Cracks resulting from cyclic wetting and drying of expansive soils create discontinuities and anisotropy in the soil.The representative elementary volume(REV)defined by the continuous-media theory cannot be applied to...Cracks resulting from cyclic wetting and drying of expansive soils create discontinuities and anisotropy in the soil.The representative elementary volume(REV)defined by the continuous-media theory cannot be applied to cracked expansive soils that are considered discontinuous media.In this study,direct shear tests of three different scales(30 cm^(2),900 cm^(2),1963 cm^(2))and crack image analysis were carried out on undisturbed soil samples subjected to drying-wetting cycles in-situ.The REV size of expansive soil was investigated using the crack intensity factor(CIF)and soil cohesion.The results show that soil cohesion decreased with increasing sample area,and the development of secondary cracks further exacerbated the size effect of sample on cohesion of the soil.As shrinkage cracks developed,the REV size of the soil gradually increased and plateaued after 3−5 cycles.Under the same drying-wetting cycle conditions,the REV size determined using soil cohesion(REV-C)is 1.75 to 2.97 times the REV size determined using CIF(REV-CIF).Under the influence of shrinkage cracks,the average CIF is positively correlated with the REV size determined using different maximum permissible errors,with the coefficient of correlation greater than 0.9.A method for determining the REV-C based on crack image analysis is proposed,and the REV-C of expansive soil in the study area under different exposure times is given.展开更多
Representative elementary volume(REV)is the key to study the heterogeneity of digital coal and characterize its macroscopic and microscopic properties.The permeability evolution law of digital coal based on REV analys...Representative elementary volume(REV)is the key to study the heterogeneity of digital coal and characterize its macroscopic and microscopic properties.The permeability evolution law of digital coal based on REV analysis can provide theoretical support for the application of permeability prediction model in multi-scale reservoirs.This study takes typical coal samples from Bofang and Sihe coal mines in Qinshui Basin as research object.First,the nondestructive information of two samples is scanned and visualized.Secondly,the calculation methods of two-dimensional(2D)and threedimensional(3D)fractal dimensions of pores and fractures are illustrated.Then,the determination methods of REV based on porosity and fractal dimension are compared.Finally,the distribution pattern of fractal dimension and porosity curves is studied,the relationship between 2D and 3D fractal dimension is characterized,and the application of fractal permeability model in permeability analysis of multi-scale reservoir is further discussed.The REV size varies greatly in different vertex directions of the same sample and between samples,so REV analysis can only be performed in specific directions.When the REV based on fractal dimension is determined,the porosity curve continues to maintain a downward trend and then tends to be stable.The 2D fractal dimension has a positive linear correlation with the 3D fractal dimension,and the porosity can be expressed as a linear function of the fractal dimension.The permeability through REV analysis domain is mainly affected by fractal dimension,dip angle,azimuth angle and maximum fracture length,which is of great significance for exploring permeability evolution law of coal reservoir at different scales.This study is of great significance for enriching the determination methods of REV in digital coal and exploring the permeability evolution law of multi-scale reservoirs.展开更多
The representative elementary volume （REV） for three-dimensional polydisperse granular packings was determined using discrete element method simulations. Granular mixtures of various sizes and particle size distribu...The representative elementary volume （REV） for three-dimensional polydisperse granular packings was determined using discrete element method simulations. Granular mixtures of various sizes and particle size distributions were poured into a cuboid chamber and subjected to uniaxial compression, Findings showed that the minimum REV for porosity was larger compared with the REV for parameters such as coordination number, effective elastic modulus, and pressure ratio. The minimum REV for porosity and other parameters was found to equal 15,10, and 5 times the average grain diameter, respectively. A study of the influence of sample size on energy dissipation in random packing of spheres has also confirmed that the REV size is about 15 times the average grain diameter. The heterogeneity of systems was found to have no effect on the REV for the parameters of interest for the narrow range of coefficient of uniformity analyzed in this paper. As the REV approach is commonly applied in both experimental and numerical studies, determining minimum REV size for polydisperse granular packings remains a crucial issue.展开更多
