Daichao Sheng

Refined explicit integration of elastoplastic models with automatic error control

Effective explicit algorithms for integrating complex elastoplastic constitutive models, such as those belonging to the Cam clay family, are described. These automatically divide the applied strain increment into subincrements using an estimate of the local error and attempt to control the global integration error in the stresses. For a given scheme, the number of substeps used is a function of the error tolerance specified, the magnitude of the imposed strain increment, and the non‐linearity of the constitutive relations. The algorithms build on the work of Sloan in 1987 but include a number of important enhancements. The steps required to implement the integration schemes are described in detail and results are presented for a rigid footing resting on a layer of Tresca, Mohr‐Coulomb, modified Cam clay and generalised Cam clay soil. Explicit methods with automatic substepping and error control are shown to be reliable and efficient for these models. Moreover, for a given load path, they are able to control the global integration error in the stresses to lie near a specified tolerance. The methods described can be used for exceedingly complex constitutive laws, including those with a non‐linear elastic response inside the yield surface. This is because most of the code required to program them is independent of the precise form of the stress‐strain relations. In contrast, most of the implicit methods, such as the backward Euler return scheme, are difficult to implement for all but the simplest soil models.

EFFECTS OF END RESTRAINT AND STRAIN RATE IN TRIAXIAL TESTS

Abstract Inhomogeneities caused by end restraint and insufficient drainage during conventional compression triaxial tests are analysed by a numerical method. A finite element model is presented to simulate the testing procedure. The soil-platen interaction is represented by contact elements which allow frictional sliding between contacting nodes. The soil mass is represented by the modified Cam clay model. Coupled hydro-mechanical analyses are carried out in order to simulate both drained and undrained tests. The distributions of stresses and strains in the specimen for different end conditions are compared with the ideal case where no end restraint exists, in order to find representative measuring positions in the sample. Different rates of axial strain are tested in order to study the inhomogeneities caused by insufficient drainage during drained tests. Simulated results show that both end restraint and insufficient drainage can cause the barrel-shape deformation of the specimen. Stress-strain and strength properties based on global measurements are not a good representation of the true material behaviour of one single soil element at constitutive level.

Load stepping schemes for critical state models

This paper investigates the performance of various load-stepping schemes for finite element analysis with critical state soil models. The accuracy of simple incremental schemes is found to be strongly influenced by the load increment size, the type of flow rule, and the overconsolidation ratio. Similarly, these factors are shown to have a pronounced effect on the efficiency and stability of some classical iterative schemes. Unless they are performed with small load steps, critical state analyses with fixed increment sizes frequently exhibit non-convergent behaviour or lead to inaccurate solutions. The automatic incrementation schemes developed by Abbo and Sloan (International Journal for Numerical Methods in Engineering 1996; 39:1737–1759; Proceedings of 5th International Conference, Owen DRJ, Onate E, Hinton E. International Center for Numerical Methods in Engineering, Barcelona, 1997; 1:325–333), which are based on standard methods for integrating systems of ordinary differential equations, are shown to be efficient, accurate and robust solution techniques for a wide variety of critical state problems. Copyright

An Elastoplastic Model for Granular Materials Exhibiting Particle Crushing

A practical elastoplastic constitutive model for granular materials is presented. And the model is suitable for description of the material behaviour for a wide range of stresses, including those sufficient to cause particle crushing. With a limited number of model parameters, the model can predict the confining-pressure dependent stress-strain relation and shear strength of granular materials in three-dimensional stresses, especially of variation of shear strength and dilatancy characteristics due to particle crushing under high confining pressure. The model parameters, which have clear physical meanings, can be determined from the results of isotropic compression test and conventional triaxial compression tests. The model performance is demonstrated for triaxial compression tests of a sand for a wide range of the confining-pressure from 0.2MPa to 8.0MPa.

Analytic solutions to the advective contaminant transport equation with non‐linear sorption

This paper considers advective transport of a soluble contaminant through saturated soil with non-linear sorption of the contaminant onto a stationary porous media. The non-linear sorption isotherms considered in the transport analysis are the Langmuir and Freundlich sorption isotherms. A special case of the Freundlich sorption isotherm is the linear sorption isotherm, and it is shown that in this case transport through a homogeneous soil results in the initial concentration profile simply being translated in the direction of the groundwater flow. However, when the sorption isotherm is non-linear the initial concentration profile distorts as it is translated with the groundwater flow, leading to the development of concentration shock fronts and rarefactions. Analytic solutions to the non-linear first-order hyperbolic equations are developed for a number of contaminant transport problems of practical significance. It is shown that in the case of the Langmuir sorption isotherms, shock fronts develop at the leading edge of the concentration profile while for the Freundlich sorption isotherm shock fronts may develop at either the leading or trailing edge of the concentration profile. Copyright

