A stepwise damping‐solvent extraction method for large‐scale dynamic soil–structure interaction analysis in time domain

Time‐domain analysis of dynamic soil–structure interaction based on the substructure method plays an increasing role in practical applications as compared with the frequency‐domain analysis. Efficient and accurate modelling of the unbounded soil or rock medium has been a key issue in such an analysis. This paper presents a subregional stepwise damping‐solvent extraction formulation for solving large‐scale dynamic soil–structure problems in the time domain. Accuracy and efficiency of the formulation are evaluated in detail for a classical problem involving a rigid strip foundation embedded in a half‐space. A practical large‐scale soil–structure interaction problem, which represents a high concrete gravity dam subjected to seismic load, is then analysed using the proposed method. Various responses of the dam, including time histories of the crest displacement and acceleration and contours of the peak principal stresses within the dam body, are presented. Comparisons are also made between these results with those obtained using other models for the unbounded medium. Copyright © 2007 John Wiley & Sons, Ltd.     

Analysis of soil–pile–structure interaction in a two‐layer ground during earthquakes considering liquefaction

This study is conducted with a numerical method to investigate the seismic behaviour among certain soils, single piles, and a structure. A series of numerical simulations of the seismic behaviour of a single‐pile foundation constructed in a two‐layer ground is carried out. Various sandy soils, namely, dense sand, medium dense sand, reclaimed soil, and loose sand, are employed for the upper layer, while one type of clayey soil is used for the lower layer. The results reveal that when a structure is built in a non‐liquefiable ground, an amplification of the seismic waves is seen on the ground surface and in the upper structure, and large bending moments are generated at the pile heads. When a structure is built in a liquefiable ground, a de‐amplification of the seismic waves is seen on the ground surface and in the upper structure, and large bending moments are generated firstly at the pile heads and then in the lower segment at the boundary between the soil layers when liquefaction takes place. Copyright © 2007 John Wiley & Sons, Ltd.     

Elastoplastic medium for foundation settlements and monotonic soil–structure interaction under combined loadings

Foundation settlements and soil–structure interaction are important problems to structural and geotechnical engineers. This study introduces a novel elastoplastic three‐degree‐of‐freedom medium which models foundations settlements under combined loadings. A soil–structure interaction problem can then be solved by replacing the soil mass with this three‐degree‐of‐freedom elastoplastic medium, thus reducing significantly the size of the problem. The model was developed by extending the classical plasticity concepts to the force‐deformation level. Its ability to predict foundation deformations was evaluated using finite element solutions of a typical shallow foundation problem and was found reasonably accurate while producing significant time savings. Copyright © 2006 John Wiley & Sons, Ltd.     

An efficient finite–discrete element method for quasi‐static nonlinear soil–structure interaction problems

An efficient finite–discrete element method applicable for the analysis of quasi‐static nonlinear soil–structure interaction problems involving large deformations in three‐dimensional space was presented in this paper. The present method differs from previous approaches in that the use of very fine mesh and small time steps was not needed to stabilize the calculation. The domain involving the large displacement was modeled using discrete elements, whereas the rest of the domain was modeled using finite elements. Forces acting on the discrete and finite elements were related by introducing interface elements at the boundary of the two domains. To improve the stability of the developed method, we used explicit time integration with different damping schemes applied to each domain to relax the system and to reach stability condition. With appropriate damping schemes, a relatively coarse finite element mesh can be used, resulting in significant savings in the computation time. The proposed algorithm was validated using three different benchmark problems, and the numerical results were compared with existing analytical and numerical solutions. The algorithm performance in solving practical soil–structure interaction problems was also investigated by simulating a large‐scale soft ground tunneling problem involving soil loss near an existing lining. Copyright © 2011 John Wiley & Sons, Ltd.     

