An Invesitigation Of Small Strain Shear-Modulus Anisotropy Based On Experiments And Numerical Smulation

Many previous researches have found that: soil, as a kind of engineering materials, exhibits anisotropy in physical and mechanical properties. It can be divided into two categories due to different causes: fabric-induced anisotropy and stress-induced anisotropy. Fabric-induced anisotropy is dependent on the virgin fabrics which are governed by the minerals and the particle characteristics during the soil sedimentation. While stress-induced anisotropy refers to the changes of mechanical properties due to stress state variations when the soil is subject to complex loading conditions. Although the two kinds of anisotropies demonstrate in the identical manner in macro scale, soil mechanical parameters vary with directions, and the rules of such variations of the two types of anisotropies are different. This paper studies the variation rules of strength anisotropy caused by fabric and stress changes based on experiments and numerical simulation-Discrete Element Method (DEM).Existing studies have found that the relationship between shear-modulus (G) and shear-strain (ε) is nonlinear, which implies that it is inadequate to determined shear -modulus (G) through classical stress-strain (σ-ε) curve. It is generally accepted that, under small shear strain (less than 10-4) conditions, shear-modulus (G) virtually keeps constant. As a significant parameter in soil dynamics, small strain shear-modulus G0 is indispensable in seismic safety assessment of any construction site.However, due to the special characteristics of soil (relative to other materials, such as metal) and also limitations of appropriate experimental devices, studies on the problem are not easy. In view of the fact that shear wave induced strain (10-5) falls in the range of small strain, and shear wave velocity can be related to small strain shear-modulus, this paper uses shear wave velocity to measure the small strain shear-modulus of soil. In conventional effective stress seismic reaction analysis, the Hardin empirical formula is usually used to calculate the small strain shear-modulus. However, due to soil anisotropy, the small strain shear-modulus is also anisotropic. Therefore, it is crucially important to take account of soil anisotropy if physical-mechanical parameters that can accurately reflect soil properties are to be obtained.In view of the two reasons of soil anisotropy, this paper studies the small strain shear-modulus in different directions and its variation rules with stress of Toyoura sand ( mainly comprises of sharp angled particles) prepared by air pluviation under isotropic loading conditions in a true tri-axial apparatus. The effect of stress history was also considered. It is found that the small strain shear-modulus differs in the vertical and horizontal directions. Under normal consolidated conditions, small strain shear-modulus in all directions are proportional to exponential values of isotropic confining stress, which agrees with many other research findings in literature. Further study also shows that the values of exponents in all directions are similar, falling in the range of 0.42-0.45. However, when soil is over-consolidated, the exponent values (0.2-0.3) in all directions are significantly smaller than those for normal consolidated soil. This manifests that the small strain shear-modulus of soil is obviously impacted by stress history.Under anisotropic loading, this paper studied the variation rule of small strain shear-modulus with stress state using Leighton Buzzard (E) sand, which mainly comprises of quasi-round particles. It is found that the shear-modulus is essentially controlled by the stress in the shear plane, whereas shows no obvious link to the stress out of plane (normal to shear surface). It is observed that the exponent value of the exponential proportional relation of small strain shear-modulus and deviatoric component of stress in the shear plane ranges from 0.6 to 0.65, while the counterpart value is 0.14-0.17 for the small strain shear-modulus in the normal direction.For natural soils, the formation process often lasts a long geological period. The time effect on soil's physical-mechanical parameters is obvious. Therefore, the time effect on soil small shear-modulus is also included in this paper. The findings are: under stable loading conditions, shear-modulus in all directions increase with time until reaching stable values; for relatively low level of isotropic loading, small strain shear-modulus in the horizontal direction increases faster than in the vertical direction, however, under relatively high isotropic loading, small strain shear-modulus increases at similar rate with time in all directions.For sand, as the granular material, the stress history effect on small strain shear- modulus and stress and fabric induced anisotropy are investigated by the software of PFC3D based on the discrete element method. The simulation reveals the micro mechanism of the stress and fabric induced anisotropic phenomena which are shown in the experimental tests. For fabric induced anisotropy, with the increase of the ratio of particle length to width, contact normal force between particles becomes more evenly distributed, which in turn make more contact normal along the preferential direction of the particle arrangement. For stress induced anisotropy, both contact normal force and contact normal tend to align with the direction of deviatoric stress component. Therefore, from the micro mechanics point, the fabric and stress induced soil anisotropy can be united again, which all demonstrate through the anisotropy of contact normal force and contact normal distribution.The previous research on the anisotropy mainly focused on the experimental tests. Though there were some reported results based on the 2D numerical simulations, this can not reflect the variations of the inherent structures and the mechanisms for 3D materials. So in this paper, partial experimental progress is simulated by 3D discrete element method. The mechanism of soil anisotropy is enclosed by the simulation from the heterogeneity of contact normal force and contact normal points, which can give a reference for more reasonable constitutive models.