The kinetics of fluoride sorption by zeolite: Effects of cadmium, barium and manganese

Industrial wastewaters often consist of a complex chemical cocktail with treatment of target contaminants complicated by adverse chemical reactions. The impact of metal ions (Cd(2+), Ba(2+) and Mn(2+)) on the kinetics of fluoride removal from solution by natural zeolite was investigated. In order to better understand the kinetics, the pseudo-second order (PSO), Hill (Hill 4 and Hill 5) and intra-particle diffusion (IPD) models were applied. Model fitting was compared using the Akaike Information Criterion (AIC) and the Schwarz Bayesian Information Criterion (BIC). The Hill models (Hill 4 and Hill 5) were found to be superior in describing the fluoride removal processes due to the sigmoidal nature of the kinetics. Results indicate that the presence of Mn (100 mg L(-1)) and Cd (100 mg L(-1)) respectively increases the rate of fluoride sorption by a factor of ~28.3 and ~10.9, the maximum sorption capacity is increased by ~2.2 and ~1.7. The presence of Ba (100 mg L(-1)) initially inhibited fluoride removal and very poor fits were obtained for all models. Fitting was best described with a biphasic sigmoidal model with the degree of inhibition decreasing with increasing temperature suggesting that at least two processes are involved with fluoride sorption onto natural zeolite in the presence of Ba.

A Micropenetrometer for Detecting Structural Strength Inside Soft Soils

A micropenetrometer is developed to measure structural strength inside soft soils. Different from the traditional detective technology for soil structure, the micropenetrometer is an intrusion technology to estimate the characteristics of soft soils. The work principle and main configuration of the micropenetrometer are introduced, followed by its calibration and some operation techniques. Finally, two application tests are carried out. Different soil textures such as sandy soil or clayey soil have different types of penetration curves. Through the end resistance variation, detailed description of the structural strength along penetration depth can be obtained. In addition, three-dimensional strength distribution on the vertical or transverse sections can be achieved from the penetration data evenly arranged on the grid nodes of the same surface through interpolation method. Such a technique is of significance for checking the effectiveness of soil improvement or monitoring the moisture movement in soil.

Effect of Density on the Soil-Water-Retention Behaviour of Compacted Soil

This paper presents a series of experimental results obtained from wetting and/or drying cyclic tests and constant suction triaxial tests on unsaturated compacted clay with different initial densities using two suction-controllable triaxial apparatus. The primary objective of this research is to investigate the influence of the soil density on the soil-water-retention behaviour. The initial density and initial degree of saturation were controlled by changing the compaction energy using clay powders with almost the same water content. The test results contain the water-retention curves and deformation behavior at different initial densities using different specimens and one specimen before and after collapse. The test data indicate that the measured water-retention curves vary with the current specimen density. A denser specimen results in a higher degree of saturation at the same imposed suction, which implies that the water-retention curve shifts to the right in the ln s-S r plane.

Interpretation of Cone Factor in Undrained Soils via Full-Penetration Finite-Element Analysis

AbstractThe cone penetration test is widely used to interpret the undrained shear strength of soil. The interpretation methods are commonly based on bearing capacity, cavity expansion, or strain-path methods. In this paper, the cone penetration test is analyzed using the large deformation FEM and contact mechanics. The full penetration process from the ground surface is modeled. The three-parameter Tresca model is used to represent the undrained soil behavior in a total stress analysis, to derive a cone factor equation for interpretation of the undrained shear strength. This equation is then compared with existing solutions in the literature as well as experimental data. The complexities that arise in more sophisticated soil models are elaborated in an effective stress analysis using the Modified Cam Clay model.

Finite element analysis for convective heat diffusion with phase change

Abstract Whereas phase-change problems associated with heat conduction have been well studied during the last three decades, very little attention has been paid to phase changes taking place in convective heat diffusion. Numerical methods dealing with conventional phase change problems do not directly work in cases where a fluid is concerned. In this paper, an enthalpy method is extended to solve phase-change problems associated with fluids. By using the concept enthalpy, the governing equations are first reformulated into a single quasi-linear partial differential equation that implicitly takes into account the condition of phase change. This equation together with appropriate initial and boundary conditions are then decomposed into two sets of equations respectively representing a convection and a diffusion problem. The decomposition is accomplished in such a way that no phase contradiction occurs between the two separate problems. The convection problem is solved by the method of step by step characteristics and the diffusion problem by a Galerkin finite element method. Numerical examples demonstrate that the numerical method produces reasonable results.