Poul V. Lade

Elasto-plastic stress-strain theory for cohesionless soil with curved yield surfaces

Abstract An elasto-plastic stress-strain theory for cohesionless soil with curved yield surfaces is developed on the basis of soil behavior observed in laboratory tests. This theory is applicable to general three-dimensional stress conditions, but the parameters required to characterize the soil behavior can be derived entirely from results of isotropic compression and conventional drained triaxial compression tests. The theory is shown to predict soil behavior under various loading conditions with good accuracy. Of special interest is its capability of predicting soil behavior under drained as well as undrained conditions over a range of confining pressures where the behavior changes from that typical of dense sand to that typical of loose sand. Work-hardening as well as work-softening is incorporated in the theory.

Effects of Non-Plastic Fines on Minimum and Maximum Void Ratios of Sand

The role of non-plastic fines content on minimum and maximum void ratios, compressibility, and static liquefaction potential of sand and the relationships between these quantities are not well understood. This paper presents a study of the effects of non-plastic fines on the extreme void ratios of sand. Included in this paper is a review of previous theoretical and experimental studies of minimum and maximum void ratios of single spherical grains, packings of spheres of several discrete sizes, as well as optimum grain-size ratios to produce maximum densities. A systematic experimental study of the variation of minimum and maximum void ratios with contents of fines for sands with smoothly varying particle size curves and a large variety of size distributions is performed. It is shown that the fines content plays an important role in determining the sand structure and the consequent minimum and maximum void ratios. It is indicated how the fines content and sand structure affects the compressibility and the static liquefaction potential of the sand.

Single hardening constitutive model for frictional materials: I. Plastic potential Function

Based on review and evaluation of a large number of test data, a general three-dimensional plastic potential function expressed in terms of stress invariants is proposed. Three parameter values are required in this function, but one is redundant with one of the failure surface parameters. The plastic potential surface resembles an asymmetric cigar in the principal stress space. It includes tensile behavior of materials with effective cohesion. Its capabilities are examined by comparisons with experimental data from two-and three-dimensional tests on different frictional materials, (sand, painted rock material, basalt, Edgar kaolinite clay, plain concrete and steel fibre reinforced concrete). For part 2 of this article see IRRD 818226, and for part 3 see IRRD 818227.

Single hardening constitutive model for frictional materials II. Yield critirion and plastic work contours

Abstract A review of numerous experimental data sets for frictional materials has led to a reformulation of the condition for plastic yielding in such materials. A yield function is proposed such that yield surfaces are equivalent to plastic work contours. Two parameters are required in this function. The yield surface resembles an asymmetric tear drop in the principal stress space. It includes tensile behavior of materials with effective cohesion. Work hardening and softening behavior can be simulated through the formulation of plasticity proposed herein. The capabilities of this mathematically consistent formulation are examined by comparisons with experimental data from two- and three-dimensional tests on different frictional materials.

Modelling rock strength in three dimensions

Abstract A general, three-dimensional failure criterion for rock is proposed. This criterion is formulated in terms of the first and third stress invariants of the stress tensor, and it involves only three independent material parameters. Although these parameters interact with one another, each parameter corresponds to one of the three failure characteristics of rock behaviour. These material parameters may be determined from simple tests such as uniaxial compression and triaxial compression tests. For the purpose of including reasonable values of tensile strengths in the failure criterion, it may be advantageous to include the uniaxial tensile strength in the parameter determination. A simple expression for evaluation of the uniaxial tensile strength on the basis of the uniaxial compressive strength is given. Thirty-six sets of good quality data for different types of rock have been included in this study, and comparisons between the proposed failure criterion and the experimental data are made in triaxial, biaxial and octahedral planes. The ability of this criterion to capture the characteristics of failure in rock appears to be quite good with accuracies within the range of the natural scatter of the test data.

