J. Cent. South Univ. Technol. (2008) 15: 75-80 

DOI: 10.1007/s11771-008-0016-9 

3D finite element analysis on pile-soil interaction of passive pile group

  ZHAO Ming-hua(赵明华), LIU Dun-ping(刘敦平), ZHANG Ling (张 玲), JIANG Chong(蒋 冲)

 (Institute of Geotechnical Engineering, Hunan University, Changsha 410082, China)

Abstract：The interaction between pile and soft soil of the passive pile group subjected to soil movement was analyzed with three-dimensional finite element model by using ANSYS software. The soil was assumed to be elastic-plastic complying with the Drucker-Prager yield criterion in the analysis. The large displacement of soil was considered and contact elements were used to evaluate the interaction between pile and soil. The influences of soil depth of layer and number of piles on the lateral pressure of the pile were investigated, and the lateral pressure distributions on the (2×1) pile group and on the (2×2) pile group were compared. The results show that the adjacent surcharge may result in significant lateral movement of the soft soil and considerable pressure on the pile. The pressure acting on the row near the surcharge is higher than that on the other row, due to the “barrier” and arching effects in pile groups. The passive load and its distribution should be taken into account in the design of the passive piles.

Key words：pile-soil interaction; passive pile group; soft soil; lateral pressure; deformation; 3D finite element analysis

1 Introduction

The majority of piles are designed to support “active” loads, that is, loads from superstructure are directly transferred to the pile foundation by the cap. However, in many cases, piles are not designed to withstand “passive” loads, which are created by the deformation and movement of soil surrounding the piles due to the weight of soil and the surcharge. These passive loads may lead to structural distress or failure. Examples of these cases include piles supporting bridge abutments adjacent to embankment, existing pile foundations adjacent to pile driving, excavation or tunneling operations, and pile foundations in moving slopes.

Several empirical and numerical methods have been proposed for analyzing the response of single pile and pile group subjected to lateral loading from horizontal soil movements. A comprehensive review on these methods has been made by STEWART et al^[1]. Most of the numerical methods that have been proposed utilize the finite element method^[2-11] or the finite differential method^[12-13]. For pile groups, the plane strain finite element method was adopted by STEWART et al^[2]. In the study by STEWART et al, the piles were represented by equivalent sheet-pile walls. The behavior of sheet-pile wall system was assumed to be dependent on predetermined relationship between the pressure and relative soil displacement (soil movement past piles), and the soil-pile interaction was not modeled. In a later study, BRANSBY and SPRINGMAN^[9] used three-dimensional finite element method, in which relatively coarse mesh was used due to limited computing capacity at that time, and the distribution of soil contact stress around piles was not investigated. In fact, this type of pile-soil interaction involves nonlinearities such as plasticity of soil, large displacement and pile-soil contact. The influencing factors of the nonlinearity include properties and depth of soft soil layer, diameter, number and spacing of piles, and constraints from upper structure.  Up to date, limited studies on these influencing factors have been found.

In this work, the distribution of soil contact stress around piles and the lateral pressure were  obtained, the pile groups deformations in different rows were investigated, and the lateral pressures on the (2×1) pile group and on the (2×2) pile group were compared.

2 Analytical model

The basic problem of a passive pile group subjected to soil movement is shown in Fig.1, where h₁ is the depth of the soft soil layer, h₂ is the depth of stiffer stratum, and L is the total pile embedded length.

In reality, both vertical and lateral soil movements always concurrently occur^[14-16]. In order to simplify the problem, only the lateral soil movement was analyzed in this paper. In the analysis, pile was modeled as elastic material, whereas soil was assumed to be elastic-plastic complying with the Drucker-Prager yield criterion. The surface-surface contact elements were used to evaluate the interaction between pile and soil. The pile surface was established as “target” surface (Targe 170), and the soil surface contacting the pile as “contact” surface (Contac 174), these two surfaces got together to comprise the “contact pair”. Processing of the three-dimensional problem was carried out by ANSYS software in a high-powered computer workstation. The normal contact stresses acting on the pile are shown in Fig.2.

Fig.1 Schematic diagram of pile group subjected to  soil movement

Fig.2 Schematic diagram of normal contact stresses on pile

By projecting the normal contact stresses on the x-axis, the resultant force per unit length, F, in that direction was calculated. The average lateral pressure on pile was then p=F/d, as illustrated in Fig.3.

Fig.3 Schematic diagram of average lateral pressure   

Two types of pile groups were investigated in this paper, and the arrangement of piles is shown in Fig.4.

