Due to the high degeneracy and singularity of the entropy equation,the physical entropy for viscous and heat-conductive polytropic gases behaves singularly in the presence of vacuum,and it is thus a challenge to study...Due to the high degeneracy and singularity of the entropy equation,the physical entropy for viscous and heat-conductive polytropic gases behaves singularly in the presence of vacuum,and it is thus a challenge to study its dynamics.It is shown in this paper that the uniform boundedness of the entropy and the inhomogeneous Sobolev regularities of the velocity and temperature can be propagated for viscous and heat-conductive gases in R3,provided that the initial vacuum occurs only at far fields with suitably slow decay of the initial density.Precisely,it is proved that for any strong solution to the Cauchy problem of the heat-conductive compressible Navier-Stokes equations,the corresponding entropy remains uniformly bounded,and the L2 regularities of the velocity and temperature can be propagated,up to the existing time of the solution,as long as the initial density vanishes only at far fields with a rate not faster than O(1/|x|^(2)).The main tools are some singularly weighted energy estimates and an elaborate De Giorgi-type iteration technique.We apply the De Giorgi-type iterations to different equations in establishing the lower and upper bounds of the entropy.展开更多
The boundary between the near and far fields is generally defined as the distance from the vibration source beyond which ground vibrations are mainly dominated by Rayleigh waves. It is closely related to the type of v...The boundary between the near and far fields is generally defined as the distance from the vibration source beyond which ground vibrations are mainly dominated by Rayleigh waves. It is closely related to the type of vibration source and the soil properties. Based on the solutions of the Lamb＇s problem, the boundary at the surface between the near and far fields of ground vibration was investigated for a harmonic vertical concentrated load and an infinite line load at the surface of a visco-elastic half-space. Particularly, the variation of the boundary with the material damping was investigated for both cases. The results indicate that the material damping slightly contributes to the attenuation of vibrations in the near-source region, but significantly reduces the vibrations in the region that is at some distance away from the source. When taking the material damping into consideration, the boundary between the near and far fields tends to move towards the vibration source. Compared with the vibrations caused by a concentrated load, the vibrations induced by an infinite line load can affect a larger range of the surrounding environment, and they attenuate more slowly. This means the boundary between the near field and far field should move fitrther away from the source. Finally, the boundaries are defined in terms of R-wave length （2R） and Poisson ratio of the ground （o）. For the case of a point load, the boundary is located at the distance of （5.0-6.0）2R for v≤0.30 and at the distance of （2.0--3.0）2R for v≥0.35. For the case of an infinite line load, the boundary is located at the distance （5.5-6.5）2rt for v≤0.30 and at the distance （2.5--3.5）2R for v≥0.35.展开更多
On the assumption that seismic source is simplified as linear rupture fault with finite length, this paper qualitatively studies the seismic source effects on space correlation of strong ground motion. Based on expand...On the assumption that seismic source is simplified as linear rupture fault with finite length, this paper qualitatively studies the seismic source effects on space correlation of strong ground motion. Based on expanding expression of Fourier spectrum of strong ground motion with space coordinate variables, this paper also gives a expression of describing correlation of strong ground motion field. According to far-field condition, the theoretical formula of the expression can be obtained. Furthermore, this paper presents a theoretical formula of estimation the radius of strong ground motion field, which depends on expansion condition of Fourier spectrum of strong ground motion, with space variables. At last, taking one earthquake as an example, this paper gives three-dimension patterns of radius of the field with epicenter distance and azimuth as well as frequency.展开更多
Accidents such as support failure and excessive deformation of roadways due to drastic changes in strata behaviors are frequently reported when mining the extra-thick coal seams Nos.3e5 in Datong coal mine with top-co...Accidents such as support failure and excessive deformation of roadways due to drastic changes in strata behaviors are frequently reported when mining the extra-thick coal seams Nos.3e5 in Datong coal mine with top-coal caving method,which significantly hampers the mine's normal production.To understand the mechanism of strata failure,this paper presented a structure evolution model with respect to strata behaviors.Then the behaviors of strata overlying the extra-thick coal seams were studied with the combined method of theoretical analysis,physical simulation,and field measurement.The results show that the key strata,which are usually thick-hard strata,play an important role in overlying movement and may influence the mining-induced strata behaviors in the working face using top-coal caving method.The structural model of far-field key strata presents a 'masonry beam' type structure when'horizontal O-X' breakage type happens.The rotational motion of the block imposed radial compressive stress on the surrounding rock mass of the roadway.This can induce excessive deformation of roadway near the goaf.Besides,this paper proposed a pre-control technology for the hard roof based on fracture holes and underground roof pre-splitting.It could effectively reduce stress concentration and release the accumulated energy of the strata,when mining underground coal resources with top-coal caving method.展开更多
基金supported by National Natural Science Foundation of China(Grant No.12131010)the Guangdong Basic and Applied Basic Research Foundation(Grant No.2020B1515310002)+2 种基金supported by National Natural Science Foundation of China(Grant Nos.11971009 and 11871005)the Guangdong Basic and Applied Basic Research Foundation(Grant Nos.2019A1515011621 and 2020B1515310005)supported by the Zheng Ge Ru Foundation and the Hong Kong RGC Earmarked Research Grants(Grant Nos.CUHK-14305315,CUHK-14300917 and CUHK-14302819).
