Cavity unloading in brittle-plastic rock using the Mohr-Coulomb criterion 145 5.3.2 Cavity unloading in brittle-plastic rock using the Hoek-Brown criterion

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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. © 1998 John Wiley & Sons, Ltd.

Soil anchors are commonly used as foundation systems for structures requiring uplift resistance, such as transmission towers, or for structures requiring lateral resistance, such as sheet pile walls. To date, the design of these anchors has been largely based on empiricism. This paper applies numerical limit analysis to rigorously evaluate the stability of vertical and horizontal strip anchors in undrained clay. Rigorous bounds on the ultimate pull-out capacity are obtained by using two numerical procedures that are based on ®nite element formulations of the upper and lower bound theorems of limit analysis. These formulations follow standard procedure by assuming a rigid perfectly plastic clay model with a Tresca yield criterion, and generate large linear programming problems. By obtaining both upper and lower bound estimates of the pull-out capacity, the true pullout resistance can be bracketed from above and below. Results are presented in the familiar form of break-out factors based on various soil strength pro®les and geometries, and are compared with existing numerical and empirical solutions.

In this paper, some practical aspects of the ®nite element implementation of critical state models are discussed. Improved automatic algorithms for stress integration and load and time stepping are presented. The implementation of two generalized critical state soil models, with one described ®rst in this paper and the other recently published elsewhere, is discussed. The robustness and correctness of the proposed numerical algorithms are illustrated through both coupled and uncoupled analyses of geotechnical problems.