Joint roughness coefficient(JRC)is the most commonly used parameter for quantifying surface roughness of rock discontinuities in practice.The system composed of multiple roughness statistical parameters to measure JRC...Joint roughness coefficient(JRC)is the most commonly used parameter for quantifying surface roughness of rock discontinuities in practice.The system composed of multiple roughness statistical parameters to measure JRC is a nonlinear system with a lot of overlapping information.In this paper,a dataset of eight roughness statistical parameters covering 112 digital joints is established.Then,the principal component analysis method is introduced to extract the significant information,which solves the information overlap problem of roughness characterization.Based on the two principal components of extracted features,the white shark optimizer algorithm was introduced to optimize the extreme gradient boosting model,and a new machine learning(ML)prediction model was established.The prediction accuracy of the new model and the other 17 models was measured using statistical metrics.The results show that the prediction result of the new model is more consistent with the real JRC value,with higher recognition accuracy and generalization ability.展开更多
Two pairs of approximation operators, which are the scale lower and upper approximations as well as the real line lower and upper approximations, are defined. Their properties and antithesis characteristics are analyz...Two pairs of approximation operators, which are the scale lower and upper approximations as well as the real line lower and upper approximations, are defined. Their properties and antithesis characteristics are analyzed. The rough function model is generalized based on rough set theory, and the scheme of rough function theory is made more distinct and complete. Therefore, the transformation of the real function analysis from real line to scale is achieved. A series of basic concepts in rough function model including rough numbers, rough intervals, and rough membership functions are defined in the new scheme of the rough function model. Operating properties of rough intervals similar to rough sets are obtained. The relationship of rough inclusion and rough equality of rough intervals is defined by two kinds of tools, known as the lower （upper） approximation operator in real numbers domain and rough membership functions. Their relative properties are analyzed and proved strictly, which provides necessary theoretical foundation and technical support for the further discussion of properties and practical application of the rough function model.展开更多
In view of certain defects of common rough communication, using the S-rough sets, this article presents a S-rough communication model. The S-rough communication model is the extension of the common rough communication...In view of certain defects of common rough communication, using the S-rough sets, this article presents a S-rough communication model. The S-rough communication model is the extension of the common rough communication model. S-rough communication has two kinds of forms： one-direction S-rough communication and two-direction S-rough communication. The mathematical structure and characteristics of the one-direction S-rough communication and the two-direction S-rough communication, the relationship theorem between the one-direction S-rough communication and the two-direction S-rough communication are also presented. The S-rough communication is a dynamic communication method, and it is a novel research direction in rough sets field.展开更多
By using function one direction S-rough sets （function one direction singular rough sets）, this article presents the concepts of F-law, F-rough law, and the relation metric of rough law; by using these concepts, thi...By using function one direction S-rough sets （function one direction singular rough sets）, this article presents the concepts of F-law, F-rough law, and the relation metric of rough law; by using these concepts, this article puts forward the theorem of F-law relation metric, two orders theorem of F-rough law relation metric, the attribute theorem of F-rough law band, the extremum theorem of F-rough law relation metric, the discovery principle of F-rough law and the application of F-rough law.展开更多
Rough set is a new approach to uncertainties in spatial analysis.In this paper,rough set symbols are simplified and standardized in terms of rough interpretation and specialized indication.Rough spatial entities and t...Rough set is a new approach to uncertainties in spatial analysis.In this paper,rough set symbols are simplified and standardized in terms of rough interpretation and specialized indication.Rough spatial entities and their topological relationships are also proposed in rough space,thus a universal intersected equation is developed,and rough membership function is further extended with the gray scale in our case study.We complete three works.First,a set of simplified rough symbols is advanced on the basis of existing rough symbols.Second,rough spatial entity is put forward to study the real world as it is,without forcing uncertainties into crisp set.Third,rough spatial topological relationships are studied by using rough matrix and their figures.The relationships are divided into three types,crisp entity and crisp entity (CC),rough entity and crisp entity (RC),and rough entity and rough entity (RR).A universal intersected equation is further proposed.Finally,the maximum and minimum maps of river thematic classification are generated via rough membership function and rough relationships in our case study.展开更多
