Closed-form solution for cavity expansion in sand based on strain gradient plasticity

As a simple and applicable theoretical tool, cavity expansion theory has been widely used in the research of geotechnical engineering problems such as tunnel, geotechnical in-situ test, bearing capacity design of pile foundation and anchor plate. The existing expansion theory cannot consider the size effect of soil with small radius expansion. This paper takes the expansion of cylindrical and spherical cavity in sand as the research object to investigate this issue. Based on the strain gradient plasticity theory, this paper introduces and explains the mechanical parameter that can consider the size effect of soil, i.e., soil characteristic length 1; meanwhile, considering the large deformation characteristics of soil, a closed solution of cavity expansion that can take the size effect of soil microstructure into account is derived. The correctness of the theoretical solution in this paper is verified by reducing the normalized characteristic length of soil l/ao (ao is the initial radius of circular hole) to 0 (i.e., without considering the size effect), and thus the solution is reduced to the classical expansion solution without considering the size effect. Then, the effects of normalized characteristic length, friction coefficient, dilatancy coefficient and shape coefficient of soil on pressure expansion relationship, stress distribution around hole, strain gradient around hole and ultimate expansion stress are discussed in detail. Finally, the theoretical solution proposed in this paper is applied to the practical problems such as micro cone penetration test (MCPT), and the formula for calculating the penetration resistance of MCPT is proposed. By comparing with the existing test results, the applicability of this solution is verified.