On the excavation-induced stress drop in damaged coal considering a coupled yield and failure criterion

Investigating the stress drop of abutment pressure is the key to a deep quantitative analysis of the discontinuous stress redistribution under mining.In the present study,uniaxial and triaxial compression tests are carried out separately to determine the bulk and shear moduli,the cohesion,and the internal friction angle of the coal samples.By extending the meaning of Mohr’s circle referring to yield stress instead of the maximum principal stress,a yield line is introduced to illustrate the stress drop of Mohr’s circle referring to yield stress instead of the maximum principal stress at the elastoplastic boundary.Furthermore,a theoretical solution of the stress drop as a function of the damage is proposed to investigate how the abutment pressure differs considering the yield line and failure line.In addition,applying the stress drop at the yield line in non-pillar mining,top coal mining,and protective coal mining shows that the damage has a nonlinearly positive influence on the stress drop.The results shows that the bulk modulus and internal friction angle have a more sensitive influence on the stress drop than do the shear modulus and cohesion.Finally,the stress drop is divided into a discontinuous stress drop at the yield line and a structural stress drop at the failure line.The stress drop is effective in describing the discontinuous stress redistribution and shows a clear difference in the movement direction of Mohr’s circle considering the unloading pressure.

Spatial and Temporal Variations in Earthquake Stress Drops between the 2008 Wenchuan and 2013 Lushan Earthquakes

As a case study of spatial and temporal variations in earthquake stress drops between the 2008 Ms 8.0 Wenchuan and 2013 Ms 7.0 Lushan earthquakes,we computed 1828 stress-drop values for earthquakes with magnitudes 1.7≤ML≤5.0 during an eight-year time span before and after major earthquakes.We divide the study area into three subregions(the southern segment of the Longmen Shan fault zone;the southwestern junction of the Longmen Shan and Sichuan Basin;and the southwestern margin of the Sichuan Basin)and calculate individual event stress drops in each.The results show that regions of alternating high and low stress drop are found on either side of the southwestern segment of the Longmen Shan fault zone.During the two-year period after the 2008 Ms 8.0 Wenchuan earthquake,the stress state of the southern Longmen Shan fault shows no significant change.A marked increase in stress level appears about 18 months before the 2013 Ms 7.0 Lushan earthquake near the Lushan hypocenter zone.Two months after the Ms 7.0 event,the stress drops suddenly attenuate,with significantly less seismic energy release per event.We find that changes in the patterns of high and low stress drop values are consistent with the process of stress accumulation or transfer from the pre-mainshock to postmainshock periods.The results indicate that major earthquakes are the dominant cause of temporal and spatial evolution in stress levels.Stress drop variations show obvious temporal and spatial patterns that may suggests subtle changes in the character of stress fields on faults and spatial variations related to local intense compression and tectonic effects.

Stress drop assessment of the August 8, 2017, Jiuzhaigou earthquake sequence and its tectonic implications

By using a broadband Lg attenuation model developed for the Tibetan Plateau,we isolate source terms by removing attenuation and site effects from the observed Lg-wave displacement spectra of the M 7.0 earthquake that occurred on August 8,2017,in Jiuzhaigou,China,and its aftershock sequence.Thus,the source parameters,including the scalar seismic moment,comer frequency and stress drop,of these events can be further estimated.The estimated stress drops vary from 47.1 kPa to 7149.6 kPa,with a median value of 59.4 kPa and most values falling between 50 kPa and 75 kPa.The estimated stress drops show significant spatial variations.Lower stress drops were mainly found close to the mainshock and on the seismogenic fault plane with large coseismic slip.In contrast,the highest stress drop was 7.1 MPa for the mainshock,and relatively large stress drops were also found for aftershocks away from the major seismogenic fault and at depths deeper than the zone with large coseismic slip.By using a statistical method,we found self-similarity among some of the aftershocks with a nearly constant stress drop.In contrast,the stress drop increased with the seismic moment for other aftershocks.The amount of stress released during earthquakes is a fundamental characteristic of the earthquake rupture process.As such,the stress drop represents a key parameter for improving our understanding of earthquake source physics.

Study on determination of stress level by seismic stress drops and the stress axis de-flections before and after large earthquakes

To obtain the stress level at the earthquake source, this paper sets forth the solution of the stress magnitude at the earthquake source by seismic stress drop and the stress axis deflections before and after large earthquakes. The pre-seismic and post-seismic stress direction can be statistically determined by a large collection of foreshock and aftershock focal mechanism data while the stress drop can be determined through the source fracture inversion from seismic wave data or crust deformation data. The paper attempts to make a fundamental contribution to seismic dynamics.