The three-dimensional(3 D) structures of pores directly affect the CH4 flow.Therefore,it is very important to analyze the3 D spatial structure of pores and to simulate the CH4 flow with the connected pores as the carr...The three-dimensional(3 D) structures of pores directly affect the CH4 flow.Therefore,it is very important to analyze the3 D spatial structure of pores and to simulate the CH4 flow with the connected pores as the carrier.The result shows that the equivalent radius of pores and throats are 1-16 μm and 1.03-8.9 μm,respectively,and the throat length is 3.28-231.25 μm.The coordination number of pores concentrates around three,and the intersection point between the connectivity function and the X-axis is 3-4 μm,which indicate the macro-pores have good connectivity.During the single-channel flow,the pressure decreases along the direction of CH4 flow,and the flow velocity of CH4 decreases from the pore center to the wall.Under the dual-channel and the multi-channel flows,the pressure also decreases along the CH4 flow direction,while the velocity increases.The mean flow pressure gradually decreases with the increase of the distance from the inlet slice.The change of mean flow pressure is relatively stable in the direction horizontal to the bedding plane,while it is relatively large in the direction perpendicular to the bedding plane.The mean flow velocity in the direction horizontal to the bedding plane(Y-axis) is the largest,followed by that in the direction horizontal to the bedding plane(X-axis),and the mean flow velocity in the direction perpendicular to the bedding plane is the smallest.展开更多
According to Cubic law and incompressible fluid law of mass conservation, the seepage character of the fracture surface was simulated with the simulation method of fractal theory and random Brown function. Furthermore...According to Cubic law and incompressible fluid law of mass conservation, the seepage character of the fracture surface was simulated with the simulation method of fractal theory and random Brown function. Furthermore, the permeability coefficient of the single fracture was obtained. In order to test the stability of the method, 500 simulations were conducted on each different fractal dimension. The simulated permeability coefficient was analyzed in probability density distribution and probability cumulative distribution statistics. Statistics showed that the discrete degree of the permeability coefficient increases with the increase of the fractal dimension. And the calculation result has better stability when the fractal dimension value is relatively small. According to the Bayes theory, the characteristic index of the permeability coefficient on fractal dimension P（Dfi｜ Ri） is established. The index, P（Dfi｜ Ri）, shows that when the simulated permeability coefficient is relatively large, it can clearly represent the fractal dimension of the structure surface, the probability is 82%. The calculated results of the characteristic index verify the feasibility of the method.展开更多
From the continuum mechanics perspective, an attempt was made to clarify the role of Terzaghi's effective stress in the theoretical analysis of saturated soil subjected to seepage. The necessity of performing a co...From the continuum mechanics perspective, an attempt was made to clarify the role of Terzaghi's effective stress in the theoretical analysis of saturated soil subjected to seepage. The necessity of performing a coupled hydromechanical analysis to solve the seepage-deformation interaction problem was illustrated by examining the equations of static equilibrium among the effective stress, seepage force, pore-water pressure and total stress. The conceptual definition of stress variable that satisfies the principles of continuum mechanics is applied in the coupled hydromechanical analysis. It is shown that Terzaghi's effective stress is in fact not a stress variable under seepage conditions, and the seepage force acting on the soil skeleton cannot be viewed as a body force. This offers a clue to the underlying cause of a paradox between the real Pascal's hydrostatic state and the hydrostatic state predicted by a class of continuum hydromechanical theories.展开更多
The continuum approach in fluid flow modeling is generally applied to porous geological media, but has limited applicability to fractured rocks. With the presence of a discrete fracture network relatively sparsely dis...The continuum approach in fluid flow modeling is generally applied to porous geological media, but has limited applicability to fractured rocks. With the presence of a discrete fracture network relatively sparsely distributed in the matrix, it may be difficult or erroneous to use a porous medium fluid flow model with continuum assumptions to describe the fluid flow in fractured rocks at small or even large field scales. A discrete fracture fluid flow approach incorporating a stochastic fracture network with numerical fluid flow simulations could have the capability of capturing fluid flow behaviors such as inhomogeneity and anisotropy while reflecting the changes of hydraulic features at different scales. Moreover, this approach can be implemented to estimate the size of the representative elementary volume (REV) in order to find out the scales at which a porous medium flow model could be applied, and then to determine the hydraulic conductivity tensor for fractured rocks. The following topics are focused on in this study: (a) conceptual discrete fracture fluid flow modeling incorporating a stochastic fracture network with numerical flow simulations; (b) estimation of REV and hydraulic conductivity tensor for fractured rocks utilizing a stochastic fracture network with numerical fluid flow simulations; (c) investigation of the effect of fracture orientation and density on the hydraulic conductivity and REV by implementing a stochastic fracture network with numerical fluid flow simulations, and (d) fluid flow conceptual models accounting for major and minor fractures in the 2 D or 3 D flow fields incorporating a stochastic fracture network with numerical fluid flow simulations.展开更多
