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
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
Objective:To establish the quality standards for the preparation of Xiao’er Qingre enema in hospitals.Method:Thin-layer chromatography(TLC)was used to identify Radix Isatidis and Glycyrrhizae in the prescription.The ...Objective:To establish the quality standards for the preparation of Xiao’er Qingre enema in hospitals.Method:Thin-layer chromatography(TLC)was used to identify Radix Isatidis and Glycyrrhizae in the prescription.The content of(R,S)-Goitrin was determined by high-performance liquid chromatography(HPLC).Results:In TLC identification,there was no interference between the negative controls of Radix Isatidis and glycyrrhizae,and the spots were well-separated.The HPLC results of(R,S)-Goitrin showed a good linear relationship between the peak area and concentration within the range of 0.476-95.2μg·mL-1(r=0.9999).Conclusion:The TLC and HPLC methods established in this experiment are simple,reproducible,and specific,making them suitable for the quality control Xiao’er Qingre enema preparation in hospitals.展开更多
应变-旋转(Strain-Rotation,S-R)和分解定理为分析几何非线性问题提供了合理可靠的理论基础,但用有限元求解时会遇到大变形发生后的网格畸变问题。近年提出的虚单元法(Virtual element method,VEM)适用于一般的多边形网格,因此,该文尝...应变-旋转(Strain-Rotation,S-R)和分解定理为分析几何非线性问题提供了合理可靠的理论基础,但用有限元求解时会遇到大变形发生后的网格畸变问题。近年提出的虚单元法(Virtual element method,VEM)适用于一般的多边形网格,因此,该文尝试使用一阶虚单元求解基于S-R和分解定理的二维几何非线性问题,以克服网格畸变的影响。基于重新定义的多项式位移空间基函数,推演获得一阶虚单元分析线弹性力学问题时允许位移空间向多项式位移空间的投影表达式;按照虚单元法双线性格式的计算规则,分析处理基于更新拖带坐标法和势能率原理的增量变分方程;进而建立离散系统方程及其矩阵表达形式,并编制MATLAB求解程序;采用常规多边形网格和畸变网格,应用该文算法分析均布荷载下的悬臂梁和均匀内压下的厚壁圆筒变形。结果与已有文献和ANSYS软件的对比表明:该文算法在两种网格中均可有效执行且具备足够数值精度。总体该文算法为基于S-R和分解定理的二维几何非线性问题求解提供了一种鲁棒方法。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
In gas turbines, thermal barrier coatings (TBCs) applied by air plasma spraying are widely used to lower the temperature of hot components. To analyze the characteristics of TBCs such as residual stress, bond streng...In gas turbines, thermal barrier coatings (TBCs) applied by air plasma spraying are widely used to lower the temperature of hot components. To analyze the characteristics of TBCs such as residual stress, bond strength, fracture toughness, and crack propagation ratio, the Young's modulus and Poisson's ratio are important parameters. For TBC is a brittle and thin film, it is desirable to evaluate those properties while the coatings are bonded to a substrate. An atmospheric plasma spray MCrAIY bond coat and Yttria stabilized zirconia (YSZ) top coat are deposited onto a nickel-base superalloy GH150 substrate. The Young's modulus and Poisson's ratio are measured by cantilever beam bending with NDI. The method will be developed to test the Young' s modulus and Poisson ratio of other multilayer systems.展开更多
The attenuation factor or quality factor(Q-factor or Q) has been used to measure the energy attenuation of seismic waves propagating in underground media. Many methods are used to estimate the Q-factor. We propose a m...The attenuation factor or quality factor(Q-factor or Q) has been used to measure the energy attenuation of seismic waves propagating in underground media. Many methods are used to estimate the Q-factor. We propose a method to calculate the Q-factor based on the prestack Q-factor inversion and the generalized S-transform. The proposed method specifies a standard primary wavelet and calculates the cumulative Q-factors; then, it finds the interlaminar Q-factors using the relation between Q and offset(QVO) and the Dix formula. The proposed method is alternative to methods that calculate interlaminar Q-factors after horizon picking. Because the frequency spectrum of each horizon can be extracted continuously on a 2D time–frequency spectrum, the method is called the continuous spectral ratio slope(CSRS) method. Compared with the other Q-inversion methods, the method offers nearly effortless computations and stability, and has mathematical and physical significance. We use numerical modeling to verify the feasibility of the method and apply it to real data from an oilfield in Ahdeb, Iraq. The results suggest that the resolution and spatial stability of the Q-profile are optimal and contain abundant interlaminar information that is extremely helpful in making lithology and fluid predictions.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
