## 1 Introduction  
Achievement of the stability of an excavation is the main design objective in order to avoid failure. In such a case, soldier piles are frequently used to support structures in geotechnical engineering applications that are constructed to resist lateral earth pressures caused by vertical excavation works or to restrain the movement of inclined ground. The ease and speed of construction works of soldier piles increase their preferability, and no advanced exclusive techniques are required for structuring [1]. In the design process of all retaining structures, it is a basic application to determine the lateral earth pressures that are affecting as active and passive for the acquirement of resisting and destabilizing forces. It will be proper to say that the active lateral earth pressure is the major effective force that is leading the structure to fail. The passive lateral earth pressure can be defined as the resisting force to failure occurrence. These lateral pressures and their distribution through the depth can be changed depending on the nature of the surrounding soil profile and environmental conditions [2]. Therefore, it is necessary to obtain the soil characterization of the site and to predict the geotechnical propertiesof related soil layers accurately to acquire a stable system and sustainable usage life. Following in the development process of lateral earth pressure theories; several theoretical, experimental, and empirical studies are conducted to determine the generation of lateral pressures through the pile depth depending on the soil properties, depth of excavation, and environmental conditions [3; 4; 5; 6; 7]. In most of these studies, the limit equilibrium method is selected as a premise prediction tool to design soldier pile retaining walls [8; 9; 10; 11; 12; 13], and it is typically proposed that the stability of cantilever soldier piles can be supplied outermost approximately within 4-8 m excavations [14; 15]. Deeper excavation works commonly necessitate external supports such as wales and struts [6]. Nevertheless, strutted excavations seems not to be an economical solution when an open-cut excavation is done that is necessitated for a large area. At this stage, the installation and cancellation works are conducted for struts, while the construction process reduces the construction efficiency [5]. Thus, if circumstances allow, it is mostly preferred to solve lateral earth pressure problems with the use of cantilever soldier piles. Although there are differences between their structures, soldier pile retaining walls are sometimes being designed similar to sheet pile walls [4; 5; 16; 17]. It is supposed as a sheet pile wall to ensure both force and moment equilibrium concurrently with the use of two equations. These equations when coupled can be written with the functions of the embedment depth and the location of the pivot point where it is assumed that the wall rotates under the effect of unbalanced forces [2; 16]. In addition to this mentioned method, another perspective is presented in the related literature. The soldier piles can be assumed to behave similar to beams on elastic soil, and the piles are considered to locate tangent [5; 18; 19; 20; 21; 22]. However, it has to be noted that all these mentioned methods can give conservative results by not considering the deformation profile of the soil, which is playing a key role both in design and sustainable usage term. Recently, according to the ignorance of deformation determination, advanced methods based on new computer technologies are preferred to be used at the geotechnical design stage to enable faster and more accurate results [1; 23; 24; 25; 26; 27]. From this point of view, most of the geotechnical engineering software that are used to model the cantilever soldier piles only depends on the calculation of lateral balance through the wall system according to the defined cross-sections.