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
Inspired by Cardano＇s method for solving cubic scalar equations, the addi- tive decomposition of spherical/deviatoric tensor （DSDT） is revisited from a new view- point. This decomposition simplifies the cubic tenso...Inspired by Cardano＇s method for solving cubic scalar equations, the addi- tive decomposition of spherical/deviatoric tensor （DSDT） is revisited from a new view- point. This decomposition simplifies the cubic tensor equation, decouples the spher- ical/deviatoric strain energy density, and lays the foundation for the von Mises yield criterion. Besides, it is verified that under the precondition of energy decoupling and the simplest form, the DSDT is the only possible form of the additive decomposition with physical meanings.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
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
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
We investigate the accuracy and robustness of moment tensor(MT)and stress inversion solutions derived from acoustic emissions(AEs)during the laboratory fracturing of prismatic Barre granite specimens.Pre-cut flaws in ...We investigate the accuracy and robustness of moment tensor(MT)and stress inversion solutions derived from acoustic emissions(AEs)during the laboratory fracturing of prismatic Barre granite specimens.Pre-cut flaws in the specimens introduce a complex stress field,resulting in a spatial and temporal variation of focal mechanisms.Specifically,we consider two experimental setups:(1)where the rock is loaded in compression to generate primarily shear-type fractures and(2)where the material is loaded in indirect tension to generate predominantly tensile-type fractures.In each test,we first decompose AE moment tensors into double-couple(DC)and non-DC terms and then derive unambiguous normal and slip vectors using k-means clustering and an unstructured damped stress inversion algorithm.We explore temporal and spatial distributions of DC and non-DC events at different loading levels.The majority of the DC and the tensile non-DC events cluster around the pre-cut flaws,where macro-cracks later develop.Results of stress inversion are verified against the stress field from finite element(FE)modeling.A good agreement is found between the experimentally derived and numerically simulated stress orientations.To the best of the authors’knowledge,this work presents the first case where stress inversion methodologies are validated by numerical simulations at laboratory scale and under highly heterogeneous stress distributions.展开更多
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
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.
When plants respond to drought stress,dynamic cellular changes occur,accompanied by alterations in gene expression,which often act through trans-regulation.However,the detection of trans-acting genetic variants and ne...When plants respond to drought stress,dynamic cellular changes occur,accompanied by alterations in gene expression,which often act through trans-regulation.However,the detection of trans-acting genetic variants and networks of genes is challenged by the large number of genes and markers.Using a tensor decomposition method,we identify trans-acting expression quantitative trait loci(trans-eQTLs)linked to gene modules,rather than individual genes,which were associated with maize drought response.Module-to-trait association analysis demonstrates that half of the modules are relevant to drought-related traits.Genome-wide association studies of the expression patterns of each module identify 286 trans-eQTLs linked to drought-responsive modules,the majority of which cannot be detected based on individual gene expression.Notably,the trans-eQTLs located in the regions selected during maize improvement tend towards relatively strong selection.We further prioritize the genes that affect the transcriptional regulation of multiple genes in trans,as exemplified by two transcription factor genes.Our analyses highlight that multidimensional reduction could facilitate the identification of trans-acting variations in gene expression in response to dynamic environments and serve as a promising technique for high-order data processing in future crop breeding.展开更多
A new unified strength criterion in the principal stress space has been proposed for use with normal strength concrete （NC） and high strength concrete （HSC） in compressioncompression-tension, compression-tension-t...A new unified strength criterion in the principal stress space has been proposed for use with normal strength concrete （NC） and high strength concrete （HSC） in compressioncompression-tension, compression-tension-tension, triaxial tension, and biaxial stress states. The study covers concrete with strengths ranging from 20 to 130 MPa. The conception of damage Poisson＇s ratio is defined and the expression for damage Poisson＇s ratio is determined basically. The failure mechanism of concrete is illustrated, which points out that damage Poisson＇s ratio is the key to determining the failure of concrete. Furthermore, for the concrete under biaxial stress conditions, the unified strength criterion is simplified and a simplified strength criterion in the form of curves is also proposed. The strength criterion is physically meaningful and easy to calculate, which can be applied to analytic solution and numerical solution of concrete structures.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
