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.

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.

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.

Confirmation of the First Law of Thermodynamics in Theory and Extended Bernoulli Equation

The internal energy change of ideal gas does not depend on the volume and pressure. The internal energy change of real gas has not any relation with the volume and pressure, which had been proved. If the internal energy change had not any relation with the volume and pressure, we could confirm the first law of thermodynamics in theory. Simultaneously, the internal energy change is the state function that shall be able to be proved in theory. If the internal energy change depended on the volume and pressure, we could not prove that the internal energy change is the state function and the chemical thermodynamics theory is right. The extended or modified Bernoulli equation can be derived from the energy conservation law, and the internal energy change, heat, and friction are all considered in the derivation procedure. The extended Bernoulli equation could be applied to the flying aircraft and mechanical motion on the gravitational field, for instance, the rocket and airplane and so on. This paper also revises some wrong ideas, viewpoints, or concepts about the thermodynamics theory and Bernoulli equation.

基于地磁场重复观测资料分析玛多M_(W)7.3地震前地磁场变化

基于玛多地震周边的地磁场重复观测资料,使用泰勒多项式空间参考场方法和自然正交分量方法分别对观测资料进行日变通化和长期变化改正,获得了玛多地震前后地磁场变化特征。通过对观测和数据处理的分析,获得了各期计算结果的误差,并基于误差对地磁场变化进行了部分修正。结果表明,玛多地震1~2年岩石圈磁场年变化会出现明显的趋势转折,变化量为5~10nT。根据速度—状态依赖的摩擦定律的地震周期分析发现,震前断层滑动量较小,因此岩石圈磁场年变化并非由地震前断层滑动引起的应力扰动产生。玛多地震前地下流体的变化产生的电磁效应更可能是产生岩石圈磁场变化的原因。

阻燃输送带火灾早期温度变化与烟气成分研究

为实现带式输送机火灾早期预警,改进滚筒摩擦实验平台并监测阻燃输送带温度。利用质谱(MS)技术,分析钢丝绳芯阻燃输送带在摩擦事故早期的升温规律与烟气成分。研究表明,随着摩擦持续进行,阻燃输送带表面温度分布呈现出较强的对称性,最高温度区域逐渐向输送带中心集聚,烟气成分随温度变化而改变。根据实验中烟气产物主要成分以及对应的反应过程,将钢丝绳芯阻燃输送带升温过程分为氧化反应阶段(环境温度至100℃)、取代反应阶段(100~160.2℃)和热解反应阶段(160.2℃以后)。当阻燃输送带处于氧化反应阶段时,输送带热容量较小、升温快,产物多为烷基和酯类化合物;取代反应阶段热容量逐渐增加,升温放缓,产物多为硝基、醚类、羧酸类化合物;热解反应阶段输送带内部热容量基本稳定,升温速率最小,在160.2℃时在烟气成分中首次检测到含氯化合物。

2018年日本北海道M_(W)6.6地震震源动力学破裂过程

2018年9月5日日本北海道东胆振地区发生了M_(W)6.6地震,震源深度37 km,超过了地壳与上地幔脆韧性边界的深度,且在地表产生了较强的破坏.为研究北海道地震震源区发震构造及产生强地面运动的物理机制,本文基于此次地震的震源运动学模型,针对其震源动力学模型开展了研究,尝试反演了动力学破裂过程.首先,由北海道地震运动学模型分析计算了断层面上的剪切应力,确定其破裂过程基本上是遵循滑动弱化摩擦准则,并由此获得初始模型的震源动力学参数,然后通过试错法反演了这次地震的震源动力学破裂过程.研究结果显示,北海道地震动力学破裂为自破裂起始处以走滑为主,先NE后SW,最终向断层面上倾方向传播,并在断层几何的弯折处产生逆冲破裂.在逆冲破裂的位置,滑动速率和滑动量达到最大值,结合运动学和动力学反演结果分析,推断该区域为强运动生成区,在地面产生的高频地震动是该中等、较深震源地震破坏性较强的主因.

