Tensionless–frictionless interaction of flexible annular foundation with a transversely isotropic multi‐layered half‐space

A transversely isotropic multi‐layered half‐space, with axis of material symmetry perpendicular to the free surface, supports a flexible either annular or solid circle foundation. The contact area of the foundation and the half‐space is considered to be both frictionless and tensionless. The foundation is assumed to be affected by a vertical static axisymmetric load. Detailed analysis of the interaction of these two systems with different thickness of layers is the target of this paper. With the use of ring load Green's functions for both the foundation and the continuum half‐space, an integral equation accompanied with some inequalities is introduced to model the complex BVP. With the incorporation of ring‐shape FEM, we are capable of capturing both regular and singular solution smoothly. The validity of the combination of the analytical and numerical method is proved with comparing the results of this paper with a number of benchmark cases of both linear and nonlinear interaction of circular and annular foundation with half‐space. Some new illustrations are presented to portray the aspect of the anisotropy and layering of the half‐space. Copyright © 2014 John Wiley & Sons, Ltd.     

Validation of a three‐dimensional constitutive model for nonlinear site response and soil‐structure interaction analyses using centrifuge test data

The capability of a bounding surface plasticity model with a vanishing elastic region to capture the multiaxial dynamic hysteretic responses of soil deposits under broadband (eg, earthquake) excitations is explored by using data from centrifuge tests. The said model was proposed by Borja and Amies in 1994 (J. Geotech. Eng., 120, 6, 1051‐1070), which is theoretically capable of representing nonlinear soil behavior in a multiaxial setting. This is an important capability that is required for exploring and quantifying site topography, soil stratigraphy, and kinematic effects in ground motion and soil‐structure interaction analyses. Results obtained herein indicate that the model can accurately predict key response data recorded during centrifuge tests on embedded specimens—including soil pressures and bending strains for structural walls, structures' racking displacements, and surface settlements—under both low‐ and high‐amplitude seismic input motions, which was achieved after performing only a basic material parameter calibration procedure. Comparisons are also made with results obtained using equivalent linear models and a well‐known pressure‐dependent multisurface plasticity model, which suggested that the present model is generally more accurate. The numerical convergence behavior of the model in nonlinear equilibrium iterations is also explored for a variety of numerical implementation and model parameter options. To facilitate broader use by researchers and practicing engineers alike, the model is implemented as a “user material” in ABAQUS Standard for implicit time stepping.     

冻融条件下模型桩基水平动力试验研究

基于自制的冻土-桩动力相互作用模型试验系统,对-5℃、-3℃及上层融化多年冻土中模型桩基进行了水平向动力试验,主要研究了冻结及上层融化冻土中模型桩基的桩头位移-荷载关系、桩基水平动刚度变化及桩身弯矩分布情况。结果表明：冻土中桩基动力响应特性与土体温度密切相关;正冻土中桩基有较大的侧向刚度,当冻土与桩接触面出现较大间隙时,桩头位移-荷载曲线呈反S形;桩基动力性能随多年冻土温度降低将有所改善;当冻土上部出现融化层时,桩基动响应变化显著,桩头动刚度明显减小,桩基在较小动载下可发生较大侧向位移,同时桩身最大弯矩值较正冻土中偏大,且此弯矩点埋深较大。对于多年冻土区桩基工程,应特别重视夏季上层冻土融化时可能出现的震害。     

Hybrid FE‐DQ for dynamic analysis of multilayered half‐space subjected to concentrated point impulsive loading

A hybrid finite element method and differential quadrature method (DQM) is developed to estimate the dynamic response of two‐dimensional multilayered half‐spaces subjected to impulsive point loading. Nonreflecting absorbing boundary conditions consist of appropriate springs, and dampers are considered. The capabilities of the finite element method for solving boundary value problems with general domain, loading and systematic boundary treatment are combined with accurate and stable time marching capabilities of the DQM to develop an accurate and efficient numerical technique. The capability, efficiency, robustness and convergence of the DQM for solving the dynamic problem are demonstrated through numerical simulations of various half‐spaces with different time increments and layer arrangement. Also, comparison study when using Newmark's time integration scheme for the same problem is done. It can be concluded that the DQM as an unconditionally stable method is suitable for solving such a problem. Also, parametric study is performed to show the effect of the absorbing boundary conditions on the dynamic response. Copyright © 2012 John Wiley & Sons, Ltd.     

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.     

