Analytical solutions for stresses and displacements of cylindrical cavity expansion based on extended SMP criterion

摘要

Exact and closed-form solutions were obtained for the elastoplastic analyses in terms of stresses and displacements due to cylindrical cavity expansion in soil mass governed by the extended SMP failure criterion. A non-associated flow rule was used with respect to large strain in plastic region and small strain in elastic region. And also solutions involving limited cavity expansion, radial stresses including strains and hoop stresses including strains around an expanding cavity were obtained. Additionally, the exact solutions presented in this paper are relatively simple and do not need any transformation. In addition, the solutions are on a basis of a theoretically consistent method, which are more analytical and physical comparing with numerical method. Also, comparison was made between the present solution and current solution both of which are based on Mohr-Coulomb criterion in order to investigate the influences of intermediate principal stress. The results indicated that soil shear dilatancy and the intermediate stress play a significant role on ultimate cavity pressure and maximum radius of plastic region in the cylindrical cavity expansion. Then, the several example cases analyzed for practical problems in this paper showed that the effect of large strain on the results of cavity expansion pressure and radius in plastic region is more than that of small strain. Thus, the innovative approximation technique can be utilized to derive the relatively simple solutions with respect to some common complex plasticity problems in soil mechanics.