Discontinuity development patterns and the challenges for 3D discrete fracture network modeling on complicated exposed rock surfaces

Natural slopes usually display complicated exposed rock surfaces that are characterized by complex and substantial terrain undulation and ubiquitous undesirable phenomena such as vegetation cover and rockfalls.This study presents a systematic outcrop research of fracture pattern variations in a complicated rock slope,and the qualitative and quantitative study of the complex phenomena impact on threedimensional(3D)discrete fracture network(DFN)modeling.As the studies of the outcrop fracture pattern have been so far focused on local variations,thus,we put forward a statistical analysis of global variations.The entire outcrop is partitioned into several subzones,and the subzone-scale variability of fracture geometric properties is analyzed(including the orientation,the density,and the trace length).The results reveal significant variations in fracture characteristics(such as the concentrative degree,the average orientation,the density,and the trace length)among different subzones.Moreover,the density of fracture sets,which is approximately parallel to the slope surface,exhibits a notably higher value compared to other fracture sets across all subzones.To improve the accuracy of the DFN modeling,the effects of three common phenomena resulting from vegetation and rockfalls are qualitatively analyzed and the corresponding quantitative data processing solutions are proposed.Subsequently,the 3D fracture geometric parameters are determined for different areas of the high-steep rock slope in terms of the subzone dimensions.The results show significant variations in the same set of 3D fracture parameters across different regions with density differing by up to tenfold and mean trace length exhibiting differences of 3e4 times.The study results present precise geological structural information,improve modeling accuracy,and provide practical solutions for addressing complex outcrop issues.

Automatic identification of rock discontinuity and stability analysis of tunnel rock blocks using terrestrial laser scanning

Local geometric information and discontinuity features are key aspects of the analysis of the evolution and failure mechanisms of unstable rock blocks in rock tunnels.This study demonstrates the integration of terrestrial laser scanning(TLS)with distinct element method for rock mass characterization and stability analysis in tunnels.TLS records detailed geometric information of the surrounding rock mass by scanning and collecting the positions of millions of rock surface points without contact.By conducting a fuzzy K-means method,a discontinuity automatic identification algorithm was developed,and a method for obtaining the geometric parameters of discontinuities was proposed.This method permits the user to visually identify each discontinuity and acquire its spatial distribution features(e.g.occurrences,spac-ings,trace lengths)in great detail.Compared with hand mapping in conventional geotechnical surveys,the geometric information of discontinuities obtained by this approach is more accurate and the iden-tification is more efficient.Then,a discrete fracture network with the same statistical characteristics as the actual discontinuities was generated with the distinct element method,and a representative nu-merical model of the jointed surrounding rock mass was established.By means of numerical simulation,potential unstable rock blocks were assessed,and failure mechanisms were analyzed.This method was applied to detection and assessment of unstable rock blocks in the spillway and sand flushing tunnel of the Hongshiyan hydropower project after a collapse.The results show that the noncontact detection of blocks was more labor-saving with lower safety risks compared with manual surveys,and the stability assessment was more reliable since the numerical model built by this method was more consistent with the distribution characteristics of actual joints.This study can provide a reference for geological survey and unstable rock block hazard mitigation in tunnels subjected to complex geology and active rockfalls.

A non-contact measurement method for rock mass discontinuity orientations by smartphone

Smartphones are usually packed with a large number of features.An increasing number of researchers are paying attention to the technological capabilities of smartphones,which is a new topic and research interest.This paper proposes a method using smartphones and digital photogrammetry to measure the discontinuity orientation of a rock mass.Smartphone photos satisfying a certain overlap rate provide an efficient method for generating point cloud models of rock outcrops based on image matching.Using the target and the generated point cloud model allows for determining actual geographic coordinates and the measurement of discontinuity orientations.The method proposed has been applied to two different study areas.The discontinuity orientations measured by the proposed method are compared with those measured by the manual method in two cases.The results show a good agreement,verifying the reliability and accuracy of the proposed method.The main contribution of this paper is to use knowledge of coordinate rotation to determine the actual geographic location of the model through a square target.The equipment used in this study is simple,and photogrammetric field surveys are easy to carry out.

