The engineering behaviour of ballast is an important factor to determine the stability and safety of railway tracks. This paper examines the stress–strain, shear strength, peak deflection stress and reinforcement strength ratio of different reinforcement materials and reinforcement locations in ballast track bed layers based on large scale static triaxial shear tests. The results show that geogrid and waste tyre reinforcement have a significant effect on the peak deviator stress of railway track bed layers and the stress–strain relationship is strain-hardened. The peak deviator stress and shear strength of geogrid reinforcement are greater under the same conditions compared with waste tyres. The reinforcement of geogrid and waste tires increases the shear strength of the track bed significantly. The more layers of geogrid reinforcement, the more energy is required for the deformation of the track bed. The energy required for deformation is greater in the centre of the waste tyre than in the other reinforced forms, and the energy required for deformation is minimal in the fully reinforced form. Excessive tyre reinforcement changes the stiffness of the track bed layer, leading to an increase in the settlement rate. The reinforcement strength ratio between geogrid and waste tyre increases significantly with the increasing of the confining pressure and reinforcement layers. Moreover, the reinforcement strength ratio of the geogrid is significantly higher than that of the waste tyre.

Applying random field theory involves two important issues: the statistical homogeneity (or stationarity) and determination of random field parameters and correlation function. However, the profiles of soil properties are typically assumed to be statistically homogeneous or stationary without rigorous statistical verification. It is also a challenging task to simultaneously determine random field parameters and the correlation function due to a limited amount of direct test data and various uncertainties (e.g., transformation uncertainties) arising during site investigation. This paper presents Bayesian approaches for probabilistic characterization of undrained shear strength using cone penetration test (CPT) data and prior information. Homogeneous soil units are first identified using CPT data and subsequently assessed for weak stationarity by the modified Bartlett test to reject the null hypothesis of stationarity. Then, Bayesian approaches are developed to determine the random field parameters and simultaneously select the most probable correlation function among a pool of candidate correlation functions within the identified statistically homogeneous layers. The proposed approaches are illustrated using CPT data at a clay site in Shanghai, China. It is shown that Bayesian approaches provide a rational tool for proper determination of random field model for probabilistic characterization of undrained shear strength with consideration of transformation uncertainty.

Determination of scale of fluctuation (SOF) is a necessary prerequisite for describing the inherent spatial variability (ISV) of design soil properties (i.e., effective friction angle φ’) using a stationary random field in geotechnical reliability analysis. It is very important to select an appropriate method to enable an accurate estimate of SOF. However, it has been a challenging task due to the fact that the true SOF is actually unknown. In addition, when the number of direct test data of design soil properties are too limited to generate meaningful statistics, the design soil properties are indirectly estimated through transformation models which involve transformation uncertainty. This paper investigates the validity and accuracy of three commonly-used calculation methods (e.g., Bayesian approaches, mean average method, and fitting sample autocorrelation function (ACF) method) for estimating SOF of φ’ using indirect cone penetration test (CPT) data. It is found that Bayesian approaches provide more accurate estimates of λ of φ’ because it takes the transformation uncertainty from empirical regression models into reasonable consideration. The mean average method and fitting sample ACF method underestimate λ of φ’.