Proceedings of Indian Geotechnical Conference December 22-24,2013, Roorkee
COMPARISON OF LATERAL LOAD CAPACITY OF PILE USING SIMPLIFIED LINEAR SPRING APPROACH AND IS: 2911 (2010) J.C. Shukla, L&T – Sargent & Lundy Ltd. Vadodara, India. E mail:
[email protected] [email protected] P.J Shukla , App. Mech. Dept , K.J. Polytechnic, Polytechnic, Bharuch, India.
[email protected] [email protected] D.L. Shah , Professor, App. Mech. Dept., M.S. University of Baroda, Vadodara, India.
[email protected] [email protected] ABSTRACT: There are many approaches to estimate the lateral capacity of piles however, Beams on elastic foundation still very popular in the practice. In present study relatively simple iterative procedure is adopted to estimate the lateral load capacity of the piles using beams on elastic foundations. The instrumented pile history of Mustang Island is selected to demonstrate the efficiency of the method and compared with the actual measured response of the pile. In order to demonstrate the applicability in the Indian context, the results are also compared with the lateral pile analysis recommendations given in IS:2911 Part 1 (2010). The approach uses the SAP2000 computer code for the estimation of the lateral response against the applied load. The comparison reveals that the present approach is efficient efficient and can be used for preliminary estimation of the lateral response of the piles. Case of small loading and high loading are also incorporated in the present study to investigate its applicability. It is observed that for both of the level of loading (high and low) the present approach is efficient compared to the equivalent cantilever approach of IS: 2911. The estimated lateral displacement, shear force and bending moment response are compared with the actual observed response at the end of the paper.
INTRODUCTION Laterally loaded piles can readily be idealized and analyzed as beams on an elastic foundation using the Winkler soil model in order to obtain acceptable values of bending moment and shear force. This approach is relatively crude and is obviously not as sophisticated as analyses based on elastic continuum theories. It does, however, provide a useful means of carrying out preliminary designs. Soil is an intrinsically variable material, even in the same location and at the same depth. Accordingly, the idea of estimating the deformation characteristics of the soil for analytical purposes must be considered from a practical viewpoint, with the intention of formulating a representative mathematical model. It must be understood that the Winkler soil model does not pretend to predict the real behavior of the soil as it does not allow for continuity within the soil mass. The sensitivity of the modulus of horizontal subgrade reaction (k h), the parameter central to the analysis, is not usually great. It is always advisable, however, to carry out sensitivity analyses using a wide range of k h values. Values of k h may be assessed by reference to indirect parameters relating to soil stiffness, e.g.
SPT N- values, California bearing ratios and undrained shear strengths. Alternatively, they may be estimated using empirical formulae that have been proved to be reasonably representative of the soil(s) under consideration. Assessments or choices of k h for single piles, pile groups and continuous sheet piling are understandably somewhat different. The software like SAP2000/STAAD allows user to model spring supports for subgrade reaction and can, therefore, be used to analyze each of these constructions using whatever variations of let, are considered appropriate by the designer(s). In the subsections which follow, the generally accepted estimations of k h are described and used in the following illustrative examples, with kh set to allow tension. . Single Piles Consider a single pile of width b (b is the diameter of a circular pile or b is the width of a square/rectangular pile which is normal to the applied loading) with an embedded length of L subjected to lateral loading as shown in Figure 1 The assumed variation of the modulus of
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Shukla J. C., Shukla, P. J., and Shah D. L.
horizontal subgrade reaction (let,) is dependent on the soil type and site conditions (Fig. 1(b) and (c)). In general, the modulus of horizontal subgrade reaction k, accounting for the width b of the pile, is given by k= k h*b where k h, is the modulus of horizontal subgrade reaction for a pile of unit width, and b is the width 2 of pile.(Units: k in kN/m2 , k h in kN/m /mm and b in mm) The variation of kh shown in Figure 1 (b) can be expressed as
k h
=
z n h ( ) ; where nh is the rate of increase of b
k), with depth z measured from ground level for a single pile (Units: nh in kN/m2/mm and z, bin nun).