Estimation of seismic stress drop from the peak velocity of ground motion

According to the source dislocation model suggested by Brune(1970), the authors have calculated the displacement spectra of S wave and source parameters of the Heqing M S 5 3 earthquake sequence, using the digital data of this sequence obtained in the Western Yunnan Earthquake Prediction Experimental Field (WYEPEF). Based on this calculation we have studied the dependence of the peak velocity ( rv ) of ground motion on the seismic stress drop Δ σ . From the seismic scaling law we obtained ( rv )∝Δ σ 2/3 , thus the three formulae of calculating seismic stress drop Δ σ using the peak velocity parameters can be derived: lg( rv)=d 1+13lg M 0+23lgΔ σ ; lg( rv) =d 2+13 M L+23lgΔ σ ; lgΔ σ =-1 0+1 5lg( rv ) Assuming that the average stress drop Δ σ =3.0×10 6 Pa for great and small earthquakes, then the constants d 1=-3 88 and d 2=-0 38 are determined by the observational data of the Heqing M S5 3 sequence. Results of the source parameters for this sequence show that the seismic moment M 0 is between 10 11 N·m and 10 15 N·m, the rupture radius a of the source is between 200 m and 600 m, the stress drop Δ σ is between 0 1 MPa and 10 MPa and the average stress drop Δ σ =3 7 MPa calculated from the peak velocity parameter of the ground motion. Δσ values measured from these scaling relations are basically in agreement with the results given by Brune′s method( 1970). Results of this study show that the dependence of the ground motion peak velocity parameter (rv) on the stress drop Δσ is even stronger than that on the seismic moment M 0 .

Variation of stress during the rupture process of the 1995 M_L=4.1 Shacheng, Hebei, China, earthquake sequence

According to the rupture dynamics of earthquakes, variations of the apparent stress and the difference between the static stress drop and the dynamic stress drop during the rupture of earthquakes are analyzed for the July 20, 1995 ML=4.1 Shacheng, Hebei, China, earthquake sequence. Results obtained show that the apparent stress for main-shock is about 5 MPa, and the average apparent stress for aftershocks 0.047 MPa. During the rupture of the main-shock, the dynamic stress drop is approximately 1.6 times greater than the static stress drop with the difference of nearly 2.7 MPa. The dynamic stress drop is less than the static stress drop for all aftershocks with the average difference of -0.75 MPa. Therefore, when the mainshock occurs the final stress on the focal fault is higher than the dynamic frictional stress, corresponding to that the fault is abruptly locked. When the aftershocks occur the final stress on the focal fault is lower than the dynamic frictional stress, corresponding to that the fault overshoots. It can be seen from the above results that there could be some differences in the physic processes between the mainshock and the aftershocks.

Research on Stress Drops and the Focal Mechanisms of the Xinyuan- Hejing ML6.8 Earthquake Sequences

Based on the digital waveform data recorded by Xinjiang Digital Seismic Network for the Xinyuan-Hejing M_L6.8 earthquake sequences of June 30,2012,this paper analyzes the stress drops of earthquake sequences and the correlation coefficients of focal mechanisms significant for strong aftershocks.Firstly,the source parameters of the Xinyuan-Hejing M_L6.8 earthquake sequences are obtained by applying the spectrum analysis and the Brunes source model.Then,the correlation coefficients of spectral amplitudes are calculated using the low-frequency spectral amplitude recorded by the same station for the different events.Finally,based on the results of the correlation coefficients of spectral amplitudes,the events with similar focal mechanisms are grouped using the clustering method.The results show that:(1)The stress drop values show a steady trend in the aftershock sequence calm period and the stress drop values show a rise-fall in strong aftershocks.(2)The moving average correlation coefficient of amplitude spectrum begins to spread after the main shock.It shows that the correlation decreases between the main shock and the aftershocks in mechanisms.(3)The results of focal mechanism groups show that the earthquake sequences are mainly strike slips.The stress distribution of the main pressure axis is nearly NS,which is the same as the structural stress field.(4)The magnitude and mechanism show that there is an agreement before the strong aftershock,which shows that the regional stress field is enhanced.

Energy dissipation rate: An indicator of coal deformation and failure under static and dynamic compressive loads

Dynamic disasters in Chinese coal mines pose a significant threat to coal productivity. Thus, a thorough understanding of the deformation and failure processes of coal is necessary. In this study, the energy dissipation rate is proposed as a novel indicator of coal deformation and failure under static and dynamic compressive loads. The relationship between stress-strain, uniaxial compressive strength, displacement rate, loading rate, fractal dimension, and energy dissipation rate was investigated through experiments conducted using the MTS C60 tests(static loads) and split Hopkinson pressure bar system(dynamic loads). The results show that the energy dissipation rate peaks are associated with stress drop during coal deformation, and also positively related to the uniaxial compressive strength. A higher displacement rate of quasi-static loads leads to an initial increase and then a decrease in energy dissipation rate, whereas a higher loading rate of dynamic loads results in larger energy dissipation rate. Theoretical analysis indicates that a sudden increase in energy dissipation rate suggests partial fracture occurring within coal under both quasi-static and dynamic loads. Hence, the energy dissipation rate is an essential indicator of partial fracture and final failure within coal, as well as a prospective precursor for catastrophic failure in coal mine.

