Elastic-plastic solutions for expanding cavities embedded in two different cohesive-frictional materials

An analytical solution of cavity expansion in two different concentric regions of soil is developed and investigated in this paper. The cavity is embedded within a soil with finite radial dimension and surrounded by a second soil, which extends to infinity. Large-strain quasi-static expansion of both spherical and cylindrical cavities in elastic-plastic soils is considered. A non-associated Mohr–Coulomb yield criterion is used for both soils. Closed-form solutions are derived, which provide the stress and strain fields during the expansion of the cavity from an initial to a final radius. The analytical solution is validated against finite element simulations, and the effect of varying geometric and material parameters is studied. The influence of the two different soils during cavity expansion is discussed by using pressure–expansion curves and by studying the development of plastic regions within the soils. The analytical method may be applied to various geotechnical problems, which involve aspects of soil layering, such as cone penetration test interpretation, ground-freezing around shafts, tunnelling, and mining

Two-dimensional elastoplastic analysis of cylindrical cavity problems in Tresca materials

This paper presents analytical elastic-plastic solutions for static stress loading analysis and quasi-static expansion analysis of a cylindrical cavity in Tresca materials, considering biaxial far-field stresses and shear stresses along the inner cavity wall. The two-dimensional static stress solution is obtained by assuming that the plastic zone is statically determinate and using the complex variable theory in the elastic analysis. A rigorous conformal mapping function is constructed, which predicts that the elastic-plastic boundary is in an elliptic shape under biaxial in situ stresses, and the range of the plastic zone extends with increasing internal shear stresses. The major axis of the elliptical elastic-plastic boundary coincides with the direction of the maximum far-field compression stress. Furthermore, considering the internal shear stresses, an analytical large-strain displacement solution is derived for continuous cavity expansion analysis in a hydrostatic initial stress filed. Based on the derived analytical stress and displacement solutions, the influence of the internal shear stresses on the quasi-static cavity expansion process is studied. It is shown that additional shear stresses could reduce the required normal expansion pressure to a certain degree, which partly explains the great reduction of the axial soil resistance due to rotations in rotating cone penetration tests. In addition, through additionally considering the potential influences of biaxial in situ stresses and shear stresses generated around the borehole during drillings, an improved cavity expansion approach for estimating the maximum allowable mud pressure of horizontal directional drillings (HDDs) in undrained clays is proposed and validated

A cavity expansion–based solution for interpretation of CPTu data in soils under partially drained conditions

A cavity expansion–based solution is proposed in this paper for the interpretation of CPTu data under a partially drained condition. Variations of the normalized cone tip resistance, cone factor, and undrained‐drained resistance ratio are examined with different initial specific volume and overconsolidation ratio, based on the exact solutions of both undrained and drained cavity expansion in CASM, which is a unified state parameter model for clay and sand. A drainage index is proposed to represent the partially drained condition, and the critical state after expansion and stress paths of cavity expansion are therefore predicted by estimating a virtual plastic region and assuming a drainage‐index–based mapping technique. The stress paths and distributions of stresses and specific volume are investigated for different values of drainage index, which are also related to the penetration velocity with comparisons of experimental data and numerical results. The subsequent consolidation after penetration is thus predicted with the assumption of constant deviatoric stress during dissipation of the excess pore pressure. Both spherical and cylindrical consolidations are compared for dissipation around the cone tip and the probe shaft, respectively. The effects of overconsolidation ratio on the stress paths and the distributions of excess pore pressure and specific volume are then thoroughly investigated. The proposed solution and the findings would contribute to the interpretation of CPTu tests under a random drained condition, as well as the analysis of pile installation and the subsequent consolidation

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

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 semianalytical 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.The research was initiated as part of GEO-INSTALL (Modelling Installation Effects in Geotechnical Engineering, PIAP-GA-2009-230638) and CREEP (Creep of Geomaterials, PIAP-GA-2011-286397) projects supported by the European Community through the programme Marie Curie Industry-Academia Partnerships and Pathways (IAPP) under the 7th Framework Programme

Numerical Check of the Meyerhof Bearing Capacity Equation for Shallow Foundations

In 1920 Prandtl published an analytical solution for the bearing capacity of a strip load on a weightless infinite half-space. This solution was extended with a surrounding surcharge by Reissner and with the soil weight by Keverling Buisman. It was Terzaghi who wrote this with three separate bearing capacity factors for the cohesion, surcharge and soil-weight. Meyerhof extended this to the equation which is nowadays used; with shape and inclination factors. He also proposed equations for the inclination factors, based on his own laboratory experiments. Since then, several people proposed updated equations for the soil-weight bearing capacity factor, and also for the shape and inclination factors. The common idea is that failure of a footing occurs in all cases with a Prandtl-wedge failure mechanism. In order to check the failure mechanisms and the currently used equations for the bearing capacity factors and shape factors, a large number of finite element calculations of strip and circular footings have been made. These calculations proof that for some cases there are also a few other failure mechanisms possible. Also the currently used bearing capacity factors and shape factors are not correct. In fact, for footings on a soil with a higher friction angle, all three bearing capacity factors and all three shape factors can be much lower than the currently used values. This means that the currently used equations for the soil-weight bearing capacity factors and the shape factors are inaccurate and unsafe. Therefore, based on the finite element calculations, new equations have been presented in this paper