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The geometric design of a waterway embankment depends on several factors like soil and subsoil properties, loading conditions, geometric constraints, climate & weather conditions, etc. Surface wind velocity (V) and fetch length (F) are two control factors that help to determine the wave height (H) utilizing the Taguchi Factorial design method. A non-linear equation was generated by integrating optimized H with the upstream water pressure (P). In the JAVA environment, a pseudo-code was created to solve the non-linear equation and determine the resulting hydrostatic height (hw) and crest width (b). The calculated hw and b were validated utilizing the Honey-Badger algorithm by initializing all the control factors along with P. The outcomes from the experimental analysis of Taguchi showcase that lower control factors helped to obtain the maximum hw along with b for the embankment. As per Analysis of Variance (ANOVA), maximum V was found to be the most significant control factor influencing the determination of H, hw and b of the earthen embankment. The regression squared (R²) value from the Design of Experiment (DoE) of the Taguchi method was found to be 99.21% which shows that the observed data were well fitted to the developed model for evaluating the contribution of Signal to Noise (S/N) ratio and verify the validity of optimal factor settings through confirmation experiments. The confirmatory test was piloted to check the similarity index between the two methods and the outcomes were found to be nearly similar with an error of 2.62%. [ABSTRACT FROM AUTHOR]