Bounding of near-fault ground motion based on radiated seismic energy with a consideration of fault frictional mechanisms

The energy radiated as seismic waves strongly depends on the fault rupture process associated with rupture speed and dynamic frictional mechanisms involved in the fault slip motion. Following McGarr and Fletcher approach, we derived a physics-based relationship of the weighted average fault slip velocity vs apparent stress, rupture speed and static stress drop based on a dynamic circular fault model. The resultant function can be approximately used to bound near-fault ground motion and seismic energy associated with near-fault coseismic deformation. Fault frictional overshoot and under- shoot mechanisms governed by a simple slip-weakening constitutive relation are included in our consideration by using dy- namic rupture models named as M- and D-models and proposed by Madariaga （1976） and Boatwright. We applied the above function to the 2008 great Wenchuan earthquake and the 1999 Jiji （Chi-Chi） earthquake to infer the near-fault ground motion called slip weighted average particle velocity and obtained that such model-dependent prediction of weighted average ground velocities is consistent to the results derived from the near-fault strong motion observations. Moreover, we compared our re- sults with the results by McGarr and Fletcher approach, and we found that the values of the weighted average particle veloci- ties we obtained for these two earthquakes are generally smaller and closer to the values by direct integration of strong mo- tion recordings of the near-fault particle velocity waveform data. In other words, if this result comes to be true, it would be a straightforward way used to constrain the near-fault ground motion or to estimate source parameters such as rupture speed, static and dynamic stress drops.

Fracture characteristics of the 1997 Jiashi,Xinjiang, China, earthquake swarm inferred from source spectra

Broadband P and S waves source spectra of 12 M_s≥5.0 earthquakes of the 1997 Jiashi, Xinjiang, China. earthquake swarm recorded at 13 GDSN stations have been analyzed. Rupture size and static stress drop of these earthquakes have been estimated through measuring the corner frequency of the source spectra. Direction of rupture propaga- tion of the earthquake faulting has also been inferred from the azimuthal variation of the comer frequency. The main results are as follows: ① The rupture size of M_s≥6.0 strong earthquakes is in the range of 10~20 km, while that of Ms_=5.0~5.5 earthquakes is 6~10 km. ② The static stress drop of the swarm earthquakes is rather low, being of the order of 0.1 MPa. This implies that the deformation release rate in the source region may be low. ③ Stress drop of the earthquakes appears to be proportional to their seismic moment, and also to be dependent on their focal mechanism. The stress drop of normal faulting earthquakes is usually lower than that of strike-slip type earth quakes. ④ For each M_s≥6.0 earthquake there exists an apparent azimuthal variation of the comer frequencies. Azimuthally variation pattern of comer frequencies of different earthquakes shows that the source rupture pattern of the Jiashi earthquake swarm is complex and no uniform rupture expanding direction exists.

A single-station coda solution for source,attenuation and site factors

ased on the empirical formulation formed from coda observations, the digital waveforms from 33 local events with magnitude ML ranging between 2.1 and 3.5, recorded at Changli station of Beijing Telemetered Seismographic Network from 1989 to 1991, are used to compute coda Q for the Changli region and the source factors of all earthquakes by single-station coda method. Furthermore, assuming a certain source model, we have obtained the station site frequency response and source spectra, as well as source parameters such as corner frequencies, seismic moments and stress drops and so on. Their variations with time are monitored before and after larger earthquakes. Because the coda method can more effectively reduce the influence of source radiation pattern and a particular propagation path than direct wave method, more data can be used and more accurate results can be obtained, which provided a possible approach to study the source properties and reveal the variation of source parameters before larger earthquakes.

Constraints on rupture speed of the 2001 MS 8.1 West Kunlun Mountain Pass earthquake by co-seismic surface rupture slip displacements based on the slip-weakening mechanism with frictional undershoot involved

With co-seismic surface rupture slip displacements provided by the field observation for the 2001 MS8.1 West Kunlun Mountain Pass earthquake, this paper estimates the rupture speed on the main faulting segment with a long straight fault trace on the surface based on a simple slip-weakening rupture model, in which the frictional overshoot or undershoot are involved in consideration of energy partition during the earthquake faulting. In contrast to the study of Bouchon and Vallée, in which the rupture propagation along the main fault could exceed the local shear-wave speed, perhaps reach the P-wave speed on a certain section of fault, our results show that, under a slip-weakening assumption combined with a frictional undershoot (partial stress drop model), average rupture speed should be equal to or less than the Rayleigh wave speed with a high seismic radiation efficiency, which is consistent with the result derived by waveform inversion and the result estimated from source stress field. Associated with the surface rupture mechanism, such as partial stress drop (frictional undershoot) associated with the apparent stress, an alternative rupture mechanism based on the slip-weakening model has also been discussed.

