural water content), are useful in predicting whether a cohesive soil mass is preconsolidated. Since an overconsolidated soil is more dense, the void ratio is smaller than in the soil remolded for the Atterberg limit tests. If the soil is located below the groundwater table (GWT) where it is saturated, one would therefore expect that smaller void ratios would have less water space and the w N value would be smaller. From this we might deduce the following:  If wN is close to wL, soil is normally consolidated  If wN is close to wP, soil is some- to heavily overconsolidated

 

If wN is intermediate, soil is somewhat overconsolidated If wN is greater than wL, soil is on verge of being a viscous liquid

Although the foregoing gives a qualitative indication of overconsolidation, other methods must be used if a quantitative value of OCR is required. Overconsolidation Ratio (OCR) The degree of overconsolidation may be expressed numerically as the overconsolidation ratio (OCR) which is defined as follows: ' OCR  c  'v Where: OCR = overconsolidation ratio  ’c = pre-consolidation ratio  ’v = vertical effective stress The OCR of a normally consolidated soil is equal to 1; in a lightly overconsolidated soil, it is typically between 1 and 3; a heavily overconsolidated soil may have an OCR as high as 8. Preconsolidation stress can be determined by consolidation test. The following empirical relationship (U.S. Navy, 1982a) can be useful when estimating it or when checking test result for reasonableness: cu  'c  0.11  0.0037 PI Where: ’c = pre-consolidation ratio cu = undrained shear strength PI = Plasticity Index Synthesis of Field and Laboratory Data Investigation and testing programs often generate large amounts of information that can be difficult to sort through and synthesize. Real soil profiles are nearly always very complex, so the borings will not correlate and the test results will often vary significantly. Therefore, we must develop a simplified soil profile before proceeding with the analysis. In many cases, the simplified profile is the best defined in terms of a one-dimensional function of soil type and engineering properties vs. depth; an idealized boring log. However, when the soil profile varies significantly across the site, one or more vertical cross-sections may be in ordered, The development of these simplified profiles requires a great deal of engineering judgment along with interpolation and extrapolation of the data. It is important to have a feel for the approximate magnitude of the many uncertainties in this process and reflect them in an appropriate degree of conservatism. This judgment comes primarily with experience combined with a through understanding of the field and laboratory methodologies.

Organic Soil Organic soils are usually found in low-lying areas where the water table is near or above the ground surface. The presence of a high water table helps in the growth of aquatic plants that, when decomposed, form organic soil. This type of soil deposit is usually encountered in coastal areas and in glaciated regions. Organic soils show the following characteristics:  Their natural moisture content may range from 200% to 300%  They are highly compresible  Laboratory tests have shown that, under loads, a large amount of settlement is derived from secondary consolidation Expansive Soil When geotechnical engineers refer to expansive soils, we usually are thinking about clays or sedimentary rocks derived from clays, and the volume changes that occur as a result of changes in moisture content. Clays are fundamentally very different from gravels, sands, and silts. All of the later consist of relatively inert bulky particles and their engineering properties depend primarily on the size, shape, and texture of these particles. In contrast, clays are made of very small particles that are usually plate-shaped. The engineering properties of clays are strongly influenced by the very small size and large surface area of these particles and their inherent electrical charges. Several different clay minerals occur in nature, the differences being defined by their chemical makeup and structural configuration. Three of the most common clay minerals are kaolinite, illite, and montmorillonite (part of the smectite group). The different chemical compositions and crystalline structures of these minerals give each a different susceptibility to swelling, as shown in table below. Table 12.

Swell Potential Of Pure Clay Minerals (Budge et al., 1964)

Sucharge Load (lb/ft2) (kPa) 200 9.6 400 19.1

Kaolinite Negligible Negligible

Swell Potential (%) Illite Montmorillonite 350 1500 150 350

Swelling occurs when water infiltrates between and within the clay particles, causing them to separate. Kaolinite is essentially nonexpansive because of the presence of strong hydrogen bonds that hold the individual clay particles together. Illite contains weaker potassium bonds that allow limited expansion, and montmorillonite particles are only weakly linked. Thus, water can easily flow into montmorillonite clays and separate the particles. Field observations have confirmed that the greatest problems occur in soils with a high montmorillonite content. Several other forces also act on clay particles, including the following:  Surface tension in the menisci of water contained between the particles (tends to pull the particles together, compressing the soil).  Osmotic pressures (tend to bring water in, thus pressing the particles further apart and expanding the soil).  Pressures in entrapped air bubles (tend to compress the soil).

 

Effective stresses due to external loads (tend to compress the soil). London-Van Der Waals intermolecular forces (tend to compress the soil).

Expansive clays swell or shrink in response to changes in these forces. For example, consider the effects of changes in surface tension and osmotic forces by imagining a montmorillonite clay that is initially saturated, as shown if figure (a). If this soil dries, the remaining moisture congregates near the particle interfaces, forming menisci, as shown in figure (b), and the resulting surface tension forces pull the particles closer together causing soil to shrink. We could compare the soil in this stafe to a compressed spring: both would expand if it were not for forces keeping them compressed. The soil in figure (b) has a great affinity for water and will draw in available water using osmosis. We would say that it has a very high soil suction at this stage. If water becomes available, the suction will draw it into spaces between the particles and the soil will swell, as shown in figure (c). Internal Friction ( ) Internal friction is used to analyze the bearing capacity of a foundation on Sand layer. This chart shows relationships between angle of friction and (N1)60.

Figure 37.

Relationship Between Angle of Friction and N-Value for Sandy Soil (K. Terzaghi)

Based on the chart above, we propose to use Dunham’s (1954) equation as:   12 N1  60  15 

Where:  = angle of friction ( 0)

(N1)60 = N-SPT value corrected for field procedures and overburden stress DeMello (1971) suggested a correlation between SPT data results and the effective friction angle of uncemented sands, ’, as shown in Figure below. This correlation should be used only at depths greater than about 2 m.

Figure 38.

Empirical correlation between N60 and ’ for uncemented sands (DeMello, 1971)

The CPT results also have been correlated with shear strength parameters, especially in sands. Figure below presents Robertson and Campanella’s 1983 correlation for uncemented, normally consolidated quartz sands. For overconsolidated sands, subtract 1 0 to 20 from the effective friction angle obtained from this figure.

Figure 39.

Relationship Between CPT Results, Overburden Stress and Effective Friction Angle for Uncemented, Normally Consolidated Quartz Sand (Robertson and Campanella, 1983)

On the basis of experimental results, Robertson and Campanella (1983) suggested the variation of ’ for normally consolidated quartz sand. The figure above can also be expressed into a relationship as (Kulhawy and Mayne, 1990)

  q    '  tan 1  0,1  0,38. log c     ' 0   

 = effective angle of friction ( 0) qc = cone resistance ’0 = effective vertical stress Cohesion (cu)

Cohesion is one of the soil properties for clay that can be used to analyze the bearing capacity of a foundation. The chart shows the relationships between undrained cohesion and corrected NSPT value :

Figure 40.

Relationship Between Cohesion with N-Value for Cohesive Soil (K. Terzaghi)

The chart above is used to determine the undrained shear strength for cohesive soils and we proposed to use: c u  6,67.N 60 ( kN / m 2 )

Where: cu = undrained shear strength N60 = N-SPT value corrected for field procedures The literature contains many correlations between the standard penetration number and the undrained shear strength of clay, cu. On the basis of results of undrained triaxial tests conducted on insensitive clays, Stroud (1974) suggested that c u  K .N 60 ( kN / m 2 )

Where: cu = undrained shear strength N60 = N-SPT value corrected for field procedures K = constant = 3,5 – 6,5 Hara et al. (1971) also suggested that

0,72 c u ( kN / m 2 )  29.N 60

As in the case of standard penetration tests, several correlations have been developed between qc and other soil properties. According to Mayne and Kemper (1988), in clayey soil the undrained cohesion cu, can be correlated via the equation cu 

qc   0 NK

Where: cu = undrained shear strength qc = cone resistance 0 = total vertical stress NK = 15 for an electric cone = 20 for a mechanical cone Values of the undrained shear strength cu corresponding to various degrees of consistency are as follows (Terzaghi & Peck, 1967 and ASTM D2488-90) :  Very Soft: cu < 12 kPa. The clay is easily penetrated several centimeters by the thumb. The clay oozes out between the fingers when squeezed in the hand.  Soft: 12 kPa ≤ cu < 25 kPa. The clay is easily penetrated 2 to 3 cm by the thumb. The clay can be molded by slight finger pressure.  Medium: 25 kPa ≤ cu < 50 kPa. The clay can be penetrated about 1 cm by the thumb with moderate effort. The clay can be molded by strong finger pressure.  Stiff: 50 kPa ≤ cu < 100 kPa. The clay can be indented about 0.5 cm by the thumb with great effort.  Very Stiff: 100 kPa ≤ cu < 200 kPa. The clay cannot be indented by the thumb, but can be readily indented with the thumbnail.  Hard: cu ≥ 200 kPa. With great difficulity, the clay can only be indented with the thumbnail. Relative Density (Dr) The following approximate relationship between CPT results and the relative density of sands (Adapted from Kulhawy and Mayne, 1990) : Dr 





qc



 . 100.kPa x100% z'

 315.Q .OCR 0.18  c  

Where: qc = cone resistance Qc = compressibility factor = 0.91 for highly compressible sands = 1.00 for moderately compressible sands = 1.09 for slightly compressible sands

OCR = overconsolidation ratio z’ = vertical effective stress A relationship between consistency of sands and gravels and relative density is shown in Table below.

Table 13.

Consistency of coarse-grained soils various relative densities (Lambe and Whitman, 1969)

Relative Density, Dr (%) 0 – 15 15 - 35 35 – 65 65 – 85 85 – 100

Classification Very Loose Loose Medium Dense Dense Very Dense

qc vs N-SPT Value Since the SPT and CPT are the two most common in-situ tests, it often is useful to convert results from one to the other. The ratio qc/N60 as a function of the mean grain size, D50, is shown in Figure below. Note that N60 does not include an overburden correction.

Figure 41.

Correlation between qc/N60 and the mean grain size, D50 (Kulhawy and Mayne, 1990)

Be cautious about converting CPT data to equivalent N values, and then using SPT based analysis methods. This technique compounds the uncertainties because it uses two correlations – one to convert to N, and then another to compute the desired quantity. Correlation with Soil Classification

Because the CPT does not recover any soil samples, it is not a substitute for conventional exploratory borings. However, it is possible to obtain an approximate soil classification using the correlation shown in Figure below:

Figure 42.

Classification of Soil Based On CPT Test Results (Robertson and Campanella, 1983)

Design N-SPT Value Early recommendations were to use the smallest N value in the boring or an average of all of the values for the particular stratum. Current practice is to use an average N but in the zone of major stressing. For example, for a spread footing the zone of interest is from about one-half the footing width B above the estimated base location to a depth of about 2B below. Weighted averaging using depth increment multiplied by N may be preferable to an ordinary arithmetic average; that is,

N av 

 N.z i  zi

and not  Ni    i 

N av   

For pile foundations there may be merit in the simple averaging of blow count N for any stratum unless it is very thick – thick being a relative term. Here it may be better to subdivide the thick stratum into several “strata” and average the N count for each subdivision. Correction for N-SPT Value Deep tests in a uniform soil deposit will have higher N values than shallow tests in the same soil, so the overburden correction adjusts the measure N values to what they would have been if the vertical effective stress, ’v, was 100 kPa. In granular soils, the value of N is affected by the effective overburden pressure, ’0. For that reason, the value of N60 obtained from field exploration under different effective overburden pressure should be changed to correspond to a standard value of ’0. So that, the corrected value (Liao and Whitman, 1985), (N1)60 is:

 N1  60

 C N .N 60

Where: (N1)60 = N-SPT value corrected for field procedures and overburden stress CN = overburden correction factor (see figure below)  ’0 = vertical effective stress in ton/ft2, which is based on water table during SPT testing. If fill is paced after SPT testing, fill does not affect ’0

SPT overburden stress correction factor, CN (Liao and Whitman, 1986)

Figure 43.

Liao and Whitman’s relationship (1986): C N  9,78.

1 for  ' v  25 kN / m 2  'v

Skempton’s relationship (1986):

CN 

2 1   'v

for  'v  25 kN / m 2 9,78

Seed et al.’s relationship (1975):   'v  C N  1  1,25. log  for  ' v  25 kN / m 2  9,78 

Peck et al.’s relationship (1974): 

 20    'v       9,78 

 for  '  25 kN / m 2 v





C N  0,77. log

  

We can improve the raw SPT data by applying certain correction factors. The variations in testing procedures may be at least partially compensated by converting the measured N to N60 as follows (Skempton, 1986):

N 60 

Em Cb Cs Cr N N60  ’v Pa

E m .C b .C s .C r .N 0,60

= hammer efficiency = borehole diameter correction = sampling method correction = rod length correction = N-SPT value from field test = N-SPT value corrected for field procedures = vertical effective stress at the test location = reference stress = 100 kN/m2 Table 14.

SPT Hammer Effeciences (Clayton, 1990)

Country

Hammer Type

Hammer Release Mechanism

Argentina Brazil

Donut Pin weight Automatic Donut Donut Donut Donut Donut Automatic Safety Donut Donut

Cathead Hand dropped Trip Hand dropped Cathead Cathead Tombi trigger Cathead 2 turns + special release Trip 2 turns on cathead 2 turns on cathead Cathead

China Colombia Japan UK US Venezuela

Hammer Effeciency, Em 0.45 0.72 0.60 0.55 0.50 0.50 0.78 – 0.85 0.65 – 0.67 0.73 0.55 – 0.60 0.45 0.43

Figure 44.

Table 15.

Type of SPT hammers

Borehole, Sampler and Rod Correction Factors (Skempton, 1986)

Factor Borehole diameter factor, CB Sampling method factor, CS Rod length factor, CR

Equipment Variables 65 – 115 mm (2.5 – 4.5 in) 150 mm (6 in) 200 mm (8 in) Standard sampler Sampler without liner (not recommended) 3 – 4 m (10 – 13 ft) 4 – 6 m (13 – 20 ft) 6 – 10 m (20 – 30 ft) > 10 m (> 30 ft)

Value 1.00 1.05 1.15 1.00 1.20 0.75 0.85 0.95 1.00

Although Liao and Whitman did not place any limits in this correction, it is probably best to keep (N1)60 ≤ 2.N60. This limit avoids excessively high (N1)60 values at shallow depths. The use of correction factors is often a confusing issue. Corrections for field procedures are always appropriate, but the overburden correction may or may not be appropriate depending on the procedures used by those who developed the analysis method under consideration. The N-SPT value, as well as many other test results, is only an index of soil behavior. It does not directly measure any of the conventional engineering properties of soil and is useful only when appropriate correlations are available. Many such correlation exist, all of which were obtained

empirically. Be especially cautious when using correlations between SPT results and engineering properties of clays because these functions are especially crude. In general, the SPT should be used only in sandy soils. Adhesion Factor ( ) Recommended values of  for drilled shafts in clay (After Reese and O’Neill, 1986): Adhesion Value for Drilled Shaft in Clay (After Reese and O’Neill,1986) Undrained Shear Strength (cu) ; Location Along Drilled Shaft Value of  1 tsf = 95,76 kPa From Ground surface to depth 0 along drilled shaft of 5 ft Bottom 1 diameter of the drilled shaft or 1 stem diameter above the 0 top of the bell All other points along the sides of < 2 tsf < 191,52 kPa 0,55 the drilled shaft 2 – 3 tsf 191,52 – 287,28 kPa 0,49 3 – 4 tsf 287,28 – 383,04 kPa 0,42 4 – 5 tsf 383,04 – 478,80 kPa 0,38 5 – 6 tsf 478,80 – 574,56 kPa 0,35 6 – 7 tsf 574,56 – 670,32 kPa 0,33 7 – 8 tsf 670,32 – 766,08 kPa 0,32 8 – 9 tsf 766,08 – 861,85 kPa 0,31 > 9 tsf > 861,85 kPa Treat as Rock Table 16.

