High water pressure and seepage are root causes of embankment failure due in peak flood. Likewise improper soil material selection and compaction also decreases shear strength of the earthen embankments. Embankments built with purely cohesive soil have negligible seepage, whereas use of the cohesionless soil as embankment construction material affects variation of factor of safety (FOS) with geometry, friction angle and the pore pressure distribution. Current work aims to develop a chart that will decide the geometry of embankment under critical steady seepage condition. Bishop and Morgenstern’s (1960) method were adopted to develop a non-dimensional parameter between height of embankment (H) to that of assumed vertical slice (h) represented as \(\frac{H}{h}\) by taking pore pressure ratio \(\left({r_{u}} \right)\) , slope angle \(\left(\alpha \right)\) , angle of internal friction \(\left(\emptyset \right)\) and slope stability number (SN) as variables. A MATLAB programming code has been formulated as per for-loop to find out coefficients for non-dimensional parameter \(\left(\frac{H}{h} \right)\) . Three non-dimensional charts have been prepared by taking these parameters and variables. Box-Behnken Design (BBD) of Response Surface Methodology (RSM) was employed to evaluate the effect of \(\emptyset,r_{u}\) , \(\alpha\) , and SN on the non-dimensional parameter. Furthermore, Material Generation Algorithm (MGA) is used to generate a fitness function which helps to predict the best possible values of \(\frac{H}{h}\) . The variables corresponding to the obtained results are analyzed and validated using PLAXIS 2D. It is ascertained that when the pore pressure rises, the embankment’s height maximizes to maintain stability, which modifies its shape.