Preliminary Study on Characteristics of Source Parameters of Earthquakes in the Nuozhadu Reservoir Area,Yunnan Province

We computed source parameters for 143 earthquakes with M_L≥ 1. 0 occurring from January,2011 to March,2014 using waveform data recorded by the Nuozhadu and Jinghong Reservoir Seismic Networks. Then,the variation of seismic activity and the characteristics of source parameters before and after the impoundment of the reservoir were investigated. The results show that:( 1) the seismic activity increased obviously after the impoundment,especially during the 3- 4 months after impoundment;( 2) the focal depths of the earthquakes occurring in the reservoir area are shallower than the earthquakes occurring outside the reservoir area in the initial stage of impoundment,but after a time,the difference was gradually reduced;( 3) corner frequency varies with the seismic moment and the log-linear relationship is more obvious after impounding;( 4)stress drop and apparent stress increase with increasing seismic moment,moreover they are lower for the earthquakes occurring in the reservoir area after impounding than those occurring outside the reservoir area or before impounding with the same seismic moment;( 5) the effect of reservoir impoundment on an earthquake can reach a depth of 10 km,and the maximum effect is seen at a depth of 3km- 6km,and the differences of seismic activity and average apparent stress between the inside and outside of the reservoir are significant.

Study on Precise Location and Structure of Earthquakes in the Shanxi Reservoir,Zhejiang Province

The Shanxi reservoir earthquakes are significant seismic events in southern Zhejiang Province in recent years, an area with fewer and weaker earthquakes. The seismicity showed an intermittent characteristic and group distribution. The epicenters located by the seismic network did not show a predominant direction and the seismogenic structure is not clear. In the study, the nonlinear imaginary wave travel time equation was linearized and solved, and the source position, initial imaginary velocity and travel time residuals were obtained. Then by doubling the standard deviation as time residuals, the maximum error generated from longitude, latitude, depth and imaginary velocity was calculated. The genetic population was structured using the maximum error and the end result of earthquake location was obtained by genetic algorithm. The result of relocation of the Shanxi reservoir earthquakes with this method shows that earthquakes are largely concentrated on a near-vertical, northwest oriented fault plane, and the included angles between the normal of the plane and the due north, due east and vertical directions are 46~, 44~, and 87~, respectively. The result is in agreement with that of comprehensive fault plane solutions of small earthquakes. The average depth of the earthquakes was 4.7km, the maximum depth 9.5kin, and the minimum depth 1.7km. The epicenters showed a northwestward narrow banded distribution, and the focal depth increased along the northwest direction. There was a discontinuous seismic gap of about 3.5km long at the northwest end of the strip. The characteristics of source parameters obtained by using the Borun model were not significantly different from that of tectonic earthquakes. Seismic stress drop was about 0.33MPa, and the average stress drop was 0.88MPa. According to the stress drop＇ spatial distribution, the seismic discontinuities segment at the northwest end of the strip is in a low stress drop zone.

Research on the Source Parameters and Correlation Coefficients of Focal Mechanisms for the Yingjiang Earthquake Sequences in 2008

The source parameters of the Yingjiang earthquake sequences in 2008 are obtained by applying spectral analysis and Brunes source model,based on the digital waveform data recorded by the Yunnan Digital Seismic Network.The correlation coefficients are calculated using the low-frequency spectral amplitudes of 2 events recorded by a same station,then,events with similar focal mechanism are grouped using the clustering analysis method.Compared to the obtained focal mechanisms,it is found that there are good correlations with the azimuth of P axes in each clustering group,and the larger the correlation coefficient,the closer the azimuths of P axes.We divide the Yingjiang area into 3 regions to analyze the stress level and stress direction by combining the source parameters and the mean focal mechanism of each group.The results show:The change and transformation of the focal mechanism types at different stages can represent the temporal characteristics of the regional stress field.If the earthquake focal mechanism types are concentrated in a time period and switch to the direction of regional stress field,it may be a sign of strong earthquake.There is some relationship between the stress drop and the type of focal mechanism.Those earthquakes with stress fields revealed by focal mechanism types closer to the regional tectonic stress field will have higher stress drop,while those with the focal mechanism-revealed stress fields differing a lot from the regional tectonic stress field will generally have a lower stress drop.