Adhesion factor () as function of undrained shear strength (su) for drilled shafts foundation in clay is presented below:

Figure 45.

Adhesion Factor ( ) vs Undrained Shear Strength (su) for drilled shaft

Recommended values of  for pile in clay (API):  For cu < 25 kPa   1,0



For 25 kPa < cu < 75 kPa  c  25.kPa    1,0  0,5. u  50.kPa  



For cu > 75 kPa   0,5

Figure 46.

Adhesion Factor ( ) vs Undrained Shear Strength (su) for driven pile (API)

All of the  factors presented above are for insensitive clays (St < 4). In sensitive clays, full-scale static load tests, special lab tests, or some other method of verification are appropriate (O’Neill and Reese, 1999). O’Neill and Reese (1989) also ignore the skin friction resistance in the upper 5 ft (1,5 m) of the shaft and along the bottom one diameter of straight shaft because of interaction with the end bearing.

Soil Modulus Subgrade Reaction and Soil Strain According to Reese (1987), modulus subgrade reaction and soil strain can be determained from the table below:  For Clays Table 17.



Modulus Subgrade Reaction and Soil Strain Value for Clay (after Reese, 1987) Consistency cu (kPa) k (kPa/m)  50 Soft 12 – 24 8140 0,02 Medium 24 – 48 27150 0,01 Stiff 48 – 96 136000 0,007 Very Stiff 96 – 192 271000 0,005 Hard 192 - 383 543000 0,004

For Sands Modulus subgrade reaction (ks) kPa/m Table 18.

Modulus Subgrade Reaction and Soil Strain Value for Clay (after Reese, 1987) Relative Density Loose Medium Dense Submerged Sand 5430 16300 33900 Sand Above Water Table 6790 24430 61000

In general, the coefficient of subgrade reaction which is also known as the modulus of subgrade reaction, or the subgrade modulus could be approached by using formula below : ks 

q 

Where: ks = coefficient of subgrade reaction (kPa/m) q = bearing pressure (kN/m2 or kPa)  = settlement (m) Basic Theory Shallow Foundation Shallow foundations transmit the applied structural loads to the near-surface soils. In the process of doing so, they induce both compressive and shear stresses in these soils. The magnitudes of these stresses depend largely on the bearing pressure and the size of the footing. If the bearing pressure is large enough, or the footing is small enough, the shear stresses may exceed the shear strength of the soil or rock, resulting in a bearing capacity failure. Researchers have identified three types of bearing capacity failures:  General shear failure It occurs in soils that are relatively incompressible and reasonably strong, in rock, and in saturated, normally consolidated clays that are loaded rapidly enough that the undrained condition prevails. The failure surface is well defined and failure occurs quite suddenly. A clearly formed bulge appears on the ground surface adjacent to the foundation. Although





bulges may appear on both sides of the foundation, ultimate failure occurs on one side only, and it is often accompanied by rotations of the foundation. Local shear failure Local shear failure is an intermediate case. The shear surfaces are well defied under the foundation, and then become vague near the ground surface. A small bulge may occur, but considerable settlement, perhaps on the order of half the foundation width, is necessary before a clear shear surface form near ground. Even then, a sudden failure does not occur, as happens in the general shear case. The foundation just continues to sink ever deeper into the ground. Punching shear failure The opposite extreme is the punching shear failure. It occurs in very loose sands, in a thin crust of strong soil underlain by a very weak soil, or in weak clays loaded under slow, drained conditions. The high compressibility of such soil profiles causes large settlements and poorly defined vertical shear surfaces. Little or no bulging occurs at the ground surface and failure develops gradually.

Figure 47.

(a) General shear failure; (b) Local shear failure; (c) Punching shear failure (after Vesic, 1973)

Complete quantitative criteria have yet to be developed to determine which of these three modes of failure will govern in any given circumstance, but the following guidelines are helpful:  Shallow foundations in rock and undrained clays are governed by the general shear case

  

Shallow foundations in dense sands are governed by the general shear case. In this context, a dense sand is one with a relative density, Dr, greater than about 67% Shallow foundations on loose to medium dense sands (30% < D r < 67%) are probably governed by local shear Shallow foundations on very loose sand (Dr < 30%) are probably governed by punching shear.

For nearly all practical shallow foundation design problems, it is only necessary to check the general shear case, and then conduct settlement analyses to verify that the foundation will not settle excessively. These settlement analyses implicitly protect against local and punching shear failures. Bearing Capacity Analyses in Soil – General Shear Case Ultimate capacity for shallow foundation design is calculated by using the formula taken from Terzaghi (1943): q ult  c '.N c  q '.N q  0,5. '.B.N 

(for continuous foundation)

q ult  1,3.c '.N c  q '.N q  0,4. '.B.N 

(for square foundation)

q ult  1,3.c '.N c  q '.N q  0,3. '.B.N 

(for circular foundation)

Where: c’ = effective cohesion of soil ’ = effective unit weight of soil q’ = vertical effective overburden pressure Nc, Nq, N = bearing capacity factors The Terzaghi bearing capacity factors are:

Nq 

a2

2. cos 2  45   '  2 

a  e

  0 , 75 ' 360  . tan   '   

N c  5,7

Nc 

N 

Nq 1

tan   '

for ’ = 0 for ’ > 0

2. N q  1. tan   ' 1  0,4. sin  4. '

The formula developed in Vesic (1973, 1975) is based on theoretical and experimental findings from these and other sources and is an excellent alternative to Terzaghi. It produces more accurate bearing values and it applies to a much broader range of loading and geometry conditions. The primary disadvantage is its added complexity. Vesic retained Terzaghi’s basic format and added the following additional factors: sc, sq, s = shape factors dc, dq, d = depth factors ic, iq, i = load inclination factors bc, bq, b = base inclination factors gc, gb, g = ground inclination factors He incorporated these factors into the bearing capacity formula as follows: q ult  c '.N c .s c .d c .ic .bc .g c  q '.N q .s q .d q .i q .bq .g q  0,5. '.B.N  .s .d  .i .b .g 

Terzaghi’s formulas consider only vertical loads acting on a footing with a horizontal base with a level ground surface, whereas Vesic factors allow any or all of these to vary. The notation for these factors is shown in figure below:

Figure 48.

Notation for Vesic’s load inclination, base inclination, and ground inclination factors. All angles are expressed in degrees

Shape Factors Vesic considered a broader range of footing shapes and defined them in his s factors:  B   N q  .  L   N c 

sc  1  

 B  . tan   L

sq  1  

 B s  1  0,4.   L For continous footings, B/L  0, so sc, sq, and s become equal to 1. This means the s factors may be ignored when analyzing continous footings. Depth Factors Unlike Terzaghi, Vesic has no limitations on the depth of the footing. The depth of footing is considered in the following depth factors: d c  1  0,4.k

d q  1  2.k . tan  .1  sin  

2

d  1

For relatively shallow foundations (D/B ≤ 1), use k  D

 B with the tan

k  tan 1 D

function at D

B

-1

B . For deeper footings (D/B > 1), use

term expresses in radians. Note that this produces a discontinues

 1.

Load Inclination Factors The load inclination factors are for loads that do not act perpendicular to the base of the footing, but still act through its centroid. The variable P refers to the component of the load that acts perpendicular to the bottom of the footing, and V refers to the component that acts parallel to the bottom. The load inclination factors are: ic  1 

m.V 0 A.cu .N c m



 V iq   1  A.cu  P  tan 

  

0  

 V i   1  A.c u  P  tan  





m 1



0  

For loads inclined in the B direction:

m

2 B 1 B

L L

For loads inclined in the L direction:

m

2 L 1 L

B B

Where: V = applied shear load P = applied normal load A = base area of footing cu = cohesion  = friction angle B = foundation width L = foundation length If the load acts perpendicular to the base of the footing, the i factors equal 1 and may be neglected. The i factors also equal 1 when  = 0. Base Inclination Factors The vast majority of footings are built with horizontal bases. However, if the applied load is inclined at a large angle from the vertical, it may be better to incline the base of the footing to the same angle so the applied load acts perpendicular to the base. However, keep in mind that such footings may be difficult to construct. The base inclination factors are: bc  1 

 147 0

 . tan   bq  b   1   57 0   

2

If the base of the footing is level, which is the usual case, all of the b factors become equal to 1 and may be ignored. Ground Inclination Factors Footings located near the top of a slope have a lower bearing capacity than those on level ground. Vesic ground inclination factors, presented below, account for this. However, there are also other considerations when placing footings on or near slopes.

gc  1 

 147 0

g q  g   1  tan  

2

If the ground surface is level ( = 0), the g factors become equal to 1 and may be ignored. Bearing Capacity Factors Vesic used the following formulas for computing the bearing capacity factors Nq, Nc and N :

  N q  e  . tan  . tan 2  45   2  Nc 

Nq 1 tan 

N c  5,14

for  > 0 for  = 0

N   2. N q  1. tan 

Bearing Capacity Analysis in Soil – Local and Punching Case Engineers rarely need to compute the local or punching shear bearing capacities because settlement analyses implicity protect against this type of failure. In addition, a complete bearing capacity analysis would be more complex because of the following:  These modes of failure do not have well-defined shear surfaces, such as those shown in figures above, and are therefore more difficult to evaluate.  The soil can no longer be considered incompressible (Ismael and Vesic, 1981).  The failure is not catastrophic, so the failure load is more difficult to define.  Scale effects make it difficult to properly interpret model footing tests. Terzaghi (1943) suggested a simplified way to compute the local shear bearing capacity using the general shear formulas with appropriately reduced values of c and : c adj  0,67.c

 adj  tan 1  0,67. tan  

Vesic (1975) expanded upon this concept and developed the following adjustment formula for sands with a relative density, Dr, less than 67%:



 adj  tan 1  0,67  Dr  0,75.Dr2 . tan 



Where: cadj = adjusted cohession adj = adjusted friction angle c = cohession  = friction angle Dr = relative density of sand, expressed in decimal form (0 ≤ Dr ≤ 67%) Although the Vesic (1975) formula was confirmed with a few model footing tests, both methods are flawed because the failure mode is not being modeled correctly. However, local or punching shear will normally only govern the final design with shallow, narrow footings on loose sands, so an approximate analysis is acceptable. An important exception to this conclusion is the case of a footing supported by a thin crust of strong soil underlain by very weak soil. This would likely be governed by punching shear and would justify a custom analysis. Sliding Capacity Analysis Resistance against sliding in soils : W  PV . tan   c a .Abase Fs   1 .5 PH W  PV . tan   c a .Abase  Pp Fs   2 .0 PH Where : Fs = minimum factor of safety against sliding potential W = foundation weight including soil above footing PV = vertical force PH = horizontal force Pp = passive force Abase = base area ca = adhesion factor tan δ = friction factor between soil and base  = friction angle tan  = tan δ Adhesion factor (NAVFAC DM-7.02) Adhesion, ca Interface Materials (Cohesion) (kPa) Very soft cohesive soil (0 – 12.5 kPa) 0 – 12.5 Soft cohesive soil (12.5 – 20 kPa) 12.5 – 20 Medium stiff cohesive soil (20 – 50 kPa) 20 – 37.5 Stiff cohesive soil (50 – 100 kPa) 37.5 – 47.5 Very stiff cohesive soil (100 – 200 kPa) 47.5 – 65 Table 19.

Pile Foundation Bearing capacity calculation can be determined by using analysis of such this condition:

1. 2.

Bearing capacity of single pile Pile-soil interaction and pile group

Figure 49.

Pile Foundation Analysis

Bearing Capacity of Single Pile

QS

QP Figure 50.

Bearing Capacity of Pile

In general, the ultimate axial capacity of bored pile / driven pile can be obtained as the summation of end bearing capacity plus skin friction resistance, or : Qu  Qs  Q p

Where: Qu = ultimate pile capacity Qp = ultimate end bearing capacity Qs = ultimate skin friction resistence

Analyses Based on SPT Results Toe-Bearing

The ultimate end bearing capacity (Qp) can be determined as: Q p  q p . Ap

Where: Qp = ultimate end bearing capacity qp = unit end bearing capacity Ap = area of bored pile / driven pile cross section The calculation of unit end bearing capacity (qp) must refer to the soil condition. Below are several equations for its conditions:  Because of their low hydraulic conductivity, we assumed undrained conditions exist in clays beneath the toe of deep foundation. Therefore, we compute qp using the undrained shear strength, cu. For deep foundations which have ratio D/B > 3 with cu ≤ 250 kPa : q p  N c* .cu  (3800kPa )

Where: qp = unit end bearing capacity Nc* = bearing capacity factor (O’Neill and Reese, 1999) = 6,5 at cu = 25 kPa = 8,0 at cu = 50 kPa = 9,0 at cu  100 kPa cu = undrained shear strength in the soil between the base of the shaft/pile and a distance 2Bb below the base D = depth to the bottom of the shaft/pile Bb = diameter of shaft/pile base Clays with cu > 250 kPa should be evaluated as intermediate geo-materials. If the base diameter, Bb, is greater than 1900 mm, the value of qp could produce settlements greater than 25 mm, which would be unacceptable for most buildings. To keep settlements within tolerable limits, reduce the value of qp and use this value (O’Neill and Reese, 1999): q pr  Fr .q p

Fr 

2,5  1,0  1 .Bb  2.5 2

 1  0,28 Bb  0,083 D B  b   2  0,065 cu

Where: qpr = reduced unit toe-bearing resistance qp = unit toe-bearing resistance Bb = diameter at base of foundation D = depth of embedment

cu = undrained shear strength in the soil between the base of the foundation and a depth 2Bb below the base 

Reese and O’Neill (1999) recommend the following function for end bearing in cohesionless soils which base diameter of drilled shaft is less than 1200 mm and with N60 ≤ 50: q p  57,5.N 60  ( 4300 kPa )