Elastic lateral dynamic impedance functions for a rigid cylindrical shell type foundation

Elastic lateral dynamic impedance functions are defined as the ratio of the lateral dynamic force/moment to the corresponding lateral displacement/rotation at the top ending of a foundation at very small strains. Elastic lateral dynamic impedance functions have a defining influence on the natural frequencies of offshore wind turbines supported on cylindrical shell type foundations, such as suction caissons, bucket foundations, and monopiles. This paper considers the coupled horizontal and rocking vibration of a cylindrical shell type foundation embedded in a fully saturated poroelastic seabed in contact with a seawater half‐space. The formulation of the coupled seawater–shell–seabed vibration problem is simplified by treating the shell as a rigid one. The rigid shell vibration problem is approached by the integral equation method using ring‐load Green's functions for a layered seawater‐seabed half‐space. By considering the boundary conditions at the shell–soil interface, the shell vibration problem is reduced to Fredholm integral equations. Through an analysis of the corresponding Cauchy singular equations, the intrinsic singular characteristics of the problem are rendered explicit. With the singularities incorporated into the solution representation, an effective numerical method involving Gauss–Chebyshev method is developed for the governing Fredholm equations. Selected numerical results for the dynamic contact load distributions, displacements of the shell, and lateral dynamic impedance functions are examined for different shell length–radius ratio, poroelastic materials, and frequencies of excitation. Copyright © 2016 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.     

Rocking vibrations of a rigid embedded foundation in a poroelastic half‐space

This paper presents an analysis of the rocking vibrations of a rigid cylindrical foundation embedded in poroelastic soil. The foundation is subjected to time‐harmonic rocking excitation and is perfectly bonded to the surrounding soil. The soil underlying the foundation base is represented by a homogeneous poroelastic half‐space, whereas the soil along the side of the foundation is modeled as an independent poroelastic stratum composed of a series of infinitesimally thin layers. The behavior of the soil is governed by Biot's poroelastodynamic theory. The contact surface between the foundation base and the poroelastic soil is assumed to be smooth and either fully permeable or impermeable. The dynamic interaction problem is solved by employing a simplified analytical method. Some numerical results for the nondimensional rocking dynamic impedance and nondimensional angular displacement amplitude of the foundation are presented to show the effect of nondimensional frequency of excitation, poroelastic material parameters, hydraulic boundary condition, depth ratio and mass ratio of the foundation. Copyright © 2009 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.     

Numerical stability for modelling of dynamic two‐phase interaction

Dynamic two‐phase interaction of soil can be modelled by a displacement‐based, two‐phase formulation. The finite element method together with a semi‐implicit Euler–Cromer time‐stepping scheme renders a discrete equation that can be solved by recursion. By experience, it is found that the CFL stability condition for undrained wave propagation is not sufficient for the considered two‐phase formulation to be numerically stable at low values of permeability. Because the stability analysis of the two‐phase formulation is onerous, an analysis is performed on a simplified two‐phase formulation that is derived by assuming an incompressible pore fluid. The deformation of saturated porous media is now captured in a single, second‐order partial differential equation, where the energy dissipation associated with the flow of the fluid relative to the soil skeleton is represented by a damping term. The paper focuses on the different options to discretize the damping term and its effect on the stability criterion. Based on the eigenvalue analyses of a single element, it is observed that in addition to the CFL stability condition, the influence of the permeability must be included. This paper introduces a permeability‐dependent stability criterion. The findings are illustrated and validated with an example for the dynamic response of a sand deposit. Copyright © 2015 John Wiley & Sons, Ltd.     

Vertical dynamic response of a rigid foundation embedded in a poroelastic soil layer

A simplified analytical method is presented for the vertical dynamic analysis of a rigid, massive, cylindrical foundation embedded in a poroelastic soil layer. The foundation is subjected to a time‐harmonic vertical loading and is perfectly bonded to the surrounding soil in the vertical direction. The soil underlying the foundation base is represented by a single‐layered poroelastic soil based on rigid bedrock while the soil at the side of the foundation is modeled as an independent poroelastic layer composed of a series of infinitesimally thin layers. The behavior of the soil is governed by Biot's poroelastodynamic theory and its governing equations are solved by the use of Hankel integral transform. The contact surface between the foundation base and the soil is smooth and fully permeable. The dynamic interaction problem is solved following standard numerical procedures. The accuracy of the present solution is verified by comparisons with the well‐known solutions obtained from other approaches for both the elastodynamic interaction problem and poroelastodynamic interaction problem. Numerical results for the vertical dynamic impedance and response factor of the foundation are presented to demonstrate the influence of nondimensional frequency of excitation, soil layer thickness, poroelastic material parameters, depth ratio and mass ratio on the dynamic response of a rigid foundation embedded in a poroelastic soil layer. Copyright © 2008 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.     

Analytical solutions for dynamic pressures of coupling fluid–porous medium–solid due to SV wave incidence

This paper presents the results of theoretical investigation on the dynamic coupling of an ideal fluid‐porous medium‐elastic half‐space system subjected to SV waves to study the effect of sediment on the seismic response of dams for reservoirs that are deposited with a significant amount of sediment after a long period of operation. The effects of the porous medium and the incident wave angle on dynamic pressures in the overlying ideal fluid are analyzed, and the reflection and transmission coefficients of the wave at the material interfaces are derived using an analytical solution in terms of displacement potentials. The numerical test of modeling shows that the dynamic pressures significantly depend on the properties of porous medium. The fully saturated porous medium reduces the response peaks slightly, while the partially saturated porous medium causes a considerable increase in the resonance peaks. Copyright © 2009 John Wiley & Sons, Ltd.     

