3D DEM simulation of hard rock fracture in deep tunnel excavation induced by changes in principal stress magnitude and orientation

To achieve the loading of the stress path of hard rock,the spherical discrete element model(DEM)and the new flexible membrane technology were utilized to realize the transient loading of three principal stresses with arbitrary magnitudes and orientations.Furthermore,based on the deep tunnel of China Jinping Underground Laboratory II(CJPL-II),the deformation and fracture evolution characteristics of deep hard rock induced by excavation stress path were analyzed,and the mechanisms of transient loading-unloading and stress rotation-induced fractures were revealed from a mesoscopic perspective.The results indicated that the stressestrain curve exhibits different trends and degrees of sudden changes when subjected to transient changes in principal stress,accompanied by sudden changes in strain rate.Stress rotation induces spatially directional deformation,resulting in fractures of different degrees and orientations,and increasing the degree of deformation anisotropy.The correlation between the degree of induced fracture and the unloading magnitude of minimum principal stress,as well as its initial level is significant and positive.The process of mechanical response during transient unloading exhibits clear nonlinearity and directivity.After transient unloading,both the minimum principal stress and minimum principal strain rate decrease sharply and then tend to stabilize.This occurs from the edge to the interior and from the direction of the minimum principal stress to the direction of the maximum principal stress on theε1-ε3 plane.Transient unloading will induce a tensile stress wave.The ability to induce fractures due to changes in principal stress magnitude,orientation and rotation paths gradually increases.The analysis indicates a positive correlation between the abrupt change amplitude of strain rate and the maximum unloading magnitude,which is determined by the magnitude and rotation of principal stress.A high tensile strain rate is more likely to induce fractures under low minimum principal stress.

Moment magnitudes of two large Turkish earthquakes on February 6,2023 from long-period coda

Two large earthquakes(an earthquake doublet)occurred in south-central Turkey on February 6,2023,causing massive damages and casualties.The magnitudes and the relative sizes of the two mainshocks are essential information for scientific research and public awareness.There are obvious discrepancies among the results that have been reported so far,which may be revised and updated later.Here we applied a novel and reliable long-period coda moment magnitude method to the two large earthquakes.The moment magnitudes(with one standard error)are 7.95±0.013 and 7.86±0.012,respectively,which are larger than all the previous reports.The first mainshock,which matches the largest recorded earthquakes in the Turkish history,is slightly larger than the second one by 0.11±0.035 in magnitude or by 0.04 to 0.18 at 95%confidence level.

Earthquake Magnitude Probability and Gamma Distribution

The earthquake magnitude probability distribution is one of the underlying input data for certain earthquake analyses, such as probabilistic seismic hazard analysis. Nowadays, the method proposed by McGuire and Arabasz (1990) is commonly used for obtaining the (simulated) earthquake magnitude probability distributions. However, based on the observed earthquake data in 5 regions (Taiwan, Japan, California, Turkey, and Greece), the model did not fit the observation well. Instead, all of the case studies show that using the newly proposed gamma distribution can improve the simulation significantly compared to the conventional method.

Scaling relations of moment magnitude, local magnitude,and duration magnitude for earthquakes originated in northeast India

In this study, we aim to improve the scaling between the moment magnitude （Mw）, local magnitude （ME）, and the duration magnitude （MD） for 162 earthquakes in Shillong-Mikir plateau and its adjoining region of northeast India by extending the Mw estimates to lower magnitude earthquakes using spectral analysis of P-waves from vertical component seismograms. The Mw-ML and Mw-MD relationships are determined by linear regression analysis. It is found that, Mw values can be considered consistent with ME and My, within 0.1 and 0.2 magnitude units respectively, in 90 % of the cases. The scaling relationships investigated comply well with similar relationships in other regions in the world and in other seismogenic areas in the northeast India region.

