The hydraulic testing of pre-existing fractures(HTPF)is one of the most promising in situ stress measurement methods,particularly for three-dimensional stress tensor determination.However,the stress tensor determinati...The hydraulic testing of pre-existing fractures(HTPF)is one of the most promising in situ stress measurement methods,particularly for three-dimensional stress tensor determination.However,the stress tensor determination based on the HTPF method requires at least six tests or a minimum of 14-15 tests(under different conditions)for reliable results.In this study,we modified the HTPF method by considering the shear stress on each pre-existing fracture,which increased the number of equations for the stress tensor determination and decreased the number of tests required.Different shear stresses were attributed to different fractures by random sampling;therefore,the stress tensors were obtained by searching for the optimal solution using the least squares criterion based on the Monte Carlo method.Thereafter,we constrained the stress tensor based on the tensile strength criterion,compressive strength criterion,and vertical stress constraints.The inverted stress tensors were presented and analyzed based on the tensorial nature of the stress using the Euclidean mean stress tensor.Two stress-measurement campaigns in Weifang(Shandong Province,China)and Mercantour road tunnel(France)were implemented to highlight the validity and efficiency of the modified HTPF(M-HTPF)method.The results showed that the M-HTPF method can be applied for stress tensor inversion using only three to four tests on pre-existing fractures,neglecting the stress gradient.The inversion results were confined to relatively small distribution dispersions and were significantly reliable and stable due to the shear stresses on the fractures and the stress constraints employed.The M-HTPF method is highly feasible and efficient for complete stress tensor determination in a single borehole.展开更多
Stress field plays a key role in geodynamics. In this study, an algorithm to determine the stress tensor and its confidence range from focal mechanism data by using grid search method was proposed. The experiment uses...Stress field plays a key role in geodynamics. In this study, an algorithm to determine the stress tensor and its confidence range from focal mechanism data by using grid search method was proposed. The experiment uses artificial focal mechanism data which were generated by extensional, compression and strike-slip stress regime and different level of noise, shows that the precision of the estimated stress tensor based on this algorithm is greatly improved compared with traditional algorithms. This algorithm has three advantages：（1） The global optimal solution of the stress tensor is determined by fine grid search of 1o×1o×1o×0.01 and local minimum value is avoided; （2） precision of focal mechanism data can be considered, i.e., different weight of the focal mechanism data contributes differently to the process of determining stress tensor; （3） the confidence range of the determined stress tensor can be obtained by using F-test. We apply this algorithm in the boundary zone of China, Vietnam and Laos, and obtain the stress field with SSE-NNW compressive stress direction and NEE-SWW extensional stress direction. The stress ratio is 0.6, which shows that the eigen values of the stress tensor are nearly in arithmetic sequence. The stress field in this region is consistent with the left-lateral strike slip of the Dienbien-Lauangphrabang arc fault. The result will be helpful in studying the geological dynamic process in this region.展开更多
The distributions of the wave-induced radiation stress tensor over depth are studied by us- ing the linear wave theory, which are divided into three regions, i. e., above the mean water level, be- low the wave trough ...The distributions of the wave-induced radiation stress tensor over depth are studied by us- ing the linear wave theory, which are divided into three regions, i. e., above the mean water level, be- low the wave trough level, and between these two levels. The computational expressions of the wave-in- duced radiation stress tensor at the arbitrary wave angle are established by means of the Eulerian coordi- nate transformation, and the asymptotic forms for deep and shallow water are also presented. The verti- cal variations of a 30°incident wave-induced radiation stress tensor in deep water, intermediate water and shallow water are calculated respectively. The following conclusions are obtained from computations. The wave-induced radiation stress tensor below the wave trough level is induced by the water wave parti- cle velocities only, whereas both the water wave particle velocities and the wave pressure contribute to the tensor above the wave trough level. The vertical variations of the wave-induced radiation stress ten- sor are influenced substantially by the velocity component in the direction of wave propagation. The dis- tributions of the wave-induced radiation stress tensor over depth are nonuiniform and the proportion of the tensor below the wave trough level becomes considerable in the shallow water. From the water surface to the seabed, the reversed variations occur for the predominant tensor components.展开更多
