Two-dimensional numerical modelling of wave propagation in soil media

Wave propagation in soil media is encountered in many engineering applications. Given that the soil is unbounded, any numerical model of finite size must include absorbing boundary conditions implemented at the artificial boundaries of the domain to allow waves to radiate away to infinity. In this work, a finite element model is developed under plane strain conditions to simulate the effects of harmonic loading induced waves. The soil can be homogeneous or multi-layered where the soil properties are linear elastic. It may overlay rigid bedrock or half-space. It may also incorporate various discontinuities such as foundations, wave barriers, embankments, tunnels or any other structure. For the case of soil media over rigid bedrock, lateral wave radiation is ensured through the implementation of the consistent transmitting boundaries, using the Thin Layer Method (TLM), which allow replacing the two semi-infinite media, on the left and right of a central domain of interest, by equivalent nodal forces simulating their effect. Those are deduced from an eigenvalue problem formulated in the two semi-infinite lateral media. In the case of soil media over half-space, the Thin Layer Method is combined to the Paraxial Boundary Conditions to allow the incoming waves to radiate away to infinity laterally and in-depth. The performance of this coupled model is enhanced by incorporating a buffer layer between the soil medium and the underlain half-space. For extensive analyses, the eigenvalue problem related to the TLM may become computationally demanding, especially for soil media with multi-wavelength depths. As the TLM involves thin sub-layers, in comparison to the wavelength, the size of the eigenvalue problem increases with increasing depth. A modified version of the TLM is proposed in this work to reduce the computational effort of the related eigenvalue problem. This dissertation work led to the development of a Fortran computer code capable of simulating wave propagation in two-dimensional soil media models with either structured or unstructured triangular mesh grids. This latter option allows considering soil-structure problems with geometrical complexities, different soil layering configurations and various loading conditions. The pre- and post-processing as well as the analysis stages are all user friendly and easy

Dynamic soil-structure interaction analysis using the scaled boundary finite-element method.

This thesis presents the development of a reliable and efficient technique for the numerical simulation of dynamic soil-structure interaction problems in anisotropic and nonhomogeneous unbounded soils of arbitrary geometry. Such a technique is indispensable in the seismic analysis of large-scale engineering constructions and, to my best knowledge, does not exist at present. The theoretical framework of the research is based on the scaled boundary finite-element method. The following advances are achieved: The scaled boundary finite-element method is extended to simulate the dynamic response of non-homogeneous unbounded domains. The scaled boundary finite element equations in the frequency and time domains are derived for power-type non-homogeneity frequently employed in geotechnical engineering. A high-frequency asymptotic expansion of the dynamic-stiffness matrix is developed. The frequency domain analysis is performed by integrating the scaled boundary finite-element equation in dynamic stiffness. In the time domain, the scaled boundary finite-element equation including convolution integrals is solved for the unit-impulse response at discrete time stations. A Padé series solution for the scaled boundary finite-element equation in dynamic stiffness is developed. It converges over the whole frequency range as the order of the approximation increases. The computationally expensive task of numerically integrating the scaled boundary finite-element equation is circumvented. Exploiting the sparsity of the coefficientmatrices in the scaled boundary finite-element equation leads to a significant reduction in computer time and memory requirements for solving large-scale problems. Furthermore, lumped coefficient matrices are obtained by adopting the auss-Lobatto-Legendre shape functions with nodal quadrature, which avoids the eigenvalue problem in determining the asymptotic expansion. A high-order local transmitting boundary constructed from a continued-fraction solution of the dynamic-stiffness matrix is developed. An equation of motion as occurring in standard structural dynamics with symmetric and frequency-independent coefficient matrices is obtained. This transmitting boundary condition can be coupled seamlessly with standard finite elements. Transient responses are evaluated by using a standard timeintegration scheme. The expensive task of evaluating convolution integrals is circumvented. The advances developed in this thesis are applicable in other disciplines of engineering and science to the analysis of scalar and vector waves in unbounded media

Recent advances on the fast multipole accelerated boundary element method for 3D time-harmonic elastodynamics

International audienceThis article is mainly devoted to a review on fast BEMs for elastodynamics, with particular attention on time-harmonic fast multipole methods (FMMs). It also includes original results that complete a very recent study on the FMM for elastodynamic problems in semi-infinite media. The main concepts underlying fast elastodynamic BEMs and the kernel-dependent elastodynamic FM-BEM based on the diagonal-form kernel decomposition are reviewed. An elastodynamic FM-BEM based on the half-space Green's tensor suitable for semi-infinite media, and in particular on the fast evaluation of the corresponding governing double-layer integral operator involved in the BIE formulation of wave scattering by underground cavities, is then presented. Results on numerical tests for the multipole evaluation of the half-space traction Green's tensor and the FMM treatment of a sample 3D problem involving wave scattering by an underground cavity demonstrate the accuracy of the proposed approach. The article concludes with a discussion of several topics open to further investigation, with relevant published work surveyed in the process

