FINITE ELEMENT ANALYSIS 1 OF A FULL-SCALE …Zhang, Abu-Farsakh, Voyiadjis 1 1 FINITE ELEMENT...

Zhang, Abu-Farsakh, Voyiadjis

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FINITE ELEMENT ANALYSIS OF A FULL-SCALE LATERAL LOAD TEST ON 1

BATTER PILE GROUP FOUNDATION 2

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Yida Zhang 5

Graduate Student 6

Department of Civil and Environmental Engineering 7

Louisiana State University 8

Baton Rouge, LA 70803 9

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Murad Y. Abu-Farsakh, Ph.D., P.E. (Corresponding Author) 11

Research Associate Professor 12

Louisiana Transportation Research Center 13


4101 Gourrier Avenue 15


E-mail: [email protected] 17

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and 19

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George Z. Voyiadjis, Ph.D. 21

Boyd Professor 22

Department of Civil and Environmental Engineering 23



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Submitted to: 32

91th Transportation Research Board Annual Meeting 33

January 2012 34

Washington, D.C. 35

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TRB 2012 Annual Meeting Paper revised from original submittal.


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FINITE ELEMENT ANALYSIS OF A FULL-SCALE LATERAL LOAD TEST ON 1

BATTER PILE GROUP FOUNDATION 2

ABSTRACT 3

This paper presents a three-dimensional (3D) finite element analysis (FEA) model that was 4

developed to numerically simulate the full-scale lateral load test on a batter pile group 5

foundation conducted on M19 pier of the I-10 Twin Span Bridge. The results of 3D FEA were 6

compared with the measured field data from lateral load test and those predicted using the 7

FB-MultiPier software. The soil resistance profiles, deduced from the FE model, were used to 8

generate the p-y curves at different depths. The results of FE analysis show that the predicted 9

lateral deformation profiles are in good agreement with the IPI measurements; and the 10

estimated moments are also in good agreement with the moments calculated from strain 11

gauge measurements. The results of FB-MultiPier showed good agreement with the measured 12

lateral deformations near the pile head; however the deflection drifts away from measured 13

values as depth increase. The moments obtained from the FB-MultiPier analysis are in good 14

agreement with moments calculated from the strain gage data. 15

INTRODUCTION 16

Pile foundations are primarily designed for vertical support of structures, while specific 17

consideration should be taken on their lateral response for supporting high buildings, bridges 18

and offshore structures due to wind loads, frequent wave loads, possible huge lateral impact 19

and earthquake loadings. According to Rao et al. (1), lateral loads are in the order of 10-15% 20

of the vertical loads in case of onshore structures and 25-30% in case of costal and offshore 21

structures. The lateral load capacity and maximum lateral deflection of the pile foundation are 22

the two most concerned aspects for engineers. It is believed that the later one is the major 23

criterion on the design (2). To reduce the lateral deflection of foundations, batter piles are 24

often used in foundation design. 25

The behavior of single/group pile has been studied by many researchers through 26

different means. The well-known p-y method developed by Reese and his coworkers (e.g., 3, 27

4) is the most widely used method for designing of laterally loaded piles. In this approach the 28

soil surrounding the piles are simplified by a series of nonlinear springs with their mechanical 29

behavior described by p-y curves. Later, the p-y method was implemented into nonlinear 30

finite difference or finite element softwares such as LPile and FB-MultiPier for designing 31

laterally loaded piles. The p-y method has certain limitations such as the p-y curves are 32

semi-empirical in describing the soil behavior, inappropriate modeling the pile-soil interface, 33

and that the pile group interaction is included as input parameter. Therefore, a 3D 34

continuum-based analysis is desirable for better understanding the problem. 35

Continuum-based methods treat the soil surrounding the piles as elastic or elasto-plastic 36

continuum. Continuum-based solutions have been attempted by many scholars, both 37

analytically and numerically. The analytical solution is highly complex, so only few 38

analytical or semi-analytical elastic solutions were developed. Poulos (5) proposed an 39

analytical solution of laterally loaded piles based on theory of elasticity. The solution was 40

achieved through equating the soil displacement given by Mindlin equation for horizontal 41

displacement, and the pile displacement obtained from the equation of flexure of a thin strip. 42