Fig.4 Arrangement of piles: (a) (2×1) Pile group; (b) (2×2) Pile group

3 (2?1) Pile group

The finite element mesh of (2×1) pile group is shown in Fig.5. In order to investigate the response of the pile group in soft soil layer, the smaller elements were used in the mesh. The geometry and material parameters were employed in the study by BRANSBY and SPRINGMAN^[9], d=1.27 m, L=19 m, h₁=6 m, h₂=  13 m, q=200 kPa. The material parameters can be seen in Table 1.　

Fig.5 3D finite element model for analysis of (2×1) pile group

Table 1 Material parameters for pile and soil

Fig.6(a) shows that the bending deformations of the piles are very serious, especially in the soft soil layer. In addition, the surrounding soil reaches its plastic state, as shown in Fig.6(b).

Average lateral pressures on the piles are shown in Fig.7 for a surcharge of 200 kPa. The pressure distributions of this study agree well with the deduced values from the double differentiation of centrifuge bending moment data^[9]. The results are also in accor- dance with the those of BRANSBY and SPRINGMAN

Fig.6 Schematic diagrams of deformed piles(a) and plastic zone of soil(b)

Fig.7 Average lateral pressure on (2×1) pile group: (a) Rear pile; (b) Front pile

in the soft soil layer^[9]. The pile behavior in the stiffer stratum is not very well replicated due to both the coarse mesh and the simplistic constitutive model used in the study by BRANSBY and SPRINGMAN^[9], adapting to limited computing capacity. In practice engineering, lateral pressures on the piles embedded in stiffer stratum will decrease with increasing embedding depth. A finer mesh combined with a more complex constitutive model for the stiffer stratum can solve this problem in this work.

Three different horizontal cross-sections of the piles were investigated. In the first case, the cross-section is  2 m below the cap (in the soft soil layer); in the second case, the cross-section is 8 m below the cap (in the stiffer stratum); and in the third case, the cross-section is 16 m below the cap (near the pile bottom). The distributions of normal contact stresses are shown in Fig.8. Separation appears between soil and pile, where the contact stresses come to zero. This phenomenon exists only when the contact elements are used between the soil and pile. Due to resistance to soil movement of the rear pile, which functions as a “barrier” around the front pile, the contact stresses and lateral pressures on the front pile are less than those on the rear pile.

Fig.9 shows the pressures acting mainly on the rear pile due to the “barrier” effect from the rear pile near the surcharge in the stiffer ground. For the soft ground, soil will move laterally past the piles under the action of surcharge, causing passive lateral pressures both on rear pile and front pile. The “barrier” effect is weakened, as shown in Figs.10 and 11. It is also been found that the pressures on the piles are rightward in the soft soil layer. In contrast, the pressures are leftward below the interface between the soft soil layer and the stiffer stratum.

4 (2×2) Pile group

The finite element mesh of (2×2) pile group is shown in Fig.12. The geometry and material parameters are the same as those of the (2×1) pile group. The deformation of the (2×2) pile group is shown in Fig.13.

Compared with the (2×1) pile group, the resistance to soil movements of the (2×2) pile group is more noticeable. The reasons cover two important aspects. On the one hand, the (2×2) pile group stiffness is greater than that of the (2×1) pile group as a whole, on the other hand, for the (2×2) pile group, the soil arching effect is formed between the pile and pile in the same row^[17], except for the “barrier” effect from the rear piles. However, the soil arching effect will not come into being for the (2×1) pile group. For the same pile rows, the pressures distributions of the (2×2) pile group are very similar to those of the (2×1) pile group, but the values are less than those on the (2×1) pile group, as shown in Figs.14 and 15.

Fig.8 Distributions of normal contact stresses on (2×1) pile group (in kPa): (a) 2 m Below pile cap of rear pile; (b) 2 m Below pile cap of front pile; (c) 8 m Below pile cap of rear pile; (d) 8 m Below pile cap of front pile; (e) 16 m Below pile cap of rear pile;       (f) 16 m Below pile cap of front pile

Fig.9 Average lateral pressures on piles for stiffer ground

Fig.10 Average lateral pressures on piles for 10 m-thickness soft ground

Fig.11 Average lateral pressures on piles for soft ground

Fig.12 3D finite element model for analysis of (2×2) pile group

Fig.13 Schematic diagram of deformed (2×2) pile group

Fig.14 Comparison of average lateral pressures on rear piles for different pile groups

Fig.15 Comparison of average lateral pressures on front piles for different pile groups

5 Conclusions

1) Three-dimensional finite element modeling of method (2×1) and (2×2) passive pile groups loaded by lateral soil movements due to adjacent surcharge is presented, in which the nonlinearities of the plasticity of soil, large displacement and pile-soil contact are considered. The normal pile-soil contact stress and the average lateral pressure along the pile are obtained.

