# Research on Shear Behavior of Sand-Structure Interface Based on Monotonic and Cyclic Tests
## 4 Cyclic Shear Tests
### Analysis and Discussion  
#### 4.2.1. Residual Deformation of Cyclic Shear  
The point in the shear displacement-shear stress ratio curve after each loading and unloading cycle is taken as the research base point. Through the normalization method, the ratio of \(u_{sr}\) and \(u_{sy}\) is used to measure the degree of residual deformation in this cycle test. Where \(u_{sr}\) is the residual displacement accumulated after each cycle, \(u_{sy}=\tau_{y}/K_{in}\) and \(\tau_{y}\) is the peak strength in the monotonic shear test. Figure 8 shows the most significant situation in which the residual deformation phenomenon occurs in the above-mentioned cycle, which is the 90% stress level amplitude. When the interface is relatively smooth, the residual displacements of loose sand and dense sand both increase with the increase in the number of cycles. However, the residual displacement increment between each cycle gradually decreases. As the normal stress increases, the residual deformation of the interface between loose sand and dense sand will decrease. When the normal stress is constant, the residual deformation at the interface of loose sand is larger than that of dense sand. For example, when loose sand is subjected to normal stresses of 200 kPa and 400 kPa, the cumulative shear deformation after the 10 th cycle increases by 8.92% and 5.08%, respectively, compared with that after the first cycle. When the normal stress is both 200 kPa, the final residual deformation of loose sand and dense sand differs by 7.67%. Figure 8 b reflects the residual deformation when the interface is rough. It is basically consistent with the morphological trend when the interface is relatively smooth. However, under the same conditions, the residual deformation of rough interface sand is smaller than that of the relatively smooth interface. This means that the residual deformation of the cohesionless soils in the cyclic shearing process gradually increases. Additionally, the weekly residual displacement increment gradually decreases. As the normal stress increases, the residual deformation of the same density sand will become smaller. Compared with dense sand, when the normal stress is the same, the residual deformation of loose sand will be greater. If the relative density of sand is the same as the normal stress, the residual deformation of the rough interface is smaller than that of the relatively smooth interface. The residual deformation under different stress level amplitudes when the normal stress is controlled at 300 kPa (Figure 9). It is observed that the residual deformation at the sand-steel interface at stress level amplitudes of 30% and 60% is extremely small. The proportion of residual deformation does not exceed 3% of the displacement that reaches  
Figure 8: The development law of residual deformation with the number of cycles (Stress level amplitude: 90%): (**a**) \(R_{n1}\). (**b**) \(R_{n3}\). the peak shear strength. Therefore, the residual deformation generated in the cycle for the stress level amplitude below 60% has very little impact on the actual project. Therefore, this article will not go into detail. The change in the trend of the residual deformation and the cumulative residual displacement increment is obtained above. The main reason for the residual deformation is the inconsistency of the shear stiffness during the cycle. In previous studies on the response of similar hysteresis loops, the secant stiffness of the loading and unloading hysteresis curves of [PERSON]'s model [22] was the same. Therefore, there is no residual deformation. On this basis, if the study uses the loading and unloading criteria proposed by [PERSON] [23] (the characteristic of the model is that the stiffness of each loading is only related to the current turning point), although it is also possible to simulate the case where the loading stiffness is less than the unloading stiffness, the loading stiffness is the same every time. This may cause excessive residual deformation.