Negative Poisson’s ratio(NPR)metamaterials are attractive for their unique mechanical behaviors and potential applications in deformation control and energy absorption.However,when subjected to significant stretching...Negative Poisson’s ratio(NPR)metamaterials are attractive for their unique mechanical behaviors and potential applications in deformation control and energy absorption.However,when subjected to significant stretching,NPR metamaterials designed under small strain assumption may experience a rapid degradation in NPR performance.To address this issue,this study aims to design metamaterials maintaining a targeted NPR under large deformation by taking advantage of the geometry nonlinearity mechanism.A representative periodic unit cell is modeled considering geometry nonlinearity,and its topology is designed using a gradient-free method.The unit cell microstructural topologies are described with the material-field series-expansion(MFSE)method.The MFSE method assumes spatial correlation of the material distribution,which greatly reduces the number of required design variables.To conveniently design metamaterials with desired NPR under large deformation,we propose a two-stage gradient-free metamaterial topology optimization method,which fully takes advantage of the dimension reduction benefits of the MFSE method and the Kriging surrogate model technique.Initially,we use homogenization to find a preliminary NPR design under a small deformation assumption.In the second stage,we begin with this preliminary design and minimize deviations in NPR from a targeted value under large deformation.Using this strategy and solution technique,we successfully obtain a group of NPR metamaterials that can sustain different desired NPRs in the range of[−0.8,−0.1]under uniaxial stretching up to 20% strain.Furthermore,typical microstructure designs are fabricated and tested through experiments.The experimental results show good consistency with our numerical results,demonstrating the effectiveness of the present gradientfree NPR metamaterial design strategy.展开更多
Static Poisson’s ratio(vs)is crucial for determining geomechanical properties in petroleum applications,namely sand production.Some models have been used to predict vs;however,the published models were limited to spe...Static Poisson’s ratio(vs)is crucial for determining geomechanical properties in petroleum applications,namely sand production.Some models have been used to predict vs;however,the published models were limited to specific data ranges with an average absolute percentage relative error(AAPRE)of more than 10%.The published gated recurrent unit(GRU)models do not consider trend analysis to show physical behaviors.In this study,we aim to develop a GRU model using trend analysis and three inputs for predicting n s based on a broad range of data,n s(value of 0.1627-0.4492),bulk formation density(RHOB)(0.315-2.994 g/mL),compressional time(DTc)(44.43-186.9 μs/ft),and shear time(DTs)(72.9-341.2μ s/ft).The GRU model was evaluated using different approaches,including statistical error an-alyses.The GRU model showed the proper trends,and the model data ranges were wider than previous ones.The GRU model has the largest correlation coefficient(R)of 0.967 and the lowest AAPRE,average percent relative error(APRE),root mean square error(RMSE),and standard deviation(SD)of 3.228%,1.054%,4.389,and 0.013,respectively,compared to other models.The GRU model has a high accuracy for the different datasets:training,validation,testing,and the whole datasets with R and AAPRE values were 0.981 and 2.601%,0.966 and 3.274%,0.967 and 3.228%,and 0.977 and 2.861%,respectively.The group error analyses of all inputs show that the GRU model has less than 5% AAPRE for all input ranges,which is superior to other models that have different AAPRE values of more than 10% at various ranges of inputs.展开更多
In recent years,there is a scenario in urban tunnel constructions to build super-large-span tunnels for traffic diversion and route optimization purposes.However,the increased size makes tunnel support more difficult....In recent years,there is a scenario in urban tunnel constructions to build super-large-span tunnels for traffic diversion and route optimization purposes.However,the increased size makes tunnel support more difficult.Unfortunately,there are few studies on the failure and support mechanism of the surrounding rocks in the excavation of supported tunnel,while most model tests of super-large-span tunnels focus on the failure characteristics of surrounding rocks in tunnel excavation without supports.Based on excavation compensation method(ECM),model tests of a super-large-span tunnel excavation by different anchor cable support methods in the initial support stage were carried out.The results indicate that during excavation of super-large-span tunnel,the stress and displacement of the shallow surrounding rocks decrease,following a step-shape pattern,and the tunnel failure is mainly concentrated on the vault and spandrel areas.Compared with conventional anchor cable supports,the NPR(negative Poisson’s ratio)anchor cable support is more suitable for the initial support stage of the super-large-span tunnels.The tunnel support theory,model test materials,methods,and the results obtained in this study could provide references for study of similar super-large-span tunnels。展开更多
