Expansion And Contraction Of A Thick-Walled Cylinder/Sphere Of Soil:Theory And Application

Cavity expansion theory in geomechanics,which serves as a simple yet useful tool,has been widely applied to many geotechnical problems,such as tunnelling,in-situ tests and bearing capacity of geo-structures.However,very limited studies have focused on the finite boundary effect of cavities on the cavity expansion/contraction behaviour,which may be important for stability and deformation analysis of shallow tunnels and the calibration chamber test for the pressuremeter test and the cone penetration test(CPT).To fill the gap,this thesis obtains quasi-static analytical/semi-analytical solutions for cavity expansion/contraction in finite soil mass that is modelled by elastic-perfectly plastic model and the critical state model,respectively.The influence of soil constitutive models,drainage conditions and boundary effect of the hollow cylinder and sphere on cavity expansion/contraction behaviour are discussed.Then the cavity expansion/contraction solutions for finite soil mass are successfully applied to the design of tunnel stability and deformation,the prediction of thick-walled cylinder tests,and evaluation of boundary effect of calibration chambers for CPT.The main research contents and conclusions are summerised as follows:1.Adopting the non-associated Mohr-Coulomb(MC)model,the large-strain solution for cavity contraction is obtained and both the stresses and displacement can be derived analytically.After validation of the solution,the influence of boundary effect,soil strength and dilatancy on the cavity contraction curve,distribution of stresses and the stress path are discussed.It is found that the cavity contraction behaviour is mainly affected by the boundary effect and soil strength.Based on the analogue between tunnel collapse and cavity contraction,a simple method is proposed to assess shallow tunnel stability in clay and sand.The predicted results are compared with 32 experimental results and 112 numerical simulation results and it is found that the method can provide a quite reasonable estimation for shallow stability in clay.2.Using Clay and Sand Model(CASM)as an example,the large-strain solution for cavity expansion/contraction in undrained conditions is proposed and thus the stresses,displacement and excess pore pressure can be calculated analytically.The solution is validated by comparison with published solutions for infinite soil mass.The changes of cavity expansion/contraction curves,distribution of stresses and stress paths with the cavity thickness and stress history are discussed to investigate the mechanism of boundary effect.The solution is adopted to predict the thick-walled cylinder tests and convergence of shallow tunnels in clay.It is found that the predicted results agree well with experimental and numerical results with consideration of the boundary effect,which extends the application of cavity expansion theory in geotechnical engineering.3.Using the critical state model,such as CASM,a new semi-analytical method,named the Eulerian-Lagrangian method,is proposed for drained cavity expansion in a finite critical state soil mass.In the elastic region,stresses and displacement can be derived analytically in small-strain theory,while in the plastic region a set of partial differential equations(PDEs)is established in large-strain theory.The stress path of the soil particle and field movement are combined by the movement of the elastic-plastic boundary and then the PDEs are solved by the second-order Eulerian method.The accuracy of the new method is verified by comparison with various published studies.Then the boundary effect on stress paths and distribution are analysed and the non-self-similar phenomenon for finite soil mass is discussed in detail.It is found that for finite soil mass,the soil particles do not follow the same stress path any more and the cavity expands in a non-self-similar manner,which is the typical difference between cavity expansion in the finite and infinite soil mass.Finally,the drained solution for cavity expansion is applied to calibration chamber tests for CPT and the results indicated the present solution can describe in some degree the relationship between the cone tip resistance and the scale of the chamber.