By using function S-rough sets（function singular rough sets）, this paper gives rough law generation and the theorem of rough law generation.Based on these results above, the paper proposes rough law separation, the ...By using function S-rough sets（function singular rough sets）, this paper gives rough law generation and the theorem of rough law generation.Based on these results above, the paper proposes rough law separation, the theorem of rough law separation, the compound generation theorem of rough law bands, and the principle of rough law bands.In the end, an application of rough law separation in recognizing the risk law of profit is presented.展开更多
The roughness of the fracture surface directly affects the strength,deformation,and permeability of the surrounding rock in deep underground engineering.Understanding the effect of high temperature and thermal cycle o...The roughness of the fracture surface directly affects the strength,deformation,and permeability of the surrounding rock in deep underground engineering.Understanding the effect of high temperature and thermal cycle on the fracture surface roughness plays an important role in estimating the damage degree and stability of deep rock mass.In this paper,the variations of fracture surface roughness of granite after different heating and thermal cycles were investigated using the joint roughness coefficient method(JRC),three-dimensional(3D)roughness parameters,and fractal dimension(D),and the mechanism of damage and deterioration of granite were revealed.The experimental results show an increase in the roughness of the granite fracture surface as temperature and cycle number were incremented.The variations of JRC,height parameter,inclination parameter and area parameter with the temperature conformed to the Boltzmann's functional distribution,while the D decreased linearly as the temperature increased.Besides,the anisotropy index(Ip)of the granite fracture surface increased as the temperature increased,and the larger parameter values of roughness characterization at different temperatures were attained mainly in directions of 20°–40°,60°–100°and 140°–160°.The fracture aperture of granite after fracture followed the Gauss distribution and the average aperture increased with increasing temperature,which increased from 0.665 mm at 25℃to 1.058 mm at 800℃.High temperature caused an uneven thermal expansion,water evaporation,and oxidation of minerals within the granite,which promoted the growth and expansion of microfractures,and reduced interparticle bonding strength.In particular,the damage was exacerbated by the expansion and cracking of the quartz phase transition after T>500℃.Thermal cycles contributed to the accumulation of this damage and further weakened the interparticle bonding forces,resulting in a significant increase in the roughness,anisotropy,and aperture of the fracture surface after five cycles.展开更多
LetΩbe homogeneous of degree zero,integrable on S^(d−1) and have vanishing moment of order one,a be a function on R^(d) such that ∇a∈L^(∞)(R^(d)).Let T*_(Ω,a) be the maximaloperator associated with the d-dimensional...LetΩbe homogeneous of degree zero,integrable on S^(d−1) and have vanishing moment of order one,a be a function on R^(d) such that ∇a∈L^(∞)(R^(d)).Let T*_(Ω,a) be the maximaloperator associated with the d-dimensional Calder´on commutator defined by T*_(Ωa)f(x):=sup_(ε>0)|∫_(|x-y|>ε)^Ω(x-y)/|x-y|^(d+1)(a(x)-a(y))f(y)dy.In this paper,the authors establish bilinear sparse domination for T*_(Ω,a) under the assumption Ω∈L∞(Sd−1).As applications,some quantitative weighted bounds for T*_(Ω,a) are obtained.展开更多
Let Ω be homogeneous of degree zero,integrable on S^(n−1) and have mean value zero,T_(Ω) be the homogeneous singular integral operator with kernel Ω(x)/|x|^(n) and[b,T_(Ω)]be the commutator of T_(Ω)with symbol b∈BMO(...Let Ω be homogeneous of degree zero,integrable on S^(n−1) and have mean value zero,T_(Ω) be the homogeneous singular integral operator with kernel Ω(x)/|x|^(n) and[b,T_(Ω)]be the commutator of T_(Ω)with symbol b∈BMO(R^(n)).In this paper,the authors prove that if sup ζ∈S^(n−1)∫Sn−1^(|Ω(θ)|log^(β)(1/|θ·ζ|)dθ<∞ with β>2,then[b,T_(Ω)]is bounded on Triebel–Lizorkin space F^(0,q)p(R^(n))provided that 1+1/β−1<p,q<β.展开更多
As the dominant seepage channel in rock masses,it is of great significance to study the influence of fracture roughness distribution on seepage and heat transfer in rock masses.In this paper,the fracture roughness dis...As the dominant seepage channel in rock masses,it is of great significance to study the influence of fracture roughness distribution on seepage and heat transfer in rock masses.In this paper,the fracture roughness distribution functions of the Bakhtiary dam site and Oskarshamn/Forsmark mountain were fitted using statistical methods.The COMSOL Multiphysics finite element software was utilized to analyze the effects of fracture roughness distribution types and empirical formulas for fracture hydraulic aperture on the seepage field and temperature field of rock masses.The results show that:(1)The fracture roughness at the Bakhtiary dam site and Oskarshamn/Forsmark mountain follows lognormal and normal distributions,respectively;(2)For rock masses with the same expected value and standard deviation of fracture roughness,the outflow from rock masses with lognormal distribution of fracture roughness is significantly larger than that of rock masses with normal distribution of fracture roughness;(3)The fracture hydraulic aperture,outflow,and cold front distance of the Li and Jiang model are significantly larger than those of the Barton model;(4)The outflow,hydraulic pressure distribution,and temperature distribution of the Barton model are more sensitive to the fracture roughness distribution type than those of the Li and Jiang model.展开更多
