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Seepage is one of the most challenging issues in some procedures such as design, construction, and operation of embankment or earth fill dams. The purpose of this research is to develop a new solution based on governing equations to solve the seepage problem in an effective way. Therefore, by implementing the equations in the programming environment, more than 24,000 models were designed to be applicable to different conditions. Input data included different parameters such as slopes in upstream and downstream, embankment width, soil permeability coefficient, height, and freeboard. With the use of this big data, a new process was developed to provide simple mathematical models for the seepage rate analysis. The study first used intelligent models to simulate the seepage behavior. Finally, the accuracy of the models was optimized using a new metaheuristic algorithm. This led to the ultimate flexibility of the final model presented as a new solution capable of evaluating different conditions. Finally, using the best model, new mathematical relationships were developed based on this methodology. This new solution can be used as a proper alternative to the governing equations of seepage rate estimation. Another advantage of the proposed model is its high flexibility that can be well applied to engineering design in this field, which was not possible using the initial equations.