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Open access

Petia Dineva, Frank Wuttke and George Manolis

Elastic Wavefield Evaluation in Discontinuous Poroelastic Media by Bem: Sh-Waves

This work examines the anti-plane strain elastodynamic problem for poroelastic geological media containing discontinuities in the form of cavities and cracks. More specifically, we solve for: (i) a mode III crack; (ii) a circular cylindrical cavity, both embedded in an infinite poroelastic plane; and (iii) a mode III crack in a finite-sized poroelastic block. The source of excitation in all cases are time-harmonic, horizontally polarized shear (SH) waves. These three cases depict a situation whereby propagating elastic waves are diffracted and scattered by the presence of discontinuities in poroelastic soil, and this necessitates the computation of stress concentration factors (SCF) and stress intensity factors (SIF). Thus, the sensitivity of the aforementioned factors to variations in the material parameters of the surrounding poroelastic continuum must be investigated. Bardet's model is introduced by assuming saturated soils as the computationally efficient viscoelastic isomorphism to Biot's equations of dynamic poroelasticity, and stress fields are then evaluated for an equivalent one-phase viscoelastic medium. The computational itool employed is an efficient boundary element method (BEM) defined in terms of the non-hypersingular, traction-based formulation. Finally, the results obtained herein demonstrate a marked dependence of the SIF and the SCF on the mechanical properties of the poroelastic continuum, while the advantages of the proposed method as compared to alternative analytical and/or numerical approaches are also discussed.

Open access

Petia Dineva and Tsviatko Rangelov

Abstract

Elastic wave scattering by cracks at macro- and nano-scale in anisotropic plane under conditions of plane strain is studied in this work. Furthermore, time-harmonic loads due to incident plane longitudinal P- or shear SV- wave are assumed to hold. In a subsequent step, the elastodynamic fundamental solution for general anisotropic continua derived in closed-form via the Radon transform is implemented in a numerical scheme based on the traction boundary integral equation method (BIEM). The surface elasticity effect in the case of nano-crack is taken into consideration via non-classical boundary condition along the crack surface proposed by Gurtin and Murdoch [1]. The numerical results obtained herein reveal substantial differences between anisotropic materials containing a macro- and a nano-crack in terms of their dynamic stress response, where the latter case demonstrates clearly the strong influence of the size-effects. Finally, these types of examples serve to illustrate the present approach and to show its potential for evaluating the stress concentration fields (SCF) inside cracked nanocomposites. The obtained results concern the reliability and safety of the advancing nanomaterials.

Open access

Tsviatko Rangelov, Marin Marinov and Petia Dineva

Abstract

Anti-plane cracked functionally graded finite piezoelectric solid under time-harmonic elecromechanical load is studied by a non-hypersingular traction boundary integral equation method (BIEM). Exponentially varying material properties are considered. Numerical solutions are obtained by using Mathematica. The dependance of the intensity factors (IF) - mechanical stress intensity factor (SIF) and electrical field intensity factor (FIF) on the inhomogeneous material parameters, on the type and frequency of the dynamic load and on the crack position are analyzed by numerical illustrative examples

Open access

Frank Wuttke, Petia Dineva and Ioanna-Kleoniki Fontara

Abstract

Elastic wave propagation in 3D poroelastic geological media with localized heterogeneities, such as an elastic inclusion and a canyon is investigated to visualize the modification of local site responses under consideration of water saturated geomaterial. The extended computational environment herein developed is a direct Boundary Integral Equation Method (BIEM), based on the frequency-dependent fundamental solution of the governing equation in poro-visco elastodynamics. Bardet’s model is introduced in the analysis as the computationally efficient viscoelastic isomorphism to Biot’s equations of dynamic poroelasticity, thus replacing the two-phase material by a complex valued single-phase one. The potential of Bardet’s analogue is illustrated for low frequency vibrations and all simulation results demonstrate the dependency of wave field developed along the free surface on the properties of the soil material.

Open access

Tsviatko V. Rangelov, Petia S. Dineva and George D. Manolis

Abstract

The aim of this study is to develop an efficient numerical technique using the non-hypersingular, traction boundary integral equation method (BIEM) for solving wave propagation problems in an anisotropic, viscoelastic plane with cracks. The methodology can be extended from the macro-scale with certain modifications to the nano-scale. Furthermore, the proposed approach can be applied to any type of anisotropic material insofar as the BIEM formulation is based on the fundamental solution of the governing wave equation derived for the case of general anisotropy. The following examples are solved: (i) a straight crack in a viscoelastic orthotropic plane, and (ii) a blunt nano-crack inside a material of the same type. The mathematical modelling effort starts from linear fracture mechanics, and adds the fractional derivative concept for viscoelastic wave propagation, plus the surface elasticity model of M. E. Gurtin and A. I. Murdoch, which leads to nonclassical boundary conditions at the nano-scale. Conditions of plane strain are assumed to hold. Following verification of the numerical scheme through comparison studies, further numerical simulations serve to investigate the dependence of the stress intensity factor (SIF) and of the stress concentration factor (SCF) that develop in a cracked inhomogeneous plane on (i) the degree of anisotropy, (ii) the presence of viscoelasticity, (iii) the size effect with the associated surface elasticity phenomena, and (iv) finally the type of the dynamic disturbance propagating through the bulk material.

Open access

P. Dineva, S. Parvanova, G. Vasilev and F. Wuttke

Abstract

Two-dimensional elastodynamic problem for seismic response of unlined and lined tunnels located in a layered half-plane with free surface relief is solved. The computation tool uses the idea of the global matrix propagator method which allows derivation of a relation between the wave field quantities along different interfaces in the layered half- plane. The numerical realization of this idea is performed with the help of the sub-structured boundary element method (BEM) well suited when objects with arbitrary geometry are considered. A relation between dis- placements and tractions along the free surface and arbitrary interface of the soil stratum is derived. It works for arbitrary geometry of the interfaces between soil layers. Finally, in the companion paper, numerical results are presented which show both a validation study of the pro- posed computational methodology and extensive numerical simulations demonstrating the influence of some important factors as type and characteristics of the incident wave, dynamic tunnels interaction, soil-tunnel interaction, free surface relief, type of the tunnel construction and mechanical properties of the layered half-plane on the complex seismic field near and far-away from the underground structures.

Open access

P. Dineva, S. Parvanova, G. Vasilev and F. Wuttke