# Analysis of Earth Pressure Variation for Partial Displacement of Retaining Wall
## 1 Introduction  
Retaining wall has been widely used in transportation, water conservancy, and construction projects [1]. However, part of the retaining wall might produce differential movement due to the influence of different stiffness of wall, embedding depth, foundation overload, and the constraint of the wall end [2]. According to [PERSON] et al. [3, 4], the displacement pattern of the retaining wall was simplified into three types: translation (T), rotation around the top (RT), and rotation around the base (RB). The movement of the retaining wall can lead to subgrade disasters such as longitudinal cracking, settlements, and slip of embankment, as shown in Figure 1 and further cause serious engineering accidents. In realistic roads, there is usually a part of the retaining wall producing displacement along the longitudinal road. However, previous research has mainly focused on the movement of the entire longitudinal retaining wall [5], which is inconsistent with the reality. The partial moveable wall could heavily affect the adjacent stationary wall, but there are still only a few studies concentrating on the influence of the partial displacement of the retaining wall [6]. Meanwhile, when the partial wall produces displacement, there is usually uneven deformation of the soil behind the retaining wall. As a result, the soil arching effect can be generated [7], which causes the variation of earth pressure behind both the moveable wall and adjacent stationary wall. Changes in earth pressure could cause significant impact on the stability of the wall. Thus, to reveal the relationship between uneven deformation of soil and earth pressure behind the wall, the concept of the soil arching effect was raised [8; 9; 10]. The soil arching effect is widespread in the field of geotechnical engineering. [PERSON] [11] first verified the existence of the soil arching by the trap-door test, and defined it as the phenomenon of stress transformation from the yielding soil to the stationary soil. Then, [PERSON] [12], [PERSON] and [PERSON] [13], and [PERSON] and [PERSON] [14] obtained similar results to [PERSON] by conducting trap-door tests. [PERSON] [15] and [PERSON] [16] revealed the mechanism and influencing factors of soil arching both in sand and clay by considering active and passive displacement modes. [PERSON] et al. [17] found that the soil arch changed with the development of the deformation of the trap-door. On the contrary, it underwent the process of formation-destruction-reformation. As a result, the earth pressure on the trap-door first decreased, then increased until it was stabilized in the end. [PERSON] et al. [18], [PERSON] et al. [19], and [PERSON] et al. [20] also verified this phenomenon. Most of the studies about soil arching have been based on the vertical trap-door test. For the retaining wall, the horizontal soil arching can control the distribution of the lateral load. In order to verify the existence of the lateral soil arching effect, [PERSON] et al. [21], [PERSON] et al. [22], [PERSON] et al. [23], and [PERSON] and [PERSON] [24] did a lot of analysis by adopting theoretical analysis, scaled model experiments, numerical simulation, or field monitoring. [PERSON] and [PERSON] [25] carried out the horizontal arching test in slope and found the load on the gate between piles first decreased and then increased to a steady value with the increasing gate deformation. [PERSON] et al. [26] found that the distribution of earth pressure presented as an inverted-bell curve along the horizontal direction due to soil arching. Similarly, [PERSON] et al. [27] discovered that the lateral soil arching between piles could cause the nonlinear distribution of active earth pressure on sheet pile walls. [PERSON] et al. [28] presented a three-dimensional model of the load sharing ratio based on horizontal soil arching, which could reflect the reduction of the pressure of the surrounding soil and the enlargement of the load exertion on piles. In summary, the earth pressure would be greatly influenced by the lateral soil arching.