measurements by different investigators have indicated that the values in Table 1 are very much on the low side. Elson (1994) recommends that Terzaghi (1955) values are used as a lower limit and that values calculated from the following relationship attributed to Reese et al. (1974) should be used as an initial upper limit for sands
n
'
h
= 0.19 D
1.16
Where n’h is the initial value of n h 2
at small strain expressed in kN/m /mm and D is the relative density of soil expressed as a percentage. Some observed values of nh for normally consolidated clays lie in the range of0-35 to 0·70 2 kN/m /mm. In order to account for the non-linear behavior of piles at higher loads, Garassino et al. (1976) suggested the following relationship for sands and normally consolidated clays
y b ' nh = n h y b
q
g
'
g
where nh is the modulus of horizontal subgrade 2 reaction for a pile of unit width (in kN/m /mm), yg is the lateral deflection of the pile at ground level (in mm), y’g is the limiting value of lateral deflection of the pile at ground level for which n’ h, applies (in mm), and q is the dimensionless exponent (in the range - 0·5 to -0·7). Typical values of y’g, expressed as a percentage, are given in Table 2. Fig. 1 (a) single pile; (b) generally assumed variation of horizontal subgrade reaction modulus for sands, normally consolidated days and variable over-consolidated clays (where the effect of local yield at ground level and /or surface weathering are significant); (c) assumed variation of horizontal subgrade reaction modulus for uniform overconsolidated clays (where the effect if local yield at ground level and /or surface weathering are not significant)
In the case of sands, Terzaghi (1955) has suggested the values of n h given in Table 1. These are valid for stresses up to one half of the ultimate soil pressure and include an allowance for long term movements. However, interpretations of in-situ
Table 1 Terzaghi (1955) values of n h for sands in 2 kN/m /mm
Relative density Loose Medium dense SPT (blows 4 to 10 10 to 30 / 300 mm) Dry moist 3 6 sand Submerged 1 4 sand
Dense 30 17 10
Note : The above values of nh may be modified to allow for difference in the width b (mm) of the pile
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Comparison of lateral load capacity of pile using simplified linear spring approach and IS: 2911 (2010)
and the 305 mm square plate used in the tests to determine above values; nh(modified)= nh(from Table) X -0.75 (b/305) Table 2 Typical values of lateral deflection of the pile at ground level
to derive the above values k h(modified) h(modified)= k h(from h(from Table) X -0.75 (b/305) IS: 2911 Recommendations on values of k /η h (after Table 4 Values of constant for sand (ηh)
Soil Type y'g/b (%) Sands 0.2 to 1.0 Normally consolidated 0.2 to 0.5 clays A suitable value of yg/b is chosen by following the iterative procedure listed below. 1. Choose a trial value of y g/b 2. Calculate nh using equation given by Garassino et al. (1976) 3. Use any good analysis package /software (SAP 2000 / STAAD) to analyze the pile (beam supported on springs) to obtain a value of yg 4. Calculate yg/b If this calculated value of yg/b is significantly different (say 10%) from that the assumed, revise the value of yg/b and go back to step 2. In the case of stiff, over consolidated clays, the value of the modulus of horizontal subgrade 2 reaction k (in kN/m ) for short term loading can be assumed to be in the range 200 C u ≤ k ≤ 400 C u where Cu is the undrained shear strength of clay (in 2 kN/m ). Moreover, for long term loading and for stresses up to 50 % of ultimate load, one third of the above values may be appropriate. Terzaghi (1955) recommended values of modulus k h (k/b) for different values of C u, are given in Table 3. Table 3 Terzaghi (1955) values of k h for clays in 2 kN/m /mm Consistency of clay Firm to Stiff Very Hard stiff Stiff Cu 50 to 100 to 200 to >400 2 (kN/m ) 100 200 400 *k h (305 15 27 54 >108 mm plate) Note: The above values of k h may be modified to allow for the difference in the width of the pile b (mm) and the 305 mm square plate used in the tests
Types of soil
Loose Sand Medium Dense Sand Dense Sand
Above Water Table (kPa/m) IS:29 Recom 11 mended by Author 2600 6790
Submerged in (kPa/m) IS:29 Recomm 11 ended by Author 1460
5430
7750
24430
5250
16300
20750
61000
12450
33900
Table 5 Values of constant for Clay (k)
Unconfined compressive strength in 2 kg/cm (kPa) (Cu) 0.2 to 0.4 (20 to 40) 1 to 2 (100 to 200) 2 to 4 (200 to 400) More than 4 (400)
Value in k= 67*Cu 2 kg/cm (kPa) (Prakash and Sharma ) (kPa) 7.75 (775)
1340 to 2680
48.80 (4880)
6700 to 13400
97.75 (9775)
13400 26800 >26800
195.50 (19550)
to
Example Problem The problem presented by Reese et al. (1974) for instrumented piles in Mustang Island is selected to demonstrate the methodology and will be compared with IS:2911 procedure and actual measurements.
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Shukla J. C., Shukla, P. J., and Shah D. L.
