Petia Dineva

A hyper-singular traction boundary integral equation method for stress intensity factor computation in a finite cracked body

Abstract This paper attempts to answer the commonly raised question: what are the parameters controlling the solution accuracy and stability when the hyper-singular traction boundary-integral equations (BIEs) are used for the dynamic (time-harmonic) linear elastic fracture analysis of a finite cracked structure. The usage of the traction BIEs together with the parabolic discretization mesh leads to hyper-singularity, when the crack lies on the boundary, even after application of a regularization procedure. In this paper two new ways, average method and shifted point method to overcome this difficulty, are proposed and compared. It is shown by numerical experiments on the examples of a cracked rectangular plate and of a cracked infinite plane that the accuracy and the convergence of the method solution depends mainly on the smoothness requirements of the solution at all collocation points.

Scattering of seismic waves by cracks in multi-layered geological regions. I. Mechanical model

In this work, a hybrid boundary integral equation method (BIEM) is developed, based on both displacement and hypersingular traction formulations, for the analysis of time-harmonic seismic waves propagating through cracked, multi-layered geological regions with surface topography and under plane strain conditions. Specifically, the displacement-based BIEM is used for a multi-layered deposit with interface cracks, while the regularized, traction-based BIEM is used when internal cracks are present within the layers. The standard uni-dimensional boundary element with parabolic shape functions is employed for discretizing the free surface and the layer interfaces, while special discontinuous boundary elements are placed near the crack tips to model the asymptotic behaviour of both displacements and tractions. This formulation yields displacement amplitudes and phase angles on the free surface of a geological deposit, as well as stress intensity factors near the tips of the cracks. Finally, in the companion paper, numerical results are presented which show that both scattered wave and stress concentration fields are sensitive to the incidence seismic wave parameters and to specific site conditions such as surface topography, layering, the presence of cracks and crack interaction.

Scattering of seismic waves by cracks in multi-layered geological regions: II. Numerical results

The mechanical model for plane strain, time-harmonic seismic wave propagation problems in cracked, multi-layered geological regions with surface topography and non-parallel interfaces was described in the first part of this work. Here, this model is used to investigate the response of such a region to the presence of traveling elastic waves generated by a seismic source. The computational methodology that was developed in the first part is based on a combination of both the regular (displacement-based) and the hypersingular (traction-based) Boundary Integral Equation Method (BIEM). First, the accuracy and convergence characteristics of this hybrid BIEM are studied. Then, a series of problems involving four different configurations of a reference geological deposit with both interface and internal cracks are solved, for a loading that is due to a seismically-induced pressure wave propagating upwards from the underlying rigid half-plane. The purpose of the numerical study is to investigate the influence of various key parameters of the problem, such as frequency and incidence angle of the incoming wave, size of the surface relief, location and size of the buried cracks, interaction effects between cracks and finally the presence of layers, on both the scattered displacement field and the stress concentration field.

Seismic response of lined tunnels in the half-plane with surface topography

In this work, we examine the seismic response of multiple tunnels reinforced with liners and buried within the elastic homogeneous half-plane in the presence of surface relief. The seismic waves are upward propagating, time-harmonic, horizontally polarized shear (SH) waves. More specifically, we examine: (a) the scattered wave fields along the free surface and inside the half-plane with the embedded tunnels; (b) the dynamic stress concentration factors that develop at the soil-liner interfaces; (c) the stresses and displacements that develop inside the tunnel liners. We use a sub-structuring technique that is based on the direct boundary element method to model each constituent part of the problem separately. Then, assembly of the full problem is accomplished through the imposition of compatibility and equilibrium conditions at all interfaces. Next, a detailed verification study is carried out based on comparisons against available analytical and/or numerical results for a series of test examples. Subsequently, detailed numerical simulations are conducted and the results of these parametric studies reveal the influence of the following key parameters on the soil-tunnel system response: (a) the shape of the free-surface relief; (b) the depth of placement of the tunnels and their separation distance; (c) the SH-wavelength to tunnel diameter ratio; (d) the elastic properties of the tunnel lining rings and (e) the dynamic interaction effects between the free-surface relief and the tunnels.

