Hai-Sui Yu

Cavity expansion methods in geomechanics

Foreword. Preface. 1. Introduction. Part I: Fundamental Solutions. 2. Elastic Solutions. 3. Elastic-Perfectly Plastic Solutions. 4. Critical State Solutions. 5. Further Elastoplastic Solutions. 6. Time-Dependent Solutions. 7. Finite Elements Solutions. Part II: Geotechnical Applications. 8. In-Situ Soil Testing. 9. Pile Foundations and Earth Anchors. 10. Underground Excavations and Tunnelling. 11. Wellbore Instability. Index.

CASM: a unified state parameter model for clay and sand

The purpose of this paper is to present a simple, unified critical state constitutive model for both clay and sand. The model, called CASM (Clay And Sand Model), is formulated in terms of the state parameter that is defined as the vertical distance between current state (v, p′) and the critical state line in v–ln p′ space. The paper first shows that the standard Cam-clay models (i.e. the original and modified Cam-clay models) can be reformulated in terms of the state parameter. Although the standard Cam-clay models prove to be successful in modelling normally consolidated clays, it is well known that they cannot predict many important features of the behavior of sands and overconsolidated clays. By adopting a general stress ratio-state parameter relation to describe the state boundary surface of soils, it is shown that a simple, unified constitutive model (CASM) can be developed for both clay and sand. It is also demonstrated that the standard Cam-clay yield surfaces can be either recovered or approximated as special cases of the yield locus assumed in CASM. The main feature of the proposed model is that a single set of yield and plastic potential functions has been used to model the behaviour of clay and sand under both drained and undrained loading conditions. In addition, it is shown that the behaviour of overconsolidated clays can also be satisfactorily modelled. Simplicity is a major advantage of the present state parameter model, as only two new material constants need to be introduced when compared with the standard Cam-clay models.

UNDRAINED CAVITY EXPANSIONS IN CRITICAL STATE SOILS

Boundary value problems for hardening/softening soils, such as Cam-Clay, usually require the extensive use of finite element methods. Here analytical and semi-analytical solutions for the undrained expansion of cylindrical and spherical cavities in critical state soils are presented. The strain is finite, the initial cavity radius is arbitrary and the procedure applicable to any isotropically hardening materials. In all cases only simple quadratures are involved, and in the case of the original Cam-Clay a complete analytical solution can be found. In addition to providing models of the behaviour of displacement piles and pressuremeters these results also provide valuable benchmark solutions for verifying various numerical methods.

Lower bound limit analysis of unreinforced masonry shear walls

Abstract This paper describes a new technique for computing the lower bound limit loads in unreinforced masonry shear walls under conditions of plane strain. From a macroscopic point of view, masonry displays similar behaviour to jointed rock or reinforced earth, which have already been successfully modelled using the lower bound theorem. The overall behaviour of the masonry shear wall is controlled by the mechanical properties of the intact unit (brick/block) and the discontinuities or joints, as well as the relative positions and orientation of the joint sets. As a result, masonry needs to be treated as an anisotropic, inhomogeneous material. In order to make use of the lower bound theorem of classical plasticity, two basic assumptions have to be made. Firstly, the material exhibits perfect plasticity, and obeys an associated flow rule without strain hardening or softening. Secondly, the body is assumed to undergo only small deformation at the limit load, and so the geometric description of the body at collapse remains unchanged. Both of these assumptions are reasonable in the case of unreinforced masonry shear walls. In the present paper, the yield surfaces of the intact brick units and of the head and bed joints are expressed separately. By using a Mohr–Coulomb approximation of the yield surfaces, the proposed numerical procedure computes a statically admissible stress field via linear programming and finite elements. The stress field is modelled using linear three-noded triangular elements and allowing statically admissible stress discontinuities at the edges of each triangle. By imposing equilibrium, yield criterion and stress boundary conditions, an expression of the collapse load is formed, which can be maximized subject to a large number of linear constraints on the nodal stresses. Because all the requirements are met for a statically admissible stress field, the solution obtained is a rigorous lower bound on the actual collapse load. The numerical solutions obtained from the lower bound formulation are compared with available experimental and finite element results from the literature. The lower bound approach developed in the present paper is shown to give good approximations to the ultimate collapse load for the two examples presented.