2

The finite element numerical modeling is another continuum-based approach, in which 1

complex soil properties such as hypoelastic, elastoplastic and fluid/solid coupling can be 2

simulated via different constitutive models. Many researchers have used the FEM to analyze 3

the behavior of laterally loaded piles (6, 7, 8). Brown and Shie (6) performed a FE parametric 4

study on laterally loaded piles to investigate the effect of in-situ stresses and pile-soil friction, 5

etc. on soil response. P-y curves were extracted from their model and compared to those 6

predicted by COM624 software. Trochanis et al. (7) performed a 3D FE analysis of laterally 7

loaded piles and revealed the significant influence of slippage/separation effect at pile-soil 8

interface to the piles’ lateral behavior. Yang and Jeremic (8) developed a FE model to 9

investigate the influence of soil layering on laterally loaded piles. 10

Full-scale load tests are always desirable by researchers for providing direct field 11

measurements that can be used to verify their models or to develop empirical analysis 12

methods. However, very few full-scale lateral load tests on piles were reported in the 13

literature (9,10,11, 12) due to their high cost and difficulties. Recently a full-scale lateral load 14

test was performed on the foundation supporting pier M19 of the new I-10 Twin Span Bridge 15

(13) to assess the method used to design this pile foundation and to evaluate its performance 16

under lateral loading. The details of the test were previous reported in Abu-Farsakh et al. (13). 17

This full-scale test provided valuable data for evaluating the current design methodology. 18

In this paper, a 3D FE model was developed to simulate the full-scale lateral load test 19

conducted on M19 batter pile group foundation using the FEA software ABAQUS. The 20

profiles of piles’ lateral deflections, bending moments, and soil resistances obtained from 21

FEM were compared with the field measurements and the results of FB-MultiPier analyses. 22

The soil resistance profiles, deduced from the FE analysis, were used to generate the p-y 23

curves. 24

DESCRIPTION OF THE LATERAL LOAD TEST 25

A full-scale lateral load test was conducted at M19 eastbound pier of the new I-10 Twin Span 26

Bridge to evaluate the performance of batter pile group under lateral loading. The foundations 27

of M19 piers consist of 24 36-inch square precast prestressed concrete (PPC) piles of 110-ft 28

long. All piles are battered with a slope of 1:6; half of them are negative or reverse batter and 29

the rest are positive or forward batter. The piles were designed to have center to center 30

spacings of 4.3 times the pile width (13 feet) in the direction of lateral loading and 2.5 times 31

the pile width (7.5 feet) in the other direction. The average embedded length of the piles was 32

87 ft. The size of M19 pile cap (or footing) is 44 ft long × 42.5 ft wide × 7 ft deep. The water 33

depth is 11 ft. Figure 1 presents a photo of the M19 eastbound and westbound piers. The test 34

was conducted by pulling the M19 eastbound and the westbound piers toward each other 35

using high strength steel tendons that connect the pile caps via PVC pipes. Figure 2a presents 36

the schematic of the lateral load test. 37

A maximum of 1870 kips lateral load was incrementally applied to the pile cap. The 38

duration per load increment ranged from 5 min. to 30 min. Eight selected piles were 39

instrumented with Micro-Electro-Mechanical Sensor (MEMS) In-Place Inclinometers (IPIs) 40

to measure pile deflection profiles and twelve selected piles were instrumented with sister bar 41

strain gauges. The locations of instrumented piles are presented in Figure 2b. Here the 42

instrumented piles are numbered to facilitate the comparison with the results of finite element 43


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FINITE ELEMENT MODEL 1

A three-dimensional finite element model was developed using ABAQUS (14) to numerically 2

simulate the full-scale lateral load test. The FE mesh is shown in Figure 3. The model 3

simulates only half of the foundation due to the symmetric nature of this problem. The size of 4

the mesh was selected such that the length of soil media is 220 ft, which is 5 times the size of 5

pile cap (44 ft), and the depth of the soil media is 165 ft, which is 1.7 times the embedded 6

depth of the piles (97 ft). The boundary conditions for the FE model included restraining the 7

horizontal movement along the side boundaries (ux or uz = 0) and restraining the vertical 8

movement along the bottom boundary (uY = 0). The final FE mesh consists of a total of 9