Comparison between different earthquake magnitudes determined by China Seismo-graph Network

By linear regression and orthogonal regression methods, comparisons are made between different magnitudes （local magnitude ML, surface wave magnitudes Ms and MsT, long-period body wave magnitude mB and short-period body wave magnitude mb） determined by Institute of Geophysics, China Earthquake Administration, on the basis of observation data collected by China Seismograph Network between 1983 and 2004. Empirical relations between different magnitudes have been obtained. The result shows that： ① As different magnitude scales reflect radiated energy by seismic waves within different periods, earthquake magnitudes can be described more objectively by using different scales for earthquakes of different magnitudes. When the epicentral distance is less than 1000 km, local magnitude ME can be a preferable scale; In case M〈4.5, there is little difference between the magnitude scales; In case 4.5〈M〈6.0, mB〉Ms, i.e., Ms underestimates magnitudes of such events, therefore, mB can be a better choice; In case M〉6.0, Ms〉mB〉mb, both mB and mb underestimate the magnitudes, so Ms is a preferable scale for determining magnitudes of such events （6.0〈M〈8.5）; In case M〉8.5, a saturation phenomenon appears in Ms, which cannot give an accurate reflection of the magnitudes of such large events; ② In China, when the epicentral distance is less than 1 000 km, there is almost no difference between ME and Ms, and thus there is no need to convert between the two magnitudes in practice; ③ Although Ms and Ms7 are both surface wave magnitudes, Ms is in general greater than Ms7 by 0.2～0.3 magnitude, because different instruments and calculation formulae are used; ④ mB is almost equal to mb for earthquakes around mB4.0, but mB is larger than mb for those of mB〉4.5, because the periods of seismic waves used for measuring mB and mb are different though the calculation formulae are the same.

Discussion on the Relationship between Different Earthquake Magnitude Scales and the Effect of Seismic Station Sites on Magnitude Estimation

Based on the earthquake catalog reported by the Chinese digital seismic network in recent years,we select the earthquakes with both surface wave magnitude and local magnitude and fit them into a relationship between the two magnitudes.The systematic difference is found from the formula which has been used for 30 years.Because of a large dynamic range and wide frequency range of the current digital observation system,in addition to a larger number of stations and earthquakes being used compared to before,the relation obtained in this paper seems more reliable.Our calculation shows that there is no significant difference before and after magnitude conversion so we suggest the abandonment of magnitude conversion.The site response of a station consists of amplification at different frequencies.The amplification is equal to about 1 and changes little with frequency at stations located on basement rock,and it is greater than 1 at low frequency ranges and less than 1 at high frequency ranges at stations located on sediment layers.The difference between magnitudes from single station located on sediment layer and the average magnitude from the whole network increases from negative to positive with period.It seems that there is no fixed station correction factor and the station correction method does not work to improve the accuracy and magnitude estimates.

Expected magnitude and distance of potential source area and the estimating method

Magnitude and distance of major potential source are needed in order to determine duration time of artificial ground motion and to determine the type of response spectrum (near field or far field) when using the seismic intensity zonation map. The magnitude probabilistic distribution function of seismic belt and the magnitude and space joint distribution function for given intensity of the site in a potential Source are provided. Then the basicformula of calculating expected magnitude and expected distance are developed. Several examples for calculating expected magnitude and expected distance in northern China are discussed. These results show that expected magnitude and expected distance are related not only to geometry of potential source and magnitude but also to the intensity of the site with certain exceeding probability.

Study on the Calibration Function of Local Earthquake Magnitude in the Gansu Region

To calculate the deviations between single station magnitudes and average ones by the magnitude residual statistical method,the paper selects 13086 seismic events recorded by the Gansu broadband digital seismic network from January 2009 to December 2012. The frequency distribution and quantitative statistics of the deviations of earthquake magnitude are analyzed. The MLcalibration function is modified and a uniform local magnitude system characteristic of the Gansu region,is obtained.

