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 numerical manifold method) that is based on the nonlinear GHB (Generalized Hoek-Brown) failure criterion. To effectively implement the proposed 3D-NSRNMM, two methods are adopted to convert the GHB parameters into the average and instantaneous equivalent MC parameters. With the proposed 3D-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 proposed 3D-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.
•A 3D-NSRNMM that is on the basis of the nonlinear GHB criterion is proposed.•Two methods are adopted to convert GHB parameters into equivalent MC parameters.•Stability analyses of 3D rock slopes are investigated using the 3D-NSRNMM.•Boundary conditions significantly influence the safety factor and failure mode of 3D rock slopes.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPUK, ZAGLJ, ZRSKP
To investigate the stability of a soil-rock-mixture (SRM) slope subjected to sequential excavation, two modifications are made to the numerical manifold method (NMM). One modification is the ...implementation of sequential excavation algorithms including an algorithm to find the excavated manifold elements and an algorithm named as “manifold element birth and death” to remove the excavated manifold elements in the excavation simulation. The other modification is the implementation of an improved shear strength reduction technique to evaluate the stability of a slope, as well as to obtain the factor of safety (FOS). In this technique, apart from the shear strength parameters, the Poisson's ratio υ is also adjusted for the purpose of eliminating the spurious plastic deformation that may happen in the deep areas of the slope. Two criterions including the NC criterion (Non-convergence criterion) and DPZ criterion (The criterion based on the distribution of plastic zones) are used to define the critical equilibrium state of the slope. With the improved NMM, three numerical examples including a homogeneous slope under one step of excavation, a slope under three steps of excavation and a SRM slope under two steps of excavation are solved. The simulation results show that: (1) the improved NMM is able to accurately simulate the excavation process of slopes, and predict the FOSs of slopes; (2) the FOSs based on the NC criterion are usually greater than or equal to those based on the DPZ criterion; (3) it is very difficult to form a slipping surface passing from the toe of the SRM slope to the top of the SRM slope; (4) rock blocks have some positive effects on the stability of a SRM slope.
•The NMM is used to simulate sequential excavation of a soil-rock-mixture (SRM) slope.•The sequential excavation algorithms are proposed to simulate the process of sequential excavation.•An improved shear strength reduction technique is adopted and implemented into the NMM.•Results obtained from NC criterion and DPZ criterion are compared.•The advantages of the NMM in discretization and accuracy are demonstrated.
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•An improved NMM with multiple layers of mathematical cover systems is proposed for the soil-rock-mixture(SRM) slopes.•An improved shear strength reduction technique is adopted and implemented into ...the improved NMM.•The FOSs based on the NC criterion is greater than those based on the DPZ criterion for SRM slopes.•The advantages of the improved NMM in discretization and accuracy are demonstrated.
In order to carry out stability analysis of soil-rock-mixture(SRM) slopes, an improved numerical manifold method (NMM) with multiple layers of mathematical cover systems is proposed. For SRM problems, the computational cost of the improved NMM is smaller than that of the traditional NMM. Besides, an improved shear strength reduction technique(ISSRT) which can eliminate spurious plastic deformation of the slopes is implemented. Based on the improved NMM with multiple layers of mathematical cover systems, the stability of three slopes, namely, a homogeneous slope and two SRM slopes with different contents of rock blocks is analyzed. The numerical results about the three slopes indicate that: 1) the proposed numerical model can obtain the FOS of a slope with high accuracy; 2) the bigger the content of rock blocks, the larger the FOS of the SRM slope will be; 3) due to the existence of rock blocks, the failure mode of a SRM slope is different from that of a homogeneous soil slope.
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•The numerical manifold method (NMM) is further developed to solve 2D rock hydraulic fracturing problems.•A “cubic law” is incorporated into the NMM for modeling fluid flow through fractures.•The ...asymptotic fracture-tip functions are used to enrich the global displacement function space of NMM.•The present results agree well with the existing experimental and analytical results.•The advantages of the NMM in discretization and accuracy are demonstrated.
Recent attempts to solve rock mechanics problems using the numerical manifold method (NMM) have been regarded as fruitful. In this paper, a coupled hydro-mechanical (HM) model is incorporated into the enriched NMM to simulate fluid driven fracturing in rocks. In this HM model, a “cubic law” is employed to model fluid flow through fractures. Several benchmark problems are investigated to verify the coupled HM model. The simulation results agree well with the analytical and experimental results, indicating that the coupled HM model is able to simulate the hydraulic fracturing process reliably and correctly.
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•A phase field numerical manifold method (PFNMM) is proposed for crack propagation.•The advantages of both the numerical manifold method (NMM) and the phase field method (PFM) are integrated in the ...PFNMM.•The proposed PFNMM is suitable for multiple crack propagation problems.
In the present work, a phase field numerical manifold method (PFNMM) is proposed for crack growth in brittle materials. The advantages of the phase field method (PFM) in modeling crack initiation and crack branching, and those of the numerical manifold method (NMM) in discretizing the computational model are integrated together in the proposed numerical model. The proposed numerical model is very suitable for simulating multiple crack propagation problems. The implementation details of the proposed numerical model are well presented. Several benchmark examples are adopted to validate the proposed numerical approach. The results indicate that the crack propagation topologies and force-displacement curves obtained by the proposed numerical model are in good agreement with others, e.g. Miehe et al. (2010) and Molnar and Gravouil (2017) 3. The convergence of numerical solution from the proposed numerical model is also investigated. The PFNMM deserves a further investigation.
