S. Valliappan

Dynamic soil–structure interaction analysis via coupled finite-element–boundary-element method

Abstract In this paper, a study on the transient response of an elastic structure embedded in a homogeneous, isotropic and linearly elastic half-plane is presented. Transient dynamic and seismic forces are considered in the analysis. The numerical method employed is the coupled Finite-Element–Boundary-Element technique (FE–BE). The finite element method (FEM) is used for discretization of the near field and the boundary element method (BEM) is employed to model the semi-infinite far field. These two methods are coupled through equilibrium and compatibility conditions at the soil–structure interface. Effects of non-zero initial conditions due to the pre-dynamic loads and/or self-weight of the structure are included in the transient boundary element formulation. Hence, it is possible to analyse practical cases (such as dam–foundation systems) involving initial conditions due to the pre-seismic loads such as water pressure and self-weight of the dam. As an application of the proposed formulation, a gravity dam has been analysed and the results for different foundation stiffness are presented. The results of the analysis indicate the importance of including the foundation stiffness and thus the dam–foundation interaction.

Numerical modelling of mass transport problems in porous media: A review

Abstract To seek the numerical solution to the contaminant transport problem in a porous medium, numerous publications on this aspect have emerged during the last three decades. Among them the finite difference method and finite element method have been widely used in this process of solution. Thus, the finite difference method for dealing with contaminant transport problems in porous media is briefly outlined in this paper. Considering the certain advantages of the finite element method over the finite difference method, the finite element method and its formulation for modelling contaminant transport problems are discussed in great detail. Finally, a numerical example has been given to show how the finite element method is applied to solve contaminant transport problems in engineering practice.

NUMERICAL MODELLING OF METHANE GAS MIGRATION IN DRY COAL SEAMS

This paper presents the development of a mathematical model for methane gas migration in coal seams. The major focus of this model is the coupling between the gas flow and deformation of solid coal. The effect of diffusion of adsorbed methane gas from the solid matrix to the voids has been taken into account. The adsorption of gas in the coal seam causes a two-phase state of gas flow. The governing equation for the two-phase gas flow is a non-linear partial differential equation with non-linear boundary conditions. A finite element model has been developed for simulation of the distribution of pressure and concentration of methane gas due to gas migration in coal seams.

Non‐linear seismic behaviour of concrete gravity dams using coupled finite element–boundary element technique

In this paper, the seismic response of concrete gravity dams is presented using the concept of Continuum Damage Mechanics (CDM) and adopting the hybrid Finite Element–Boundary Element technique (FE–BE). The finite element method is used for discretization of the near field and the boundary element method is employed to model the semi-infinite far field. Because of the non-linear nature of the discretizied equations of motion modified Newton–Raphson approach has been used at each time step to linearize them. Damage evolution based on tensile principal strain using mesh-dependent hardening modulus technique is adopted to ensure the mesh objectivity and to calculate the accumulated damage. The methodology employed is shown to be computationally efficient and consistent in its treatment of both damage growth and damage propagation in gravity dams. Other important features considered in the analysis are: (1) realistic damage modelling for concrete that allows isotropic as well as anisotropic damage state and exhibits stiffness recovery upon load reversals. (2) softening initiation and strain softening criteria for concrete, and (3) proper modelling of semi-infinite foundation using FE–BE method that allows to consider dam–foundation interaction analysis. As an application of the proposed formulation a gravity dam has been analysed and the results are compared with different foundation stiffnesses. The results of the analysis indicate the importance of including rock foundation in the seismic analysis of dams. Copyright

Seismic analysis of arch dams—a continuum damage mechanics approach

In this paper, the non-linear seismic response of arch dams is presented using the concept of Continuum Damage Mechanics (CDM). The analysis is performed using the finite element technique and appropriate non-linear material and damage models in conjunction with the α-algorithm for time marching. Because of the non-linear nature of the discretizied equations of motion, modified Newton–Raphson approach has been used at each time step. Damage evolution based on tensile principal strain using mesh-dependent hardening modulus technique is adopted to ensure the mesh objectivity and to calculate the accumulated damage. The methodology employed is shown to be computationally efficient and consistent in its treatment of both damage growth and damage propagation. As an application of the proposed formulation, a double curvature arch dam has been analysed and the results are compared with the solutions from linear analysis and it is shown that the structural response of arch dams varies significantly in terms of damage evolution. Copyright

