SUMMARYA granular material consists of an assemblage of particles with contacts newly formed or disappeared, changing the micromechanical structures during macroscopic deformation. These structures are idealized through a strain space multiple mechanism model as a twofold structure consisting of a multitude of virtual two-dimensional mechanisms, each of which consists of a multitude of virtual simple shear mechanisms of one-dimensional nature. In particular, a second-order fabric tensor describes direct macroscopic stressstrain relationship, and a fourth-order fabric tensor describes incremental relationship. In this framework of modeling, the mechanism of interlocking defined as the energy less component of macroscopic strain provides an appropriate bridge between micromechanical and macroscopic dilative component of dilatancy. Another bridge for contractive component of dilatancy is provided through an obvious hypothesis on micromechanical counterparts being associated with virtual simple shear strain. It is also postulated that the dilatancy along the stress path beyond a line slightly above the phase transformation line is only due to the mechanism of interlocking and increment in dilatancy due to this interlocking eventually vanishing for a large shear strain. These classic postulates form the basis for formulating the dilatancy in the strain space multiple mechanism model. The performance of the proposed model is demonstrated through simulation of undrained behavior of sand under monotonic and cyclic loading.

SUMMARYThis paper reviews fundamental behaviour of a strain space multiple mechanism model for granular materials. Although this model has previously been implemented in a finite element program and used in the analysis of numerous practical problems for evaluating seismic performance of geotechnical works, most of the application was limited to the two dimensional boundary value problems. This paper reviews the theoretical link between the micromechanical and macroscopic behaviour of granular materials and discusses the relationship between the two and three dimensional behaviour of the model. The strain space multiple mechanism model characterizes a twofold structure of an assemblage of particles: the first is a multitude of virtual two dimensional mechanisms, the second a multitude of virtual simple shear mechanisms of one dimensional nature. Due to the twofold structure, a yield criterion specified in the micromechanical level does not reproduce the same yield criterion at the macroscopic level. There is an effect of the intermediate principal stress. Based on this finding, the paper proposes a methodology to introduce various macroscopic yield criteria, including Tresca, von Mises, extended Tresca, DruckerPrager, Mohr-Coulomb, and extended Mohr-Coulomb criteria within the framework of the strain space multiple mechanism model. Performance of this model incorporating various yield criteria is demonstrated for monotonic and cyclic loading, under drained and undrained conditions.

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SUMMARYThe strain space multiple mechanism model idealizes the behavior of granular materials based on a multitude of virtual simple shear mechanisms oriented in arbitrary directions. Within this modeling framework, the virtual simple shear stress is defined as a quantity that depends on the contact distribution function as well as the normal and tangential components of inter-particle contact forces, which evolve independently during the loading process. In other terms, the virtual simple shear stress is an intermediate quantity in the upscaling process from the microscopic level (characterized by the contact distribution and inter-particle contact forces). The stress space fabric (i.e. the orientation distribution of the virtual simple shear stress) produces macroscopic stress through the tensorial average. Thus, the stress space fabric characterizes the fundamental and higher modes of anisotropy induced in granular materials. Comparing an induced fabric associated with the biaxial shear of plane granular assemblies obtained via a simulation using Discrete Element Method to the strain space multiple mechanism model suggests that the strain space multiple mechanism model has the capability to capture the essential features in the evolution of an induced fabric in granular materials.

SUMMARYThe strain space multiple mechanism model idealizes the behavior of granular materials on the basis of a multitude of virtual simple shear mechanisms oriented in arbitrary directions. Within this modeling framework, the virtual simple shear stress is defined as a quantity dependent on the contact distribution function as well as the normal and tangential components of interparticle contact forces, which evolve independently during the loading process. In other terms, the virtual simple shear stress is an intermediate quantity in the upscaling process from the microscopic level (characterized by contact distribution and interparticle contact forces) to the macroscopic stress. The stress space fabric produces macroscopic stress through the tensorial average. Thus, the stress space fabric characterizes the fundamental and higher modes of anisotropy induced in granular materials. Herein, the induced fabric is associated with monotonic and cyclic loadings, loading with the rotation of the principal stress, and general loading. Upon loading with the rotation of the principal stress axis, some of the virtual simple shear mechanisms undergo loading whereas others undergo unloading. This process of fabric evolution is the primary cause of noncoaxiality between the axes of principal stresses and strains. Although cyclic behavior and behavior under the rotation of the principal stress axis seem to originate from two distinct mechanisms, the strain space multiple mechanism model demonstrates that these behaviors are closely related through the hysteretic damping factor.