Method Of Asymptotic Homogenization For Evaluation Of Deformation And Strength Properties Of Layered Rock

Deformation and strength parameters of rock masses, and of layered rock masses in particular, are needed for engineering practice in mountainous regions. These parameters are usually determined experimentally in-situ. However, layered rocks are frequently anisotropic, which creates difficulties in experimental determination of mechanical properties and makes evaluation of the shear modules and Poisson ratios impossible. Great difficulties also occur with evaluation of the yield surface and its parameters. Anisotropic rocks are frequently represented by transversely-isotropic bodies. In this case elastic stress/strain condition is well described by Young moduli, shear moduli and Poisson ratios Ell, E.1, G.1, V II,, G II (or VII,II), where subscripts II and I denote directions parallel and perpendicular to strata, respectively. Here we consider effective deformation parameters, i.e. quantities generally describing deformation of an imaginary homogeneous transversely-isotropic material in the volume of analyzed rock mass and representative in deformation of the real rock mass. The values of effective mechanical parameters greatly depend on correctness of averaging of actual parameters of rock layers.

Recently many different analytical and numerical-analytical methods proposed for evaluation of effective deformation parameters of layered rocks appeared. We use the approach, which was proposed by N. S. Bakhvalov (Bakhvalov 1975, Bakhvalov & Panasenko 1984) and is based on asymptotic averaging of differential equations in partial derivatives with fast oscillating coefficients. Here exact equations of the theory of elasticity with fast oscillating coefficients are replaced by the averaged ones. The values of effective deformation parameters obtained by this approach provide adequate description of the pre-limit deformation of the real rock mass (the principle of equivalent homogeneity is fulfilled). Moreover it permits determination of displacements and stresses with any afore given precision, which in full measure is not possible with any other method (Bakhvalov & Panasenko 1984).

Rock fracture is activated by local physical processes, i.e. processes on the micro level. Thus we need the exact description of the stress and strain fields. The most important are stress (strain) concentrations.

Now we shortly give an account of the method for evaluation of strength parameters of rocks which is being developed by the authors (Vlasov et al 2001, Vlasov 2001). For this we consider an infinite equivalent domain with given boundary conditions at the infinity in which we apportion a volume corresponding to the typical element of structure. This procedure can be realized for any loading path right up to the failure of the typical structure element. Sections of linear and nonlinear deformation are distinguished.