Calibration of Constitutive Models

Numerous constitutive models have been developed over the past forty years for modeling the stress-strain behavior of soils. These models are to be used with finite element and/or finite difference calculations of soil structures and soil/structure interaction problems under axisymmetric, plane strain, and/or general three-dimensional conditions. Simple as well as advanced models have been formulated on the basis of principles of mechanics, some more rigorous than others, some based on experimental evidence, and others based on theoretical principles. The capabilities and the shortcomings of these models are not always easy to ascertain, and the requirements for determination of parameters are not uniform. It is consequently difficult to determine which model to select for a particular task. Presented here is an overview of the principles, main characteristic features, and components of existing, widely available constitutive models. Their requirements in terms of experimental data for calibration are presented, and their capabilities are reviewed.

Finite element analysis of geotechnical materials is contingent on the proper constitutive model to represent the soil. These models often range in complexity from simple linear elastic to complex hardening and consolidation behavior. Even though many models have been derived, there is little guidance for the selection of input parameters for such models. In this study, four constitutive models are considered the Mohr-Coulomb and Hardening Soil from Plaxis and the Drucker-Prager and Sandler Dimaggio from PlasFEM. A series of six consolidated drained triaxial tests are used to verify constitutive model parameters for sand. The laboratory derived strength and stiffness parameters, the results of a parametric study, and limited guidance from the literature are assembled to provide a best estimate of inputs for four constitutive models. The of plots of the finite element simulations using each of the four models versus the actual triaxial tests show good agreement, respective to the model behavior. A summary table of the parameters details the results.

Submarine landslides pose considerable hazards to coastal communities and offshore structures. The difficulty and cost of obtaining undisturbed samples of offshore soils for determining material properties required for slope stability analyses contribute to the complexity of the problem. There are significant advantages in using a simplified model for the seismic response of submarine slopes, compatible with the limited amount of information that can be realistically gathered, but still able to capture the key elements of clay behavior. This paper illustrates the process of parameter determination and calibration of the SIMPLE DSS model, developed for the study of seismic triggering of submarine slope instabilities. The selection of parameters and predictions of monotonic and cyclic simple shear response are carried out for Boston Blue Clay, a marine clay extensively studied and with a large experimental database available in the literature. The results show that the simplified model is able to reproduce the important trends in the response of the soil, especially in accounting for the effect of the slope.

This paper presents a thorough calibration study for a recently developed constitutive model for coarse granular materials. The calibration was performed using true-triaxial experimental results for pea-gravels. Soil responses under various and complex stress paths were considered to verify the capability of the model to describe general constitutive behavior of soils. Stress paths used in the calibration process include: (1) monotonic stress paths in a deviatoric plane, (2) monotonic conventional triaxial compression (CTC) stress path, (3) cyclic simple shear (SS) stress path, and (3) circular cyclic stress path on a deviatoric plane with varying Lode angle and constant mean stress. Comparisons of the model simulations to the experimental results show that the model is capable of capturing the behavior of pea-gravel under monotonic and cyclic loading conditions.

Dilatancy is an essential sand response. Experimental and microstructural investigations have shown that whether a sand is in a dilative or contractive state depends on its density, confining pressure, stress ratio, as well as the soil fabric. In the past decade, a number of researchers have tackled the dilatancy issue from the perspective of constitutive modeling. It has been shown by Manzari and Dafalias and Li and Dafalias that, in order to model sand behavior over a full range of density states, additional dependence of dilatancy on the internal state of the sand is needed, and the material state must be described in reference to the critical/steady state line in the e-p-η space. This concept is referred to as the state-dependent dilatancy. In addition, due mainly to the process of deposition under earth gravity, the behavior of sand is very likely to be inherently anisotropic, meaning the stress-strain-strength relations for the same sand may vary as the stress tensor rotates in reference to the orientation of soil fabric. Experimental investigations in the past 15 years on flow liquefaction of earth structures have revealed that the influence of inherent fabric anisotropy on the residual strength of a granular soil is so drastic that the inherent anisotropy can no longer be ignored. On the basis of these observations, Li & Dafalias proposed an anisotropic sand model aimed at describing these features. This paper briefly reviews the issue of sand dilatancy and the impact of fabric anisotropy, and the model developed by Li and Dafalias. The focus will be placed on the calibration and determination of several important material constants, including the critical state parameters and the fabric anisotropic index.

A simplified constitutive model based on a multi-plane concept is presented for monotonic and cyclic soil response including liquefaction. The proposed model uses only two mobilized planes; a maximum shear stress plane, and a horizontal plane. The application of more than one mobilized plane can intrinsically handle anisotropy as well as rotation of principal planes without additional parameters. The soil skeleton behaviour observed in cyclic drained simple shear tests, including compaction during unloading and dilation at large strain is considered in the model. Undrained and partially drained monotonic and cyclic response can be predicted by considering the volumetric constraint of the water on the drained or skeleton behaviour. The rotation effect associated with simple shear loading from a K₀ consolidated state is incorporated in the proposed model. This constitutive model is incorporated into the dynamic coupled stress-flow finite difference program FLAC (Fast Lagrangian Analysis of Continua). The model is calibrated by capturing the undrained cyclic behaviour of Fraser River sand, and can be used in the design of liquefaction remediation measures involving densification and drainage.

A single hardening model (proposed by Lade and co-workers) is calibrated using 12 model parameters, which can be determined from one isotropic consolidation test (with unloading and reloading), and three triaxial shear tests; however, the process of calibrating these parameters is relatively complex. In this paper, the authors have calibrated this model for the purpose of predicting the experimentally observed 3-D mechanical behavior of Kaolin clay through advanced laboratory testing. During this calibration process, several interesting issues were observed for the specific Kaolin clay used in the study. These issues are discussed in light of the concepts behind relevant calibration parameters and their significance to the model predictions. Based on the definition of plastic work, a modified approach for calibrating the work hardening parameters is presented and shows some promise. Various aspects of this model are also presented in the context of predicting the mechanical behavior of soils including the sensitivity of the model parameters over the prediction of the complex mechanical behavior under generalized state of stress/strain.

A material model for soft, wet soil was generated to simulate the deformation behavior of thawing soil under vehicle loading on paved and unpaved roads. The soil modeled, a frost-susceptible fine sand called Lebanon Sand, was subjected to a full suite of saturated and unsaturated triaxial testing duplicating conditions experienced during large-scale freeze—thaw testing. Material parameters were generated for a capped Drucker—Prager plasticity model with hardening. These were calibrated in triaxial test simulations using the commercial finite element code ABAQUS. The material model was then implemented in several three-dimensional finite element simulations for validation and robustness.