Seismic wave scattering effects under different canyon topographic and geological conditions

Abstract Based on our numerical model for wave scattering problems due to P and SV wave incidences and the frequency domain analysis procedure, the effect of canyon topographic and geologic conditions on ground motion due to P and SV earthquake wave incidences has been extensively studied in this paper. The numerical results from this research illustrated that: (1) canyon topographic and geologic conditions can dramatically affect both peak value and frequency contents of the free field motion along the canyon surface during an earthquake; (2) a canyon may be subjected to stronger ground motion when its predominant frequency is in coincidence with the predominant frequency of the incident earthquake wave; (3) a stronger wave mode conversion effect can be induced by a steeper canyon bank or a softer weathered stratum on the canyon surface in the case of an earthquake wave incidence; (4) compared with harmonic wave incidences, the amplification effect of a canyon on the incident earthquake wave is a little weaker due to the average self-healing effect of the earthquake wave.

Wave propagation analysis of two-phase saturated porous media using coupled finite-infinite element method

Abstract A fully coupled two-dimensional infinite element for frequency domain analysis of wave propagation problems in unbounded saturated porous media is presented. The decay function of the element is derived based on the analytical solution of Biot (Theory of propagation of elastic waves in fluid-saturated porous solid. 1. Low-frequency range. Journal of the Acoustical Society of America 1956;28(2):168–78) formulation for a one-dimensional configuration. After a detailed description of the element formulation, the effectiveness and the accuracy of the present infinite element in simulating unbounded domains are demonstrated through two numerical examples. Extremely good agreements are obtained between the results from a very large mesh and those from the coupled finite–infinite element method. It is shown that the accuracy of the solutions deteriorate significantly when the infinite elements are removed and fixed to free displacement boundary conditions are introduced at the truncated boundaries.

Effect of impervious members and reservoir bottom sediment on dynamic response of embankment dams

Abstract In this paper, a systematic investigation into the effect of both the type of impervious members and the reservoir bottom sediment on the dynamic response of embankment dams has been carried out using the finite and infinite element coupled method. It has been demonstrated from the numerical results that: (1) the resonant frequencies of an embankment dam—foundation system with an upstream inclined concrete apron are different from those with a central clay core; (2) the type of impervious members has a significant influence on the amplification factors of the system in the low frequency range of excitation, but has little effect in the high frequency range of excitation; (3) the foundation material of an embankment dam affects the dynamic response of the dam drastically; (4) the inclusion of the reservoir bottom sediment has a considerable effect on amplification factors of embankment dams in the case of P-wave incidences, but has little influence in the case of SV-wave vertical incidences; and (5) the reservoir bottom sediment also has a profound effect on the deformed shape of the embankment dam for both P-wave and SV-wave incidences.

Seismic response of concrete gravity dams including water-dam-sediment-foundation interaction

Abstract Using the finite and infinite element coupled method, an investigation into the effect of reservoir bottom sediment on the seismic response of concrete gravity dams has been carried out in this paper. From the related numerical results, it has been concluded that: (1) the finite and infinite element coupled method is more suitable for the seismic analysis of a concrete gravity dam; (2) the reservoir bottom sediment has a significant effect on the seismic response of concrete gravity dams; (3) the neglect of the reservoir bottom sediment in the analysis may be conservative for seismic SV-wave vertical incidences, but it is very dangerous for P-wave vertical incidences.

Finite element modelling of methane gas migration in coal seams

Abstract From the related physical principles, the governing equations of methane gas migration in coal seams have been derived and outlined in this paper. The effect of the medium deformation, two-phase flow and mass/gas transfer on the methane gas transport process in the porous medium has been considered in the analysis. Owing to the complicated nature and nonlinear behaviour of the equations, the finite element method was suggested to solve the methane gas migration problem in the porous medium. Further, the finite element formulations related to this problem have been derived and given in great detail.