Where: qp = unit end bearing capacity (kPa) N60 = N-SPT value corrected for field procedures between toe and a depth of 2Bb below the toe Bb = base diameter of drilled shaft If N60 > 50, the ground is classified as an intermediate geo-material Shaft with base diameters larger than about 1200 mm, require about 60 mm of settlement to develop the “full” toe-bearing resistance as defined by O’Neill and Reese. Shaft with larger base diameters may experience excessive settlements, especially if toe bearing represents a large portion of the total capacity. There are two ways to deal with this problem by reducing the unit toe-bearing resistance and perform the settlement analysis to adjust the design so the settlement under working loads within tolerable limits. 1200 qp Bb

q pr 

Where: qpr = reduce of unit end bearing capacity qp = unit end bearing capacity Bb = base diameter of drilled shaft 

According to Meyerhof (1976), the unit end (point or tip) resistance qp in tons per square feet (tsf) of driven piles in cohesionless soils can be estimated by the following relationship :  0,4.N ' avg 

q p   

B

 .Df   4.N ' avg . tsf   

Where: qp = unit end bearing capacity (tsf), this value should be multiplied by a conversion factor of 95,8 to obtain qp in kPa N’avg = average N-SPT value corrected for field procedures and overburden test near the pile tip B = base diameter of pile Df = depth of pile into granular stratum, which is the pile length (L) in homogeneous cohesionless soils Intermediate geo-material is a new term used to describe hard soils and soft rocks. O’Neill and Reese (1999) define them as cohesive or cemented materials, such as shale or mudstones, with 250 kPa < cu < 2500 kPa or non-cohesive materials, such as glacial till, with N60 > 50. These

materials can be difficult to evaluate because they have engineering properties between those of soil and rock. For cohesive intermediate geo-material and rock we know the RQD (Rock Quality Designation). RQD is a measure of the integrity of rock or intermediate geo-material obtained from coring. It is computed by summing the lengths of all pieces of the core (NX size) equal to or longer than 4 in. (10 cm) and dividing by the total length of the core run. The RQD is multiplied by 100 and expressed as a percentage. When calculating the RQD, only the natural fractures should be counted and any fresh fractures due to the sampling process should be ignored. RQD measurements can provide valuable data on the quality of the in situ rock mass, and can be used to locate zones of extensively fractured or weathered rock. The mass rock quality can be defined as follows: o RQD = 0 – 25%, rock quality is defined as very poor o RQD = 25 – 50%, rock quality is defined as poor o RQD = 50 – 75%, rock quality is defined as fair o RQD = 75 – 90%, rock quality is defined as good o RQD = 90 – 100%, rock quality is defined as excellent In addition to determining the type of rock, it is often important to determine the quality of the rock, which is related to its degree of weathering, defined as follows: o Fresh, no discoloration or oxidation. o Slightly Weathered, discoloration or oxidation is limited to surface of, or short distance from, fractures; some feldspar crystals are dull. o Moderately Weathered, discoloration or oxidation extends from fractures, usually throughout, Fe and Mg minerals are rusty and feldspar crystals are cloudy. o Intensely Weathered, discoloration or oxidation throughout; all feldspars and Fe and Mg minerals are altered to clay to some extent; or chemical alteration produces in situ disaggregation. o Decomposed, discolored or oxidized throughout, but resistant minerals such as quartz may be unaltered; all feldspars and Fe and Mg minerals are completely altered to clay. The unconfined compressive strength (qu) is usually measured in the laboratory on core samples using a technique similar to that for measuring the compressive strength of concrete. This value also is equal to twice the undrained shear strength, cu. O’Neill and Reese use the RQD and the unconfined compressive strength between the bottom of the foundation and a depth of about 2B below the bottom to evaluate toe-bearing resistance.  Cohesive Intermediate Geo-material and Rock – If RQD = 100% and the foundation extends to a depth of at least 1,5B into the intermediate geo-material or rock q p  2,5.q u

Where: qp = unit end bearing capacity qu = unconfined compressive strength

–

If 70% < RQD < 100%, all joints are closed (i.e., not containing voids are soft infill material) and nearly horizontal, and qu > 500 kPa q p  4830.(q u ) 0.51

Where: qp = unit end bearing capacity qu = unconfined compressive strength –

If the material is jointed, the joints have random orientation, and the condition of the joints can be evaluated in the area or from test excavation:





q p  t 0,5  (m.t 0, 5  t ) 0,5 .qu

Where m and t are determined from tables below: Table 20.

Description of Rock and Intermediate Geo-material Types (O’Neill and Reese, 1999) Rock or Intemediate Descreption Geomaterial Type A Carbonate rocks with well-developed crystal cleavage (e. g., dolostone, limestone, marble) B Lithified argillaeous rocks (e. g., mudstone, siltstone, shale, slate) C Arenaceous rocks (e. g., sandstone, quartz) D Fine-grained igneous rocks (e. g., andesite, dolerite, diabase, rhyolite) E Coarse-grained igneous and metamorphic rocks (e. g., amphibole, gabro, gneiss, granite, norite, quartz diorite)

Table 21.

Quality of Rock or Intermediate Geomaterial Excellent

m Joint Descreption

Very Good Good Fair Poor Very Poor



Values of m and t (O’Neill and Reese, 1999)

Intact (closed) Interlocking Slightly weathered Moderately weathered Weathered with gouge Heavily weathered

Joint Spacing

t

Type A

Type B

Type C

Type D

Type E

> 3m

1

7

10

25

17

25

1 – 3m

0.1

3,5

5

7,5

8,5

12,5

1 – 3m

0.04

0,7

1

1,5

1,7

2,5

0,1 – 1m

10-4

0,14

0,2

0,3

0,34

0,5

30 – 300mm

10-5

0,04

0,05

0,08

0,09

0,13

< 50mm

0

0,007

0,01

0,015

0,017

0,025

Non-cohesive Intermediate Geo-material q p  0,59. ( N 1 ) 60 

0,8

. ' zD

Where: qp = unit end bearing capacity (N1)60 = N-SPT value corrected for field procedures and overburden stress ≤ 100 σ’zD = vertical effective stress at base of foundation

The purpose of this section is to provide a brief introduction to rock classification. There are three basic types of rocks: igneous, sedimentary and metamorphic. Because of their special education and training, usually the best person to classify rock is the engineering geologist. Below a simplified rock classification and common rock types: Simplified Rock Classification Common igneous rocks Major division Secondary divisions Rock types Extrusive Volcanic explosion debris (fragmental) Tuff (litihified ash) and volcanic breccia Lava flows and hot siliceous clouds Obsidian (glass), pumice and scoria Lava flows (fine-grained) texture Basalt, andesite and rhyolite Intrusive Dark minerals dominant Gabbro Intemediate (25-50% dark minerals) Diorite Light color (quartz and feldspar) Granite Common sedimentary rocks Major division Texture (grain size) or chemical composition Rock types Clastic rocks* Grain size lager than 2 mm (pebbles, gravel, Conglomerate (rounded cobbles) or cobbles, and boulders) breccia (angular rock fragments) Sand-size grains, 0.062 - 2 mm Sandstone Silt-sizq grains, 0.004 – 0.062 mm Siltstone Clay-size grains, less than 0.004 mm Claystone and shale Chemical and organic Carbonate minerals (e.g., calcite) Limestone rocks Halite minerals Rock salt Sulfate minerals Gypsum Iron-rich minerals Hematite Siliceous minerals Chert Organic products Coal Common metamorphic rocks Major division Structure (foliated or massive) Rock types Coarse crystalline Foliated Gneiss Massive Metaquartzite Medium crystalline Foliated Schist Massive Marble, quartzite, serpentine, soapstone Fine to microscopic Foliated Phyllite, slate Massive Hornfels, anthracite coal *Grain sizes correspond to the Modified Wentworth scale Table 22.

Hardness of rock versus unconfined compressive strength (Basic Soils Engineering (Hough, 1969); Engineering Geology Field Manual, 1987) Hardness qu Rock description Very soft 1 – 25 MPa The rock can be readily indented, grooved, or gouged with fingernail, or carved with a knife. Breaks with light manual pressure. The rock disintegrates upon the single blow of a geologic hammer Soft 25 – 50 MPa The rock can be grooved of gouged easily by a knife or sharp pick with light pressure. Can be scratched with a fingernail. Breaks with light to moderate manual pressure Hard 50 – 100 MPa The rock can be scratched with a knife or sharp pick with great difficulity (heavy pressure is needed). A heavy hammer blow is required to break the rock Very Hard 100 – 200 MPa The rock cannot be scratched with a knife or a sharp pick. The rock can be broken with several solid blows of a geologic hammer Extremelly hard >200 MPa The rock cannot be scratched with a knife or sharp pick. The rock can only be chipped with repeated heavy hammer blows NOTES: 1. Besides degree of weathering, a measure of the quality of rock is its hardness, which has been correlated with the unconfined compressive strength of rock specimens. Because the unconfined compressive strength is performed on small rock specimens, in most cases, it will not represent the actual condition of in situ rock. The

Table 23.

2.

reason is due to the presence of joints, fractures, fissures, and plane of weakness in the actual rock mass that govern its engineering properties, such as deformation characteristics, shear strength and permeability. The unconfined compressive test also does not consider other rock quality factors, such as its resistance to weathering or behavior when submerged in water. qu = unconfined compressive strength (MPa) of the rock.

Open-Section Foundations Open-section foundations are deep foundations that have poorly defined foundation-soil contacts. These include open-end steel pipe piles and steel H-piles. These poorly defined contacts make it more difficult to compute At (toe-bearing contact areas) and As (side-friction contact areas). When open-end pipe piles are driven, they initially tend to “cookie out” into the ground, and the toe-bearing area, At, is equal to the cross-sectional area of the steel. Soil enters the pipe interior as the pile advances downward. At some point, the soil inside the pile becomes rigidly embedded and begins moving downward with the pile. It has then become a soil plug, as shown in Figure below, and the toe-bearing area then becomes the cross-sectional area of the pile and the soil plug. In other words, the pile now behaves the same as a closed-end pipe (i.e., one that has a circular steel plate welded to the bottom). Many factors affect the formation of soil plugs (Paikowsky and Whitman, 1990; Miller and Lutenegger, 1997), including the soil type, soil consistency, in-situ stresses, pile diameter, pile penetration depth, method of installation, rate of penetration, and so forth. In open-end steel pipe piles, the soil plug may be considered rigidly embedded when the penetration-to-diameter ratio, D/B is greater than 10 to 20 (in clays) or 25 to 35 (in sands) (Paikowsky and Whitman, 1990). Many piles satisfy these criteria. Once they become plugged, open-end pipe piles have the same side-friction area, As, as closedend piles. Use only the outside of pipe piles when computing the side-friction area. Do not include the friction between the plug and the inside of the pile. With H-piles, soil plugging affects both toe-bearing and side-friction contact areas. The space between the flanges of H-piles is much smaller than the space inside pipe piles, so less penetration is required to form a soil plug. For analysis purpose, we usually can compute At and As in H-piles based on the assumption they become fully plugged as shown in Figure below. If open-section foundations are driven to bedrock, the relative stiffness of the steel, soil plug and bedrock are such that the toe-bearing probably occurs primarily between the steel and the rock. Therefore, in this case it is generally best to use At equal to the cross-sectional area of the steel, As, and ignore any plugging in the toe-bearing computations.

Figure 51.

Soil plugging in open-ended steel pipe piles and steel H-piles

Side Friction Then, the ultimate skin friction resistance (Qs) is determined as: Qs   f s . p.L

Where: Qs = ultimate skin friction resistance fs = unit skin friction resistance p = perimeter of bored pile / driven pile L = length of bored pile / driven pile In several cases the unit skin friction resistance (fs) could be obtained by using the equations below:  For cohesive soils, the unit skin friction (fs) is obtained based on -method equation:

f s   .cu  260 kPa

Where: fs = unit skin friction resistance  = factor of adhesion (refers to the sub-chapter “adhesion factor” before) cu = undrained shear strength In clays, the side-friction resistance within 1,5 m (5 ft) of the ground surface should be ignored because of clay shrinkage cause by drying, foundation movement produced by lateral loads, pile wobble during driving, and other factors. 

For cohesionless soils, the unit skin friction (fs) is obtained based on -method (Burland, 1973): f s   . 'v  190 kPa

Where: fs = unit skin friction resistance (kPa) β = betha factor σ’v = vertical effective stress at base of foundation For drilled shaft in sand with N60  15, O’Neill and Reese (1999) recommends:   1,5  0,245 z

If N60 < 15, multiply the  values obtained from equation above by the ratio N60/15. And the  values should be 0,25 ≤  ≤ 1,20 Then, the unit skin friction of a driven pile in cohesionless soils is given by the following relationship (Meyerhof, 1976, 1983) : fs 

N ' avg 50

 1 tsf

Where: fs = unit skin friction (tsf), this value should be multiplied by a conversion factor of 95,8 to obtain fs in kPa N’avg = average N-SPT value corrected for field procedures and overburden test This function reaches its limits at depths of 1.5 m and 26 m, so layer boundaries should be placed at these two depths. Another boundary should be placed at the ground water table. Additional boundaries should be placed every 6 m and where the sand strata end and it becomes necessary to begin using clay or rock analyses. Rollins, Clayton, and Mikesell (1997) used a series of full-scale static load tests to develop a revised version of equation derived from O’Neill and Reese (1999) in gravels (>50% gravel size):   3,4.e 0 , 085. z

And the  values should be 0,25 ≤  ≤ 3,0 For gravelly sands (25-50% gravel size):   2,0  0,15.z 0, 75

And the  values should be 0,25 ≤  ≤ 1,80 Where: fs = unit skin friction resistance z = depth below ground surface (m) ’v = vertical effective stress e = base of natural logarithms = 2,718

 for piles in gravelly soils also should be 20 to 30 percent higher than that in sandy soils. Reese and O’Neill’s (1989) also ignore the skin friction resistance in the upper 5 ft (1,5 m) of the shaft and along the bottom one diameter of straight shaft because of interaction with the end bearing. Analyses Based on CPT Results Engineers also have developed analytic methods based on cone penetration test (CPT) results. These methods are very attractive because of the similarities between the CPT and the load transfer mechanism in deep foundations. The cone resistance, qc, is very similar to the unit toebearing resistance, qp, and the cone side friction, fsc, is very similar to the unit side-friction resistance, fs. The CPT is essentially a miniature pile load test, and was originally developed partially as a tool for predicting pile capacities. Although we still must use empirical correlations to develop design values of qp and fs from CPT data, these correlations should be more precise than those based on parameters that have more indirect relationships to deep foundations. Eslami and Fellinius method (Eslami and Fellinius, 1997) takes advantage of the additional data gained through the use of a piezocone (also known as CPTU test) which is a standard CPT probe equipped with a piezometer to measure the pore water pressure near the cone tip while the test is in progress. This pore water pressure is the sum of the hydrostatic pore water pressure (such as could be measured using a conventional stationary piezometer) and any excess pore water pressure induced by the advancing cone. In sandy soils, the excess pore water pressure is usually very small, but in clays it can be large. The Eslami and Fellinius method requires application of an additional pore water pressure correction to the qT values as follows: q E  qT  u 2