Topographic amplification of seismic motion

Seismic hazard assessment relies increasingly on the numerical simulation of ground motion, since recent advances in numerical methods and computer architectures have made it ever more practical to obtain the surface response to idealized or realistic seismic events. The key motivation stems from the need to assess the performance of sensitive components of the civil infrastructure (nuclear power plants, bridges, lifelines, etc.), when subjected to realistic scenarios of seismic events. To date, most simulation tools rely on a flat-earth assumption, which ignores topography and its effects on seismic motion amplification. In an attempt to narrow the gap between modeling and physical reality, in this dissertation we study systematically the effects topographic features have on the surface motion when compared against motion obtained using a at-surface assumption. To this end, we discuss first an integrated approach that deploys best-practice tools for simulating seismic events in arbitrarily heterogeneous formations, while also accounting for topography. Specifically, we describe an explicit forward wave solver based on a hybrid formulation that couples a single-field formulation for the computational domain with an unsplit mixed-field formulation for Perfectly-Matched-Layers (PMLs or M-PMLs) used to limit the computational domain. We use spectral elements for spatial discretization, and an efficient Runge-Kutta explicit solver for time integration. Due to the material heterogeneity and the contrasting discretization needs it imposes, we also use an adaptive Runge-Kutta-Fehlberg time-marching scheme to optimally adjust the time step so that the local truncation error rests below a predefined tolerance. To account for the seismic load, we use the Domain- Reduction-Method to introduce the incoming seismic motion in the computational domain whenever the introduction of the actual seismic source would make the computational domain unnecessarily large. Lastly, we couple the DRM with the PMLs to complete the seismic motion simulation engine. Using the developed toolchain, we then report results of parametric studies involving idealized topographic features, which show motion amplification that depends, as expected, on the relation between the topographic features' characteristics and the dominant wavelength. More interestingly, we also report motion de-amplification patterns. Given the prevalence of lower dimensionality models for seismic risk assessment, we also report on the effects model dimensionality has in the presence of heterogeneity and topography. The results reported herein, support the thesis that, for purposes of seismic risk assessment, topography and heterogeneity are best treated when fully accounted for in three-dimensional models. Even this is only a first and necessary step towards higher fidelity modeling of seismic motion effects.Civil, Architectural, and Environmental Engineerin

Advanced BEM-based methodologies to identify and simulate wave fields in complex geostructures

To enhance the applicability of BEM for geomechanical modeling numerically optimized BEM models, hybrid FEM-BEM models, and parallel computation of seismic Full Waveform Inversion (FWI) in GPU are implemented. Inverse modeling of seismic wave propagation in inhomogeneous and heterogeneous half-plane is implemented in Boundary Element Method (BEM) using Particle Swarm Optimization (PSO). The Boundary Integral Equations (BIE) based on the fundamental solutions for homogeneous elastic isotropic continuum are modified by introducing mesh-dependent variables. The variables are optimized to obtain the site-specific impedance functions. The PSO-optimized BEM models have significantly improved the efficiency of BEM for seismic wave propagation in arbitrarily inhomogeneous and heterogeneous media. Similarly, a hybrid BEM-FEM approach is developed to evaluate the seismic response of a complex poroelastic soil region containing underground structures. The far-field semi-infinite geological region is modeled via BEM, while the near-field finite geological region is modeled via FEM. The BEM region is integrated into the global FEM system using an equivalent macro-finite-element. The model describes the entire wave path from the seismic source to the local site in a single hybrid model. Additionally, the computational efficiency of time domain FWI algorithm is enhanced by parallel computation in CPU and GPU

Development of Time-Domain Green’s Functions and Boundary Element Techniques for Transient Elastodynamics of Multi-Layered Media

Time-domain boundary element method (TD-BEM) is a powerful tool for transient elastodynamic modeling of soil and structures especially for unbounded domain problems. Aimed to add to the advancement of this class of methods and facilitate its coupling with other numerical approaches, a number of new analytical and computational formulations are developed and explored in this study. The work includes the development of a regularized convolution-type boundary integral equation in the time domain for 3-D elastodynamics, the formulation of a rigorous stability analysis via a hybrid amplification matrix of direct TD-BEMs, an extension of a displacement potential-integral transform method from the frequency- to the time-domain, a generalization of the classical Cagniard-de Hoop method in wave propagation theory for Laplace transform's inversion, and the derivation of exact as well as asymptotic forms of the time-domain point-load Green's functions for a homogeneous and a multi-layered half-space. The theoretical developments are employed to develop new computational algorithms such as the new variable-weight multi-step collocation TD-BEM scheme with higher-order time projections and a new numerical contour integration method to compute the fundamental integrals in exact half-space time-domain Green's functions. The efficacy and performance of these developments are evaluated with respect to benchmark elastodynamic problems for both bounded and unbounded domains. The formulation and effectiveness of coupling the proposed TD-BEM approach with a local finite element zone for dynamic soil-structure interaction problems as a rigorous form of wave-absorbing boundary are also investigated