The authors propose a combined approach for definition of the shear rigidity of the multilayered soil which is cut through by a pile. The solution for the vertical direction is presented in the view of an axisymmetric problem. As to the horizontal direction, the solution is presented in view of a beam on elastic subsoil with genetically non-linear transition to equivalent horizontal rigidity of the wide pile field in condition of dynamic forces action. The axisymmetric solution provides visual clarity in the analysis of the stress-strain state of the pile and near-pile soil in comparison with the approved analytical methods. To speed up calculations at the stage of the main combination of constant and long-term impacts, the vertical rigidity of the base under the foot of the pile can be calculated analytically as for a stamp on an elastic-plastic base. The horizontal rigidity is considered as for a discrete single bent pile in the medium of an elastic layered half-space at the stage of formation of the stress-strain state of the system under the main combination of static loads. These methods of numerical modeling of deformations of a single pile make it possible to expand the algorithm of analytical calculation of a large pile field, which in turn is modified by the authors by excluding deformations of the pile body due to its natural consideration in the finite element formulation, as well as by introducing the parameter of the limiting radius of the influence of a single pile on the settlement of neighboring piles. The considered numerical approaches to the calculation of the pile field are applicable in a complex calculation taking into account the history of loading at the stage of the main combination of permanent and long-term impacts. At the stages of short-term or special dynamic impacts an integral rigidity of pile cells is proposed, which will be considered in the next publication of the authors.

vertically loaded pile axisymmetric model, bended pile rod model, large pile field model.