In this paper, the generalized Prandtl-Reuss (P-R) constitutive equations of elastic-plastic material in the presence of finite deformations through a new approach are studied. It analyzes the generalized P-R equation...In this paper, the generalized Prandtl-Reuss (P-R) constitutive equations of elastic-plastic material in the presence of finite deformations through a new approach are studied. It analyzes the generalized P-R equation based on the material corotational rate and clarifies the puzzling problem of the simple shear stress oscillation mentioned in some literature. The paper proposes a modified relative rotational rate with which to constitute the objective rates of stress in the generalized P-R equation and concludes that the decomposition of total deformation rate into elastic and plastic parts is not necessary in developing the generalized P-R equations. Finally, the stresses of simple shear deformation are worked out.展开更多
We will be looking at the energy of a graviton, based upon the Stress energy tensor, and from there ascertaining how fluctuations in early universe conditions impact the mass of a graviton. Physically the mass of the ...We will be looking at the energy of a graviton, based upon the Stress energy tensor, and from there ascertaining how fluctuations in early universe conditions impact the mass of a graviton. Physically the mass of the graviton would be shrinking right after Planck time and presumably it would be going to its equilibrium value of about 10<sup>-62</sup> grams, for its present day value. It, graviton mass, would increase up to the Plank time of about 10<sup>-44</sup> seconds. Note that the result that graviton mass shrinks to 10<sup>-62</sup> grams for its present day value works only for relic gravitons.展开更多
Utilizing stress-energy tensors which allow for a divergence-free formulation, we establish Pohozaev＇s identity for certain classes of quasilinear systems with variational structure.
An explicit algebraic stress model (EASM) has been formulated for two-dimensional turbulent buoyant flows using a five-term tensor representation in a prior study. The derivation was based on partitioning the buoyant ...An explicit algebraic stress model (EASM) has been formulated for two-dimensional turbulent buoyant flows using a five-term tensor representation in a prior study. The derivation was based on partitioning the buoyant flux tensor into a two-dimensional and a three-dimensional component. The five-term basis was formed with the two-dimensional component of the buoyant flux tensor. As such, the derived EASM is limited to two-dimensional flows only. In this paper, a more general approach using a seven-term representation without partitioning the buoyant flux tensor is used to derive an EASM valid for two- and three-dimensional turbulent buoyant flows. Consequently, the basis tensors are formed with the fully three-dimensional buoyant flux tensor. The derived EASM has the two-dimensional flow as a special case. The matrices and the representation coefficients are further simplified using a four-term representation. When this four-term representation model is applied to calculate two-dimensional homogeneous buoyant flows, the results are essentially identical with those obtained previously using the two-dimensional component of the buoyant flux tensor. Therefore, the present approach leads to a more general EASM formulation that is equally valid for two- and three-dimensional turbulent buoyant flows.展开更多
Focal mechanism solutions and centroid depths of 312 M≥4 aftershocks from the 2008 Wenchuan earthquake sequence have been derived by CAP （Cut and Paste） method from broadband waveform data with relatively high sign...Focal mechanism solutions and centroid depths of 312 M≥4 aftershocks from the 2008 Wenchuan earthquake sequence have been derived by CAP （Cut and Paste） method from broadband waveform data with relatively high signal-to-noise ratio （SNR）. Following this, we have analyzed the distribution of focal depths and the stress tensors, as well as the types of focal mechanisms. The major results are： （1） different cross-sections show that the depth ranges of the aftershocks at the southern and northern ends of the aftershock area along the Longmenshan fault zone are wider than those on the central segment, where rare M≥4 aftershocks occurred at depths shallower than 10 kin. The main faults trend to the NW on the southern and central segments, and for the northern segment, no dominant trend direction has been determined; （2） stress tensor distribution demonstrates that the majority of the aftershock areas on the cross-section along the major axis are mainly under compressive stress perpendicular to the profile; however, for the areas near Lixian, Beichuan, Qingchuan and the shallow parts of its northern segment, large principal stress components are parallel to the major axis profile direction. On the cross-sections perpendicular to the major axis, the three areas above can be divided into two parts： one with dominantly compressional stress near the major faults of the Longmenshan fault zone on the SE side, and the other with NE-direction push along the fault zone on the NW side; （3） the stress tensor distribution in map view is very similar to those on the vertical cross-sections. In map view, the orientation of the principal compressional stress axis $1 on the central segment of the aftershock area presents an SE-trending arc shape; （4） the stress tensor slices at different depths show that the orientation of S1 axis mainly changes on the central segment and at the northern end, indicating that the two segments have different seismogenic structures at different depths; （5） with the exception of the northern end of the aftershock region, the orientation of the $1 axis changes little during the early and late stages, illustrating the seismogenic structures are relatively stable; （6） preliminary analyses for the seismogenic structures at the northern end indicated that deeper strike-slip quakes occurred on the ENE-striking branch at first, and then the NNE-striking branch faults at the northern end were activated and generated a series of relatively shallow strike-slip earthquakes due to subsequent stress-triggering; （7） the aftershock triggering mechanism that occurred near Lixian is different between the shallow and deep depths, and between the early and late stages, indicating that the main faults and the branch faults responsible for aftershocks are at different depths. Consequently, the relaxation effect of the main shock particularIy impacts the branch faults.展开更多
