Micromechanical approach to effective viscoelastic behavior of jointed rocks

Abstract

Assessing the overall instantaneous behavior and strength properties of jointed materials have been the subject of important investigations in the last decades, including phenomenological or micromechanics-based contributions. However, less attention has been dedicated to delayed component of deformation in such media. This issue is addressed in this paper, which is devoted to the formulation of a micromechanical approach to effective viscoelastic properties of jointed rocks with consideration of constituents aging. At the scale of representative elementary volume (REV), the joints are modeled as planar interfaces whose behavior is described by means of generalized viscoelastic state equations under normal and shear loading conditions. Closed-form expressions for the homogenized creep tensor are derived from solving an appropriate viscoelastic concentration problem stated on the REV. The local strain and displacement jump fields are analyzed by extending the concept of strain concentration to relate the components of joint displacement jump to macroscopic strain. Main features of the theoretical overall creep behavior, such as the anisotropy associated with the privileged joint orientations, are highlighted through explicit formulations in some particular configurations of the jointed medium. Finally, the ability of the approach to accurately reproduce the creep behavior of jointed media is assessed by comparison with experimental data as well as with finite element solutions derived in the context of multilayered stratified composite modeling.

A micromechanics‐based approach to damage propagation criterion in viscoelastic fractured materials regarded as homogenized media

“…The results of Figure 8 indicate that for the considered strain loading history, the viscous component of the constituents behavior do not affect the damage propagation condition since 𝑡 →  (𝑡) is a decreasing function, so that its maximum value is obtained for the instantaneous elastic response  0 =  (𝑡 = 0 + ), which is the same for both the complete expression ( 77) and the simplified one (78). As expected, the critical value to damage propagation  0 =  (𝑡 = 0 + ) reveals higher for cracks, thus emphasizing that cracks propagation is easier than that of fractures.…”

“…The viscoelastic concentration problem (11) may be reformulated adopting the homogeneous stress boundary condition (2). In that case, the creep behavior of the fractured material can be assessed as follows 78 :…”

“…Once the homogenized elastic stiffness is evaluated for a single family of fractures by resorting to the Mori-Tanaka homogenization scheme, the contribution of the whole families to overall stiffness is achieved by integration over all fracture orientations. 73,78 The second step of the approach consists in the determination of the homogenized relaxation tensor ℝ hom (𝑡) from application of the elastic-viscoelastic correspondence principle. As expected, the effective medium is isotropic and expresses as…”

“…Once the above quantities are computed, the numerical value of energy release rate  is evaluated considering either the complete expression (77) or simplified expression (78). The damage threshold  𝑐 is also computed by ( 76) at this stage.…”

Study on Mechanical Problems of Complex Rock Mass by Composite Material Micromechanics Methods: A Literature Review

“…In representative units, the constitutive relations of rock mass and joints are given. The macroscopic equivalent mechanical parameters and constitutive model of jointed rock mass can be obtained by using the coordination conditions between macro and meso stress-strain and the mesomechanical method [Zhang Wu et al (Zhang and Zhang, 1987); Yang Haitian et al (Yang and Wu, 1991)], such as the elastic constants and joint occurrence parameters of jointed material and complete rock mass (Zhang and Zhang, 1987), and the composite creep model of jointed rock mass (Yang and Wu, 1991;Maghous et al, 20212021).…”