Dynamic Soil-structure Interaction Problems Research Articles

Space–time finite element method with domain reduction techniques for dynamic soil–structure interaction problems

AbstractDesign of earth structures, such as dams, tunnels, and embankments, against the vibrational loading caused by high‐speed trains, road traffic, underground explosions, and, more importantly, earthquake motion, demands solutions of the dynamic soil–structure Interaction (SSI) problem. This paper presents a velocity‐based space–time finite element procedure, v‐ST/finite element method (FEM), to solve dynamic SSI problems. The main goal of this study is to present the computation details of implementing viscous boundary conditions of Lysmer–Kuhlemeyer to truncate the unbounded soil domain. Furthermore, additional time‐dependent boundary conditions, in terms of the free‐field response, are included to facilitate energy flow from the far field to the computation domain at the vertical truncated boundaries. In the FEM, seismic input motion is applied to an effective nodal force vector, which can be obtained explicitly in the numerical simulations. Finally, the response of a concrete gravity dam resting on an elastic half‐space to the horizontal component of earthquake motion is computed and successfully compared with the results of semidiscrete FEM using the Newmark‐ method.

Material damping in a stratified soil deposit

Due to the extensive use of one-dimensional equivalent linear analyses to determine the free-field response of nonlinear soil deposits, dynamic numerical simulations able to reproduce an analogous response to equivalent linear codes are of great value for practical engineering, particularly for dynamic soil-structure interaction problems. An appealing alternative, for problems not close to a failure condition, is to assume a linear elastic behaviour of the soil but with stiffness parameters derived from one-dimensional equivalent linear analyses, i.e. consistent with the level of deformation induced by the input motion. In this approach, energy dissipation has to be artificially incorporated through material damping formulations. In this work, local, Rayleigh, and hysteretic damping formulations in FLAC were assessed to emulate results from one-dimensional equivalent linear analysis. A main feature of the analyses is that they consider a site having a considerably stratified soil deposit, in which the shear wave velocity profile displays significant variations and where the selection of some parameters in the damping formulations is not a trivial task. Results provide relevant insights into the performance of the adopted damping formulations and the selection of material damping parameters to reproduce results of equivalent linear analyses.

Numerically study of SSSI effect on nuclear power plant on layered soil

In typical dynamic soil-structure interaction (SSI) problems, the dynamic response a structure can be affected by the existence of some nearby structures, which is sometimes referred to as the dynamic structure-soil-structure interaction (SSSI). This effect is especially important in the earthquake engineering design of adjacent nuclear power plants, as the safety risk is relatively high. However, the current understanding on the SSSI of nuclear power plants is still insufficient. In this work, we use the finite element method to investigate the SSSI of two nuclear power plants located at a specific distance under earthquake excitation. Four nuclear-power-plant-soil systems are designed to account for the SSI and SSSI respectively, where the soil properties are obtained from drilling data. The effect of the SSSI on the nuclear power plants is studied by comparing the dynamic responses of four nuclear power plants-soil systems in vertical and horizontal directions, in which both layered soils and local weak interlayer soils are considered. The results of numerical study show that the presence of one nuclear power plant has a favorable effect on the seismic response of an adjacent nuclear power plant, such as reducing the displacement response, but this effect is limited. In addition, the SSSI effect is related to not only the soil properties, but also the direction of ground motion. Furthermore, the existence of soft soil layers complicates the SSSI effect. The results provide important insights for the construction and expansion of nuclear power plants.

Numerical Modeling of a Pile Group Subjected to Seismic Loading Using the Hypoplasticity Model

Various simple and complicated models have been utilized to simulate the stress-strain behavior of the soil. These models are used in Finite Element Modeling (FEM) for geotechnical engineering applications and analysis of dynamic soil-structure interaction problems. These models either can't adequately describe some features, such as the strain-softening of dense sand, or they require several parameters that are difficult to gather by conventional laboratory testing. Furthermore, soils are not completely linearly elastic and perfectly plastic for the whole range of loads. Soil behavior is quite difficult to comprehend and exhibits a variety of behaviors under various circumstances. As a result, a more realistic constitutive model is needed, one that can represent the key aspects of soil behavior using simple parameters. In this regard, the powerful hypoplasticity model is suggested in this paper. It is classified as a non-linear model in which the stress increment is stated in a tonsorial form as a function of strain increment, actual stress, and void ratio. Eight material characteristics are needed for the hypoplastic model. The hypoplastic model has a unique way to keep the state variables and material parameters separated. Because of this property, the model can implement the behavior of soil under a variety of stresses and densities while using the same set of material properties.