68,229 eight-node solid elements. The lateral load was applied on the east side of pile cap and 10

directed horizontally to the west. 11

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13 Figure 3. Finite element mesh 14

Material Constitutive Models and Parameters 15

The piles and pile cap was simulated using a linear elastic model. In this study, the elastic 16

Young’s modulus was estimated based on the average results of 28-day concrete compressive 17

strength based on cylinder specimens ( = 9064 psi). Since the lateral load test was 18

conducted six months after pile construction, the average compressive strength was increased 19

by 20% to account for the additional curing time after 28 days. The Young’s modulus of the 20

concrete was then estimated using the following equation: 21

57,000 (1) 22

The value of pile Young’s modulus was then estimated to be 8.56 × 108 psf. 23

The clay soil layers were simulated using the Mohr-Coulomb (MD) constitutive 24

model, as expressed by the following equation: 25 F (2) 26

where is the magnitude of shear stress, is the cohesion, is the internal friction angle 27

of the material, and is the normal stress. The CPT data were used to estimate the 28

undrained shear strength of the clay layers. Since the duration time per load increment in the 29



5

field test ranged from 5 min to 30 min, compared to the consolidation process, this time is 1

considered short and thus an undrained condition can be assumed for clay soil in the FE 2

analysis. For saturated clay soils under undrained condition, the friction angle is set to be 3

zero and the cohesion is set to be equal to the undrained shear strength estimated from the 4

CPT data. 5

The sand soil layers were simulated using the Drucker-Prager DP) model with 6

non-associated flow rule. The Drucker-Prager yield function includes the effect of hydrostatic 7

stress, which is expressed as follows: 8

0tan =−β⋅−= dptF (3) 9

⋅

−−+⋅⋅=

31111

21

qr

KKqt (4) 10

where is a function describing the shape of the yield stress on the π plane, β describes the 11

slope of the yield surface in the p–t plane and is referred as the angle of friction, d describe 12

the cohesion of the material, p is the mean stress, q is the Mises equivalent stress, is the is 13

the ratio of the yield stress in triaxial tension to the yield stress in triaxial compression, and r 14

is the third invariant of deviatoric stress. In this study, the friction angle φ of sand layers was 15

estimated from the corrected SPT-N values, and the cohesion d is artificially set small value 16

to avoid convergence problem. 17

Both the MC and DP models require proper estimation of the Young’s modulus and 18

Poisson's Ratio. In this study, the elastic parameters were estimated from results of in-situ 19

tests and soil type via some empirical formulas. The Young’s modulus of cohesionless soil 20

was estimated from the corrected SPT-N value using the formula proposed by Kulhawy and 21

Mayne (15). The Young’s modulus of cohesive soil was estimated based on the undrained 22

shear strength of the clay according to the U.S. Army Corps of Engineers Engineering 23

Manual 1110-1-1904 (16). The Poisson’s ratio of both cohesionless and cohesive soil was 24

determined according to the type of the soil as suggested by Bowles (17). 25

The final soil parameters interpreted from the in-situ tests at M19 eastbound pier are 26

listed in Table 1 for use in both the finite element analysis and the FB-MultiPier prediction. It 27

should be noted here that the soil strength values were increased by 20% to include the effect 28

of soil densification caused by driving of the 24 piles and subsequent soil consolidation. 29

Soil-Pile Interface Model 30

In this study, the ABAQUS contact interaction feature was used to model the pile-soil 31

interface friction. The pile-soil interface was assigned master/slave surface contact 32

formulation with small sliding assumption. The interface in the normal direction is assumed 33

to be “hard” contact, while the tangential interaction behavior is governed by Coulomb 34

friction model. Separation is allowed after contact and slippage can happen when the 35

tangential stress reached certain limit. A pile-soil interface friction of 0.424 has been assigned 36

to the tangential behavior, which corresponds to an angle of interface friction of 23o between 37

the soil and the piles. 38

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Table 1. Summary of models’ soil parameters 1

