Boundary integral formulation and two-dimensional fundamental solutions for dynamic behavior analysis of unsaturated soils

In this paper the coupled equations governing the dynamic behavior of unsaturated soils are derived based on the poromechanics theory within the framework of the suction-based mathematical model presented by Gatmiri (1997) [Gatmiri B. Analysis of fully coupled behavior of unsaturated porous medium under stress, suction and temperature gradient. Final report of CERMES-EDF, 1997] and Gatmiri et al. (1998) [Gatmiri B, Delage P, Cerrolaza M, UDAM: a powerful finite element software for the analysis of unsaturated porous media. Adv Eng Software 1998; 29(1): 29–43]. In this formulation, the solid skeleton displacements, water pressure and air pressure are presumed to be independent variables. The Boundary Integral formulations as well as fundamental solutions for such a dynamic u–p_w–p_a theory are presented in this paper for the first time. The boundary integral equations are derived via the use of the weighted residuals method in a way that permits an easy discretization and implementation in a Boundary Element code. Also, the associated two dimensional (2D) fundamental solutions for such deformable porous medium with linear elastic behavior are derived in Laplace transform domain using the method of Hörmander. Finally, some numerical results are presented to show the accuracy of the proposed solutions. The derived results are verified analytically by comparison with the previously introduced corresponding fundamental solutions in elastodynamic limiting case.     

Three‐dimensional transient thermo‐hydro‐mechanical fundamental solutions of unsaturated soils

The governing differential equations of unsaturated soils considering the thermo‐poro‐mechanical behaviour consist of equilibrium, moisture air and heat transfer equations. In this paper at first, following some necessary simplifications, the thermal three‐dimensional fundamental solution for an unsaturated deformable porous medium with linear elastic behaviour in Laplace transform domain is presented. Subsequently, the closed‐form time domain fundamental solutions are derived by analytical inversion of the Laplace transform domain solutions. Then a set of numerical results are presented, which demonstrate the accuracies and some salient features of the derived analytical transient fundamental solutions. Finally, the closed‐form time domain fundamental solution will be verified mathematically by comparison with the previously introduced corresponding fundamental solution. Copyright © 2009 John Wiley & Sons, Ltd.     

GeoNDT: a fast general-purpose computational tool for geotechnical non-destructive testing applications

The non-destructive testing (NDT) plays a crucial role in geotechnical engineering and geophysical applications, especially in the design of earthquake-resistant foundations, geotechnical field investigation, and material characterization and detection of underground anomaly. Currently, the existing signal interpretation methods in NDT measurements still predominantly rely on empirical relations or subjective judgements. In this paper, we present the GeoNDT software, which is developed to provide an advanced physics-based signal interpretation method for NDT characterization of multiphase geomaterials. GeoNDT is able to model the propagation of stress waves and dispersion relations in dry (elastodynamic), saturated (two-phase poroelastodynamic), and three-phase frozen (multiphase poroelastodynamic) geomaterials using the meshless spectral element method. GeoNDT is flexible, general-purpose, and can be used seamlessly for advanced signal interpretation in geophysical laboratory testing including the bender element and ultrasonic pulse velocity tests, characterization of complex multiphase geomaterials, and in situ shallow seismic geophysics including the falling weight deflectometer and multichannel analysis of surface waves tests. The advanced physics-based signal interpretation feature of GeoNDT allows the quantitative characterization of geophysical and geomechanical properties of geomaterials and multilayered geosystems independently without making any simplified assumptions as common in the current practice.

     

Site-specific spectral response of seismic movement due to geometrical and geotechnical characteristics of sites

It is well-known that the response of a site to a seismic solicitation depends on local topographical and geotechnical characteristics. Many aspects of seismic site effect still need to be studied in more detail and they can be incorporated in the seismic norms after quantification. The purpose of this paper is to contribute to establishment of a simple method to include complex site effects in a building code. Horizontal ground movements in various points of two-dimensional (2D) irregular configurations subjected to synthetic SV waves of vertical incidence are calculated. The parametric studies are achieved by means of HYBRID program combining finite elements in the near field and boundary elements in the far field (FEM/BEM). The results are shown in the form of pseudo-acceleration response spectra. For the empty valleys, we can classify the spectral response according to a unique geometric criterion: the “surface/angle” ratio, where surface is the area of the valley opening, and angle denotes the angle between the slope and horizontal line in the above corner. To assess the influence of the 2D effect on the spectral response of filled valleys, the response of alluvial basins are compared with the response of one-dimensional columns of soil. Finally, an offset criterion is proposed to choose a relevant computation method for the spectral acceleration at the surface of alluvial basins.