Keywords: railway track spatial variability, finite element method, Monte Carlo simulation, dynamic cone penetration test, track equivalent stiffness, static load.

The influence of the spatial variability of the mechanical properties of the railway track components on the equivalent track stiffness measured between sleepers is studied in this paper. Field results show that the mechanical properties of different soil layers vary randomly along the track therefore a deterministic approach seems not to be the most appropriate approach when dealing with such materials. SNCF has recently made a series of dynamic cone penetrometer tests in order to establish a probabilistic description regarding the cone resistance. Results obtained from a classical line site are used in this paper in order to obtain statistical characteristics for each substructure layer, i.e. fresh and crushed ballast, intermediate layer and supporting soil. Lognormal distribution is the best to fit the data for all layers using the Kolmogorov-Smirnov test. Empirical correlations are used to relate the cone resistance to the Young's Modulus, which depends on the soil nature and amplifies the input data uncertainty. A squared exponential auto-correlation function is considered with different correlation lengths. A random field is obtained using the covariance decomposition and the inverse cumulative distribution function (CDF) method. Discretization is made considering the midpoint method. The track model is a two and a half dimensioanl finite element model with a modified plane-strain approach for the soil. Linear elastic behaviour is considered and static load is applied at the middle of the model as a first approach. Two different soil behaviours are considered in order to assess the influence of the correlation function on the scatter of the model's response. A Monte Carlo scheme is implemented and several simulations are performed for each considered case. Results show that even a large coefficient of variation in the input data leads to a small coefficient of variation on the equivalent track stiffness distribution. Correlation lengths of 1m and 5m are considered and compared to a homogeneous layer. Results show little difference between a homogeneous layer and the 5m case, and smaller correlation length leads to a smaller coefficient of variation of the response. The correlation function has great influence on the equivalent stiffness response, both in terms of the mean and the coefficient of variation values. The correlation length is a key parameter which is not yet well characterized for the railway field. Considering dynamic moving loads and non-linear soil behavior will certainly bring a better comprehension of the railway track response.

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