# Deformation Behavior of Saturated Soft Clay under Cyclic Loading with Principal Stress Rotation
## 1 Introduction
In order to study the influence of principal stress rotation on the pore pressure, it is necessary to introduce cycles \(N\) as an objective reference quantity that does not change with various influencing factors. The relationship between the increase in pore pressure and loading cycles, taking into account the rotation of the principal stress axis, is established. The relationship between pore pressure and strain in the soil under the principal stress rotation is determined indirectly through loading cycles, which can reflect the actual situation of pore pressure and strain changes more objectively. The backbone curve is one of the most important indicators of the nonlinear stress-strain relationship in research on the cyclic behavior of soil. [PERSON] et al. [19; 20] and [PERSON] et al. [21] gave expressions for the variation in dynamic elastic mode and dynamic damping ratio with shear stress amplitude. [PERSON] et al. [22] found that if the stress amplitude is maintained constant, the increase in amplitude of cyclic confining pressure will promote the development of both permanent volumetric strain and axial strain significantly. [PERSON] et al. [23] found that the backbone curve for the stress-strain relationship in soils subjected to cyclic loading in most cases can be assumed to be a hyperbolic model. [PERSON] et al. [8], [PERSON] et al. [24], and [PERSON] et al. [25] pointed out the variation in the backbone curve of soils based on the results of cyclic loading tests under different loading conditions. They gave expressions for the dynamic stress-strain relationship. [PERSON] et al. [26] used a bidirectional triaxial apparatus to simulate traffic loading. They proposed a model for the backbone curve of soft clay in Ningbo, considering the cyclic surrounding pressure and the number of vibrations. Currently, based on the research of a large number of scholars, the backbone curve models are mainly classified into three types: Hardin-Drnevich hyperbolic model [19; 20; 27], Ramberg-Osgood model [6], and Martin-Darvidenkov model [28]. Among them, the Hardin-Drnevich (H-D) model is commonly used to describe the dynamic properties of soft clay. In addition, the above studies are all based on triaxial test results, and the cyclic loading under the triaxial stress state does not truly reflect the rotational effect of the principal stress axis in the traffic loading. The period of the above studies is limited, and the study of soil backbone curves under long-term cyclic loading is rare. To better understand the deformation properties of soft clays under traffic loading with principal stress axis rotation, a corresponding investigation was performed in this study. A series of cyclic torsional shear tests on saturated soft clay simulating traffic loading were conducted through a GDS hollow cylinder apparatus. The influence of principal stress rotation on the development of permanent strain and pore pressure have been interpreted and discussed with their practical implications to analyze the effect of principal stress rotation on the mechanical properties of soil. Finally, a pore pressure model and a H-D backbone curve model were modified considering the principal stress rotation and cycles for the deformation behavior of soft clay under cyclic traffic loading.