Frictional contact algorithms in SPH for the simulation of soil–structure interaction

Simulation of frictional contact between soils and rigid or deformable structure in the framework of smoothed particle hydrodynamics (SPH) is presented in this study. Two algorithms are implemented into the SPH code to describe contact behavior, where the contact forces are calculated using the law of conservation of momentum based on ideal plastic collision or using the criteria of partial penetrating. In both algorithms, the problem of boundary deficiency inherited from SPH is properly handled so that the particles located at contact boundary can have precise acceleration, which is critical for contact detection. And the movement and rotation of the rigid structure are taken into account so that it is easy to simulate the process of pile driving or movement of a retaining wall in geotechnical engineering analysis. Furthermore, the capability of modeling deformability of a structure during frictional contact simulations broadens the fields of SPH application. In contrast to previous work dealing with contact in SPH, which usually use particle‐to‐particle contact or ignoring sliding between particles and solid structure, the method proposed here is more efficient and accurate, and it is suitable to simulate interaction between soft materials and rigid or deformable structures, which are very common in geotechnical engineering. A number of numerical tests are carried out to verify the accuracy and stability of the proposed algorithms, and their results are compared with analytical solutions or results from finite element method analysis. Good agreement obtained from these comparisons suggests that the proposed algorithms are robust and can be applied to extend the capability of SPH in solving geotechnical problems. Copyright © 2013 John Wiley & Sons, Ltd.     

Cyclic macro‐element for soil–structure interaction: material and geometrical non‐linearities

This paper presents a non‐linear soil–structure interaction (SSI) macro‐element for shallow foundation on cohesive soil. The element describes the behaviour in the near field of the foundation under cyclic loading, reproducing the material non‐linearities of the soil under the foundation (yielding) as well as the geometrical non‐linearities (uplift) at the soil–structure interface. The overall behaviour in the soil and at the interface is reduced to its action on the foundation. The macro‐element consists of a non‐linear joint element, expressed in generalised variables, i.e. in forces applied to the foundation and in the corresponding displacements. Failure is described by the interaction diagram of the ultimate bearing capacity of the foundation under combined loads. Mechanisms of yielding and uplift are modelled through a global, coupled plasticity–uplift model. The cyclic model is dedicated to modelling the dynamic response of structures subjected to seismic action. Thus, it is especially suited to combined loading developed during this kind of motion. Comparisons of cyclic results obtained from the macro‐element and from a FE modelization are shown in order to demonstrate the relevance of the proposed model and its predictive ability. Copyright © 2001 John Wiley & Sons, Ltd.     

A macro‐element for a circular foundation to simulate 3D soil–structure interaction

This paper presents a non‐linear interface element to compute soil–structure interaction (SSI) based on the macro‐element concept. The particularity of this approach lies in the fact that the foundation is supposed to be infinitely rigid and its movement is entirely described by a system of global variables (forces and displacements) defined in the foundation's centre. The non‐linear behaviour of the soil is reproduced using the classical theory of plasticity. Failure is described by the interaction diagram of the ultimate bearing capacity of the foundation under combined loads. The macro‐element is appropriate for modelling the cyclic or dynamic response of structures subjected to seismic action. More specifically, the element is able to simulate the behaviour of a circular rigid shallow foundation considering the plasticity of the soil under monotonic static or cyclic loading applied in three directions. It is implemented into FedeasLab, a finite element Matlab toolbox. Comparisons with experimental monotonic static and cyclic results show the good performance of the approach. Copyright © 2007 John Wiley & Sons, Ltd.     

Beam–solid contact formulation for finite element analysis of pile–soil interaction with arbitrary discretization

This paper presents an embedded beam formulation for discretization independent finite element (FE) analyses of interactions between pile foundations or rock anchors and the surrounding soil in geotechnical and tunneling engineering. Piles are represented by means of finite beam elements embedded within FEs for the soil represented by 3D solid elements. The proposed formulation allows consideration of piles and pile groups with arbitrary orientation independently from the FE discretization of the surrounding soil. The interface behavior between piles and the surrounding soil is represented numerically by means of a contact formulation considering skin friction as well as pile tip resistance. The pile–soil interaction along the pile skin is considered by means of a 3D frictional point‐to‐point contact formulation using the integration points of the beam elements and reference points arbitrarily located within the solid elements as control points. The ability of the proposed embedded pile model to represent groups of piles objected to combined axial and shear loading and their interactions with the surrounding soil is demonstrated by selected benchmark examples. The pile model is applied to the numerical simulation of shield driven tunnel construction in the vicinity of an existing building resting upon pile foundation to demonstrate the performance of the proposed model in complex simulation environments. Copyright © 2014 John Wiley & Sons, Ltd.     

