Numerical modeling of changes in anisotropy during liquefaction using a generalized constitutive model

Abstract

A constitutive model with rotation hardening was generalized from the triaxial compression state to a general stress state. With the generalized model, numerical simulations of cyclic and monotonic undrained triaxial tests were conducted to reproduce the phenomenon of continuous, orderly and rapid changes in anisotropy during liquefaction. The simulated results demonstrated that when sand enters the liquefaction stage, the yield surface in the stress space rotates quickly, causing continuous and rapid changes in anisotropy. Through comparison of the simulated and experimental results, the generalized constitutive model was shown to be able to capture the fundamental behaviors of sand demonstrated by the experimental data, and the rotational hardening rule adopted in the generalized model was proven suitable for describing the continuous, orderly and rapid changes in anisotropy that occur during liquefaction.

Introduction

There are two different kinds of anisotropy in geomaterials; the first of these is the inherent anisotropy formed by the long-term sedimentary process of the geomaterial, which will not change unless the bonding of the material has reached a failure state. Modeling of inherent anisotropy using a special ‘fabric tensor’ can be found in literature, such as in the works by Boehler and Sawczuk [1], Boehler [2], Li and Dafalias [3], Oka et al. [4] and Dafalias et al. [5]. From the micro-structure perspective, the multi-laminate model [6] and the microplane model [7], [8] were proposed to describe the inherent anisotropic behavior of soils. The other form of anisotropy is stress-induced anisotropy, which is an important factor that influences the mechanical behavior of soft soil. Unlike inherent anisotropy, stress-induced anisotropy may change with plastic deformation during the loading process, not necessarily in the failure state. In this paper, the focus is on the stress-induced anisotropy in soft soil, which is referred to simply as ‘anisotropy’. There have been many previous studies related to the anisotropy of soil, but the development of anisotropy during liquefaction, a state in which the effective stress and stiffness of soil are extremely low, is still a controversial problem. Some researchers assume that anisotropy disappears during liquefaction because soil behaves like liquid in this stage, gradually losing its fabric and structure, including anisotropy. Alternatively, some researchers argue that anisotropy increases during liquefaction because large plastic deformations often occur during this stage. Through triaxial tests, several past research studies (e.g., the works by Finn et al. [9], Ishihara and Okada [10], [11], Suzuki and Toki [12] and Oda et al. [13]) have shown that if a sand has a prior liquefaction history, it will exhibit totally different behaviors in triaxial compression and extension tests under undrained conditions, which indicates that a high level of anisotropy has developed during the previous liquefaction history. These reports, however, did not note how anisotropy develops during liquefaction. In a recent study on the post-liquefaction resistance of sand, Yamada et al. [14] proved convincingly that the anisotropy of soil changes during liquefaction in a “continuous”, “orderly” manner with “dizzying rapidity”.

Because anisotropy changes greatly during liquefaction, it is reasonable to account for its effects when developing constitutive models to describe the liquefaction behaviors of sand. A large number of constitutive models have been previously proposed to simulate the liquefaction behaviors of sand, such as the works by Pastor et al. [15], Prevost [16], Nishi and Kanatani [17], Oka et al. [18], Li [19], Wang et al. [20] and Elgamal et al. [21]. The researchers made significant efforts to model the complex behavior of cyclic mobility, which is a typical phenomenon of sand during liquefaction [22]. Although these constitutive models are successful in describing the liquefaction behavior, most of them do not consider anisotropy as a primary factor. Therefore, it is difficult for these models to simulate the behavior of soil with a liquefaction history, in which the previously developed anisotropy will play a significant role in the subsequent loading process.

Zhang et al. [23] proposed an elasto-plastic constitutive model that included rotational hardening to describe the liquefaction behavior of soil. In the model, the anisotropy of soil was assumed to change continuously and rapidly during liquefaction, and a new approach was adopted to describe this kind of anisotropy development. The description coincides completely with the experimental phenomenon observed by Yamada et al. [14]. Hence, the constitutive model provides a potential method to correctly describe the changes in anisotropy during liquefaction. In the original model, however, the extended Von-Mises failure criterion is implicitly adopted. Under the triaxial compression condition, the model predicts the test results well; however, under general stress conditions, such as the triaxial extension tests, the model often overestimates its prediction for soil strength. Therefore, to better predict the test results under the triaxial extension condition, the constitutive model should be generalized from the triaxial compression state to the three-dimensional stress state. Some mathematical methods have been proposed to generalize constitutive relations, such as the g(θ) method proposed by Zienkiewicz and Pande [24], the t_ij method proposed by Nakai and Mihara [25], and the transformed stress (TS) method proposed by Yao et al. [26], [27]. In the present study, the original model proposed by Zhang et al. [23] was generalized using the TS method. The advantage of the TS method is that the constitutive model established in the p–q stress space can be easily extended to a general stress condition without either changing or adding any material parameters. Based on the proposed generalized model, the triaxial tests conducted by Yamada et al. [14] were simulated. Through comparison of the simulated and experimental results, it can be seen that the generalized constitutive model can capture the fundamental behavior of soil during liquefaction and that the evolution rule for the anisotropy adopted in the generalized model is suitable for describing the continuous and rapid changes in anisotropy during liquefaction.

This paper first briefly describes the original model proposed by Zhang et al. [23], paying particular attention to how the anisotropy is modeled by the yield surface rotation during liquefaction. Secondly, the mathematical formulations used by the TS method to generalize the constitutive model are presented. Next, using the proposed generalized model, a numerical simulation is conducted under the same loading conditions as the triaxial tests performed by Yamada et al. [14]. Finally, the simulated and experimental results are compared to show the capability of the generalized model to predict the experimental results.