Evaluation of the rotation of the main axes of stress and strain and their misalignment in the liquefaction prediction model of non-cohesive soils

Soil and soil mechanics trend

Abstract

Study of soil behavior due to different loadings is one of the most important issues in geotechnical engineering. The behavior of soils depends on several parameters such as grain size, grain type, loading method, stress history, etc. Non-alignment of main stress and main strain directions is a phenomenon that has attracted a lot of attention in recent years. This phenomenon is caused by heterogeneity in soil behavior. The behavioral models that operate based on independent stress and strain are not able to present the misalignment of the soil in different directions.

In this thesis, multi-plane theory is used to investigate the misalignment. In addition to the ability to apply soil micrometric properties such as porosity ratio, grain type and expansion and contraction behavior of soil, this theory is able to apply loading in different directions. In other words, this theory is the link between macroscopic and microscopic properties. In this thesis, the results obtained from the rotation of the main axes in the behavior of the soil are first examined and then its non-coaxiality is shown.  1- Chapter 1: Introduction and generalities Covering the earth's surface with these materials and their behavioral complexities have caused their stress-strain behavior to be studied carefully. One of the main factors of these complications is their multi-phase and deformability. Deformation of soils depends on many factors such as shape and size of particles, porosity, adhesion and friction of grains, percentage of moisture, percentage of saturation, drainage, lateral consolidation, path and history of stress, speed of loading and homogeneity of materials. For this reason, it is difficult to predict the behavior or deformation of soils [1].

In geotechnical engineering, non-coaxiality, asymmetry in the direction of the main stress and the direction of the development of the main strain is defined. This important phenomenon is observed both in engineering problems and in the laboratory results of direct cutting tests and cylindrical cylinder devices [1]. Numerical analysis performed by Yu [2] and Yuan [3] [2], [3] and Yu and Yang [4] [4] showed that the non-coaxiality of granular soil has important effects on geotechnical design. They concluded that the design of surface foundations without considering the lack of concentricity can be against the direction of reliability. The importance of considering the lack of concentricity in the geotechnical design of structures has been acknowledged [2]. Models that consider the non-coaxiality of soil behavior have been developed by many researchers ([5] Yatomi[5] and [6] Gutierrez[6] and [7] Li[7] and Dafilias[8] and [8] Lashkari and Latifi and [9], [10] Jiang[9] etc.).

For the first time in 1967, [11], [12] Roscoe [10] He reported the non-coaxial direction of principal stresses and the direction of strain development in the simple shear test. Based on micromechanical laboratory research using an optical disk as a two-dimensional simulation of the grain environment, [13] Drescher [11] and Jocelyn de Jong [12] reported further evidence of misalignment. [9] Arthur[13] and Wong[14] showed by using simple shear test that in sand samples under continuous rotation of the principal stress axis, the deviation between the directions of principal stress development and principal strain development can be more than 30. Experiments conducted with HCA [15] showed that granular materials show non-coaxiality in their behavior when subjected to pure rotation of the principal axes ([10] Sims[16], [11] Ishihara[17] and Tohata[18], [12] Miura[19]). Misalignment is dependent on material inhomogeneity and loading history.

(Images available in main file)

Figure 1?1 shows an example of inhomogeneity. In Figure 1-1(a), if the loading direction is perpendicular to the layers, the direction of principal stress and principal strain development will be coaxial, even if the specimen is inhomogeneous. As shown in Figure 1-1 (b), when the loading direction and the layers are not perpendicular to each other, the axis of the strain development deviates from the main stress axis and misalignment occurs.

Predicting the magnitude and direction of soil deformation accurately is very important when installing a structure on it. Therefore, it is necessary to use the laws of misalignment in the development of plastic strains. 1-1- Objectives of the thesis The main objective of this thesis is to investigate the misalignment of principal stresses and the development of principal strains using multi-plane theory. In this theory, the elastoplastic model with the uniform hardening law is used.One of the advantages of this theory is the dependence of soil behavior on different directions of loading and the ability to apply heterogeneity to soil in different directions. Also, this model is able to predict the rupture plane under different loadings.

1-2- Thesis structure

This thesis is compiled in six chapters. The first chapter includes the introduction, objectives of the thesis, and the structure of the thesis. In the second chapter, the past studies on the lack of concentricity, cylindrical cylinder device and the studies done with it are given. In the third chapter, the basics of multi-page theory and the model used are explained. In the fourth chapter of this thesis, the results of this theory in the beam sand [1] in two states, drained and undrained, are presented and the lack of concentricity is examined, and in the fifth chapter, the results obtained are again presented and the suggestions are stated. Cod yield applied in the problem of plasticity of metals, it has been used. Therefore, these assumptions are also called Saint Venant. However, it has been known for a long time that it is not appropriate to use coaxiality in heterogeneous materials. 2-1-1- Definition of non-coaxiality: Non-coaxiality is defined as the difference in direction between the axes of the main stress and the development of the main strain. Considering the same axes of the two tensors of stress ( ) and strain growth ( ) are defined as follows: (formulas and images are available in the main file) 1-1-1- Studies conducted on non-coaxiality Among numerous researches on granular materials, it has been concluded that the assumption of co-axiality is valid only for isotropic media. The theoretical origin of non-coaxiality can be found in some plasticity models for the behavior of granular materials at the threshold of rupture, such as hypoplastic models [1] ([13] Wong and [20] Kolimbas [2]) and multi-plane models ([14] Yai [3] and [22] Rodaniki [4] and Rice [5]). Rodanicki and Rice focused on the strain position of materials and showed that misalignment plays an important role in the formation of fracture boundaries in sand. In addition, by introducing the vertices of the yield surface (different from the soft and continuous yield surface), soil flow became dependent on the direction and development of stress and behaved as non-coaxial for indirect loading.

Non-coaxial is the characteristic of plastic models that describe the fully developed plastic flow plane for granular materials by kinematic theory. Early kinematic models for granular material flow were developed by Jocelyn de Jong [15] with graphical methods. The double-slip, free-rotation model for planar flow is based on the assumption that shear flow occurs on two surfaces whose shear resistance is depleted. Then [16] Spencer [6] presented a set of kinematic relationships called the double shear model with a different rotation term using this concept. A similar model was also presented independently by [17] Mendel [7], which was further investigated by [26] Mendel and Fernandez [8] about the co-axiality between principal stress and principal strain development. These models were developed for inelastic, rigid, plastic and post-peak flow materials. Other researchers developed these models by considering dilation, elastoplasticity and pre-peak hardening (Joer [18], [9]), however, these models were not able to account for the results of Roscoe's [12] simple shear test.

Figure 2-1 shows Roscoe's laboratory results. Before that, Roscoe had shown in 1967 that in the simple shear test, the main axes of stress and strain development before the sand reaches the shear peak are not co-axial. According to Figure 2-1, it is observed that at the beginning of loading, the rotation of the main axes of stress and plastic strain are not coaxial, and then at high strains, the axes tend to become coaxial.

One of the first evidences of non-coaxiality was reported by [13] Drescher and Jocelyn de Jong in 1972 based on micromechanical laboratory studies of the photoelastic disk as a two-dimensional simulator of the grain environment. The lack of concentricity was also observed in the experiments conducted with the cylinder cylinder device (HCA) which allows full rotation of the main stress axes ([6], [10], [16] and [19]). And these studies included drained and non-drained tests on different types of sand.