## 1 Introduction  
Several theories of lateral earth pressure acting on retaining walls and based on the classical theories of [PERSON] [1] and [PERSON] [2] are currently used. [PERSON]'s theory [1], taking into account the friction at the wall-soil interface, is considered a more realistic model than [PERSON]'s theory [2]. However, [PERSON] did not cover the passive earth pressure, but later, [PERSON]'s theory was used by others to develop a formula for the passive earth pressure [3]. [PERSON] [4] incorporated the cohesion factor of cohesive soils in the computations of lateral earth pressure. [PERSON] and [PERSON] [5] developed a presumptive and conservative earth pressure model using the soil classification and the observed performance of real walls. However, for the stability of walls, [PERSON] et al. [6] indicated that the exact distribution of earth pressure at the lower portion of a retaining wall is not easily determined due to the presence of passive earth pressure in front of the wall and, if any wall rotation, at the wall back. According to the classification of earth-retaining structures by [PERSON] and [PERSON] [7], a pile-wall is considered to act as an in situ, cantilevered wall of an externally stabilized system, and based on Coduto [3], the pile-wall depends on its flexural stiffness and embedment length to resist the lateral earth pressure without any additional supports. [PERSON] et al. [6] indicated that the embedment length of a cantilevered wall is considered critical for wall design and concluded that the soil type, retained soil height, and loading configuration have significant impact on wall behavior. [PERSON] [8] and [PERSON] [9] described an alternative conventional method to calculate the embedment length of a cantilevered wall. This conventional method simplifies the active and passive earth pressures acting on a wall to net pressures with the equilibrium of moments and forces. For practical use, a conservative factor of safety is applied with this approach to either reduce the coefficient of passive earth pressure or increase the embedment length of the wall. [PERSON] [3] suggested that a pile is deemed to be long when its embedment length is greater than 35 times its diameter or width. For the inter-dependent effects between a pile-wall and a sloped backfill, [PERSON] [10] pointed out that the lateral pressure acting on the piles depends on factors, such as pile lateral capacity, pile flexural deformation, and the relative displacement between pile and soil. [PERSON] et al. [11] observed that the lateral earth pressure behind a retaining structure is non-linearly or curved distributed due to the soil arching phenomena caused by the large displacement of the retaining structure. By the classical theories and for a cohesionless backfill soil, the resultant force of lateral earth pressure acts at the lower one-third point of the embedded part of a retaining structure due to the assumption of linearly distributed earth pressure. In contrast to the results predicted by the classical theories, [PERSON] [12] reported that the resultant force acts at 40% to 45% of the embedded part of a retaining structure from the bottom due to the soil-arching phenomena. As a result of this soil-arching phenomena, the classical solutions are not always conservative. [PERSON] et al. [13] later related the cause of the soil-arching phenomena to the non-homogeneous displacement in soil that causes stress release and particle rearrangement. [PERSON] [3] stated that a retaining structure is significantly influenced by an adjacent surcharge load applied at a distance less than the exposed height of a retaining structure. [PERSON] [14] proposed a solution using the elastic theory of Boussinesq to estimate the lateral pressure induced by an adjacent strip surface load on both flexible and rigid retaining walls. However, [PERSON]'s solution results in greater lateral pressure due to a lack of consideration of soil properties and wall stiffness and movement [14].