The conventional cavity expansion method is based on the assumption of uniform radial pressure applied at the cavity wall boundary without considering the shear stress. However, in practice, shear stress may exist at the cavity wall, such as during the drilling process of drilled displacement piles. This note presents an analysis of the influence of shear stress on cylindrical cavity expansion in an undrained elastic-perfectly plastic soil. The problem is formulated by assuming large strain in the plastic zone and small strain in the elastic zone around the cavity, with a plane-strain condition under the cavity expansion process. Plastic yielding is determined by the Tresca failure criterion and an associated flow rule. A closed-form solution for the pressure-expansion relation is given to modify the conventional pressure-expansion relation without considering the influence of the shear stress. The plastic zone radius, cavity wall limit pressure, stress and excess pore pressure are also obtained. Furthermore, parametric studies are carried out to investigate the influence of shear stress on the cavity wall limit pressure, stress, excess pores pressure distributions around an expanding cylindrical cavity and the plastic zone radius. The results show that shear stress at the cavity wall boundary has a significant influence on the pressure-expansion relation and cannot be neglected when deriving the cavity wall pressure or excess pore pressure. However, the plastic zone radius is not sensitive to the shear stress. The present work provides a more general solution and improves the conventional cavity expansion theoretical framework.
This paper presents an analytical solution for cavity expansion in thermoplastic soil considering non-isothermal conditions. The constitutive relationship of thermoplasticity is described by Laloui's advanced and unified constitutive model for environmental geomechanical thermal effect (ACMEG-T), which is based on multi-mechanism plasticity and bounding surface theory. The problem is formulated by incorporating ACMEG-T into the theoretical framework of cavity expansion, yielding a series of partial differential equations (PDEs). Subsequently, the PDEs are transformed into a system of first-order ordinary differential equations (ODEs) using a similarity solution technique. Solutions to the response parameters of cavity expansion (stress, excess pore pressure, and displacement) can then be obtained by solving the ODEs numerically using mathematical software. The results suggest that soil temperature has a significant influence on the pressure-expansion relationships and distributions of stress and excess pore pressure around the cavity wall. The proposed solution quantifies the influence of temperature on cavity expansion for the first time and provides a theoretical framework for predicting thermoplastic soil behavior around the cavity wall. The solution found in this paper can be used as a theoretical tool that can potentially be employed in geotechnical engineering problems, such as thermal cone penetration tests, and nuclear waste disposal problems.
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