Frictional sliding of infilled planar granite fracture under oscillating normal stress

This paper investigates the frictional behavior of the infilled rock fracture under dynamic normal stress.A series of direct shear tests were conducted on saw-cut granite fractures infilled with quartz using a selfdeveloped dynamic shear apparatus,and the effects of normal load oscillation amplitude,normal load oscillation period and sliding velocity were studied.The test results reveal that the shear response can be divided into three stages over a whole loading-unloading process,characterized by different time spans and stress variations.Generally,a smaller oscillation amplitude,a longer oscillation period and a fast shear velocity promote the stability of the friction system,which is also confirmed by the Coulomb failure criterion calculated based on the observed periodic apparent friction coefficient.The dynamic strengthening/weakening phenomenon is dependent on the oscillation amplitude and product of sliding velocity and oscillation period(vT).Also,the rate and state friction law incorporating the parameter a that characterizes the normal stress variation is employed to describe the dynamic friction coefficient but exhibits an incompetent performance when handling intensive variation in normal stress.Finally,the potential seismicity induced by oscillating normal stress based on the observed stress drop is analyzed.This work helps us understand the sliding process and stability evolution of natural faults,and its benefits for relative hazard mitigation.

A numerical study of comparison of two one-state-variable,rate-and state-dependent friction evolution laws

The two one-state-variable, rate- and state-dependent friction laws, i.e., the slip and slowness laws, are com- pared on the basis of dynamical behavior of a one-degree-of-freedom spring-slider model through numerical simulations. Results show that two （normalized） model parameters, i.e., A （the normalized characteristic slip distance） and β-α （the difference in two normalized parameters of friction laws）, control the solutions. From given values of △, β, and α, for the slowness laws, the solution exists and the unique non-zero fixed point is stable when △〉（β-α）, yet not when △ 〈（β-α）. For the slip law, the solution exists for large ranges of model parameters and the number and stability of the non-zero fixed points change from one case to another. Results suggest that the slip law is more appropriate for controlling earthquake dynamics than the slowness law.

Experimental study on the slip evolution of planar fractures subjected to cyclic normal stress

The frictional rupture mechanisms of rock discontinuities considering the dynamic load disturbance still remain unclear.This paper investigates the transitional behaviors of slip events happened on a planar granite fracture under cyclic normal stress with diferent oscillation amplitudes.The experimental results show that the activations of fast slips always correlate with unloading of normal stress.Besides,the intensive normal stress oscillation can weaken the shear strength which is recoverable when the normal stress return to constant.The rupture patterns are quantifed by stress drop,slip length and slip velocity.With the efect of small oscillation amplitudes,the slip events show chaotic shapes,compared to the regular and predictable style under constant normal stress.When the amplitude is large enough,the big and small slip events emerge alternately,showing a compound slip style.Large amplitude of the cyclic normal stress also widens the interval diferences of the slip events.This work provides experimental supports for a convincible link between the dynamic stress disturbance and the slip behavior of rock fractures.

Transient postseismic slip and aftershock triggering:A case study of the 2008 M_W7.9 Wenchuan Earthquake,China

In this study,we investigate how a stress variation generated by a fault that experiences transient postseismic slip(TPS)affects the rate of aftershocks.First,we show that the postseismic slip from Rubin-Ampuero model is a TPS that can occur on the main fault with a velocity-weakening frictional motion,that the resultant slip function is similar to the generalized Jeffreys-Lomnitz creep law,and that the TPS can be explained by a continuous creep process undergoing reloading.Second,we obtain an approximate solution based on the Helmstetter-Shaw seismicity model relating the rate of aftershocks to such TPS.For the Wenchuan sequence,we perform a numerical fitting of the cumulative number of aftershocks using the Modified Omori Law(MOL),the Dieterich model,and the specific TPS model.The fitting curves indicate that the data can be better explained by the TPS model with a B/A ratio of approximately 1.12,where A and B are the parameters in the rate-and state-dependent friction law respectively.Moreover,the p and c that appear in the MOL can be interpreted by the B/A and the critical slip distance,respectively.Because the B/A ratio in the current model is always larger than 1,the model could become a possible candidate to explain aftershock rate commonly decay as a power law with a p-value larger than 1.Finally,the influence of the background seismicity rate r on parameters is studied;the results show that except for the apparent aftershock duration,other parameters are insensitive to r.