Regression discontinuity design and its applications to Science of Science:A survey

Purpose:With the availability of large-scale scholarly datasets,scientists from various domains hope to understand the underlying mechanisms behind science,forming a vibrant area of inquiry in the emerging“science of science”field.As the results from the science of science often has strong policy implications,understanding the causal relationships between variables becomes prominent.However,the most credible quasi-experimental method among all causal inference methods,and a highly valuable tool in the empirical toolkit,Regression Discontinuity Design(RDD)has not been fully exploited in the field of science of science.In this paper,we provide a systematic survey of the RDD method,and its practical applications in the science of science.Design/methodology/approach:First,we introduce the basic assumptions,mathematical notations,and two types of RDD,i.e.,sharp and fuzzy RDD.Second,we use the Web of Science and the Microsoft Academic Graph datasets to study the evolution and citation patterns of RDD papers.Moreover,we provide a systematic survey of the applications of RDD methodologies in various scientific domains,as well as in the science of science.Finally,we demonstrate a case study to estimate the effect of Head Start Funding Proposals on child mortality.Findings:RDD was almost neglected for 30 years after it was first introduced in 1960.Afterward,scientists used mathematical and economic tools to develop the RDD methodology.After 2010,RDD methods showed strong applications in various domains,including medicine,psychology,political science and environmental science.However,we also notice that the RDD method has not been well developed in science of science research.Research Limitations:This work uses a keyword search to obtain RDD papers,which may neglect some related work.Additionally,our work does not aim to develop rigorous mathematical and technical details of RDD but rather focuses on its intuitions and applications.Practical implications:This work proposes how to use the RDD method in science of science research.Originality/value:This work systematically introduces the RDD,and calls for the awareness of using such a method in the field of science of science.

Topography of the 660-km discontinuity within the Izu-Bonin subduction zone and evidence of slab penetration near the Bonin Super Deep Earthquake(~680 km)

The Izu-Bonin subduction zone in the Northwest Pacific is an ideal location for understanding mantle dynamics such as cold lithosphere subduction. The slab produces a lateral thermal anomaly, inducing local topographic changes at the boundary of a post-spinel phase transformation, considered to be the origin of the ‘660-km discontinuity.’ In this study, the short-period(1–2 Hz) S-to-P conversion phase S660P was used to obtain the fine-scale structure of the discontinuity. More than 100 earthquakes that occurred from the 1980s to the 2020s and were recorded by high-quality seismic arrays in the United States and Europe were analyzed. A discontinuity in the ambient mantle with an average depth of ~670 km was found beneath the 300–400-km event zone in the northern Bonin region near 33°N. Meanwhile, the ‘660-km discontinuity’ has been pushed upward, away from the slab, possibly because of a hot upwelling mantle plume. In the central part of the subduction zone, the 660-km discontinuity is depressed to an average depth of(690 ± 5) km within the slab at approximately 150 km below the coldest slab core, indicating a(300 ± 100) ℃ cold anomaly estimated using a post-spinel transformation Clapeyron slope of(-2.0 ± 1.0) MPa/K. In southern Bonin near 28°N, the discontinuity was found to be further depressed at an average depth of(695 ± 5) km below the deepest event and with a focal depth of ~550 km. The discontinuity is located where the slab bends abruptly to become sub-horizontal toward the west-southwest. Near the zone of the isolated Bonin Super Deep Earthquake, which occurred at ~680 km on May 30,2015, the discontinuity is depressed to ~700 km, suggesting a near-vertical penetrating slab and an S-to-P conversion in the coldest slab core, where a large low-temperature anomaly should exist.

Scale-space effect and scale hybridization in image intelligent recognition of geological discontinuities on rock slopes

Geological discontinuity(GD)plays a pivotal role in determining the catastrophic mechanical failure of jointed rock masses.Accurate and efficient acquisition of GD networks is essential for characterizing and understanding the progressive damage mechanisms of slopes based on monitoring image data.Inspired by recent advances in computer vision,deep learning(DL)models have been widely utilized for image-based fracture identification.The multi-scale characteristics,image resolution and annotation quality of images will cause a scale-space effect(SSE)that makes features indistinguishable from noise,directly affecting the accuracy.However,this effect has not received adequate attention.Herein,we try to address this gap by collecting slope images at various proportional scales and constructing multi-scale datasets using image processing techniques.Next,we quantify the intensity of feature signals using metrics such as peak signal-to-noise ratio(PSNR)and structural similarity(SSIM).Combining these metrics with the scale-space theory,we investigate the influence of the SSE on the differentiation of multi-scale features and the accuracy of recognition.It is found that augmenting the image's detail capacity does not always yield benefits for vision-based recognition models.In light of these observations,we propose a scale hybridization approach based on the diffusion mechanism of scale-space representation.The results show that scale hybridization strengthens the tolerance of multi-scale feature recognition under complex environmental noise interference and significantly enhances the recognition accuracy of GD.It also facilitates the objective understanding,description and analysis of the rock behavior and stability of slopes from the perspective of image data.

