f On application of analytical solutions of consolidation problems for interpretation of geophysical studies

Values and the character of distribution of pore pressure and effective stresses should be taken into account in interpretation of results of geophysical studies, in particular velocities of compression and shear waves relation in fluid-saturated porous media. Possible application of efficient analytical solutions of consolidation problems for classical domains (in the report as an example is considered plane strain for a strip, half-strip or rectangle) at various types of boundary conditions is discussed, basing on recently obtained results. The process of consolidation of fluid-saturated elastic isotropic porous layer accounting for compressibility of the fluid and solid constituents is analyzed applying Biot equations [1] in the form [2]. The application of an integral Laplace transformation in time and bilateral Laplace transformation in coordinate provides general solution using the functions of parameters of these transformations μ and s correspondingly. The arbitrary constants in the general solution are determined by boundary conditions on the upper and lower boundaries of a layer, which represent conditions of elasticity in displacements or (and) stresses and conditions of diffusion in pressures or velocities for pore fluid, as well as in the derivatives of these variables. In particular it may be conditions of contact of a layer with punch and raft, Winkler or drainage layer, etc. [3, 4]. The mentioned groups of conditions generally do not depend each other, and may be considered in various combinations producing appropriate characteristic equations Nm(μ,s) = 0 for eigenvalues of the problem sk(μ), k = 0, ±1, ±2,..., with a number of similar properties.