As an important indicator parameter of fluid identification,fluid factor has always been a concern for scholars.However,when predicting Russell fluid factor or effective pore-fluid bulk modulus,it is necessary to intr...As an important indicator parameter of fluid identification,fluid factor has always been a concern for scholars.However,when predicting Russell fluid factor or effective pore-fluid bulk modulus,it is necessary to introduce a new rock skeleton parameter which is the dry-rock VP/VS ratio squared(DVRS).In the process of fluid factor calculation or inversion,the existing methods take this parameter as a static constant,which has been estimated in advance,and then apply it to the fluid factor calculation and inversion.The fluid identification analysis based on a portion of the Marmousi 2 model and numerical forward modeling test show that,taking the DVRS as a static constant will limit the identification ability of fluid factor and reduce the inversion accuracy.To solve the above problems,we proposed a new method to regard the DVRS as a dynamic variable varying with depth and lithology for the first time,then apply it to fluid factor calculation and inversion.Firstly,the exact Zoeppritz equations are rewritten into a new form containing the fluid factor and DVRS of upper and lower layers.Next,the new equations are applied to the four parameters simultaneous inversion based on the generalized nonlinear inversion(GNI)method.The testing results on a portion of the Marmousi 2 model and field data show that dynamic DVRS can significantly improve the fluid factor identification ability,effectively suppress illusion.Both synthetic and filed data tests also demonstrate that the GNI method based on Bayesian deterministic inversion(BDI)theory can successfully solve the above four parameter simultaneous inversion problem,and taking the dynamic DVRS as a target inversion parameter can effectively improve the inversion accuracy of fluid factor.All these results completely verified the feasibility and effectiveness of the proposed method.展开更多
Bivalve shell fossils,cemented by authigenic carbonates,are widely spread in the Haima cold seep,Qiongdongnan Basin of the South China Sea(SCS).In this study,we examined an element profile of Gigantidas platifrons in ...Bivalve shell fossils,cemented by authigenic carbonates,are widely spread in the Haima cold seep,Qiongdongnan Basin of the South China Sea(SCS).In this study,we examined an element profile of Gigantidas platifrons in the Haima cold seeps at a water depth of 1381 m.Based on the scanning electron microscope(SEM)analyses,the prismatic layer and nacreous layer were identified,which are characterized by prismatic structure and stratified structure,respectively.In addition,the profile can be subdivided into two parts:altered and unaltered zones.Laser inductively coupled plasma mass spectrometry(LA-ICP-MS)mapping shows that the element concentrations of the altered zones were influenced by the authigenic carbonate rocks,whereas the element concentrations of unaltered zones remain stable.In-situ X-ray diffraction(XRD)analyses show that the mineral constituent of the prismatic layer is mainly composed of aragonite.Along with the growth profile,Mg/Ca ratios of unaltered zones have minor variations,ranging 0.72-0.97 mmol/mol(mean=0.87 mmol/mol),with estimated temperatures of 3.8-4.1℃,indicating that the temperature of the surrounding seawater remains constant and agree with the measured data of 3.9℃which was conducted by a conductivity-temperature-depth system(CTD).The minor variations of Ba/Ca ratios(0.01-0.06 mmol/mol;mean=0.04 mmol/mol)indicate a relatively stabilized salinity of the surrounding seawater.S/Ca ratios show large variations of 0.04-4.15 mmol/mol(mean=1.37 mmol/mol).S/Ca ratios have regular variations which generally correspond to the variations of the Mg/Ca ratios,highlighting that the S/Ca ratios of bivalve shells show the potential to reflect the growth rate of the Gigantides.However,further studies should be carried out on the understanding of the links between the S/Ca ratios and seepage intensity of cold-seep fluids.展开更多