Based on rough similarity degree of rough sets and close degree of fuzzy sets, the definitions of rough similarity degree and rough close degree of rough fuzzy sets are given, which can be used to measure the similar ...Based on rough similarity degree of rough sets and close degree of fuzzy sets, the definitions of rough similarity degree and rough close degree of rough fuzzy sets are given, which can be used to measure the similar degree between two rough fuzzy sets. The properties and theorems are listed. Using the two new measures, the method of clustering in the rough fuzzy system can be obtained. After clustering, the new fuzzy sample can be recognized by the principle of maximal similarity degree.展开更多
Pavement condition monitoring and its timely maintenance is necessary to ensure the safety and quality of the roadway infrastructure. The International Roughness Index (IRI) is a commonly used measure to quantify road...Pavement condition monitoring and its timely maintenance is necessary to ensure the safety and quality of the roadway infrastructure. The International Roughness Index (IRI) is a commonly used measure to quantify road surface roughness and is a critical input to asset management. In Indiana, the IRI statistic contributes to roughly half of the pavement quality index computation used for asset management. Most agencies inventory IRI once a year, however, pavement conditions vary much more frequently. The objective of this paper is to develop a framework using crowdsourced connected vehicle data to identify and detect temporal changes in IRI. Over 3 billion connected vehicle records in Indiana were analyzed across 30 months between 2022 and 2024 to understand the spatiotemporal variations in roughness. Annual comparisons across all major interstates in Indiana showed the miles of interstates classified as “Good” decreased from 1896 to 1661 miles between 2022 and 2024. The miles of interstate classified as “Needs Maintenance” increased from 82 to 120 miles. A detailed case study showing monthly and daily changes of estimated IRI on I-65 are presented along with supporting dashcam images. Although the crowdsourced IRI estimates are not as robust as traditional specialized pavement profilers, they can be obtained on a monthly, weekly, or even daily basis. The paper concludes by suggesting a combination of frequent crowdsourced IRI and commercially available dashcam imagery of roadway can provide an agile and responsive mechanism for agencies to implement pavement asset management programs that can complement existing annual programs.展开更多
Flow and transport properties of fractured crystalline rock are of great interest for different geotechnical ap-plications,such as storage of carbon dioxide,extraction of geothermal energy,or geologic storage of hazar...Flow and transport properties of fractured crystalline rock are of great interest for different geotechnical ap-plications,such as storage of carbon dioxide,extraction of geothermal energy,or geologic storage of hazardous waste.For the long-term safety assessment of geological storage of hazardous waste,the understanding of flow and transport properties through the network of fractures is essential.The flow and transport behaviour can be explored using numerical models to investigate what parameters that affect the results.In this work a pilot study is carried out for multiple realizations of single realistic fractures,using fractal theories,which then are nu-merically sheared using a semi-analytical algorithm.The aperture field is calculated using the average distance of the volume integral of the void that a 1 mm lateral displacement of the sheared surfaces generates.The flow field through the aperture field is solved using Reynolds lubrication equation in linear triangular finite elements.The transport properties,travel length,travel time,transport resistance and specific flow wetted surface,are calculated in a Lagrangian framework using 10,000 particles for each of the 128 flow fields.Evaluating these four metrics,varying initial roughness,4<JRC<10 and normal stress between 0.2 and 20 MPa during shearing,it is concluded that an increase in normal stress generally results in longer travel paths,longer travel times,higher transport resistance and larger specific flow wetted surface while an increase of initial roughness will generally result in longer travel paths,shorter travel times,lower transport resistance and smaller specific flow wetted surface.展开更多
基金funding from the National Natural Science Foundation of China (Grant No.42277175)the pilot project of cooperation between the Ministry of Natural Resources and Hunan Province“Research and demonstration of key technologies for comprehensive remote sensing identification of geological hazards in typical regions of Hunan Province” (Grant No.2023ZRBSHZ056)the National Key Research and Development Program of China-2023 Key Special Project (Grant No.2023YFC2907400).