Physical mechanisms and influencing factors on the effective stress coefficient for rock/soil-like porous materials are investigated, based on which equivalent connectivity index is proposed. The equivalent connectivi...Physical mechanisms and influencing factors on the effective stress coefficient for rock/soil-like porous materials are investigated, based on which equivalent connectivity index is proposed. The equivalent connectivity index, relying on the meso-scale structure of porous material and the property of liquid, denotes the connectivity of pores in Representative Element Area （REA）. If the conductivity of the porous material is anisotropic, the equivalent connectivity index is a second order tensor. Based on the basic theories of continuous mechanics and tensor analysis, relationship between area porosity and volumetric porosity of porous materials is deduced. Then a generalized expression, describing the relation between effective stress coefficient tensor and equivalent connectivity tensor of pores, is proposed, and the expression can be applied to isotropic media and also to anisotropic materials. Furthermore, evolution of porosity and equivalent connectivity index of the pore are studied in the strain space, and the method to determine the corresponding functions in expressions above is proposed using genetic algorithm and genetic programming. Two applications show that the results obtained by the method in this paper perfectly agree with the test data. This paper provides an important theoretical support to the coupled hydro-mechanical research.展开更多
Moment tensor inversion was carried out to myert the source mechanism and source time function of the Ms=7.6November 6. 1988, Lancang-Gengma. Yunnan Province, Chin4 earthquake. Waveforms of long-period bodywaves recor...Moment tensor inversion was carried out to myert the source mechanism and source time function of the Ms=7.6November 6. 1988, Lancang-Gengma. Yunnan Province, Chin4 earthquake. Waveforms of long-period bodywaves recorded by China Digital Seismograph Network (CDSN) were used in the inversion. The inverted resultshows one nodal plane of right-lateral strike-slip faulting and another of left-lateral strike-slip faulting and a simplesource time function of a duration of about 15 s and scalar seismic moment of 6.4x 102oN-N-m From the geologicaldata and tectonic settings and also from field observations and epicentral distribution of aftershocks, the nodalplane striking in the azimuth of 313° is preferred as the fault plane. The pressure axis lies almost horizontally innorth-south direction.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
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
In deep hard rock excavation, stress plays a pivotal role in inducing stress-controlled failure. While the impact of excavation-induced stress disturbance on rock failure and tunnel stability has undergone comprehensi...In deep hard rock excavation, stress plays a pivotal role in inducing stress-controlled failure. While the impact of excavation-induced stress disturbance on rock failure and tunnel stability has undergone comprehensive examination through laboratory tests and numerical simulations, its validation through insitu stress tests remains unexplored. This study analyzes the three-dimensional stress changes in the surrounding rock at various depths, monitored during the excavation of B2 Lab in China Jinping Underground Laboratory Phase Ⅱ(CJPL-Ⅱ). The investigation delves into the three-dimensional stress variation characteristics in deep hard rock, encompassing stress components and principal stress. The results indicate changes in both the magnitude and direction of the principal stress during tunnel excavation. To quantitatively describe the degree of stress disturbance, a series of stress evaluation indexes are established based on the distances between stress tensors, including the stress disturbance index(SDI), the principal stress magnitude disturbance index(SDIm), and the principal stress direction disturbance index(SDId). The SDI indicates the greatest stress disturbance in the surrounding rock is 4.5 m from the tunnel wall in B2 Lab. SDIm shows that the principal stress magnitude disturbance peaks at2.5 m from the tunnel wall. SDId reveals that the largest change in principal stress direction does not necessarily occur near the tunnel wall but at a specific depth from it. The established relationship between SDI and the depth of the excavation damaged zone(EDZ) can serve as a criterion for determining the depth of the EDZ in deep hard rock engineering. Additionally, it provides a reference for future construction and support considerations.展开更多