Poisson’s ratio changes during the tensile stress of technical fabric samples due to the anisotropy of technical fabrics.This paper examines the effects of the type of weave and the anisotropic characteristics of the...Poisson’s ratio changes during the tensile stress of technical fabric samples due to the anisotropy of technical fabrics.This paper examines the effects of the type of weave and the anisotropic characteristics of the technical fabric on maximum tensile force,corresponding elongation,work-to-maximum force,elasticity modulus,and Poisson’s ratio when axial tensile forces are applied to samples cut at various angles in the direction of the weft yarns of the technical fabric.In the lab,3 cotton fabric samples of constant warp and weft density with different structural weave types(plain weave,twill weave,atlas weave)were subjected to the tensile force until they broke at the following angles:0°,15°,30°,45°,60°,75°,90°.Based on the different measured values of technical fabric stretching in the longitudinal direction and lateral narrowing,Poisson’s ratio is calculated.The Poisson’s ratio was calculated up to a relative elongation of the fabric of 8%,as the buckling of the fabric occurs according to this elongation value.According to the results presented in this paper,the type of weave of the fabric,the direction of tensile force,and the relative narrowing of the technical fabrics all play important roles in the Poisson’s ratio value.The Poisson’s ratio curve of a technical fabric under tensile stress(i.e.elongation)is primarily determined by its behaviour in the opposite direction of the elongation.The change in the value of the Poisson’s ratio is represented by a graph that first increases nonlinearly and then decreases after reaching its maximum value.展开更多
The samples of the C-S-H series were synthesized by hydrothermal reaction of fumed silica, CaO and deionized water at initial C/S ratios between 1.0-1.7. Phase composition and structural and morphology characteristics...The samples of the C-S-H series were synthesized by hydrothermal reaction of fumed silica, CaO and deionized water at initial C/S ratios between 1.0-1.7. Phase composition and structural and morphology characteristics of C-S-H samples were analyzed by XRD, IR and SEM. The experimental results showed that the d-spacing of （002）, （110） and （020） decreased, the d-spacing of （200） increased, and the d-spacing of （310） varied randomly, the polymerization of silica tetrahedra of C-S-H decreased, and morphology of C-S-H samples varied from sheet shapes to long reticular fibers as C/S ratio increased.展开更多
The experimental test of co-incinerating Chinese raw municipal solid waste （MSW） and coal in a laboratory-scale tubular reactor was first reported in present study, and the emission of normal gas components and the ...The experimental test of co-incinerating Chinese raw municipal solid waste （MSW） and coal in a laboratory-scale tubular reactor was first reported in present study, and the emission of normal gas components and the effects of the S/Cl molar ratio or coal mixing percentages on polychlorinated dibenzo-p-dioxins and dibenzofurans （PCDDs/Fs） emission were investigated and discussed. The results indicated that OCDD was the only PCDD homologues since others like TCDD-HpCDD was hardly detected, while as the categories of PCDF homologues were comparatively much more general. The amount of PCDD was much larger than that of PCDF in all operating conditions. Since ZPCDF/∑PCDD〈〈1, the dominant role of the precursor formation was proven in our experimental conductions. With increasing the coal addition to MSW （from 0 to 16%）, PCDD and PCDF were reduced considerably. Coal and MSW may suppress the PCDD/F emissions efficiently （over 95%） during the MSW incineration process. The PCDD/F suppression results of the present study could be helpful guidance to the industrial application of Chinese MSW and auxiliary coal co-incineration processes. The PCDD/F stack emission data of two industrial incinerators using co-incineration technology in China seem to have a great positive reduction of PCDDs/Fs.展开更多
The generalized mixture rule(GMR) is used to provide a unified framework for describing Young’s(E),shear(G) and bulk(K) moduli, Lame parameter(l), and P- and S-wave velocities(Vpand Vs) as a function of porosity in v...The generalized mixture rule(GMR) is used to provide a unified framework for describing Young’s(E),shear(G) and bulk(K) moduli, Lame parameter(l), and P- and S-wave velocities(Vpand Vs) as a function of porosity in various isotropic materials such as metals, ceramics and rocks. The characteristic J values of the GMR for E, G, K and l of each material are systematically different and display consistent correlations with the Poisson’s ratio of the nonporous material(v0). For the materials dominated by corner-shaped pores, the fixed point at which the effective Poisson’s ratio(n) remains constant is at v0=0.2, and J(G) > J(E) > J(K) > J(l) and J(G) < J(E) < J(K) < J(l) for materials with v0> 0.2 and v0< 0.2, respectively.J(Vs) > J(Vp) and J(Vs) < J(Vp) for the materials with v0> 0.2 and v0< 0.2, respectively. The effective n increases, decreases and remains unchanged with increasing porosity for the materials with v0< 0.2,v0> 0.2 and v0=0.2, respectively. For natural rocks containing thin-disk-shaped pores parallel to mineral cleavages, grain boundaries and foliation, however, the n fixed point decreases nonlinearly with decreasing pore aspect ratio(a: width/length). With increasing depth or pressure, cracks with smaller a values are progressively closed, making the n fixed point rise and finally reach to the point at v0=0.2.展开更多
基金the support of the National Science Foundation of China(12372120,12172075)the Liaoning Revitalization Talents Program(XLYC2007027)Fundamental Research Funds for the Central Universities(DUT21RC(3)067).