A comprehensive study on regional stress field around the Taigu fault zone in Shanxi Province, China, was performed in this study. To get a better understanding of the present-day stress status in this area, 31 focal ...A comprehensive study on regional stress field around the Taigu fault zone in Shanxi Province, China, was performed in this study. To get a better understanding of the present-day stress status in this area, 31 focal mecha- nisms of ML 〉3 earthquakes since 1965 were compiled, and the best stress tensor was then inverted based on the database. Additionally, magnetic fabrics along the Taigu fault zone were investigated to get an indication of the regional stress field in the past. Our results show that the present-day stress field around the Taigu fault zone is characterized by astable NW-SE extension with a strike- slip component, consistent with the geological surveys and recent GPS data. Results from magnetic fabrics indicate that the orientations of principal stress axes from magnetic fabrics of sedimentary rocks in Neogene coincide to the orientations of principal stress axes from focal mecha- nisms. The south segment of the Taigu fault displays more complicated magnetic fabrics and more activity of mod- erate earthquakes. It is connected with the Mianshan west fault and intersects with NW-SE striking Fenyang fault and the north fault of the Lingshi uplift at the south edge of Taiyuan basin. This may be the area needing more atten- tion in terms of seismic risk along the Taigu fault.展开更多
It has been well recognized that, due to anisotropic packing structure of granular material, the true stress in a specimen is different from the applied stress. However, very few research efforts have been focused on ...It has been well recognized that, due to anisotropic packing structure of granular material, the true stress in a specimen is different from the applied stress. However, very few research efforts have been focused on quantifying the relationship between the true stress and applied stress. In this paper, we derive an explicit relationship among applied stress tensor, material-fabric tensor, and force-fabric tensor; and we propose a relationship between the true stress tensor and the applied stress tensor. The validity of this derived relationship is examined by using the discrete element simulation results for granular material under biaxial and triaxial loading con- ditions.展开更多
The intersection is a widely used traffic line structure from the shallow tunnel to the deep roadway,and determining the subsidence hidden danger area of the roof is the key to its stability control.However,applying t...The intersection is a widely used traffic line structure from the shallow tunnel to the deep roadway,and determining the subsidence hidden danger area of the roof is the key to its stability control.However,applying traditional maximum equivalent span beam(MESB)theory to determine deformation range,peak point,and angle influence poses a challenge.Considering the overall structure of the intersection roof,the maximum equivalent triangular plate(METP)theory is proposed,and its geometric parameter calculation formula and deflection calculation formula are obtained.The application of the two theories in 18 models with different intersection angles,roadway types,and surrounding rock lithology is verified by numerical analysis.The results show that:1)The METP structure of the intersection roof established by the simulation results of each model successfully determined the location of the roof’s high displacement zone;2)The area comparison method of the METP theory can be reasonably explained:①The roof subsidence of the intersection decreases with the increase of the intersection angle;②The roof subsidence at the intersection of different roadway types has a rectangular type>arch type>circular type;③The roof subsidence of the intersection with weak surrounding rock is significantly larger than that of the intersection with hard surrounding rock.According to the application results of the two theories,the four advantages of the METP theory are compared and clarified in the basic assumptions,mechanical models,main viewpoints,and mechanism analysis.The large deformation inducement of the intersection roof is then explored.The J 2 peak area of the roof drives the large deformation of the area,the peak point of which is consistent with the center of gravity position of the METP.Furthermore,the change in the range of this peak is consistent with the change law of the METP’s area.Hence,this theory clarifies the large deformation area of the intersection roof,which provides a clear guiding basis for its initial support design,mid-term monitoring,and late local reinforcement.展开更多
基金supported by the National Natural Science Foundation of China(Grant No.42174118)a research grant(Grant No.ZDJ 2020-7)from the National Institute of Natural Hazards,Ministry of Emergency Management of China.
