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"Bottom friction"
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Experimental evaluation of gentle anti-dip slope deformation and fracture network under the action of underground mining
To gain a deep understanding of the interaction between underground mining and mountain deformation, based on historical deformation and the UAV video, we analyzed the evolution process of deformation and failure in detail and comprehensively evaluated the slope deformation and fracture network under the action of underground mining via the bottom friction physical simulation test, DPDM technology, fractal theory, and percolation theory. We simulated the whole process of mining, deformation, and failure of the Pusa collapse. DPDM technology was employed to obtain the evolution process of the total displacement, maximum shear strain (γmax), and volumetric strain εv of the Pusa collapse and establish a relationship between the fractal dimension and settlement. Simultaneously, the fractal dimension, fracture number, fracture rate, and percolation probability of the fracture network were calculated in MATLAB software. The research results of the bottom friction physical simulation test and DPDM technology indicated that after the M10 coal seam was mined, the maximum total displacement and maximum shear strain γmax were mainly located in the direct roof, resulting in volume expansion due to the direct roof collapse. After the M14 coal seam was mined, the maximum total displacement and volume strain εv developed towards the slope top, and the maximum shear strain was located in the middle and lower parts of the model surface and the leading and trailing edges of the slope top, respectively. The research results of fractal dimension and percolation probability indicated that after the M10 coal seam was mined, the development form of the fracture network at this stage mainly entailed the formation of new fractures. After the M14 coal seam was mined, the fracture network developed from beyond this stage mainly included fracture expansion and opening. The test results are consistent with the historical change process and the UAV video showing the method and signs of deformation. These research results help to better explain the deformation evolution process of a given slope under the action of underground mining and provide a technical reference for accurate assessment and proper mitigation of similar landslide disasters.
Journal Article
Modeling Wave Energy Dissipation by Bottom Friction on Rocky Shores
Rocky shores are characterized by rough, multi-scale bathymetric variations that result in enhanced wave energy dissipation by bottom friction compared to sandy beaches. Realistic SWAN simulations of surface gravity waves across the rocky shores of Monterey (CA, USA) are conducted, and model results are compared to 20 inner-shelf observational sites spanning 34–5 m water depth. The wave field was highly variable during the study, including alternately low energy waves dominated by southern swell and higher energy local waves aligned with strong north-westerly winds. Including a modified bottom friction parameterization is required for the model to reproduce bulk wave statistics with high skill across the entire inner shelf. The SWAN simulation with the default bottom friction parameterization overestimates significant wave height relative to observations because the friction factor fe parameterization has a maximum value of 0.3. Additional simulations included two empirical formulations relating fe to the normalized wave excursion Ab/kN in the large roughness regime Ab/kN<1. Both simulations incorporate a higher fe that is required to model strong bottom friction dissipation over rocky seabeds. The higher friction factors, with 80% falling within the range 0.43 to 5.38, are associated with variability in the normalized orbital excursion within 0.1
Journal Article
Deformation and Failure Mechanism of Bedding Slopes Induced by Underground Mining: Case Study from Yanwan Village, Guizhou Province, China
The deformation and instability disasters of mining slopes in the Southwest China mountainous area are frequent. Moreover, geological disasters are characterized by large-scale, strong destructiveness and complex failure modes. To research the collapse in Yanwan Village, Qingzhen City, Guizhou Province, the deformation and failure process of the slope is physically simulated by a bottom friction test. Digital photographic deformation measurement technology is used to monitor the displacement change of the slope. The results show that in addition to the unloading fissures formed by the stream trenching, which affects the stability of the slope, the mining of underground coal seams is the main factor leading to the deformation and failure of the slope. After underground mining, the overlying rock in the goaf first subsides and deforms, so that the stress is readjusted, and tensile stress is concentrated at the top of the slope, and finally a tensile crack is formed. At the same time, the stress above the goaf is distributed in an arched shape, and a horizontal stress concentration zone is formed. The horizontal stress pushes the slope body to move towards the free face, which eventually leads to the collapse of the rock mass at the top of the slope. Therefore, the collapse mechanism of the slope dangerous rock mass under the action of underground mining is cracking-toppling (collapse).
