# Macro-Meso Mechanical Behavior of Loose Sand under Multi-Directional Cyclic Simple Shear Tests
## 1 Introduction  
During the liquefaction of saturated soils, the pore water pressure is rapidly built up and the bearing capacity of soils is dramatically decreased, resulting in many instances of catastrophic damage such as the uneven settlement of foundations and the collapse of marine structures. Therefore, understanding the mechanics of sand liquefaction and taking reasonable measures are of great significance to preventing liquefaction-related disasters. In most scenarios, the greenfield condition is too ideal; the existing structure and even a seabed slope could create a rather complex stress state for sand. As a result, research on sand liquefaction must consider the complex shear state of sand; however, due to the limitations of experimental instruments, most studies have not systematically considered this significant factor. With the continuous iteration of geotechnical experimental instruments, a dynamic simple shear apparatus is capable of applying multi-directional and multi-stage shears, which helps to study the liquefaction mechanism of a complex initial stress state [1,2]. A multi-directional dynamic simple shear device has two perpendicular loading motors located on the horizontal plane, and the combined action of the two motors can generate shear stress in any direction and complex shear paths (such as circular, elliptical, figure-8-shaped, etc.) on the horizontal plane. With the ability to apply bi-directional shear stress, [PERSON] and [PERSON] [1] first performed a series of undrained bi-directional cyclic simple shear tests on saturated medium-dense sand, and the testing involved oval and \"alternating cycle\" (two perpendicular circles)-shaped cyclic shear paths. The authors found that the second shear direction lowered the liquefaction resistance at different levels. At a shear strain of 5%, frequently recorded bi-directional cyclic shear stresses are 30% smaller than uni-directional cyclic shear stress. However, a follow-up study reported severe rocking motion problems in the device, which may cause inaccurate measurements. Its tendency to rock is mainly due to the lack of complementary shear stresses [3]. To evaluate the effect of initial driving shear stress, [PERSON] et al. conducted a series of cyclic simple shear tests with an initial driving shear stress parallel or perpendicular to cyclic loading [4; 5; 6]. Results showed that in parallel conditions, stress reversal increases the liquefaction resistance (except loose sand), while in perpendicular conditions, the initial driving shear stress can decrease the liquefaction resistance due to additionally introduced large permanent strain. Follow-up tests were performed by [PERSON] [7] on medium-dense and dense sand, in which linear, circle, oval, and figure-8-shaped shear paths were used. Results showed that without an initial driving shear stress, the pore water pressure generation and strain development under bi-directional cyclic shear stresses were generally faster than those in the uni-directional condition, and the bi-directional cyclic shear stresses generally decreased the liquefaction resistance at different levels, in which the figure-8-shaped cyclic shear tests had a rapid accumulation of permanent strains and the lowest liquefaction resistance. Similar results have been reported by different researchers using different materials, which are mainly dense sand and clay [8; 9; 10; 11; 12; 13; 14; 15]. In addition, [PERSON] et al. [11] conducted a series of bi-directional cyclic simple shear tests to study the effect of different directions of consolidation shear stress on the liquefaction characteristics of sand. It was found that the direction of consolidation shear stress had a significant impact on the stiffness of the sample. With the increase in the angle between consolidation shear stress (also known as initial driving shear stress) and dynamic shear stress, the stiffness decreased, and the sample liquefied faster.