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.

Geophysical Significance of the Senegalo-Mali Discontinuity: Evidence from Secondary Structures, Kédougou-Kéniéba Inlier, Western Mali

The present study focuses on the analysis and description of lineaments interpreted as secondary structures to describe the nature of Senegalo Malian Discontinuity. These lineaments cross-cut the large north-south oriented transcurrent lithospheric structure known as the Senegalo Malian Discontinuity (SMD). Two lineaments were selected oriented NNE (N15˚ to N25˚), one at Dialafara and one at Sadiola. Four profiles on each lineament of these 2 zones, so that there were 2 on each side of the SMD. The ground data collected were processed using proper parameter and software. Some filters were applied to enhance the signal level. These ground data were later compared to the existing airborne magnetic data for consistency and accuracy using the upward continuation filter. The results show that the quality of ground data is good. In addition, the ground magnetic data show the presence of certain local anomalies that are not visible in the regional data. The analytical signal was also used to determine domain boundaries or possible contact zones. The contact zone can be highlighted on certain profiles such as L300 and L600. The study showed that the west and east sides of the SMD are not the same. Secondary structures become wide when approaching the SMD on both sides. They are also duplicated to the east of the SMD when we move progressively away. In the Dialafara area, the ground magnetic data intersect an interpreted fold. The results of this work confirm the presence of the secondary structures and their evolution in relation to the SMD. The relationships between the secondary structures in the Dailafara and Sadiola zones and their relations with the SMD are highlighted. The technique used in this study, is an important approach to better description and interpreting of regional structures using the secondary structures and proposing a structural model.

The Effect of Blood Lipid Profiles on Chronic Kidney Disease in a Prospective Cohort:Based on a Regression Discontinuity Design

Objective Previous studies on the association between lipid profiles and chronic kidney disease(CKD)have yielded inconsistent results and no defined thresholds for blood lipids.Methods A prospective cohort study including 32,351 subjects who completed baseline and follow-up surveys over 5 years was conducted.Restricted cubic splines and Cox models were used to examine the association between the lipid profiles and CKD.A regression discontinuity design was used to determine the cutoff value of lipid profiles that was significantly associated with increased the risk of CKD.Results Over a median follow-up time of 2.2(0.5,4.2)years,648(2.00%)subjects developed CKD.The lipid profiles that were significantly and linearly related to CKD included total cholesterol(TC),triglycerides(TG),high-density lipoprotein cholesterol(HDL-C),TC/HDL-C,and TG/HDL-C,whereas lowdensity lipoprotein cholesterol(LDL-C)and LDL-C/HDL-C were nonlinearly correlated with CKD.TC,TG,TC/HDL-C,and TG/HDL-C showed an upward jump at the cutoff value,increasing the risk of CKD by 0.90%,1.50%,2.30%,and 1.60%,respectively,whereas HDL-C showed a downward jump at the cutoff value,reducing this risk by 1.0%.Female and participants with dyslipidemia had a higher risk of CKD,while the cutoff values for the different characteristics of the population were different.Conclusion There was a significant association between lipid profiles and CKD in a prospective cohort from Northwest China,while TG,TC/HDL-C,and TG/HDL-C showed a stronger risk association.The specific cutoff values of lipid profiles may provide a clinical reference for screening or diagnosing CKD risk.

No basalt accumulation and segregation atop the 660-km discontinuity beneath the Sea of Okhotsk

Recent seismic evidence shows that basalt accumulation is widespread in the mantle transition zone(MTZ),yet its ubiquity or sporadic nature remains uncertain.To investigate this phenomenon further,we characterized the velocity structure across the 660-km discontinuity that separates the upper mantle from the lower mantle beneath the Sea of Okhotsk by modeling the waveform of the S660P phase,a downgoing S wave converting into a P wave at the 660-km interface.These waves were excited by two regional>410-km-deep events and were recorded by stations in central Asia.Our findings showed no need to introduce velocity anomalies at the base of the MTZ to explain the S660P waveforms because the IASP91 model adequately reproduced the waveforms.This finding indicates that the basalt accumulation has not affected the bottom of the MTZ in the study area.Instead,this discontinuity is primarily controlled by temperature or water content variations,or both.Thus,we argue that the basalt accumulation at the base of the MTZ is sporadic,not ubiquitous,reflecting its heterogeneous distribution.