Discrete element method simulations of the seismic response of shallow foundations including soil‐foundation‐structure interaction

A novel three‐dimensional particle‐based technique utilizing the discrete element method is proposed to analyze the seismic response of soil‐foundation‐structure systems. The proposed approach is employed to investigate the response of a single‐degree‐of‐freedom structure on a square spread footing founded on a dry granular deposit. The soil is idealized as a collection of spherical particles using discrete element method. The spread footing is modeled as a rigid block composed of clumped particles, and its motion is described by the resultant forces and moments acting upon it. The structure is modeled as a column made of particles that are either clumped to idealize a rigid structure or bonded to simulate a flexible structure of prescribed stiffness. Analysis is done in a fully coupled scheme in time domain while taking into account the effects of soil nonlinear behavior, the possible separation between foundation base and soil caused by rocking, the possible sliding of the footing, and the dynamic soil‐foundation interaction as well as the dynamic characteristics of the superstructure. High fidelity computational simulations comprising about half a million particles were conducted to examine the ability of the proposed technique to model the response of soil‐foundation‐structure systems. The computational approach is able to capture essential dynamic response patterns. The cyclic moment–rotation relationships at the base center point of the footing showed degradation of rotational stiffness by increasing the level of strain. Permanent deformations under the foundation continued to accumulate with the increase in number of loading cycles. Copyright © 2011 John Wiley & Sons, Ltd.     

Robust partitioned block preconditioners for large‐scale geotechnical applications with soil–structure interactions

Soil–structure interaction problems are commonly encountered in geotechnical practice and remarkably characterized with significant material stiffness contrast. When solving the soil–structure interaction problems, the employed Krylov subspace iterative method may converge slowly or even fail, indicating that the adopted preconditioning method may not suit for such problems. The inexact block diagonal preconditioners proposed recently have been shown effective for the soil–structure interaction problems; however, they haven't been exploited to full capabilities. By using the same partition strategy according to the structure elements and soil elements, the partitioned block symmetric successive over‐relaxation preconditioners or partitioned block constraint preconditioners are proposed. Based on two pile‐group foundation problems and a tunnel problem, the proposed preconditioners are evaluated and compared with the available preconditioners for the consolidation analysis and the drained analysis, respectively. In spite of one additional solve associated with the structure block and multiplications with off‐diagonal blocks in the preconditioning step, numerical results reveal that the proposed preconditioners obviously possess better performance than the recently developed inexact block preconditioners. Copyright © 2013 John Wiley & Sons, Ltd.     

Embedded beam element with interaction surface for lateral loading of piles

This paper presents a numerical formulation of a three dimensional embedded beam element for the modeling of piles, which incorporates an explicit interaction surface between soil and pile. The formulation is herein implemented for lateral loading of piles but is able to represent soil–pile interaction phenomena in a general manner for different types of loading conditions or ground movements. The model assumes perfect adherence between beam and soil along the interaction surface. The paper presents a comparison of the results obtained by means of the present formulation and by means of a previously formulated embedded pile element without interaction surface, as well as reference semi‐analytical solutions and a fully 3D finite element (FE) model. It is seen that the proposed embedded element provides a better convergence behavior than a previously formulated embedded element and is able to reproduce key features of a full 3D FE model. Copyright © 2015 John Wiley & Sons, Ltd.     

结构-地基动力相互作用的时域模型

结构-地基动力相互作用是结构地震响应分析及安全评估的一个非常重要课题。基于比例边界有限元法,提出了一种新颖的结构-地基动力相互作用的时域模型,即采用比例边界有限元子域模拟近场有限域部分,采用高阶透射边界模拟远场无限域部分。通过采用连分式展开和引入辅助变量,有限域的动力方程采用高阶的静力刚度矩阵和质量矩阵表示。高阶透射边界精确满足无限远处的辐射边界条件,具有全局精确、时间局部和收敛速度快等优点。它是基于改进的连分式法求解无限域动力刚度矩阵而建立的,在时域里表示为一阶常微分方程组。通过联立有限域和无限域的运动方程,建立了结构-地基相互作用的标准动力学方程,采用Newmark法可直接求解。3个算例结果表明,该算法在时域里比黏弹性边界更精确、有效。     

