This paper presents a novel unified solution to drained expansion of a spherical cavity in both clay and sand. The large-strain theory and a critical state model with a unified hardening parameter are used to describe the elastoplastic behavior of the soils after yielding. The elastoplastic constitutive tensor of the critical state model is developed to be a system of first-order differential equations for the drained expansion of a spherical cavity. The problem is formulated as an initial value problem in terms of the Lagrangian scheme by introducing an auxiliary variable and is solved numerically. With the present solution, curves for the expansion pressures, the distributions of stress components, and the stress paths are plotted to illustrate the different expansion responses in clay and sand. The proposed solution not only incorporates the dilatancy and peak strength of dense sand, but it can also reduce to the solution for clay and loose sand when ignoring the dilatancy and peak strength. Therefore, the present solution can be applied to interpret the cone penetration test and the pile installation, as well as to evaluate the pile end bearing capacity in various kinds of soils.


Geosciences and Geological and Petroleum Engineering


National Natural Science Foundation of China, Grant 41272288

Keywords and Phrases

Auxiliary variable; Dilatancy; Drained expansion; Elastoplastic; Expansion response

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Document Type

Article - Journal

Document Version


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Publication Date

01 Aug 2017