Journal Article
An empirical formula of bottom friction coefficient with a dependence on the current speed for the tidal models
Tides are of great importance for ocean mixing and nearshore ocean engineering. Bottom friction is a major factor in tidal dissipation and is usually parameterized by the bottom friction coefficient (BFC). BFC is a critical parameter in numerical tidal models and is known to vary with time and space, as calculated with measured data. However, it is difficult to accurately adjust the spatially-temporally varying BFC in numerical tidal models. Based on the relationship between the spatially-temporally varying BFC estimated by adjoint data assimilation and the simultaneously simulated current speed, an empirical formula of BFC with a dependence on the current speed is proposed. This new empirical formula of BFC is compared with several traditional empirical formulas, including the constant BFC, the Chezy-Manning BFC, and two depth-dependent BFCs. When the four principal tidal constituents ( M 2 , S 2 , K 1 , and O 1 ) in the Bohai, Yellow and East China Seas (BYECS) are simulated, the mean vector error between the simulated results obtained using the current speed-dependent BFC and the TOPEX/Poseidon satellite altimetry data (the tidal gauge data) is 8.81 cm (10.62 cm), which is decreased by up to 8.1% (18.2%) compared with those using the several commonly used empirical formulas of BFC. Furthermore, in the sensitivity experiments where only the M 2 tide in the BYECS, the M 2 , S 2 , K 1 , and O 1 tides in the Bohai and Yellow Sea (BYS), and the M 2 , S 2 , K 1 , and O 1 tides in the South China Sea (SCS) are simulated, the errors between the simulated results obtained by using current speed-dependent BFC and the tidal gauge data are less than those using the other empirical formulas of BFC, further demonstrating the superiority of the current speed-dependent BFC proposed in this study. From numerical model experiments, the current speed-dependent BFC can adequately reflect the spatial and temporal variations of BFC and improve the simulation accuracy of tides, thus having a broad application scope.
Journal Article
Tide-Surge Interaction in the Pearl River Estuary: A Case Study of Typhoon Hato
In this study, the characteristics and mechanisms of tide-surge interaction in the Pearl River Estuary (PRE) during Typhoon Hato in August 2017 are studied in detail using a 3D nearshore hydrodynamic model. The wind field of Typhoon Hato is firstly reconstructed by merging the Holland parametric tropical cyclone model results with the CFSR reanalysis data, which enables the model to reproduce the pure astronomical tides and storm tides well; especially the distinctive oscillation pattern in the measured water levels due to the passage of the typhoon has been captured. Three different types of model runs are conducted in order to separate the water level variations due to the astronomical tide, storm surge and tide-surge interactions in the Pearl River Estuary. Results show the strong tidal modulation of the surge level, as well as alteration of the phase of surge which also changes the peak storm tidal level, in addition to the tidal modulation effects. In order to numerically assess the contributions of three nonlinear processes in the tide-surge interaction and quantify their relative significance, the widely used ``subtraction\" approach and a new “addition\" approach are tested in this study. The widely used “subtraction'' approach is found unsuitable for the assessment due to the ``rebalance\" effect and thus a new “addition'' approach is proposed along with a new indicator to represent the tide-surge interaction, from which more reasonable results are obtained. Detailed analysis using the ``addition'' approach indicates that the quadratic bottom friction, shallow water effect and nonlinear advective effect play the first, second and third most important roles in the tidal-surge interaction in the estuary, respectively.
Journal Article
Estimation of the Manning’s n coefficient in multi-constituent tidal models by assimilating satellite observations with the adjoint data assimilation
The bottom friction is critical for the dissipation of the global tidal energy. The bottom friction coefficient is traditionally determined using the Manning’s n formulation in tidal models. The Manning’s n coefficient in the Manning’s n formulation is vital for the accurate simulation and prediction of the tide in coastal shallow waters, but it cannot be directly measured and contains large amounts of uncertainties. Based on a two-dimensional multi-constituent tidal model with the adjoint data assimilation, the estimation of the Manning’s n coefficient is investigated by assimilating satellite observations in the Bohai, Yellow and East China Seas with the simulation of four principal tidal constituents M 2 , S 2 , K 1 and O 1 . In the twin experiments, the Manning’s n coefficient is assumed to be constant, and it is estimated by assimilating the synthetic observations at the spatial locations of the satellite tracks. Regardless the inclusion of artificial random observational errors associated with synthetic observations, the model performance is improved as evaluated by the independent synthetic observations. The prescribed ‘real’ Manning’s n coefficient is reasonably estimated, indicating that the adjoint data assimilation is an effective method to estimate the Manning’s n coefficient in multi-constituent tidal models. In the practical experiments, the errors between the independent observations at the tidal gauge stations and the corresponding simulated results of the four principal tidal constituents are substantially decreased under both scenarios of the constant and spatially-temporally varying Manning’s n coefficient estimated by assimilating the satellite observations with the adjoint data assimilation. In addition, the estimated spatial and temporal variation trend is robust and not affected by the model settings. The spatially-temporally varying Manning’s n coefficient is negatively correlated with the current speed and shows significant spatial variation in the shallow water areas. This study demonstrates that the Manning’s n coefficient can be reasonably estimated by the adjoint data assimilation, which allows significant improvement in accurate simulation of the ocean tide.
