The development of vehicle-terrain interaction models to assess the performance of off-road vehicles has been one of the focuses of the terramechanics community. In this context, the inputs and accuracy of the terrain models play a vital role. Given the operation of military and agricultural vehicles on challenging, plastic, and non-linear terrain, the adoption of physics-based terrain modeling allows for advanced understanding, providing an opportunity for high-fidelity results. In particular, the navigation of these vehicles on soft clay has been modeled to a limited extent in the literature. Research majorly employing the total stress framework (i.e., considering the soil and water behavior collectively) has been previously noted. This study addresses the modeling of plastic clayey terrains, using the effective stress framework (i.e., the soil and water behavior are distinctly modeled). A robust FE model is developed to describe the tire-saturated clay (i.e., CL soil) interaction. The clay is modeled using a Drucker-Prager soil model with dilation. To describe the effect of the pore water, the simulation is undrained. The sensitivity analysis of the different soil parameters including the: (a) cohesion, (b) friction angle, (c) dilation angle, and (d) elastic shear modulus to the drawbar pull and tire instantaneous sinkage is studied. The pore water pressure accumulation in the sub-soil due to the plastic volumetric deformations imparted by the tire is investigated. The results highlight the influence of plastic parameters on performance, showing future implications in the development of robust virtual proving grounds.