文摘The hydraulic testing of pre-existing fractures(HTPF)is one of the most promising in situ stress measurement methods,particularly for three-dimensional stress tensor determination.However,the stress tensor determination based on the HTPF method requires at least six tests or a minimum of 14-15 tests(under different conditions)for reliable results.In this study,we modified the HTPF method by considering the shear stress on each pre-existing fracture,which increased the number of equations for the stress tensor determination and decreased the number of tests required.Different shear stresses were attributed to different fractures by random sampling;therefore,the stress tensors were obtained by searching for the optimal solution using the least squares criterion based on the Monte Carlo method.Thereafter,we constrained the stress tensor based on the tensile strength criterion,compressive strength criterion,and vertical stress constraints.The inverted stress tensors were presented and analyzed based on the tensorial nature of the stress using the Euclidean mean stress tensor.Two stress-measurement campaigns in Weifang(Shandong Province,China)and Mercantour road tunnel(France)were implemented to highlight the validity and efficiency of the modified HTPF(M-HTPF)method.The results showed that the M-HTPF method can be applied for stress tensor inversion using only three to four tests on pre-existing fractures,neglecting the stress gradient.The inversion results were confined to relatively small distribution dispersions and were significantly reliable and stable due to the shear stresses on the fractures and the stress constraints employed.The M-HTPF method is highly feasible and efficient for complete stress tensor determination in a single borehole.
基金supported by Natural Science Foundation of China(No.41674055)the Earthquake Science and Technology Spark Plan in Hebei Province(DZ20140101002)
文摘Stress field plays a key role in geodynamics. In this study, an algorithm to determine the stress tensor and its confidence range from focal mechanism data by using grid search method was proposed. The experiment uses artificial focal mechanism data which were generated by extensional, compression and strike-slip stress regime and different level of noise, shows that the precision of the estimated stress tensor based on this algorithm is greatly improved compared with traditional algorithms. This algorithm has three advantages：（1） The global optimal solution of the stress tensor is determined by fine grid search of 1o×1o×1o×0.01 and local minimum value is avoided; （2） precision of focal mechanism data can be considered, i.e., different weight of the focal mechanism data contributes differently to the process of determining stress tensor; （3） the confidence range of the determined stress tensor can be obtained by using F-test. We apply this algorithm in the boundary zone of China, Vietnam and Laos, and obtain the stress field with SSE-NNW compressive stress direction and NEE-SWW extensional stress direction. The stress ratio is 0.6, which shows that the eigen values of the stress tensor are nearly in arithmetic sequence. The stress field in this region is consistent with the left-lateral strike slip of the Dienbien-Lauangphrabang arc fault. The result will be helpful in studying the geological dynamic process in this region.
基金The project was supported by the Research Fund for the Doctoral Program of Higher Education of China under contractNo. 9802940
文摘The distributions of the wave-induced radiation stress tensor over depth are studied by us- ing the linear wave theory, which are divided into three regions, i. e., above the mean water level, be- low the wave trough level, and between these two levels. The computational expressions of the wave-in- duced radiation stress tensor at the arbitrary wave angle are established by means of the Eulerian coordi- nate transformation, and the asymptotic forms for deep and shallow water are also presented. The verti- cal variations of a 30°incident wave-induced radiation stress tensor in deep water, intermediate water and shallow water are calculated respectively. The following conclusions are obtained from computations. The wave-induced radiation stress tensor below the wave trough level is induced by the water wave parti- cle velocities only, whereas both the water wave particle velocities and the wave pressure contribute to the tensor above the wave trough level. The vertical variations of the wave-induced radiation stress ten- sor are influenced substantially by the velocity component in the direction of wave propagation. The dis- tributions of the wave-induced radiation stress tensor over depth are nonuiniform and the proportion of the tensor below the wave trough level becomes considerable in the shallow water. From the water surface to the seabed, the reversed variations occur for the predominant tensor components.
