<p>This paper aims at deriving effective poroelastic properties of an N-layered composite sphere assemblage with an imperfect interface between two consecutive layers. The Linear Spring Model (LSM) is used to describe the interface behavior, in which the stress is continuous while the displacement is discontinuous across the interface. Each layer is a porous medium, and the porosity is assumed to be connected throughout all the layers. The derivation of effective poroelastic properties is based on thermoelastic solution derived by Hashin (Hashin <CitationRef CitationID="CR25">1991</CitationRef>) (for 2 layers with imperfect interface) and generalized self-consistent homogenization scheme. The closed-form solutions of the Biot coefficient and the solid Biot modulus are drived, which are the main contribution of this study.</p><p>The solution obtained is applied to estimate the poroelastic properties of various oolitic rocks, which are constituted by an assemblage of grains (oolites) coated by a porous cement matrix. A two-step homogenization is proposed. The first step consists in the transition from the microscopic to the mesoscopic scale, where the effective properties of each phase (oolite and matrix) are estimated by using an iterative self-consistent scheme. In the second step (also called meso-macro transition/upscaling), the two phases oolite and embedding matrix are homogenized in the framework of the three-phase CSA model with interfaces. Comparisons with measurement data from various limestones are made. A sensitive study is performed to assess the role of imperfect interface parameters and to propose a reference set of parameters for all the considered materials.</p>

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Effective Poroelastic Properties of N-Layered Composite Sphere Assemblage with Imperfect Interface: Application to Oolitic Rocks

  • Thi Thu Nga Nguyen,
  • Ngoc Bien Nguyen,
  • Minh Ngoc Vu,
  • Tuan Nguyen-Sy,
  • Duc Tho Pham,
  • Nam Hung Tran

摘要

This paper aims at deriving effective poroelastic properties of an N-layered composite sphere assemblage with an imperfect interface between two consecutive layers. The Linear Spring Model (LSM) is used to describe the interface behavior, in which the stress is continuous while the displacement is discontinuous across the interface. Each layer is a porous medium, and the porosity is assumed to be connected throughout all the layers. The derivation of effective poroelastic properties is based on thermoelastic solution derived by Hashin (Hashin 1991) (for 2 layers with imperfect interface) and generalized self-consistent homogenization scheme. The closed-form solutions of the Biot coefficient and the solid Biot modulus are drived, which are the main contribution of this study.

The solution obtained is applied to estimate the poroelastic properties of various oolitic rocks, which are constituted by an assemblage of grains (oolites) coated by a porous cement matrix. A two-step homogenization is proposed. The first step consists in the transition from the microscopic to the mesoscopic scale, where the effective properties of each phase (oolite and matrix) are estimated by using an iterative self-consistent scheme. In the second step (also called meso-macro transition/upscaling), the two phases oolite and embedding matrix are homogenized in the framework of the three-phase CSA model with interfaces. Comparisons with measurement data from various limestones are made. A sensitive study is performed to assess the role of imperfect interface parameters and to propose a reference set of parameters for all the considered materials.