Constitutive modeling of anisotropic behavior in geomaterials: The role of fabric

(a) A general approach is proposed to characterize the strength anisotropy of geomaterials. A salient ingredient of the method involves the introduction of the degree of cross anisotropy and an anisotropic variable, defined by the joint invariant of the deviatoric stress tensor and the deviatoric fabric tensor, into the frictional characteristic of a popular isotropic criterion. The Lade's failure criterion and a generalized nonlinear failure criterion are employed as demonstrative examples to show the feature of this method.;(b) A novel constitutive model is proposed to describe the effect of bonding and fabric anisotropy on the behavior of artificially cemented sand. The triaxial tensile strength and a fabric tensor have been chosen as macroscopic representation of the inter-particle bonding and fabric in cemented sand respectively. The yield function adopted in the model is an extension of the generalized anisotropic failure criterion. A de-bonding law is proposed by assuming the de-bonding process is driven by the development of plastic deformation. The model is employed to predict the behavior of cemented Ottawa sand and multiple-sieving-pluviated Toyoura sand, and the predictions compare well with the experimental data.;(c) By assuming that the total strength of composite is a combination of the shear resistance of the host soil and the reinforcement of fibers, a general anisotropic failure criterion is proposed with special emphasis on the effect of anisotropically distributed fibers. An anisotropic variable, defined by the joint invariant of the deviatoric stress tensor and a deviatoric fiber distribution tensor, is introduced to quantify the fiber orientation with respect to the strain rate/stress direction at failure. With further consideration of fiber concentration and aspect ratio, the proposed criterion is applied to predict the failure of fiber-reinforced sand under conventional triaxial compression/extension tests, for both isotropically and anisotropically distributed fiber cases. The predictions are in good agreement with test results available in the literature.;(d) A three-dimensional anisotropic model for granular material is proposed based on the anisotropic critical state theory. The model features an explicit expression for the yield function in terms of the invariants and joint invariants of the normalized deviatoric stress ratio tensor and the deviatoric fabric tensor. A void-based fabric tensor is employed to characterize the anisotropic internal structure in the material. Upon plastic loading, the material fabric is assumed to evolve continuously with its principal direction tending steadily towards the loading direction. A novel fabric evolution law is proposed to describe this behavior. With these considerations, a non-coaxial flow rule is naturally obtained. The model is shown to be capable of characterizing the complex anisotropic behavior of granular materials under monotonic loading conditions, and meanwhile retains a relatively simple formulation for numerical implementation.;(e) Complex and highly nonlinear models such as the one proposed above need robust and efficient stress integration method for their finite element implement. An explicit Euler method with automatic substepping and error control is employed to implement the model proposed in Part (d) into ABAQUS via its User Material (UMAT) interface. The implemented model is further used to simulate the formation of shear band in sand under both drained and undrained plane-strain compressions. The interplay between the initiation and development of shear band and the evolution of fabric is highlighted in the study.