文摘Due to the high degeneracy and singularity of the entropy equation,the physical entropy for viscous and heat-conductive polytropic gases behaves singularly in the presence of vacuum,and it is thus a challenge to study its dynamics.It is shown in this paper that the uniform boundedness of the entropy and the inhomogeneous Sobolev regularities of the velocity and temperature can be propagated for viscous and heat-conductive gases in R3,provided that the initial vacuum occurs only at far fields with suitably slow decay of the initial density.Precisely,it is proved that for any strong solution to the Cauchy problem of the heat-conductive compressible Navier-Stokes equations,the corresponding entropy remains uniformly bounded,and the L2 regularities of the velocity and temperature can be propagated,up to the existing time of the solution,as long as the initial density vanishes only at far fields with a rate not faster than O(1/|x|^(2)).The main tools are some singularly weighted energy estimates and an elaborate De Giorgi-type iteration technique.We apply the De Giorgi-type iterations to different equations in establishing the lower and upper bounds of the entropy.
基金Project(51178342)supported by the National Natural Science Foundation of ChinaProject(KLE-TJGE-C1301)supported by the Key Laboratory of Geotechnical and Underground Engineering of Ministry of Education(Tongji University)under the International Cooperation and Exchange Program,China
文摘The boundary between the near and far fields is generally defined as the distance from the vibration source beyond which ground vibrations are mainly dominated by Rayleigh waves. It is closely related to the type of vibration source and the soil properties. Based on the solutions of the Lamb＇s problem, the boundary at the surface between the near and far fields of ground vibration was investigated for a harmonic vertical concentrated load and an infinite line load at the surface of a visco-elastic half-space. Particularly, the variation of the boundary with the material damping was investigated for both cases. The results indicate that the material damping slightly contributes to the attenuation of vibrations in the near-source region, but significantly reduces the vibrations in the region that is at some distance away from the source. When taking the material damping into consideration, the boundary between the near and far fields tends to move towards the vibration source. Compared with the vibrations caused by a concentrated load, the vibrations induced by an infinite line load can affect a larger range of the surrounding environment, and they attenuate more slowly. This means the boundary between the near field and far field should move fitrther away from the source. Finally, the boundaries are defined in terms of R-wave length （2R） and Poisson ratio of the ground （o）. For the case of a point load, the boundary is located at the distance of （5.0-6.0）2R for v≤0.30 and at the distance of （2.0--3.0）2R for v≥0.35. For the case of an infinite line load, the boundary is located at the distance （5.5-6.5）2rt for v≤0.30 and at the distance （2.5--3.5）2R for v≥0.35.
文摘On the assumption that seismic source is simplified as linear rupture fault with finite length, this paper qualitatively studies the seismic source effects on space correlation of strong ground motion. Based on expanding expression of Fourier spectrum of strong ground motion with space coordinate variables, this paper also gives a expression of describing correlation of strong ground motion field. According to far-field condition, the theoretical formula of the expression can be obtained. Furthermore, this paper presents a theoretical formula of estimation the radius of strong ground motion field, which depends on expansion condition of Fourier spectrum of strong ground motion, with space variables. At last, taking one earthquake as an example, this paper gives three-dimension patterns of radius of the field with epicenter distance and azimuth as well as frequency.
基金supported by the Special Funding Projects of“Sanjin Scholars”Supporting Plan(Grant No.2050205)
文摘Accidents such as support failure and excessive deformation of roadways due to drastic changes in strata behaviors are frequently reported when mining the extra-thick coal seams Nos.3e5 in Datong coal mine with top-coal caving method,which significantly hampers the mine's normal production.To understand the mechanism of strata failure,this paper presented a structure evolution model with respect to strata behaviors.Then the behaviors of strata overlying the extra-thick coal seams were studied with the combined method of theoretical analysis,physical simulation,and field measurement.The results show that the key strata,which are usually thick-hard strata,play an important role in overlying movement and may influence the mining-induced strata behaviors in the working face using top-coal caving method.The structural model of far-field key strata presents a 'masonry beam' type structure when'horizontal O-X' breakage type happens.The rotational motion of the block imposed radial compressive stress on the surrounding rock mass of the roadway.This can induce excessive deformation of roadway near the goaf.Besides,this paper proposed a pre-control technology for the hard roof based on fracture holes and underground roof pre-splitting.It could effectively reduce stress concentration and release the accumulated energy of the strata,when mining underground coal resources with top-coal caving method.
