Soil-rock mixtures(S-RMs) are widely distributed in the nature. The mesoscopic deformation and failure mechanisms as well as the macro-mechanical behaviors of the S-RMs depend largely upon the rate of deformation, water content and particle sizes. In this research, a series of large-scale direct shear tests with different water contents and different grain-size distributions were conducted to study the influence of the aforementioned factors on the mechanical properties of the S-RMs. Due to the effect of the rock blocks' breakage in the S-RMs, the relationship between the shear strength and the vertical stress of S-RM follows a power law instead of a linear one. It is found that there exists a threshold value for the vertical stress during the shearing process,below which the soil strength is mainly determined by the inter-locking of particles and the re-arrangement of meso-structure,and otherwise large-sized rock blocks are gradually broken into smaller fragments, resulting in a decrease in the soil strength.The shear rate can also significantly influence the degree of particle breakage and the meso-structural rearrangement of the SRMs, namely, under low shear rate, the particles of the samples are fully broken resulting in enhanced macro-strength. As a result, the lower the shear rate, the higher the macroscopic strength. So under unsaturated conditions, the water content will affect the strength of the S-RMs by reducing the strength of rock blocks. As the water content increases, the soil strength decreases gradually, and assumes a moderate value when the water content reaches 8%. At the same water content, the soil strength increases with the sizes of large rock blocks. For the occlusion, breakage and structure re-arrangement of the oversized rock blocks inside S-RM, which have a huge influence on the mechanical characteristics of the samples.
In this study, numerical manifold method(NMM) coupled with non-uniform rational B-splines(NURBS) and T-splines in the context of isogeometric analysis is proposed to allow for the treatments of complex geometries and local refinement. Computational formula for a 9-node NMM based on quadratic B-splines is derived. In order to exactly represent some common free-form shapes such as circles, arcs, and ellipsoids, quadratic non-uniform rational B-splines(NURBS) are introduced into NMM. The coordinate transformation based on the basis function of NURBS is established to enable exact integration for the manifold elements containing those shapes. For the case of crack propagation problems where singular fields around crack tips exist, local refinement technique by the application of T-spline discretizations is incorporated into NMM, which facilitates a truly local refinement without extending the entire row of control points. A local refinement strategy for the 4-node mathematical cover mesh based on T-splines and Lagrange interpolation polynomial is proposed. Results from numerical examples show that the 9-node NMM based on NURBS has higher accuracies. The coordinate transformation based on the NURBS basis function improves the accuracy of NMM by exact integration. The local mesh refinement using T-splines reduces the number of degrees of freedom while maintaining calculation accuracy at the same time.