Soil Type Depth Below Mudline Level

Effective Unit Weight Undrained Shear Strength

Friction Angle Poisson's ratio Young’s Modulus Mohr‐Coulomb Model Drucker‐Prager Model c d K

ft pcf psf psf psf psf Soft Clay 0‐15 60.6 240 0.4 71,712 0 0 240 Stiff Clay 15‐25 56.6 1560 0.45 1,307,923 0 0 1560 Medium Clay 25‐38 45.6 1104 0.45 780,000 0 0 1104 Medium Sand 38‐49 57.6 35 0.4 600,000 15.27 10 100 0.778 Stiff Clay 49‐70 50.6 1533.6 0.45 1,307,923 0 0 1533.6 Stiff Clay 70‐81 59.6 3162 0.35 2,400,192 0 0 3162 Stiff Clay 81‐89 65.6 1796.4 0.4 1,620,000 0 0 1796.4 Dense Sand >89 61.6 38 0.45 1,200,000 16.6 10 100 0.778 2

RESULTS OF NUMERICAL ANALYSIS 3

Soil Displacement Field 4

Figures 4a and 4b present the contours of the soil deformations before and after applying a 5

lateral load of 1870 kips. Initially, the deformation of the soils is purely caused by the gravity 6

of the pile and cap. After applying the lateral load to pile cap, the largest soil displacements 7

are concentrated near the ground surface and between the piles. Besides, the soils 8

surrounding the lead 1st row and 2nd row are subjected to increasing deformation; while the 9

soil deformation near the 3rd and trail 4th rows are decreasing with loading. This is because 10

the piles in 1st and 2nd rows are positive battered piles that transfer part of the lateral load to 11

downward vertical load and thus expand the deformation field; while the piles in 3rd and 4th 12

rows are negative battered piles in which part of the pile gravity will be cancelled out by the 13

transferred upward vertical load and hence reduce the deformation field. 14

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(a) Soil deformation before lateral load (b) Soil deformation after lateral load 16

Figure 4 17



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Lateral Deformation Profile 1

Figure 5a exhibits the FE deformed pile group foundation obtained at 1870 kips lateral load. 2

A scale factor of 366 is used to visualize the lateral deflections of the piles. The distribution 3

of piles’ Mises equivalent stress is shown in the figure by the contour colors, indicating that 4

the concrete near the pile cap at the most bent region of the pile experiences the highest stress. 5

Figure 5b presents the profiles of lateral deflection generated from the FE model on batter 6

pile group foundation under different lateral loads. The FE predicted maximum pile cap 7

lateral deformation is 0.80 inch at 1870 kips applied lateral load. 8

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Displacement (in)

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Dep

thbe

low

pile

cap

(ft)

Load570 kips770 kips970 kips1180 kips1580 kips1745 kips1870 kips

lead row / pile 1

9 (a) Lateral deformation of piles (b) Profiles of lateral deformation 10

Figure 5 11

Figure 6 compares the FE predicted lateral deflection profiles obtained for selected piles 12

with those measured in the field using IP inclinometers and those predicted by FB-MultiPier 13

under lateral load 1870 kips. It should be noted that p-y multipliers of 0.85, 0.6, 0.6 and 0.5 14

were used in the FB-MultiPier analysis for the leading and subsequent trailing rows, 15

respectively. Here, piles 1, 2 and 4 are battered in the direction opposite the loading and pile 5 16

is inclined in the loading direction. It could be seen that the 3D FE analysis successfully 17

captures the deflection pattern of the batter piles. The deflection profiles from FEM show 18

slightly larger deflection near the pile cap than the measured values. However, the overall 19

deflection curves along the pile match closely with the field measurement. Although the 20

FB-MultiPier shows good predictions of the measured deformations near the pile head; the 21

deformations drift away from the measured values with increasing depth along the pile. The 22