A non‐linear coupled finite element–boundary element model for the prediction of vibrations due to vibratory and impact pile driving

This paper presents a non‐linear coupled finite element–boundary element approach for the prediction of free field vibrations due to vibratory and impact pile driving. Both the non‐linear constitutive behavior of the soil in the vicinity of the pile and the dynamic interaction between the pile and the soil are accounted for. A subdomain approach is used, defining a generalized structure consisting of the pile and a bounded region of soil around the pile, and an unbounded exterior linear soil domain. The soil around the pile may exhibit non‐linear constitutive behavior and is modelled with a time‐domain finite element method. The dynamic stiffness matrix of the exterior unbounded soil domain is calculated using a boundary element formulation in the frequency domain based on a limited number of modes defined on the interface between the generalized structure and the unbounded soil. The soil–structure interaction forces are evaluated as a convolution of the displacement history and the soil flexibility matrices, which are obtained by an inverse Fourier transformation from the frequency to the time domain. This results in a hybrid frequency–time domain formulation of the non‐linear dynamic soil–structure interaction problem, which is solved in the time domain using Newmark's time integration method; the interaction force time history is evaluated using the θ‐scheme in order to obtain stable solutions. The proposed hybrid formulation is validated for linear problems of vibratory and impact pile driving, showing very good agreement with the results obtained with a frequency‐domain solution. Linear predictions, however, overestimate the free field peak particle velocities as observed in reported field experiments during vibratory and impact pile driving at comparable levels of the transferred energy. This is mainly due to energy dissipation related to plastic deformations in the soil around the pile. Ground vibrations due to vibratory and impact pile driving are, therefore, also computed with a non‐linear model where the soil is modelled as an isotropic elastic, perfectly plastic solid, which yields according to the Drucker–Prager failure criterion. This results in lower predicted free field vibrations with respect to linear predictions, which are also in much better agreement with experimental results recorded during vibratory and impact pile driving. Copyright © 2008 John Wiley & Sons, Ltd.     

LBM–DEM modeling of fluid–solid interaction in porous media

Three porous media flow problems, in which the fluid mechanical interactions are critical, are studied in a mesoscopic–microscopic coupling system. In this system, fluid flow in the pore space is explicitly modeled at mesoscopic level by the lattice Boltzmann method, the geometrical representation and the mechanical behavior of the solid skeleton are modeled at microscopic level by the particulate distinct element method (DEM), and the interfacial interaction between the fluid and the solids is resolved by an immersed boundary scheme. In the first benchmark problem, the well‐known and frequently utilized Ergun equation is validated in periodic particle and periodic pore models. In the second problem, the upward seepage problem is simulated over three stages: The settlement of the column of sphere under gravity loading is measured to illustrate the accuracy of the DEM scheme; the system is solved to hydrostatic state with pore space filled with fluid, showing that the buoyancy effect is captured correctly in the mesoscopic–microscopic coupling system; then, the flow with constant rate is supplied at the bottom of the column; the swelling of the ground surface and pore pressure development from the numerical simulation are compared with the predictions of the macroscopic consolidation theory. In the third problem, the fluid‐flow‐induced collapse of a sand arch inside a perforation cavity is tested to illustrate a more practical application of the developed system. Through comparing simulation results with analytical solutions, empirical law and physical laboratory observations, it is demonstrated that the developed lattice Boltzmann–distinct element coupling system is a powerful fundamental research tool for investigating hydromechanical physics in porous media flow. Copyright © 2012 John Wiley & Sons, Ltd.     

Dynamic analysis of a cylindrical casing–cement structure in a poroelastic stratum

The transient response of a cylindrical casing–cement structure in a poroelastic stratum under dynamic radial tractions is one of the significant issues during the analysis of downhole operations and the selection of safe material. Based on the Biot theory and general elastic mechanics, this paper gives a set of exact solutions for radial displacement, stresses for the casing–cement system and the pore pressure of the infinite surrounding poroelastic stratum in the Laplace transform space. Solutions are presented for three different types of transient radial loadings acting on the surface of casing, i.e., suddenly applied constant load, gradually applied step load and triangular pulse load. Time domain solutions are obtained using a reliable numerical method of inverse Laplace transforms. A detailed parametric study about the transient response is presented both at the casing–cement interface and the cement–stratum interface, and the distributions of the pore pressure and the effective stresses in the stratum are also examined. Copyright © 2017 John Wiley & Sons, Ltd.     