Comparative nonlinear soil-structure interaction analyses using macro-element and soil-block modelling approaches

In dynamic soil-structure interaction problems, involving the coupling of structure, foundation and soil, the use of a nonlinear macro-element modelling approach may result particularly advantageous not only to consider nonlinear effects and thus avoid the introduction of possible bias in seismic risk assessment analyses, especially when ground motion intensity levels are high, but also to greatly reduce the heavy computational effort required by 3D finite element soil-block models. In this work, a footing macro-element that models the soil nonlinear behaviour at near-field, as well as the far-field dynamic impedance and energy dissipation through radiation damping, is verified against results obtained from the analysis with OpenSees of a 3D nonlinear soil-block model, itself verified through cross-checks and cross-modelling efforts with equivalent-linear analyses in STRATA and nonlinear analyses in DEEPSOIL. Considering two soil profiles of different complexity and two records of different intensity, one of which leads to extensive soil nonlinearity, the soil-block is verified first. Then, the macro-element model, available in SeismoStruct, is verified against the soil-block model in terms of structural response of a single-degree-of-freedom (SDOF) system as well as near-field soil-footing behaviour.

Application of constitutive model in simulation analysis of tunnel construction

Application of constitutive model in simulation analysis of tunnel construction

Boundary element analysis of dynamic interaction of anisotropic elastic half-space and structure under impact load

In this paper, a direct boundary element formulation for numerical modelling of threedimensional dynamic soil-structure interaction is briefly described. Formulation is applicable to problems involving isotropic and anisotropic elastic materials. It is based on the Laplace domain regularized boundary integral equations for the displacements under assumption of vanishing initial conditions and zero body forces. Mixed boundary elements are employed for the spatial discretization of the boundary integral equations. Subdomain technique is used to tackle problems involving piecewise homogeneous material properties. The described formulation is employed for the boundary element analysis of dynamic soil-structure interaction problem involving a structure which contains a cavity with a complex geometrical form. Soil is represented by a transversely isotropic elastic half-space. Effect of material anisotropy of half-space on the transient response of the embedded structure is assessed. It is observed that the shear modulus anisotropy have substantial impact on the displacements response. Influence of the Young’s modulus in the plane of isotropy is lesser but still pronounced.

Vibration soil isolation analysis based on a 3-D frequency domain Direct Boundary Element implementation: GPGPU acceleration

A Direct Boundary Element implementation was accelerated by using General Purpose Graphics Processing Units (GPGPUs) to improve the performance in analysis of soil vibration isolation with trenches. The Boundary Element formulation is based on the 3D full space stationary fundamental (visco)elastic solutions. In this stationary Dynamic Soil-Structure Interaction (DSSI) problem, the soil is externally excited generating a propagation wave field. This resulting field induces vibrations on structures in the surrounding soil. Aiming to reduce the time required to calculate the vibration soil behavior, a code was developed with CUDA C++ and OpenMP to explore the capabilities provided by GPUs and multi-core CPUs. The performance analysis is conducted by comparing codes in two modes: one uses exclusively CPU and the other is GPU-accelerated. The implementation presents the vibration reduction as well as comparisons of computation time and speedup for two groups of CPU and GPU. The speedup ratios range from 8 to 60 comparing to the sequential version.

Shear modulus and damping ratio of a nonplastic silt at large shear strains

Site response analyses and solution of dynamic soil-structure interaction problems need determination of variation of shear modulus and damping ratio with shear strain. Since many studies in literature concern evaluation of behavior of sands and silty sands, a series of cyclic triaxial tests were performed to determine the variation of shear modulus and damping ratio of a nonplastic silt with shear strain. Stress controlled cyclic triaxial tests on silt specimens of initial relative densities ranging among 30%, 50% and 70% were performed. Tests were carried out on identical samples under different CSR levels, and the confining pressure was selected as 100 kPa. Variation of shear modulus and damping ratio of silts with cyclic stress ratio amplitude, relative density and number of cycles were investigated. It was understood that soil relative density and cyclic stress ratio amplitude has a significant influence on shear modulus and damping ratio of silts. It was also observed that, as the cyclic stress ratio amplitude is increased, greater shear modulus and lower damping ratio values were obtained.