Single hardening constitutive model for frictional materials III. Comparisons with experimental data

Abstract A unified constitutive model for the behavior of frictional materials is described. The model is based on concepts from elasticity and plasticity theories. In addition to Hookes law for the elastic behavior, the framework for the plastic behavior consists of a failure criterion, a nonassociated flow rule, a yield criterion that describes contours of equal plastic work, and a work-hardening/softening law. The functions that describe these components are all expressed in terms of stress invariants. The model incorporates twelve parameters which can all be determined from simple experiments such as isotropic compression and conventional triaxial compression tests. Validation of the model is achieved by comparison of predicted and measured stress-strain curves for various two- and three-dimensional stress-paths obtained for different types of frictional materials.

SINGLE HARDENING CONSTITUTIVE MODEL FOR SOIL, ROCK AND CONCRETE

Abstract A constitutive model with a single yield surface has been developed for the behavior of frictional materials such as clay, sand, concrete, and rock. The model is based on concepts of elasticity and plasticity theories. In addition to Hookes law for the elastic behavior, the framework for the plastic behavior consists of a failure criterion, a nonassociated flow rule, a single yield criterion that describes contours of equal plastic work, and a work-hardening/softening law. The functions that describe these components are all expressed in terms of stress invariants. The model incorporates twelve parameters for frictional materials with effective cohesion such as concrete and rock. These parameters can all be determined from simple experiments such as isotropic compression and triaxial compression tests. Examples of predictions of the behavior of sand in undrained triaxial compression and of concrete under three-dimensional loading conditions are presented.

Instability, shear banding, and failure in granular materials

Two modes of decrease in load bearing capacity of granular materials are discussed in view of experimental results. Both relate to the fact that frictional materials exhibit nonassociated plastic flow and they undergo considerable volume changes, either contraction or dilation. One mode consists of the instability that may occur in certain regions of stress space and potentially result in liquefaction of the granular material. It is the fact that loading of contracting soil (resulting in large plastic strains) can occur under decreasing stresses that may lead to unstable behavior under undrained conditions. As long as the soil remains drained, it will remain stable in the region of potential instability. The other mode is initiated by localization of plastic strains and subsequent development of shear bands, which in granular materials is followed by a decrease in load bearing capacity. These two modes are mutually exclusive and they occur for different loading and material conditions as discussed here on the basis of experimental observations.

Strain Rate, Creep, and Stress Drop-Creep Experiments on Crushed Coral Sand

The part of sand behavior that is affected by time, such as creep, relaxation, and loading rate effects are not similar to those observed for clay. To throw more light on the time effects in sand, many series of drained triaxial compression experiments have been performed on crushed coral sand. These tests were all performed with a constant effective confining pressure of 200 kPa. The test series included experiments with specimens loaded at five different strain rates with a 256-fold ratio between the extreme rates, tests with sudden changes in strain rate from slow to fast and vice versa, and tests in which axial and volumetric creep strains were observed at stress differences of 500, 700, and 900 kPa. Creep creates structuration and this has to be overcome to produce further plastic straining. Experiments were also performed in which the stress difference was dropped quickly from three different values of 500, 700, and 900 kPa followed by creep. In these stress drop-creep tests five different magnitudes of stress drops were employed: 0, 100, 200, 300, and 400 kPa. The results involving conventional creep effects and stress drop-creep effects are presented and analyzed.

ANISOTROPY OF NORMALLY CONSOLIDATED SAN FRANCISCO BAY MUD

Consolidated-undrained tests were performed on intact specimens of San Francisco Bay mud to study the anisotropic behavior of a normally consolidated clay. Large cylindrical block samples were obtained from an excavation in reclaimed tidelands south of the San Francisco International Airport. Evidence of soil fabric and its relation to the stratigraphy of the area were studied in preparation for the investigation of anisotropy. Cubical specimens were trimmed from the block samples and tested in triaxial compression with vertical and horizontal material axes. Consolidation characteristics, as well as stress-strain, pore pressure, and strength relations, were obtained along with lateral strains in two perpendicular directions. The experimental results were carefully evaluated and showed that the clay behaved as an orthotropic material, but for practical purposes could be characterized as being cross-anisotropic. The cross-anisotropic, elastic parameters were determined and related to the initial inclinations of the effective stress paths for vertical and horizontal specimens.