Undrained cylindrical cavity expansion in anisotropic critical state soils

Abstract

This paper develops a rigorous semi-analytical approach for the undrained cylindrical cavity expansion problem using an anisotropic critical state clay plasticity model. The model, originally proposed by Y. F. Dafalias in 1987, is capable of capturing the inherent anisotropy of the soil due to its initial K0 consolidation history, as well as the subsequent stress-induced anisotropy, through the proper incorporation of the rotation and/or distortion of the ellipsoidal yield surface. It is found that the cavity expansion boundary value problem can be eventually reduced to solving a system of six first-order ordinary differential equations in the plastic zone, with the radial, tangential and vertical stresses in association with the three anisotropic variables controlling the yield surface evolution being the basic unknowns. The pore water pressure can be subsequently deduced from the radial equilibrium equation. Extensive parametric studies have been made of the effects of K0 consolidation anisotropy (including also the subsequent stress-induced anisotropy) and past consolidation history (overconsolidation ratio) on the calculated distributions of stress components and excess pore pressure, the progressive development of the stress-induced anisotropy, and on the effective stress trajectory for a soil particle at the cavity surface due to the cavity expansion. The present solution on account of the natural and induced anisotropy is expected to be able to provide more realistic analyses for a variety of geotechnical problems such as the pile installation prediction and interpretation of pressuremeter tests. It can also serve as a benchmark for the finite-element numerical modelling of the cavity expansion problem involving the advanced anisotropic critical state plasticity models.

Analysis of cylindrical cavity expansion in anisotropic critical state soils under drained conditions

“…As pointed out in Chen and Liu (2018), for a cylindrical cavity expanded in ‫ܭ‬ consolidated, initially transversely isotropic soils, all the three off-diagonal components of the deviatoric anisotropic tensor ߙ , i.e., ߙ ఏ , ߙ ௭ , and ߙ ఏ௭ , must remain vanishing throughout the entire expansion process due to the axisymmetric nature of the problem. Dafalias' (1987) anisotropic Cam Clay model for such a particular boundary value problem, therefore, may be formulated as follows…”

“…The present paper continues on the theme of developing analytical solutions for cavity expansion in elastoplastic soils, this time with an extension of the work of Chen and Liu (2018) from undrained to drained loading conditions. The derivation presented in this work is again based on Dafalias' (1987) representative anisotropic Cam Clay model and on the leverage of the solution procedure originally proposed by Chen and Abousleiman (2013), which enables an innovative conversion of the radial equilibrium equation between Eulerian and Lagrangian forms.…”

“…As in Chen and Liu (2018), to simplify the mathematical derivation so as to obtain the semianalytical elastoplastic solution, no attempt will be made in the present work to incorporate the elastic anisotropy of soil behaviour. Nevertheless, it is supposed herein that the shear modulus ‫ܩ‬ and Young's modulus ‫ܧ‬ are both dependent on the mean stress ‫‬ and specific volume ‫ݒ‬ within the critical state soil mechanics framework (Schofield and Wroth, 1968), and take the following…”

“…Here ‫ܴܥܱ‬ is defined as the ratio of past maximum effective vertical stress ߪ ௩,௫ to the in situ vertical effective stress ߪ ௩ , which is different from the isotropic overconsolidatoin ratio ܴ as used in Chen and Abousleiman (2013) in terms of the mean effective stress. The soil parameters for these three cases are given in Table 2, which have the same set-up as used in Chen and Liu (2018). Fig.…”

“…Li et al (2016Li et al ( , 2017, on the other hand, following the methods proposed by Chen andAbousleiman (2012, 2013), developed semi-analytical solutions for the undrained and drained cavity expansion problems in ‫ܭ‬ consolidated, anisotropic elastoplastic soils, but the rotation of the yield surface was deemed to be relevant merely to the inherent sedimentation anisotropy and be fixed in the stress space. This limitation has been overcome in a most recent paper by Chen and Liu (2018), who offered a rigorous cavity expansion solution under undrained condition with the due consideration of both initial deposition and stress-induced anisotropy, using the well-known rotational hardening elastoplastic model proposed by Dafalias (1987). It is worthy to mention that a similar undrained solution was also simultaneously and independently derived by Sivasithamparam and Castro (2018), where a different anisotropic elastoplastic model S-CLAY1 (Wheeler et al 2003) incorporating both plastic volumetric strain and plastic shear strain within the rotational hardening rule has been employed in their formulations.…”