文摘In this paper, the generalized Prandtl-Reuss (P-R) constitutive equations of elastic-plastic material in the presence of finite deformations through a new approach are studied. It analyzes the generalized P-R equation based on the material corotational rate and clarifies the puzzling problem of the simple shear stress oscillation mentioned in some literature. The paper proposes a modified relative rotational rate with which to constitute the objective rates of stress in the generalized P-R equation and concludes that the decomposition of total deformation rate into elastic and plastic parts is not necessary in developing the generalized P-R equations. Finally, the stresses of simple shear deformation are worked out.
文摘We will be looking at the energy of a graviton, based upon the Stress energy tensor, and from there ascertaining how fluctuations in early universe conditions impact the mass of a graviton. Physically the mass of the graviton would be shrinking right after Planck time and presumably it would be going to its equilibrium value of about 10<sup>-62</sup> grams, for its present day value. It, graviton mass, would increase up to the Plank time of about 10<sup>-44</sup> seconds. Note that the result that graviton mass shrinks to 10<sup>-62</sup> grams for its present day value works only for relic gravitons.
文摘Utilizing stress-energy tensors which allow for a divergence-free formulation, we establish Pohozaev＇s identity for certain classes of quasilinear systems with variational structure.
文摘An explicit algebraic stress model (EASM) has been formulated for two-dimensional turbulent buoyant flows using a five-term tensor representation in a prior study. The derivation was based on partitioning the buoyant flux tensor into a two-dimensional and a three-dimensional component. The five-term basis was formed with the two-dimensional component of the buoyant flux tensor. As such, the derived EASM is limited to two-dimensional flows only. In this paper, a more general approach using a seven-term representation without partitioning the buoyant flux tensor is used to derive an EASM valid for two- and three-dimensional turbulent buoyant flows. Consequently, the basis tensors are formed with the fully three-dimensional buoyant flux tensor. The derived EASM has the two-dimensional flow as a special case. The matrices and the representation coefficients are further simplified using a four-term representation. When this four-term representation model is applied to calculate two-dimensional homogeneous buoyant flows, the results are essentially identical with those obtained previously using the two-dimensional component of the buoyant flux tensor. Therefore, the present approach leads to a more general EASM formulation that is equally valid for two- and three-dimensional turbulent buoyant flows.
基金supported by the projects from Ministry of National Science and Technology of China(Grant No. 2012BAK19B01-01)National Basic Research Program of China (Grant No. 2008CB425701)
文摘Focal mechanism solutions and centroid depths of 312 M≥4 aftershocks from the 2008 Wenchuan earthquake sequence have been derived by CAP （Cut and Paste） method from broadband waveform data with relatively high signal-to-noise ratio （SNR）. Following this, we have analyzed the distribution of focal depths and the stress tensors, as well as the types of focal mechanisms. The major results are： （1） different cross-sections show that the depth ranges of the aftershocks at the southern and northern ends of the aftershock area along the Longmenshan fault zone are wider than those on the central segment, where rare M≥4 aftershocks occurred at depths shallower than 10 kin. The main faults trend to the NW on the southern and central segments, and for the northern segment, no dominant trend direction has been determined; （2） stress tensor distribution demonstrates that the majority of the aftershock areas on the cross-section along the major axis are mainly under compressive stress perpendicular to the profile; however, for the areas near Lixian, Beichuan, Qingchuan and the shallow parts of its northern segment, large principal stress components are parallel to the major axis profile direction. On the cross-sections perpendicular to the major axis, the three areas above can be divided into two parts： one with dominantly compressional stress near the major faults of the Longmenshan fault zone on the SE side, and the other with NE-direction push along the fault zone on the NW side; （3） the stress tensor distribution in map view is very similar to those on the vertical cross-sections. In map view, the orientation of the principal compressional stress axis $1 on the central segment of the aftershock area presents an SE-trending arc shape; （4） the stress tensor slices at different depths show that the orientation of S1 axis mainly changes on the central segment and at the northern end, indicating that the two segments have different seismogenic structures at different depths; （5） with the exception of the northern end of the aftershock region, the orientation of the $1 axis changes little during the early and late stages, illustrating the seismogenic structures are relatively stable; （6） preliminary analyses for the seismogenic structures at the northern end indicated that deeper strike-slip quakes occurred on the ENE-striking branch at first, and then the NNE-striking branch faults at the northern end were activated and generated a series of relatively shallow strike-slip earthquakes due to subsequent stress-triggering; （7） the aftershock triggering mechanism that occurred near Lixian is different between the shallow and deep depths, and between the early and late stages, indicating that the main faults and the branch faults responsible for aftershocks are at different depths. Consequently, the relaxation effect of the main shock particularIy impacts the branch faults.
