Abstract
This paper presents a novel, exact, semi-analytical solution for the quasi-static undrained expansion of a cylindrical cavity in soft soils with fabric anisotropy. This is the first theoretical solution of the undrained expansion of a cylindrical cavity under plane strain conditions for soft soils with anisotropic behaviour of plastic nature. The solution is rigorously developed in detail, introducing a new stress invariant to deal with the soil fabric. The semi-analytical solution requires numerical evaluation of a system of six first-order ordinary differential equations. The results agree with finite element analyses and show the influence of anisotropic plastic behaviour. The effective stresses at critical state are constant, and they may be analytically related to the undrained shear strength. The initial vertical cross-anisotropy caused by soil deposition changes towards a radial cross-anisotropy after cavity expansion. The analysis of the stress paths shows that proper modelling of anisotropic plastic behaviour involves modelling not only the initial fabric anisotropy but also its evolution with plastic straining.
Highlights
IntroductionThere is a wide variety of practical problems that may be modelled as the expansion (or contraction) of a spherical or cylindrical cavity in a solid mass
There is a wide variety of practical problems that may be modelled as the expansion of a spherical or cylindrical cavity in a solid mass
The solution involves the numerical integration of a system of six first-order ordinary differential equations, three of them corresponding to the effective stresses in cylindrical coordinates and the other three to the components of the fabric tensor
Summary
There is a wide variety of practical problems that may be modelled as the expansion (or contraction) of a spherical or cylindrical cavity in a solid mass. The mathematical solutions to those problems are usually categorized within the cavity expansion theory. The first solid mechanics applications of the cavity expansion theory were for metal indentation problems Some examples comprise the interpretation of in-situ tests like pressuremeter It is useful for wellbore instability and deep tunnels because, in these cases the cavity is contracted instead of being expanded, the problem is similar mathematically The analysis limits to the quasi-static expansion of a cylindrical cavity in plane strain conditions because the solid mass is assumed as infinite. The cavity is usually expanded in a short period of time and no drainage is allowed (undrained conditions)
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