## 2 Methods  
### Background  
Several studies have dealt with the behavior of footings constructed on stabilized sand walls [52; 53; 54; 55; 56; 57; 58; 59; 60; 61; 62; 63; 64; 65; 66; 67; 68; 69; 70]. Some authors are interested in both experimental and theoretical investigations of RS structures. For example, [PERSON] et al. [71] built a few large-scale mini-pier tests using silty gravel as back-fill material, concrete masonry units as facing elements, and woven geotextiles of different tensile strengths and vertical spacing as reinforcement layers. The authors concluded that the performance of the RS mass and its behavior under loading was more dependent on reinforcement spacing than on geotextile strength. [PERSON] [72] carried out large-scale generic soil-geosynthetic composite tests under plane strain conditions. The gravel was used as back-fill material and woven geotextiles of different tensile strengths and vertical spacing were used as reinforcement layers. During the experiments, [PERSON] [72] applied different confining pressures to the two sides of the reinforced soil mass. The author [72] pointed that vertical spacing of the reinforcement had a more significant influence on the performance of the RS mass than its tensile strength. Based on published results [72; 73], it can be concluded that large-scale loading tests are very useful to investigate the real behavior of RS structures, considering their aggregate size and reinforcement spacing [74; 75]. However, it is worth bearing in mind that this kind of investigation also has some disadvantages. [PERSON] et al. [76] paid attention to two major problematic items associated with large-scale RS performance tests. Firstly, these tests require specialized equipment which is not always available. Secondly, a performance test gives results only for a specific case (for a specific RS structure model characterized by an individually selected combination of parameters). Therefore, the test results obtainedcannot be considered representative of other structures--without additional checking--when the geometry and/or materials will be changed. Additionally, it should be noted that this is a very expensive type of research that requires significant funding. Moreover, in some cases, many interesting results can be obtained by limiting activities to small-scale experiments. This is the approach that was used during this research, the results of which are presented in the article. In this study, special attention was paid to the theoretical analysis of the behavior of RS walls under serviceable loading. The main part of this investigation focused on recognizing the scope and character of these deformations. It should be noted that only limited studies concerning this aspect of the behavior of RS structures are presented in the literature. However, the deformation of RS walls is becoming an ever more important design consideration since they are built with increasingly tight tolerances. The deformation performance of these composite structures, which combine the benefits of strong soil and reinforcement, can be influenced by a large number of factors. The most important are the geometrical properties of RS structures, the time-dependent characteristics of the reinforcement, and the main parameters of the soil used as backfill and subgrade/foundation materials. During their professional activities, engineers are interested mainly in accurately predicting two types of deformations of RS structures: horizontal displacements of the RS facing and vertical displacements of the crest (Figure 1). The scope of this paper is limited to the analysis the former. It should be noted that additional information regarding the problems associated with the deformation of RS structures is available from other published articles [50; 77; 78; 79; 80]. There are two general mathematical approaches that can be used to solve the problem. The first one is based on analytical models for the calculation of deformations of RS structures.