Study on Lifted-up Length of Rail in Modified Winkler Model

Recently, various models have been widely used for analysis and design of the railway tracks. Since the rail is fixed to sleepers by fastening system and then track panel is installed directly on ballast, sub ballast and sub grade layers orderly without any bonding, so the superstructure is just embedded in the ballast and there are no adhesive or stuck layers. Many modeling for the purpose of analysis and design, railway track can be simulated by using linear or non-linear springs to represent the behavior of the rail on substructure. In the engineering society, the Beam on Elastic Foundation is the most well-known technique. Among these modelings and approaches like as Adin.et.al, Scott, Filonenko- Borodich foundation, Pasternak foundation, Reissner foundation, Vlasov and Leontiev approach, because of the simplicity of Winkler Model, this model hase been considered as one of the idealized models. Railway engineers and designers are most interested in choosing this modeling. Since in reality, the soil foundation does not sustain tensile stresses, the stiffness of tensioned springs should be set equal to zero in the Winkler model. In this work, regarding the advantages of simplicity and popularity of Winkler model in various engineering applications, the model has been developed by eliminating the limitations using Tsai and West Mann theory. In the modified Winkler model, the weight of rails and sleepers (self-weight) has been involved in the formulations and the springs in tensions have been disregarded during the calculations. Consequently, new set of beam-deflection differential equations have been written for each tension and compression segment and the closed form solution have been applied. Also sensitivity analysis is performed by using normalized variables. Specifically, it is shown that (i) the contact length is a sensitive function of the beam/rail profile type; (ii) also the non-contact length is depend on the magnitude of the load and that this function may change significantly regarding wheel-set load, (iii) sub grade modulus has a noticeable influence on the contact region consequently lifting-up zone length. Regarding the railway track conditions and traffic load in Iran, a case study presented, in which the length of no contact zone and the length of contact zone in the Winkler, Tsai and West Mann models have been compared. The result of rail deflections in the modified Winkler model shows that the length of no contact zone (2.5 times) and the height of track uplift due to the concentrated load (1.5 times) are greater than those obtained from the Winkler model including self-weight.