Research on characteristics of magnitude structure of earthquake sequences

Based on the research on 108 strictly selected earthquake sequences since 1965 in the Chinese mainland, why the magnitude structures of most of these sequences are not in accord with the G R relation has been analyzed and the fitting method with the division of the magnitude structure for the earthquake sequences has been suggested. The characteristic values of this method in the high magnitude interval have mainly been researched, and characteristic magnitude percent f and the slope ratio b 2 of the high magnitude interval, which are different for various sequence types are most obvious. The results show that the N M patterns of magnitude structures for 52.8% earthquake sequences are not in accord with the G R relation from the magnitude less than 80% of the maximum one and that for only 18.5% earthquake sequences show the decrease trend in the high magnitude interval. When b 2 <0 or 0 b 2 <3.0 and f is less, the strong aftershocks in the earthquake sequences are less; when b 2 3.0 for the sequence, several strong aftershocks often occurred; when 0b 2<3.0 and f is bigger, aftershocks with middle magnitude are more in these sequences.

Seismic Risk Assessment and Maximum Magnitudes of Potential Earthquakes on Active Faults near Lanzhou City

The Zhuanglang river and Baiyin Baiyangshu river faults are late Quaternary faults near Lanzhou city, which pose a threat to the safety of the city. However, the cause of medium- strong earthquakes along the fault is rather complicated and even uncertain. It is important for us how to assess the magnitudes of maximum potential earthquakes and the seismic risk of the faults. The authors make reference to the method that Wen Xueze, et ai. （2007） developed to assess the magnitudes of maximum potential earthquakes in sub-areas of moderately and weakly active faults in the eastern Chinese Mainland, and brought forward an empirical relationship between the maximum magnitudes Mmax and the at/b values of the sub-areas＇ frequency- magnitude relationships in the Lanzhou area. By using this empirical relationship, the authors have estimated the upper-limits Mu of the Zhuanglang river and Baiyin Baiyangshu river active faults near Lanzhou city as Ms6.9 and 6.3, respectively. In addition, they have assessed the average interval recurrence time and the probabilities of destructive earthquakes on the faults.

Study of Minimum Magnitude of Completeness in the North-South Trending Seismic Belt for the Collaboratory for the Study of Earthquake Predictability Project

To determine the studying region of China Testing Center of the Collaboratory for the Study of Earthquake Predictability （CSEP）, we adopted the Entire-Magnitude-Range （EMR） method to study the spatial distribution of minimum magnitude of completeness （Mc） in the North-South Trending Seismic Belt （NSTSB） during the period from October 1, 2008 to May 31, 2011. Also bootstrap testing was performed to estimate the uncertainty of Mc, i. e. 8Mc. The results show that Mc （EMR） = 1.6 ± 0. 03 for the whole region. From the spatial distributions of Mc we find that Mc is in the range of Mu 1.3 ±2.0 for most regions. Specifically, the spatial distribution of Mc is consistent with the distribution of stations indicating high monitoring level in the southern part and low monitoring level in the northern part. Events located with less than three stations have great influence on Me. Moreover, the uncertainty of minimum magnitude of completeness 6Mc ranges from 0. 07 to 0.22. The spatial distribution of 6Mc agrees with the seismic rate. The shorter time span may cause larger 6Mc

Definition,epidemiology and magnitude of alcoholic hepatitis

Alcoholic liver disease(ALD) is a major cause of alcoholrelated morbidity and mortality.Its presentation ranges from fatty liver to alcoholic hepatitis(AH),cirrhosis,and hepatocellular carcinoma.Although the amount and pattern of alcohol consumption is a well recognized predisposing factor for the development of serious liver pathology,environmental factors and the host's genetic makeup may also play significant roles that have not yet been entirely explored.Continuing alcohol consumption is a major factor that influences the survival of patients with AH.The presence of cirrhosis at presentation or its development on follow up is a major factor determining the outcome in the long run.This chapter deals with the epidemiology and magnitude of ALD in general and AH in particular.

