Analytical Analysis Of Two-dimensional Plane Strain Consolidation Characteristics For Unsaturated Soil

Consolidation theory is a classical project in the field of geotechnical engineering.Since Terzaghi proposed the one-dimensional consolidation theory for saturated soils,consolidation theory has been developed rapidly and many impact consolidation models have been proposed.As the soil above the water table line is unsaturated,the study of consolidation theory for unsaturated soils is,therefore,significant to instructing engineering construction in unsaturated soil areas.In the past 40 years,a series of investigations based on the theoretical framework of consolidation for unsaturated soil proposed by Fredlund and Dakshanamurthy et al.have been performed by many scholars and have made great progress.However,the established methods are too complicated in solving consolidation models containing non-ideal permeability drainage boundaries.Besides,the existing consolidation models are inadequate,and there is an urgent need to develop new consolidation models to evaluate the consolidation properties of unsaturated soils.Based on the above analysis,the main contents and conclusions of this thesis are as follows.(1)The eigenfunction method,Laplace transform,and its inverse transform technique are used to solve the two-dimensional plane strain consolidation model for unsaturated soil considering the lateral semi-permeability boundary.The correctness of the analytical solution is then verified through COMSOL Multiphysics software.Afterward,the analytical solution of this thesis is compared with the existing semi-analytical solution.The results show that the analytical solution proposed in this thesis is simpler and easier to be used by engineers.In addition,the consolidation characteristics of unsaturated soil are not only affected by the semi-permeable parameter,but also by the soil size.(2)A two-dimensional plane strain consolidation model for unsaturated soils under exponential time-dependent loading considering lateral and vertical semi-permeable drainage boundaries is proposed.The analytical solution of the model is firstly derived by using the eigenfunction method and Laplace transform and its inversion technique,and the correctness of the analytical solution is then verified by both degradation verification and finite element simulation.Based on the obtained solutions,the effects of time-dependent loading on consolidation behavior and the variation of consolidation properties of unsaturated soils along the x-and z-directions are investigated.The results show that the parameters controlling the amplitude and loading rate of time-dependent loading have significant influences on the consolidation properties of unsaturated soil.(3)To consider the effect of self-weight stress on consolidation characteristics,a two-dimensional plane strain consolidation model for unsaturated soil with horizontal and vertical semi-permeable drainage boundaries considering time-dependent loading and soil self-weight stress is further proposed.The solution of the consolidation model under four types of time-dependent loading is derived by using the eigenfunction method and Laplace transform and its inversion technique.The correctness of the obtained solution is verified by employing degradation verification and finite element simulation verification.The results show that the self-weight stress of the soil has a great influence on the consolidation behavior of unsaturated soil.The greater the self-weight stress of the soil,the larger the values of the initial excess pore-water pressure and excess pore-air pressure generated in the unsaturated soil,and the greater the final settlement value.Meanwhile,the ratio of k_a/k_walso affects the consolidation behavior of the unsaturated soil.The larger the ratio of k_a/k_w,the earlier the soil deforms,regardless of whether the self-weight stress is considered or not.(4)The governing equations for the 2D plane strain electro-osmosis-enhanced preloading consolidation model of unsaturated soil are derived.The auxiliary variable method,eigenfunction method,and Laplace transform technique are used to solve the PDEs.The correctness of the analytical solution is then verified by finite element numerical simulation.The results show that the dissipation pattern of excess pore-water pressure can be divided into two different stages under the act of the external electric field.Besides,the larger the value of k_e/k_w,the larger the value of negative excess pore-water pressure generated in the soil,but the effect on the excess pore-air pressure is very limited.What’s more,the larger the value of k_x/k_y,the faster the dissipation rate of excess pore pressures,and the faster the consolidation rate of the unsaturated soil.(5)A two-dimensional plane strain electro-osmosis-enhanced preloading consolidation model for unsaturated soils considering the nonlinear distribution of voltage and vertical semi-permeability boundary conditions is proposed.The model is solved using the eigenfunction method and Laplace transform technique.The correctness of the analytical solution is then verified by finite element numerical simulation.The results show that the excess pore-water pressure is slightly smaller during the"platform period”,and the final negative excess pore-water pressure is larger for the same k_a/k_w value when considering the nonlinear distributed voltage assumption.Besides,the dissipation pattern of excess pore-air pressure is almost independent of the value of k_e/k_w,while the average dissipation rate of excess pore-water pressure and the final negative excess pore-water pressure is smaller for the same k_e/k_w value when considering the nonlinear distributed voltage assumption.What’s more,the dissipation model of excess pore-water pressure for the same k_x/k_y value can be very different at the later stage of consolidation,and the final negative excess pore-water pressure value is smaller when considering the nonlinear distributed voltage assumption.