## 3 Response of Plastic Deformation in Model Test  
### Vertical Deformation Under Cyclic Loading  
The vertical deformation is precisely measured by the vertical displacement transducers located on the model surface in real time. When \(P_{d}\) = 100 kPa, the displacement of Model 3 measured by the No.1 vertical transducer is shown in Figure 6. Figure 6a depicts the evolvement characteristics of measured deformation in the entire cyclic loading process. Figure 6b, which shows the deformation curve from 545 s to 590 s in the initial stage, is obtained from the deformation curve in the dotted box of Figure 6a and enlarged along the x direction. The deformation development demonstrates sine shaped curve in loading and unloading cycles. It is clearly indicated that both elastic and plastic deformations occur in the loading process, while only elastic deformation is recoverable during the unloading stage. In other words, a certain level of plastic deformation is sustained and developed during each loading and unloading cycle. Therefore, plastic displacement is continuously accumulated under the effect of cyclic loading. However, the growth rate of accumulated plastic deformation is gradually decreased with elapsed time (loading times) increasing under 100 kPa cyclic amplitude, which finally leads to the stable plastic displacement when loading times reach a relatively high level, as shown in Figure 6a. Figure 5: Cyclic loading program. When cyclic loading level \(P_{d}\) ranges from 100 kPa to 700 kPa, the vertical deformation curves for Model 3 (\(K\) = 1.0) are measured by No.1 vertical transducer, as shown in Figure 7. Figure 7a-d show the curves corresponding to the condition of \(P_{d}\) = 100 kPa, \(P_{d}\) = 300 kPa, \(P_{d}\) = 500 kPa, and \(P_{d}\) = 700 kPa respectively. When \(P_{d}\) = 100 kPa and \(P_{d}\) = 300 kPa, vertical plastic deformations are finally increased quite slowly as the loading times arrive at a relatively large magnitude. Moreover, the deformations at 100,000 loading times when \(P_{d}\) equals to 100 kPa and 300 kPa are close to 0.50 mm and 0.85 mm, respectively. Obviously, as the amplitude of \(P_{d}\) increases, vertical plastic deformation is obviously improved. On the condition of \(P_{d}\) = 500 kPa and \(P_{d}\) = 700 kPa, vertical plastic deformation develops continuously with the increasing loading times. When \(P_{d}\) = 700 kPa, the vertical deformation rate of the filling model even increases with loading times, which undoubtedly leads to the soil structure collapse rapidly at the initial stage of cyclic loading process. Summarily, the development of plastic deformation tends to converge when amplitude of cyclic loading is relatively small for a given model with a certain compaction degree. As the cyclic loading amplitude increases, the converging deformation is also steadily improved. When the loading amplitude reaches to some extent, the tendency of the plastic displacement gradually become diverging and deformation will abidingly develop with the ever-increasing loading times. If the amplitude of cyclic load keeps growing, plastic deformation will develop at an amazing speed and model structure will break down rapidly. Figure 6: Vertical displacement for Model 3 (\(K\) = 1.0) under 100 kPa cyclic loading level. Except for amplitude of cyclic loading, compaction degree \(K\) of the model filling may be another factor that can obviously influence the development characteristics of plastic deformation under dynamic load. Take Figure 7b, Figure 7e, and Figure 7f to make a comparison, plastic deformation is precisely measured when amplitude of cyclic loading equals to 300 kPa for the three models. The difference is that compaction degrees for these three models are 1.0, 0.95, and 0.9 respectively. Obviously, under the effect of the same cyclic loading amplitude, plastic deformation of Model 3 (\(K=1.0\)) tends to converge towards 0.85 mm, while deformations of Model 2 (\(K=0.95\)) and Model 1 (\(K=0.9\)) remarkably show divergency.