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

Abstract

Summary Consideration of fabric anisotropy is crucial to gaining an improved understanding of the behavior of granular materials. This paper presents a constitutive model to describe the sand behavior associated with fabric anisotropy within a framework of a strain space multiple mechanism model. In the proposed model, a second‐order fabric tensor is extended by incorporating a new function that represents the effect of inherent (or initial fabric) anisotropy, along with three additional parameters: two of them, a1 and a2, control the degree of anisotropy, and the second mode of inherent anisotropy can be expressed by introducing the parameter a2 as well as the first mode by the parameter a1. The third parameter, θ0, expresses the principal direction of inherent anisotropy (eg, the normal vector direction of bedding planes relative to horizontal axis). The formulation of the dilative component of dilatancy (ie, positive dilatancy) is also extended to consider the effect of inherent anisotropy based on the interlocking mechanism. Experimental data on the complex anisotropic responses of Fraser River sand and Toyoura sand under monotonic loading is used to validate this model. The proposed model is shown to successfully capture anisotropic responses, which become contractive or dilative depending on different principal‐stress directions, with a single set of anisotropy parameters; thus, the model is considered to possess the capability to simulate the anisotropic behaviors of granular materials. In addition to different loadings on the same fabric, the effects of different fabric anisotropies upon the sand behavior under the same loadings are also investigated.

Noncoaxiality considering inherent anisotropy under various loading paths in a strain space multiple mechanism model for granular materials

“…The function * ( ) has been newly introduced to account for the effect of inherent anisotropy using three additional parameters; 1 and 2 control the degree of inherent anisotropy, whereas 0 expresses the principal direction of inherent anisotropy. 25 To express the fabric of air-pluviated samples in geotechnical laboratory tests, 0 should be set to 90 • as the normal vector direction of the bedding plane relative to the x-axis. When the anisotropic parameters are ignored, the second-order fabric tensor in Equation ( 3) is reduced to the formulation for inherently isotropic materials.…”

“…22,24 These shear strength and reference strain of virtual simple shear mechanism are identified as functions of the parameters representing inherent anisotropy. 25 Therefore, out of the three transformation steps: (a) ↦ ∕ , (b) ∕ ↦ ∕ , and (c) ∕ ↦ in Equation ( 20), steps (a) and (c) are influenced by inherent anisotropy. However, such anisotropy does not affect step (b), which represents the nonlinear evolution of stress-space fabric (ie, stress-induced anisotropy).…”

“…[9][10][11][12] These experimental outcomes have been used for the validation and verification of constitutive models, which can account for the effect of inherent anisotropy [13][14][15][16][17][18][19][20] ; a strain space multiple mechanism model [21][22][23][24] has also been expanded to represent the effect of inherent anisotropy, and its fundamental capability has been demonstrated. 25 A numerical F I G U R E 2 Mohr's circle for two-dimensional: (A) applied stress components; (B) strain responses in isotropic linear elastic materials; (C), (D) strain responses in orthotropic linear elastic materials study using these constitutive models is useful to investigate the possibility that the inherent anisotropy due to the deposition process and grain characteristics of granular materials contributes to macroscopic soil responses, including noncoaxiality. 14,15,18 Two-dimensional discrete element method simulations of granular materials [26][27][28][29][30][31] also report that noncoaxiality is dependent on the material's inherent anisotropy as well as the loading history.…”

“…The dependency of noncoaxiality on inherent anisotropy in the nonlinear (or plastic) domain is, of course, expected to be more complicated; this is because inherent anisotropy also exerts an influence on the failure surface of soils besides the initial elastic modulus (as described later in Equation 28and Figure 11). However, the strain space multiple mechanism F I G U R E 3 Contact normal , tangential direction , and contact force model accounted for inherent anisotropy 25 is one of the most promising examples for describing such behavior. This is because the model idealizes the behavior of granular materials based on a multitude of virtual simple shear mechanisms, each of which is oriented in an arbitrary direction, [21][22][23][24] and can express the tendency for larger strain components to appear in the soft and weak direction than in the hard and strong direction.…”

“…As mentioned above, the model has been expanded by incorporating a new function with additional parameters to represent the effect of inherent anisotropy; its fundamental capability to evaluate the granular material behavior under monotonic proportional loading has been demonstrated. 25 However, the behavior of inherently anisotropic materials under more complex-loading conditions (eg, nonproportional loading including the rotation of the principal stress axis) was not studied in the article; rather, it was left for future work. Hence, the present study investigates the model's capability by comparing laboratory tests under various loading conditions (ie, monotonic proportional and nonproportional loadings including the rotation of the principal stress axis) with its simulations considering inherent anisotropy.…”