A rigorous semi‐analytical solution for undrained cylindrical cavity expansion in critical state soils

Abstract

This paper presents a generalized, rigorous and simple large strain solution for the undrained expansion of a vertical cylindrical cavity in critical state soils using a rate-based plasticity formulation: the initial stress field is taken as anisotropic, that is with horizontal stresses that differ from the vertical stress, and the soil is assumed to satisfy any two-invariant constitutive model from the critical state (Cam-clay) family; no simplifying assumption is made during the mathematical derivation; calculating the effective stresses around the cavity requires the solution of a nonlinear equation by means of the Newton-Raphson method in combination with quadrature. Cavity expansion curves and stress distributions in the soil are then presented for different critical state models (including the modified Cam-clay model). The solution derived can be useful for estimating the instantaneous response of saturated low-permeability soils around piles and self-boring pressuremeters and can serve as trustworthy benchmark for numerical analysis codes.

Undrained expansion of a cylindrical cavity in clays with fabric anisotropy: theoretical solution

“…Chen & Abousleiman [8] were the first ones to obtain an exact analytical solution using the rigorous definition of the deviatoric stress, q, and a shear modulus, G, that varies with the mean pressure, p'. Vrakas [31] developed a general exact solution for different Cam-clay models and presented a critical evaluation of the various simplifying expressions used for stress invariants.…”

“…This simplifying assumption does not affect the results because in the elastic region, the strains are much smaller than in the plastic annulus. The solution by Vrakas [31] considers large-strain formulation also in the elastic zone, but the differences are negligible.…”

Spherical cavity expansion in porous rock considering plasticity and damage

“…on cavity expansion results 10,29–33 . Thus, more advanced constitutive models can also be incorporated through similarity technique 34 …”

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.…”

“…Bishop first developed equations for the quasistatic cylindrical and spherical cavity expansion and used these equations to compute forces on the conical nose punches pushed slowly into metal targets . Subsequently, a series of analytical and semianalytical solutions for quasistatic cavity expansion were presented by considering the large deformation effect and using more complex soil constitutive models, such as the hypoplasticity model, bounding surface model, and critical state model . Furthermore, some special cavity expansion problems, such as cavity expansion in two layered soils, cavity expansion under anisotropic stress conditions, pressure‐controlled elliptical cavity expansion, and cavity expansion in thermoplastic soil, are investigated.…”