# Calculation of Nonlimit Active Earth Pressure against Rigid Retaining Wall Rotating about Base
###### Abstract  
A retaining wall with sandy fill was considered as the research object in order to study the nonlimiting active earth pressure under the rotation about the base (RB mode). [PERSON]'s and [PERSON]'s earth pressure theories are no longer applicable to the above conditions (RB mode and nonlimiting active earth pressure). In order to improve the traditional earth pressure calculation methods ([PERSON] and Coulomb), a calculation method using curvilinear thin layer elements is presented with overall considerations of wall displacement, soil arching effect, and friction angle exertion coefficient to deduce the nonlimit active earth pressure under RB. Additionally, the calculation results were in good agreement with model test data (from [PERSON] and [PERSON]). Moreover, a parametric analysis was carried out. It was revealed that the developed value of the shear strength decreased with the depth, and the active earth pressure distribution curve was linear and nonlinear in the upper and lower halves, respectively. retaining wall; rotation about the base; active earth pressure; curvilinear thin layer elements; nonlimiting state +
Footnote †: journal: Applied  
method for considering the soil arch for improvement. It used the principal stress trace, which simplified the force on the differential elements by the large and small principal stresses. In particular, [PERSON] [15] studied the distribution law of active earth pressure under RB, assuming cases of circular, parabolic, and suspended chain-shaped arches, finding that the shape of the arch had little effect on the earth pressure value. Moreover, [PERSON] [16] calculated the earth pressure of the retaining wall rotating about base under static and seismic conditions. In addition to the novel computing method, [PERSON] [17] found that replacing the backfill with BDMs (building derived materials) could improve the stability of the retaining wall. [PERSON] [18] used finite element and second-order cone programming for limit analysis of lateral earth stress of geosynthetics reinforced support structures. The basic assumption of classical earth pressure theory holds that the backfill is in a limit state. However, the wall displacement is always small and cannot reach the limit state, leaving the soil in a nonlimit state [19]. At present, there are three methods for calculating earth pressure in the nonlimit state. The first method is to directly establish the functional relationship between earth pressure and displacement [20; 21]. Although it has grasped the key point that the earth pressure changes with the soil displacement, it needs to set a number of assumptions. The second method is using thin-layer elements on the basis of [PERSON]'s theory to calculate the nonlimit earth pressure [22]. However, it involves a large number of calculation parameters, and there are few universal solutions. The third method is to replace the strength parameters in the limit state earth pressure theory with the nonlimit state soil strength parameters [23; 24]. Yet, it is difficult to carry out because of the lack of measured data to reveal the relationship between shear strength parameters and displacement function. Therefore, some studies focus on the relationship between displacement and shear strength. [PERSON] [19] believed that the soil failure behind the rotating wall followed the progressive failure mechanism. [PERSON] [25] believed that the developed value of friction angle under the nonlimit state varied linearly with displacement, but the progressive failure mechanism of soil mass was not taken into account. The nonlinear relationship between the friction angle and displacement obtained by [PERSON] [26] was more accurate by using the experimental data with consideration of the progressive failure mechanism. In this study, an analytical solution using curvilinear thin layer elements of nonlimit active earth pressure in the RB of rigid retaining walls with sandy soil was obtained. It is proven that this method has strong reliability.