Journal of Shanghai Jiao Tong University

Journal of Shanghai Jiaotong University >

2016 , Vol. 50 >Issue 01: 8 - 16

DOI: https://doi.org/10.16183/j.cnki.jsjtu.2016.01.002

Modelling of Saturated Soil Dynamic Coupled Consolidation Problems Using Three-Dimensional Scaled Boundary Finite Element Method

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  • 1.College of Civil Engineering and Architecture, Nanchang Institute of Technology, Nanchang 330029, China
    2.School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiaotong University, Shanghai 200240, China

Received date: 2015-02-02

  Online published: 2016-01-29

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Abstract

Based on the Biot's dynamic coupled consolidation theory, the scaled boundary finite-element method was developed to correctly model the dynamic unbounded far-field boundary of three-dimensional (3D) fully saturated soil in this paper. Body forces and surface tractions were considered in the derivation. The concept of similarity, the compatibility equation, Biot's coupled consolidation equations, and the Galerkin's weighted-residual method were used to derive the formulation for the governing equations. The main difference from the single-phase version was the presence of pore water pressures as additional parameters to be solved, in addition to the displacements, strain and stress which were incorporated into the static-stiffness matrices by producing fully coupled matrices. Solving the resulting equations yielded a boundary condition satisfying the far-field radiation condition exactly. The computed solutions were exact in a radial direction (perpendicular to the boundary and pointing towards infinity), while converging to the exact solution in the finite element sense in the circumferential direction parallel to the soil-structure boundary interface.

Key words： three-dimensional (3D) fully saturated soil; Galerkin’s weighted-residual method; scaled boundary finite-element method; Biot’s dynamic coupled consolidation theory

Cite this article

XU Bin, XU Manqing, WANG Jianhua . Modelling of Saturated Soil Dynamic Coupled Consolidation Problems Using Three-Dimensional Scaled Boundary Finite Element Method[J]. Journal of Shanghai Jiaotong University, 2016 , 50(01) : 8 -16 . DOI: 10.16183/j.cnki.jsjtu.2016.01.002

References

[1] 陈胜立, 贺海洪. 横观各向同性层状饱和地基的轴对称二维Biot固结分析[J]. 上海交通大学学报, 2005, 39(5): 760-768.
[1] CHEN Shengli, HE Haihong. Axisymmetric consolidation of a transversely isotropic single-layered soil[J]. Journal of Shanghai Jiaotong University, 2005, 39(5): 760-768.
[2] 陆建飞, 司漪, 王建华. 层状粘弹性饱和土地基与基础和上部结构的共同作用[J]. 上海交通大学学报, 2001, 35(4): 489-492.
[2] LU Jianfei, SI Yi, WANG Jianhua. Interaction between super-structure, raft and layered viscoelastic saturated soil[J]. Journal of Shanghai Jiaotong University, 2001, 35(4): 489-492.
[3] 杜修力, 王进廷. 动水压力及其对坝体地震反应影响的研究进展[J]. 水利学报, 2001(7): 13-21.
[3] DU Xiuli, WANG Jinting. Review of studies on the hydrodynamic pressure and its effects on the seismic response of dams[J]. Journal of Hydraulic Engineering, 2001(7): 13-21.
[4] 张楚汉. 结构-地基动力相互作用问题[M]. 南京: 河海大学出版社, 1993: 243-266.
[5] SMITH W D. A non-reflecting plain boundary for wave propagation problems[J]. Journal of Computational Physics, 1974, 15(4): 492-503.
[6] ENGQUIST B, MAJDA A. Absorbing boundary conditions for the numerical simulation waves[J]. Mathematics of Computation, 1977, 31(139): 629-651.
[7] LIAO Zhenpeng, ZHOU Zhenghua, ZHANG Yanhang. Stable implementation of transmitting boundary in numerical simulation of wave motion[J]. Chinese Journal of Geophysica, 2002, 45(4): 554-568.
[8] KEYS R G. Absorbing boundary conditions for acoustic media[J]. Geophysics, 2012, 50(6): 892-902.
[9] KHALILI N, VALLIAPPAN S, TABTABAIE Y J, et al. 1Dinfinite element for dynamic problems in saturated porous media[J]. Communications in Numerical Methods in Engineering, 1997, 13(9): 727-38.
[10] 徐斌, 高亮, 雷晓燕, 等. 移动荷载与土体中孔洞相互作用的2.5D边界元法分析[J]. 西南交通大学学报, 2013, 48(4): 659-665.
[10] XU Bin, GAO Liang, LEI Xiaoyan, et al. Analysis of dynamic interaction between hole embedded in saturated soil and moving loads using 2.5Dboundary element method[J]. Journal of Southwest Jiaotong University, 2013, 48(4): 659-665.
[11] YAZDCHI M, KHALILI N, VALLIAPPAN S. Non-linear seismic behaviour of concrete gravity dams using coupled finite element-boundary element method[J]. International Journal for Numerical Methods in Engineering, 1998, 44(1): 101-130.
[12] SONG C, WOLF J P. The scaled boundary finite-element method alias consistent infinitesimal finite-element cell method[J]. Computer Methods in Applied Mechanics and Engineering, 1997, 147(3/4): 329-355.
[13] LI Miao, ZHANG Hong, GUAN Hong, et al. Three-dimensional investigation of wave-pile group interaction using the scaled boundary finite element method. Part I. Theoretical developments[J]. Ocean Engineering, 2013, 64: 174-184.
[14] SONG Hao, TAO Longbin. An efficient scaled boundary FEM model for wave interaction with a nonuniform porous cylinder[J]. International Journal for Numerical Methods in Fluids, 2010, 63(1): 96-118.
[15] BIOT M A. General theory of three-dimensional consolidation[J]. Journal of Applied Physics, 1941, 12(2): 155-164.
[16] BANERJEE P K B, MAMOON S M. A fundamental solution due to a periodic point force in the interior of an elastic half-space[J]. Earthquake Engineering and Structural Dynamics, 1990, 19(1): 91-105.
[17] KOBAYASHI S, NISHIMURA N. Green's tensors for elastic half-space: An application of boundary integral equation method[J]. Memoirs of the Faculty of Engineering, Kyoto University, 1980, 42(2): 228-241.
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