CRTSⅡ型板式无砟轨道层间摩擦参数及性能影响研究

针对CRTSⅡ型板式无砟轨道离缝后的层间相互作用关系,开展现场运营线及室内推板试验,建立CRTSⅡ型板式无砟轨道的力学特性分析模型,研究离缝条件下不同层间摩擦参数对轨道结构力学性能的影响。研究结果表明:实际运营状态下的轨道板随着顶推力不断增大,轨道板与砂浆层逐渐脱粘,完全脱粘后发生滑移,轨道板失稳发生水平位移的推力在160~200 kN之间,轨道板发生稳定滑移的水平推力在210~250 kN之间,对应摩擦系数为2.5~3.1;室内试验轨道板与砂浆层之间在无粘结力的最不利状态下,轨道板发生稳定滑移的水平推力在55~56 kN之间,对应摩擦系数为0.79~0.80;随着层间摩擦系数增加,会一定改善轨道结构受力变形,但影响程度有限,摩擦系数由0.7增加至3.1时,宽窄接缝受力最大减小6.6%,钢轨和轨道板最大上拱位移分别减小了4.19%和5.7%;对于已经出现离缝的CRTSⅡ型板式无砟轨道,层间摩擦状态影响较小,应提前预防和避免层间离缝病害的产生,保证层间粘结完好。

EFFECT OF VISCOSITY OF LUBRICANT IN FRICTION

The movement of lubricated fibres in a fibre assembly is investigated theoretically and aviscous sliding model of friction is proposed.Previous work and experimental results are discussedin relation to the model.Results of drawing experiments carried out on wool slivers are also pres-ented and discussed.

The Role of Friction in the Static Equilibrium of a Fixed Ladder: Theoretical Analysis and Experimental Test

In a recent publication the author derived and experimentally tested several theoretical models, distinguished by different boundary conditions at the contacts with horizontal and vertical supports, that predicted the forces of reaction on a fixed (i.e. inextensible) ladder. This problem is statically indeterminate since there are 4 forces of reaction and only 3 equations of static equilibrium. The model that predicted the empirical reactions correctly used a law of static friction to complement the equations of static equilibrium. The present paper examines in greater theoretical and experimental detail the role of friction in accounting for the forces of reaction on a fixed ladder. The reported measurements confirm that forces parallel and normal to the support at the top of the ladder are linearly proportional with a constant coefficient of friction irrespective of the magnitude or location of the load, as assumed in the theoretical model. However, measurements of forces parallel and normal to the support at the base of the ladder are linearly proportional with coefficients that depend sensitively on the location (although not the magnitude) of the load. This paper accounts quantitatively for the different effects of friction at the top and base of the ladder under conditions of usual use whereby friction at the vertical support alone is insufficient to keep the ladder from sliding. A theoretical model is also proposed for the unusual circumstance in which friction at the vertical support can keep the ladder from sliding.

断层相互作用与地震触发机制研究回顾与展望

断层相互作用与地震触发关系研究是震源物理学领域的热点问题,能够帮助认识强震的孕育过程与物理机理,在地震危险性分析与预测研究中也有良好的应用前景.前人的综述文章从应力触发的基本原理、方法、适用性及多个震例研究的角度,提供了详细的阐述,然而从地震活动性分析这一角度对地震触发的介绍并不详尽,也未对这两个角度的结合和互补提供进一步的探讨.本文从物理模型和统计模型两个角度,综述了过去几十年针对断层相互作用和地震触发机制研究的成果与进展;通过介绍速率-状态摩擦律,展现这一科学问题的内在统一性,并对目前存在的问题和未来的可能研究方向进行了梳理和展望.从物理模型角度,着重分析了断层相互作用来源的几个重要机制:静态应力触发、动态应力触发和黏弹性应力触发,以及计算的基本原理和方法.在统计模型方面,介绍了地震活动性分析的基本原理和方法,重点分析了ETAS模型和b值在断层相互作用和地震触发机制中的应用.从两个模型结合的角度,指出两者互相验证的统一内涵以及速率-状态摩擦律的基本原理和方法.分析指出通过库仑应力计算和ETAS模型这两种不同的角度,可以综合研究多断层或地震之间的应力相互作用,并提供交叉验证,增加结果的可靠性;应用速率-状态摩擦律可以回溯性地研究地震序列的发生过程,为认识地震触发关系和断层相互作用提供了新的视角.