Journal Article
Influence of flow resistance stresses on debris flow runout
The hydrodynamic modeling of debris flows is challenged by the complicated mechanism of debris flow and the large variability of material composition. Therefore, in the dynamic continuum modeling of debris flows it is essential to select suitable rheological and associated friction parameters. The quadratic rheological model is the most comprehensive approach because it considers the effects of viscous behavior, solid-particle resistance, turbulent properties, and friction characteristics of debris flow. Therefore, this study adopted the quadratic model as the governing flow resistance stress and analyzed the influence of various flow resistance stresses to evaluate the runout performance. The shallow-water equations with modified bottom friction were discretized and the developed model was validated against a dam break flow and a ‘spreading of circular cone’ problem. Then, to investigate the relationship between the flow resistance relations and the bottom shear stresses exerted by the cones and dry bed, the model was applied to runout in a rectangular domain with three cone-shaped obstacles. An actual field runout event that occurred in Korea in 2011 was replicated and the runout paths and flow patterns were analyzed according to the various resistance stresses. By considering both the extremely rapid runout velocity and the striking run-up height, the results obtained by the quadratic stress relation achieved the best performance. However, for the successful application of the quadratic approach, three parameters had to be adjusted with consideration to locality.
Journal Article
An operational improvement of A-4DEnVar and its application to the estimation of the spatially varying bottom friction coefficients of the M2 constituent in the Bohai and Yellow seas
The analytical four-dimensional ensemble variational (A-4DEnVar) data assimilation scheme inherits the advantages of the conventional four-dimensional variational (4D-Var) data assimilation scheme and removes the adjoint model. However, compatible operational improvements such as the reduction of the computational costs and the localization method should be considered when it is used in realistic systems. In this paper, the computational complexity of calculating the inverse of background error covariance (the B matrix) is decreased by a precondition transform method, i.e., introducing a new state variable whose product with the B matrix is the original state variable to be optimized in the cost function. Furthermore, an independent point (IP) scheme is combined to construct an implicit localization method and further decreases the computational cost. Based on the Princeton Ocean Model with the generalized coordinate system (POMgcs), the operational improved A-4DEnVar is applied to optimize the spatially varying bottom friction coefficients (BFCs) of the M 2 constituent in the Bohai and Yellow seas. A twin experiment with idealized observations is designed to validate the effectiveness of the proposed method. In practical experiments, with no more than 10 IPs, the algorithm can assimilate observations from the National Astronomical Observatory (NAO) dataset and obtain a good simulation. The experimental performances increase with the increase of either the IPs or observations, which indicates the efficacy of the proposed algorithm.
Journal Article
3D numerical computation of the tidally induced Lagrangian residual current in an idealized bay
A numerical model that solves 3D first-order Lagrangian residual velocity (uL) equations is established by modifying the HAMSOM model. With this model, uL is studied in a wide, idealized bay. The results show that the vertical eddy viscosity term of Stokes’ drift (π1) in the tidal body force determines the overall flow state of uL, and the contribution of the advection term (π2) is responsible for the small correction. In addition, two types of Coriolis effects introduced into the residual current system not only enhance the lateral flow and break the symmetry of the flow regime in the bay but also slightly correct the flow state driven by the entire tidal body force. It is also found by numerical sensitivity experiments that the increase in the aspect ratio δ, implying a decrease in the topographic gradient, can simplify the residual flow state. The increase in tidal amplitude at the open boundary significantly enhances the intensity of uL and causes the residual flow regime to be more complicated in the bay. This can be ascribed to the disproportionate increase in the tidal body force. The proportion of the vertical eddy viscosity term of Stokes’ drift in the tidal body force also varies with the vertical eddy viscosity coefficient, which leads to different residual current states. Compared with the influence of incoming tidal strength on the residual current, the effect of the bottom friction coefficient on the residual current is relatively mild. An increase in the quadratic bottom friction coefficient induces an unbalanced decrease in the tidal body force. Therefore, uL decreases, but the flow regime is more complex. The influence of the nonlinear effect of the bottom friction decreases from the bay head towards the bay mouth. The residual current only changes in magnitude near the bay mouth but changes in pattern near the bay head for different bottom friction coefficients. By keeping the bottom friction coefficient in the zeroth-order tidal equations constant, the sensitivity experiment shows that uL is insensitive to the change in bottom friction coefficient in the governing equations of uL.
Journal Article
Tsunami Damping due to Bottom Friction Considering Flow Regime Transition and Depth-Limitation in a Boundary Layer
According to recent investigations on bottom boundary layer development under tsunami, a wave boundary can be observed even at the water depth of 10 m, rather than a steady flow type boundary layer. Moreover, it has been surprisingly reported that the tsunami boundary layer remains laminar in the deep-sea area. For this reason, the bottom boundary layer under tsunami experiences two transitional processes during the wave shoaling: (1) flow regime transition in a wave-motion boundary layer from laminar to the turbulent regime, and (2) transition from non-depth-limited (wave boundary layer) to depth-limited boundary layer (steady flow boundary layer). In the present study, the influence of these two transition processes on tsunami wave height damping has been investigated using a wave energy flux model. Moreover, a difference of calculation results by using the conventional steady flow friction coefficient was clarified.
Journal Article