The three-dimensional numericalmanifoldmethod(3dNMM) method is further enriched to simulate wave propagation across homogeneous/jointed rock masses. For the purpose of minimizing negative effects from artificial bou...
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The three-dimensional numericalmanifoldmethod(3dNMM) method is further enriched to simulate wave propagation across homogeneous/jointed rock masses. For the purpose of minimizing negative effects from artificial boundaries, a viscous nonreflecting boundary, which can effectively absorb the energy of a wave, is firstly adopted to enrich 3dNMM. Then, to simulate the elastic recovery property of an infinite problem domain, a viscoelastic boundary, which is developed from the viscous nonreflecting boundary, is further adopted to enrich 3dNMM. Finally, to eliminate the noise caused by scattered waves, a force input method which can input the incident wave correctly is incorporated into 3dNMM. Five typical numerical tests on P/S-wave propagation across jointed/homogeneous rock masses are conducted to validate the enriched3dNMM. numerical results indicate that wave propagation problems within homogeneous and jointed rock masses can be correctly and reliably modeled with the enriched3dNMM.
A 3d stability analysis is essential in slope designs, since it is more in line with real situation, and can provide more reasonable results than a 2d analysis. A numerical model termed as ISR3dNMM-GPS method is propo...
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A 3d stability analysis is essential in slope designs, since it is more in line with real situation, and can provide more reasonable results than a 2d analysis. A numerical model termed as ISR3dNMM-GPS method is proposed for factor-of-safety (FOS) calculation and3d failure surface (or critical slip surface) determination involved in a 3d slope stability analysis. In the proposednumerical model, an improved strength reduction technique (ISRT) which can avoid unreasonable plastic zones appearing in the deep area of a slope is implemented into the 3d numerical manifold method (3dNMM), and an improved strength-reduction-based3dNMM (ISR3dNMM) is developed. With the proposed ISR3dNMM, the FOS and generalized plastic strain (GPS) field corresponding to slope's failure state can be obtained simultaneously. Then, a group of useful 3d points locating within the plastic zone of the slope are further determined based on the 3d slope's GPS field. With these 3d points, an improved least square method is adopted to obtain a rational 3d failure surface, which passes through the slope's weakest point. With the proposed ISR3dNMM-GPS method, the stability of two typical 3d slopes are analyzed. The numerical results indicate that 3d slopes' stability can be effectively analyzed with the proposednumerical model. The proposednumerical model deserves further investigation.
due to rock masses' nonlinear failure property, it is inappropriate to investigate the stability of rock slopes using the traditional SRM (strength reduction method) which is based on the linear MC (Mohr-Coulomb) ...
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due to rock masses' nonlinear failure property, it is inappropriate to investigate the stability of rock slopes using the traditional SRM (strength reduction method) which is based on the linear MC (Mohr-Coulomb) failure criterion. To conduct 3d analysis (three dimensional) of rock slopes, we propose a 3d-NSRNMM (3d nonlinear strength reduction numericalmanifoldmethod) that is based on the nonlinear GHB (Generalized Hoek-Brown) failure criterion. To effectively implement the proposed3d-NSRNMM, two methods are adopted to convert the GHB parameters into the average and instantaneous equivalent MC parameters. With the proposed3d-NSRNMM, the influences of different types of equivalent MC parameters, and boundary conditions on rock slopes' stability are investigated. The numerical results assessed from the proposed3d-NSRNMM indicate that: 1) boundary conditions will significantly influence the safety factor and failure mode of a rock slope obtained from 3d analysis;2) the safety factor from two-dimensional analysis is more conservative compared with 3d analysis;3) Furthermore, safety factors based on the instantaneous equivalent MC parameters are very close to those based on the average equivalent MC parameters, but 3d rock slopes' failure modes based on the two different types of equivalent MC parameters are a little different from each other.
numericalmanifoldmethod (NMM) has gained widespread application in engineering practice due to its capacity to effectively address both continuous anddiscontinuous problems in a unified framework. With the advancem...
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numericalmanifoldmethod (NMM) has gained widespread application in engineering practice due to its capacity to effectively address both continuous anddiscontinuous problems in a unified framework. With the advancement of 3d-NMM, there remains a deficiency in ready-made preprocessing tools. Hence, the generation of 3dmanifold elements (MEs) is the primary prerequisite for 3d-NMM. In this study, a parallel algorithm to generate the MEs is proposed. Firstly, a novel 3d block identification algorithm is developed to improve the modeling efficiency. Then, 3d joint networks are simulated using the geological statistical results. Thirdly, the mathematical cover system is constructed using uniformly regular hexahedral meshes. Subsequently, the physical domain is cut using the Boolean algorithm to generate the relatedmanifold blocks (MBs) and the Union -Find algorithm is used to determine the relationship of MBs with mathematical patches (MPs) and physical patches (PPs). The proposed program incorporates the OpenMP parallel library for CPU parallelization to enhance its efficiency and the OpenGL library is used to build a real-time visualization program. Finally, the proposed program is validated using several representative examples, and the obtained results demonstrate its efficient capability in generating MEs.
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