The article proposes a new approach to the method of calculating a rigid foundation on a nonlinear and rheology deformable half-space, taking into account the external load variable in time. It is proposed to take into consideration the nonlinearity and rheology of deformation on the basis of modern phenomenological theory using the integral method of successive iterations, which makes it possible to take into account the time-variable mode of external loading, which is characteristic of the stage of construction and operation of structures. An algorithm for the numerical solution of the problem under the conditions of the regime action of external loads using the method of integral estimates based on the step method and successive approximations is presented.

Keywords: rigid foundation, foundation deformation, regime loads, deformation rheology, integral method, phenomenological theory