Particle Discontinuous Deformation Analysis of Static and Dynamic Crack Propagation in Brittle Material

Crack propagation in brittle material is not only crucial for structural safety evaluation,but also has a wideranging impact on material design,damage assessment,resource extraction,and scientific research.A thorough investigation into the behavior of crack propagation contributes to a better understanding and control of the properties of brittle materials,thereby enhancing the reliability and safety of both materials and structures.As an implicit discrete elementmethod,the Discontinuous Deformation Analysis(DDA)has gained significant attention for its developments and applications in recent years.Among these developments,the particle DDA equipped with the bonded particle model is a powerful tool for predicting the whole process of material from continuity to failure.The primary objective of this research is to develop and utilize the particle DDAtomodel and understand the complex behavior of cracks in brittle materials under both static and dynamic loadings.The particle DDA is applied to several classical crack propagation problems,including the crack branching,compact tensile test,Kalthoff impact experiment,and tensile test of a rectangular plate with a hole.The evolutions of cracks under various stress or geometrical conditions are carefully investigated.The simulated results are compared with the experiments and other numerical results.It is found that the crack propagation patterns,including crack branching and the formation of secondary cracks,can be well reproduced.The results show that the particle DDA is a qualified method for crack propagation problems,providing valuable insights into the fracture mechanism of brittle materials.

THE RIEMANN PROBLEM FOR ISENTROPIC COMPRESSIBLE EULER EQUATIONS WITH DISCONTINUOUS FLUX

We consider the singular Riemann problem for the rectilinear isentropic compressible Euler equations with discontinuous flux,more specifically,for pressureless flow on the left and polytropic flow on the right separated by a discontinuity x=x(t).We prove that this problem admits global Radon measure solutions for all kinds of initial data.The over-compressing condition on the discontinuity x=x(t)is not enough to ensure the uniqueness of the solution.However,there is a unique piecewise smooth solution if one proposes a slip condition on the right-side of the curve x=x(t)+0,in addition to the full adhesion condition on its left-side.As an application,we study a free piston problem with the piston in a tube surrounded initially by uniform pressureless flow and a polytropic gas.In particular,we obtain the existence of a piecewise smooth solution for the motion of the piston between a vacuum and a polytropic gas.This indicates that the singular Riemann problem looks like a control problem in the sense that one could adjust the condition on the discontinuity of the flux to obtain the desired flow field.

Adaptive Sparse Grid Discontinuous Galerkin Method:Review and Software Implementation

This paper reviews the adaptive sparse grid discontinuous Galerkin(aSG-DG)method for computing high dimensional partial differential equations(PDEs)and its software implementation.The C++software package called AdaM-DG,implementing the aSG-DG method,is available on GitHub at https://github.com/JuntaoHuang/adaptive-multiresolution-DG.The package is capable of treating a large class of high dimensional linear and nonlinear PDEs.We review the essential components of the algorithm and the functionality of the software,including the multiwavelets used,assembling of bilinear operators,fast matrix-vector product for data with hierarchical structures.We further demonstrate the performance of the package by reporting the numerical error and the CPU cost for several benchmark tests,including linear transport equations,wave equations,and Hamilton-Jacobi(HJ)equations.

Application of modified discontinuous deformation analysis to dynamic modelling of the Baige landslide in the Jinsha River

Accurate dynamic modeling of landslides could help understand the movement mechanisms and guide disaster mitigation and prevention.Discontinuous deformation analysis(DDA)is an effective approach for investigating landslides.However,DDA fails to accurately capture the degradation in shear strength of rock joints commonly observed in high-speed landslides.In this study,DDA is modified by incorporating simplified joint shear strength degradation.Based on the modified DDA,the kinematics of the Baige landslide that occurred along the Jinsha River in China on 10 October 2018 are reproduced.The violent starting velocity of the landslide is considered explicitly.Three cases with different violent starting velocities are investigated to show their effect on the landslide movement process.Subsequently,the landslide movement process and the final accumulation characteristics are analyzed from multiple perspectives.The results show that the violent starting velocity affects the landslide motion characteristics,which is found to be about 4 m/s in the Baige landslide.The movement process of the Baige landslide involves four stages:initiation,high-speed sliding,impact-climbing,low-speed motion and accumulation.The accumulation states of sliding masses in different zones are different,which essentially corresponds to reality.The research results suggest that the modified DDA is applicable to similar high-level rock landslides.