Last Deglacial Soft-Sediment Deformation at Shawan on the Eastern Tibetan Plateau and Implications for Deformation Processes and Seismic Magnitudes

The eastern margin of the Tibetan Plateau is characterized by frequent earthquakes; however, research of paleo-earthquakes in the area has been limited^ owing to the alpine topography and strong erosion. Detailed investigations of soft-sediment deformation(SSD) structures are valuable for understanding the trigger mechanisms, deformation processes, and the magnitudes of earthquakes that generate such structures, and help us to understand tectonic activity in the region. To assess tectonic activity during the late Quaternary, we studied a well-exposed sequence of Shawan lacustrine sediments, 7.0 m thick, near Lake Diexi in the upper reaches of the Minjiang River. Deformation is recorded by both ductile structures(load casts, flame structures,pseudonodules, ball-and-pillow structures, and liquefied convolute structures) and brittle structures(liquefied breccia, and microfaults). Taking into account the geodynamic setting of the area and its known tectonic activity, these SSD structures can be interpreted in terms of seismic shocks. The types and forms of the structures,the maximum liquefaction distances, and the thicknesses of the horizons with SSD structures in the Shawan section indicate that they record six strong earthquakes of magnitude 6-7 and one with magnitude >7. A recent study showed that the Songpinggou fault is the seismogenic structure of the 1933 Ms7.5 Diexi earthquake. The Shawan section is located close to the junction of the Songpinggou and Minjiang faults, and records seven earthquakes with magnitudes of ?7. We infer,therefore, that the SSD structures in the Shawan section document deglacial activity along the Songpinggou fault.

Investigation of Induced Unbalance Magnitude on Dynamic Characteristics of High-speed Turbocharger with Floating Ring Bearings

Due to operational wear and uneven carbon absorption in compressor and turbine wheels, the unbalance(me) vibration is induced and could lead to sub?synchronous vibration accidents for high?speed turbocharger(TC). There are very few research works that focus on the magnitude e ects on such induced unbalance vibration. In this paper, a finite element model(FEM) is developed to characterize a realistic automotive TC rotor with floating ring bearings(FRBs). The nonlinear dynamic responses of the TC rotor system with di erent levels of induced unbalance magni?tude in compressor and turbine wheels are calculated. From the results of waterfall and response spectral intensity plots, the bifurcation and instability phenomena depend on unbalance magnitude during the startup of TC. The sub?synchronous component 0.12× caused rotor unstable is the dominant frequency for small induced unbalance. The nonlinear e ects of induced unbalance in the turbine wheel is obvious stronger than the compressor wheel. As the unbalance magnitude increases from 0.05 gbration 1·mm to 0.2 g·mm, the vibration component changes from mainly 0.12× to synchronous vi×. When unbalance increases continuously, the rotor vibration response amplitude is rapidly growing and the 1× caused by the large unbalance excitation becomes the dominant frequency. A suitable un?balance magnitude of turbine wheel and compressor wheel for the high?speed TC rotor with FRBs is proposed: the value of induced un?balance magnitude should be kept around 0.2 g·mm.

Determination of the local magnitudes of small earthquakes using a dense seismic array in the Changning-Zhaotong Shale Gas Field,Southern Sichuan Basin

With the development of unconventional shale gas in the southern Sichuan Basin,seismicity in the region has increased significantly in recent years.Though the existing sparse regional seismic stations can capture most earthquakes with ML≥2.5,a great number of smaller earthquakes are often omitted due to limited detection capacity.With the advent of portable seismic nodes,many dense arrays for monitoring seismicity in the unconventional oil and gas fields have been deployed,and the magnitudes of those earthquakes are key to understand the local fault reactivation and seismic potentials.However,the current national standard for determining the local magnitudes was not specifically designed for monitoring stations in close proximity,utilizing a calibration function with a minimal resolution of 5 km in the epicentral distance.That is,the current national standard tends to overestimate the local magnitudes for stations within short epicentral distances,and can result in discrepancies for dense arrays.In this study,we propose a new local magnitude formula which corrects the overestimated magnitudes for shorter distances,yielding accurate event magnitudes for small earthquakes in the Changning-Zhaotong shale gas field in the southern Sichuan Basin,monitored by dense seismic arrays in close proximity.The formula is used to determine the local magnitudes of 7,500 events monitored by a two-phased dense array with several hundred 5 Hz 3 C nodes deployed from the end of February 2019 to early May 2019 in the Changning-Zhaotong shale gas field.The magnitude of completeness(MC)using the dense array is-0.1,compared to MC 1.1 by the sparser Chinese Seismic Network(CSN).In addition,using a machine learning detection and picking procedure,we successfully identify and process some 14,000 earthquakes from the continuous waveforms,a ten-fold increase over the catalog recorded by CSN for the same period,and the MC is further reduced to-0.3 from-0.1 compared to the catalog obtained via manual processing using the same dense array.The proposed local magnitude formula can be adopted for calculating accurate local magnitudes of future earthquakes using dense arrays in the shale gas fields of the Sichuan Basin.This will help to better characterize the local seismic risks and potentials.