Plasticity solutions for soil behaviour around contracting cavities and tunnels

The action of tunnel excavation reduces the in-situ stresses along the excavated circumference and can therefore be simulated by unloading of cavities from the in-situ stress state. Increasing evidence suggests that soil behavior in the plane perpendicular to the tunnel axis can be modelled reasonably by a contracting cylindrical cavity, while movements ahead of an advancing tunnel heading can be better predicted by spherical cavity contraction theory. In the past, solutions for unloading of cavities from in-situ stresses in cohesive-frictional soils have mainly concentrated on the small strain, cylindrical cavity model. Large strain spherical cavity contraction solutions with a non-associated Mohr–Coulomb model do not seem to be widely available for tunnel applications. Also, cavity unloading solutions in undrained clays have been developed only in terms of total stresses with a linear elastic-perfectly plastic soil model. The total stress analyses do not account for the effects of strain hardening/softening, variable soil stiffness, and soil stress history (OCR). The effect of these simplifying assumptions on the predicted soil behavior around tunnels is not known. In this paper, analytical and semi-analytical solutions are presented for unloading of both cylindrical and spherical cavities from in-situ state of stresses under both drained and undrained conditions. The non-associated Mohr-Coulomb model and various critical state theories are used respectively to describe the drained and undrained stress-strain behaviors of the soils. The analytical solutions presented in this paper are developed in terms of large strain formulations. These solutions can be used to serve two main purposes: (1) to provide models for predicting soil behavior around tunnels; (2) to provide valuable benchmark solutions for verifying various numerical methods involving both Mohr–Coulomb and critical state plasticity models. Copyright

On a class of non-coaxial plasticity models for granular soils

The non-coaxiality of the directions of principal stresses and principal plastic strain rates in granular soils under stress rotations has long been observed and recognized in soil tests using both simple shear and hollow cylinder apparatuses. A few constitutive theories have also been proposed in the literature to account for the effect of stress rotations and the subsequent non-coaxial soil behaviour, particularly in the context of shear band analysis. However, the lack of corresponding general numerical methods makes it difficult to investigate the influence of non-coaxial stress–strain behaviour on the results of geotechnical boundary value problems. This paper presents a numerical evaluation of a class of non-coaxial, elastic–plastic models that are developed by combining the conventional plastic potential theory and the double shearing theory. The general non-coaxial constitutive theories are first formulated and then a finite element implementation of the theories is carried out. To evaluate the non-coaxial theories, the problem of simple shear of soils is chosen to investigate the predicted behaviour of soils under simple shear loading conditions where the axes of principal stresses rotate. In particular, the influence of initial stress states and the degree of non-coaxiality are examined. It is found that the numerical results predicted using the non-coaxial model are in general agreement with the experimental observations reported in the literature.

Noncoaxial Behavior of Sand under Various Stress Paths

AbstractIn this paper, the results of three series of drained tests carried out on sands using hollow cylinder apparatus are presented. The noncoaxiality, defined as the difference between the major principal stress direction and the corresponding principal strain increment direction, is investigated. In the first series of tests, the sand was isotropically consolidated before being sheared with the fixed principal stress direction. In the other two series of tests, the sand specimens were isotropically consolidated and then sheared by rotating the major principal stress axes while the deviator stress level was either fixed (pure stress rotation) or increased continuously (combined shear loading). The experimental results provide clear evidence for material noncoaxiality when the rotation of principal stress direction is involved. The results from these series of tests show that the degree of noncoaxiality depends on the level of deviatoric stress and the stress increment direction. It tends to decrease w...

Expansion of a thick cylinder of soils

Abstract This paper presents a unified large-strain analysis of the expansion of a thick cylinder of soil. The soil is modelled as an elastic-perfectly plastic material obeying the Mohr-Coulomb yield criterion. A non-associated plastic flow rule is used and therefore the dilatancy of the soil is fully taken into account. Closed form solutions are obtained for the stresses and the elastic-plastic deformations of arbitrary magnitude when a thick-walled cylinder of soil is subject to constant external pressure and monotonically increasing internal pressure. A rigorous small strain solution is also presented so that a direct comparison between the results of small strain and large strain analyses can be made. In addition to serving as a benchmark solution for verifying the performance of elastic-plastic finite elements, the analytical solution developed in this paper can also be used to assist the interpretation of calibration chamber tests.

Three-dimensional analytical solutions for shakedown of cohesive-frictional materials under moving surface loads

This paper develops analytical solutions for shakedown limits of a cohesive-frictional half-space under a three-dimensional moving surface load. Melans lower-bound shakedown theorem has been adopted as the theoretical basis for deriving shakedown limits. Rigorous lower-bound solutions are obtained for shakedown limits by establishing a self-equilibrated residual stress field that, together with the applied elastic stress fields, lies within the Mohr–Coulomb yield criterion throughout the half-space. By searching through the half-space, this study shows that the most critical location for satisfying the yield condition lies on the central plane. The analytical solutions derived in the paper can be used to benchmark numerical shakedown results, as well as to serve as a theoretical basis for the development of an analytical design method for pavements under moving traffic loads.

Finite element limit analysis of reinforced soils

Abstract Finite element formulations of the lower and upper bound theorems for a reinforced soil are described. The numerical methods are based on the idea that, from a macroscopic point of view, reinforced soil can be treated as a homogeneous material with anisotropic properties. In reality, reinforced soil is a composite material whose strength relies on the interaction of the fill and the reinforcement, with the latter being comprised of metal strips or geotextile. The overall behaviour of a reinforced soil is controlled by the mechanical properties of the soil and the reinforcement, as well as their relative proportions and geometrical arrangement. Several examples are given to illustrate the effectiveness of the proposed procedures for computing rigorous bound solutions for reinforced soil structures.