Dynamic soil-structure interaction in a 3D layered medium treated by coupling a semi-analytical axisymmetric far field formulation and a 3D finite element model

A strategy for dynamic soil-structure interaction problems involving three-dimensional layered soil is proposed. It is based on coupling an axisymmetric formulation for the regular layered far field region with a general three-dimensional finite element model of the near field via a cylindrical near field / far field interface. Using a virtual work statement, an axisymmetric scaled boundary finite element method (SBFEM) for the elastodynamic analysis of 3D layered continua is derived. Here, a vertical line, which is rotated around the origin of the cylindrical coordinate system is discretized in the finite element sense. A nonlinear differential equation in dynamic stiffness is obtained for each term of the Fourier series describing the circumferential variation of displacements in the far field, which must be solved numerically for each frequency of interest. While this leads to considerable savings in numerical cost compared to the effort associated with calculating a fully coupled stiffness matrix for the 3D problem, the numerical efficiency can be further increased by re-casting the problem using the method of weighted residuals. In doing so, a link with the well-known thin-layer method is established. The latter leads to a standard eigenvalue problem for the calculation of wave numbers and modes. The axisymmetric stiffness formulation obtained using one of the two aforementioned techniques is coupled with the 3D finite element model of the near field via the dynamic stiffness matrix relating nodal forces to nodal displacements at the cylindrical interface. Following a physically motivated approach, individual columns of the latter are obtained by considering situations where a unit displacement is assumed for the corresponding degree of freedom and zero displacements elsewhere and by expanding the corresponding displacement field into a Fourier series. The proposed strategy is applied to various soil-structure interaction problems involving flexible foundations of irregular shape resting on layered ground over rigid bedrock.

Study of Direct Finite Element Method of Analysing Soil–Structure Interaction in a Simply Supported Railway Bridge Subjected to Resonance

This paper presents the dynamic soil–bridge interaction under high-speed railway lines, under different soil stiffness conditions. Starting from the analysis of a simply supported Euler–Bernoulli beam model subjected to moving loads, a three-dimensional multi-body (soil–abutment–bridge–ballast–sleeper–rail) model formulated in the time domain to study the vibrations induced due to the passage of moving concentrated loads was analysed using the direct finite element method of soil–structure interaction analysis. The high-speed train was considered to be a set of concentrated loads, the rail was modelled as a Euler–Bernoulli beam (frame element), and the sleepers, ballast, bridge, abutments and soil were modelled using eight-node solid (brick) elements. Layered soil stratum’s effects on the dynamic response of the bridge deck and variation of stresses were studied. From this study, it was observed that the direct method of FE analysis can be an effective tool to solve the complex dynamic soil–structure interaction problems.

Nonlinear soil-structure interaction analysis in poroelastic soil using mid-point integrated finite elements and perfectly matched discrete layers

A numerical approach for a nonlinear analysis of soil-structure interaction in poroelastic soil is proposed. Nonlinear behavior in the near-field region of soil is considered by conventional finite elements. The far-field region of soil is represented by mid-point integrated finite elements and perfectly matched discrete layers (PMDLs) in order to consider the energy radiation into infinity. The mid-point integrated finite elements can be formulated identically to conventional finite elements. Thus, PMDLs for poroelastic media are formulated in this study. A means by which to represent a layered poroelastic half-space with conventional finite elements, mid-point integrated finite elements, and the developed PMDLs is proposed. The proposed numerical approach is verified from various perspectives. The approach is applied to a nonlinear analysis of the earthquake responses of a structural system on poroelastic soil. It is demonstrated via the application that the proposed approach can be applied successfully to nonlinear dynamic soil-structure interaction problems.

The influence of uncertain local subsoil conditions on the response of buildings to ground vibration

This paper examines the influence of imperfect knowledge of the local subsoil conditions on the prediction of building response to ground-borne vibration. The focus is on problems of environmental ground vibration in the wide frequency range between 1 Hz and 80 Hz. A probabilistic finite element-perfectly matched layers model is developed for the analysis of the dynamic soil-structure interaction problem where the shear modulus of the soil is modeled as a conditional random field. A subdomain formulation is employed to impose loading by an incident wave field in the model. The uncertainty on the subsoil properties is propagated to the response of a building by means of Monte Carlo simulation. A case study is considered to investigate the influence of the spatial correlation length of the random field representing the shear modulus of the subsoil, and the foundation type of the building. The structural response uncertainty varies over frequency bands but as a general trend increases with frequency. The foundation type of the building is a crucial parameter determining the structural response and the associated uncertainty bounds.