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The phase field method (PFM) by means of regularization fractures has become a promising and popular method for complex crack propagation, especially in geotechnical applications. Attractive as it ...is, a challenge exists for the PFM to obtain explicit representation of cracks and jump displacement field across cracks that are essential and crucial for some applications, e.g., hydraulic fracturing, leakage problems, and contact problems. In the present paper, an algorithm in which the values of phase field are regarded as the indicator to identify crack paths is proposed. Then physical patches are cut by the reconstructed crack paths to obtain explicit cracks and jump displacement field in the context of the numerical manifold method (NMM). The numerical examples investigate that various explicit cracks, including a straight crack, a curve crack, the branching cracks, and the merging cracks, predicted by the proposed method are in good agreement with the literature. Besides, the Sneddon’s example verifies that the discontinuous displacement field across explicit cracks is in line with the closed form solution. The proposed numerical model deserves a further investigation.
•A phase field numerical manifold method (PFNMM) is proposed for various explicit cracks.•Jump displacement field across cracks is obtained by the proposed method.•The explicit cracks can be freely opening and closing.
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An improved numerical manifold method (INMM) with multiple layers of mathematical cover (MC) systems is employed for a sequential excavation analysis of SRM (soil-rock-mixture) slopes. For the ...purpose of obtaining the FOS (factor of safety) of a SRM slope, an enhanced SSRT (shear strength reduction technique) is used in the INMM. Furthermore, two algorithms, i.e., an algorithm to identify the excavated MEs (manifold elements) and an algorithm to remove the excavated MEs, are incorporated into the INMM to study the effects of excavation of the SRM slopes. With the INMM, two examples, including a soil slope and two SRM slopes subjected to sequential excavation construction, are investigated. The simulation results show that 1) the excavation processes, as well as the FOSs of the slopes, can be accurately predicted with the INMM; 2) the higher the content of rock blocks, the larger the FOS of the SRM slope will be; and 3) the FOSs assessed from the INMM are the same as those from the traditional NMM (TNMM), but the memory consumption and computational cost of the INMM are smaller.
•An improved NMM (INMM) is proposed for the sequential excavation analysis of the SRM slopes.•The excavation algorithms are implemented to simulate the sequential excavation processes.•The improved shear strength reduction technique is adopted and implemented into the INMM.•Compared to the traditional NMM, computational cost of the INMM is smaller.•The advantages of the INMM in discretization and accuracy are demonstrated.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPUK, ZAGLJ, ZRSKP
Ga
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-based solar blind avalanche photodetectors exhibit low voltage operation, optical filter-free and monolithic integration of photodetector arrays, and therefore they are promising to be an ...alternative to the bulky and fragile photomultiplier tubes for weak signal detection in deep-ultraviolet region. Here, by deliberate lattice and band engineering, we construct an n-Barrier-n unipolar barrier avalanche photodetector consisting of β-Ga
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/MgO/Nb:SrTiO
heterostructure, in which the enlarged conduction band offsets fortify the reverse breakdown and suppress the dark current while the negligible valance band offsets faciliate minority carrier flow across the heterojunction. The developed devices exhibit record-high avalanche gain up to 5.9 × 10
and detectivity of 2.33 × 10
Jones among the reported wafer-scale grown Ga
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-based photodetectors, which are even comparable to the commercial photomultiplier tubes. These findings provide insights into precise manipulation of band alignment in avalanche photodetectors, and also offer exciting opportunities for further developing high-performance Ga
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-based electronics and optoelectronics.
In regard to geotechnical problems, the numerical manifold method (NMM) has many particular advantages over the finite element method (FEM) in many aspects. In the present paper, a numerical model ...called SRNMM-GPS method is further proposed for slope stability analysis. In the proposed numerical model, a strength-reduction-based NMM (SRNMM) is firstly adopted to predict slope’s safety factor and generalized plastic strain (GPS) field that corresponds to the slope’s limit equilibrium state. Then, a group of useful points locating within the plastic zone of the slope are determined. With these points, an improved version of least square method is adopted to obtain a rational critical slip surface (CSS), which passes through the point with the maximum value of GPS near the toe of the slope. The proposed SRNMM-GPS method is verified with some typical examples. The proposed method deserves further investigation.
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To increase the total power output of the Three Gorges Hydropower Station and generate greater economic benefits, it is necessary to reduce the time required for the water level of the Three Gorges ...Reservoir to drop, i.e., to increase the rate at which the water level drops. A rapid drop in the reservoir water level might result in a significant change in the reservoir bank environment, which can destabilize landslides that extend into the water, reactivate old landslide masses and form new landslide masses in the reservoir region. A typical slope that extends to the water in the Three Gorges Reservoir region was selected for study. We studied the geologic conditions of a selected landslide mass and developed an expression for the hydrodynamic pressure under the effects of groundwater within the slope area and an expression for the normal stress on a sliding surface under the effect of hydrodynamic pressures. In addition, the evolution of the stability of the slope (submerged to various depths) under the effects of the lowering of the reservoir level is investigated based on a strictly global analysis: (a) safety factor decreases about 14% as the reservoir level drops with rate of 0.6m/d and about 16% with rate of 1.2m/d at the fall of reservoir water level 30.0m; (b) an increase in the drawdown rate of the Three Gorges Reservoir from 0.6m/d to 1.2m/d is unfavourable for the stability of the slope that extends into the water, but the extent of the decrease in safety factors resulting from this increase in rate is not significant.
•Expression of the normal stress on sliding surface in condition of hydrodynamic pressures is deduced.•Evolution of the selected slope stability in Three Gorges reservoir is investigated.•Effects of drawdown rates on the stability of the slope are studied in details.
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