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

Abstract

Conventional cavity expansion theory is a one-dimensional problem and is not applicable for the two-dimensional cavity expansion issue, which is also required for geotechnical problems. This paper proposes a novel semi-analytical solution for displacement-controlled elliptical cavity expansion (DC-ECE) in undrained soil. The displacement and strain fields for DC-ECE are obtained from the strain path method (SPM) with the aid of conformal mapping theory. The effective stress can be subsequently obtained by the incremental stress-strain calculation using a suitable constitutive model such as the MCC model. Then, the computed effective stress results are substituted into the stress equilibrium equation to give the pore pressure solution. The new semi-analytical solution reveals the non-axisymmetric characteristics of DC-ECE and allows the elastic-plastic (EP) boundary, excess pore pressure, stress, and displacement to be calculated.The proposed method provides a solution to non-axisymmetric cavity expansion issues and it can be applied to geotechnical engineering problems, including vertical drain installation, flat dilatometer tests and noncylindrical pile penetration in clay.

Revisiting undrained cavity expansion problem in critical state soils: A simple graph‐based approach

“…In the last 40 years, the development of analytic technique for the analysis of cavity expansion in soils, a fundamental problem in theoretical geomechanics with many practical applications such as pressuremeter/cone penetration test interpretation and pile-driving modeling, has reached a maturity state in terms of the novelty of the solution procedure/strategy involved (e.g., [1][2][3][4][5][6][7][8][9][10][11][12] and the sophistication level of the constitutive model used. [13][14][15][16][17][18][19] The approaches commonly adopted for the solutions of cavity expansion problems, especially in the critical state soils, appear to be the similarity method (and its variants) proposed by Collins and his co-workers 4,20,21 and the rigorous Lagrangian-based solution procedure developed by Chen 22 and Chen & Abousleiman.…”

Analytical Solution for Elastic Analysis around an Ellipse with Displacement-Controlled Boundary

“…Previous solutions for the analysis around an ellipse mostly focused on the problem under the stress-controlled type of boundary conditions, for example, the analyses of an infinite elastic plate with a traction-free [8,14,24,25] or uniformly loaded [2,3,26] elliptical hole subjected to biaxial far-field loading. In fact, in some engineering problems, the inner elliptical cavity may also likely deform with specified displacements [27,28], for instance, the membrane expansion of a flat dilatometer and the radial expansion process of bio-inspired soil penetrometers/robots in the ground [29,30]. Zhou et al [17] presented an analytical solution for the elastic analysis of a flat elliptical cavity with small displacements in the direction parallel to one coordinate axis and applied the solution to the modelling of in-situ dilatometer tests.…”