Blasting-induced cracks in the rock surrounding deeply buried tunnels can result in water gushing and rock mass collapse,posing significant safety risks.However,previous theoretical studies on the range of blasting-in...Blasting-induced cracks in the rock surrounding deeply buried tunnels can result in water gushing and rock mass collapse,posing significant safety risks.However,previous theoretical studies on the range of blasting-induced cracks often ignore the impact of the in-situ stress,especially that of the intermediate principal stress.The particle displacement−crack radius relationship was established in this paper by utilizing the blasthole cavity expansion equation,and theoretical analytical formulas of the stress−displacement relationship and the crack radius were derived with unified strength theory to accurately assess the range of cracks in deep surrounding rock under a blasting load.Parameter analysis showed that the crushing zone size was positively correlated with in-situ stress,intermediate principal stress,and detonation pressure,whereas negatively correlated with Poisson ratio and decoupling coefficient.The dilatancy angle-crushing zone size relationship exhibited nonmonotonic behavior.The relationships in the crushing zone and the fracture zone exhibited opposite trends under the influence of only in-situ stress or intermediate principal stress.As the in-situ stress increased from 0 to 70 MPa,the rate of change in the crack range and the attenuation rate of the peak vibration velocity gradually slowed.展开更多
-According to basic equations of fluid mechanics, this paper presents a unified variational principle of fluid mechanics (UVPFM) by using the optimization method of weighted residuals (OMWR). The advantages are as fol...-According to basic equations of fluid mechanics, this paper presents a unified variational principle of fluid mechanics (UVPFM) by using the optimization method of weighted residuals (OMWR). The advantages are as follows, the establishment of the functional and the variational principle is easy, it can change various problems of fluid mechanics derived by basic equations into a unified optimization problem, and the solution is the optimum one in some sense. According to the OMWR for the solitary subdomain, this paper uses UVPFM onto any solitary subdomain and gives the solution of the hydrodynamics equation which is suitable only for that solitary subdomain. According to the OMWR for solitary point, this paper uses UVPFM to any solitary point and gives the solution of the hydrodynamics equation (point solution) which is suitable only for that solitary point. As the solution for the solitary subdomain or solitary point is developed independently, the compatibility with other subdomain or other points, does not need to be considered, but all the boundary conditions and the supplementary derived residual equations obtained by running the derivative operations to the differential equation should be taken into account.展开更多
The stratification processes have been studied by the application of the similarity principle, and the similarity criteria has also been derived.Two possible π-equations were deduced from the experimental results.The...The stratification processes have been studied by the application of the similarity principle, and the similarity criteria has also been derived.Two possible π-equations were deduced from the experimental results.The approach of the π-equation to predict separating results and to control the separating processes is presented with examples.展开更多
Previous theoretical studies have found that the concentration variations within a certain range have a prominent effect on inter-mineral equilibrium isotope fractionation(10^3 lna).Based on the density functional the...Previous theoretical studies have found that the concentration variations within a certain range have a prominent effect on inter-mineral equilibrium isotope fractionation(10^3 lna).Based on the density functional theory,we investigated how the average Ca–O bond length and the reduced partition function ratios(10^3 lnb)and103lna of 44 Ca/40 Ca in forsterite(Fo)are affected by its Ca concentration.Our results show that Ca–O bond length in forsterite ranges from 2.327 to 2.267 A with the Ca/(Ca+Mg)varying between a narrow range limited by an upper limit of 1/8 and a lower limit of 1/64.However,outside this narrow range,i.e.,Ca/(Ca+Mg)is lower than1/64 or higher than 1/8,Ca–O bond length becomes insensitive to Ca concentration and maintains to be a constant.Because the 10^3 lnb is negatively correlated with Ca–O bond length,the 10^3lnb significantly increases with decreasing Ca/(Ca+Mg)when 1/64<Ca/(Ca+Mg)<2/16.As a consequence,the 10^3lna between forsterite and other minerals also strongly depend on the Ca content in forsterite.Combining previous studies with our results,the heavier Ca isotopes enrichment sequence in minerals is:forsterite[orthopyroxene[clinopyroxene[calcite & diopside[dolomite[aragonite.Olivineand pyroxenes are enriched in heavier Ca isotope compared to carbonates.The 10^3lna between forsterite with a Ca/(Ca+Mg)of 1/64 and clinopyroxene(Ca/Mg=1/1,i.e.,diopside)is up to^0.64%at 1200 K.The large 103lnaFodiopsiderelative to the current analytical precision for Ca isotope measurements suggests that the dependence of10^3 lnaFo-diopsideon temperature can be used as a thermometer,similar to the one based on the 103lna of 44 Ca/40 Ca between orthopyroxene and diopside.These two Ca isotope thermometers both have a precision approximate to that of elemental thermometers and provide independent constraints on temperature.展开更多
