Abstract：This paper presents a three-dimensional numerical modeling method associated with actual mesostructures for heterogeneous geomaterials. Firstly，digital image techniques are used to extract two- dimensional material heterogeneity from material surface images. Secondly，the 2D square mesostructures are extrapolated to form 3D cuboidal mesostructures with the assumption that the material surface is a representation of the inner material distribution within a very small depth. Thirdly，an iterative milling and scanning system is set up to remove the material surface layer at a very small depth. The newly exposed surface is scanned to form the new digital representation of material heterogeneity. The milling and scanning process is repeated until the entire specimen can be represented by a series of layers of the cuboidal elements. These one-layer-thick 3D mesostructures are connected in series to form the actual 3D mesostructures. Finally，the 3D mesostructures are incorporated into traditional numerical methods to examine the mechanical behavior and fracture patterns of heterogeneous geomaterials under external loadings. A Hong Kong granite specimen is used to demonstrate the procedure of the 3D mesostructure establishment. The granite heterogeneity consists of three minerals：biotite，quartz and feldspar. A 40×118×10 cuboidal model is established. The actual size of the model is 15.00 mm×44.25 mm×3.56 mm. By adopting the commercial finite difference code FLAC3D，the 3D stress distribution，crack propagation process and failure model of rock under uniaxial compression loadings are simulated. Three homogenous cases and one heterogonous case are studied. The stress distribution and failure patterns associated with the three homogenous cases and a heterogeneous case are different. The load and displacement curves show that the compressive strength of the heterogeneous case is lower than those of the homogenous cases. The numerical results indicate that material heterogeneity can play an important role in the failure behavior as well as fracture patterns of geomaterials under external loading.
