Open Access

ARTICLE

The Influence of Non-Homogeneous Material Properties on ElasticWave Propagation in Fluid-Filled Boreholes

A. Tadeu¹, P. Stanak², J. Antonio¹, J. Sladek², V. Sladek²

1 ITeCons, University of Coimbra, Pólo II, Rua Pedro Hispano, 3030-289, Coimbra, Portugal
2 Institute of Construction and Architecture, Slovak Academy of Sciences, 84503 Bratislava, Slovakia

Computer Modeling in Engineering & Sciences 2015, 107(5), 345-378. https://doi.org/10.3970/cmes.2015.107.345

Abstract

This paper implements a numerical method based on the mutual coupling of the boundary element method (BEM) and the meshless local Petrov-Galerkin (MLPG) method to simulate elastic wave propagation in fluid-filled boreholes. The fluid-solid interaction is solved in the frequency domain assuming longitudinally invariant geometry in the axial direction (2.5D formulation).
This model is used to assess the influence of the non-homogeneous material properties of a borehole wall that can be caused by a damaged zone, construction process or the ageing of material. The BEM is used to model propagation within the unbounded homogeneous domain and the fluid domain inside the borehole and the MLPG method is used to simulate the confined, non-homogeneous, surrounding damaged borehole. The advantages of MLPG in modeling non-homogeneous bounded media and the advantage of BEM in modeling unbounded homogeneous material are thus exploited. The coupling of the two numerical techniques is accomplished directly at the nodal points located at the common interface. Boundary conditions at the interfaces are imposed through the collocation of continuity equations at the interface by means of the moving least-squares (MLS) scheme. At the solid-solid interface, continuity of stresses and displacements is imposed, while continuity of normal stresses and displacements and null shear stress are prescribed at the fluid-solid interface.
The validity of the coupled BEM-MLPG approach is confirmed against the results provided by an analytical solution developed for a circular multi-layered subdomain, in which the central fluid domain is surrounded by a circular non-homogeneous elastic region whose material properties vary radially. Finally, the example of an unbounded medium containing two fluid-filled boreholes excited by a blast load is used to illustrate the applicability of the proposed model.

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