A Provable Positivity-Preserving Local Discontinuous Galerkin Method for the Viscous and Resistive MHD Equations

In this paper,we construct a high-order discontinuous Galerkin(DG)method which can preserve the positivity of the density and the pressure for the viscous and resistive magnetohydrodynamics(VRMHD).To control the divergence error in the magnetic field,both the local divergence-free basis and the Godunov source term would be employed for the multi-dimensional VRMHD.Rigorous theoretical analyses are presented for one-dimensional and multi-dimensional DG schemes,respectively,showing that the scheme can maintain the positivity-preserving(PP)property under some CFL conditions when combined with the strong-stability-preserving time discretization.Then,general frameworks are established to construct the PP limiter for arbitrary order of accuracy DG schemes.Numerical tests demonstrate the effectiveness of the proposed schemes.

Discontinuation of therapy in inflammatory bowel disease: Current views

The timely introduction and adjustment of the appropriate drug in accordance with previously well-defined treatment goals is the foundation of the approach in the treatment of inflammatory bowel disease(IBD).The therapeutic approach is still evolving in terms of the mechanism of action but also in terms of the possibility of maintaining remission.In patients with achieved long-term remission,the question of de-escalation or discontinuation of therapy arises,considering the possible side effects and economic burden of long-term therapy.For each of the drugs used in IBD(5-aminosalycaltes,immunomodulators,biological drugs,small molecules)there is a risk of relapse.Furthermore,studies show that more than 50%of patients who discontinue therapy will relapse.Based on the findings of large studies and meta-analysis,relapse of disease can be expected in about half of the patients after therapy withdrawal,in case of monotherapy with aminosalicylates,immunomodulators or biological therapy.However,longer relapse-free periods are recorded with withdrawal of medication in patients who had previously been on combination therapies immunomodulators and anti-tumor necrosis factor.It needs to be stressed that randomised clinical trials regarding withdrawal from medications are still lacking.Before making a decision on discontinuation of therapy,it is important to distinguish potential candidates and predictive factors for the possibility of disease relapse.Fecal calprotectin level has currently been identified as the strongest predictive factor for relapse.Several other predictive factors have also been identified,such as:High Crohn's disease activity index or Harvey Bradshaw index,younger age(<40 years),longer disease duration(>40 years),smoking,young age of disease onset,steroid use 6-12 months before cessation.An important factor in the decision to withdraw medication is the success of re-treatment with the same or other drugs.The decision to discontinue therapy must be based on individual approach,taking into account the severity,extension,and duration of the disease,the possibility of side adverse effects,the risk of relapse,and patient’s preferences.

A Local Macroscopic Conservative(LoMaC)Low Rank Tensor Method with the Discontinuous Galerkin Method for the Vlasov Dynamics

In this paper,we propose a novel Local Macroscopic Conservative(LoMaC)low rank tensor method with discontinuous Galerkin(DG)discretization for the physical and phase spaces for simulating the Vlasov-Poisson(VP)system.The LoMaC property refers to the exact local conservation of macroscopic mass,momentum,and energy at the discrete level.The recently developed LoMaC low rank tensor algorithm(arXiv:2207.00518)simultaneously evolves the macroscopic conservation laws of mass,momentum,and energy using the kinetic flux vector splitting;then the LoMaC property is realized by projecting the low rank kinetic solution onto a subspace that shares the same macroscopic observables.This paper is a generalization of our previous work,but with DG discretization to take advantage of its compactness and flexibility in handling boundary conditions and its superior accuracy in the long term.The algorithm is developed in a similar fashion as that for a finite difference scheme,by observing that the DG method can be viewed equivalently in a nodal fashion.With the nodal DG method,assuming a tensorized computational grid,one will be able to(i)derive differentiation matrices for different nodal points based on a DG upwind discretization of transport terms,and(ii)define a weighted inner product space based on the nodal DG grid points.The algorithm can be extended to the high dimensional problems by hierarchical Tucker(HT)decomposition of solution tensors and a corresponding conservative projection algorithm.In a similar spirit,the algorithm can be extended to DG methods on nodal points of an unstructured mesh,or to other types of discretization,e.g.,the spectral method in velocity direction.Extensive numerical results are performed to showcase the efficacy of the method.