Reinforcing mechanism of anchors in slopes: a numerical comparison of results of LEM and FEM

This paper reports the limitation of the conventional Bishop's simplified method to calculate the safety factor of slopes stabilized with anchors, and proposes a new approach to considering the reinforcing effect of anchors on the safety factor. The reinforcing effect of anchors can be explained using an additional shearing resistance on the slip surface. A three‐dimensional shear strength reduction finite element method (SSRFEM), where soil–anchor interactions were simulated by three‐dimensional zero‐thickness elasto‐plastic interface elements, was used to calculate the safety factor of slopes stabilized with anchors to verify the reinforcing mechanism of anchors. The results of SSRFEM were compared with those of the conventional and proposed approaches for Bishop's simplified method for various orientations, positions, and spacings of anchors, and shear strengths of soil–grouted body interfaces. For the safety factor, the proposed approach compared better with SSRFEM than the conventional approach. The additional shearing resistance can explain the influence of the orientation, position, and spacing of anchors, and the shear strength of soil–grouted body interfaces on the safety factor of slopes stabilized with anchors. Copyright © 2003 John Wiley & Sons, Ltd.     

Parallel finite element analysis of seismic soil structure interaction using a PC cluster

This paper describes an implementation of a highly scalable parallel computational facility with high speedup efficiency using relatively low-cost hardware, which consists of a cluster of desktop personal computers (PCs) connected via a 10-Gigabit Ethernet. Two-levels of parallelization were implemented. Communication between different PCs was achieved using message passing interface (MPI) protocol. Domain decomposition was automated and based on element numbering. Domain continuity was assured largely by re-numbering the elements using a “front squasher” code prior to decomposition. Within each PC, the shared memory parallelization was implemented using either the open-multiprocessing (OpenMP) or the MPI protocol. Analysis of three different problems with number of degrees-of-freedom ranging from about 129,000 to about 2,260,000 shows a speedup efficiency generally above 70%. Super-linear speedup was achieved in several of the cases examined in this study, with the hybrid MPI-OpenMP approach generally performing better compared to the pure MPI method for parallelization. The results demonstrate the feasibility of acquiring a parallel computing facility with relatively modest outlay that is within the reach of consulting or engineering offices.     

Implementation of DSC model and application for analysis of field pile tests under cyclic loading

The disturbed state concept (DSC) model, and a new and simplified procedure for unloading and reloading behavior are implemented in a nonlinear finite element procedure for dynamic analysis for coupled response of saturated porous materials. The DSC model is used to characterize the cyclic behavior of saturated clays and clay–steel interfaces. In the DSC, the relative intact (RI) behavior is characterized by using the hierarchical single surface (HISS) plasticity model; and the fully adjusted (FA) behavior is modeled by using the critical state concept. The DSC model is validated with respect to laboratory triaxial tests for clay and shear tests for clay‐steel interfaces. The computer procedure is used to predict field behavior of an instrumented pile subjected to cyclic loading. The predictions provide very good correlation with the field data. They also yield improved results compared to those from a HISS model with anisotropic hardening, partly because the DSC model allows for degradation or softening and interface response. Copyright © 2000 John Wiley & Sons, Ltd.     

Pile driving by numerical cavity expansion

A cavity expansion procedure for the simulation of pile driving is presented and assessed in this paper. The analysis uses a non-linear finite-element model and the penetration of the pile into the soil is simulated by a radial opening of the soil around the pile. The case of a pile advanced by expansion will be compared to a similar pile subjected to computational driving (referred to, respectively, as ‘expanded’ and ‘driven’ piles for convenience). The state of stress and deformation, and the evolution of pore-water pressure in the soil will be monitored for the expanded and driven piles. Further computational driving will be applied to both cases and the pile response and soil resistance will be compared. The computational cost of advancing the pile by expansion will finally be investigated. Copyright © John Wiley & Sons, Ltd.