Axisymmetric interaction of a rigid disc with a transversely isotropic half‐space

A theoretical formulation is presented for the determination of the interaction of a vertically loaded disc embedded in a transversely isotropic half‐space. By means of a complete representation using a displacement potential, it is shown that the governing equations of motion for this class of problems can be uncoupled into a fourth‐order partial differential equation. With the aid of Hankel transforms, a relaxed treatment of the mixed‐boundary value problem is formulated as dual integral equations, which, in turn, are reduced to a Fredholm equation of the second kind. In addition to furnishing a unified view of existing solutions for zero and infinite embedments, the present treatment reveals a severe boundary‐layer phenomenon, which is apt to be of interest to this class of problems in general. The present solutions are analytically in exact agreement with the existing solutions for a half‐space with isotropic material properties. To confirm the accuracy of the numerical evaluation of the integrals involved, numerical results are included for cases of different degrees of the material anisotropy and compared with existing solutions. Further numerical examples are also presented to elucidate the influence of the degree of the material anisotropy on the response. Copyright © 2009 John Wiley & Sons, Ltd.     

Dynamic response of road pavement resting on a layered poroelastic half‐space to a moving traffic load

This paper is dedicated to study the dynamic response of a thin‐plate resting on a layered poroelastic half‐space under a moving traffic load. Based on the dynamic poroelastic theory of Biot, the general solutions of the homogeneous poroelastic foundation are obtained by Fourier translation. By using the transmission and reflection matrices method in the frequency domain, the equivalent stiffness of the layered poroelastic half‐space is presented. Kirchhoff's hypotheses are applied to obtain the vertical displacement of the thin plate. By using the inverse Fourier transform, the time domain solution is obtained. As an example of three layers, the influences of the load velocity, the material properties of poroelastic layers, and the flexural rigidity of the plate on the response of the pavement system are examined. Analyses show that a soft intermediate layer results in the significant increase of vertical displacement of road pavement. Comparison with the existing work validates the present model. Copyright © 2013 John Wiley & Sons, Ltd.     

Forced vertical and horizontal movements of a rectangular rigid foundation on a transversely isotropic half‐space

An analytical investigation of a half‐space containing transversely isotropic material under forced vertical and horizontal displacements applied on a rectangular rigid foundation is presented in this paper. With the goal of a rigorous solution to the shape‐ and rigidity‐ induced singular mixed boundary value problem, the formulation employs scalar potential representation, the Fourier expansion and the Hankel integral transforms method to obtain the surface arbitrary point‐load solution in cylindrical coordinate system. The obtained Green's functions are rewritten in rectangular coordinate system, allowing the response of the half‐space because of an arbitrary distributed load on a rectangular surface area be given in terms of a double integral. The numerical evaluations of stresses are done with the use of an element, which is singular at the edge and the corner of the rectangle. Upon the imposition of the rigidity displacement boundary condition for a rigid foundation and the use of a set of two‐dimensional adaptive‐gradient elements, which can capture the singular behavior in the contact stress effectively, a set of new numerical results are presented to illustrate the effect of transverse isotropy on the foundation response. Copyright © 2012 John Wiley & Sons, Ltd.     

On vertical dynamic stability and cross‐section optimization of closed‐ended hollow pile by considering soil compaction effects

This paper conducts a comprehensive study on the effects of expansion force after pile driving on the vertical vibration of the hollow pile. The initial radially inhomogeneous strain field of soil in disturbed soil region and dynamic shear modulus of remolded soil are constructed by applying the cylindrical cavity expansion method. The equation governing the incremental motion of the soil is consequently deduced on the basis of incremental deformations superposed on an underlying finite deformation. The longitudinal impedance of the top of the pile and the velocity response in frequency and time domains are also numerically studied. The relations between the expansion force after pile driving and the velocity response of the pile with different wall thickness are discussed accordingly. The results suggest that a pile has a better dynamical stability when the characteristics of the section are optimized and interacting force with soil medium gets smaller.     

Soil‐pile interaction in the pile vertical vibration considering true three‐dimensional wave effect of soil

The dynamic response of an end bearing pile embedded in a linear visco‐elastic soil layer with hysteretic type damping is theoretically investigated when the pile is subjected to a time‐harmonic vertical loading at the pile top. The soil is modeled as a three‐dimensional axisymmetric continuum in which both its radial and vertical displacements are taken into account. The pile is assumed to be vertical, elastic and of uniform circular cross section. By using two potential functions to decompose the displacements of the soil layer and utilizing the separation of variables technique, the dynamic equilibrium equation is uncoupled and solved. At the interface of soil‐pile system, the boundary conditions of displacement continuity and force equilibrium are invoked to derive a closed‐form solution of the vertical dynamic response of the pile in frequency domain. The corresponding inverted solutions in time domain for the velocity response of a pile subjected to a semi‐sine excitation force applied at the pile top are obtained by means of inverse Fourier transform and the convolution theorem. A comparison with two other simplified solutions has been performed to verify the more rigorous solutions presented in this paper. Using the developed solutions, a parametric study has also been conducted to investigate the influence of the major parameters of the soil‐pile system on the vertical vibration characteristics of the pile. Copyright © 2013 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.