# Evaluating Slope Deformation of Earth Dams Due to Earthquake Shaking Using MARS and GMDH Techniques
## 1 Introduction  
In seismic loading, the study of dams' behavior is a necessary and important issue. A wrong study of dams' behavior in these conditions may result in irreversible damages. The first method to obtain the permanent slope deformation in dams was introduced by [PERSON] [1] as the sliding block. This method simply calculates changes of slope in the earthquake conditions. Among the primary and basic assumptions of the sliding block method is considering slide mass as a rigid body as well as the greater magnitude of acceleration arising from the earthquake than the yield acceleration that can result in movement of the mass [2; 3]. This method was later modified and developed by scholars [4; 5]. For example, considering the acceleration of the block response as the input acceleration of the system, [PERSON] and [PERSON] [6] evaluated the value of displacement with modification of the blockmodel. Uncertainty of results between real cases and the suggested method has been discussed as well [7]. Moreover, using the numerical methods, such as finite element and finite difference methods, deformations in the earth slopes were obtained [5,8]. In different works, the main parameters of ground motion were used through which the changes of the slope deformation in different conditions in earth dams were studied [9,10]. [PERSON] and [PERSON] [11] have deformations of dams based on the two features of failure acceleration and maximum acceleration irrespective of the vertical section of acceleration during an earthquake. In general, earthquake issues are very complicated in different subjects [3,12]. Furthermore, other important factors, such as the fundamental period of the dam, non-homogeneity, and settlement characteristics, have different impacts on huge structures, such as an earth dam [13]. Many scholars have referred to the high complication of the precise relations of these factors in the study of deformations in the earth dam during an earthquake and have considered it as an important challenge in the geotechnical area [14, 15, 16].  
In recent years, new methods based on soft computing have been used in different engineering analyses considering the ability to solve complicated problems. These methods, in fields of civil engineering and the geotechnical area, have been applied to different issues, such as the dynamic behavior of earth, deformations of earth, tunneling, and laboratory samples of mines [17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67]. There are a few researches concerning the use of soft computing methods in the earth dams' deformations arising from earthquakes. It shows that a new methodology, based on these methods, for earth dams' deformations can be developed and implemented. Therefore, in this study, given the above discussions, two new methods of soft computing, i.e., group method of data handling (GMDH) and multivariate adaptive regression splines (MARS), were implemented to evaluate the slope deformations of earth dams. These models were selected to propose a black box model (GMDH) and mathematical formula (MARS) in predicting slope deformation. In addition, these types of intelligent models have unique features for comparison purposes. To this end, the data of different earthquakes were gathered from around the world. Then, the initial analyses were performed on them. Using the initial analyses, the intelligence models predicted the slope deformations. In the end, new models were compared with the old models. The rest of this paper will continue by giving some information about the case study and data collection. After that, the principles of MARS and GMDH models and their implementation in predicting slope deformation will be given in detail. Finally, the most appreciated model will be selected through the use of some well-known performance indices.