Induced fabric under cyclic and rotational loads in a strain space multiple mechanism model for granular materials

Abstract

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.

Constitutive modeling of inherent anisotropy in a strain space multiple mechanism model for granular materials

“…Furthermore, the necessity and advantages of introducing the second mode with the parameter a 2 in the expression are examined in Appendix A through comparison with a DEM simulation. If the anisotropic parameters are ignored and thus the function F * ( θ ) is independent of direction θ (ie, F * ( θ ) = 1) as shown in the circle in Figure , the second‐order fabric tensor in Equation is reduced to its original form without any inherent‐anisotropy effects …”

“…The transformation process in Equation is decomposed into the following three steps: (1) γ ↦ γ / γ v ; (2) γ / γ v ↦ q Iso / q v ; and (3) q Iso / q v ↦ q Iso . The effect of inherent anisotropy comes into effect in steps (1) and (3), but such anisotropy does not affect the transformation process in step (2), which is essential for describing the non‐linear evolution of stress‐space fabric (ie, stress‐induced anisotropy) …”

“…is reduced to its original form without any inherent-anisotropy effects. [28][29][30] Because of the equilibrium of momentum (ie, ∫ 2π…”

“…The model consists of a multitude of simple shear mechanisms, each oriented in an arbitrary direction. These mechanisms can idealize the internal (or micromechanical) structure of granular materials with an induced fabric anisotropy, as well as the evolution of this structure under monotonic and cyclic loadings and complicated loading paths, including the effect of rotation of the principal stress axes . The model has been implemented in a finite‐element program and used to analyze numerous practical problems involved in evaluating the seismic performances of geotechnical works, such as level ground, retaining structures, embankments, and underground structures .…”

“…These mechanisms can idealize the internal (or micromechanical) structure of granular materials with an induced fabric anisotropy, as well as the evolution of this structure under monotonic and cyclic loadings and complicated loading paths, including the effect of rotation of the principal stress axes. 29,30 The model has been implemented in a finite-element program and used to analyze numerous practical problems involved in evaluating the seismic performances of geotechnical works, such as level ground, retaining structures, embankments, and underground structures. [31][32][33][34][35][36][37][38] However, the influence of inherent anisotropy has not been incorporated into the model in an explicit form for describing the textures of granular materials.…”