# Analysis of Earth Pressure Variation for Partial Displacement of Retaining Wall
## 3 Results and Discussion
### Variation of Horizontal Earth Pressure with the Displacement of Trap-Door  
To explore the variation pattern of horizontal earth pressure with the distance of the trap-door under different movement modes, the earth pressure on the moveable plate with a width of 10 cm was selected for analysis. To be convenient, the horizontal earth pressure acting on the trap-door was marked as \(\sigma_{h}\). And the height of the load cell on the trap-door above the bottom was marked as \(h\) (see Figure 3).  
The variation of the horizontal soil pressure at different heights versus displacement in three modes is shown in Figure 14. According to [PERSON] and [PERSON] [4] and [PERSON] [30], the earth pressure behind the rigid wall might reach its minimum at the active displacement of about 0.1-0.2% \(H\), which means that the soil reached a limited state. However, it is clear from Figure 14 that the lateral soil pressure did not remain at a stable value in the soil limited state, but increased to a larger value for the displacement overpassing 0.1-0.2% \(H\). The variation of total earth pressure could be divided into three stages:  
Stage I: Reduction stage of earth pressure behind the moveable plate. For any movement mode, the earth pressure behind the trap-door is reduced from the static pressure to the active pressure in this stage. As shown in Figure 14, the lateral soil pressure reached the minimal value when the displacement of the trap-door was about 0.1-0.2% \(H\) in the three modes. The limited displacement obtained from the test was similar to [PERSON] [4] and [PERSON] [30].  
Figure 14: Variation of active earth pressure behind the moveable plate with the movement of moveable plates in three modes: (**a**) T mode, (**b**) RB mode, (**c**) RT mode.  
Stage II: Increasing stage of earth pressure behind the moveable plate. Unlike the classical earth pressure theory, the earth pressure would rise sharply with the movement of plates instead of maintaining a stable state. Furthermore, the pressure peak in the three modes was lower than the static soil pressure.  
Stage III: Stable stage of earth pressure behind the moveable plate. During this stage, the earth pressure converges to a stable state. The present tendency was in good agreement with those given by [PERSON] [20], and [PERSON] and [PERSON] [25]. It should be mentioned that the maximum stable pressure in RT mode was located at the middle height of the wall. Because the displacement was larger in the lower location in RT mode, the earth pressure would decrease more at the bottom part of the wall. However, the lower location corresponded to a larger gravity, therefore the stable earth pressure eventually emerged in the middle of the trap-door.  
Similar to that in the vertical trap-door experiment, the above phenomenon of pressure variation could be explained by the theory of soil arching evolution [17; 18; 19], as shown in Figure 15. When the displacement of the trap-door was small, the initial soil arch formed and the earth pressure decreased to a minimum. At this time, the soil mass reached the active limit equilibrium state and the soil arching effect was fully exerted. After that, with the increasing displacement of the trap-door, the slide plane gradually extended to the interior of the soil. Then, the initial soil arch was destroyed and the earth pressure increased. Finally, a stable soil arch was formed again in the soil and the earth pressure gradually decreased to a stable value. Particularly, in addition, to the horizontal displacement of the soil, there was also an impact caused by gravity and different displacement modes, therefore the strength of the soil arching at various heights was disparate.