Where: qE = effective cone resistance qT = corrected cone resistance u2 = pore water pressure measured behind the cone point This correction is intended to more closely align the analysis with the effective stresses. In sands, u2 should be approximately equal to the hydrostatic pore water pressure. Therefore, this method

could still be used in sands even if only conventional CPT data (i. e., no pore pressure data) is available, so long as the position of the groundwater table is known and no artesian conditions are present. Toe Bearing Toe bearing failures occur as a result of punching and local shear, and thus affect only the soils in the vicinity of the toe. Therefore, the analysis considers only the qE values in the following zones:  For piles installed through a weak soil and into a dense soil: 8B above the pile toe to 4B below the pile toe  For piles installed through a dense soil and into a weak soil: 2B above the pile toe to 4B below the pile toe In both cases, B is the pile diameter. The geometric average, qEg, of the n measured qE values within the defined depth range is then computed using: q Eg 

( q E )1 .( q E ) 2 .(q E ) 3 ...(q E ) n n

In general, odd spikes or troughs in the qE data should be included in the computation of qEg. However, extraordinary peaks or troughs might be “smoothed over” if they do not appear to be representative of the soil profile. For example, occasional gravel in the soil can produce false spikes. The unit toe-bearing resistance has then been empirically correlated with qEg using the load test results: q p  C t .q Eg

Where: qp = unit toe-bearing qEg = geometric average effective cone resistance Ct = toe-bearing coefficient Eslami and Fellinius recommend using Ct = 1 for pile foundations in any soil type. In addition, unlike some other methods, they do not place any upper limit on qp. Side Friction A side-friction analysis is performed for each CPT data point using the following equation: f s  C s .q E

Where: fs = unit side-friction qE = effective cone resistance

Cs

= side-friction coefficient (from table below) Side-Friction Coefficient, Cs (Eslami and Fellinius, 1997) Cs Soil Type Range Typical Design Value Soft sensitive soils 0,0737 – 0,0864 0,08 Clay 0,0462 – 0,0556 0,05 Stiff clay or mixture of clay and silt 0,0206 – 0,0280 0,025 Mixture of silt and sand 0,0087 – 0,0134 0,01 Sand 0,0034 – 0,0060 0,004 Table 24.

The Cs value depends on the soil type, and should be selected using Table above. And the soil classification may be determined directly from the CPT data using figure below.

Figure 52.

Soil Classification from CPT Data (Eslami and Fellinius, 1997)

Because CPT data is typically provided at depth intervals of 100 to 200 mm, this procedure is too tedious to use at every data point when performing computations by hand. Therefore, hand computations usually divide the soil between the ground surface to the pile tip into layers according to the CPT results, with a representative qE for each layer. For most soil profiles, five to ten layers are sufficient. Preboring (Engineering Manual, EM 1110-2-2906) A pilot or prebore hole may be required to penetrate hard nonbearing strata; to maintain accurate location and alignment when passing through materials which tend to deflect the pile; to avoid possible damage to adjacent structures by reducing vibrations; to prevent heave of adjacent buildings; or to remove a specified amount of soil when installing displacement-type piles,

thereby reducing foundation heave. Preboring normally takes place in cohesive soils and is usually required when concrete piles must penetrate man-made fills and embankments containing rock particles or other obstructions. It should be noted that on past Corps projects, concrete piles have been successfully driven through man-made fills such as levee embankments without preboring. Preboring through cohesionless soils is not recommended, since the prebored hole may not stay open and could require a casing. The most widely used method of preboring is by utilizing an auger attached to the side of the crane leads. When preboring is permitted, the hole diameter should not be grater than two-thirds the diameter or width of the pile and not extend more than three-fourths the length of the pile. Oversizing the hole will result in a loss of skin friction and a reduction in the axial capacity and lateral support, thereby necessitating reevaluation of the pile foundation. When extensive preboring is needed, consideration should be given to using a drilled-shaft system rather than a driven-pile system. Spudding (Engineering Manual, EM 1110-2-2906) Spudding is similar to preboring and may be appropriate when layers or obstructions are present near the surface that would damage the pile or present unusual driving difficulty. Spudding is accomplished by driving a spud, such as mandrel, heavy steel pipe or H-pile section, to provide a pilot hole. The spud is withdrawn and the pile inserted into the hole and driven to the required depth. Problems may result if the spud is driven too deep, since extraction becomes more difficult as penetration is increased. Spudding may sometimes entail alternately lifting a partially driven pile a short distance and redriving it when very difficult driving is encountered (e.g. for heavy piles). Because this procedure adversely affects the soil’s lateral and axial capacity, it should be avoided for friction piles and should never be permitted without the specific authoriztion of the design engineer. Pullout Capacity Pullout capacity is pile ability to hold working tensile force. If some or all of the foundation is beneath the ground water table, substract the bouyancy force from the unsubmerged weight to obtain Wf. The bouyancy force equals the submerged volume of the foundation multipiled by the unit weight of water. Formulation of uplift load capacity: Pau  0,9W f 

Rf s As F

Where: Pau = net allowable upward axial load R = reduction factor F = factor of safety fs = unit skin friction resistance As = skin friction contact area Wf = pile weight For foundation with a D/B ratio greater than 6, set the reduction factor R equal to 1. This means that the ultimate skin friction resistance of long foundations is equal in both upward and

downward loading. However, for shorter foundations, a cone of soil may form, as shown in Figure below, thus reducing the skin friction resistance (Kulhawy, 1991). Pu If D/B > 1 and  > 1 Cone breakout condition adjacent to a deep foundation loaded in uplift (Kulhawy, 1991)

R

2 3

Where:

     .cu /  ' D

= average  factor along length of foundation = average  factor along length of  foundation = average undrained shear strength along cu 

length of foundation  ' D = vertical effective stress at tip of foundation

Figure 53.

Pullout Reducing

Group Efficiency The proper spacing of piles in the group is important. If they are too close (i.e., less than 2,0-2,5 diameter or 600 mm on center), there may not be enough room for errors in positioning and alignment. Conversely, if the spacing is too wide, the pile cap will be very large and expensive. Therefore, piles are usually spaced 2,5 to 3,0 diameters on center. The interactions between piles in a group and the adjacent soil are very complex, and the ultimate capacity of the group is not necessarily equal to the ultimate capacity of a single isolated pile multiplied by the number of piles. The effect of these interactions on the axial load capacity is called the group efficiency, which depends on several factors, including the following : 1. The number, length, diameter, arrangement, and spacing of the piles 2. The load transfer mode (side friction vs. end bearing) 3. The construction procedures used to install the piles 4. The sequence of installation of the piles 5. The soil type 6. The elapsed time since the piles were driven 7. The interaction, if any, between the pile cap and the soil 8. The direction of the applied load Engineers compute the allowable downward load capacity of pile groups using a group efficiency factor, η, as follows : Pag   .N .Pa

Where: Pag = allowable downward or upward capacity of pile group η = group efficiency factor

N Pa

= number of piles in a group = allowable downward or upward capacity of a single isolated pile

Converse-Labarre formula (Bolin,1941):   1 .

(n  1).m  (m  1).n 90.m.n

Where: η = group efficiency factor m = number of rows of piles n = number of piles per row θ = tan-1 (B/s) (expressed in degrees) B = diameter of a single pile s = center to center spacing of piles (not the clear space between piles) Another approach is to compare individual failure with block failure. Individual failure means the soil between the piles remains stationary and the individual piles punch through it, whereas block failure means the soil moves with the piles, thus failing as a large single unit. Presumably block failure governs if the sum of the perimeters of the piles is greater than the circumference of the pile group, and the group efficiency factor is assumed to be the ratio of these two perimeters: 

2.s.(m  n)  4.B 1  .m.n.B s

a. Individual Failure Figure 54.

b

b. Block Failure

Typical of Group Failures

Although research conducted thus far has provided many insights, the behavior of pile groups is still somewhat mysterious, and no comprehensive method of assessing group action has yet been developed. Therefore, we must use the available information, along with engineering judgment and conservative design methods to develop design values of the group efficiency factor, η. Hannigan et. al. (1997) recommends the following guide-lines for pile groups:

In Sands:  So long as no pre-drilling of jetting is used, the piles are at least 3 diameters in center, and the group is not underlain by weak soils, use η = 1.  Avoid pre-drilling or jetting whenever possible, because the methods can significantly reduce the load capacity. If these methods must be used, they should be carefully controlled.  If a pile group founded on a firm bearing stratum of limited thickness is underlain by a weak deposit, then the ultimate group capacity is the smaller of either the sum of the ultimate capacities of the individual piles, or the group capacity against block failure of an equivalent foundation consisting of the pile group and the enclosed soil mass punching through the underlying weak soil.  Piles should be installed at center-to-center spacing of at least 3 diameters. In Clays:  Use a center-to-center spacing of at least 3 pile diameters.  Use the following procedure to estimate the allowable capacity of the pile group : o If the undrained shear strength, su, is less than 95 kPa and the pile cap is not in firm contact with the ground, use equation Pag   .N .Pa with η = 0,7 for groups with center-to-center spacing of 3 diameters, and η = 1 with center-to-center spacing of 6 diameters or more. For intermediate spacing, linearly interpolate between these two values. o If the undrained shear strength, su, is greater than 95 kPa, use equation Pag   .N .Pa with η = 1 regardless of whether of not the cap is on contact with the soil. o Compute the group capacity against block failure using the following formula : Pag  2.D.( B g  L g ).s u1  B g .L g .s u 2 .N c*

D   B   N c*  5. 1   . 1   9 5 . B 5 .L    

Where: Pag = allowable downward load capacity Bg = width of pile group Lg = length of pile group D = depth of embedment of pile group su1 = weighted average of undrained shear strength in clays over depth of embedment su2 = average undrained shear strength between the bottom of the pile group and a depth 2 Bg below the bottom Nc* = bearing capacity factor Use the lowest of the applicable values from steps 1 to 4. Because of the excess pore water pressure produced by pile driving, the short-term ultimate capacity of pile groups in saturated clay will be reduced to about 0,4 to 0,8 times the ultimate value. However, as these excess pore water pressures dissipate, the ultimate capacity will increase. The rate at which it rises depends primarily on the dissipation of excess pore water pressure. Small groups will probably reach long-term η within 1 to 2 months, which may be faster than the rate of loading, whereas larger groups may require a year or more. If the group will be subjected to the full design load before the excess pore water pressure fully o 

dissipate, then a more detailed analysis may be warranted. In some cases, it may be appropriate to install piezometers to monitor the dissipation of excess pore water pressures. Suggested minimum centre-to-centre pile spacing by several building codes are as follows : Table 25.

Pile type Friction Point bearing

BOCA, 1993 (Sec. 1013.8) 2D or 1.75H ≥ 760 mm 2D or 1.75H ≥ 610 mm

Pile spacing requirement NBC, 1976 (Sec. 912.1l) 2D or 1.75H ≥ 760 mm 2D or 1.75H ≥ 610 mm

Chicago, 1994 (Sec. 13-132-120) 2D or 2H ≥ 760 mm

Here D = pile diameter; H = diagonal of rectangular shape or HP pile. The BOCA code also stipulates that spacing for friction piles in loose sand or loose sand-gravels shall be increased 10 percent for each interior pile to a maximum of 40 percent. Optimum spacing s seems to be on the order of 2.5 to 3.5D or 2 to 3H for vertical loads; for groups carrying lateral and/or dynamic loads, larger pile spacings are usually more effecient. Maximum pile spacings are not given in building codes, but spacings as high as 8 or 10D have been used on occasion. Settlements The classical method is based on the assumption that settlement is a one-dimensional process in which all of the strains are vertical. This assumption is accurate when evaluating settlement beneath the center of wide fills, but it less accurate when applied to shallow foundations, especially spread footings, because their loaded area is much smaller. Therfore, Skempton and Bjerrum (1957) presented another method of computing the total settlement of shallow foundations. This method accounts for three-dimensional effects by dividing the settlement into two components: 1. Distortion settlement, d (also called immediate settlement, initial settlement, or undrained settlement), is that caused by the lateral distortion of the soil beneath the foundation. This settlement is similar to that which occurs when a load is placed on a bowl of Jello@, and occurs immediately after application of the load.

Figure 55.

2.

Distortion settlement beneath a spread footing

Consolidation settlement, c (also known as primary consolidation settlement), is that caused by the change in volume of the soil that results from changes in the effective stress.

In actual condition, pore water stress dissapate into lateral direction. Then, Skempton and Bjerrum (1957) proposed a 3-dimensional adjusment coeficient () as a correction factor for lateral direction. 3-D Dimentional Adjustment Coefficient ( ) Table 26. Soil Type Typical OCR Very sensitive clays 1,0 NC clays and silts 1,0 – 1,2 OC clays and silts 1,2 – 5 Heavily OC clays and silt >5

Figure 56.

 1,0 – 1,2 0,7 – 1,0 0,4 – 0,7 0,3 – 0,6

 factors for Skempton and Bjerrum method (Adopted from Loenards, 1976)

According to Skempton and Bjerrum’s method, the settlement of a shallow foundation is computed as :    e   . c

Where : δ = settlement δe = elastic settlement δc = consolidation settlement  = three-dimensional settlement Induced Stresses Due To A Concentrated Load In 1885, Boussinesq developed the mathematical relationships for determining the normal and shear stresses at any point inside homogeneous, elastic, and isotropic mediums due to a concentrated point load located at the surface. According to his analysis, the vertical stress increase at point A caused by a point load of magnitude P is given by

 

3.P   r  2. .z . 1     z 

5



2

2

2

 

Where: r 

x2  y 2

x, y, z = coordinates of the point A

Vertical stress at a point A caused by a point load on the surface

Figure 57.

Induced Stresses Due To A Circularly Loaded Area The Boussinesq equation above can also be used to determine the vertical stress below the cinter of a flexible circularly loaded area. Let the radius of the loaded area be B/2, and let q 0 be the uniformly distributed load per unit area. To determine the stress increase at a point A, located at a depth z below the center of the circular area, consider an elemental area on the circle. The load on this elemental area may be taken to be appoint load and expressed as q 0r dθ dr. The stress increase at A caused by this load can be determined as d 

3. q 0 .r .d .dr    r 2. .z . 1     z 

5



2

2

2

 

The total increase in stress caused by the entire loaded area may be obtained by integrating the equation above, or

3. q 0 .r .d .dr 

B

   d  02 rr 0 2

  r  2. .z . 1     z 

5



2

2



2

 

 

 1    q 0 . 1     B     1   2z   

Figure 58.