A nonlinear constitutive model for beam elements with cyclic degradation and damage assessment for advanced dynamic analyses of geotechnical problems. Part II: validation and application to a dynamic soil–structure interaction problem

The variation of the stiffness mismatch between soil and structural elements during ground motions is one of the most influential parameters for the assessment of the kinematic component in SSI problems. The variation of the stiffness ratio is mainly governed by material nonlinearity that can develop in either the soil or the structural parts of the system. The direct approach, which is in principle capable of accounting for both soil and structural nonlinearities, provides the “complete solution” to the SSI problem. The implementation of this approach requires the availability of general-purpose computational platforms where the modeling process is very often, particularly time-demanding. Even when using this kind of software, the substructure approach, suitable only if the system behave linearly or weakly nonlinearly, is often preferred over the direct method because it allows to split the model in two parts, simplifying the problem. The nonlinear constitutive model for beam elements presented in the companion paper (Andreotti and Lai in Bull Earthq Eng, 2017, doi:10.1007/s10518-017-0090-1) is conceived to be embedded in computer programs oriented to geotechnical applications to overcome their typical limitations in structural modeling. The proposed constitutive model is capable to simulate the cyclic degradation of stiffness and strength. Furthermore it allows to assess the damage experienced by the structure. Coupling the inelasticity of structural elements with the highly nonlinear behaviour of soils in a computer program specialized for geotechnical applications might hopefully contribute to bridging the gap between geotechnical and structural community when attempting to solve problems of soil–structure interaction. This paper presents the implementation, validation and application of the model to solve a dynamic soil–structure interaction problem by coupling the nonlinear behaviour of ground with the inelasticity of the structural elements.

A nonlinear constitutive model for beam elements with cyclic degradation and damage assessment for advanced dynamic analyses of geotechnical problems. Part I: theoretical formulation

Dynamic soil–structure interaction (SSI) represents an interdisciplinary subject characterized by complex geometrical and material nonlinearities affecting both the soil and the structural components of the system under study. In the current practice, SSI problems are often solved using the so-called substructure method based on decomposing the superstructure-foundation-soil system into two subsystems whose response is determined independently. The direct method is a more general procedure to tackle SSI problems which is in principle capable of accounting for both soil and structural nonlinearities. Despite this generality, most of the current computational platforms are specialized either for structural applications or for geotechnical applications. Whereas the formers are capable to accurately reproduce the nonlinear response of the structural elements, they are usually poor in modeling soil nonlinear behaviour especially under earthquake loading. On the other hand, the latter do the reverse: they are advanced in modeling soil response but typically rough in reproducing the behaviour of the structural components of the system. Inevitably, all structures interact with the ground and therefore the need to model material and geometric nonlinearities maybe important both in the ground and structural elements. The variation of the stiffness mismatch between soil and structural elements during ground motions is one of the most influential parameters for the assessment of the kinematic component in SSI problems. The variation of the stiffness ratio is mainly governed by material nonlinearity that can develop in either the soil or the structural parts of the system. This paper presents a nonlinear constitutive model for beam elements that is compatible with performance–based earthquake engineering principles because it is capable to simulate the cyclic degradation of mechanical properties and to assess the damage suffered by the structural system. The proposed model is based on distributed plasticity and can be easily implemented in any computational platform allowing the use of an explicit solver. The article describes the theoretical aspects of the model. Validation and application of the model to the solution of a dynamic soil–structure interaction problem where the nonlinear behaviour of geomaterials is coupled with the inelasticity of structural elements, are presented in a companion paper (Andreotti and Lai in Bull Earthq Eng 2017).

Responses of reinforced concrete pile group in two-layered liquefied soils: shake-table investigations

During earthquakes, the response of pile foundations in liquefiable sand reinforced by densification techniques is still a very complex dynamic soil-structure interaction problem. Two shake-table experiments were conducted to investigate the behavior of a reinforced concrete (RC) low-cap pile group embedded in liquefiable soils. Discussion is focused on the behavior of soil-pile-superstructure systems prior to and during liquefaction of the medium-dense and dense sand stratums, which are involved in restoring force characteristics at the superstructure and pile group effect. The test results demonstrated a stiffness reduction and dependent nonlinear behavior appearing in the liquefied medium-dense sand; however, an overall stiffening response was observed in liquefied dense sand. The pile group effect seemed insignificant in liquefied medium-dense sand, but was very significant in the liquefied dense sand.