Numerical Investigations on the Resonance Errors of Multiscale Discontinuous Galerkin Methods for One-Dimensional Stationary Schrödinger Equation

In this paper,numerical experiments are carried out to investigate the impact of penalty parameters in the numerical traces on the resonance errors of high-order multiscale discontinuous Galerkin(DG)methods(Dong et al.in J Sci Comput 66:321–345,2016;Dong and Wang in J Comput Appl Math 380:1–11,2020)for a one-dimensional stationary Schrödinger equation.Previous work showed that penalty parameters were required to be positive in error analysis,but the methods with zero penalty parameters worked fine in numerical simulations on coarse meshes.In this work,by performing extensive numerical experiments,we discover that zero penalty parameters lead to resonance errors in the multiscale DG methods,and taking positive penalty parameters can effectively reduce resonance errors and make the matrix in the global linear system have better condition numbers.

Can rifaximin for hepatic encephalopathy be discontinued during broad-spectrum antibiotic treatment?

Hepatic encephalopathy(HE)is a formidable complication in patients with decompensated cirrhosis,often necessitating the administration of rifaximin(RFX)for effective management.RFX,is a gut-restricted,poorly-absorbable oral rifamycin derived antibiotic that can be used in addition to lactulose for the secondary prophylaxis of HE.It has shown notable reductions in infection,hospital readmission,duration of hospital stay,and mortality.However,limited data exist about the concurrent use of RFX with broad-spectrum antibiotics,because the patients are typically excluded from studies assessing RFX efficacy in HE.A pharmacist-driven quasi-experimental pilot study was done to address this gap.They argue against the necessity of RFX in HE during broad-spectrum antibiotic treatment,particularly in critically ill patients in intensive care unit(ICU).The potential for safe RFX discontinuation without adverse effects is clearly illuminated and valuable insight into the optimization of therapeutic strategies is offered.The findings also indicate that RFX discontinuation during broadspectrum antibiotic therapy was not associated with higher rates of delirium or coma,and this result remained robust after adjustment in multivariate analysis.Furthermore,rates of other secondary clinical and safety outcomes,including ICU mortality and 48-hour changes in vasopressor requirements,were comparable.However,since the activity of RFX is mainly confined to the modulation of gut microbiota,its potential utility in patients undergoing extensive systemic antibiotic therapy is debatable,given the overlapping antibiotic activity.Further,this suggests that the action of RFX on HE is class-specific(related to its activity on gut microbiota),rather than drug-specific.A recent double-blind randomized controlled(ARiE)trial provided further evidence-based support for RFX withdrawal in critically ill cirrhotic ICU patients receiving broad-spectrum antibiotics.Both studies prompt further discussion about optimal therapeutic strategy for patients facing the dual challenge of HE and systemic infections.Despite these compelling results,both studies have limitations.A prospective,multi-center evaluation of a larger sample,with placebo control,and comprehensive neurologic evaluation of HE is warranted.It should include an exploration of longer-term outcome and the impact of this protocol in non-critically ill liver disease patients.

Bound-Preserving Discontinuous Galerkin Methods with Modified Patankar Time Integrations for Chemical Reacting Flows

In this paper,we develop bound-preserving discontinuous Galerkin(DG)methods for chemical reactive flows.There are several difficulties in constructing suitable numerical schemes.First of all,the density and internal energy are positive,and the mass fraction of each species is between 0 and 1.Second,due to the rapid reaction rate,the system may contain stiff sources,and the strong-stability-preserving explicit Runge-Kutta method may result in limited time-step sizes.To obtain physically relevant numerical approximations,we apply the bound-preserving technique to the DG methods.Though traditional positivity-preserving techniques can successfully yield positive density,internal energy,and mass fractions,they may not enforce the upper bound 1 of the mass fractions.To solve this problem,we need to(i)make sure the numerical fluxes in the equations of the mass fractions are consistent with that in the equation of the density;(ii)choose conservative time integrations,such that the summation of the mass fractions is preserved.With the above two conditions,the positive mass fractions have summation 1,and then,they are all between 0 and 1.For time discretization,we apply the modified Runge-Kutta/multi-step Patankar methods,which are explicit for the flux while implicit for the source.Such methods can handle stiff sources with relatively large time steps,preserve the positivity of the target variables,and keep the summation of the mass fractions to be 1.Finally,it is not straightforward to combine the bound-preserving DG methods and the Patankar time integrations.The positivity-preserving technique for DG methods requires positive numerical approximations at the cell interfaces,while Patankar methods can keep the positivity of the pre-selected point values of the target variables.To match the degree of freedom,we use polynomials on rectangular meshes for problems in two space dimensions.To evolve in time,we first read the polynomials at the Gaussian points.Then,suitable slope limiters can be applied to enforce the positivity of the solutions at those points,which can be preserved by the Patankar methods,leading to positive updated numerical cell averages.In addition,we use another slope limiter to get positive solutions used for the bound-preserving technique for the flux.Numerical examples are given to demonstrate the good performance of the proposed schemes.