   2



3

 

 

2

 

Increase in pressure under a uniformly loaded flexible circular area

Induced Stresses Below A Rectangular Area The integration technique of Boussinesq’s equation also allows the vertical stress at any point A below the corner of a flexible rectangular loaded area to be evaluated. To do so, consider an elementary area dA = dx dy on the flexible loaded area. If the load per unit area is q 0, the total load on the elemental area is dP  q 0 .dx.dy

This elemental load, dP, may be treated as a point load. The increase in vertical stress at point A caused by dP may be evaluated by using equation “stress due to a concentrated load”. Note, however, the need to substitute dP = q0 dx dy for P and x 2 + y2 for r2 in that equation. Thus, the

stress increase at A caused by dP 

3.q 0 . dx.dy .z 3

2. . x 2  y 2  z 2 

5

2

Determination of stress below the corner of a flexible rectangular loaded area

Figure 59.

The total stress increase  caused by the entire loaded area at point A may now be obtained by integrating the preceding equation:

  

L B y  0 x 0



3.q 0 . dx.dy .z 3

2. . x  y  z 2

2

2



5

2

 q 0 .I

Here, I = influence factor =

1 4

 2.m.n. m 2  n 2  1 m 2  n 2  2 2.m.n. m 2  n 2  1  . . 2  tan 1 2 2 2 2 2 2  m  n  m .n  1 m  n  1 m  n 2  1  m 2 .n 2  

When m2 + n2 +1 < m2n2, the argument of tan-1 becomes negative. In that case, I = influence factor =

Where m  And n 

L z

B z

 1  2.m.n. m 2  n 2  1 m 2  n 2  2 2.m.n. m 2  n 2  1  1  . 2 .  tan    4  m  n 2  m 2 .n 2  1 m 2  n 2  1 m 2  n 2  1  m 2 .n 2    





The stress increase at any point below a rectangular loaded area can also be found by using equation above in conjuction with Figure below. To determine the stress at a depth z below point O, divide the loaded area into four rectangles, with O the corner common to each. Then use the equation above to calculate the increase in stress at a depth z below O caused by each rectangular area. The total stress increase caused by the entire loaded are may now be expressed as

  q 0 . I 1  I 2  I 3  I 4  Where I1, I2, I3, and I4 = the influence values of rectangles 1, 2, 3, and 4, respectively

Figure 60.

Stress below any point of a loaded flexible rectangular area

In most cases, the vertical stress below the center of a rectangular area is of importance. This can be given by the relationship   q 0 .I c

Where I c 

m1 

n1 

2  .   

m1.n1 1  m12  n12

.

1  m12  n12  m1 1  1  n12 . m12  n12    sin m12  n12 . 1  n12

B z

z  B    2

Foundations engineers often use an approximate method to determine the increase in stress with depth caused by the construction of a foundation. The method is referred to as the 2:1 method. According to this method, the increase in stress at depth z is

 

q 0 .B.L  B  z . L  z 

Note that equation above is based on the assumption that the stress from the foundation spreads out along lines with a vertical-to-horizontal slope of 2:1.

Figure 61.

2:1 method of finding stress increase under a foundation

Stress Increase Under An Embankment Figure below shows the cross section of an embankment of height H. For this two deimensional loading condition, the vertical stress increase may be expressed as

 

q0  .  

  B1  B2  B   .  1   2   1 .  2   B2   B2 

Where: q0 = γ.H γ = unit weight of the embankment soil H = height of the embankment  B  B2   B   1  tan 1  1   tan 1  1  z    z   B   2  tan 1  1   z  (Note that α1 and α2 are in radians.)

Figure 62.

Embankment loading

Induced Stresses Beneath Shallow Foundations (Simplified Method) The Boussinesq equations are tedious to solve by hand, so it is useful to have simple approximate methods of computing stresses in soil for use when a quick answer is needed, or when a computer is not available. The following approximate formulas compute the induced vertical stress, σz, beneath the center of a shallow foundation. They produce answers that are within 5 percent of the Boussinesq values, which is more than sufficient for virtually all practical problems. For circular foundations (adapted from Poulos and Davis, 1974):  











1, 50







 

1

 z   1      B  1    2. z   f   

 . q   ' vD  



 

2

 



 



 



For square foundations:  









1, 76

 

   

1

 z   1      B  1    2. z   f   

 . q   ' vD  



 

2





 

 

  

For continuous foundations of width B:

 









 z



2 , 60

 



1   1     B  1    2.z   f   

 

 . q   ' vD    

2

 

 

 

 

 

For rectangular foundations of width B and length L:  





 

z

2 , 60  0 ,84. B

 



  1      1    



B   2. z f 

1, 38  0 , 62. B

   





1 



L

 . q   ' vD   

L



   

 

Where: σz = induced vertical stress beneath the center of a foundation B = width or diameter of foundation L = length of foundation zf = depth from bottom of foundation to point q = bearing pressure σ'zD = vertical effective stress at a depth D below the ground surface

Figure 63.

Distribution of induced stress, σz, in layered strata

Immediate Settlement of Shallow Foundation – Based On Laboratory Tests The elastic settlement of a shallow foundation can be estimated by using the theory elasticity. e 





q max .B . 1   2 I3 Eu

Where: e = elastic settlement qmax = maximum bearing pressure stress

B L Eu 

= width of foundation = length of foundation = undrained modulus elasticity of soil = poisson’s ratio of the soil Table 27.

Soil Type Clay

Typical values of Poisson’s ratio ( ) Description  Soft 0,35 – 0,40 Medium 0,30 – 0,35 Stiff 0,20 – 0,30

Sand

 1 I3  .    m1 n1 z

Loose Medium Dense

 1  m 2  n 2  1 1 1  ln  m1 . ln     2 2 2 2  1  m1  n1  m1   1  m1  n1  1 

0,15 – 0,25 0,25 – 0,30 0,30 – 0,35



 1 m 2  n 2  m  1 1 1 

  

= L/B = z/B = depth of foundation embedment

Total of elastic settlement would be the subtraction of each elastic settlement which have been determined while foundation embedded at depth equal with z and at depth = 0 from the existing ground level.

Janbu, Bjerrum, and Kjaernsli (1956) first proposed this formula : e 

q max .B .I1.I 2 Eu

Where: e = elastic settlement qmax = maximum bearing pressure stress B = width of foundation I1, I2 = influence factors Eu = undrained modulus elasticity of soil Since then, Christian and Carrier (1978) revised the procedure and Taylor and Matyas (1983) shed additional light on its theoretical basis. The updated influce factors (I1 and I2) are shown in Figure below.

Figure 64.

Influence factors I1 and I2 (Adapted from Christian and Carrier, 1978)

Immediate Settlement of Deep Foundation 

Single Pile

Reese and O’Neill (1999) developed the charts in Figures below to estimate the settlement of drilled shafts under service loads. These charts express the settlement in terms of the ratio of the mobilized resistance to the actual resistance. These charts provide a useful guide for estimating short-term settlement. Elastic settlement of deep foundation can be computed using : P.z c e  A.E Where: e = settlement due to elastic compression of foundation P = downward load on each foundation zc = depth to centroid of soil resistance (typically about 0,75D)

E = modulus of elasticity of the foundation = 4700. f c' MPa for concrete = 200.000 MPa for steel A = cross-sectional area of the foundation

Figure 65.

Normalized Curves for Drilled Shafts in Clay

Figure 66.

Normalized Curves for Drilled Shafts in Sand

After trialing several settlements () for both of base settlement and shaft settlement by using the chart above in which will provide the closest value to the working loads (also possible to do a linear interpolation for more accurate adjusment). Then the total settlement would be:  adj     e

Where: adj = total settlement of foundation  = settlement due to base settlement and shaft settlement e = settlement due to elastic compression of foundation 

Pile Groups

The settlement of pile group is exactly equal to the displacement of the pile plus the elastic shortening of the pile shaft between cap and point.  G   adj

B (Vesic, 1977) D

Where: G = group settlement adj = single pile settlement B = width of pile group D = pile diameter Primary Consolidation Settlement – Classical Method Certain conditions can produce excessive settlements for deep foundation design, so the the engineer must be able to recognize and evaluate them. These include the following :  The structure is especially sensitive to settlement.  The foundation has a large diameter and a large portion of the allowable capacity is due to toe bearing.  One or more highly compressible strata are present, especially if these strata are below the toe.  Downdrag loads might develop during the life of the structure.  The engineer must express the pile response in terms of an equivalent “spring” located at the bottom of the column. This analytical model is used in some sophisticated structural analyses.

Figure 67.

Imaginary Footing To Compute Settlement Of A Deep Foundation Group (Tomlinson,1977)

The imaginary footing method computes the settlement of a deep foundation group by replacing it with an imaginary footing, as shown in Figure above. This method is especially useful when the design consists of a group of deep foundations that are underlain by compressible soils such that the compression of these soils is more significant than the settlements required to mobilize the side friction and toe bearing. For foundations that rely primarily on side friction, place the imaginary footing at a depth of 0,67 D (where D is the depth of embedment). For foundations that rely principally on toe bearing, place it at the toe elevation. When both side friction and toe bearing are significant, use linear interpolation to place the imaginary footing between these two positions. Then use the techniques described later below to compute the settlement of the imaginary footing, and add the elastic compression of the foundations, e, using the equation which has been discussed before, with zc = the depth zi to the imaginary footing. This method also consider settlements produced by causes other than the structural loads on the piles. For example, the construction process may include lowering the ground water table, which increases the effective stress in the soil and thus create settlement.

A one-dimensional (1-D) consolidation test is widely used to obtain the settlement and time parameters. A 1-D test confines the soils laterally in a metal ring so that the settlement and drainage can occur only in the vertical direction. These condition are reasonably close to what occurs in situ for most loading cases. Actually some radial displacement and lateral drainage probably occur but, based on experience, these appear to be small enough that a 1-D analysis gives adequate accuracy in most cases. These equation below are directly applicable for normally consolidated soils:   C c H    H    1 e 0   

 p  p  0    p 0  







 log

  

Where: ΔH = settlement PI 74

Cc

= compression index 

e0 H

= in situ void ratio in the stratum where Cc was obtained = stratum thickness. If the stratum is very thick (say > 6 m) it should be subdevided into several sublayers of Hi = 2 to 3 m, with each having its own e0 and Cc. Compute the several values of ΔHi and then sum them to obtain the total consolidation settlement = effective overburden pressure at midheight of H = average increase in pressure from the foundation loads in layer H and in the same units as for p’0

p’0 Δp

for OC clays, based on Kulhawy and Mayne (1990)

When the soil is preconsolidated they should be adjusted as follows. Taking the stress increase as: Δp = Δp1 + Δp2 Where Δp2 is any part of Δp that is along Cc zone to the right of p’c, we have the total settlement consisting of two parts, that from p0 to p’c and that (if any) from more than p’c. These are computed as follows:

Figure 68.

Consolidation Chart for Determining Cc,Cr or p’c

Part 1 : p'  p Cr.H log 0 1  e0 p' 0

H 1 

p' 0  p1  p' c

Where: = recompression index 

Cr

PI for OC clays, based on Kulhawy and Mayne (1990) 370

Part 2 : H 2 

p '  p 2 Cc.H log c 1  e0 p'c

 p 2  p  p'c  0

The total primary consolidation settlement is: H p  H1  H 2

Therefore, settlement caused by primary consolidation is calculated by using formula as follow:

p0'  p H  c  Cc log 1  e0 p0'

 c  Cr

p '  p H log 0 ' 1  e0 p0

(for NC clays)

(for OC clays with po'+  p < pc’)

p c' p 0'  p H H  c  Cr log '  C c log 1  e0 1 e 0 p0 p c'

(for OC clays with po’ < pc’ < po’ +  p)

Where: Cc = compression index, Cr = swelling index, H = thickness of the clay layer, eo = initial void ratio, pc’ = preconsolidation pressure, p = average increase of pressure on clay layer caused by foundation construction (and fill), po’ = average effective pressure on clay layer before foundation construction Table 28.

Cc Cc = 0.046 + 0.0104 IP Cc = 0.009 wN + 0.005 wL

Compression index, Cc Requirements Source Best for IP < 50 % Nakase et al. (1988) All clays Koppula (1986)

Notes : Use IP, wN, wP, wL as percent, not decimal. Table 29.

Cr Cr = 0.00194 (IP – 4.6) Cr = 0.05 to 0.1 Cc

Recompression index, Cr Requirements Source Best for IP < 50 % Nakase et al. (1988) In desperation Leonards (1976)

Notes : Use IP, wN, wP, wL as percent, not decimal.

We compute the consolidation settlement by dividing the soil beneath the foundation into layers, computing the settlement of each layer, and summing. The top of first layer should be at the bottom of the foundation, and the bottom of the last layer should be at a depth such that σz < 0,10 σ’z0. Unless the soil is exceptionally soft, the strain below this depth is negligible, and thus may be ignored. Table 30.

Approximate thickness of soil layers for manual computation of consolidation settlement of shallow foundations Approximate Layer Thickness Layer Number Square Footing Continuous Foooting 1 B/2 B 2 B 2B 3 2B 4B

Notes: 1. Adjust the number and thickness of the layers to account for changes in soil properties. Locate each layer entirely within one soil stratum. 2. For rectangular footings, use layer thicknesses between those given for square and continuous footings. 3. Use somewhat thicker layers (perhaps up to 1,5 times the thicknesses shown) if the groundwater table is very shallow. 4. For quick, but less precise, analyses, use a single layer with a thickness of about 3B (square footings) or 6B (continuous footing).

Similar to solutions for shallow foundations, charts have been developed for estimating the distribution of stress beneath deep foundations. Figures below show the pressure distributions for pile foundations for four different soil conditions. Friction piles in CLAY

The upper left figure shows the pressure distribution for a pile group embedded in clay. The load P that the pile cap supports is the first turned into an applied stress q by using the following equation: q 0 

n.Qall P  B. A B. A

Where: q = σ0 = vertical stress applied by the deep foundation at a depth of (2/3)L L = length of the piles P = total concentric vertical load on the pile cap. The maximum load the pile cap can support is n times Qall n = number of piles that support the pile cap Qall = allowable vertical load for each pile B = width of the pile group, taken to the outside edge of the group A = length of the pile group, taken to the outside edge of the group In essence, the 2:1 approximation starts at a depth of (2/3)L below ground surface. In figure below, it is assumed that there is a hard layer located below the clay. In this case, the compression or consolidation of the clay would be calculated for the thickness of H as defined in the upper left diagram of figure. Friction piles in SAND underlain by CLAY The upper right diagram in figure shows the pile group embedded in sand with two underlying clay layers. For this situation, two conditions would have to be evaluated. The first is a bearing capacity failure of the pile group where it punches through the sand and into the upper soft clay layer. The second condition is the compression or consolidation of the two clay layers located below the pile group. Similar to the case outlined above, the 2:1 approximation is used to calculate the increase in vertical stress σz due to the pile cap loading for the two clay layers. Point bearing piles in SAND underlain by CLAY The lower left diagram in figure shows the condition of a soft clay layer underlain by a sand stratum. The sand stratum provides most of the vertical resistance and hence the pile group is considered to be point bearing (also known as end bearing). For this case, the 2:1 approximation is assumed to start at the top of the sand layer and is used to calculate the increase in vertical stress σz due to the pile cap loading for the soft clay layer. Friction piles in CLAY with RECENT FILL The lower right diagram in figure shows the condition of piles embedded in clay with the recent placement of a fill layer at ground surface. In this case, the piles woll be subjected to a downdrag load due to placement of the fill layer. The 2:1 approximation is assumed to start at a distance of L3 below the top of the clay layer, where L3 = (2/3)L2. The value of q applied at this depth includes two additional terms, the first is the total weight of fill t times the thickness of the fill L1 and the second is the downdrag load converted to a stress, defined as (n AD)/(B A). If the pile caps are spaced close together, there could be additional settlement as the pressure distribution from one pile cap overlaps with the pressure distribution from a second nearby pile cap.