Summary of Results
The two tests were carried out on the test piles
Initial Loading High Loading
Lateral force (kN) 89 220
Moment (kNm) 23 56
IS : 2911 Procedure : As per Table 4, selecting η h = 12.45 MN/m 3 2 EI = 163000 kN.m T = 5
EI nh
= 1.672
Considering load application on ground (L 1=0.305 m), referring the Figure 2 of Appendix C of IS:2911 (Part 1), for L1/T =0.18, Lf /T /T = 2.1 for fixed end condition Hence depth of fixity below ground level = L f = 2.1 * T = 3.512 m ( 5.75 D). Total Horizontal force on Pile (Q) = 89 kN + 26/3.512 26/3.512 = 96.40 (for Initial loading) = 220 kN + 15.95 = 235.95 (for High Loading) Knowing the total horizontal load on pile and length of the equivalent cantilever (length of fixity), the pile had deflection shall be computed using the equation given in IS: 2911 3 Q ( L1 + L f ) for fixed head condition Y = 12 EI Y = 2.74 mm (for Initial loading) Y=6.7 mm (for high loading)
Description
Lateral displacem ent at ground level (mm)
Actual/measur Initial ed Reese et al. Loading (1974) High Loading IS:2911, static Initial estimate using Loading provisions in High code/procedure Loading s STAAD with Initial spring constant Loading for short term High loading as per Loading by Reese et al. (1974) STAAD with Initial spring constant Loading for high High loading as per Loading Garassino et al. (1976) STAAD with Initial spring constant Loading selected from High IS:2911 Loading LPILE analysis Initial Loading High Loading
5
Estimate d Maximu m bending moment (kN.m) 125
23
374
2.74
156*
6.7
386*
4.38
105.34
10.67
253.66
7.66
118.95
18.77
287.18
7.79
119.32
19.02
288.10
5.34
136.501
22.67
398.08
Observations and recommendations: 1. The idealization of spring supports using theory of beams on elastic foundations (Winkler Model) is useful approach for preliminary / approximate analysis of the laterally loaded piles. 2. There are wide variations in the recommendations for modulus of subgrade reaction values (k) for soils. Since the k-
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Comparison of lateral load capacity of pile using simplified linear spring approach and IS: 2911 (2010)
3.
4.
5.
6.
value is not fundamental soil property, its evaluation requires geotechnical expertise and engineering judgment for appropriate solutions of the problem. The uncoupled spring idealization of soil supporting a pile is useful approach. However, sensitivity of the spring value must be attempted in order to get the better solution of the laterally loaded pile problem especially for particular loading conditions i.e. Short term/ Long term / Cyclic. The problem can be extended by bilinear approximation of the spring value and considering different spring value respective to soil layering which may increase computing effort to get more precise solutions (Fig. 2a and 2b). It is also advisable to consider the construction method, consolidation, long term settlement etc. as influencing factor for such analysis since they will in fact modify the in situ soil properties thereby modulus of subgrade reaction. The soil stiffness thereby modulus of subgrade reaction value of soil may degrade under the action of cyclic loading. Some gapping phenomena have been observed worldwide especially in clay soil which may not be possible to model using present approach and some specialized computer codes like LPILE, OPILE, FLPIER should be used. It is observed that the modulus of subgrade reaction specified in IS:2911 are lower bound values and for short term loading higher values may be selected.
7. It is also observed that IS: 2911 may predict the load very close to the actual values (especially for long term loading based on the formulae specified in IS:2911) however, it will under predict the displacement which may cause serviceability problem. In such case of long term loading, the present methodology using the value of modulus of subgrade reaction can be used to predict the displacement. 8. LPILE results are in very good agreement with the actual measured values which further indicate that the later pile analysis using p-y curve approach is better compared to other methods in all the loading cases. Figure 3 and 4 gives STADD Pro and L Pile output for lateral analysis respectively. References: 1. Terzaghi K., (1955). Evaluation of coefficient of subgrade reaction. Geotechnique, 5(4), 297-326. 2. Reese L. C., Cox W.R. and Koop F.D., (1974). Analysis of laterally loaded piles in th stiff clay. Proc. 7 offshore Tech. Conf., Houston, Texas, 473-483. 3. Garassino A., Jamilokowski M. and Pasqualini E., (1976). Soil modulus for laterally loaded piles in sand and NC clays. th Proc. 6 Europ. Conf. on Soil Mech. and Found. Engng, Vienna, 1.2, 429-434. 4. Ramasamy G., Gopal Ranjan and Jain N.K., (1987). Modification to Indian Standard code procedure on lateral capacity of piles. Indian Geotechnical Journal, 17(3), 249-258.
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Shukla J. C., Shukla, P. J., and Shah D. L.
Fig. 2a Comparison of calculated lateral displacement for pile
Fig. 2b Figure Comparison of calculated maximum bending moment for pile
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Comparison of lateral load capacity of pile using simplified linear spring approach and IS: 2911 (2010)
Fig. 3 STAAD Pro out put for lateral pile analysis anal ysis
Fig. 4 LPILE output for lateral pile analysis
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