# Research on Shear Behavior of Sand-Structure Interface Based on Monotonic and Cyclic Tests
## 4 Cyclic Shear Tests
### Analysis and Discussion
#### 4.2.3 Loading and Unloading Shear Stiffness under Different Stress Level Amplitudes  
In the tests, the normal stress is controlled at 300 kPa to observe the changing trend of cyclic loading and unloading stiffness under different stress level amplitudes (Figure 12). The development trend of the curve shape of the cyclic loading stiffness of loose sand with stress level amplitudes of 30% and 60% is almost the same as the abovementioned 90% change law. They all show a trend of increasing loading stiffness, but their increasing range gradually decreases. For example, the second loading stiffness of loose sand with a 30% stress level amplitude at the relatively smooth interface is about 1.9% higher than the first loading, while the tenth loading stiffness is only about 0.2% higher than the ninth loading. In addition, when the interface roughness is the same, as the stress level amplitude increases, the overall loading stiffness decreases. Additionally, under the same stress level amplitude, the loading stiffness of the relatively smooth interface is generally less than that of the rough interface. The behavior of dense sand is different. The loading stiffness at the 30% and 60% stress level amplitude hardly increases or decays. This means that at low or medium stress level amplitude, the load-shear stiffness of relatively dense cohesive soils hardly changes during the cycle.  
Figure 11: The development law of interface cyclic loading and unloading shear stiffness with the number of cycles (stress amplitude level: 90%). (**a**) Cyclic loading, \(D_{r}=0.3\). (**b**) Cyclic loading, \(D_{r}=0.9\). (**c**) Cyclic unloading, \(D_{r}=0.3\). (**d**) Cyclic unloading, \(D_{r}=0.9\).  
Through Figure 12c,d, it is found that the unloading stiffness of different stress level amplitude has no obvious fluctuation during the cycle. Additionally, as the stress level amplitude increases, the overall loading stiffness decreases. Under the same stress level amplitude, the loading stiffness of the rough interface is generally greater than that of the relatively smooth interface. It is worth mentioning that the loading stiffness of loose sand or dense sand under the same stress level amplitude is always lower than the unloading stiffness. Additionally, with the continuous increase of loading stiffness, it will approach and unload stiffness. This point is consistent with the above conclusion about the loading and unloading stiffness of 90% stress level amplitude.  
Figure 13 shows the unloading stiffness of the last cycle under different stress level amplitudes. It can be seen from the figure that whether it is loose sand or dense sand, under the same normal stress, the higher the stress level amplitude, the lower the final unloading stiffness. In addition, the increase in normal stress or the relative density of sand will increase the unloading stiffness. This point is almost consistent with the above experimental conclusions. Therefore, it can be seen from the comprehensive analysis of static and dynamic tests that the loading stiffness of the sand-steel interface in the cyclic shear test continues to increase, and the unloading stiffness hardly changes. The higher the stress level amplitude, the lower the corresponding loading and unloading stiffness. Additionally, the unloading stiffness is always greater than the initial stiffness. As the cycle  
Figure 12: The influence of different stress level amplitudes on the shear stiffness of cyclic loading and unloading. (**a**) Cyclic loading, \(D_{r}=0.3\). (**b**) Cyclic loading, \(D_{r}=0.9\). (**c**) Cyclic unloading, \(D_{r}=0.3\). (**d**) Cyclic unloading, \(D_{r}=0.9\).  
increases, the loading stiffness continues to increase, and it may eventually approach the unloading stiffness.