Railway embankment slopes are exposed to natural hazards such as excess rainfall, floods, earthquakes, and lake water/groundwater level variations. These are generally considered during the design, construction, and maintenance periods of the embankment. In this study, combined laboratory test methods and a computational approach were applied to assess the effect of groundwater level changes on the railway embankment. The Plackett–Burman (PBD), Box–Behnken design response surface methodology (BBD-RSM), and an artificial neural network (ANN) were used to predict the behavior of the embankment soil hydromechanical properties to determine the integrity of the embankment as water level fluctuates under varied seasonal conditions. The results show that the seepage line is concave during the rising water level (RWL) period, and the railway slope’s static stability factor surges and then stabilizes. Further analysis found that the slope’s stability is largely affected by some of the hydromechanical properties of the soil embankment material, such as the internal friction angle (ϕ), soil density (ρs), and cohesion (c). The second-order interaction factors c x s, x s, and s2 also affect the stability factor. It was observed that the four most sensitive parameters under both falling water level (FWL) and RWL conditions are ϕ, ρs, c, and rate of fall/rise in water level (H). The statistical evaluation of the RSM model produced R2 values of 0.99(99) and 0.99, with MREs of 0.01 and 0.24 under both RWL and FWL conditions, respectively, while for ANN, they produced R2 values of 0.99(99) and 0.99(98), with MRE values of 0.02 and 0.21, respectively. This study demonstrates that RSM and ANN performed well under these conditions and enhanced accuracy, efficiency, iterations, trial times, and cost-effectiveness compared to full laboratory experimental procedures.