2) The lateral soft soil movement and the pile-soil interaction are revealed using three-dimensional finite element method. The separation between pile and soil is reasonably modeled and the lateral pressure acting on the pile is properly estimated. 

3) The adjacent surcharge may result in significant lateral movement of the soft soil and considerable pressure on the pile is high due to adjacent surcharge, which should be taken into account in the design of passive piles.

4) The pressures on varying rows of pile groups are different. The pressure acting on the row near the surcharge is higher than that on the other row due to the “barrier” and arching effects in pile groups.

References

[1] STEWART D P, JEWELL R J, RANDOLPH M F. Design of piled bridge abutments on soft clay for loading from lateral soil movements[J]. Geotechnique, 1994, 44(2): 277-296.

[2] STEWART D P, JEWELL R J, RANDOLPH M F. Numerical modeling of piled bridge abutments on soft ground[J]. Computers and Geotechnics, 1993, 15(1): 21-46.

[3] ELLIS E A, SPRINGMAN S M. Modeling of soil-structure interaction for a piled bridge abutment in plane strain FEM analyses[J]. Computers and Geotechnics, 2001, 28(1): 79-98.

[4] ELLIS E A, SPRINGMAN S M. Full-height piled bridge abutments constructed on soft clay[J]. Geotechnique, 2001, 51(1): 3-14.

[5] HARA T, YUZHEN Y, KEIZO U. Behavior of piled bridge abutments on soft ground: A design method proposal based on 2D elasto-plastic-consolidation coupled FEM[J]. Computers and Geotechnics, 2004, 31(4): 339-355.

[6] GOH A T C, TEH C I, WONG, K S. Analysis of piles subjected to embankment induced lateral soil movements[J]. Journal of Geotechnical and Geoenvironment Engineering, ASCE, 1997, 123(9): 792-801.

[7] BRANSBY M F, SPRINGMAN S. Selection of load–transfer functions for passive lateral loading of pile groups[J]. Computers and Geotechnics, 1999, 24(3): 155-184.

[8] CHEN L T, POULOS H G. Piles subjected to lateral soil movements[J]. Journal of Geotechnical and Geoenvironment Engineering, ASCE, 1997, 123(9): 802-811.

[9] BRANSBY M F, SPRINGMAN S M. 3D finite element modeling of pile groups adjacent to surcharge loads[J]. Computers and Geotechnics, 1996, 19(4): 301-324.

[10] SPRINGMAN S M. Lateral loading on piles due to simulated embankment construction[D]. London: Cambridge University, 1989.

[11] STEWART D P. Lateral loading of piled bridge abutments due to embankment construction[D]. Perth: University of Western Australia, 1992.

[12] POULOS H G, DAVIS E H. Pile foundation analysis and design[M]. New York: John Wiley & Sons Inc, 1980.

[13] MARTIN G R, CHEN C Y. Response of piles due to lateral slope movement[J]. Computers and Structures, 2005, 12(2): 1-11.

[14] FAN Zhen-hui, WANG Yong-he, XIAO hong-bin. Analytical method of load-transfer of single pile under expansive soil swelling[J]. Journal of Central South University of Technology, 2007, 14(4): 575-579.

[15] ZHAO Ming-hua, LIU Yu, CAO Wen-gui. The developing regularity and forecasting of settlement in soft clay roadbed[J]. Journal of Central South University: Science and Technology, 2004, 35(1): 157-161. (in Chinese)

[16] XIAO Hong-bin, ZHANG Chun-shun, HE Jie, FAN Zhen-hui. Experiment study on expansive soil-structure interaction and its sensitive analysis[J]. Journal of Central South University of Technology, 2007, 14(3): 425-430.

[17] LI Zhong-cheng, YANG Min. Soil arching effect on passive piles and 3-D numerical analysis[J]. China Civil Engineering Journal, 2006, 39(3): 114-117. (in Chinese)

(Edited by CHEN Wei-ping)

Foundation item: Project(50378036) supported by the National Natural Science Foundation of China

Received date: 2007-06-25; Accepted date: 2007-08-19

Corresponding author: ZHAO Ming-hua, Professor; Tel: +86-731-8821590; E-mail: mhzhaohd@21cn.com