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This paper describes the numerical research that studied the macroscopic mechanical behavior and the microscopic particle movement of gangue with different gradation under different confining condition and loading rate. Two types of compression tests, confined compression tests and triaxial compression tests were simulated using the commercial numerical modeling software PFC 3D . Most of the gangues are irregular convex polyhedron in shape. When under compression, huge contact force can be generated between particles result in interlocking effect. In order to reproduce the interaction between gangues, this research used Clump Template tool in PFC 3D to generate clusters of particles to represent tailing particles. Following observations were made based on numerical modeling result: 1) reasonable particle gradation can significantly improve the anti-deformation capacity and decrease lateral stress coefficient of gangue. 2) In triaxial compression tests, the load bearing capacity of gangue increases with the increase of confining pressure. 3) Distribution of particles axial displacement showed ‘horizontal layering’ feature in confined compression tests, and showed ‘concave layering’ feature in triaxial compression tests. In triaxial compression tests, particles close to the mid-height and the sides of the sample have most significant lateral displacement, forming a triangular zone of significant lateral displacement. It is also found that smaller particles move more actively while the large particles have their own “movement inertia”. 4) With the increase of confining pressure, the number of the contact force chains and the maximum contact force between particles within the sample increases gradually, also the interpenetration degree of the contact force chains gradually increased. Meanwhile, the number of contact force chains and the maximum contact force are comparatively higher by using confined compression condition than the confining pressure at the same stress state. 5) Large size gangue particles play the main role in anti-deformation and transfer of axial stress; the surface contact force of large particles is significantly greater than that of the small particles. 6) Faster loading rate may increase the measured load bearing capacity of the gangue sample under the same confining condition.

The conformality of NURBS surfaces greatly affects the results of rendering and tessellation applications. To improve the conformality of NURBS surfaces, an optimization algorithm using general bilinear transformations is presented in this paper. The conformality energy is first formulated and its numerical approximation is then constructed using the composite simpson's rule. The initial general bilinear transformation is obtained by approximating the conformal mapping of its 3D discretized mesh using a least square method, which is further optimized by the Levenberg-Marquardt method. Examples are given to show the performance of our algorithm for rendering and tessellation applications. We give explicit representations of the general bilinear reparameterized surfaces.A scheme is given to construct the general bilinear reparameterized NURBS surfaces.An optimization method is given to improve the conformality of NURBS surfaces.