# Stability of Reinforced Retaining Wall under Seismic Loads
## 1 Introduction  
The reinforced retaining wall is a composite structure widely adopted in seismic regions due to its excellent deformation characteristics under seismic loads, such as earthquakes, owing to the friction between the reinforcement and the soil [1; 2; 3; 4; 5; 6; 7; 8; 9; 10]. [PERSON] [11] proposed the Mononobe-Okabe method, which has been applied in analyzing the stability of reinforced retaining walls under dynamic loads [12]. [PERSON] and [PERSON] [13] studied the propagation of the shear wave in the backfill of a retaining wall by the pseudodynamic method and validated the analysis by centrifuge tests. Based on the pseudostatic method, [PERSON] [14] and [PERSON] [15] investigated the vertical seismic response of reinforced soil structures under earthquake conditions. [PERSON] et al. [16] adopted the horizontal slice method (HSM) to analyze the stability of reinforced soil structures subjected to seismic loads. [PERSON] and [PERSON] [17] used the pseudostatic method to calculate the active earth pressure behind a retaining wall under seismic load. The slip surface of the reinforced retaining wall was also detected by vibration table tests [18; 19], and it was found that the slip surface was like a log spiral. However, the mechanism of collaboration between reinforcement and soil remains unclear. Calculation of the tensile force of the reinforcement is still far from being fully understood and established [20; 21]. Based on HSM and log spiral slip surface [16; 22; 23], the collaborative work of reinforcement and soils is considered in this study to establish a method of analyzing the stability of a reinforced retaining wall under seismic loads. Calculation of the tensile force of the reinforcement is carried out by considering the influence of soil parameters and loading conditions [24; 25]. The slice method is proposed to determine the critical failure angle of the backfill wedge under complex conditions, and an iterativecalculation method is presented to determine the tension crack depth of the active earth pressure under seismic loads [26; 27]. The axial stress of the anchor is greatly increased by seismic excitation, and the increment is mainly induced within the excitation period of great acceleration amplitude, evaluation of the effect of earthquake frequency content on seismic behavior of cantilever retaining wall including soil-structure interaction [28; 29]. By taking the failure surface as a plane, the analytical expression for the critical angle of the failure surface, earthquake-induced displacements of gravity retaining walls and anchor-reinforced slopes are also derived [30; 31].  
A critical review of literature shows that a very few studies have been reported for the stability analysis of a reinforced retaining wall. The present paper extends the latter work by developing a number of formulations, including a pseudostatic method of analysis. The formulations are described and compared with other published methods used for the seismic analysis of reinforced soil structures. However, no study seems to be available to quantify the effect of seismic acceleration coefficients and soil and reinforcing structure on the stability of reinforced soil walls. In view of this observation, the present study is directed to conduct a seismic stability analysis of the reinforced retaining wall using the HSM and considering the pseudo static forces. The limit equilibrium equation of a reinforced retaining wall under seismic loads is established, and the formula for calculating the tensile force in reinforcement is proposed to address the stability of reinforced retaining wall. In the end, the parametric study has been carried out to investigate the effect of various parameters like reinforcing structure, angle of internal friction and cohesion of soil, horizontal seismic loading.