Two earthquakes of Ms=6.0 and Ms=6. 1 consecutively occurred on December 31, 1994 and January 10, 1995 in Beibuwan region, China. By using the generalized reflection-transmission coefficient matrix and the discrete sl...Two earthquakes of Ms=6.0 and Ms=6. 1 consecutively occurred on December 31, 1994 and January 10, 1995 in Beibuwan region, China. By using the generalized reflection-transmission coefficient matrix and the discrete slowness integration method in the calculation of Green's functions, we obtained the focal mechanisms of these earthquakes using long-period waveforms of regional body waves recorded by the China Digital Seismograph Network (CDSN) by means of moment tensor inversion method in frequency domain. The results inverted indicate that the focal mechanisms of these two earthquakes were similar to each other. Their principal compressional stresses are in NW-SE direction and principal tensional stresses are in NE-SW direction. It turns out that the occurrence of the two earthquakes was controlled by the same tectonic environment related to the collision of the Philippine Plate and the Eurasian Plates. On the other hand, the results imply that the stress field in the seismogenic region has a significant change after the Ms=6.0 earthquake. It may be proposed that the occurrence of the Ms=6. 1 earthquake could be related to the stress field adjustment caused by the Ms=6.0 earthquake.展开更多
In recent years,finite element analysis is increasingly being proposed in slope stability problems as a competitive method to traditional limit equilibrium methods(LEMs)which are known for their inherent deficiencies....In recent years,finite element analysis is increasingly being proposed in slope stability problems as a competitive method to traditional limit equilibrium methods(LEMs)which are known for their inherent deficiencies.However,the application of finite element method(FEM)to slope stability as a strength reduction method(SRM)or as finite element limit analysis(FELA)is not always a success for the drawbacks that characterize both methods.To increase the performance of finite element analysis in this problem,a new approach is proposed in this paper.It consists in gradually expanding the mobilized stress Mohr’s circles until the soil failure occurs according to a prescribed non-convergence criterion.The present approach called stress deviator increasing method(SDIM)is considered rigorous for three main reasons.Firstly,it preserves the definition of the factor of safety(FOS)as the ratio of soil shear strength to the mobilized shear stress.Secondly,it maintains the progressive development of shear stress resulting from the increase in the principal stress deviator on the same plane,on which the shear strength takes place.Thirdly,by introducing the concept of equivalent stress loading,the resulting trial stresses are checked against the violation of the actual yield criterion formed with the real strength parameters rather than those reduced by a trial factor.The new numerical procedure was encoded in a Fortran computer code called S^(4)DINA and verified by several examples.Comparisons with other numerical methods such as the SRM,gravity increasing method(GIM)or even FELA by assessing both the FOS and contours of equivalent plastic strains showed promising results.展开更多
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.
基金supported by the National Natural Science Foundation of China(Nos.11072125 and11272175)the Specialized Research Fund for the Doctoral Program of Higher Education of China(No.20130002110044)the China Postdoctoral Science Foundation(No.2015M570035)
文摘Inspired by Cardano＇s method for solving cubic scalar equations, the addi- tive decomposition of spherical/deviatoric tensor （DSDT） is revisited from a new view- point. This decomposition simplifies the cubic tensor equation, decouples the spher- ical/deviatoric strain energy density, and lays the foundation for the von Mises yield criterion. Besides, it is verified that under the precondition of energy decoupling and the simplest form, the DSDT is the only possible form of the additive decomposition with physical meanings.
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.
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.
文摘We investigate the accuracy and robustness of moment tensor(MT)and stress inversion solutions derived from acoustic emissions(AEs)during the laboratory fracturing of prismatic Barre granite specimens.Pre-cut flaws in the specimens introduce a complex stress field,resulting in a spatial and temporal variation of focal mechanisms.Specifically,we consider two experimental setups:(1)where the rock is loaded in compression to generate primarily shear-type fractures and(2)where the material is loaded in indirect tension to generate predominantly tensile-type fractures.In each test,we first decompose AE moment tensors into double-couple(DC)and non-DC terms and then derive unambiguous normal and slip vectors using k-means clustering and an unstructured damped stress inversion algorithm.We explore temporal and spatial distributions of DC and non-DC events at different loading levels.The majority of the DC and the tensile non-DC events cluster around the pre-cut flaws,where macro-cracks later develop.Results of stress inversion are verified against the stress field from finite element(FE)modeling.A good agreement is found between the experimentally derived and numerically simulated stress orientations.To the best of the authors’knowledge,this work presents the first case where stress inversion methodologies are validated by numerical simulations at laboratory scale and under highly heterogeneous stress distributions.