Finite element–boundary element coupling algorithms for transient elastodynamics

This paper discusses the coupling of finite element (FE) and boundary element (BE) methods for the solution of transient dynamic soil–structure interaction problems in the time domain. As both the FE and the BE method impose different requirements on the time step for reasons of stability and accuracy, iterative coupling schemes are applied since they allow for a different time discretization in both subdomains. Apart from a direct coupling approach, various sequential and parallel iterative coupling strategies are investigated, imposing either Neumann or Dirichlet boundary conditions on the FE and BE subdomains. The use of interface relaxation accelerates convergence, where Aitken׳s Δ2-method provides an optimal relaxation parameter for all iterative strategies considered. It is demonstrated that the boundary conditions applied to each subdomain strongly affect the efficiency of these algorithms; the application of Neumann boundary conditions on the stiffest subdomain results in the fastest convergence. The iterative coupling strategy is useful in the case where different time steps are used in both subdomains, though a direct coupling can also be used. The iterative coupling strategy is finally applied to the computation of ground vibrations from impact pile driving.

A spatial windowing technique to account for finite dimensions in 2.5D dynamic soil–structure interaction problems

The dynamic interaction between a layered halfspace and quasi translationally invariant structures such as roads, railway tracks, tunnels, dams, and lifelines can be modelled using a computationally efficient 2.5D approach, assuming invariance of the geometry in the longitudinal direction. This assumption is not always fulfilled in practice, however. Even for elongated structures, full 3D computations may be required for an accurate solution of the dynamic soil–structure interaction problem. This paper presents a spatial windowing technique for elastodynamic transmission and radiation problems that allows accounting for the finite length of a structure, still maintaining the computational efficiency of a 2.5D formulation. The proposed technique accounts for the diffraction occurring at the structure's edges, but not for its modal behaviour resulting from reflections of waves at its boundaries. Numerical examples of a barrier for vibration transmission and a surface foundation are discussed to demonstrate the accuracy and applicability of the proposed methodology. Full 3D calculations are performed to provide a rigorous validation for each of these examples. It is demonstrated that the proposed technique is appropriate as long as the response is not dominated by the resonant behaviour of individual modes of the structure.

Coupled finite element - hierarchical boundary element methods for dynamic soil-structure interaction in the frequency domain

SUMMARY This paper discusses the coupling of finite element and fast boundary element methods for the solution of dynamic soil–structure interaction problems in the frequency domain. The application of hierarchical matrices in the boundary element formulation allows considering much larger problems compared to classical methods. Three coupling methodologies are presented and their computational performance is assessed through numerical examples. It is demonstrated that the use of hierarchical matrices renders a direct coupling approach the least efficient, as it requires the assembly of a dynamic soil stiffness matrix. Iterative solution procedures are presented as well, and it is shown that the application of such schemes to dynamic soil–structure interaction problems in the frequency domain is not trivial, as convergence can hardly be achieved if no relaxation procedure is incorporated. Aitken's Δ2-method is therefore employed in sequential iterative schemes for the calculation of an optimized interface relaxation parameter, while a novel relaxation technique is proposed for parallel iterative algorithms. It is demonstrated that the efficiency of these algorithms strongly depends on the boundary conditions applied to each subdomain; the fastest convergence is observed if Neumann boundary conditions are imposed on the stiffest subdomain. The use of a dedicated solver for each subdomain hence results in a reduced computational effort. A monolithic coupling strategy, often used for the solution of fluid–structure interaction problems, is also introduced. The governing equations are simultaneously solved in this approach, while the assembly of a dynamic soil stiffness matrix is avoided. Copyright © 2013 John Wiley & Sons, Ltd.

A MATLAB toolbox for soil–structure interaction analysis with finite and boundary elements

In this work the numerical model SSIFiBo developed in MATLAB to study dynamic soil-structure interaction problems is presented. The model is based on a three dimensional boundary element-finite element coupled formulation in time domain. This model allows computing structural forced-vibrations, as well as seismic responses. Two numerical examples are solved with the proposed technique: ground-borne isolation with open and filled trench, and the seismic response of a tall chimney.