Superconvergence of Direct Discontinuous Galerkin Methods:Eigen-structure Analysis Based on Fourier Approach

This paper investigates superconvergence properties of the direct discontinuous Galerkin(DDG)method with interface corrections and the symmetric DDG method for diffusion equations.We apply the Fourier analysis technique to symbolically compute eigenvalues and eigenvectors of the amplification matrices for both DDG methods with different coefficient settings in the numerical fluxes.Based on the eigen-structure analysis,we carry out error estimates of the DDG solutions,which can be decomposed into three parts:(i)dissipation errors of the physically relevant eigenvalue,which grow linearly with the time and are of order 2k for P^(k)(k=2,3)approximations;(ii)projection error from a special projection of the exact solution,which is decreasing over the time and is related to the eigenvector corresponding to the physically relevant eigenvalue;(iii)dissipative errors of non-physically relevant eigenvalues,which decay exponentially with respect to the spatial mesh sizeΔx.We observe that the errors are sensitive to the choice of the numerical flux coefficient for even degree P^(2)approximations,but are not for odd degree P^(3)approximations.Numerical experiments are provided to verify the theoretical results.

HetNets Under Decoupled Uplink and Downlink Access with UE Random Discontinuous Transmission: Local Delay and Energy Efficiency

Due to the limited uplink capability in heterogeneousnetworks (HetNets), the decoupled uplinkand downlink access (DUDA) mode has recently beenproposed to improve the uplink performance. In thispaper, the random discontinuous transmission (DTX)at user equipment (UE) is adopted to reduce the interferencecorrelation across different time slots. By utilizingstochastic geometry, we analytically derive themean local delay and energy efficiency (EE) of an uplinkHetNet with UE random DTX scheme under theDUDA mode. These expressions are further approximatedas closed forms under reasonable assumptions.Our results reveal that under the DUDA mode, there isan optimal EE with respect to mute probability underthe finite local delay constraint. In addition, with thesame finite mean local delay as under the coupled uplinkand downlink access (CUDA) mode, the HetNetsunder the DUDA mode can achieve a higher EE witha lower mute probability.

High-Order Decoupled and Bound Preserving Local Discontinuous Galerkin Methods for a Class of Chemotaxis Models

In this paper,we explore bound preserving and high-order accurate local discontinuous Galerkin(LDG)schemes to solve a class of chemotaxis models,including the classical Keller-Segel(KS)model and two other density-dependent problems.We use the convex splitting method,the variant energy quadratization method,and the scalar auxiliary variable method coupled with the LDG method to construct first-order temporal accurate schemes based on the gradient flow structure of the models.These semi-implicit schemes are decoupled,energy stable,and can be extended to high accuracy schemes using the semi-implicit spectral deferred correction method.Many bound preserving DG discretizations are only worked on explicit time integration methods and are difficult to get high-order accuracy.To overcome these difficulties,we use the Lagrange multipliers to enforce the implicit or semi-implicit LDG schemes to satisfy the bound constraints at each time step.This bound preserving limiter results in the Karush-Kuhn-Tucker condition,which can be solved by an efficient active set semi-smooth Newton method.Various numerical experiments illustrate the high-order accuracy and the effect of bound preserving.

Performance of inclined pillars with a major discontinuity

Discontinuities are an inherent part of the rock mass and majorly affect the stability of the excavation skin and pillars.The dip of the discontinuities and their properties also have a significant effect on the strength of the pillars.Empirical approaches are commonly used to determine the pillar strength but can overestimate the strength and don’t consider the inclination of the pillars and the strength reduction caused by discontinuities.Numerical modeling is a powerful tool and if calibrated can be used to evaluate the strength of the pillars with discontinuities having a range of properties.The effect of a discontinuity on inclined pillars was conducted which has been seldom considered in evaluating the pillar strength.Three-dimensional vertical pillars were simulated,and the pillar strength was calibrated to accepted theoretical results and then the discontinuities were introduced in different pillar inclinations with distinct width to height ratios to gain an insight into the effective pillar strength reduction.Based upon the results,it was found that the discontinuities have a significant effect with the increase in the inclination of the pillars even at a higher width to height ratios.