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.
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.
基金supported by the Biological Breeding-National Science and Technology Major Project(2023ZD04076)the Guangxi Key Research and Development Projects of China(GuikeAB21238004)the Agricultural Science and Technology Innovation Program.
文摘When plants respond to drought stress,dynamic cellular changes occur,accompanied by alterations in gene expression,which often act through trans-regulation.However,the detection of trans-acting genetic variants and networks of genes is challenged by the large number of genes and markers.Using a tensor decomposition method,we identify trans-acting expression quantitative trait loci(trans-eQTLs)linked to gene modules,rather than individual genes,which were associated with maize drought response.Module-to-trait association analysis demonstrates that half of the modules are relevant to drought-related traits.Genome-wide association studies of the expression patterns of each module identify 286 trans-eQTLs linked to drought-responsive modules,the majority of which cannot be detected based on individual gene expression.Notably,the trans-eQTLs located in the regions selected during maize improvement tend towards relatively strong selection.We further prioritize the genes that affect the transcriptional regulation of multiple genes in trans,as exemplified by two transcription factor genes.Our analyses highlight that multidimensional reduction could facilitate the identification of trans-acting variations in gene expression in response to dynamic environments and serve as a promising technique for high-order data processing in future crop breeding.
基金Project supported by the National Natural Science Foundation of China (Nos. 50438020 and 50578162).
文摘A new unified strength criterion in the principal stress space has been proposed for use with normal strength concrete （NC） and high strength concrete （HSC） in compressioncompression-tension, compression-tension-tension, triaxial tension, and biaxial stress states. The study covers concrete with strengths ranging from 20 to 130 MPa. The conception of damage Poisson＇s ratio is defined and the expression for damage Poisson＇s ratio is determined basically. The failure mechanism of concrete is illustrated, which points out that damage Poisson＇s ratio is the key to determining the failure of concrete. Furthermore, for the concrete under biaxial stress conditions, the unified strength criterion is simplified and a simplified strength criterion in the form of curves is also proposed. The strength criterion is physically meaningful and easy to calculate, which can be applied to analytic solution and numerical solution of concrete structures.
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supported by the Yalongjiang River Joint Fund by the National Natural Science Foundation of China(NSFC)Ertan Hydropower Development Company,LTD(Nos.50579091 and 50539090)+1 种基金NSFC(No.10772190)Major State Basic Research Project of China(No.2002CB412708)
文摘Physical mechanisms and influencing factors on the effective stress coefficient for rock/soil-like porous materials are investigated, based on which equivalent connectivity index is proposed. The equivalent connectivity index, relying on the meso-scale structure of porous material and the property of liquid, denotes the connectivity of pores in Representative Element Area （REA）. If the conductivity of the porous material is anisotropic, the equivalent connectivity index is a second order tensor. Based on the basic theories of continuous mechanics and tensor analysis, relationship between area porosity and volumetric porosity of porous materials is deduced. Then a generalized expression, describing the relation between effective stress coefficient tensor and equivalent connectivity tensor of pores, is proposed, and the expression can be applied to isotropic media and also to anisotropic materials. Furthermore, evolution of porosity and equivalent connectivity index of the pore are studied in the strain space, and the method to determine the corresponding functions in expressions above is proposed using genetic algorithm and genetic programming. Two applications show that the results obtained by the method in this paper perfectly agree with the test data. This paper provides an important theoretical support to the coupled hydro-mechanical research.
文摘Moment tensor inversion was carried out to myert the source mechanism and source time function of the Ms=7.6November 6. 1988, Lancang-Gengma. Yunnan Province, Chin4 earthquake. Waveforms of long-period bodywaves recorded by China Digital Seismograph Network (CDSN) were used in the inversion. The inverted resultshows one nodal plane of right-lateral strike-slip faulting and another of left-lateral strike-slip faulting and a simplesource time function of a duration of about 15 s and scalar seismic moment of 6.4x 102oN-N-m From the geologicaldata and tectonic settings and also from field observations and epicentral distribution of aftershocks, the nodalplane striking in the azimuth of 313° is preferred as the fault plane. The pressure axis lies almost horizontally innorth-south direction.