“Fixed point” predicted with FB-MultiPier is shallower than those predicted by FEM and 23

field measurements. Such discrepancies were also reported by McVay et al. (12) in their 24

barge impact tests on a bridge pier at St. George Island Causeway. The authors believe that 25

these disagreements are partially due to simplifying the group effect in FB-MultiPier and the 26

effect of pile spacing in perpendicular direction. In FEA using the FB-MultiPier program, the 27

group effect is empirically considered using the p-y multiplier concept, which is determined 28

by comparing the group pile cap movement with the single pile head movement. This reason 29

in addition to not considering 3D continuum in software modeling might be the reason for 30

discrepancies in deflection pattern. 31



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0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8Displacement (in)

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Pile 2FEMMeasuredFB-Multipier

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8Displacement (in)

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0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8Displacement (in)

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Figure 6. Profiles of lateral deformations at 1870 Kips 2

Bending Moment Profile 3

The distributions of bending moments with depth for the different piles were determined 4

from the FE analysis at different load increments. The predicted FE moments were compared 5

with the moments deduced from the strain gauge measurements and those calculated using 6

the FB-MultiPier software. As stated earlier, two pairs of strain gauges were installed on each 7

of the 12 selected piles at two different locations. The strain gauge data for each pair was 8

used to calculate the bending moment and axial load. The moments can be calculated using 9

the following equation: 10

M (5) 11

where is the tensile strain and is te compressive strain and h is the horizontal distance 12

between the two gauges, and EI is the flexural stiffness of the pile. 13

Figures 7 present the comparison of bending moments generated from FEM, strain 14

gauges and FB-MultiPier, for piles 1 and 8, respectively, determined at two different load 15

increments, 970 kips and 1745 kips. The comparison is limited since there are only two pairs 16

of strain gauges instrumented in each pile. However, at these two points, both the FEM and 17

FB-MultiPier predicted bending moments agree very well with those deduced from strain 18

gauges data. The figures show that the maximum positive bending moment occurs at the 19

pile-cap joint, the maximum negative bending moment is located at 29 ft to 31.5 ft below the 20

pile cap, and the point of zero bending moment occurs at about 18 ft below pile cap, which 21

corresponding to the inflection point of the deflection curves. The maximum positive 22

moments predicted by the FEM are 10%-15% higher than those predicted by FB-MultiPier; 23

while the maximum negative bending moments from FEM are 20%-30% lower than those 24

predicted by FB-MultiPier. Besides, the location of maximum negative moment from FEM 25

occurs at slightly shallower depth (29 ft below pile cap) than the location from FB-MultiPier 26

analysis (31.5 ft below pile cap). 27



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-700 -600 -500 -400 -300 -200 -100 0 100 200 300 400 500 600 700 800 900 1000

Moment (kips-ft)

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Depthbelowpilecap(ft)

LoadFEM 970 kipsFEM 1745 kipsFB 970 kipsFB 1745 kipsSG 970 kipsSG 1745 kips

Trail row/ Pile 1

-700 -600 -500 -400 -300 -200 -100 0 100 200 300 400 500 600 700 800 900 1000

Moment (kips-ft)

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LoadFEM 970 kipsFEM 1745 kipsFB 970 kipsFB 1745 kipsSG 970 kipsSG 1745 kips

Trail row/ Pile 8

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Figure 7. Comparison of FE bending moment profiles with FB-MultiPier 2

Soil Resistance Profile 3

Figures 8a and 8b present the comparison of soil resistance profiles obtained from 3D FEM 4

for piles arranged perpendicular and parallel to the loading direction, respectively, and the 5

