Drained and undrained analyses of cylindrical cavity contractions by bounding surface plasticity

Abstract

This paper develops a rigorous semi-analytical approach for drained–undrained cylindrical cavity contraction problems in bounding surface elastoplastic geomaterials. For undrained situations, the effective radial, tangential, and vertical component stresses can be solved directly from the constitutive governing differential equations as an initial value problem, the excess pore pressure subsequently being determined from the radial equilibrium equation. In contrast, for the drained case the Eulerian radial equilibrium equation must be first transformed into an equivalent one in a Lagrangian description via the introduction of an auxiliary variable, then solved together with the elastoplastic constitutive relation for the three stress components as well as the specific volume. It is observed that during drained–undrained contraction processes, plastic deformations occur immediately as a direct result of employing the bounding surface model, so outside the cavity there exists no purely elastic zone. The computed stress distributions and in particular the stress path prediction through an example analysis capture well the anticipated elastoplastic and failure behaviour of the geomaterials surrounding the cavity. The validity and accuracy of the proposed semi-analytical elastoplastic solutions are justified through comparison with ABAQUS numerical results, and their applicability to the tunnel excavation and wellbore drilling problems is also demonstrated.

Computational implementation of bounding surface model and its verification through cavity benchmark problems

“…Other than the specific loading conditions of triaxial tests, as usually being employed in the literature, here the developed UMAT is used for the ABAQUS analysis of the fundamental cavity geomechanics problem and validated with the recently available analytical solutions for wellbore drilling/tunnel excavation. [ 25,26 ] The predictions from the ABAQUS simulations are found in general in excellent agreement with the analytical solutions, thus demonstrating the validity and accuracy of the currently proposed integration scheme.…”

A semi‐analytical solution for displacement‐controlled elliptical cavity expansion in undrained MCC soil

“…Russell et al 9 adopted the similarity solution methodology and derived a semi-analytical solution for unsaturated soils using bounding surface plasticity theory. Chen et al [10][11][12][13][14] obtained a series of exact solutions for drained or undrained CCE in isotropic or anisotropic critical state soils with rigorous definitions of deviatoric stresses. Li et al 15,16 presented rigorous numerical solutions for undrained CCE in K 0 -consolidated clay under plain strain condition and SANICLAY under plane stress condition based on Chen et al's method 11 .…”

Closed-form solutions for large strain analysis of cavity contraction in a bounded Mohr-Coulomb medium

“…Meanwhile, the elastic initial stress state is relatively simple. Hence, many relevant analytical/semi-analytical contraction solutions have been developed in this case over the years (Brown et al, 1983;Chen & Abousleiman, 2016;Mo & Yu, 2017;Park, 2014;Sharan, 2008;Vrakas & Anagnostou, 2014;Yu & Rowe, 1999;Yu et al, 2019). Likewise, most of them concentrated on the case of a cavity embedded in an infinite soil mass, which represents a reasonable simplification for the problem of deep tunnels and un-reinforced boreholes.…”