Abstract—The design of a gravity dam is performed through an interactive process involving a preliminary layout of the structure followed by a stability and stress analysis. This study presents a method to define the optimal top width of gravity dam with genetic algorithm. To solve the optimization task (minimize the cost of the dam), an optimization routine based on genetic algorithms (GAs) was implemented into an Excel spreadsheet. It was found to perform well and GA parameters were optimized in a parametric study. Using the parameters found in the parametric study, the top width of gravity dam optimization was performed and compared to a gradient-based optimization method (classic method). The accuracy of the results was within close proximity. In optimum dam cross section, the ratio of is dam base to dam height is almost equal to 0.85, and ratio of dam top width to dam height is almost equal to 0.13. The computerized methodology may provide the help for computation of the optimal top width for a wide range of height of a gravity dam. Keywords—Chromosomes, dam, genetic algorithm, global optimum, preliminary layout, stress analysis, theoretical profile. I. INTRODUCTION ASICALLY, gravity dams are solid concrete structures that maintain their stability against design loads from the geometric shape and the mass and strength of the concrete. Generally, they are constructed on a straight axis, but may be slightly curved or angled to accommodate the specific site conditions. Gravity dams typically consist of a nonoverflow section(s) and an overflow section or spillway. The two general concrete construction methods for concrete gravity dams are conventional placed mass concrete and RCC. Dam profiles consist of nonoverflow and overflow section. The configuration of the nonoverflow section is usually determined by finding the optimum cross section that meets the stability and stress criteria for each of the loading conditions. The design cross section is generally established at the maximum height section and then used along the rest of the nonoverflow dam to provide a smooth profile. The upstream face is generally vertical, but may include a batter/fillet to increase sliding stability or in existing projects provided to meet prior stability criteria for construction requiring the resultant to fall within the middle third of the base. The downstream face will usually be a uniform slope transitioning to a vertical face near the crest. Based on U.S. Army Corps of Engineers [1], the slope will usually be in the range of 0.7H-1V and 0.8H-1V, depending on uplift and the seismic zone, to meet the stability requirements. Two basic loading conditions are used in gravity dam design. Loadings that are not indicated should be included where applicable [2]: F. Salmasi is with the water engineering department, faculty of agriculture, Tabriz university, Tabriz, IRAN (e-mail: Salmasi@Tabrizu.ac.ir). • Load condition No. 1: unusual loading condition- construction - Dam structure completed - No headwater or tailwater • Load condition No. 2: usual loading condition normal operating - Pool elevation at top of closed spillway gates where spillway is gated and at spillway crest where spillway is ungated - Minimum tailwater - Uplift - Ice and silt pressure, if applicable The procedure of the design of a solid gravity dam involves the determination of theoretical profile initially and then the modification from practical point of view. The basic modifications required in the theoretical profile are: • The sufficient freeboard is provided to avoid over flow from the dam. The requirement of free board is decided from the wave action created at the water surface. The minimum free board should be provided as 0.9 m. The sufficient top width is provided which is required for the provision of road above the dam for inspection purposes.Due to above provisions, extra material is required at the top of the dam, which results in shifting of resultant towards the heel in reservoir empty condition and chances of development of tension at the toe. To avoid this tension, base width of the dam is increased at the upstream side and upstream batter is provided. Hence material is increased on the upstream side of the dam.In reservoir full condition, the resultant remains in middle third portion due to provision of top width and the section remains quite safe, hence the material from the downstream side may be removed to bring resultant in the outer middle third point.The material required in modification of theoretical profile consists of the material required at the top plus the material required at the upstream bottom minus material removed from downstream side. The net material required is a function of top width. Hence a particular top width is to be decided for which the net material required is the minimum. This top width is known as the optimal top width [3]. Creager [4] had proposed that the economical top width of gravity dam can be adopted as 14% of height of the dam. He had not considered earthquake forces. Several researchers have studied genetic algorithm in engineering application. In the study of Sarabian and Lee [5], Non- oriented case of Two-Dimensional Rectangular Bin Packing Problem (2DRBPP) was investigated. The objective of this problem was to pack a given set of small rectangles, which may be rotated by 90°, without overlaps into a minimum numbers of identical large rectangles. Aim was to improve the performance of the MultiCrossover Genetic Algorithm (MXGA) proposed from the literature for solving the problem. Rayner [6], proposed a genetic semi-supervised clustering technique as a means of aggregating data stored in Farzin Salmasi Design of Gravity Dam by Genetic Algorithms B International Journal of Civil and Environmental Engineering 3:3 2011 187