工况及配缸间隙对活塞敲击力影响规律

针对发动机的运行工况及配缸间隙对活塞敲击力的影响规律展开研究。采用EXCITE软件搭建了活塞运动仿真模型与发动机多体动力学仿真模型。基于验证后的模型研究了活塞二次运动及活塞敲击力的特点,分析了转速及转矩等运行工况及配缸间隙的影响规律。研究结果表明:在压缩上止点附近活塞的二次运动最为明显,主推力面上存在最大活塞敲击力;随着转速的增加,活塞惯性力增大,使活塞敲击力增大;随转矩的增加,活塞所受侧向力增大,使得活塞敲击能量增加;随着配缸间隙的增加,活塞二次运动加剧,活塞敲击力相应增加。

新型变摩擦滑橇式飞行器滑跑纠偏

相较于轮式起落架,结构轻巧紧凑的滑橇式起落架更适用于扁平化的高超声速飞行器,然而前轮后橇布局所固有的地面力学特性使得飞行器在中速滑跑阶段存在严重的航向失稳问题。针对滑橇式飞行器滑跑航向稳定性较差的问题,提出了一种具备航向增稳功能的新型变摩擦滑橇式起落架。建立了滑橇式飞行器的非线性地面滑跑动力学模型,考虑了气动载荷、地面载荷和纠偏机构模型;基于摩擦特性试验结果得到了滑橇及摩擦材料摩擦系数的多参数拟合公式,并将其代入所提滑跑模型以提高精度;引入积分视线(ILOS)法建立了滑橇式飞行器滑跑纠偏控制系统,并采用粒子群算法优化控制参数。试验结果表明:滑橇及摩擦材料的摩擦系数均随速度和压强的增加先增大后减小;典型初始工况下的滑跑仿真结果验证了基于变摩擦滑橇纠偏控制的有效性;当摩擦材料摩擦系数从0.3增至0.4时,飞行器地面滑跑安全边界提升16.6%。

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.

熔化焊和摩擦焊残余应力分布规律分析

为了研究熔化焊和摩擦焊焊接方法残余应力的分布规律,分别对4 mm厚的低合金高强钢采用手工电弧焊和摩擦焊进行焊接实验,焊接后采用盲孔法测量钢板的残余应力,得到了残余应力的分布曲线。再通过有限元仿真模拟出熔化焊和摩擦焊的加热和冷却过程,分析残余应力的分布规律。讨论了转速与焊接速度对残余应力分布的影响机理,进一步提高了搅拌摩擦焊接头性能、质量和可靠性。

基于纳米划痕试验的砂岩结构面宏-微观摩擦系数关系研究

基本摩擦系数是影响岩体结构面抗剪强度的重要参数。常规室内试验方法所确定的基本摩擦系数往往受矿物成分、温度等因素影响,为系统揭示结构面的基本摩擦性质,分别研究了砂岩宏观摩擦系数与微观摩擦系数,并建立了两者的关系。首先,通过X射线衍射、纳米压痕试验确定砂岩矿物组分与力学参数。其次,采用倾斜试验、直剪试验开展摩擦系数的宏观尺度研究,对规格为10 cm×10 cm×5 cm的平直结构面试样开展直剪试验,分别施加1、2、3、8、12 MPa的恒定法向应力,研究表明,摩擦系数随法向应力增加呈对数降低趋势,随剪切速率增加呈对数增长趋势。再次,采用纳米划痕试验开展摩擦系数的微观尺度研究,研究表明,低荷载条件下,长石矿物摩擦系数随荷载增加表现出先降低后保持不变的趋势,石英矿物摩擦系数随荷载增加表现出先降低后增加的趋势;此外,随着剪切速率的增加,两种矿物的摩擦系数在低荷载条件下呈增长的趋势,在高荷载条件下基本保持稳定。最后,基于摩擦系数的宏-微观摩擦系数试验结果,采用速度-状态摩擦(RSF)定律建立红砂岩基本摩擦系数与矿物摩擦系数的线性回归方程,并通过直剪试验验证了该经验关系的可靠性,其误差范围为0.17%~0.91%。研究结果为基本摩擦系数的测定与取值提供了新思路。

基于摩擦补偿的柔性关节机器人分级滑模控制

针对柔性关节机器人中存在的非线性摩擦问题,提出一种基于摩擦补偿的柔性关节机器人分级滑模控制方法。首先,通过线性化参数的方法对柔性关节机器人受到的摩擦进行建模,并对模型中未知参数设计自适应律以实现摩擦的估计;然后,针对摩擦模型的误差,进一步设计观测器进行估计,结合摩擦的自适应和模型误差估计实现对摩擦的补偿;最后,利用电机侧和关节侧的位置误差和速度误差设计一级滑模面,再根据一级滑模面设计二级滑模面,从而得到分级滑模控制器,进一步实现柔性关节机器人的位置轨迹跟踪控制。通过Lyapunov函数证明了机器人关节轨迹跟踪误差的收敛性。仿真结果表明:该控制方法结合参数自适应和模型误差观测器可以有效地对摩擦进行补偿,在有限时间内实现柔性关节机器人的位置轨迹对期望位置轨迹的跟踪。