General Decay Synchronization of Competitive Fuzzy Neural Networks Involving Time Delays and Right-Hand Discontinuous Activation

This paper discusses the general decay synchronization problem for a class of fuzzy competitive neural networks with time-varying delays and discontinuous activation functions. Firstly, based on the concept of Filippov solutions for right-hand discontinuous systems, some sufficient conditions for general decay synchronization of the considered system are obtained via designing a nonlinear feedback controller and applying discontinuous differential equation theory, Lyapunov functional methods and some inequality techniques. Finally, one numerical example is given to verify the effectiveness of the proposed theoretical results. The general decay synchronization considered in this article can better estimate the convergence rate of the system, and the exponential synchronization and polynomial synchronization can be seen as its special cases.

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.

An extended displacement discontinuity method for analysis of stress wave propagation in viscoelastic rock mass

An extended displacement discontinuity method (EDDM) is proposed to analyze the stress wave propagation in jointed viscoelastic rock mass (VRM).The discontinuities in a rock mass are divided into two groups.The primary group with an average geometrical size larger than or in the same order of magnitude of wavelength of a concerned stress wave is defined as 'macro-joints',while the secondary group with a high density and relatively small geometrical size compared to the wavelength is known as 'micro-defects'.The rock mass with micro-defects is modeled as an equivalent viscoelastic medium while the macro-joints in the rock mass are modeled explicitly as physical discontinuities.Viscoelastic properties of a micro-defected sedimentary rock are obtained by longitudinally impacting a cored long sedimentary rod with a pendulum.Wave propagation coefficient and dynamic viscoelastic modulus are measured.The EDDM is then successfully employed to analyze the wave propagation across macro-joint in VRM.The effect of the rock viscosity on the stress wave propagation is evaluated by comparing the results of VRM from the presented EDDM with those of an elastic rock mass (ERM) from the conventional displacement discontinuity method (CDDM).The CDDM is a special case of the EDDM under the condition that the rock viscosity is ignored.Comparison of the reflected and transmitted waves shows that the essential rock viscosity has a significant effect on stress wave attenuation.When a short propagation distance of a stress wave is considered,the results obtained from the CDDM approximate to the EDDM solutions,however,when the propagation distance is sufficiently long relative to the wavelength,the effect of rock viscosity on the stress wave propagation cannot be ignored.

ASYMPTOTIC BEHAVIOR OF SOLUTIONS TOWARD THE SUPERPOSITION OF CONTACT DISCONTINUITY AND SHOCK WAVE FOR COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH FREE BOUNDARY

A free boundary problem for the one-dimensional compressible Navier-Stokes equations is investigated. The asymptotic behavior of solutions toward the superposition of contact discontinuity and shock wave is established under some smallness conditions. To do this, we first construct a new viscous contact wave such that the momentum equation is satisfied exactly and then determine the shift of the viscous shock wave. By using them together with an inequality concerning the heat kernel in the half space, we obtain the desired a priori estimates. The proof is based on the elementary energy method by the anti-derivative argument.

ZERO DISSIPATION LIMIT TO CONTACT DISCONTINUITY FOR THE COMPRESSIBLE NAVIER-STOKES SYSTEM OF GENERAL GAS

The zero dissipation limit to the contact discontinuities for one-dimensional com- pressible Navier-Stokes equations was recently proved for ideal polytropic gas （see Huang et al. [15, 22] and Ma [31]）, but there is few result for general gases including ideal polytropic gas. We prove that if the solution to the corresponding Euler system of general gas satisfying （1.4） is piecewise constant with a contact discontinuity, then there exist smooth solutions to Navier-Stokes equations which converge to the inviscid solutions at a rate of k1/4 as the heat-conductivity coefficient k tends to zero. The key is to construct a viscous contact wave of general gas suitable to our proof （see Section 2）. Notice that we have no need to restrict the strength of the contact discontinuity to be small.

