Non-self-similar Cavity Expansion in Elastoplastic Soils: Theory and Applications

Cavity expansion theory (CET) is a simplified theoretical method in geomechanics and has been widely applied to many geotechnical problems. Traditional CET are mainly concentrated on self-similar cavity expansion problems, in which all material points follow the same stress/deformation paths. However, non-self-similar CET is developed much more slowly due to limitations of traditional methods, especially when constitutive models are complex and multi-fields are taken into consideration. In this thesis, three three non-self-similar cavity expansion problems are investigated by developing novel solution methods, where the non-self-similarity is induced by finite cylinder thickness, hydro-mechanical coupling and thermo-mechanical coupling, respectively. The main work of the thesis is briefly summarised as follows.

A hybrid Eulerian-Lagrangian (HEL) approach is proposed and applied to analyse the non-self-similar expansion process of a hollow cylinder with critical state models, considering arbitrary saturation states of soils under both drained and undrained conditions. A closed-form solution for the stresses and displacements in the elastic zone is presented, taking the state-dependent soil moduli and outer boundary effect of the soil cylinder into account. Adopting large strain theory in the plastic zone, the non-self-similar cavity expansion process is formulated into a set of partial differential equations (PDEs) in terms of both Eulerian and Lagrangian descriptions, which is solved by a newly proposed algorithm. Then, the expansion process is proven to be non-self-similar by showing the stress and deformation paths, and the finite thickness of soil cylinders may greatly influence the cavity expansion behaviour, especially with a small thickness ratio. Finally, an example application of the new solution shows that the boundary effect in pressuremeter tests can be generally captured by the cavity expansion solution in bounded soils.

A hydro-mechanical coupled solution is proposed for cylindrical cavity expansion under partially drained conditions. The mechanical behaviour of soils is modelled by the perfectly elastoplastic model with the Tresca yield criterion and water flow within porous soils is assumed to obey Darcy’s law. Two PDEs are established in the elastic and plastic zones, respectively, transforming the cavity expansion analysis under partially drained conditions into a typical Stefan problem with moving boundary conditions. Then an approximate solution for the PDEs is derived by the variable transformation method. Based on the new solution, a novel normalised penetration rate is defined considering the rigidity index of soils, with which a unique backbone curve for CPTU is found. Finally, the backbone curve is compared with a database consisting of 109 in-situ experimental tests, 101 centrifuge modelling tests, and numerical simulation results.

Considering the thermo-mechanical coupling, a cavity expansion solution is developed to investigate the radial interaction between energy piles and soils (RIEPS). Firstly, transient temperature distributions are shown by assuming heat conduction in the radial direction and constant temperature at the pile-soil interface. Then the temperature distributions are applied to soils to obtain an analytical solution for thermo-elastic stresses and displacements. It is found that the solution under the combined thermal-mechanical loading pattern is the linear superposition of those under the purely thermal loading and mechanical loading. Hence, the stresses, strains and displacements in soils are determined by the competitive relationships between thermal loading and mechanical loading. Finally, the expression for radial stress change at the pile-soil interface is revisited by the cavity expansion analysis and comparison with field data. This expression could be quite general for typical soil and pile parameters considering transient temperature distributions and soil/pile moduli.