Figure 69.

Pressure distribution for deep foundations (NAVFAC DM-7.2, 1982)

Secondary Consolidation Settlement At the end of primary consolidation (i.e., after the complete dissipation of excess pore water pressure) some settlement is observed that is due to the plastic adjustment of soil fabrics. This stage of consolidation is called secondary consolidation. A plot of deformation against the logarithm of time during secondary consolidation is practically linear as shown in figure. From this figure, the secondary compression index can be defined as

C 

e  log t 2   log t 1 

e  t  log 2   t1 

Where: Cα = secondary compression index e = change of void ratio t1, t2 = time

Figure 70.

Variation of e with log t under a given load increment, and definition of secondary compression index Table 31.

Cα Cα = 0.00168 + 0.00033 IP Cα = 0.0001 wN Cα = 0.032 Cc Cα = 0.06 to 0.07 Cc Cα = 0.015 to 0.03 Cc

Secondary compression index, Cα Requirements Source Nakase et al. (1988) NAFAC DM7.1 p. 7.1-237 0.025 < Cα < 0.1 Mesri and Godlewski (1977) Peats and organic soil Mesri (1986) Sandy clays Mesri et al. (1990)

Notes : Use IP and wN as percent, not decimal.

The magnitude of the secondary consolidation can be calculated as  t  S c ( s )  C '  .H c . log 2   t1 

Where: C’α = Cα/(1+ep) ep = void ratio at the end of primary consolidation (see figure above) Hc = thickness of clay layer The general magnitudes of C’α as observed in various natural deposits are given in figure below.

Figure 71.

C’α for natural soil doposits (after Mesri, 1973)

Secondary consolidation settlement is more important in the case of all organic and highly compressible inorganic soils. In overconsolidated inorganic clays, the secondary compression index is very small and of less practical significance. There are several factors that might affect the magnitude of secondary consolidation, some of which are not yet very clearly understood (Mesri, 1973). The ratio of secondary to primary compression for a given thickness of soil layer is dependent on the ratio of the stress increment, ’, to the initial overburden stress, ’0. For small ’/’0 ratios, the secondary-to-primary compression ratio is larger. Settlement Analyses (Schmertmann’s Method) – Based On In-Situ Tests The second category of settlement analysis techniques consists of those based on in-situ tests. Most of these analyses use results from the standard penetration test (SPT) or the cone penetration test (CPT). However, other in-situ tests, especially the dilatometer test (DMT) and the pressuremeter test (PMT) also may be used. 

Equivalent Modulus of Elasticity

The classical method of computing foundation settlements described the stress-strain properties using the compression index, Cc, for normally consolidated soils, or the recompression index, Cr, for overconsolidation soils. Both of these parameters are logarithmic. Schmertmann’s method uses the equivalent modulus of elasticity, Es, which is a linear function and thus simplifies the computations. However, soil is not a linear material (i.e., stress and strain are not proportional), so the value of Es must reflect that of an equivalent unconfined linear material such that the computed settlement will be the same as in the real soil. The design value of Es implicitly reflects the lateral strains in the soil. Thus, it is larger than the modulus of elasticity, E (also known as Young’s Modulus), but smaller than the confined modulus, M. 

Table 32.



Es from Cone Penetration Test (CPT) results Schmertmann developed empirical correlations between Es and the cone resistance, qc, from a cone penetration test (CPT). This method is especially useful because the CPT provides a continuous plot of qc vs. depth, so our analysis can model Es as a function of depth. Table below presents a range of recommended design values of Es/qc. It is usually best to treat all soils as being young and normally consolidated unless there is compelling evidence to the contrary. Such evidence might include: 1. Clear indications that the soil is very old. This might be established by certain geological evidence. 2. Clear indications that the soil is overconsolidated. Such evidence would not be based on consolidation tests on the sand (because of soil sampling problems), but might be based on consolidation tests performed on samples from interbedded clay strata. Alternatively, overconsolidation could be deduced from the origin of the soil deposit. For example, lodgement till and compacted fill are clearly overconsolidated. Es-values from CPT results {adapted from Schmertmann, et al. (1978), Robertson and Campanella (1989), and other sources} USCS Soil Type Group Es/qc Symbol Young, normally consolidated clean silica sands (age < 100 years) SW or SP 2,5 – 3,5 Aged, normally consolidated clean silica sands (age > 3000 years) SW or SP 3,5 – 6,0 Overconsolidated clean silica sands SW or SP 6,0 – 10,0 Normally consolidated silty or clayey sands SM or SC 1,5 Overconsolidated silty or clayey sands SM or SC 3

Es from Standard Penetration Test (SPT) results Schmertmann’s method also may be used with Es values based on the standard penetration test. However, these values are not as precise as those obtained from the cone penetration test because: 1. The standard penetration test is more prone to error, and is less precise measurement. 2. The standard penetration test provides only a series of isolated data points, whereas the cone penetration test provides a continuous plot.

Nevertheless, SPT data is adequate for many projects, especially those in which the loads are small and the soil conditions are good. Several direct correlations between Es and N60 have been developed, often producing widely disparate results (Anagnostopoulos, 1990; Kulhawy and Mayne, 1990). This scatter is probably caused in part by the lack of precision in the SPT, and in part to the influence of other factors beside N60. Nevertheless, the following relationship should produce approximate, if somewhat conservative, values of Es: E s   0 . OCR   1 .N 60

Where: Es = equivalent modulus of elasticity 0, 1 = correlation factors from table below OCR = overconsolidation ratio N60 = SPT N-value corrected to field procedures Once again, most analyses should use OCR = 1 unless there is clear evidence of overconsolidation.  0,  1 factors 0 Soil Type (kPa) Clean sands (SW and SP) 5000 Silty sands and clayey sands (SM and SC) 2500 Table 33.



1 (kPa) 1200 600

Strain Influence Factor Schmertmann conducted extensive research on the distribution of vertical strain, z, below spread footings. He found the greatest strains do not occur immediately below the footing, as one might expect, but at a depth of 0,5B to B below the bottom of the footing, where B is the footing width. This distribution is described by the strain influence factor, Ie, which is a type of weighting factor. The distribution of Ie with depth has been idealized as two straight lines, as shown in figure below:

Distribution of strain influence factor with depth under square and continuous footings (Adapted from Schmertmann 1978; used with permission of ASCE)

Figure 72.

The peak value of the strain influence factor, Iep, is: I ep  0,5  0,1.

q   ' zD  ' zp

Where: Iep = peak strain influence factor q = bearing pressure σ’zD = vertical effective stress at a depth D below the ground surface σ’zp = initial vertical effective stress at depth of peak strain influence factor For square and circular foundation (L/B = 1), compute σ’zp at a depth of {D+(B/2)} below the ground surface. For continuous footing (L/B  10), compute σ’zp at a depth of (D+B) below the ground surface. The exact value of Ie at any given depth may be computed using the following equations:  Square and circular foundations (L/B = 1): For zf = 0 to B/2 : I e  0,1   z f B . 2.I ep  0,2 

For zf = B/2 to 2B : I e  0,667.I ep . 2  z f B 



Continuous foundations (L/B  10): For zf = 0 to B :

I e  0,2   z f B . I ep  0,2 

For zf = B to 4B : I e  0,333.I ep . 4  z f B 



Rectangular foundations (1 < L/B < 10): I e  I es  0,111 . I ec  I es . L B  1

Where: zf = depth from bottom of foundation to midpoint of layer Ie = strain influence factor Iec = Ie for a continuous foundation Iep = peak Ie Ies = Ie for a square foundation Schmertmann’s method also includes empirical corrections for the depth of embedment, secondary creep in the soil, and footing shape. These are implemented through the factors C 1, C2, and C3:   ' zD C1  1  0,5.  q   ' zD   



t   0  ,1 

C 2  1  0,2. log

C 3  1,03  0,03. L B  0,73

Where:  = settlement of footing C1 = depth factor C2 = secondary creep factor C3 = shape factor = 1 for square and circular foundations q = bearing pressure σ’zD = vertical effective stress at a depth D below the ground surface Ie = influence factor at midpoint of soil layer H = thickness of soil layer Es = equivalent modulus of elasticity in soil layer t = time since application of load (yr) (t 0,1 yr) B = foundation width L = foundation length These formulas may be used with any consistent set of units, except that t must be expressed in years. If no time is given, use t = 50 yr (C2 = 1,54).

Finally, this information is combined using the following formula to compute the settlement, :

  C1 .C 2 .C 3 . q   ' zD . 

I e .H Es

Analysis Procedure The Schmertmann method uses the following procedures: 1. Perform appropriate in-situ tests to define the subsurface conditions. 2. Consider the soil from the base of the foundation to the depth of influence below the base. This depth ranges from 2B for square footings or mats to 4B for continuous footings. Divide this zone into layers and assign a representative E s value to each layer. The required number of layers and the thickness of each layer depend on the variations in the E vs. depth profile. Typically 5 to 10 layers are appropriate. 3. Compute the peak strain influence factor, Iep. 4. Compute the strain influence factor, Ie, at the midpoint of each layer. 5. Compute the correction factors, C1, C2, and C3. 6. Compute the settlement.

Pile Foundation Analyses Under Lateral Load Lateral capacity analysis of bored pile is using computer program LPILE Plus 4.0 (Ensoft, 1980). This program use load transfer method and assume that soil reaction is nonlinear under lateral load. When designing deep foundaions, we divide these loads into two categories: axial loads and lateral loads. Axial loads are those that act parallel to the axis of the foundation; lateral loads are those that act perpendicular to the axis. Thus, if the axis is vertical, the applied uplift and downward loads from the structure induce axial loads in the foundation, whereas applied shear and moment loads induce lateral loads. Torsional loads are rarely a concern in deep foundation design. The type of connection between the pile and the structure is also important because it determines the kinds of restraint, if any, acting on the pile. Engineers usually assume that one of the following conditions prevails:  The free-head condition, means that the top of the pile may freely move laterally and rotate when subjected to shear and/or moment loads.  The restrained-head condition (also known as the fixed-head condition), means that the top of the pile may move laterally, but is not pemitted to rotate. Piles connected to a very stiff pile cap closely approximate this condition.  The pure moment condition, occurs when there is an applied moment load, but no applied shear load. It results in rotation of the top of the pile, but no lateral movement.

Figure 73.

Lateral Movement Under Load Combination

Pile failure mode is determined as two part. First, failure as a short pile and second one as a long pile. A short foundation is one does not have enough embedment to anchor the toe against rotations, whereas a long foundation is one in which the toe is essentially fixed. Inclination point for long pile is depend on load combinations. In general, flexible foundations, such as timber piles, are long if D/B greater than about 20, while stiffer foundations, such as those made of steel or concrete, typically require D/B greater than about 35. The ultimate lateral capacity of short foundations is controlled primarily by the soil. In other words, the soil fails before the foundation reach its flexural capacity. Conversely, the ultimate lateral capacity of long foundations is controlled primarily by the flexural strength of the foundation because it will fail structurally before the soil fails. And the lateral deflection is only occured at pile cap. For further information can be seen on the illustration below:

Figure 74.

Load Transfer of Pile Group

Pile Failure Mode

The axial tension or compression load at a depth z in a foundation subjected to axial and/or lateral load is: P1 

Pg n



M gx .y i n

 yi2

i 1



M gy .x i n

 xi 2

i 1

Figure 75.

Load Transfer of Pile Groups

Where: P1 = axial or compression load for each pile Pg = subjected axial load from the upper structure n = number of pile Mgx = moment which occured in x-direction Mgy = moment which occured in y-direction y = distance from neutral axis in y-direction x = distance from neutral axis in x-direction Those formula is used to transfer the moment loads into axial loads. This calculation is required by the LPile program to defined the internal forces such as lateral deflection, moments, and shear force. Then, the internal force will be used to determine the reinforcement and confinement design. LIQUEFACTION ANALYSIS

The typical subsurface condition that is susceptible to liquefaction is a loose or very loose sand that has been newly deposited or placed, with a groundwater table near ground surface. During an earthquake, the ground shaking causes the loose sand to contract, resulting in an increase in pore water pressure. Because the seismic shaking occurs so quickly, the cohesionless soil is subjected to an undrained loading (total stress analysis). The increase in pore water pressure causes an upward flow of water to the ground surface, where it emerges in the form of mud spouts or sand boils. The development of high pore water pressures due to the ground shaking (i.e., the effective stress becomes zero) and the upward flow of water may turn the sand into a liquefied condition, a process that has been termed liquefaction. Structures on top of a loose sand deposit that has liquefied during an earthquake will sink or fall over, and buried tanks will float to the surface when the loose sand liquefies (Seed 1970). Main factors that govern the liquefaction process : 1. Earthquake intensity and duration It is the earthquake induced shear strains and subsequent contraction of the soil particles that lead to the development of excess pore water pressures and ultimately liquefaction. Sites located near the epicenter of major earthquakes will be subjected to the largest intensity and duration of ground shaking (i.e., higher number of applications of cyclic shear strain). Besides earthquakes, other conditions can cause liquefaction, such as subsurface blasting. 2. Groundwater table The condition most conducive to liquefaction is a near-surface groundwater table. Unsaturated soil located above the groundwater table will not liquefy. 3. Soil type The soil types susceptible to liquefaction are nonplastic (cohesionless) soils. Seed et al. (1983) state that, on the basis of both laboratory testing and field performance, the great majority of clayey soils will not liquefy during earthquakes. An approximate listing of cohesionless soils from least to most resistant to liquefaction are clean sands, nonplastic silty sands, nonplastic silt, and gravels. 4. Soil relative density (Dr) Cohesionless soils in a very loose relative density state are susceptible to liquefaction while the same soil in a very dense relative density state will not liquefy. Very loose nonplastic soils will contract during the seismic shaking, which will cause the development of excess pore water pressures. Very dense soils will dilate during seismic shaking and are not susceptible to liquefaction. 5. Particle size gradation Poorly graded nonplastic soils tend to form more unstable particle arrangements and are more susceptible to liquefaction than well-graded soils 6. Placement conditions Hydraulic fills (fill placed under water) are more susceptible to liquefaction because of the loose and segregated soil structure created by the soil particles falling through water. 7. Drainage conditions If the excess pore water pressure can quickly dissipate, the soil may not liquefy. Thus gravel drains or gravel layers can reduce the liquefaction potential of adjacent soil. 8. Confining pressures The greater the confining pressure, the less susceptible the soil is to liquefaction. Conditions that can create a higher confining pressure are a deeper groundwater table, soil that is located at a deeper depth below ground surface, and a surcharge pressure applied at a ground surface. Case studies have shown that the possible zone of liquefaction usually extends from the ground surface to a maximum depth about 15 m. Deeper soils generally do not liquefy because of the higher confining pressures.