A modified method of discontinuity trace mapping using three-dimensional point clouds of rock mass surfaces

This paper presents an automated method for discontinuity trace mapping using three-dimensional point clouds of rock mass surfaces.Specifically,the method consists of five steps:(1)detection of trace feature points by normal tensor voting theory,(2)co ntraction of trace feature points,(3)connection of trace feature points,(4)linearization of trace segments,and(5)connection of trace segments.A sensitivity analysis was then conducted to identify the optimal parameters of the proposed method.Three field cases,a natural rock mass outcrop and two excavated rock tunnel surfaces,were analyzed using the proposed method to evaluate its validity and efficiency.The results show that the proposed method is more efficient and accurate than the traditional trace mapping method,and the efficiency enhancement is more robust as the number of feature points increases.

CONVERGENCE RATE OF SOLUTIONS TO STRONG CONTACT DISCONTINUITY FOR THE ONE-DIMENSIONAL COMPRESSIBLE RADIATION HYDRODYNAMICS MODEL

This paper is concerned with a singular limit for the one-dimensional compress- ible radiation hydrodynamics model. The singular limit we consider corresponds to the physical problem of letting the Bouguer number infinite while keeping the Boltzmann number constant. In the case when the corresponding Euler system admits a contact discontinuity wave, Wang and Xie （2011） [12] recently verified this singular limit and proved that the solution of the compressible radiation hydrodynamics model converges to the strong contact 1 discontinuity wave in the L∞-norm away from the discontinuity line at a rate of ε1/4, as the reciprocal of the Bouguer number tends to zero. In this paper, Wang and Xie＇s convergence rate is improved to ε7/8 by introducing a new a priori assumption and some refined energy estimates. Moreover, it is shown that the radiation flux q tends to zero in the L∞-norm away from the discontinuity line, at a convergence rate as the reciprocal of the Bouguer number tends to zero.

Machine learning-based classification of rock discontinuity trace:SMOTE oversampling integrated with GBT ensemble learning

This paper presents a hybrid ensemble classifier combined synthetic minority oversampling technique(SMOTE),random search(RS)hyper-parameters optimization algorithm and gradient boosting tree(GBT)to achieve efficient and accurate rock trace identification.A thirteen-dimensional database consisting of basic,vector,and discontinuity features is established from image samples.All data points are classified as either‘‘trace”or‘‘non-trace”to divide the ultimate results into candidate trace samples.It is found that the SMOTE technology can effectively improve classification performance by recommending an optimized imbalance ratio of 1:5 to 1:4.Then,sixteen classifiers generated from four basic machine learning(ML)models are applied for performance comparison.The results reveal that the proposed RS-SMOTE-GBT classifier outperforms the other fifteen hybrid ML algorithms for both trace and nontrace classifications.Finally,discussions on feature importance,generalization ability and classification error are conducted for the proposed classifier.The experimental results indicate that more critical features affecting the trace classification are primarily from the discontinuity features.Besides,cleaning up the sedimentary pumice and reducing the area of fractured rock contribute to improving the overall classification performance.The proposed method provides a new alternative approach for the identification of 3D rock trace.

EXISTENCE OF MINIMISERS FOR A CLASS OF FREE DISCONTINUITY PROBLEMS IN THE HEISENBERG GROUP H^n

The purpose of this paper is to prove existence of minimisers of the functional where Ω is an open set of the Heisenberg group Hn, K runs over all closed sets of Hn, u varies in C_H^1(Ω\ K), α,β> 0,q≥1, g ∈ Lq(Ω) ∩ L∞(Ω) and f : R2n→R is a convex function satisfying some structure conditions (H1)(H2)(H3) (see below).