Magnitude-frequency relationship of debris flows in the Jiangjia Gully, China

The magnitude-frequency(MF) relationship of debris flows is the basis for engineering designs and risk quantification. However, because of the lack of debris flow monitoring data, research progress in this area has been relatively slow. The MF relationship of debris flows in Jiangjia Gully, Yunnan Province was evaluated based on a regression analysis of 178 debris flow events that occurred from 1987-2004. The magnitude-cumulative frequency(MCF) relationship of the debris flows in the Jiangjia Gully is consistent with the linear logarithmic transformation function. Moreover, observed data for debris flows in Hunshui Gully of Yunnan Province and Huoshao Gully, Liuwan Gully, and Niwan Gully of Gansu Province were used to verify the function. The results showed that the MCF relationship of highfrequency debris flows is consistent with the power law equation, although the regression coefficients in the equation are considerably different. Further analysis showed a strong correlation between the differences in the constants and the drainage area and daily maximum precipitation.

Earthquake probabilities and magnitude distribution (M≥6.7) along the Haiyuan fault, northwestern China

In recent years, some researchers have studied the paleoearthquake along the Haiyuan fault and revealed a lot of paleoearthquake events. All available information allows more reliable analysis of earthquake recurrence interval and earthquake rupture patterns along the Haiyuan fault. Based on this paleoseismological information, the recur- rence probability and magnitude distribution for M≥6.7 earthquakes in future 100 years along the Haiyuan fault can be obtained through weighted computation by using Poisson and Brownian passage time models and consid- ering different rupture patterns. The result shows that the recurrence probability of MS≥6.7 earthquakes is about 0.035 in future 100 years along the Haiyuan fault.

Relationships between moment magnitude and fault parameters:theoretical and semi-empirical relationships

Fault parameters are important in earthquake hazard analysis.In this paper,theoretical relationships between moment magnitude and fault parameters including subsurface rupture length,downdip rupture width,rupture area,and average slip over the fault surface are deduced based on seismological theory.These theoretical relationships are further simplified by applying similarity conditions and an unique form is established.Then,combining the simplified theoretical relationships between moment magnitude and fault parameters with seismic source data selected in this study,a practical semi-empirical relationship is established.The seismic source data selected is also to used to derive empirical relationships between moment magnitude and fault parameters by the ordinary least square regression method.Comparisons between semi-empirical relationships and empirical relationships show that the former depict distribution trends of data better than the latter.It is also observed that downdip rupture widths of strike slip faults are saturated when moment magnitude is more than 7.0,but downdip rupture widths of dip slip faults are not saturated in the molnent magnitude rangcs of this study.

Bh序列和Magnitude错误标准下m元纠错码构造

文献对Bh序列和Magnitude错误标准下m元t-sEC/AUED码的关系进行了讨论,在此基础上提出了一种Magnitude错误标准下m元可纠t个对称错的纠错码的构造方法,并相应地给出了可纠t个对称错的纠错码码字个数的下界。

Magnitude错误标准下m元非对称错纠错码的构造(英文)

基于多项式的剩余类环理论,给出了magnitude错误标准下m元可纠小于等于t个非对称错纠错码的构造方法.由此构造方法给出了这类码码字个数的下界.