文摘Negative Poisson’s ratio(NPR)metamaterials are attractive for their unique mechanical behaviors and potential applications in deformation control and energy absorption.However,when subjected to significant stretching,NPR metamaterials designed under small strain assumption may experience a rapid degradation in NPR performance.To address this issue,this study aims to design metamaterials maintaining a targeted NPR under large deformation by taking advantage of the geometry nonlinearity mechanism.A representative periodic unit cell is modeled considering geometry nonlinearity,and its topology is designed using a gradient-free method.The unit cell microstructural topologies are described with the material-field series-expansion(MFSE)method.The MFSE method assumes spatial correlation of the material distribution,which greatly reduces the number of required design variables.To conveniently design metamaterials with desired NPR under large deformation,we propose a two-stage gradient-free metamaterial topology optimization method,which fully takes advantage of the dimension reduction benefits of the MFSE method and the Kriging surrogate model technique.Initially,we use homogenization to find a preliminary NPR design under a small deformation assumption.In the second stage,we begin with this preliminary design and minimize deviations in NPR from a targeted value under large deformation.Using this strategy and solution technique,we successfully obtain a group of NPR metamaterials that can sustain different desired NPRs in the range of[−0.8,−0.1]under uniaxial stretching up to 20% strain.Furthermore,typical microstructure designs are fabricated and tested through experiments.The experimental results show good consistency with our numerical results,demonstrating the effectiveness of the present gradientfree NPR metamaterial design strategy.
基金The authors thank the Yayasan Universiti Teknologi PETRONAS(YUTP FRG Grant No.015LC0-428)at Universiti Teknologi PETRO-NAS for supporting this study.
文摘Static Poisson’s ratio(vs)is crucial for determining geomechanical properties in petroleum applications,namely sand production.Some models have been used to predict vs;however,the published models were limited to specific data ranges with an average absolute percentage relative error(AAPRE)of more than 10%.The published gated recurrent unit(GRU)models do not consider trend analysis to show physical behaviors.In this study,we aim to develop a GRU model using trend analysis and three inputs for predicting n s based on a broad range of data,n s(value of 0.1627-0.4492),bulk formation density(RHOB)(0.315-2.994 g/mL),compressional time(DTc)(44.43-186.9 μs/ft),and shear time(DTs)(72.9-341.2μ s/ft).The GRU model was evaluated using different approaches,including statistical error an-alyses.The GRU model showed the proper trends,and the model data ranges were wider than previous ones.The GRU model has the largest correlation coefficient(R)of 0.967 and the lowest AAPRE,average percent relative error(APRE),root mean square error(RMSE),and standard deviation(SD)of 3.228%,1.054%,4.389,and 0.013,respectively,compared to other models.The GRU model has a high accuracy for the different datasets:training,validation,testing,and the whole datasets with R and AAPRE values were 0.981 and 2.601%,0.966 and 3.274%,0.967 and 3.228%,and 0.977 and 2.861%,respectively.The group error analyses of all inputs show that the GRU model has less than 5% AAPRE for all input ranges,which is superior to other models that have different AAPRE values of more than 10% at various ranges of inputs.
基金supported by the Innovation Fund Research Project of State Key Laboratory for Geomechanics and Deep Underground Engineering,China University of Mining and Technology(Grant No.SKLGDUEK202201)the Foundation for the Opening of State Key Laboratory for Geomechanics and Deep Underground Engineering,China University of Mining and Technology(Grant No.SKLGDUEK2129)the Open Research Fund of State Key Laboratory of Geomechanics and Geotechnical Engineering,Institute of Rock and Soil Mechanics,Chinese Academy of Sciences(Grant No.Z020007)。
文摘In recent years,there is a scenario in urban tunnel constructions to build super-large-span tunnels for traffic diversion and route optimization purposes.However,the increased size makes tunnel support more difficult.Unfortunately,there are few studies on the failure and support mechanism of the surrounding rocks in the excavation of supported tunnel,while most model tests of super-large-span tunnels focus on the failure characteristics of surrounding rocks in tunnel excavation without supports.Based on excavation compensation method(ECM),model tests of a super-large-span tunnel excavation by different anchor cable support methods in the initial support stage were carried out.The results indicate that during excavation of super-large-span tunnel,the stress and displacement of the shallow surrounding rocks decrease,following a step-shape pattern,and the tunnel failure is mainly concentrated on the vault and spandrel areas.Compared with conventional anchor cable supports,the NPR(negative Poisson’s ratio)anchor cable support is more suitable for the initial support stage of the super-large-span tunnels.The tunnel support theory,model test materials,methods,and the results obtained in this study could provide references for study of similar super-large-span tunnels。
基金the National Natural Science Foundation of China(41904116,41874156,42074167 and 42204135)the Natural Science Foundation of Hunan Province(2020JJ5168)the China Postdoctoral Science Foundation(2021M703629)for their funding of this research.