BACKGROUND In spite of developing medical technologies to discover the etiopathogenesis of diseases and developments in the treatment of coronary artery disease, acute coronary syndromes(ACS) continue to be the main c...BACKGROUND In spite of developing medical technologies to discover the etiopathogenesis of diseases and developments in the treatment of coronary artery disease, acute coronary syndromes(ACS) continue to be the main cause of mortality and morbidity worldwide. New cardiac biomarkers and techniques are needed to help provide rapid diagnosis in order to evaluate risk in coronary artery patients.AIM To evaluate the effects of R to S ratio(RSR) in the electrocardiograph of patients with ACS, from the point of the arising complication after myocardial infarction(MI), to three-vessel disease(TVD) and mortality.METHODS The data of 1,296 patients with ACS, who presented to the emergency department of our hospital with chest pain between January 2014 and December2018 and were admitted to the cardiology clinic, were retrospectively included in this cross-sectional cohort study. Patients with an RSR value less than I were assigned to group Ⅰ, while those with an RSR value greater than Ⅰ were assigned to group Ⅱ.RESULTS In our study, 466(35.9%) of the 1,296 patients, 357(38.3%) in group 1 and 109(29.9%) in group 2, were female, with a mean age of 61.56 ± 9.42. ST-elevation MI 573(44.2%), unstable angina(UA) 502(38.7%) and non ST-elevation MI 220(17%)were more prevalent in group Ⅰ. Acute anterior MI 263(20.3) in group Ⅰ, and acute inferior MI 184(14.2) in group Ⅱ was higher. Ischemic heart failure was the most common complication. In group Ⅱ, the red cell distribution width(RDW) was 15.42 ± 1.82, the gensini score was 48.39 ± 36.44, the left ventricular ejection fraction was 41.17 ± 10.41, the TVD was 111(8.5), and the mortality rate was 72(5.6), which was significantly higher than group Ⅰ RDW; in MI with ST and nonST-elevation, in TVD, mortality and complications were high and low in UA. In single and multivariate regression analyses, the variables were associated with ACS risk.CONCLUSION RSR levels may be an auxiliary predictive value in ACS in terms of complications developing after MI, TVD, and mortality.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 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Xi’an Science and Technology Plan Project(Project number:23YXYJ0163)Education and Teaching Reform Research Project of Xi,an Medical University in(2023)(Project number:S202311840061)First Affiliated Hospital of Xi’an Medical University of China(Fund number:XYYFY-2023-01).
文摘Objective:To establish the quality standards for the preparation of Xiao’er Qingre enema in hospitals.Method:Thin-layer chromatography(TLC)was used to identify Radix Isatidis and Glycyrrhizae in the prescription.The content of(R,S)-Goitrin was determined by high-performance liquid chromatography(HPLC).Results:In TLC identification,there was no interference between the negative controls of Radix Isatidis and glycyrrhizae,and the spots were well-separated.The HPLC results of(R,S)-Goitrin showed a good linear relationship between the peak area and concentration within the range of 0.476-95.2μg·mL-1(r=0.9999).Conclusion:The TLC and HPLC methods established in this experiment are simple,reproducible,and specific,making them suitable for the quality control Xiao’er Qingre enema preparation in hospitals.
文摘应变-旋转(Strain-Rotation,S-R)和分解定理为分析几何非线性问题提供了合理可靠的理论基础,但用有限元求解时会遇到大变形发生后的网格畸变问题。近年提出的虚单元法(Virtual element method,VEM)适用于一般的多边形网格,因此,该文尝试使用一阶虚单元求解基于S-R和分解定理的二维几何非线性问题,以克服网格畸变的影响。基于重新定义的多项式位移空间基函数,推演获得一阶虚单元分析线弹性力学问题时允许位移空间向多项式位移空间的投影表达式;按照虚单元法双线性格式的计算规则,分析处理基于更新拖带坐标法和势能率原理的增量变分方程;进而建立离散系统方程及其矩阵表达形式,并编制MATLAB求解程序;采用常规多边形网格和畸变网格,应用该文算法分析均布荷载下的悬臂梁和均匀内压下的厚壁圆筒变形。结果与已有文献和ANSYS软件的对比表明:该文算法在两种网格中均可有效执行且具备足够数值精度。总体该文算法为基于S-R和分解定理的二维几何非线性问题求解提供了一种鲁棒方法。
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.
