Abstract
SUMMARYAn analytical solution of cavity expansion in two different concentric regions of soil is developed and investigated in this paper. The cavity is embedded within a soil with finite radial dimension and surrounded by a second soil, which extends to infinity. Large‐strain quasi‐static expansion of both spherical and cylindrical cavities in elastic‐plastic soils is considered. A non‐associated Mohr–Coulomb yield criterion is used for both soils. Closed‐form solutions are derived, which provide the stress and strain fields during the expansion of the cavity from an initial to a final radius. The analytical solution is validated against finite element simulations, and the effect of varying geometric and material parameters is studied. The influence of the two different soils during cavity expansion is discussed by using pressure–expansion curves and by studying the development of plastic regions within the soils. The analytical method may be applied to various geotechnical problems, which involve aspects of soil layering, such as cone penetration test interpretation, ground‐freezing around shafts, tunnelling, and mining. © 2014 The Authors. International Journal for Numerical and Analytical Methods in Geomechanics published by John Wiley & Sons Ltd.
Highlights
Cavity expansion theory has been extensively developed and widely used for the study of many engineering problems
The results presented illustrate that the cavity expansion method can be effectively used to study problems involving two concentric regions of different soils
The closed-form solutions are an extension of the cavity expansion solutions developed by Yu and Houlsby [4] and provide the stress and strain distributions within the two soils for both elastic and plastic states using a Mohr–Coulomb yield criterion, a non-associated flow rule, and a large-strain analysis
Summary
Cavity expansion theory has been extensively developed and widely used for the study of many engineering problems. Yu and Houlsby [4] provided a unified analytical solution of cavity expansion in dilatant elastic-plastic soils, using the Mohr–Coulomb yield criterion with a non-associated flow rule. Sayed and Hamed [24] were the first to apply analytical cavity expansion analyses of concentrically layered media to the field of geomechanics In their analysis, the medium was assumed to be a frictionless linear-elastic solid and did not account for the plastic behaviour of soils. The development of an analytical cavity expansion method for application to geotechnical problems involving aspects of soil layering is the main motivation for the work described in this paper. The following section considers the most general expansion problem for a cavity embedded in two different concentric regions of soil and derives expressions for stresses, strains, and displacements within elastic and plastic zones. A discussion of the application of the proposed method and its limitations is provided, followed by concluding remarks
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