Influences of across-strike heterogeneous viscosity on the earthquake cycle in a three-dimensional strike-slip fault model

Geodetic observations have shown that there exist large differences in the viscosity of the deep lithosphere across many large strike-slip faults.Heterogeneity in lithospheric viscosity structure can influence the efficiency of stress transfer and thus may have a significant effect on the earthquake cycle.Until now,how the lateral viscosity variation across strike-slip faults affects the earthquake cycles is still not well understood.Here,we investigate the effects of across-strike viscosity variation on long-term earthquake behaviors with a three-dimensional strike-slip fault model.Our model is a quasi-static model which is controlled by the slip-weakening friction law and powerlaw rheology.By comparing with the reference case,we find that low viscosity on one side of the fault results in a smaller rupture area but with a higher Coulomb stress drop on the ruptured fault region.In addition,low viscosity also leads to a small Coulomb stress accumulation rate.These combined effects increase the earthquake recurrence interval by approximately 10%and the earthquake moments by about 30%when the low viscosity is related to a geothermal gradient of 30 K/km.In addition,across-strike viscosity variation causes asymmetric interseismic ground surface deformation rate.As the viscosity contrast increases,the difference in the interseismic ground surface deformation rate between the two sides of the fault gradually increases,although the asymmetric feature is not pronounced.This asymmetry of interseismic ground deformation rate across a strike-slip fault is supposed to result in asymmetric coseismic deformation if the long-term plate motion velocity is invariant.As a result,this kind of asymmetry of interseismic deformation may influence the evaluation of potential earthquake hazards along large strike-slip faults with lateral viscosity contrast.

Advances in experiments and numerical simulations on the effects of stress perturbations on fault slip

Laboratory experiments and numerical simulations on rock friction perturbations,an important means for understanding the mechanism and influencing factors of stress-triggered earthquakes,are of great significance for studying earthquake mechanisms and earthquake hazard analysis.We reviews the experiments and numerical simulations on the effects of stress perturbations on fault slip,and the results show that stress perturbations can change fault stress and trigger earthquakes.The Coulomb failure criterion can shed light on some questions about stress-triggering earthquakes but cannot explain the time dependence of earthquake triggering nor be used to investigate the effect of heterogeneous stress perturbations.The amplitude and period are important factors affecting the correlation between stress perturbation and fault instability.The effect of the perturbation period on fault instability is still controversial,and the effect of the high-frequency perturbation on earthquakes may be underestimated.Normal and shear stress perturbation can trigger fault instability,but their effects on fault slip differ.It is necessary to distinguish whether the stress perturbation is dominated by shear or normal stress change when it triggers fault instability.Fault tectonic stress plays a decisive effect on the mode of fault instability and earthquake magnitude.Acoustic emission activity can reflect the changes in fault stress and the progression of fault nucleation,and identify the meta-instability stage and precursor of fault instability,providing a reference for earthquake prediction.

An approach to evaluate ground surface rupture caused by reverse fault movement

An approach for estimating ground surface rupture caused by strong earthquakes is presented in this paper, where the finite element （FE） method of continuous and discontinuous coalescent displacement fields is adopted. The onset condition of strain localization is introduced to detect the formation of the slippage line. In the analysis, the Drucker-Prager constitutive model is used for soils and the rate- and state-dependent friction law is used on the slippage line to simulate the evolution of the sliding. A simple application to evaluate the ground surface rupture induced by a reverse fault movement is provided, and the numerical simulation shows good agreement with failure characteristics observed in the field after strong earthquakes.

Mechanical genesis of Henan(China) Yima thrust nappe structure

Considering the serious coal and rock dynamic disasters around the main slip plane called F16 in the coal mining area) of Henan Yima(China) thrust nappe structure,the mechanical genesis of the Yima thrust nappe structure was studied comprehensively using geomechanics,fault mechanics,elastic mechanics,and Coulomb's law of friction.First,using the centrifugal inertia force of Earth's rotation as a source,a mechanical model of N-S compression superimposed with W-E reverse torsion was established to explain the formation of the early Yima coal basin and Jurassic Yima Group coal measures.Second,an equation for the ultimate stress in the forming stage of F16 was derived using the plastic slip-line field theory and the parabolic Mohr failure criterion.Moreover,the distribution of ultimate stress and the geometric characteristics of the fault profile were obtained using the field model parameters.Finally,the stress field of F16 and the mechanical genesis of the large-scale reverse thrust sheet were discussed based on elastic mechanics theory and Coulomb's law of friction.The results show that the tectonic framework of the early Yima coal basin and the formation pattern of Jurassic Yima Group coal measures given by the model are consistent with the in-situ explorations.The geometric characteristics of the fault profile obtained by numerical calculation can better reflect the shape of F16 in its forming stage,and the mechanical genesis of the large-scale reverse thrust sheet also concurred with the field situations.Thus,this work can provide a foundation for further studies on the genesis of the thrust nappe structure,the mechanism of rock bursts induced by F16,and the characteristics of the residual stress field in the Yima mining area.

Combined approach of poroelastic and earthquake nucleation applied to the reservoir-induced seismic activity in the Val d’Agri area,Italy

In this work,an approach is developed to study the seismicity associated with the impoundment and level changes of a water reservoir(reservoir induced seismicity e RIS).The proposed methodology features a combination of a semi-analytical poroelastic model with an earthquake nucleation approach based on rate-and-state frictional law.The combined approach was applied to the case of the Pertusillo Lake,located in the Val d’Agri area(Italy),whose large seasonal water level changes are believed to induce protracted micro-seismicity(local magnitude ML<3).Results show that the lake impoundment in 1962 could have produced up to 0.5 bar(1 bar=100 kPa)changes in Coulomb failure stress(DCFS),while the seasonal water level variation is responsible for variation up to 0.05 bar.Modeling results of the seismicity rates in 20012014 show that the observed earthquakes are well correlated with the modeled DCFS.Finally,the reason that the seismicity is only observed at southwest of the Pertusillo Lake is provided,which is likely attributed to different rock lithologies and depletion caused by significant hydrocarbon exploitation in the northeastern sector of the lake.