Dynamic behavior of a bi-material interface-cracked plate

The hyper-singular traction boundary integral equation method (BIEM) has been developed to analyze the dynamic behavior of two-dimensional finite bi-material plates with one or more interface cracks under uniform time-harmonic tension. The multi-region BEM technique is employed. Fracture parameters and scattered wave field far from the crack-tips are computed. The numerical results show the dependence of these dynamic characteristics on the frequency of the applied load, on the Dundurs bi-material constants, on the crack length and on the existence of other neighboring cracks.

Seismic response of buried metro tunnels by a hybrid FDM-BEM approach

In this work, we present a 2D elastodynamic model for the seismic response of subway tunnels embedded in a laterally inhomogeneous, multilayered geological region overlying the half-plane. To this end, a finite difference-boundary element methodology (FDM-BEM) is developed, with the latter method embedded in the former so as to capture near-site field effects. More specifically, the FDM is used for simulating in-plane elastic wave propagation from the underlying bedrock through the overlying soil deposits to the surface. A ‘box’ area is then defined within the original FDM mesh and contains lined tunnels. The ‘box’ is modeled by the BEM and its upper boundary coincides with the free surface of the geological deposit. This way, seismically-induced motions are imparted from the FDM mesh to the ‘box’ perimeter, so that the BEM may now be used to efficiently model the near-site layers which contain the tunnels. Verification studies are then successfully conducted for upward moving Gabor pulses, using the FDM alone, the present hybrid FDM-BEM and a hybrid FDM-finite element method formulation. Given that the FDM is defined in the time domain and the BEM in the frequency domain, the fast Fourier transform is used for linking these two constituent parts of the hybrid approach. This methodology is finally applied to a north–south geological cross-section of Thessaloniki, Greece, which contains two Metro tunnels placed directly below an important Roman-era monument known as the Arch of Galerius. Results are then given in the form of free-surface motions stemming from the Thessaloniki 5 July 1978 aftershock recorded at bedrock so as to establish the influence of the ongoing Metro line construction, now temporarily halted because of the economic crisis, on the free surface motions in the city centre where a number historical monuments besides the Arch of Galerius still survive.

Seismic Soil-Tunnels Interaction Via Bem Part I. Mechanical Model

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.

Design sensitivity analysis for shape optimization by the BEM

Abstract In this paper the shape optimization problem for an inelastic case by the hybrid utilization of the BEM and design sensitivity analysis is examined. Gourevichs model for describing the inelastic behaviour of the solid is used. As a numerical example, the problem for determining the optimal shape of the free boundary of a hole in a rectangular elastic and inelastic metal plate unaxial tension is solved.

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

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. Bardets model is introduced by assuming saturated soils as the computationally efficient viscoelastic isomorphism to Biots 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.

Interface Behavior of a Bimaterial Plate under Dynamic Loading

The paper deals with interface behavior of bimaterial ceramic-metal composites under dynamic time-harmonic load. The first plate is precracked with a normal crack touching the interface between the plates. It is assumed that the respective restriction for the ratio of energy release rates of the plates allowing the occurrence of an interface single delamination before the initiation of the normal crack in the second plate is satisfied. The growth of interface delamination is not considered. The used approximate shear-lag dynamic approach gives a possibility to obtain solutions in a closed form for axial and shear stresses of the structure. At an elastic-brittle interface behavior theoretical predictions for single debond length of two bimaterial structures are calculated. The parametric analysis reveals the sensitivity of the interface single debond length and shear stress to the type of bimaterial structure and to the characteristics of the dynamic load—in particular its frequency and amplitude. All results are illustrated in figures and tables and are discussed.