The constitutive model and equivalent deformation modulus of an arbitrary column in representative elementary volume （REV） of fractured rock mass are derived. The deformation of fractured rock mass is com- posed of ...The constitutive model and equivalent deformation modulus of an arbitrary column in representative elementary volume （REV） of fractured rock mass are derived. The deformation of fractured rock mass is com- posed of the rock part and the fracture part. The elasto-visco-plastic property is considered in this model. For the convenience in engineering practice, the complex elasto-visco-plastic model and its equivalent modulus are degraded, and tbe rock is taken as an elastic body. By statistical analysis of the geometric positions of the column and the fracture, the equivalent modulus of rock mass with arbitrary fractures is obtained.展开更多
The size of the rock specimen affects the stress concentrates in the vicinity of the top/bottom of the rock specimen during the evaluation of the geomechanical parameters in the laboratory,which causes un-reliable res...The size of the rock specimen affects the stress concentrates in the vicinity of the top/bottom of the rock specimen during the evaluation of the geomechanical parameters in the laboratory,which causes un-reliable results.However,the appropriate size for geomechanical evaluation is not well understood yet because of limitations in the sampling and analysis.In this study,a series of numerical simulations using a finite element package was conducted to investigate the effect of sample aspect ratio,fluid saturation,and porosity,on the mechanical behavior of the rock under elastic and poroelastic conditions.In addition,two concepts,stress/strain homogeneity index(SHI)and representative elementary volume(REV),were developed to find out the appropriate sample size.The results show that the presence of stiff platens,which are dissimilar to the specimen material,causes significant stress concentration in the two ends of the specimen.The concentration of stress in the specimen reduces when the aspect ratio increases.An optimum aspect ratio(length-to-diameter equal to 3)was observed by SHI analysis which after that the changes in stress concentration are insignificant.The REV size analysis confirms the obtained optimum aspect ratio by SHI analysis.The saturated specimens show a lower magnitude of stress than applied stress because of the presence of pore pressure,which can carry a portion of the stress.The higher void ratio results in lower strength of the specimen.This study could be beneficial for the better design of geomechanical tests to have reliable results.展开更多
基金Project(41472240)supported by the National Natural Science Foundation of ChinaProjects(2015B25514,2015B17214)supported by the Fundamental Research Funds for the Central Universities,China。
文摘Cracks resulting from cyclic wetting and drying of expansive soils create discontinuities and anisotropy in the soil.The representative elementary volume(REV)defined by the continuous-media theory cannot be applied to cracked expansive soils that are considered discontinuous media.In this study,direct shear tests of three different scales(30 cm^(2),900 cm^(2),1963 cm^(2))and crack image analysis were carried out on undisturbed soil samples subjected to drying-wetting cycles in-situ.The REV size of expansive soil was investigated using the crack intensity factor(CIF)and soil cohesion.The results show that soil cohesion decreased with increasing sample area,and the development of secondary cracks further exacerbated the size effect of sample on cohesion of the soil.As shrinkage cracks developed,the REV size of the soil gradually increased and plateaued after 3−5 cycles.Under the same drying-wetting cycle conditions,the REV size determined using soil cohesion(REV-C)is 1.75 to 2.97 times the REV size determined using CIF(REV-CIF).Under the influence of shrinkage cracks,the average CIF is positively correlated with the REV size determined using different maximum permissible errors,with the coefficient of correlation greater than 0.9.A method for determining the REV-C based on crack image analysis is proposed,and the REV-C of expansive soil in the study area under different exposure times is given.
基金supported by the National Natural Science Foundation of China(Grant No.42102217)the University Synergy Innovation Program of Anhui Province(No.GXXT-2021-018)+2 种基金the Natural Science Research Project of Anhui University(Nos.KJ2020A0315 and KJ2020A0317)the Natural Science Foundation of Anhui Province(No.2108085MD134)the Foundation of State Key Laboratory of Petroleum Resources and Prospecting,China University of Petroleum,Beijing(No.PRP/open-2005).