Effect of the time-weakening friction law during the nucleation process

Based on dynamic rupture simulations on a planar fault in a homogeneous half-space, we investigated the nucleation processes using the time-weakening friction law. Both the characteristic time and the rupture speed in the nucleation asperity play an important role in determining rupture behaviors on a fault plane following the time-weakening friction law, with which rupture starts from a single point in the nucleation asperity and propagates at a given speed toward the boundary of the nucleation area. Rupture with a small characteristic time or a large rupture speed in the nucleation asperity propagates earlier from the hypocenter. Rupture following the slipweakening friction law requires a smaller radius of nucleation patch to have similar rupture front contours of the time-weakening friction law. Even if the rupture velocity in the nucleation patch of the time-weakening friction law increases to infinity, the peak slip rate in the nucleation asperity is smaller than that of the slip-weakening law. The peak ground velocity distributions of ruptures following the two friction laws are also compared.

Coulomb stress changes due to the 2021 MS7.4 Maduo Earthquake and expected seismicity rate changes in the surroundings

On May 22 nd,2021,an MS7.4 earthquake occurred near the Maduo county of the Qinghai Province,China,within the Bayan Har Block.Seismic activities have been intense in this block,thus whether the Maduo Earthquake will bring subsequent seismic hazards to its surrounding regions raises wide concerns.In this paper,we first calculated the Coulomb failure stress changes caused by the Maduo Earthquake on nearby faults,and estimated how much these faults are brought closer or further from their next failures based on their stressing rates.Next,we combined the Coulomb failure stress changes with the rate-state frictional law to estimate the seismicity rate in the study region in the next decade.A declustered catalogue before the Maduo Earthquake was adopted to calculate background seismicity rate,and rate-state parameters are constrained by fault slip rates.Our results show that the Maduo Earthquake increases stress accumulations in the northwestern portion of the Qingshuihe fault(0.02 MPa at maximum),the two ends of the Kunlun Mountain Pass-Jiangcuo fault(0.01 MPa at maximum),and the northwestern portion of the Maduo-Gande fault(on average~0.09 MPa),and seismicity rates are expected to increase near these faults.What is especially worth noting is the seismic hazard in the region extending from the eastern end of the Kunlun Mountain Pass-Jiangcuo fault to the Maqin-Maqu seismic gap on the Eastern Kunlun fault,which is calculated to have experienced a maximum stress increase of 0.67 MPa after the Maduo Earthquake.On the other hand,stress accumulations are reduced in the southern end of the Elashan fault,the Eastern Kunlun fault segment to the west of Maduo,and the northwestern portion of the Dari fault.Seismic hazards are expected to be low in these regions.For the study region as a whole,the probability of an M≥6 earthquake taking place in the next decade is estimated to be 59%,about twice the value calculated for the time period before the Maduo Earthquake.

Effect of tidal stress on fault nucleation and failure of the 2007 Ms6.4 Ning＇er earthquake

Based on calculations of the tidal Coulomb failure stress and investigations of the correlation between the Earth tide and the Ning＇er earthquake sequence, the processes of fault nucleation and failure were simulated. In these simulations we consider the influence of tidal stresses using the rate- and state-dependent friction laws. Furthermore, the effects on tidal trig- gering due to the stress amplitude and periodic oscillation properties were investigated, and the triggering effects between the tidal normal and tidal shear stresses were compared. The results showed that the Ning＇er earthquake sequence was a physical consequence of tidal effects. A transition period To exists between the nucleation and failure processes of a seismic fault. When the period T of stress is equal to or becomes larger than To, the fault response becomes dependent on the periodic features of the loading stress; however, for T 〈 To, the response of the fault is nearly independent of the period. Both the tidal normal and tidal shear stresses have similar effect in the nucleation and failure processes; the clock changes generally increase with the maximum amplitudes of the tidal stresses. Tidal normal and tidal shear stresses with positive amplitudes mainly induce earth- quake triggering; however, the triggering effects induced by negative tidal stresses are smaller and faults are not sensitive to negative tidal stresses. Our results primarily reveal the physical mechanisms of tidal stress triggering.

A BOUNDARY ELEMENT APPROXIMATION OF A SIGNORINI PROBLEM WITH FRICTION OBEYING COULOMB LAW

In this work, a Signorini problem with Coulomb friction in two dimensional elasticity is considered. Based on a new representation of the derivative of the double-layer potential, the original problem is reduced to a system of variational inequalities on the boundary of the given domain. The existence and uniqueess of this system are established for a small frictional coefficient. The boundary element approximation of this system is presented and an error estimate is given.