FB-MultiPier profiles. The figures show that the first peak of positive soil resistance occurs 6

close to ground surface, and the second peak occurred at about 27 ft below pile cap, which is 7

just below the interface of the soft clay layer and stiff clay layer. The positive soil resistance 8

reduced to zero at a depth of 34 ft below pile cap. Below this depth, the soils offer resistance 9

to the negative deflection of the pile down to a depth of about 55ft, below which the soil has 10

negligible resistance. 11

It is also noticed that the soil resistance profile near mudline varied significantly from 12

pile to pile. Comparison of piles arranged perpendicular to loading direction shows that the 13

side pile # 1 has higher resistance near the mudline than the piles located in the middle and 14

inner piles. It also has slightly higher maximum positive soil resistance at 27 ft depth than the 15

middle and inner piles. Figure 8b shows that the piles located in the lead and trail rows have 16

higher soil resistance near the mudline than the 2nd and 3rd row piles. The lead row also has 17

higher maximum positive soil resistance at 27 ft depth than the other 3 piles. 18

The profiles of soil resistance predicted from the FB-MultiPier are generally in 19

agreement with those generated by the FE model. The comparison shows that the 20

FB-MultiPier predicted less soil resistance than the FEM near the mudline, while predicted 21

greater soil resistance provided by the sandy layer at the depth of 49-60ft below pile cap than 22

the FE model. 23



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-10 -8 -6 -4 -2 0 2 4 6 8 10 12 14 16 18 20 22 24 26

Soil resistance (kips)

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-5


Side column/ pile 1Middle column/ pile 2Inner column/ pile 3FB-trail row

-10 -8 -6 -4 -2 0 2 4 6 8 10 12 14 16 18 20 22 24 26

Soil resistance (kips)

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Lead row/ pile 62nd row/ pile 53rd row/ pile 4Trail row/ pile 2FB-lead rowFB-triail row

1 (a) Piles perpendicular to loading (b) Piles parallel to loading 2

Figure 8. Comparison of soil resistance profiles at 1870 Kips load 3

CONCLUSION 4

In this study, a 3D FEM was developed and used to simulate the full-scale lateral load test 5

that was conducted on a batter pile group foundation at M19 eastbound pier of I-10 Twin 6

span bridge. The results of 3D FE analysis were compared with the measured field data from 7

the lateral load test and those predicted using the FB-MultiPier software. Based on this study, 8

the following conclusions can be made: 9

• The predicted lateral deformation profiles from 3D FEM were compared with the 10

measured field deformations and the results showed good agreement. The estimated 11

moments from FE analysis were also compared with the moments calculated from strain 12

gauge data, and the results also showed good agreement. 13

• The FB-MultiPier results shows good agreement with the measured lateral deformations 14

near the pile head; however, it has some discrepancy from measured deformations as the 15

depth increases below 25 ft. The “fixed point” determined from the FB-Multi-Pier is 16

shallower than those determined by 3D FEM and field measurements. The comparison 17

between the moments estimated from FB-Multi-Pier with the moments calculated from 18

strain gauge measurements showed good agreement. 19

• The soil resistance profiles deduced from the FEM indicated that the piles located at the 20

corner of the leading row experiences more soil resistance than the other piles, which is in 21

agreement with the observations from other literatures. 22

• The soil resistance profiles predicted by FB-MultiPier analysis are generally in agreement 23

with those generated by the FE model. The FB-MultiPier predicted less soil resistance 24

near the mudline and greater soil resistance at depths 49-60 ft below pile cap. 25

ACKNOWLEGMENTS 26

This research was funded by the Louisiana Transportation Research Center (LTRC) and the 27

Louisiana Department of Transportation and Development. The authors would like to express 28

their thanks to Zhongjie Zhang and Mark Morvant at LTRC for providing valuable help and 29

support in this study. 30



11

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bridge geotechnical investigation. Report Number 4910 4554 016-12, Florida Department of 28

Transportation, Tallahassee, FL., 150 p. 29 13. Abu-Farsakh, M., Yu X., Pathak B., and Zhang, Z., 2011 “Field Testing and Analyses of a Batter 30

Pile Group Foundation under Lateral Loading,” in press, Journal of Transportation Board. 31

14. Hibbitt, Karlson and Sorensen, 2002. ABAQUS Standard User’s Manuals, Version 6.3-1, 32

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FINITE ELEMENT ANALYSIS 1 OF A FULL-SCALE …Zhang, Abu-Farsakh, Voyiadjis 1 1 FINITE ELEMENT...

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