Effects of Area Discontinuity at Nozzle Inlet on the Characteristics of Self-resonating Cavitating Waterjet

The current research on self-resonating cavitating waterjet（SRCW） mainly focuses on the generation mechanism and structure optimization.Researches relating to the influences of disturbances at nozzle inlet on the characteristics of the jet are rarely available.In order to further improve the performance of SRCW,effects of area discontinuity（enlargement and contraction） are experimentally investigated using three organ-pipe nozzles.Axial pressure oscillation peak and amplitude as well as aggressive erosion intensity of the jet are used to evaluate the effects.The results reveal that area enlargement and contraction affect the peak differently,depending on the inlet pressure,nozzle geometry,and standoff distance;while area contraction always improves the amplitude regardless of these factors.At inlet pressures of 10 MPa and 20 MPa,area discontinuity improves the peak at almost all the testing standoff distances,while this only happens at smaller standoff distances with the inlet pressure increased to 30 MPa.The capability of area discontinuity for improving the amplitude is enhancing with increasing inlet pressure.Moreover,the cavitation erosion ability of the jet can be largely enhanced around the optimum standoff distance,depending on the type of area discontinuity and nozzle geometry.A preliminary analysis of the influence of area discontinuity on the disturbance waves in the flow is also performed.The proposed research provides a new method for effectively enhancing the performance of SRCW.

A state-of-the-art review of automated extraction of rock mass discontinuity characteristics using three-dimensional surface models

In the last two decades,significant research has been conducted in the field of automated extraction of rock mass discontinuity characteristics from three-dimensional(3D)models.This provides several methodologies for acquiring discontinuity measurements from 3D models,such as point clouds generated using laser scanning or photogrammetry.However,even with numerous automated and semiautomated methods presented in the literature,there is not one single method that can automatically characterize discontinuities accurately in a minimum of time.In this paper,we critically review all the existing methods proposed in the literature for the extraction of discontinuity characteristics such as joint sets and orientations,persistence,joint spacing,roughness and block size using point clouds,digital elevation maps,or meshes.As a result of this review,we identify the strengths and drawbacks of each method used for extracting those characteristics.We found that the approaches based on voxels and region growing are superior in extracting joint planes from 3D point clouds.Normal tensor voting with trace growth algorithm is a robust method for measuring joint trace length from 3D meshes.Spacing is estimated by calculating the perpendicular distance between joint planes.Several independent roughness indices are presented to quantify roughness from 3D surface models,but there is a need to incorporate these indices into automated methodologies.There is a lack of efficient algorithms for direct computation of block size from 3D rock mass surface models.

Regionalized difference of the 660 km discontinuity beneath Izu-Bonin

Digital waveform data recorded by the vertical component short period stations at the American networks of SCSN, NCSN and PNSN and three components broadband stations at the Germany and Swiss networks and arrays of GRFN, GRSN and SDSNet for the events between 1981 and 2000 under Izu-Bonin are used as data sets. The N-th root slant stack method was used to pick up the SdP phase converted at the velocity interface beneath source and the regionalized difference of the 660 km discontinuity beneath Izu-Bonin is studied. It is found that while the dip angles of the subducting slab and the maximal depths of sources increase gradually from 35N to 26N, the 660 km discontinuity appears regionalized differences. The discontinuity exists at 660 km while there is no effect from subducting slab, but it is depressed to the depth of 720 km while there are obvious effects. The dispersion of converted points is still an unsolved problem which maybe result from the complex structure of the discontinuity, converted phases which were misjudged, or the assumption of one dimensional spherical earth model.

