Computational homogenization for mechanical properties of sand cobble stratum based on fractal theory

Sandy cobble strata is one of the most commonly encountered engineering geological body. A further research into the stability of ground and underground structure demands for precise modeling of actual formation. In this paper, a meso-scale numerical method for modelling sandy cobble strata is presented, which considers rock blocks and soil matrix as separate constituents. In the approach, the particle size distribution and spatial distribution of rock blocks are two crucial points. For the first point, i.e. the particle size distribution of rocks, the fractal scaling theory is included in particle size distribution description and design. In the log-log plots, 60 sets of particle size distributions of sandy cobble soil in Beijing are examined for fractal behavior. For the second point, i.e. the spatial distribution of rocks, the Monte-Carlo principle is used to generate random spatial distribution of rocks in soil matrix, while the rock shape is assumed to be circular in two dimension, or sphere in three dimension. Based on the compassion of rock volume content between the numerical model and theoretical calculation value, it is validated that the meso-scale method could basically be used to establish the meso model of sandy cobble strata. Then, the present sandy cobble strata model is extended to investigate tunnel excavation in such a formation. Based on the simulation results, the deformation characteristics on transverse section and longitudinal profile are explored respectively, and their variations with fractal dimension or the maximum rock size are discussed subsequently.