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552.52,624.131.54 The rheological properties of water-saturated clays have been studied based on the model described in [1,2]. The problem on shrinkage of a clay layer under strain has been reduced to the well-known problem of N. N. Verigin. The numerical solution of the problem on squeezing of water from a clay layer has been found and analyzed. The distinctive features of the model, which are important for explanation of certain characteristic features of the rheology of clays, have been investigated. It has been shown that the solutions obtained are in qualitative agreement with experimental results.Introduction. Study of the rheological properties of clays is traditionally of interest from both the applied viewpoint (clays are a raw material for manufacture of drilling muds, ceramics, and brick) and the theoretical viewpoint. In the latter case, the problem is reduced, as a rule, to the following one: to put forward a system of hypotheses for the structure and properties of a medium and processes occurring in it such that none of them is inconsistent with the available experimental facts and to formulate, based on it, a mathematical model which could be realized for a standard set of known phenomenological constants for clays and processes in them and would lead to numerical results consistent with experiment. The difficulties of mathematical modeling of the rheological properties of clays are associated with the necessity of allowing for the processes of mechanical straining of a medium and changes in the packing of clay particles and the distinctive features of the motion of water in macro-and micropores of a clay rock. These problems have been studied in many works, including [1]. In it, it was, in particular, proposed that the problem obtained for the simplest case of one-dimensional shrinkage of a clay layer under a constant load be reduced to the Verigin problem [2]. Physically this corresponds to the appearance of two shrinkage zones in the clay layer, in one of which the pores of the clay rock are only partially filled with clay particles and consequently the permeability of this zone is relatively high, whereas in the other, clay particles entirely fill the pores of the rock and the permeability of this zone is lower than that of the first zone. Thus, any process associated with the straining of clay rocks can be subdivided into two stages, in which (1) the fraction of pores free from clay particles (free porosity) is not equal to zero and (2) free porosity is equal to zero, i.e., clay particles have entirely filled all the pores.In the simplest case, in the first stage, the process of shrinkage of a porous medium with an elastic skeleton due to the squeezing of a fluid from the pores of the rock [3] is described by the piezoconductivity equation [4]

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