文摘Joint roughness coefficient(JRC)is the most commonly used parameter for quantifying surface roughness of rock discontinuities in practice.The system composed of multiple roughness statistical parameters to measure JRC is a nonlinear system with a lot of overlapping information.In this paper,a dataset of eight roughness statistical parameters covering 112 digital joints is established.Then,the principal component analysis method is introduced to extract the significant information,which solves the information overlap problem of roughness characterization.Based on the two principal components of extracted features,the white shark optimizer algorithm was introduced to optimize the extreme gradient boosting model,and a new machine learning(ML)prediction model was established.The prediction accuracy of the new model and the other 17 models was measured using statistical metrics.The results show that the prediction result of the new model is more consistent with the real JRC value,with higher recognition accuracy and generalization ability.
基金the Scientific Research and Development Project of Shandong Provincial Education Department(J06P01)the Science and Technology Fundation of University of Jinan (XKY0703).
文摘Two pairs of approximation operators, which are the scale lower and upper approximations as well as the real line lower and upper approximations, are defined. Their properties and antithesis characteristics are analyzed. The rough function model is generalized based on rough set theory, and the scheme of rough function theory is made more distinct and complete. Therefore, the transformation of the real function analysis from real line to scale is achieved. A series of basic concepts in rough function model including rough numbers, rough intervals, and rough membership functions are defined in the new scheme of the rough function model. Operating properties of rough intervals similar to rough sets are obtained. The relationship of rough inclusion and rough equality of rough intervals is defined by two kinds of tools, known as the lower （upper） approximation operator in real numbers domain and rough membership functions. Their relative properties are analyzed and proved strictly, which provides necessary theoretical foundation and technical support for the further discussion of properties and practical application of the rough function model.
基金This project was supported by the Natural Science Foundation of Shandong Province of China (Y2004A04)the Natural Science Foundation of Fujian Province of China (A0410026).
文摘In view of certain defects of common rough communication, using the S-rough sets, this article presents a S-rough communication model. The S-rough communication model is the extension of the common rough communication model. S-rough communication has two kinds of forms： one-direction S-rough communication and two-direction S-rough communication. The mathematical structure and characteristics of the one-direction S-rough communication and the two-direction S-rough communication, the relationship theorem between the one-direction S-rough communication and the two-direction S-rough communication are also presented. The S-rough communication is a dynamic communication method, and it is a novel research direction in rough sets field.
基金supported by the Natural Science Foundation of Shandong Province(Y2007H02)Natural Science Foundation of Fujian Province(S0650031)
文摘By using function one direction S-rough sets （function one direction singular rough sets）, this article presents the concepts of F-law, F-rough law, and the relation metric of rough law; by using these concepts, this article puts forward the theorem of F-law relation metric, two orders theorem of F-rough law relation metric, the attribute theorem of F-rough law band, the extremum theorem of F-rough law relation metric, the discovery principle of F-rough law and the application of F-rough law.
文摘Rough set is a new approach to uncertainties in spatial analysis.In this paper,rough set symbols are simplified and standardized in terms of rough interpretation and specialized indication.Rough spatial entities and their topological relationships are also proposed in rough space,thus a universal intersected equation is developed,and rough membership function is further extended with the gray scale in our case study.We complete three works.First,a set of simplified rough symbols is advanced on the basis of existing rough symbols.Second,rough spatial entity is put forward to study the real world as it is,without forcing uncertainties into crisp set.Third,rough spatial topological relationships are studied by using rough matrix and their figures.The relationships are divided into three types,crisp entity and crisp entity (CC),rough entity and crisp entity (RC),and rough entity and rough entity (RR).A universal intersected equation is further proposed.Finally,the maximum and minimum maps of river thematic classification are generated via rough membership function and rough relationships in our case study.