文摘As an important indicator parameter of fluid identification,fluid factor has always been a concern for scholars.However,when predicting Russell fluid factor or effective pore-fluid bulk modulus,it is necessary to introduce a new rock skeleton parameter which is the dry-rock VP/VS ratio squared(DVRS).In the process of fluid factor calculation or inversion,the existing methods take this parameter as a static constant,which has been estimated in advance,and then apply it to the fluid factor calculation and inversion.The fluid identification analysis based on a portion of the Marmousi 2 model and numerical forward modeling test show that,taking the DVRS as a static constant will limit the identification ability of fluid factor and reduce the inversion accuracy.To solve the above problems,we proposed a new method to regard the DVRS as a dynamic variable varying with depth and lithology for the first time,then apply it to fluid factor calculation and inversion.Firstly,the exact Zoeppritz equations are rewritten into a new form containing the fluid factor and DVRS of upper and lower layers.Next,the new equations are applied to the four parameters simultaneous inversion based on the generalized nonlinear inversion(GNI)method.The testing results on a portion of the Marmousi 2 model and field data show that dynamic DVRS can significantly improve the fluid factor identification ability,effectively suppress illusion.Both synthetic and filed data tests also demonstrate that the GNI method based on Bayesian deterministic inversion(BDI)theory can successfully solve the above four parameter simultaneous inversion problem,and taking the dynamic DVRS as a target inversion parameter can effectively improve the inversion accuracy of fluid factor.All these results completely verified the feasibility and effectiveness of the proposed method.
基金Supported by the Key Research and Development Project of Guangdong Province(No.2020B1111510001)the National Natural Science Foundation of China(No.U2244224)+1 种基金the PI Project of Southern Marine Science and Engineering Guangdong Laboratory(Guangzhou)(No.GML2020GD0802)the Guangdong Special Support Team Program(No.2019BT02H594)。
文摘Bivalve shell fossils,cemented by authigenic carbonates,are widely spread in the Haima cold seep,Qiongdongnan Basin of the South China Sea(SCS).In this study,we examined an element profile of Gigantidas platifrons in the Haima cold seeps at a water depth of 1381 m.Based on the scanning electron microscope(SEM)analyses,the prismatic layer and nacreous layer were identified,which are characterized by prismatic structure and stratified structure,respectively.In addition,the profile can be subdivided into two parts:altered and unaltered zones.Laser inductively coupled plasma mass spectrometry(LA-ICP-MS)mapping shows that the element concentrations of the altered zones were influenced by the authigenic carbonate rocks,whereas the element concentrations of unaltered zones remain stable.In-situ X-ray diffraction(XRD)analyses show that the mineral constituent of the prismatic layer is mainly composed of aragonite.Along with the growth profile,Mg/Ca ratios of unaltered zones have minor variations,ranging 0.72-0.97 mmol/mol(mean=0.87 mmol/mol),with estimated temperatures of 3.8-4.1℃,indicating that the temperature of the surrounding seawater remains constant and agree with the measured data of 3.9℃which was conducted by a conductivity-temperature-depth system(CTD).The minor variations of Ba/Ca ratios(0.01-0.06 mmol/mol;mean=0.04 mmol/mol)indicate a relatively stabilized salinity of the surrounding seawater.S/Ca ratios show large variations of 0.04-4.15 mmol/mol(mean=1.37 mmol/mol).S/Ca ratios have regular variations which generally correspond to the variations of the Mg/Ca ratios,highlighting that the S/Ca ratios of bivalve shells show the potential to reflect the growth rate of the Gigantides.However,further studies should be carried out on the understanding of the links between the S/Ca ratios and seepage intensity of cold-seep fluids.