文摘Representative elementary volume(REV)is the key to study the heterogeneity of digital coal and characterize its macroscopic and microscopic properties.The permeability evolution law of digital coal based on REV analysis can provide theoretical support for the application of permeability prediction model in multi-scale reservoirs.This study takes typical coal samples from Bofang and Sihe coal mines in Qinshui Basin as research object.First,the nondestructive information of two samples is scanned and visualized.Secondly,the calculation methods of two-dimensional(2D)and threedimensional(3D)fractal dimensions of pores and fractures are illustrated.Then,the determination methods of REV based on porosity and fractal dimension are compared.Finally,the distribution pattern of fractal dimension and porosity curves is studied,the relationship between 2D and 3D fractal dimension is characterized,and the application of fractal permeability model in permeability analysis of multi-scale reservoir is further discussed.The REV size varies greatly in different vertex directions of the same sample and between samples,so REV analysis can only be performed in specific directions.When the REV based on fractal dimension is determined,the porosity curve continues to maintain a downward trend and then tends to be stable.The 2D fractal dimension has a positive linear correlation with the 3D fractal dimension,and the porosity can be expressed as a linear function of the fractal dimension.The permeability through REV analysis domain is mainly affected by fractal dimension,dip angle,azimuth angle and maximum fracture length,which is of great significance for exploring permeability evolution law of coal reservoir at different scales.This study is of great significance for enriching the determination methods of REV in digital coal and exploring the permeability evolution law of multi-scale reservoirs.
文摘The representative elementary volume （REV） for three-dimensional polydisperse granular packings was determined using discrete element method simulations. Granular mixtures of various sizes and particle size distributions were poured into a cuboid chamber and subjected to uniaxial compression, Findings showed that the minimum REV for porosity was larger compared with the REV for parameters such as coordination number, effective elastic modulus, and pressure ratio. The minimum REV for porosity and other parameters was found to equal 15,10, and 5 times the average grain diameter, respectively. A study of the influence of sample size on energy dissipation in random packing of spheres has also confirmed that the REV size is about 15 times the average grain diameter. The heterogeneity of systems was found to have no effect on the REV for the parameters of interest for the narrow range of coefficient of uniformity analyzed in this paper. As the REV approach is commonly applied in both experimental and numerical studies, determining minimum REV size for polydisperse granular packings remains a crucial issue.
基金financially supported by the National Key Research and Development Plan(No.2018YFB0605601)the National Natural Science Foundation of China(No.41972168)。
文摘The three-dimensional(3 D) structures of pores directly affect the CH4 flow.Therefore,it is very important to analyze the3 D spatial structure of pores and to simulate the CH4 flow with the connected pores as the carrier.The result shows that the equivalent radius of pores and throats are 1-16 μm and 1.03-8.9 μm,respectively,and the throat length is 3.28-231.25 μm.The coordination number of pores concentrates around three,and the intersection point between the connectivity function and the X-axis is 3-4 μm,which indicate the macro-pores have good connectivity.During the single-channel flow,the pressure decreases along the direction of CH4 flow,and the flow velocity of CH4 decreases from the pore center to the wall.Under the dual-channel and the multi-channel flows,the pressure also decreases along the CH4 flow direction,while the velocity increases.The mean flow pressure gradually decreases with the increase of the distance from the inlet slice.The change of mean flow pressure is relatively stable in the direction horizontal to the bedding plane,while it is relatively large in the direction perpendicular to the bedding plane.The mean flow velocity in the direction horizontal to the bedding plane(Y-axis) is the largest,followed by that in the direction horizontal to the bedding plane(X-axis),and the mean flow velocity in the direction perpendicular to the bedding plane is the smallest.
基金Project(50934006) supported by the National Natural Science Foundation of ChinaProject(CX2012B070) supported by Hunan Provincial Innovation Foundation for Postgraduate,ChinaProject(1343-76140000024) Supported by Academic New Artist Ministry of Education Doctoral Post Graduate in 2012,China
文摘According to Cubic law and incompressible fluid law of mass conservation, the seepage character of the fracture surface was simulated with the simulation method of fractal theory and random Brown function. Furthermore, the permeability coefficient of the single fracture was obtained. In order to test the stability of the method, 500 simulations were conducted on each different fractal dimension. The simulated permeability coefficient was analyzed in probability density distribution and probability cumulative distribution statistics. Statistics showed that the discrete degree of the permeability coefficient increases with the increase of the fractal dimension. And the calculation result has better stability when the fractal dimension value is relatively small. According to the Bayes theory, the characteristic index of the permeability coefficient on fractal dimension P（Dfi｜ Ri） is established. The index, P（Dfi｜ Ri）, shows that when the simulated permeability coefficient is relatively large, it can clearly represent the fractal dimension of the structure surface, the probability is 82%. The calculated results of the characteristic index verify the feasibility of the method.
