An elastoplastic solution for spherical cavity undrained expansion in overconsolidated soils

Abstract

In this paper, a novel elastoplastic solution is developed for the undrained expansion of a spherical cavity in overconsolidated soils, with the aim of providing a mechanical model for the interpretation of cone penetration tests in overconsolidated soils. The well-established unified hardening (UH) model is adopted in the present solution to represent the unique mechanical behaviors of the overconsolidated soil during cavity expansion. The problem considered is formulated as a system of first order partial differential equations in terms of a Lagrangian description; these equations are solved as an initial value problem with the code developed based on the Runge-Kutta algorithm. The results, including the expansion-pressure curves, the distributions of the stress components, and the evolution of the potential strength during cavity expansion are presented to show the expansion responses in overconsolidated soils. The results reveal that the unique expansion responses in overconsolidated soil during cavity expansion, such as the development of a negative excess pore water pressure, the strain-hardening and softening behavior, the peak strength and the decay of the potential strength during cavity expansion could be well represented by the present solution.

Introduction

Cavity expansion theory, which primarily concerns the changes in the stress, porewater pressure and displacement caused by cavity expansion, has versatile applications in modeling a variety of geotechnical problems (Yu, 2000). With appropriate assumptions and abstractions, cavity expansion theory can be applied to interpret the cone penetration and pressuremeter tests (Salgado et al., 1997, Burns and Mayne, 1998, Cudmani and Osinov, 2001, Chang et al., 2001, Russell and Khalili, 2002, Mo et al., 2016, Agaiby and Mayne, 2018); model pile installation effects (Carter et al., 1986, Chai et al., 2005, Randolph, 2003, Randolph et al., 1979, Li et al., 2017, Li et al., 2017, Rezania et al., 2017), determine the end-bearing and shaft capacities of driven piles, and predict the effects of tunneling (Yu and Rowe, 1999, Mo and Yu, 2016, Vrakas and Anagnostou, 2014, Vrakas and Anagnostou, 2015, Liang et al., 2020).

Cavity expansion theory has been well developed during the past few decades, by either developing new solution techniques (Collins et al., 1992, Chen and Abousleiman, 2012, Chen and Abousleiman, 2013, Vrakas, 2016, Cao et al., 2001, Zhuang and Yu, 2019) or applying advanced soil models in cavity expansion solutions (Collins and Stimpson, 1994, Collins and Yu, 1996, Russell and Khalili, 2006, Zhou et al., 2018, Li et al., 2016, Chen and Abousleiman, 2016, Chen and Liu, 2019, Chen et al., 2019, Sivasithamparam and Castro, 2018, Chen et al., 2020, Mo and Yu, 2017, Li et al., 2017, Yang et al., 2020). For the spherical cavity expansion problem, Collins and Yu (Collins and Yu, 1996) presented a general analytical framework that is applicable to any isotropic critical soil model and cavity with an arbitrary initial cavity radius. Recently, Mo and Yu (Mo and Yu, 2017) further examined the spherical cavity expansion problem in both clay and sand with the advanced unified state parameter model of Yu (Yu, 1998). Nearly at the same time, Li et al. (Li et al., 2017) also developed a semi-analytical solution using a simple unified hardening parameter-based critical state model (UH model) of Yao et al. (Yao et al., 2008) for the drained expansion of a spherical cavity in clay and sand. Although the cavity expansion theory has been well developed at present, no elastoplastic solution has been developed, especially for cavity expansion in overconsolidated soils (Sully et al., 1999). It is well known that most natural clays show overconsolidated and unsaturated properties due to the changes in the deposition environment (Gao et al., 2019). Compared with normally consolidated soils, overconsolidated soils exhibit some apparently unique features, such as a lower void ratio, higher peak strength, strain hardening and softening behavior during loading. However, although the available solutions based on the modified Cam-clay (MCC) model can reflect the general expansion responses, they are incapable of representing the unique behavior of overconsolidated soil in the expansion process. As a consequence, the available MCC model-based solutions would result in inaccurate predictions for the cone penetration tests and pile installation effects in overconsolidated soils. Therefore, it is of great significance to develop an elastoplastic solution for cavity expansion to accurately interpret the cone penetration tests and pile installation effects in overconsolidated soils.

In this study, a novel elastoplastic solution is presented for the undrained expansion of a spherical cavity in overconsolidated soils. The behavior of the overconsolidated soil is properly modeled by the well-established UH model of Yao et al. (Yao et al., 2012, Yao et al., 2009), which could reasonably represent the strain hardening/softening, shear dilatancy, and peak strength of the overconsolidated soils. The problem considered is formulated as a system of first-order differential equations following the analytical framework of Chen and Abousleiman (Chen and Abousleiman, 2012) and is solved as an initial value problem with the code developed based on the Runge-Kutta algorithm. The analytical framework of the present solution is similar to but simpler than the general approach presented by Collins and Yu (Collins and Yu, 1996). Notably, the present solution is different from the previous solution of Li et al. (Li et al., 2017); which was developed for the drained expansion of a spherical cavity in clay and sand, as the soil model and drainage condition are totally different. The key contribution of the present solution lies in that the UH model of Yao et al. (Yao et al., 2012, Yao et al., 2009), which is capable of representing the unique behavior of overconsolidated soil, is used to develop the solution; thus, the solution could better model the undrained expansion responses in overconsolidated soils. The expansion response results of soils with different overconsolidation ratios are presented to show the expansion responses in different overconsolidated soils. In particular, the expansion-pressure curves, the distributions of the stress components, and the effective stress paths calculated from the present solution are selectively compared with those generated from the available MCC model-based solution to highlight the unique expansion responses in overconsolidated soil. The results show that the proposed solution can properly reflect the development of the negative excess pore water pressure, strain-hardening and softening behaviors, and the decay of the potential strength of overconsolidated soil during cavity expansion.