The micromechanics of friction in a granular layer

A grain bridge model is used to provide a physical interpretation of the rate- and state-dependent friction parameters for the simple shear of a granular layer. This model differs from the simpler asperity model in that it recognizes the difference between the fracture of a grain and the fracture of an adhesion between grains, and it explicitly accounts for dilation in the granular layer. The model provides an explanation for the observed differences in the friction of granular layers deformed between rough surfaces and those deformed between smooth surfaces and for the evolution of the friction parameters with displacement. The observed evolution from velocity strengthening to velocity weakening with displacement is interpreted as being due to the change in the micromechanics of strain accommodation from grain crushing to slip between adjacent grains; this change is associated with the observed evolution of a fractal grain structure.     

Ion--neutral friction as a model for magnetic relaxation

It is generally admitted that a plasma in the absence of forcing will relax to a minimum energy state compatible with appropriate constraints. Usually this is a force-free state, which, in two dimensions, implies a potential magnetic field except by the possible presence of current sheets. The precise mechanism of this relaxation, and in particular the plasma velocity, are generally ignored. There exists, however, a physically well-defined process that should produce magnetic relaxation: ion--neutral (or ambipolar) friction. While there is no guarantee of the existence of a limit of this process when t?→?∞, there exists a family of sequential limits for whom the Lorentz force tends to zero. To analyze the configuration of these limit states, we study the evolution of several moments of the magnetic energy. We prove that for as long as the enstrophy remains bounded, the current density energy also remains bounded in two dimensions: this excludes all classical configurations of current sheets across which the magnetic field reverses direction. Hence, these sheets cannot be the limit of ion--neutral diffusion unless the flow becomes increasingly irregular over time.     

一种SMA复合摩擦阻尼器的设计与性能研究

利用形状记忆合金(SMA)的超弹性特性,将SMA丝与摩擦阻尼器复合,提出了一种SMA复合摩擦阻尼器,给出了SMA复合摩擦阻尼器的工作机理和设计方法,建立了其理论模型,确定了SMA复合摩擦阻尼器的力-位移滞回曲线,并对一SMA复合摩擦阻尼器控震单自由度体系在地震作用下的动力响应进行了数值模拟。结果表明,提出的SMA复合摩擦阻尼器具有优良的耗能减振性能。     

Extreme behavior in a triple friction pendulum isolated frame

While isolation can provide significantly enhanced performance compared to fixed‐base counter parts in design level or even maximum considered level earthquakes, there is still uncertainty over the performance of isolation systems in extreme events. Researchers have looked at component level stability of rubber bearings and on the effect of moat impact on behavior of structures isolated on general bilinear isolators. However, testing of triple friction pendulum (TFP) sliding bearings has not been done dynamically or incorporated into a building system. Here, one‐third scale laboratory tests were conducted to on a 2‐story 2‐bay TFP‐isolated structure. Input motions were increasingly scaled until failure occurred at the isolation level. As the superstructure was designed with a yield force equivalent to the force of the bearing just at their ultimate displacement capacity, there was minimal yielding. A numerical model is presented to simulate the isolated building up to and including bearing failure. Forces transferred to the superstructure in extreme motions are examined using both experimental and numerical data. Additionally, the effect of the hardening stage of the TFP bearing is evaluated using the numerical model, finding slight benefits.     