基金Project(51278171)supported by the National Natural Science Foundation of ChinaProject(B13024)supported by the"111"Project,China+1 种基金Projects(2014B04914,2011B02814,2010B28114)supported by the Fundamental Research Funds for the Central Universities of ChinaProject(617608)supported by the Research Grants Council of the Hong Kong Special Administrative Region of China
文摘From the continuum mechanics perspective, an attempt was made to clarify the role of Terzaghi's effective stress in the theoretical analysis of saturated soil subjected to seepage. The necessity of performing a coupled hydromechanical analysis to solve the seepage-deformation interaction problem was illustrated by examining the equations of static equilibrium among the effective stress, seepage force, pore-water pressure and total stress. The conceptual definition of stress variable that satisfies the principles of continuum mechanics is applied in the coupled hydromechanical analysis. It is shown that Terzaghi's effective stress is in fact not a stress variable under seepage conditions, and the seepage force acting on the soil skeleton cannot be viewed as a body force. This offers a clue to the underlying cause of a paradox between the real Pascal's hydrostatic state and the hydrostatic state predicted by a class of continuum hydromechanical theories.
基金ChinaCommitteeofEducation theUniver sityofArizonaandtheMetropolitanWaterDistrictofSouthernCaliforni a.
文摘The continuum approach in fluid flow modeling is generally applied to porous geological media, but has limited applicability to fractured rocks. With the presence of a discrete fracture network relatively sparsely distributed in the matrix, it may be difficult or erroneous to use a porous medium fluid flow model with continuum assumptions to describe the fluid flow in fractured rocks at small or even large field scales. A discrete fracture fluid flow approach incorporating a stochastic fracture network with numerical fluid flow simulations could have the capability of capturing fluid flow behaviors such as inhomogeneity and anisotropy while reflecting the changes of hydraulic features at different scales. Moreover, this approach can be implemented to estimate the size of the representative elementary volume (REV) in order to find out the scales at which a porous medium flow model could be applied, and then to determine the hydraulic conductivity tensor for fractured rocks. The following topics are focused on in this study: (a) conceptual discrete fracture fluid flow modeling incorporating a stochastic fracture network with numerical flow simulations; (b) estimation of REV and hydraulic conductivity tensor for fractured rocks utilizing a stochastic fracture network with numerical fluid flow simulations; (c) investigation of the effect of fracture orientation and density on the hydraulic conductivity and REV by implementing a stochastic fracture network with numerical fluid flow simulations, and (d) fluid flow conceptual models accounting for major and minor fractures in the 2 D or 3 D flow fields incorporating a stochastic fracture network with numerical fluid flow simulations.
基金Foundation item： the Western Transport Construction Science and Technology Project of the Ministry of Transport of the People＇s Republic of China （No. 2009318000046）
文摘The constitutive model and equivalent deformation modulus of an arbitrary column in representative elementary volume （REV） of fractured rock mass are derived. The deformation of fractured rock mass is com- posed of the rock part and the fracture part. The elasto-visco-plastic property is considered in this model. For the convenience in engineering practice, the complex elasto-visco-plastic model and its equivalent modulus are degraded, and tbe rock is taken as an elastic body. By statistical analysis of the geometric positions of the column and the fracture, the equivalent modulus of rock mass with arbitrary fractures is obtained.
文摘The size of the rock specimen affects the stress concentrates in the vicinity of the top/bottom of the rock specimen during the evaluation of the geomechanical parameters in the laboratory,which causes un-reliable results.However,the appropriate size for geomechanical evaluation is not well understood yet because of limitations in the sampling and analysis.In this study,a series of numerical simulations using a finite element package was conducted to investigate the effect of sample aspect ratio,fluid saturation,and porosity,on the mechanical behavior of the rock under elastic and poroelastic conditions.In addition,two concepts,stress/strain homogeneity index(SHI)and representative elementary volume(REV),were developed to find out the appropriate sample size.The results show that the presence of stiff platens,which are dissimilar to the specimen material,causes significant stress concentration in the two ends of the specimen.The concentration of stress in the specimen reduces when the aspect ratio increases.An optimum aspect ratio(length-to-diameter equal to 3)was observed by SHI analysis which after that the changes in stress concentration are insignificant.The REV size analysis confirms the obtained optimum aspect ratio by SHI analysis.The saturated specimens show a lower magnitude of stress than applied stress because of the presence of pore pressure,which can carry a portion of the stress.The higher void ratio results in lower strength of the specimen.This study could be beneficial for the better design of geomechanical tests to have reliable results.