文摘In gas turbines, thermal barrier coatings (TBCs) applied by air plasma spraying are widely used to lower the temperature of hot components. To analyze the characteristics of TBCs such as residual stress, bond strength, fracture toughness, and crack propagation ratio, the Young's modulus and Poisson's ratio are important parameters. For TBC is a brittle and thin film, it is desirable to evaluate those properties while the coatings are bonded to a substrate. An atmospheric plasma spray MCrAIY bond coat and Yttria stabilized zirconia (YSZ) top coat are deposited onto a nickel-base superalloy GH150 substrate. The Young's modulus and Poisson's ratio are measured by cantilever beam bending with NDI. The method will be developed to test the Young' s modulus and Poisson ratio of other multilayer systems.
基金supported by The National Key Research and Development Program Plane(No.2017YFC0601505)National Natural Science Foundation(No.41672325)Science&Technology Department of Sichuan Province Technology Project(No.2017GZ0393)
文摘The attenuation factor or quality factor(Q-factor or Q) has been used to measure the energy attenuation of seismic waves propagating in underground media. Many methods are used to estimate the Q-factor. We propose a method to calculate the Q-factor based on the prestack Q-factor inversion and the generalized S-transform. The proposed method specifies a standard primary wavelet and calculates the cumulative Q-factors; then, it finds the interlaminar Q-factors using the relation between Q and offset(QVO) and the Dix formula. The proposed method is alternative to methods that calculate interlaminar Q-factors after horizon picking. Because the frequency spectrum of each horizon can be extracted continuously on a 2D time–frequency spectrum, the method is called the continuous spectral ratio slope(CSRS) method. Compared with the other Q-inversion methods, the method offers nearly effortless computations and stability, and has mathematical and physical significance. We use numerical modeling to verify the feasibility of the method and apply it to real data from an oilfield in Ahdeb, Iraq. The results suggest that the resolution and spatial stability of the Q-profile are optimal and contain abundant interlaminar information that is extremely helpful in making lithology and fluid predictions.
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BACKGROUND In spite of developing medical technologies to discover the etiopathogenesis of diseases and developments in the treatment of coronary artery disease, acute coronary syndromes(ACS) continue to be the main cause of mortality and morbidity worldwide. New cardiac biomarkers and techniques are needed to help provide rapid diagnosis in order to evaluate risk in coronary artery patients.AIM To evaluate the effects of R to S ratio(RSR) in the electrocardiograph of patients with ACS, from the point of the arising complication after myocardial infarction(MI), to three-vessel disease(TVD) and mortality.METHODS The data of 1,296 patients with ACS, who presented to the emergency department of our hospital with chest pain between January 2014 and December2018 and were admitted to the cardiology clinic, were retrospectively included in this cross-sectional cohort study. Patients with an RSR value less than I were assigned to group Ⅰ, while those with an RSR value greater than Ⅰ were assigned to group Ⅱ.RESULTS In our study, 466(35.9%) of the 1,296 patients, 357(38.3%) in group 1 and 109(29.9%) in group 2, were female, with a mean age of 61.56 ± 9.42. ST-elevation MI 573(44.2%), unstable angina(UA) 502(38.7%) and non ST-elevation MI 220(17%)were more prevalent in group Ⅰ. Acute anterior MI 263(20.3) in group Ⅰ, and acute inferior MI 184(14.2) in group Ⅱ was higher. Ischemic heart failure was the most common complication. In group Ⅱ, the red cell distribution width(RDW) was 15.42 ± 1.82, the gensini score was 48.39 ± 36.44, the left ventricular ejection fraction was 41.17 ± 10.41, the TVD was 111(8.5), and the mortality rate was 72(5.6), which was significantly higher than group Ⅰ RDW; in MI with ST and nonST-elevation, in TVD, mortality and complications were high and low in UA. In single and multivariate regression analyses, the variables were associated with ACS risk.CONCLUSION RSR levels may be an auxiliary predictive value in ACS in terms of complications developing after MI, TVD, and mortality.
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.