Degree
Doctor of Philosophy (PhD)
Department
Department of Civil and Environmental Engineering
Document Type
Dissertation
Abstract
The cavity expansion theory has been introduced to geomechanics and geotechnical engineering for over sixty years to predict the relationship between stress and displacement during cavity expansion in geomaterials. Over the past forty years, many analytical solutions have been proposed and developed for the fundamental cavity expansion problem in geomechanics, accounting for various elastoplastic models and boundary conditions. Recently, a novel and simple yet rigorous analytical approach, called the graphical method, was proposed to directly predict the limiting undrained cavity expansion pressure in modified Cam Clay critical state soils. The advantage of this graph-based analytical method lies in its ability to determine the ultimate cavity expansion pressure through the equilibrium equation in Lagrangian form with the mean effective stress as the only variable.
This dissertation aims to extend this novel graph-based analytical method to investigate the stress and displacement responses during undrained cavity expansion in various elastoplastic yield models. These models include both models with smooth yield and potential surfaces, such as original and modified Cam Clay models and shear strain-hardening Drucker-Prager models with both associated and non-associated flow rules, and those with non-smooth yield and potential surfaces, such as the perfect Mohr-Coulomb yield model. For elastoplastic models with smooth yield and potential surfaces, the limit cavity expansion can be readily solved through the Lagrangian description of the radial equilibrium function with respect to the mean effective pressure as the only variable. For those with non-smooth yield and potential surfaces, such as the perfect Mohr-Coulomb yield model addressed in this dissertation, the limit cavity expansion pressure is obtained through the radial equilibrium equation after solving the effective stress components from the constitutive equation in Lagrangian form. Rigorous analytical solutions for stresses and displacements in undrained cavity expansion for perfect Mohr-Coulomb soils can be derived in completely explicit forms, and the intermediacy assumption for the vertical stress commonly adopted in previous formulations is removed.
Date
4-3-2025
Recommended Citation
Wang, Xu, "Graph-Based Analytical Solutions for Undrained Cylindrical Cavity Expansion in Elastoplastic Soils" (2025). LSU Doctoral Dissertations. 6767.
https://repository.lsu.edu/gradschool_dissertations/6767
Committee Chair
Chen, Sheng-Li