Spatial variations of the 660-km discontinuity in the western Pacific subduction zones observed from CEArray triplication data

We examined the spatial variation of velocity structures around the 660-kin discontinuity at the western Pacific subduction zones by waveform modeling of triplication data. Data from two deep earthquakes beneath Izu-Bonin and Northeast China are used. Both events were well recorded by a dense broadband seismic network in China （CEArray）. The two events are located at approximately the same distance to the CEArray, yet significant differences are observed in their records： （1） the direct arrivals traveling above the 660-km discontinuity （AB branch） are seen in a different distance extent： -29° for the NE China event, -23° for Izu-Bonin event; （2） the direct （AB） and the refracted waves at the 660-km （CD branch） cross over at 19.5° and 17° for the NE China and the Izu-Bonin event, respectively. The best fitting model for the NE China event has a broad 660-km discontinuity and a constant high velocity layer upon it; while the Izu-Bonin model differs from the standard IASP91 model only with a high velocity layer above the 660-km discontinuity. Variations in velocity models can be roughly explained by subduction geometry.

Dynamic evolution of shear rate-dependent behavior of rock discontinuity under shearing condition

Rock blocks sliding along discontinuities can cause serious disasters,such as landslides,earthquakes,or rock bursts.The shear rate-dependent behavior is a typical time-dependent behavior of a rock discontinuity,and it is closely related to the stability of a rock block.To further study the shear rate-dependent behavior of rock discontinuities,shear tests with alternating shear rates(SASRs)were conducted on rock discontinuities with various surface morphologies.The dynamic evolution of the shear rate dependency was studied in detail based on the shear test results,and three stages were identified with respect to the shear stress and shear deformation states.The test results revealed that dynamic changes in shear stiffness and the energy storage abilities of the rock discontinuities occurred in relation to the shear rate-dependent behavior of crack growth,which increased with an increase in normal stress and/or the joint roughness coefficient.The stage of decreasing shear stiffness corresponded to a stage of noticeable shear rate-dependency,and the shear rate was found to have no influence on the initial crack stress.

On the accuracy of higher order displacement discontinuity method(HODDM) in the solution of linear elastic fracture mechanics problems

The higher order displacement discontinuity method(HODDM) utilizing special crack tip elements has been used in the solution of linear elastic fracture mechanics(LEFM) problems. The paper has selected several example problems from the fracture mechanics literature(with available analytical solutions) including center slant crack in an infinite and finite body, single and double edge cracks, cracks emanating from a circular hole. The numerical values of Mode Ⅰ and Mode Ⅱ SIFs for these problems using HODDM are in excellent agreement with analytical results(reaching up to 0.001% deviation from their analytical results). The HODDM is also compared with the XFEM and a modified XFEM results. The results show that the HODDM needs a considerably lower computational effort(with less than 400 nodes) than the XFEM and the modified XFEM(which needs more than 10000 nodes) to reach a much higher accuracy. The proposed HODDM offers higher accuracy and lower computation effort for a wide range of problems in LEFM.

Sharpness of the paired 660-km discontinuity beneath the Izu-Bonin area

The 660-km discontinuity that separates the Earth's upper and lower mantle has primarily been attributed to phase changes in olivine and other minerals.Resolving the sharpness is essential for predicting the composition of the mantle and for understanding its dynamic effects.In this study,we used S-to-P conversions from the 660-km interface,termed S660P,arriving in the P-wave coda from one earthquake in the Izu–Bonin subduction zone recorded by stations in Alaska.The S660P signals were of high quality,providing us an unprecedented opportunity to resolve the sharpness of the discontinuity.Our study demonstrated,based on the impedance contrast given by the IASP91 model,that the discontinuity has a transitional thickness of^5 km.In addition,we observed a prominent arrival right after the S660P,which was best explained by S-to-P conversions from a deeper discontinuity at a depth of^720 km with a transitional thickness of^20 km,termed S720P.The 720-km discontinuity is most likely the result of a phase transition from majoritic garnet to perovskite in the segregated oceanic crust(mainly the mid-oceanic ridge basalt composition)at the uppermost lower mantle beneath this area.The inferred phase changes are also consistent with predictions from mineral physics experiments.