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The objective of this paper is to develop a foundation model which idealizes a ballasted railway track along with geosynthetic reinforcement considering soft clay as founding soil. The suggested foundation model incorporated various aspects of the behavior of geosynthetic reinforced ballasted track system which become quintessential in field situations. Some of the aspects include time dependent behavior of soft subgrade, compressibility of ballast and sub-ballast layers and predicting settlement at desired instants of time. The model uses a rough stretched elastic membrane to idealize the behavior of the geosynthetic layer. The burger model has been used to characterize the soft viscoelastic subgrade. Numerical solutions have been obtained by adopting the finite difference method combined with non-dimensionalizing the governing equations of the proposed model. It was observed that at a wheel load of 250 tonnes, there is a reduction of 4.9% in the settlement of the reinforced system when compared with the settlement values of the unreinforced system. The reduction in the settlement is due to the mobilized tensile load of geosynthetic provided in between ballast and sub-ballast layers. This study reveals that the geosynthetic reinforcement can play a major role in reducing the track settlements and thereby improving the current unreinforced ballasted railway tracks by increasing their efficiency.