9.

Aging Newly deposited soils tend to be more susceptible to liquefaction than old deposits of soil. Older soil deposits may already have been subjected to seismic shaking, or the soil particles may have deformed or been compressed into more stable arrangements.

The most common type of analysis to determine the liquefaction potential is to use the standard penetration test (SPT) or the cone penetration test (CPT) (Seed et al. 1985, Stark and Olson 1995). The analysis is based on the simplified method proposed by Seed and Idriss (1971). The first step in the liquefaction analysis is to determine the seismic shear stress ratio (SSR). The seismic shear stress ration (SSR) induced by the earthquake at any point in the ground is estimated as follows (Seed and Idriss 1971):

a SSR  0,65.rd . max 

 .  v 0  g    ' v 0 

Where : SSR = seismic shear stress ratio (dimensionless parameter) amax = peak acceleration measured or estimated at the ground surface of the site (m/s2) g = acceleration of gravity (9,81 m/s2) Ussually the engineering geologist will determine the peak acceleration at the ground surface at the site from fault, seismicity, and attenuation studies. Typically the engineering geologist provides a peak ground acceleration in the form of a max/g = a constant, in which case the value of a constant (dimensionless) is substituted into the above equation in place of amax/g. v0 = total vertical stress at a particular depth where the liquefaction analysis is being performed (kPa) ’v0 = vertical effective stress at that same depth in the soil deposit where v0 was calculated (kPa) rd = depth reduction factor, which can be estimated in the upper 10 m of soil as (Kayen et al. 1992) rd = 1 – 0,012z, where z = depth in meters below the ground surface where the liquefaction analysis is being performed (i.e., the same depth used to calculate v0 and ’v0) The second step is to determine the seismic shear stress ratio (SSR) that will cause liquefaction of the in situ soil. A chart (from Stark and Olson 1995) will be used to determine the seismic shear stress ratio (SSR) that will cause liquefaction of the in situ soil. In order to use this chart, the results of the standard penetration test (SPT) must be expressed in terms of the N’-SPT value. So that, the corrected value (Liao and Whitman, 1985), N’-SPT is: N '  C N .N 60

Where: N’ = N-SPT value corrected for field procedures and overburden stress CN = overburden correction factor Liao and Whitman’s relationship (1986):

C N  9,78.

1 for  ' v  25 kN / m 2  'v

Skempton’s relationship (1986): 2 CN  for  ' v  25 kN / m 2  'v 1 9,78 Seed et al.’s relationship (1975):   'v  C N  1  1,25. log  for  ' v  25 kN / m 2 9 , 78   Peck et al.’s relationship (1974): 

 20    'v       9,78 

 for  '  25 kN / m 2 v





C N  0,77. log

  

We can improve the raw SPT data by applying certain correction factors. The variations in testing procedures may be at least partially compensated by converting the measured N to N60 as follows (Skempton, 1986): N 60 

Em Cb Cs Cr N N60  ’v Pa

E m .C b .C s .C r .N 0,60

= hammer efficiency (for U.S. equipment, E m equals 0,6 for safety hammer and equals 0,45 for a doughnut hammer) – Adapted from Clayton, 1990 = borehole diameter correction (Cb = 1,0 for boreholes of 65 to 115 mm diameter ; 1,05 for 150 mm diameter ; 1,15 for 200 mm diameter of hole) – Adapted from Skempton, 1986 = sampling method correction (Cs = 1,00 for standard sampler ; 1,20 for sampler without liner – not recommended) – Adapted from Skempton, 1986 = rod length correction (Cr = 0,75 for up to 4 m of drill rods ; 0,85 for 4 to 6 m of drill rods ; 0,95 for 6 to 10 m of drill rods ; 1,00 for drill rods over 10 m) – Adapted from Skempton, 1986 = N-SPT value from field test = N-SPT value corrected for field procedures = vertical effective stress at the test location = reference stress = 100 kN/m2

Once the corrected N’-SPT has been calculated, the chart can be used to determine the seismic shear stress ratio (SSR) that will cause liquefaction of the in situ soil. For a given N’-SPT value, soils with more fines have a higher seismic shear stress ratio (SSR) that will cause liquefaction of the in situ soil. As an alternative to the second step, the cone penetration test (CPT) can be used instead of the standard penetration test (SPT). The procedure consists of multiplying the cone penetration tip resistance qc by a correction factor Cq to account for the overburden pressure, in order to calculate the corrected CPT tip resistance qc1, or:

q c1  C q .q c 

1,8.qc '  0,8   v 0  100  

Where : qc1 = corrected CPT tip resistance (corrected for the overburden pressure) Cq = correction factor to account for the overburden pressure ’v0 = vertical effective stress in kPa qc = cone penetration tip resistance Once the corrected CPT tip resistance qc1 has been calculated, the chart can be used to determine the seismic shear stress ratio (SSR) that will cause liquefaction of the in situ soil. For a given q c1 value, soils with more fines have a higher seismic shear stress ratio (SSR) that will cause liquefaction of the in situ soil. The third step in the liquefaction analysis is to compare the seismic shear stress ratio (SSR) values. If the SSR induced by the earthquake is greater than the SSR value obtained from the chart, then liquefaction could occur during the earthquake, and vice versa. When in fact the entire analysis is only a gross approximation, the analysis should be treated as such and engineering experience and judgment are essential in the final determination of whether or not a site has liquefaction potential.

Note: M = 7,5 is equal 6,7 Richter. BMS (Vehicle Load)

Figure 76.

Vehicle load based on BMS

Dynamic Driving Resistance (Pile Driving Formula) The two methods of estimating ultimate capacity of piles on the basis of dynamic driving resistance are pile-driving formulas and wave equation analysis. Pile capacities based on piledriving formulas are not always reliable. They should therefore be supported by local experience or testing and should be used with caution. Pile capacities estimated on the basis of wave equation analysis have more rational approach than the estimation on the basis of pile driving formulas. Pile hammers are the devices used to impart sufficient energy to the pile so that it penetrates the soil. Several pile hammers are described in the following paragraph. a. Drop hammers Drop hammers are still occasionally used for small, relatively inaccessible jobs. The drop hammer consists of a metal weight fitted with a lifting hook and guides for traveling down the leads (or guides) with reasonable freedom and alignment. The hook is connected to a cable, which fits over a sheave block and is connected to a hoisting drum. The weight is lifted and tripped, freely falling to a collision with the pile. The impact drives the pile into the ground. Principal disadvantages are the slow rate of blows and length of leads required during the early driving to obtain a sufficient height of fall to drive the pile. b. Single-acting hammers Steam or air pressure is used to lift the ram to the necessary height. The ram then drops by gravity onto the anvil, which transmits the impact energy to the capblock, then to the pile. The hammer is characterized by a relatively slow rate of blows. The hammer length must be such as to obtain a reasonable impact velocity (h or height of ram fall), or else the driving energy will be small. The blow rate is considerably higher than that of the drop hammer. In general the ratio of ram weight to pile weight including appurtenances should be on the order of 0.5 to 1.0.

c.

Double-acting hammers These hammers use steam both to lift the ram and to accelerate it downward. Differentialacting hammers are quite similar except that more control over the steam (or air) is exerted to maintain an essentially constant pressure (nonexpansion) on the accelerating side of the ram piston. This increase in pressure results in a greater energy output per blow than with the conventional double-acting hammer. The blow rate and energy output are usually higher for double-acting or differential hammers (at least for the same ram weight), but steam consumption is also higher than for the single-acting hammer. The length may be a meter or more shorter for the double-acting hammer than for the single-acting hammer with length ranges on the order of 2 to 4.5 m. The ratio of ram weight to pile weight should be between 0.50 and 1. When compressed air instead of steam is used with single- or double-acting hammers, there is the additional problem of the system icing up at temperatures close to freezing.

d.

Diesel hammers Diesel hammers consist of a cylinder or casing, ram, anvil block, and simple fuel injection system. To start the operation, the ram is raised in the field as fuel is injected near the anvil block, then the ram is released. As the ram falls, the air and fuel compress and become hot because of the compression; when the ram is near the anvil, the heat is sufficient to ignite the air-fuel mixture. The resulting explosion (1) advances the pile and (2) lifts the ram. If the pile advance is very great as in soft soils, the ram in not lifted by the explosion sufficiently to ignite air-fuel mixture on the next cycle, requiring that the ram be again manually lifted. It is thus evident that the hammer works most efficiently in hard soils or where the penetration is quite low (point-bearing piles when rock or hardpan is encountered) because maximum ram lift will be obtained. Diesel hammers are highly mobile, have low fuel consumption (on the order of 4 to 16 L/hr), are lighter than steam hammers, and operate efficiently in temperatures as low as 0C. There is no need for a steam or air supply generation unit and the resulting hoses. The diesel hammer has a length varying from about 3.5 to 8.2 m (4.5 to 6 m average). The ratio of ram weight should be on the order of 0.25 to 1.0.

e.

f.

Jetting or preaugering A water jet is sometimes used to assist in inserting the pile into the ground. That is, a highpressure stream of water is applied at the pile point to displace the soil. This method may be used to loosen sand or small gravel where for some reason the pile must penetrate to a greater depth in the material than necessary for point bearing. Care must be exercised that the jetting does not lower the point-bearing value. Some additional driving after the jet is halted should ensure seating the point in firm soil. Preaugering is also sometimes used where a firm upper stratum overlies a compressible stratum, which in turn overlies firmer material into which it is desired to seat the pile point. Preaugering will reduce the driving effort through the upper firm material. For both jetting and preaugering, considerable engineering judgment is required to model the dynamic pile capacity equations (and static equations) to the field system. Vibratory hammers

Pile driving leads, sometimes called leaders, are usually fabricated of steel and function to align the pile head and hammer concentrically, maintain proper pile position and alignment continuously during the driving operation, and also to provide lateral support for the pile when required. Proper hammer alignment is extremely important to prevent eccentric loadings on the pile. Otherwise driving energy transferred to the pile may be reduced considerably and structural pile damage due to excessive stresses near the top of the pile may result from eccentric loading. Typical lead systems are shown below :

Figure 77.

Typical fixed or extended leads

Figure 78.

Typical swinging lead system

To develop the desired load-carrying capacity, a point bearing pile must be penetrate the dense soil layer sufficiently or have sufficient contact with a layer of rock. This requirement cannot always be satisfied by driving a pile to a predetermined depth, because soil profiles vary. For that reason, several equations have been developed to calculate the ultimate capacity of a pile during driving. These dynamic equations are widely used in the field to determine whether a pile has reached a satisfactory bearing value at the predetermined depth. One of the earliest such equations – commonly reffered to as the Engineering News (EN) Record formula – is derived from the work – energy theory. That is, Energy imparted by the hammer per blow = (pile resistance) (penetration per hammer blow) W R .h  Qu .S

Equation above is quite inappropriate, however, because it does not include a number of practical considerations, for example :  Energy loss due to friction  Energy loss due to pile bounce  Energy loss due to compression of hammer parts  Energy loss due to compression of pile  Uncertainties in soil response  Uncertainties in pore water response  Nonuniformity of pile resistance along shaft  Nonuniformity of pile resistance at tip A widely used (and abused) formula, originally developed for end-bearing piles driven through soft soil sediments in New Jersey, is the Engineering News Record (ENR) formula. It assumes the losses are a constant, C, which allows for the following equation for ultimate pile capacity :

Qu 

W R .h S C

Where : WR = weight of the ram h = height of fall of the ram S = penetration of pile per hammer blow C = a constant The pile penetration, S, is usually based on the average value obtained from the last few driving blows. In the equation’s original form, the following values of C were recommended :  For drop hammers, C = 25,4 mm if S and h are in mm ; 1 in. if S and h are in inches 

For steam hammers, C = 2,54 mm if S and h are in mm ; 0,1 in. if S and h are in inches

Also, a factor of safety FS = 6 was recommended for estimating the allowable pile capacity. Note that, for single- or double-acting hammers, the term WR h can be replaced by E HE, where E is the efficiency of the hammer and HE is the rated energy of the hammer. Thus, Qu 

E.H E S C

The EN formula has been revised several times over the years, and other pile-driving formulas also have been suggested. Some of them are showed below : 

Modified EN formula (use SF = 6) Qu 

2 1,25.eh .H E WR  n .W p . or S C WR  W p

Qu 

2 1,25.W R .h WR  n .W p . S C WR  W p

Where : eh = efficiency of hammer HE = rated energy of the hammer h = height of fall of the ram C = 25,4 mm if the units of S and h are in mm or 1,0 in. if the units of S and h are in in. (for drop hammers) C = 2,54 mm if the units of S and h are in mm or 0,1 in. if the units of S and h are in in. (for steam hammers) Wp = weight of the pile WR = weight of the ram S = penetration of pile per hammer blow n = coefficient of restitution between the ram and the pile cap h = height of ram fall Typical values of eh

Single-acting hammers Double-acting or differential hammers Diesel hammers Drop hammers

0,70 – 0,85 0,85 0,80 – 0,90 0,70 – 0,90

Typical values for n (After ASCE - 1941) Broomed wood Wood piles (nondeteriorated end) Compact wood cushion on steel pile Compact wood cushion over steel pile Steel-on-steel anvil on either steel or concrete pile Cast-iron hammer on concrete pile without cap

0,00 0,25 0,32 0,40 0,50 0,40

The Hiley equation is obtained (use SF = 4) :  



  W r  n 2 .W p  .  s  1 . k  k  k    W r  W p 1 2 3 2   e h .W r .h

Pu  

  

Values for k1 – temporary elastic compression of pile head and cap (After Chellis, 1961) Driving stress P/A on pile head or cap, MPa (ksi) Pile Material 3,5 (0,5) 7,0 (1,0) 10,5 (1,5) 14,0 (2,0) k1, mm (in.) Steel piling or pile Directly on head 0 0 0 0 Directly in head of timber pile 1,0 (0,05) 2,0 (0,10) 3,0 (0,15) 5,0 (0,20) Precast concrete pile with 3,0 (0,12) 6,0 (0,25) 9,0 (0,37) 12,5 (0,50) 75-100 mm packing inside cap Steel-covered cap containing wood 1,0 (0,04) 2,0 (0,05) 3,0 (0,12) 4,0 (0,16) packing for steel HP or pipe piling 5-mm fiber disk between two 0,5 (0,02) 1,0 (0,04) 1,5 (0,06) 2,0 (0,08) 10-mm steel plates

Table 34.

