Constitutive Modelling – Development , Implementation , Evaluation , and Application

A comparative study of different constitutive models able to predict drained sand behaviour has been studied in this research. Comparisons have been made within the frame work defined by characteristics state of sand. These characteristics state include steady state line, quasi steady state line, upper reference line etc. The steady state line of Bagmati (Nepal) river sand has been determined from both the empirical relationship and from triaxial tests. Results from both methods show very good correlation. The steady state line has been used for constitutive modelling of drained behaviour of the sand. Existing Ishihara’s model has been modified to fit the drained triaxial results. The modelling results are quite satisfactory and match with experimental results. Besides using state index as a model parameter, the state parameter and state pressure index have been used in basic hyperbolic equation proposed by Ishihara to model the drained behaviour of sand. Prevost and Duncan models have also been studied in this research. It has been found that these models can simulate strain hardening behaviour more accurately. For strain softening behaviour, the performance of these models is not satisfactory. INTRODUCTION There are several constitutive models characterizing the behaviour of sands. Some of the models that are commonly available are Kondener Model, Duncan Model, Prevost Model and Ishihara Model. Most models use elastic and elastoplastic concept. With the development of computer, numerical techniques such as finite element method, finite difference methods etc. are gaining popularity. These numerical techniques are widely used in geotechnical engineering. In geomechanics, to determine the response of a geologic material to a given loading situation, a predictive capability is used. For predictive capability, a material model describing the material behaviour, a method for evaluating the model parameters inputs and a computational procedure for the application to a particular problem are required. The material model describes the material through the constitutive equations, which is generally in an increment form relating stresses and strains. Kondener (1963) has given the functional relationship between shear stress (τ) and shear strain (γ). This model is applicable to both sand and clay. This function is simple but is not able to model failure accurately (Pyke 1979). Further Prevost proposed the modified hyperbolic function with power terms. This function is shown to offer more versatility for modelling stress strain behaviour in both monotonic and cyclic loading conditions at both low and high strain levels. An elastoplastic deformation law for sands incorporating the state concept is formulated (Cubrinovski and Ishihara 1998). These fundamental concepts for characterization and modelling of sand behaviour are unified in order to build a rational sand model that enables integral modelling over a wide range of density and normal stress state. The characterization of sand behaviour is based on the state concept using state index (Is). A modified hyperbolic relation is used to establish a rational stress strain model that captures the dependence of sand behaviour on the relative initial e-p state. 1 Department of Civil and Environmental Engineering, Saitama University, Japan. 2 Geotechnical Engineer, Department of Civil Engineering, Pulchowk, Lalitpur, Nepal.