Nonuniform friction as a physical basis for earthquake mechanics

A review of simple models and observations suggests that the main first-order features of active faulting-mechanical instability, the frequency-magnitude relations, seismic and aseismie slip, seismic radiation, incoherency and rupture stoppage — may be explained by a single characteristic of crustal faults: the spatial variation of the effective frictional stress, which resists slippage on faults. Faultoffset data suggest that rupture propagation ceases in regions of high resistance which act, as barriers. In these regions slippage is associated with negative stress drop. The spacing and the amplitudeA() of the barriers, as inferred from the frequency-magnitude and moment relation for earthquakes, obeys a simple statistical relationA()^p. On the scale of particle motion, this variability of frictional stress provides a mechanical instability which may be associated with the concept of dynamic friction. Invariably, the rapid particle motion in the model is always preceded by accelerated creep. The particle acceleration is highly irregular, giving rise to an almost random acceleration record on the fault. The particle displacement is relatively smooth, giving rise to simple displacement time function in the far field. Rupture propagation time is approximately proportional to the gradient of frictional stress along the fault. Consequently sharp changes of this stress may cause multiple events and other long period irregularities in the fault motion.The power density spectrum associated with the frictional stress implies that stress may be related to a Poisson distribution of lengths. The autocorrelation of such type of distribution yields a correlation lengthk _L ^–1 , similar perhaps toHaskell's (1964) andAki's (1967) correlation lengths inferred from spectral analysis of seismic waves. The partial incoherency of faulting implies that preseismic deformation may be significantly incoherent, consequently the prediction of small moderate earthquakes may be subject to inherent uncertainties. We conclude that frictional stress heterogeneities may be necessary and sufficient to explain active faulting associated with small and moderate earthquakes.     

Seismicity simulation with a rate- and state-dependent friction law

The dynamic motions and stabilities of a single-degree-of-freedom elastic system controlled by different friction laws are compared. The system consists of a sliding block connected to an elastic spring, driven at a constant velocity. The friction laws are a laboratory-inferred friction law called the rate-and-state-dependent friction law, proposed by Dieterich and Ruina, and a simple friction law described by dynamic and static frictions. We further extend the solution to a one-dimensional mass-spring model which is an analog of a fault controlled by the rate-and-state-dependent friction law. This model predicts non uniform slip and stress drop along the rupture length of a heterogeneous fault. This result is very different from some earlier modelings based on the simple friction law and a slip weakening friction law. In those earlier modelings the stress and slip functions become smoother with time along the length of the fault rupture, owing to the interactions between fault segments during slip. Because of this smoothing process the number of small events will decrease with time, and the universilly observed stationary magnitude-frequency relation cannot be explained. The interaction between a fault segment and its neighboring segments can be measured when the post-slip stress on this segment is compared with the stress on an identical segment (represented by a block in this modeling) without neighboring segments. If the post-slip stress of the former is much higher than that of the latter, strong interaction exists; if the two are close, only weak interaction exists. The interaction is determined by the relative motion between fault segments and the time duration of interaction. Our new modeling with the rate-and-state-dependent friction law appears to show no such smoothing effect and provides a physical mechanism for the roughening process in the difference between the fault strength and stress that is necessary to explain the observed stationary magnitude-frequency relation. The noninstantaneous healing predicted by the rate-and-state-dependent friction law may be repsonsible for the recurring nonuniform slip and stress drop, and may be explained by the reduction of interaction among fault segments due to the low frictional strength during the fault stopping. The very low friction during slip stopping allows much longer times than does the higher friction due to instantaneous healing for the fault segments to adjust their motions from an upper-limit slip velocity to almost rest. According to newton's second law, a process with fixed masses and constant velocity changes involves low forces and weak interactions if it is accomplished in a long time period, and vice versa. Our modeling also indicates that the existence of strong patches with higher effective stress on a fault is needed for the occurrence of major events. The creeping section of a fault, such as the one along the San Andreas fault in central California, on the other hand, can be simulated with the rate-and-state-dependent friction law by certain model parameters, which, however, must not include strong patches. In this case small earthquakes and aseismic creep relieve the accumulating strain without any large events.     

Seismicity simulation with a mass-spring model and a displacement hardening-softening friction law

Dieterich simulated aftershocks numerically, using a one-dimensional mass-spring model with a time-dependent friction law. But an important precursory phenomenon called quiescence cannot be produced by this model unless, as Mikumo and Miyatake showed with a three-dimensional continuum model, a somewhat arbitrary bimodal distribution of frictional strength is assumed. Here we used the friction law proposed by Stuart, which is a displacement hardening-softening model, and simulated the quiescence. By varying the parameters of the friction law in our mass-spring model, we found a variety of seismicity patterns. When we choose extremely large critical displacement we get a recurrent sequence of creep followed by mainshock without small earthquakes. But when we choose a critical displacement in the same order of magnitude as the slip-weakening critical displacement estimated by Papageorgiou and Aki from strong motion data, we get a normal seismicity pattern, including quiescence before large events. This simple model points to a promising approach for the interpretation of the rupture process during an earthquake by the same physical model.     

