# Deformation Behavior of Saturated Soft Clay under Cyclic Loading with Principal Stress Rotation
## 1 Introduction  
Wenzhou soft clay is a typical soft clay. It has a high water content, low shearing strength, low permeability, and high compressibility. The soft clay was formed in the late Quaternary period and is widely distributed in the coastal areas of China [1]. In this region, rapid economic development has led to a significant increase in transportation construction, most of which is built on the soft ground. The traffic loading exerted by the transportation is a typical cyclic loading. Under the long-term action of traffic loading, the soil structure under the subgrade is disturbed, easily producing deformation, stability reduction, and other problems. The soft clay has poor engineering properties and is more sensitive to disturbance [2]. Therefore, to improve the service performance of traffic facilities in coastal areas and to control the maintenance costs, it is necessary to study the cyclic behavior of saturated soft clay under traffic loading. During a certain vehicle wheel passing, the changes in the stress components of the soil element in subgrade are more complex. As shown in Figure 1, the vertical cyclic stress \(\sigma_{11}\), the horizontal cyclic stress \(\sigma_{22}\), and the shear stress \(\tau_{12}\) are constantly changing, and the shear stress \(\tau_{12}\) changes both in magnitude and direction. Therefore, the principal stress axis on the soil element rotates continuously [3, 4]. The stress path of the traffic loading in the \(\sigma\)-\(\tau\) plane can be simplified as a cardioid (see Figure 2). According to [PERSON] et al. [5], the shear stress in subgrade decays faster with depth than the normal stresses do. Therefore, the ratio of shear stress to axial stress of the soil under traffic loading decreases with depth,  
Soil dynamics is one of the most popular studies in soil mechanics. Many researchers have researched the factors that may affect the dynamic characteristics of soil, such as the frequency, loading rate, amplitude, overconsolidation ratio, and loading times. Some scholars believe that low-frequency cyclic loading can better reflect the actual situation of soil, and the pore pressure development is more uniform [6; 7; 8]. The strain rate affects the shear strength of soil, while the loading rate affects the shear modulus of soil [9; 10; 11]. The influence of the cyclic number and overconsolidation ratio on soil dynamic characteristics has also been studied by many scholars [12; 13; 14]. The effects on the soil can be attributed to the different loading histories of soil, and different stress paths were found to be the main influence on the cyclic behavior of soil. Pore pressure is one of the important characteristics of saturated soft clay under cyclic loading. The development of pore pressure can soften the stiffness and strength of soil, which leads to the destruction of soil structure. Many factors affect the variation in pore pressure of saturated clay under cyclic loadings, such as the cycles, the magnitude of deviator stress, cyclic stress ratio, and frequency [15; 16]. Therefore, the cumulative pore pressure model needs to be further studied. Among the existing pore pressure models, there are many models of pore pressure for saturated clay under dynamic load, and many scholars have directly established the relationship model between pore pressure and strain [17; 18]. These models are mainly of exponential, bilinear, and polynomial types. However, there are many factors affecting pore pressure and soil strain, and the relationship between pore pressure and strain is different under different factors. Even if a relationship between pore pressure and strain is established, the results are not universal, due to the many factors involved. Given the current state of research on pore pressure in clays, it is difficult to establish a pore pressure model that reflects the mechanism of pore pressure variation and the influence of various factors, which can only be focused on in specific situations.