Note :  For driving stresses larger than 14 MPa use k1 in last column  Where P is equal with working weight of hammer (around 1,68 to 2,28 times of Ram weight), should be provided by manufacturers. The term k2 is computed as

Pu .L , and one may arbitrarily take the k3 term (quake) as : A.E

k3 = 0,0 for hard soil (rock, very dense sand, and gravels) = 2,5 to 5 mm (0,1 to 0,2 in.) For double-acting or differential steam hammers, Chellis (1941, 1961) suggested the following form of the Hiley equation : 



  W  n 2 .W p   .   s  1 . k  k  k    W  W p  1 2 3   2

Pu  



e h .E h

According to Chellis, the manufacturer’s energy rating of Eh is based on an equivalent hammer weight term W and height of ram fall h as follows : E h  W .h  W r  W ca sin g .h

Inspection of the derivation of the Hiley equation indicates the energy loss fraction should be modified to W as shown in Hiley equation also. A careful inspection of the Hiley equation, together with a separation of terms, result in Energy in = work + impact loss + cap loss + pile loss + soil loss e h .W r .h  Pu .s  eh .W .h.

W p .1  n 2  W p  Wr

 Pu .k 1  Pu .k 2  Pu .k 3

For small wood piles on the order of 100 to 150 mm used to support small buildings on soil with a water table at or very near the ground surface Yttrup et al. (1989) suggest using : Pu 

0,4.W .h s

Where : W = weight of the ram h = height of fall of the ram S = penetration of pile per hammer blow This formula is applicable for drop hammers mounted in small conventional tractors.

Plug Weight. Open-end pipe piles always cut a soil plug. The plug usually does not fill the pipe when observed from above since it is much compressed both from vibration and from side friction on the interior walls. The plug weight can be estimated as : W plug   '.V pipe

Where Vpipe = internal pipe volume. This weight may be critical when the pile is nearly driven to the required depth since it is a maximum at that time. HP piles will also have a plug of unknown dimensions; however, it would not be a great error to assume the plug length Lplug is one-half the embedded length of the pile (when blow counts are taken for pile capacity of for penetration resistance). The plug weight is this case is : W plug  0,5.L pile .bf .d . '

This equation includes the web tw and flange thickness tf in the soil volume but the plug length is an estimate, so the computation as shown is adequate. Use effective unit weight γ’ for the soil, as the water will have a floatation effect for both the soil and the pile. The “pile” weight should be the actual weight Wp plus plug, or W p  W p  W plug

for use in any of the equations given that uses a pile weight term Wp.

The plug weight was not included in the past because few persons ever checked the derivation of the equations to see how the pile weight term was treated. Do not include the plug weight unless the equation you are using includes the pile weight in a term similar to the second term in the Hiley equation. A major problem with using statistical analyses primarily based on piles reported in technical literature is that although on can obtain a large data base it is not of much value. The reason is that there are not sufficient data given for the reader to make a reliable judgment of significant parameters to consider. Where the person making the analysis uses a self-generated data base (as in the case of Gates) results are generally more reliable. Table 35.

Summary of safety factor range for equations used in the Michigan Pile Test Program Upper and lower limits of SF = Pu/Pd Formula Range of Pu, kips 0 to 900 900 to 1800 1800 to 3100 Engineering News 1,1 – 2,4 0,9 - 2,1 1,2 – 2,7 Hiley 1,1 – 4,2 3,0 – 6,5 4,0 – 9,6 Pacific Coast Uniform Building Code 2,7 – 5,3 4,3 – 9,7 8,8 – 16,5 Redtenbacher 1,7 – 3,6 2,8 – 6,5 6,0 – 10,9 Eytelwein 1,0 – 2,4 1,0 – 3,8 2,2 – 4,1 Navy-McKay 0,8 – 3,0 0,2 – 2,5 0,2 – 3,0 Rankine 0,9 – 1,7 1,3 – 2,7 2,3 – 5,1 Canadian National Building Code 3,2 – 6,0 5,1 – 11,1 10,1 – 19,9 Modified Engineering News 1,7 – 4,4 1,6 – 5,2 2,7 – 5,3 Gates 1,8 – 3,0 2,5 – 4,6 3,8 – 7,3 Rabe 1,0 – 4,8 2,4 – 7,0 3,2 – 8,0

Note: 1 kips = 4,536 kN General Comments On Pile Driving Alignment of piles can be difficult to get exactly correct, and often the driven piles are not exactly located in plan. A tolerance of 50 to 100 mm is usually considered allowable. Larger deviations may require additional substructure design to account for eccentricities, or more piles may have to be driven. Alignment of pipe piles may be checked by lowering a light into the tube. If the light source disappears, the alignment is not true. Pile groups should be driven from the interior outward because the lateral displacement of soil may cause excessively hard driving and heaving of already driven piles. Damage to piles may be avoided or reduced by squaring the driving head with the energy source. Appropriate pile-driving caps and/or cushions should be used. When the required driving resistance is encountered, driving should be stopped. These driving resistances may be arbitrarily taken as : Table 36.

Blow per 25 mm penetration requirement to avoid pile damage Pile Type Blow per 25 (mm) Penetration Timber piles 4–5 blows/25 mm Concrete piles 6–8 blows/25 mm Steel piles 12–15 blows/25 mm Driving stress requirement to avoid pile damage Pile Type Requirements Timber piles 0,7 fu

Table 37.

Concrete piles Steel piles

0,6 f’ c 0,85 fy

Plate Load Test (Shallow Foundation) The ultimate load-bearing capacity of a foundation, as well as the allowable bearing capacity based on tolerable settlement considerations, can be effectively determined from the field load test, generally referred to as the plate load test (ASTM, 2000; Test Designation D-1194-94). The plates that are used for tests in the field are usually made of steel and are 25 mm (1 in.) thick and 150 mm to 762 mm (6 in. to 30 in.) in diameter. Occasionally, square plates that are 305 mm x 305 mm (12 in. x 12 in.) are also used. To conduct a plate load test, a hole is excavated with a minimum diameter of 4B (B is the diameter of the test plate) to a depth of D f, the depth of the proposed foundation. The plate is placed at the center of the hole, and a load that is about one-fourth to one-fifth of the estimated ultimate load is applied to the plate in steps by means of a jack. A schematic diagram of the test arrangement is shown in figure below. During each step of the application of the load, the settlement of the plate is observed on dial gauges. At least one hour is allowed to elapse between each application. The test should be conducted until failure, or at least until the plates has gone through 25 mm (1 in.) of settlement. Figure below shows the nature of the load-settlement curve obtained from such tests, from which the ultimate load per unit area can be determined.

Figure 79.

Test arrangement for Plate Load Test

Figure 80.

Nature of load – settlement curve

For tests in clay, qu  F   qu  P 

Where: qu(F) = ultimate bearing capacity of the proposed foundation qu(P) = ultimate bearing capacity of the test plate From the equation above implies that the ultimate bearing capacity in clay is virtually independent of the size of the plate. The ultimate load is defined as the point where the load displacement becomes practically linear. For tests in sandy soils, qu  F   qu  P  .

BF BP

Where: BF = width of the foundation BP = width of the test plate The allowable bearing capacity of a foundation, based on settlement considerations and for a given intensity of load, q0, is SF  SP .

and

BF BP

(for clayey soil)

 2.BF S F  S P .  BF  BP

2







(for sandy soil)

The preceding relationship is based on the work of Terzaghi and Peck (1967). D’Appolonia et al. (1970) compiled several field-test results in sandy soils to establish the applicability of equation for Sandy Soil, and these are summarized in Figure below. On the basis of the results, it can be said that equation above is a fairly good approximation.

Figure 81.

Comparison of test results with equation for Sandy Soil (After D’Appolonia et. Al., 1970)

Pile-Load Test The most reliable method to determine the load capacity of a pile is to load-test it. This consists in driving the pile to the design depth and applying a series of loads by some means. The usual procedure is to drive several of the piles in a group and use two or more of adjacent piles for reactions to apply the load. A rigid beam spans across the test pile and is securely attached to the reaction piles. A large-capacity jack is placed between the reaction beam and the top of the test pile to produce the test load increments. The test has been standardized as ASTM D 1143; however, local building codes may stipulate the load increments and time sequence.

Figure 82.

Typical pile load test setup using adjacent piles in group of reaction

The ultimate pile load is commonly taken as the load where the load-settlement curve approaches a vertical asymptote. The load-settlement curve must be drawn to a suitably large settlement scale so that the shape (and slope) is well defined. An alternative method of interpreting load-settlement curve is based on the concept that the load is carried mostly by skin resistance until the shaft slip is sufficient to mobilize the limiting value. When the limiting skin resistance is mobilized, the point load increases nearly linearly until the ultimate point capacity is reached. At this point further applied load results in direct settlement (load curve becomes vertical).

Figure 83.

Pile load-test data

Referring to figure 28 (Pile load test data), these statements translate as follows : 1. From 0 to point a the capacity is based on the skin resistance plus any small point contribution. The skin resistance capacity is the principal load-carrying mechanism in this region. Point a usually requires some visual interpretation since there is seldom a sharp break in the curve. 2. From point a to b the load capacity is the sum of the limiting skin resistance (now a constant) plus the point capacity 3. From point b the curve becomes vertical as the ultimate point capacity is reached. Often the vertical asymptote is anticipated (or the load to some value is adequate) and the test terminated before a “vertical” curve branch is established. This concept was introduced by Van Weele (1957) and has since been used by others [e.g., Brierley et al. (1979), Leonards and Lovell (1979), among others]. According to Van Weele, if we draw the dashed line 0 to c through the origin and parallel to the point capacity region from a to b, the load-carrying components of the pile are as shown on Fig. 28 (Pile load test data). In this figure we have at settlement δ = 25 mm the load carried as follows : Point = 250 kN Skin resistance = 1350 kN = 1600 – 250 kN Total = 1600 kN (shown on figure) Piles in granular soils are often tested 24 to 48 hr after driving when load test arrangements have been made. This time lapse is usually sufficient for excess pore pressures to dissipate; however, Samson and Authier (1986) show that up to a 70 percent capacity gain may occur if load tests are made two to three weeks after driving. Piles in cohesive soils should be tested after sufficient lapse for excess pre pressures to dissipate. This time lapse is commonly on the oreder of 30 to 90 days giving also some additional strength gain from thixotropic effects.

In any soil sufficient time should elapse before testing to allow partial dissipation of residual compression stresses in the lower shaft and point load from negative skin resistance on the upper shaft caused by shaft expansion upward as the hammer energy is released. Residual stersses and/or forces have been observed in a number of reports and summarized by Vesic (1977). It appears that pile load testing of the load-unload-reload type is more likely to produce residual stresses than driving. Soil Reinforcement The use of reinforced earth is a recent development in the design and construction of foundations and earth-retaining structures. Reinforced earth is a construction material made from soil that has been strengthened by tensile elements such as metal rods or strips, nonbiodegradable fabrics (geotextiles), geogrids, and the like. The beneficial effects of soil reinforcement derive from (a) the soil’s increased tensile strength and (b) the shear resistance developed from the friction at the soil-reinforcement interfaces. Such reinforcement is comparable to that of concrete structures. Currently, most reinforced-earth design is done with free-draining granular soil only. Thus, the effect of pore water development in cohesive soils, which, in turn, reduces the shear strength of the soil, is avoided. The general design procedure of any mechanically stabilized retaining wall can be divided into two parts: 1. Satisfying internal stability requirements. 2. Checking the external stability of the wall. The internal stability checks involve determining tension and pullout resistance in the reinforcing elements and ascertaining the integrity of facing elements. The external stability checks include checks for overturning, sliding, and bearing capacity failure. Retaining walls with geotextile reinforcement, the facing of the wall is formed by lapping the sheets as shown with a lap length of l1. When construction is finished, the exposed face of the wall must be covered; otherwise, the geotextile will deteriorate from exposure to ultraviolet light. Bitumen emulsion or Gunite is sprayed on the wall face. A wire mesh anchored to the geotextile facing maybe necessary to keep the coating on.

Negative Skin Friction Pada saat pondasi tiang ditempatkan pada lapisan tanah yang mengalami konsolidasi maka penurunan tanah yang terjadi disekeliling tiang tersebut akan menimbulkan gaya geser ke bawah pada tiang. Gaya ini dikenal dengan istilah negative skin friction. Gaya ini akan menambah beban aksial yang bekerja pada tiang pondasi. Besarnya negative negative skin friction dapat ditentukan dengan menggunakan persamaan sebagai berikut:

FNS    D   K   0 ' tan e   Le dimana, K

=

koefisien tekanan tanah lateral

e

=

sudut geser dalam tanah

0’ =

tekanan overburden efektif

Le

ketebalan efektif dari lapisan tanah yang terkonsolidasi

=

Prakash dan Sarma (1990) mengusulkan nilai dari ketebalan efektif lapisan tanah yang terkonsolidasi adalah sebagai berikut:

Le=0.75Lc (1) dimana, Lc

=

ketebalan total lapisan tanah terkonsolidasi

Unit skin friction dari tiang yang diberi lapisan maupun yang tidak diberi lapisan anti karat dapat dilihat pada tabel di bawah ini : Unit Skin Friction Untuk Pondasi Tiang (Prakash & Sharma, 1990)

Table 38.

Soil & Pile Condition

Unit Negative Skin Friction

Uncoated pile: - Soft compressible layer of silt and clay

0.15 – 0.30  0’

- Loose sand

0.30 – 0.80  0’

Coated pile

0.01 – 0.05  0’

Durability Main Wall (Arcelor Piling Handbook, 8th Edition) Table 39.

Loss of thickness (mm) due to corrosion for piles and sheet piles in soils, with or without groundwater

Required design working life

5 years

25 years

50 years

75 years

100 years

Undisturbed natural soils (sand, silt, clay, schist, …)

0.00

0.30

0.60

0.90

1.20

Polluted natural soils and industrial grounds

0.15

0.75

1.50

2.25

3.00

Aggressive natural soils (swamp, marsh, peat, ...)

0.20

1.00

1.75

2.50

3.25

Non-compacted and non-aggressive fills (clay, schist, sand, silt, …)

0.18

0.70

1.20

1.70

2.20

Non-compacted and aggressive fills (ashes, slag, …)

0.50

2.00

3.25

4.50

5.75

Table 40.

Loss of thickness (mm) due to corrosion for piles and sheet piles in fresh water or in sea water

Required design working life

5 years

25 years

50 years

75 years

100 years

Common fresh water (river, ship canal, …) in the zone of high attack (water line)

0.15

0.55

0.90

1.15

1.40

Very polluted fresh water (sewage, industrial effluent, …) in the zone of high attack (water line)

0.30

1.30

2.30

3.30

4.30

Sea water in temperate climate in the zone of high attack (low water and splash zones)

0.55

1.90

3.75

5.60

7.50

Sea water in temperate climate in the zone permanent immersion of in the intertidal zone

0.25

0.90

1.75

2.60

3.50