Elastic‐plastic solutions for expanding cavities embedded in two different cohesive‐frictional materials

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.

Centrifuge modelling of cone penetration tests in layered soils

“…Also included in Fig. 5 are predictions of resistance ratio using the Mo et al (2014aMo et al ( , 2014b) method for interpretation of CPT data in layered soils. This method involves the prediction of the transition of penetration resistance in layered soils using analytical solutions for expanding cavities embedded in two different cohesive-frictional materials.…”

“…The first analytical solution for penetration in layered soils was proposed by Vreugdenhil et al (1994), which is an approximate solution for simple linear-elastic media. Elastic-plastic solutions for expanding cavities embedded in two different cohesive-frictional materials were proposed by Mo et al (2014b), which were shown to provide an effective method for the interpretation of CPT data in layered soils in Mo et al (2014a).…”

Analysis of dynamic spherical cavity expansion in undrained modified Cam Clay soil

“…1 Subsequently, a series of analytical and semianalytical solutions for quasistatic cavity expansion were presented by considering the large deformation effect [2][3][4][5][6][7][8][9] and using more complex soil constitutive models, such as the hypoplasticity model, 10 bounding surface model, 11 and critical state model. [12][13][14] Furthermore, some special cavity expansion problems, such as cavity expansion in two layered soils, 15,16 cavity expansion under anisotropic stress conditions, [17][18][19][20] pressure-controlled elliptical cavity expansion, [21][22][23][24] and cavity expansion in thermoplastic soil, 25 are investigated. A review of these published solutions for geomaterials indicates that the previous cavity expansion analyses neglected the influence of cavity expansion velocity (dynamic effect) by using the quasistatic assumption.…”

Elastoplastic Analysis of Circular Tunnel Based on Drucker–Prager Criterion

“…Pinto and Whittle [6] predicted and expound the deformation of shallowly buried tunnel in the soft soil layer, based on the cavity expansion theory. Mo et al [7] deduced the theoretical solution of the concentric regions of two different rock soils and also carried out the finite element simulation. For a long time, the elastoplastic analysis of the tunnel has been conducted by adopting the Mohr-Coulomb criterion [4,[8][9][10] or Hoek-Brown criterion [11][12][13], based on the fact that the internal friction angle of the surrounding soil is a constant.…”