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financial support for this work from the National Natural Science Foundation of China(Nos.42202320 and 42102266)the Open Project of Engineering Research Center of Phosphorus Resources Development and Utilization of Ministry of Education(No.LKF201901).
文摘In deep hard rock excavation, stress plays a pivotal role in inducing stress-controlled failure. While the impact of excavation-induced stress disturbance on rock failure and tunnel stability has undergone comprehensive examination through laboratory tests and numerical simulations, its validation through insitu stress tests remains unexplored. This study analyzes the three-dimensional stress changes in the surrounding rock at various depths, monitored during the excavation of B2 Lab in China Jinping Underground Laboratory Phase Ⅱ(CJPL-Ⅱ). The investigation delves into the three-dimensional stress variation characteristics in deep hard rock, encompassing stress components and principal stress. The results indicate changes in both the magnitude and direction of the principal stress during tunnel excavation. To quantitatively describe the degree of stress disturbance, a series of stress evaluation indexes are established based on the distances between stress tensors, including the stress disturbance index(SDI), the principal stress magnitude disturbance index(SDIm), and the principal stress direction disturbance index(SDId). The SDI indicates the greatest stress disturbance in the surrounding rock is 4.5 m from the tunnel wall in B2 Lab. SDIm shows that the principal stress magnitude disturbance peaks at2.5 m from the tunnel wall. SDId reveals that the largest change in principal stress direction does not necessarily occur near the tunnel wall but at a specific depth from it. The established relationship between SDI and the depth of the excavation damaged zone(EDZ) can serve as a criterion for determining the depth of the EDZ in deep hard rock engineering. Additionally, it provides a reference for future construction and support considerations.
文摘Two earthquakes of Ms=6.0 and Ms=6. 1 consecutively occurred on December 31, 1994 and January 10, 1995 in Beibuwan region, China. By using the generalized reflection-transmission coefficient matrix and the discrete slowness integration method in the calculation of Green's functions, we obtained the focal mechanisms of these earthquakes using long-period waveforms of regional body waves recorded by the China Digital Seismograph Network (CDSN) by means of moment tensor inversion method in frequency domain. The results inverted indicate that the focal mechanisms of these two earthquakes were similar to each other. Their principal compressional stresses are in NW-SE direction and principal tensional stresses are in NE-SW direction. It turns out that the occurrence of the two earthquakes was controlled by the same tectonic environment related to the collision of the Philippine Plate and the Eurasian Plates. On the other hand, the results imply that the stress field in the seismogenic region has a significant change after the Ms=6.0 earthquake. It may be proposed that the occurrence of the Ms=6. 1 earthquake could be related to the stress field adjustment caused by the Ms=6.0 earthquake.
文摘In recent years,finite element analysis is increasingly being proposed in slope stability problems as a competitive method to traditional limit equilibrium methods(LEMs)which are known for their inherent deficiencies.However,the application of finite element method(FEM)to slope stability as a strength reduction method(SRM)or as finite element limit analysis(FELA)is not always a success for the drawbacks that characterize both methods.To increase the performance of finite element analysis in this problem,a new approach is proposed in this paper.It consists in gradually expanding the mobilized stress Mohr’s circles until the soil failure occurs according to a prescribed non-convergence criterion.The present approach called stress deviator increasing method(SDIM)is considered rigorous for three main reasons.Firstly,it preserves the definition of the factor of safety(FOS)as the ratio of soil shear strength to the mobilized shear stress.Secondly,it maintains the progressive development of shear stress resulting from the increase in the principal stress deviator on the same plane,on which the shear strength takes place.Thirdly,by introducing the concept of equivalent stress loading,the resulting trial stresses are checked against the violation of the actual yield criterion formed with the real strength parameters rather than those reduced by a trial factor.The new numerical procedure was encoded in a Fortran computer code called S^(4)DINA and verified by several examples.Comparisons with other numerical methods such as the SRM,gravity increasing method(GIM)or even FELA by assessing both the FOS and contours of equivalent plastic strains showed promising results.
