After the liquefaction of sand, the prediction of anisotropy and heterogeneity is one of the complexities of constitutive law. This study aimed to develop a method to more effectively assess anisotropy and strain and stress distributions, and determine their history in cohesionless soil. To achieve this objective, instead of defining all the direction-dependent events on the three orthogonal planes of the Cartesian coordinate system, numerical integration was utilized to make use of 17 planes with pre-defined directions. This leads to a more accurate and powerful assessment of anisotropy and its effects. The constitutive equations of the proposed model were adjusted with a multilaminate framework, and its result for different monotonic and cyclic loading, drained and undrained conditions, and different pressures and void ratios were verified using the experimental data. Finally, the model’s performance in predicting induced anisotropy is demonstrated under cyclic mobility conditions on the 17 planes.

Introduction

The constitutive characteristics of sand as a basic geomaterial have a significant effect on its applications. Developing a constitutive model for sand, and especially its liquefaction, is a challenging task. Under monotonic or cyclic loading conditions, sandy soils tend to exhibit dilatancy. In undrained conditions, this behavior leads to increased pore pressure and decreased effective stress, and this reduction can sometimes lead to liquefaction. Another important parameter that can affect soil liquefaction resistance under cyclic loads is inherent and induced anisotropy due to plastic deformation, which can be defined as the properties of soil fabric. Some studies have tried to establish a relationship between the important microscopic and macroscopic properties of sand, and incorporate the result into their constitutive models [1,2]. There are essentially two types of anisotropy in granular material, inherent anisotropy and induced anisotropy. Inherent anisotropy is created during the sedimentation of geomaterials as a result of the placement of the soil particles, the void ratio, and the inter-particle contact [3,4]. Inherent anisotropy remains unchanged as long as the material is in its elastic state. Induced anisotropy occurs under the influence of plastic strain and loading history, and it plays a significant role in the mechanical behavior of granular soils [2,5]. Unlike inherent anisotropy, induced anisotropy evolves with plastic deformation over the course of the loading process. While many studies have examined soil anisotropy, the development of anisotropy during liquefaction and the ensuing effects, including changes in effective stress and soil stiffness, are still under debate. Anisotropy in granular soils subjected to cyclic or monotonic loading has also been extensively studied [6–۱۰]. Some researchers have studied the inter-particle contact level and have also predicted the effects of anisotropy on the behavior of granular soil using micromechanical models, such as the discrete element model [11–۱۷].