文摘Poisson’s ratio changes during the tensile stress of technical fabric samples due to the anisotropy of technical fabrics.This paper examines the effects of the type of weave and the anisotropic characteristics of the technical fabric on maximum tensile force,corresponding elongation,work-to-maximum force,elasticity modulus,and Poisson’s ratio when axial tensile forces are applied to samples cut at various angles in the direction of the weft yarns of the technical fabric.In the lab,3 cotton fabric samples of constant warp and weft density with different structural weave types(plain weave,twill weave,atlas weave)were subjected to the tensile force until they broke at the following angles:0°,15°,30°,45°,60°,75°,90°.Based on the different measured values of technical fabric stretching in the longitudinal direction and lateral narrowing,Poisson’s ratio is calculated.The Poisson’s ratio was calculated up to a relative elongation of the fabric of 8%,as the buckling of the fabric occurs according to this elongation value.According to the results presented in this paper,the type of weave of the fabric,the direction of tensile force,and the relative narrowing of the technical fabrics all play important roles in the Poisson’s ratio value.The Poisson’s ratio curve of a technical fabric under tensile stress(i.e.elongation)is primarily determined by its behaviour in the opposite direction of the elongation.The change in the value of the Poisson’s ratio is represented by a graph that first increases nonlinearly and then decreases after reaching its maximum value.
基金Funded by the National Basic Research Program of China (973 Program) (No. 2009CB623201)the National Natural Science Foundation of China (No.51072150)
文摘The samples of the C-S-H series were synthesized by hydrothermal reaction of fumed silica, CaO and deionized water at initial C/S ratios between 1.0-1.7. Phase composition and structural and morphology characteristics of C-S-H samples were analyzed by XRD, IR and SEM. The experimental results showed that the d-spacing of （002）, （110） and （020） decreased, the d-spacing of （200） increased, and the d-spacing of （310） varied randomly, the polymerization of silica tetrahedra of C-S-H decreased, and morphology of C-S-H samples varied from sheet shapes to long reticular fibers as C/S ratio increased.
基金Project supported by the National Basic Research Program (973) of China(No.G1999022211)the National Natural Science Foun-dation of China(No.59836210).
文摘The experimental test of co-incinerating Chinese raw municipal solid waste （MSW） and coal in a laboratory-scale tubular reactor was first reported in present study, and the emission of normal gas components and the effects of the S/Cl molar ratio or coal mixing percentages on polychlorinated dibenzo-p-dioxins and dibenzofurans （PCDDs/Fs） emission were investigated and discussed. The results indicated that OCDD was the only PCDD homologues since others like TCDD-HpCDD was hardly detected, while as the categories of PCDF homologues were comparatively much more general. The amount of PCDD was much larger than that of PCDF in all operating conditions. Since ZPCDF/∑PCDD〈〈1, the dominant role of the precursor formation was proven in our experimental conductions. With increasing the coal addition to MSW （from 0 to 16%）, PCDD and PCDF were reduced considerably. Coal and MSW may suppress the PCDD/F emissions efficiently （over 95%） during the MSW incineration process. The PCDD/F suppression results of the present study could be helpful guidance to the industrial application of Chinese MSW and auxiliary coal co-incineration processes. The PCDD/F stack emission data of two industrial incinerators using co-incineration technology in China seem to have a great positive reduction of PCDDs/Fs.
文摘The generalized mixture rule(GMR) is used to provide a unified framework for describing Young’s(E),shear(G) and bulk(K) moduli, Lame parameter(l), and P- and S-wave velocities(Vpand Vs) as a function of porosity in various isotropic materials such as metals, ceramics and rocks. The characteristic J values of the GMR for E, G, K and l of each material are systematically different and display consistent correlations with the Poisson’s ratio of the nonporous material(v0). For the materials dominated by corner-shaped pores, the fixed point at which the effective Poisson’s ratio(n) remains constant is at v0=0.2, and J(G) > J(E) > J(K) > J(l) and J(G) < J(E) < J(K) < J(l) for materials with v0> 0.2 and v0< 0.2, respectively.J(Vs) > J(Vp) and J(Vs) < J(Vp) for the materials with v0> 0.2 and v0< 0.2, respectively. The effective n increases, decreases and remains unchanged with increasing porosity for the materials with v0< 0.2,v0> 0.2 and v0=0.2, respectively. For natural rocks containing thin-disk-shaped pores parallel to mineral cleavages, grain boundaries and foliation, however, the n fixed point decreases nonlinearly with decreasing pore aspect ratio(a: width/length). With increasing depth or pressure, cracks with smaller a values are progressively closed, making the n fixed point rise and finally reach to the point at v0=0.2.
