Analysis of undrained cavity expansion in elasto‐plastic soils with non‐linear elasticity

Abstract

SUMMARYA large strain analysis of undrained expansion of a spherical/cylindrical cavity in a soil modelled as non-linear elastic modi"ed Cam clay material is presented. The stress}strain response of the soil is assumed to obey non-linear elasticity until yielding. A power-law characteristic or a hyperbolic stress}strain curve is used to describe the gradual reduction of soil sti!ness with shear strain. It is assumed that, after yielding, the elasto-plastic behaviour of the soil can be described by the modi"ed Cam clay model. Based on a closedform stress}strain response in undrained condition, a numerical solution is obtained with the aid of simple numerical integration technique. The results show that the stresses and the pore pressure in the soil around an expanded cavity are signi"cantly a!ected by the non-linear elasticity, especially if the soil is overconsolidated. The di!erence between large strain and small strain solutions in the elastic zone is not signi"cant. The stresses and the pore pressure at the cavity wall can be expressed as an approximate closed-form solution.

On the problem of cavity expansion in unsaturated soils

“…These include closed form solutions [6,10,19,38] in which the soil was assumed to be incompressible; semi-analytical solutions for dilative soils within MohrCoulomb yield criterion and non-associative flow rule [4,9,12,42,44,45]; numerical solutions for large strain cavity expansion in strain hardening-softening soils [1,7,8,37,43]; and the semi-analytical solutions of Collins and his coworkers [12,13,14,15] using the similarity technique.…”

Prediction of stone column ultimate bearing capacity using expansion cavity model

“…The analytical methods were developed by assuming that the medium around the cavity followed various behaviour laws such as linear elastic, elastic perfectly plastic, either by not taking account of volume variation (Chadwick, 1959;Gibson and Anderson, 1961;Hill, 1950;Ménard, 1957) or by considering volume variation (Carter et al, 1986;Hughes et al, 1975;Ladanyi, 1963;Manassero, 1989;Mecsi, 1991;Salençon, 1966;Vésic, 1972;Yu and Houlsby, 1991). In the analytical contributions, hypotheses were adopted for the soil behaviour either in small strains (Bishop et al, 1945;Gibson and Anderson, 1961;Hill, 1950;Hughes et al, 1975;Ladanyi, 1963;Ménard, 1957;Vésic, 1972;Windle and Wroth, 1977) or in large strains (Cao et al, 2002;Carter et al, 1986;Chadwick, 1959;Yu and Houlsby, 1991, etc.). Note that Hughes et al (1975) proposed neglecting the elastic strain with respect to the plastic component, whereas Carter et al (1986) demonstrated that for a strain level beyond 10%, the elastic strain component should not be neglected.…”

“…Equation 5 is derived from the work of Ménard (1957), Bishop et al (1945) or Houlsby and Withers (1988), using ideal MohrCoulomb elastic-plastic assumptions Cao et al (2002) studies the non-linear elastic response prior to yielding on the expansion of the cylindrical cavity in a soil that is modelled as a non-linear modified Cam Clay material. Large strain formulation is adopted for both the elastic and the plastic regions.…”

“…The calibration of the equations aims to determine the following quantities j the best value of multiplier L using empirical results j the best fit of coefficient ä in Equation 23 from the Cao et al (2002) model j the values of AE and k in Equation 24 from the model.…”

Potential role of compressional structures in generating submarine slope failures in the Niger Delta

“…The cavity expansion is a simple theory that has found many applications in geotechnical engineering. Analytical solution of spherical/cylindrical cavity in a soil modelled as elastic, non-linear elastic or elasto-plastic are now available in literature (Cao and Chang, 2002).…”