Considering that at present the regular waves in common use have the profile symmetrized to a vertical axis, which are different from actual wind-driven sea waves, and based on deriving linear wave, solitary wave, fif...Considering that at present the regular waves in common use have the profile symmetrized to a vertical axis, which are different from actual wind-driven sea waves, and based on deriving linear wave, solitary wave, fifth order Stokes wave and stream function wave by using Unified Variational Principle of Water Gravity Wave (UVPWGW), this paper derives wind-driven slanting profile wave by using UVPWGW. Its feature is that under the action of wind pressure, the wave profile is not symmetrized to a vertical axis, but that it is in the forward slanting form.展开更多
Based on the linear wave, solitary wave and fifth order stokes wave derived by use of the Unified Variational Principle of Water Gravity Wave (UVPWGW), this paper derives stream function wave theory by using UVPWGW. T...Based on the linear wave, solitary wave and fifth order stokes wave derived by use of the Unified Variational Principle of Water Gravity Wave (UVPWGW), this paper derives stream function wave theory by using UVPWGW. This paper will handle the Kinematic Free Surface Boundary Condition (KFSBC) and Dynamic Free Surface Boundary Condition (DFSBC) directly and give the optimum solution, instead of the conditions Sigma(Q(av) - Q(i))(2) = min, and the related equations of stational condition. When the wave height H, period T and water depth D are given, the original stream function wave will be determined, and can not be adjusted if it does not agree with the real case; in the present method, the adjustment can be done by adding several constraint conditions, for example, the wave profile can be adjusted according to the condition of accurate peak position. The examples given in this paper show that for the original stream function wave, the DFSBC can be fairly well satisfied, but the KFSBC can not; however, the stream function wave derived by UVPWGW is better than the original one in the sense of minimum error squares in the aspect of the level at which KFSBC and DFSBC are satisfied.展开更多
In order to study the mechanism of bearing behavior at the tip of a pile embedded in rock, the generalized nonlinear unified strength criterion and slip line principle for resolving the differential equation systems w...In order to study the mechanism of bearing behavior at the tip of a pile embedded in rock, the generalized nonlinear unified strength criterion and slip line principle for resolving the differential equation systems which govern the stress field were applied to derive the ultimate end beating capacity based on some reasonable hypothesis and failure plane model. Both numerical simulation and test results were compared with the theoretic solution. The results show good consistency with each other and verify the validity of the present approach. The depth effect with respective to embedment ratio and other influence factors like geological strength index, intermediate principal stress, overburden factor, and damage on end bearing capacity were discussed in the analytical solution. The results show that the proposed yield criterion can be much better for investigating the ultimate end bearing performance of rock-socketed pile. The end bearing capacity increases with embedment ratio and the increasing degree is influenced intensely by the above parameters. Furthermore, ignoring intermediate stress effect would underestimate the strength properties of the rock material and lead to a very conservative estimation value.展开更多
In this paper, we study blow-up solutions of the Cauchy problem to the L2 critical nonlinear Schrdinger equation with a Stark potential. Using the variational characterization of the ground state for nonlinear Schrdin...In this paper, we study blow-up solutions of the Cauchy problem to the L2 critical nonlinear Schrdinger equation with a Stark potential. Using the variational characterization of the ground state for nonlinear Schrdinger equation without any potential, we obtain some concentration properties of blow-up solutions, including that the origin is the blow-up point of the radial blow-up solutions, the phenomenon of L2-concentration and rate of L2-concentration of blow-up solutions.展开更多
Stochastic Quantum Space (SQS) theory is a new version of unified field theory based on three fundamental postulations: Gaussian Probability Postulation, Prime Numbers Postulation, Vacuon Postulation. It build a frame...Stochastic Quantum Space (SQS) theory is a new version of unified field theory based on three fundamental postulations: Gaussian Probability Postulation, Prime Numbers Postulation, Vacuon Postulation. It build a framework with theoretical results agree with many experimental data well. For more information, please refer to the PDF.展开更多