基金partly funded by Open Fund of State Key Laboratory of Earthquake Dynamics,CEA(LED2011B05)the Foundation for the Returned Overseas of Shanxi Province(121)the National Science Fund of Shanxi Province(Youth,2010021005)
文摘A comprehensive study on regional stress field around the Taigu fault zone in Shanxi Province, China, was performed in this study. To get a better understanding of the present-day stress status in this area, 31 focal mecha- nisms of ML 〉3 earthquakes since 1965 were compiled, and the best stress tensor was then inverted based on the database. Additionally, magnetic fabrics along the Taigu fault zone were investigated to get an indication of the regional stress field in the past. Our results show that the present-day stress field around the Taigu fault zone is characterized by astable NW-SE extension with a strike- slip component, consistent with the geological surveys and recent GPS data. Results from magnetic fabrics indicate that the orientations of principal stress axes from magnetic fabrics of sedimentary rocks in Neogene coincide to the orientations of principal stress axes from focal mecha- nisms. The south segment of the Taigu fault displays more complicated magnetic fabrics and more activity of mod- erate earthquakes. It is connected with the Mianshan west fault and intersects with NW-SE striking Fenyang fault and the north fault of the Lingshi uplift at the south edge of Taiyuan basin. This may be the area needing more atten- tion in terms of seismic risk along the Taigu fault.
基金the financial support of the National Natural Science Foundation of China(51178044)Program for New Century Excellent Talents in University (NCET-11-0579)
文摘It has been well recognized that, due to anisotropic packing structure of granular material, the true stress in a specimen is different from the applied stress. However, very few research efforts have been focused on quantifying the relationship between the true stress and applied stress. In this paper, we derive an explicit relationship among applied stress tensor, material-fabric tensor, and force-fabric tensor; and we propose a relationship between the true stress tensor and the applied stress tensor. The validity of this derived relationship is examined by using the discrete element simulation results for granular material under biaxial and triaxial loading con- ditions.
基金Project(52204164)supported by the National Natural Science Foundation of ChinaProject(2021QNRC001)supported by the Young Elite Scientists Sponsorship Program by CAST,China。
文摘The intersection is a widely used traffic line structure from the shallow tunnel to the deep roadway,and determining the subsidence hidden danger area of the roof is the key to its stability control.However,applying traditional maximum equivalent span beam(MESB)theory to determine deformation range,peak point,and angle influence poses a challenge.Considering the overall structure of the intersection roof,the maximum equivalent triangular plate(METP)theory is proposed,and its geometric parameter calculation formula and deflection calculation formula are obtained.The application of the two theories in 18 models with different intersection angles,roadway types,and surrounding rock lithology is verified by numerical analysis.The results show that:1)The METP structure of the intersection roof established by the simulation results of each model successfully determined the location of the roof’s high displacement zone;2)The area comparison method of the METP theory can be reasonably explained:①The roof subsidence of the intersection decreases with the increase of the intersection angle;②The roof subsidence at the intersection of different roadway types has a rectangular type>arch type>circular type;③The roof subsidence of the intersection with weak surrounding rock is significantly larger than that of the intersection with hard surrounding rock.According to the application results of the two theories,the four advantages of the METP theory are compared and clarified in the basic assumptions,mechanical models,main viewpoints,and mechanism analysis.The large deformation inducement of the intersection roof is then explored.The J 2 peak area of the roof drives the large deformation of the area,the peak point of which is consistent with the center of gravity position of the METP.Furthermore,the change in the range of this peak is consistent with the change law of the METP’s area.Hence,this theory clarifies the large deformation area of the intersection roof,which provides a clear guiding basis for its initial support design,mid-term monitoring,and late local reinforcement.
