## 3 Response of Plastic Deformation in Model Test
### Vertical Plastic Deformation Under Different Cyclic Loading Amplitude  
Since vertical plastic deformation can be quantitatively determined by the deformation curves, the No.1 and No.2 vertical displacement transducers could give two groups of experimental data for the plastic deformation of a given model. Therefore, plastic displacement can be precisely calculated by  
Figure 7: Vertical displacement for the three models under cyclic loading. averaging the two groups of testing data. The development law of vertical accumulative deformation against loading times is shown in Figure 8. Figure 8a shows the evolutive law of vertical deformation for Model 1 (\(K\) = 0.9). When \(P_{d}\leq\) 100 kPa, the deformation curves present almost horizontal status when the loading times increase from 80,000 to 100,000. It can be deduced that vertical deformation finally converges towards a constant value, which indicates that plastic displacement tends to be steady under a large amount of cyclic loading times. As \(P_{d}\) increases to 200 kPa or 250 kPa, plastic deformation seems to abidingly develop with the increasing loading times. It can be deduced that the filling model will collapse when loading times are large enough to destroy the filling structure. When \(P_{d}\) = 300 kPa, plastic deformation develops at an overwhelming speed and reaches to 5 mm with only 10,000 loading times, and filling structure is broken with relatively fewer loading times. Figure 8b,c show the plastic deformation curves for Model 2 (\(K\) = 0.95) and Model 3 (\(K\) = 1.0) respectively. Similarly, the deformation curves for the two models firstly converge to some constant value when loading amplitude is relatively low. Then, cumulative deformation is inclined to develop continuously with increasing loading times at relatively higher loading amplitude. Finally, cumulative deformation increases sharply and lead to soil structure broken down instantaneously when amplitude is close to the bearing capacity of the filling model. Obviously, plastic deformation shows quite different developing characteristics under a wide variety of cyclic amplitudes for a given model. The evolutive characteristics of plastic deformation can be further revealed by analyze the deformation rate under cyclic loading. Plastic deformation rate is determined by calculating the  
Figure 8: Vertical plastic deformation against loading times for (a) Model 1, (b) Model 2, and (c) Model 3.  
plastic deformation developed every 10,000 loading times. Model 1 with compaction degree of 0.9 is taken as the example to analyze the developing law of plastic deformation rate under cyclic loading. Plastic deformation develops quite rapidly when \(P_{d}\) = 300 kPa. Actually, the deformation rate remains larger than 5 mm per 10,000 loading times at initial loading stage. With loading times increasing, although deformation decreases slightly for a while, it still remains larger than 3 mm per 10,000 loading times. Finally, the filling structure breaks down when cyclic loading reaches to 10,000 times. However, plastic deformation rate seems to decrease gradually with increasing loading times when \(P_{d}\)\(\leq\) 250 kPa, as shown in Figure 9. Since the deformation rate corresponding to \(P_{d}\) = 300 kPa is so large that it is not plotted in the figure. Especially, when \(P_{d}\) < 100 kPa, evolutive rate of plastic deformation levels off to a small magnitude when loading times reaches to 100,000 times. This phenomenon demonstrates that plastic deformation will finally become steady under low amplitude of cyclic loading. More importantly, deformation rate almost reduces to zero at first 10,000 loading times when \(P_{d}\) = 50 kPa. Therefore, the lower amplitude of cyclic loading, the larger rate of convergence for plastic deformation. On the condition of \(P_{d}\) = 200 kPa and \(P_{d}\) = 250 kPa, plastic deformation develops continuously in spite of the decreasing deformation rate.