Realization of uniform deformation of soil specimen under undrained plane strain condition based on soil–water coupled finite deformation analysis considering inertia forces

Based on a soil–water coupled finite deformation analysis, theoretical considerations and numerical calculations were carried out under the undrained plane strain condition in order to reproduce a uniform deformation field. Rather than the “quasi-static” equation of motion, which does not include inertia forces, a dynamic equation of motion which includes inertia forces was used. At first, a theoretical consideration was carried out to realize uniform deformation for a saturated soil that satisfied the element-wise undrained/constant-volume condition. This presents an “infinitely slow loading” case without ignoring the inertia term based on the u–p formulation. In other words, it can be seen that under general slow loading that is not infinitely slow, a gradient in the pore water pressure will always be produced, resulting in the migration of pore water and loss/collapse of uniformity. This first conclusion is useful for verifying numerical analysis code made in the finite deformation regime. Next, the uniform deformation of a plane strain rectangular soil specimen was measured under constant cell pressure and undrained boundary conditions using a dynamic soil–water coupled analysis in which the SYS Cam-clay model was employed as the elasto-plastic constitutive model for the soil skeleton. In addition, the effects of the loading rates as well as loading applications, with/without inertia forces, on the loss of uniformity in deformation were shown to have a significant influence on the inertia term even though the loss itself was extremely small.     

Development and verification of a soil–water coupled finite deformation analysis based on u–w–p formulation with fluid convective nonlinearity

Most soil–water coupled analyses of saturated soil are based on the u–p formulation, where a set of equations is reduced by assuming that the acceleration of the fluid phase relative to that of the solid phase is less than that of the solid phase. Therefore, this analysis cannot be used for a coupled analysis with dynamic water flow in highly permeable soil. This study aims to present a soil–water coupled finite deformation analysis method based on full formulation, or u–w–p formulation. This method differs from conventional methods in the following ways: (1) the governing equations explicitly include the equation of motion for the fluid phase, (2) a relative convective term is used to describe a change in the relative configuration between the two phases, and (3) the moving/inclined discharge boundary is directly implemented to the discretized governing equations. Herein, one/two dimensional seepage and plane-strain deformation analysis results are reported. In the seepage analysis, accelerating permeation of pore water is obtained and the undrained constraint condition is verified. In the deformation analysis, dynamic migration in a high permeable soil specimen, i.e., wave propagation and rotational flow of pore water, is observed.     

A three-dimensional soil–water coupled FE analysis of hollow cylinder test concerning non-uniform deformation

The hollow cylinder shear test is somewhat controversial due to its non-uniform stresses and strains, and has been analyzed by simple theoretical methods and two-dimensional FE calculations. In this paper, the hollow cylinder test under strain control was carried out numerically by treating the specimen as a three-dimensional initial-boundary value problem considering the inertial forces. At first, besides the known nonuniform strain, the non-uniformities of excess pore water pressure and overconsolidation ratio have been shown to benefit from a soil–water coupled analysis that employs the SYS Cam-clay model. Then, the influence of the specimen geometries, including wall thicknesses, heights and outer diameters on the non-uniformity was investigated sequentially. A new method for evaluating non-uniformity was proposed, which is suitable for the three-dimensional analysis. The response under a uniform deformation field, which is indicated by “the perfect path”, was presented to draw a comparison with the apparent behaviors, with non-uniformities taken into consideration. It should be noted that there is a critical height to prevent failure at the specimen ends according to the apparent behavior. Finally, the torque-controlled experiment indicated that 4 ribs could not transfer the torque reliably while 6 or 8 ribs were feasible.     

Numerical simulation based heuristic investigation of inertia-induced phenomena and theoretical solution based verification by the damped wave equation for the dynamic deformation of saturated soil based on the u–w–p governing equation

The theoretical and numerical solutions for the one-dimensional dynamic deformation of saturated ground were obtained using the u–w–p governing equation. The numerical analysis was performed based on the finite element method, and the occurrence of superficially peculiar phenomena, i.e., S-shaped settlement–time relation, non-harmonic oscillation in the settlement/pressure–time relation in highly permeable soil, and inconsistency in the vertical load and immediate pressure was identified heuristically. The theoretical solution of the damped wave equation was derived from the original governing equation expressed as the superposition of several modes with different eigenvalues, and this solution could successfully explain the phenomena observed heuristically. It was noted that the phenomena were induced by the presence of inertia, because the static solution and u–p analysis did not exhibit such phenomena. The verification of the analysis was conducted owing to the correspondence of the theoretical solutions of the damped wave equation and the u–w–p analysis results.     

Effects of principal stress rotation on stress–strain behaviors of saturated clay under traffic–load–induced stress path

A series of cyclic torsional shear tests using hollow cylinder apparatus (HCA) were performed to investigate the effect of principal stress rotation (PSR) on the stress–strain behaviors of saturated soft clay. The traffic–load–induced shear stress path was used in the cyclic test and the investigation mainly concerned the influence of PSR on the shear stiffness and non-coaxiality. It indicated that the effects of PSR substantially depends on the magnitude of deviatoric stress (q?=?{[(σ₁???σ₂)²?+?(σ₂???σ₃)²?+?(σ₁???σ₃)²]/2}^1/2) as well as the intermediate principal stress ratio (b?=?(σ₂???σ₃)/(σ₁???σ₃)). At low deviatoric stress, the trajectory envelope of deviatoric strain path translates with a nearly constant size, showing constant shear stiffness and strong non-coaxiality. However, at high deviatoric stress, the trajectory envelope of deviatoric strain rapidly expands towards instability, showing degenerating shear stiffness and weak non-coaxiality. Moreover, the excess pore water pressure increases and the shear stiffness decreases more rapidly as b value increases. The results can provide an experimental basis for constitutive modelling of clays under traffic–induced loadings.     

Mixture design concept and mechanical characteristics of PS ash–cement-treated clay based on the water absorption and retention performance of PS ash

In an attempt to reduce environmental impact, paper sludge ash (PS ash) has recently been studied for its complementary reuse with cement for soil stabilization. In order to establish the optimal mixture design for combining PS ash and cement in soils, a detailed investigation into the stabilizing mechanism is required. To assess the combined effects of PS ash and cement on the strength development of stabilized clay soil, referred to as PS ash–cement-treated clay, a new critical parameter, the unabsorbed and unretained clay-water/cement ratio W*/C, was proposed. To determine W*/C, a new testing method for evaluating the water absorption and retention performance of PS ash was developed. It was revealed that the water absorption and retention rate W_ab of PS ash increased with curing time. Unconfined compression tests conducted on the PS ash–cement-treated clay with various water-cement–PS ash mixture proportions and different curing times affirmed that the strength development was fundamentally governed by the parameter W*/C. This suggests that the water absorption and retention rate W_ab obtained by the developed method is an essential material parameter in the mixture design for the PS ash–cement-treated clay. It was also found that the effect of the hybrid treatment method, which uses both cement and PS ash, was better than that of the method which uses cement alone, particularly under high W*/C conditions. This indicates that the water absorption and retention performance of PS ash can be fully utilized when the mixture has sufficient unabsorbed and unretained water for cement hydration.