基金supported partly by the Natural Science Foundation of Shandong Province of China (Y2007Ho2)the Elementary and Advanced Technology Foundation of Henan Province of China (082300410040)
文摘By using function S-rough sets（function singular rough sets）, this paper gives rough law generation and the theorem of rough law generation.Based on these results above, the paper proposes rough law separation, the theorem of rough law separation, the compound generation theorem of rough law bands, and the principle of rough law bands.In the end, an application of rough law separation in recognizing the risk law of profit is presented.
基金funding support from the National Natural Science Foundation of China(Grant No.52274082)the Program of Qingjiang Excellent Young Talents,Jiangxi University of Science and Technology(Grant No.JXUSTQJBJ2020003)the Innovation Fund Designated for Graduate Students of Jiangxi Province(Grant No.YC2023-B215).
文摘The roughness of the fracture surface directly affects the strength,deformation,and permeability of the surrounding rock in deep underground engineering.Understanding the effect of high temperature and thermal cycle on the fracture surface roughness plays an important role in estimating the damage degree and stability of deep rock mass.In this paper,the variations of fracture surface roughness of granite after different heating and thermal cycles were investigated using the joint roughness coefficient method(JRC),three-dimensional(3D)roughness parameters,and fractal dimension(D),and the mechanism of damage and deterioration of granite were revealed.The experimental results show an increase in the roughness of the granite fracture surface as temperature and cycle number were incremented.The variations of JRC,height parameter,inclination parameter and area parameter with the temperature conformed to the Boltzmann's functional distribution,while the D decreased linearly as the temperature increased.Besides,the anisotropy index(Ip)of the granite fracture surface increased as the temperature increased,and the larger parameter values of roughness characterization at different temperatures were attained mainly in directions of 20°–40°,60°–100°and 140°–160°.The fracture aperture of granite after fracture followed the Gauss distribution and the average aperture increased with increasing temperature,which increased from 0.665 mm at 25℃to 1.058 mm at 800℃.High temperature caused an uneven thermal expansion,water evaporation,and oxidation of minerals within the granite,which promoted the growth and expansion of microfractures,and reduced interparticle bonding strength.In particular,the damage was exacerbated by the expansion and cracking of the quartz phase transition after T>500℃.Thermal cycles contributed to the accumulation of this damage and further weakened the interparticle bonding forces,resulting in a significant increase in the roughness,anisotropy,and aperture of the fracture surface after five cycles.
文摘LetΩbe homogeneous of degree zero,integrable on S^(d−1) and have vanishing moment of order one,a be a function on R^(d) such that ∇a∈L^(∞)(R^(d)).Let T*_(Ω,a) be the maximaloperator associated with the d-dimensional Calder´on commutator defined by T*_(Ωa)f(x):=sup_(ε>0)|∫_(|x-y|>ε)^Ω(x-y)/|x-y|^(d+1)(a(x)-a(y))f(y)dy.In this paper,the authors establish bilinear sparse domination for T*_(Ω,a) under the assumption Ω∈L∞(Sd−1).As applications,some quantitative weighted bounds for T*_(Ω,a) are obtained.
基金Supported by NSFC(No.11971295)Guangdong Higher Education Teaching Reform Project(No.2023307)。
文摘Let Ω be homogeneous of degree zero,integrable on S^(n−1) and have mean value zero,T_(Ω) be the homogeneous singular integral operator with kernel Ω(x)/|x|^(n) and[b,T_(Ω)]be the commutator of T_(Ω)with symbol b∈BMO(R^(n)).In this paper,the authors prove that if sup ζ∈S^(n−1)∫Sn−1^(|Ω(θ)|log^(β)(1/|θ·ζ|)dθ<∞ with β>2,then[b,T_(Ω)]is bounded on Triebel–Lizorkin space F^(0,q)p(R^(n))provided that 1+1/β−1<p,q<β.