Based on the measured activities, the phase diagrams and the annexation principle, the calculating models of mass action concentrations for Ag-Bi and Ag-Bi-In melts have been formulated. The calculated results agree w...Based on the measured activities, the phase diagrams and the annexation principle, the calculating models of mass action concentrations for Ag-Bi and Ag-Bi-In melts have been formulated. The calculated results agree with practice and obey the mass action law, showing that the models formulated can reflect the structural characteristics of both melts. Meanwhile, it confirms that annexation principle is applicable to the Ag-Bi-In metallic melts. The melts involving eulectic which give rise to phase separation, and in which activities exhibit positive deviation from Raoult's law is the basic cause of melts transforming from homogeneous to heterogeneous ones.展开更多
Based on the principle of annexation and phase diagrams, the structural units of In Pb Sb and In Bi Pb melts were determined, and their calculating models of mass action concentrations were formulated. Calculated resu...Based on the principle of annexation and phase diagrams, the structural units of In Pb Sb and In Bi Pb melts were determined, and their calculating models of mass action concentrations were formulated. Calculated results agree well with practical values, which in turn show that the models deduced can reflect the structural realities of corresponding melts and the principle of annexation is applicable not only to some binary metallic melts, but also to ternary metallic melts.展开更多
Based on the measured activities,the phase diagrams and the annexation principle,the calculating models of mass action concentrations for Ag-Bi and Ag-Bi-In melts have been formulated.The calculated results agree with...Based on the measured activities,the phase diagrams and the annexation principle,the calculating models of mass action concentrations for Ag-Bi and Ag-Bi-In melts have been formulated.The calculated results agree with practice and obey the mass action law,showing that the models formulated can reflect the structural characteristics of both melts.Meanwhile,it confirms that annexation principle is applicable to the Ag-Bi-In metallic melts.The melts involving eutectic which give rise to phase separation,and in which activcities exhibit positive deviation from Raoult's law is the basic cause of melts transforming from homogeneous to heterogeneous ones.展开更多
Based on the equivalence principle of deflection and stress, the concentrated vehicle load which acts on the center of continuously reinforced concrete pavement (CRCP) is translated into the equivalent half-wave sin...Based on the equivalence principle of deflection and stress, the concentrated vehicle load which acts on the center of continuously reinforced concrete pavement (CRCP) is translated into the equivalent half-wave sine load by the Fourier transform. On the basis of this transform and the small deflection theory of elastic thin plates, the deflection and stress formulae of CRCP under the concentrated vehicle load with a hollow foundation are put forward. The sensitivity of parameters is analyzed. The results show that maximum deflection is directly proportional to the concentrated vehicle load and the slab width, and inversely proportional to the lateral bending stiffness and slab thickness. The effects of slab width and thickness are significant with regard to maximum deflection. Maximum stress is directly proportional to the concentrated vehicle load and the slab width as well as inversely proportional to slab thickness. The effect of slab thickness is significant with regard to maximum stress. According to the calculation results, the most effective measure to reduce maximum deflection and stress is to increase slab thickness.展开更多
基金Project(2021JJ10063)supported by the Natural Science Foundation of Hunan Province,ChinaProject(202115)supported by the Science and Technology Progress and Innovation Project of Hunan Provincial Department of Transportation,ChinaProject(2021K094-Z)supported by the Science and Technology Research and Development Program of China Railway Guangzhou Group Co.,Ltd。
文摘Blasting-induced cracks in the rock surrounding deeply buried tunnels can result in water gushing and rock mass collapse,posing significant safety risks.However,previous theoretical studies on the range of blasting-induced cracks often ignore the impact of the in-situ stress,especially that of the intermediate principal stress.The particle displacement−crack radius relationship was established in this paper by utilizing the blasthole cavity expansion equation,and theoretical analytical formulas of the stress−displacement relationship and the crack radius were derived with unified strength theory to accurately assess the range of cracks in deep surrounding rock under a blasting load.Parameter analysis showed that the crushing zone size was positively correlated with in-situ stress,intermediate principal stress,and detonation pressure,whereas negatively correlated with Poisson ratio and decoupling coefficient.The dilatancy angle-crushing zone size relationship exhibited nonmonotonic behavior.The relationships in the crushing zone and the fracture zone exhibited opposite trends under the influence of only in-situ stress or intermediate principal stress.As the in-situ stress increased from 0 to 70 MPa,the rate of change in the crack range and the attenuation rate of the peak vibration velocity gradually slowed.
文摘-According to basic equations of fluid mechanics, this paper presents a unified variational principle of fluid mechanics (UVPFM) by using the optimization method of weighted residuals (OMWR). The advantages are as follows, the establishment of the functional and the variational principle is easy, it can change various problems of fluid mechanics derived by basic equations into a unified optimization problem, and the solution is the optimum one in some sense. According to the OMWR for the solitary subdomain, this paper uses UVPFM onto any solitary subdomain and gives the solution of the hydrodynamics equation which is suitable only for that solitary subdomain. According to the OMWR for solitary point, this paper uses UVPFM to any solitary point and gives the solution of the hydrodynamics equation (point solution) which is suitable only for that solitary point. As the solution for the solitary subdomain or solitary point is developed independently, the compatibility with other subdomain or other points, does not need to be considered, but all the boundary conditions and the supplementary derived residual equations obtained by running the derivative operations to the differential equation should be taken into account.
文摘The stratification processes have been studied by the application of the similarity principle, and the similarity criteria has also been derived.Two possible π-equations were deduced from the experimental results.The approach of the π-equation to predict separating results and to control the separating processes is presented with examples.
基金financially supported by the Natural Science Foundation of China (Nos. 41721002, 41473011)Special Program for Applied Research on Super Computation of the NSFC-Guangdong Joint Fund
文摘Previous theoretical studies have found that the concentration variations within a certain range have a prominent effect on inter-mineral equilibrium isotope fractionation(10^3 lna).Based on the density functional theory,we investigated how the average Ca–O bond length and the reduced partition function ratios(10^3 lnb)and103lna of 44 Ca/40 Ca in forsterite(Fo)are affected by its Ca concentration.Our results show that Ca–O bond length in forsterite ranges from 2.327 to 2.267 A with the Ca/(Ca+Mg)varying between a narrow range limited by an upper limit of 1/8 and a lower limit of 1/64.However,outside this narrow range,i.e.,Ca/(Ca+Mg)is lower than1/64 or higher than 1/8,Ca–O bond length becomes insensitive to Ca concentration and maintains to be a constant.Because the 10^3 lnb is negatively correlated with Ca–O bond length,the 10^3lnb significantly increases with decreasing Ca/(Ca+Mg)when 1/64<Ca/(Ca+Mg)<2/16.As a consequence,the 10^3lna between forsterite and other minerals also strongly depend on the Ca content in forsterite.Combining previous studies with our results,the heavier Ca isotopes enrichment sequence in minerals is:forsterite[orthopyroxene[clinopyroxene[calcite & diopside[dolomite[aragonite.Olivineand pyroxenes are enriched in heavier Ca isotope compared to carbonates.The 10^3lna between forsterite with a Ca/(Ca+Mg)of 1/64 and clinopyroxene(Ca/Mg=1/1,i.e.,diopside)is up to^0.64%at 1200 K.The large 103lnaFodiopsiderelative to the current analytical precision for Ca isotope measurements suggests that the dependence of10^3 lnaFo-diopsideon temperature can be used as a thermometer,similar to the one based on the 103lna of 44 Ca/40 Ca between orthopyroxene and diopside.These two Ca isotope thermometers both have a precision approximate to that of elemental thermometers and provide independent constraints on temperature.
文摘Considering that at present the regular waves in common use have the profile symmetrized to a vertical axis, which are different from actual wind-driven sea waves, and based on deriving linear wave, solitary wave, fifth order Stokes wave and stream function wave by using Unified Variational Principle of Water Gravity Wave (UVPWGW), this paper derives wind-driven slanting profile wave by using UVPWGW. Its feature is that under the action of wind pressure, the wave profile is not symmetrized to a vertical axis, but that it is in the forward slanting form.
文摘Based on the linear wave, solitary wave and fifth order stokes wave derived by use of the Unified Variational Principle of Water Gravity Wave (UVPWGW), this paper derives stream function wave theory by using UVPWGW. This paper will handle the Kinematic Free Surface Boundary Condition (KFSBC) and Dynamic Free Surface Boundary Condition (DFSBC) directly and give the optimum solution, instead of the conditions Sigma(Q(av) - Q(i))(2) = min, and the related equations of stational condition. When the wave height H, period T and water depth D are given, the original stream function wave will be determined, and can not be adjusted if it does not agree with the real case; in the present method, the adjustment can be done by adding several constraint conditions, for example, the wave profile can be adjusted according to the condition of accurate peak position. The examples given in this paper show that for the original stream function wave, the DFSBC can be fairly well satisfied, but the KFSBC can not; however, the stream function wave derived by UVPWGW is better than the original one in the sense of minimum error squares in the aspect of the level at which KFSBC and DFSBC are satisfied.