基金College Students Innovation and Entrepreneurship Project of Guangzhou Railway Polytechnic(2025CXCY015)。
文摘As the dominant seepage channel in rock masses,it is of great significance to study the influence of fracture roughness distribution on seepage and heat transfer in rock masses.In this paper,the fracture roughness distribution functions of the Bakhtiary dam site and Oskarshamn/Forsmark mountain were fitted using statistical methods.The COMSOL Multiphysics finite element software was utilized to analyze the effects of fracture roughness distribution types and empirical formulas for fracture hydraulic aperture on the seepage field and temperature field of rock masses.The results show that:(1)The fracture roughness at the Bakhtiary dam site and Oskarshamn/Forsmark mountain follows lognormal and normal distributions,respectively;(2)For rock masses with the same expected value and standard deviation of fracture roughness,the outflow from rock masses with lognormal distribution of fracture roughness is significantly larger than that of rock masses with normal distribution of fracture roughness;(3)The fracture hydraulic aperture,outflow,and cold front distance of the Li and Jiang model are significantly larger than those of the Barton model;(4)The outflow,hydraulic pressure distribution,and temperature distribution of the Barton model are more sensitive to the fracture roughness distribution type than those of the Li and Jiang model.
基金the Fujian Provincial Natural Science Foundation of China (Z0510492006J0391)
文摘Based on rough similarity degree of rough sets and close degree of fuzzy sets, the definitions of rough similarity degree and rough close degree of rough fuzzy sets are given, which can be used to measure the similar degree between two rough fuzzy sets. The properties and theorems are listed. Using the two new measures, the method of clustering in the rough fuzzy system can be obtained. After clustering, the new fuzzy sample can be recognized by the principle of maximal similarity degree.
文摘Pavement condition monitoring and its timely maintenance is necessary to ensure the safety and quality of the roadway infrastructure. The International Roughness Index (IRI) is a commonly used measure to quantify road surface roughness and is a critical input to asset management. In Indiana, the IRI statistic contributes to roughly half of the pavement quality index computation used for asset management. Most agencies inventory IRI once a year, however, pavement conditions vary much more frequently. The objective of this paper is to develop a framework using crowdsourced connected vehicle data to identify and detect temporal changes in IRI. Over 3 billion connected vehicle records in Indiana were analyzed across 30 months between 2022 and 2024 to understand the spatiotemporal variations in roughness. Annual comparisons across all major interstates in Indiana showed the miles of interstates classified as “Good” decreased from 1896 to 1661 miles between 2022 and 2024. The miles of interstate classified as “Needs Maintenance” increased from 82 to 120 miles. A detailed case study showing monthly and daily changes of estimated IRI on I-65 are presented along with supporting dashcam images. Although the crowdsourced IRI estimates are not as robust as traditional specialized pavement profilers, they can be obtained on a monthly, weekly, or even daily basis. The paper concludes by suggesting a combination of frequent crowdsourced IRI and commercially available dashcam imagery of roadway can provide an agile and responsive mechanism for agencies to implement pavement asset management programs that can complement existing annual programs.
文摘Flow and transport properties of fractured crystalline rock are of great interest for different geotechnical ap-plications,such as storage of carbon dioxide,extraction of geothermal energy,or geologic storage of hazardous waste.For the long-term safety assessment of geological storage of hazardous waste,the understanding of flow and transport properties through the network of fractures is essential.The flow and transport behaviour can be explored using numerical models to investigate what parameters that affect the results.In this work a pilot study is carried out for multiple realizations of single realistic fractures,using fractal theories,which then are nu-merically sheared using a semi-analytical algorithm.The aperture field is calculated using the average distance of the volume integral of the void that a 1 mm lateral displacement of the sheared surfaces generates.The flow field through the aperture field is solved using Reynolds lubrication equation in linear triangular finite elements.The transport properties,travel length,travel time,transport resistance and specific flow wetted surface,are calculated in a Lagrangian framework using 10,000 particles for each of the 128 flow fields.Evaluating these four metrics,varying initial roughness,4<JRC<10 and normal stress between 0.2 and 20 MPa during shearing,it is concluded that an increase in normal stress generally results in longer travel paths,longer travel times,higher transport resistance and larger specific flow wetted surface while an increase of initial roughness will generally result in longer travel paths,shorter travel times,lower transport resistance and smaller specific flow wetted surface.