基金Project(2007AA11Z134) supported by the National High-tech Research and Development Program of ChinaProject(10JJ4035) supported by Hunan Provincial Natural Science Foundation of ChinaProject(04SK2008) supported by Hunan Provincial Science and Technology Department,China
文摘In order to study the mechanism of bearing behavior at the tip of a pile embedded in rock, the generalized nonlinear unified strength criterion and slip line principle for resolving the differential equation systems which govern the stress field were applied to derive the ultimate end beating capacity based on some reasonable hypothesis and failure plane model. Both numerical simulation and test results were compared with the theoretic solution. The results show good consistency with each other and verify the validity of the present approach. The depth effect with respective to embedment ratio and other influence factors like geological strength index, intermediate principal stress, overburden factor, and damage on end bearing capacity were discussed in the analytical solution. The results show that the proposed yield criterion can be much better for investigating the ultimate end bearing performance of rock-socketed pile. The end bearing capacity increases with embedment ratio and the increasing degree is influenced intensely by the above parameters. Furthermore, ignoring intermediate stress effect would underestimate the strength properties of the rock material and lead to a very conservative estimation value.
基金supported by National Science Foundation of China (11071177)
文摘In this paper, we study blow-up solutions of the Cauchy problem to the L2 critical nonlinear Schrdinger equation with a Stark potential. Using the variational characterization of the ground state for nonlinear Schrdinger equation without any potential, we obtain some concentration properties of blow-up solutions, including that the origin is the blow-up point of the radial blow-up solutions, the phenomenon of L2-concentration and rate of L2-concentration of blow-up solutions.
文摘Stochastic Quantum Space (SQS) theory is a new version of unified field theory based on three fundamental postulations: Gaussian Probability Postulation, Prime Numbers Postulation, Vacuon Postulation. It build a framework with theoretical results agree with many experimental data well. For more information, please refer to the PDF.
文摘Based on the measured activities, the phase diagrams and the annexation principle, the calculating models of mass action concentrations for Ag-Bi and Ag-Bi-In melts have been formulated. The calculated results agree with practice and obey the mass action law, showing that the models formulated can reflect the structural characteristics of both melts. Meanwhile, it confirms that annexation principle is applicable to the Ag-Bi-In metallic melts. The melts involving eulectic which give rise to phase separation, and in which activities exhibit positive deviation from Raoult's law is the basic cause of melts transforming from homogeneous to heterogeneous ones.
文摘Based on the principle of annexation and phase diagrams, the structural units of In Pb Sb and In Bi Pb melts were determined, and their calculating models of mass action concentrations were formulated. Calculated results agree well with practical values, which in turn show that the models deduced can reflect the structural realities of corresponding melts and the principle of annexation is applicable not only to some binary metallic melts, but also to ternary metallic melts.
文摘Based on the measured activities,the phase diagrams and the annexation principle,the calculating models of mass action concentrations for Ag-Bi and Ag-Bi-In melts have been formulated.The calculated results agree with practice and obey the mass action law,showing that the models formulated can reflect the structural characteristics of both melts.Meanwhile,it confirms that annexation principle is applicable to the Ag-Bi-In metallic melts.The melts involving eutectic which give rise to phase separation,and in which activcities exhibit positive deviation from Raoult's law is the basic cause of melts transforming from homogeneous to heterogeneous ones.
基金The Science Foundation of Ministry of Transport of the People's Republic of China(No.200731822301-7)
文摘Based on the equivalence principle of deflection and stress, the concentrated vehicle load which acts on the center of continuously reinforced concrete pavement (CRCP) is translated into the equivalent half-wave sine load by the Fourier transform. On the basis of this transform and the small deflection theory of elastic thin plates, the deflection and stress formulae of CRCP under the concentrated vehicle load with a hollow foundation are put forward. The sensitivity of parameters is analyzed. The results show that maximum deflection is directly proportional to the concentrated vehicle load and the slab width, and inversely proportional to the lateral bending stiffness and slab thickness. The effects of slab width and thickness are significant with regard to maximum deflection. Maximum stress is directly proportional to the concentrated vehicle load and the slab width as well as inversely proportional to slab thickness. The effect of slab thickness is significant with regard to maximum stress. According to the calculation results, the most effective measure to reduce maximum deflection and stress is to increase slab thickness.