Chaotic seismic faulting with a mass-spring model and velocity-weakening friction

We present a systematic analysis of the dynamical behavior introduced by fault zone heterogeneities, using a simple mass-spring model with velocity-weakening friction. The model consists of two sliding blocks coupled to each other and to a constant velocity driver by clastic springs. The state of this system can be characterized by the positions of the two blocks relative to the driver. Symmetry stabilizes the system and generates only cyclic behavior. For an asymmetric system where the frictional forces for the two blocks are not equal, the solutions exhibit chaotic behavior. The transition from stable cyclic behavior to chaos is characterized by the period-doubling route to chaos. Lyapunov exponents are computed to quantify the deterministic chaos and to locate the onset of the chaotic evolution in parameter space. In many examples of deterministic chaos, chaotic behavior of a low-order system implies chaos in similar higher order systems. Thus, our results provide substantial evidence that crustal deformation is an example of deterministic chaos.     

新型自复位变摩擦阻尼器试验研究

目前阻尼器运用广泛,但传统摩擦阻尼器无法适应不同的振动强度,且在地震作用后损坏严重,没有自复位功能。文章利用形状记忆合金的超弹性,提出一种新型的自复位变摩擦阻尼器,介绍了阻尼器的构造、基本工作原理并推导了其力学模型,之后对阻尼器进行了力学试验。得到如下结论：该阻尼器不仅能在不同等级地震作用下满足耗能要求,还具有良好的自复位能力;力学试验得到的滞回曲线与理论推导的力学模型吻合较好,印证了力学模型的正确性;该阻尼器耗能能力随着合金丝直径、螺栓预紧力和坡面坡度的增大而增强;残余位移随着合金丝直径和坡面坡度增大而减小、随着预紧力增大而增大。     

Seismic analysis of a LNG storage tank isolated by a multiple friction pendulum system

The seismic response of an isolated vertical, cylindrical, extra-large liquefi ed natural gas (LNG) tank by a multiple friction pendulum system (MFPS) is analyzed. Most of the extra-large LNG tanks have a fundamental frequency which involves a range of resonance of most earthquake ground motions. It is an effective way to decrease the response of an isolation system used for extra-large LNG storage tanks under a strong earthquake. However, it is diff icult to implement in practice with common isolation bearings due to issues such as low temperature, soft site and other severe environment factors. The extra-large LNG tank isolated by a MFPS is presented in this study to address these problems. A MFPS is appropriate for large displacements induced by earthquakes with long predominant periods. A simplifi ed fi nite element model by Malhotra and Dunkerley is used to determine the usefulness of the isolation system. Data reported and statistically sorted include pile shear, wave height, impulsive acceleration, convective acceleration and outer tank acceleration. The results show that the isolation system has excellent adaptability for different liquid levels and is very effective in controlling the seismic response of extra-large LNG tanks.     

摩擦阻尼器的研究进展

摩擦阻尼器是一种运用摩擦阻尼原理耗散由振动输入到结构中能量的减震装置.相比传统的减震(振)阻尼器,摩擦阻尼器具有以下几点优势:工程结构安装的便利性、构造加工组装的简易性、较大的初始刚度及性能方面的稳定性等.整理并总结国内外学者在摩擦阻尼器方面取得的大量研究成果,包括摩擦阻尼器的类型、性能影响因素、试验研究以及国内外摩擦...     

Tidal friction in a sea with two equal semidiurnal tidal constituents

The effect of quadratic friction on tidal currents consisting of equal M₂ and S₂ constituents is considered. It is shown by two separate arguments—one based on an energy balance, the other on harmonic analysis of the frictional force—that, for rectilinear and parallel currents, the drag coefficient applicable to either constituent considered in isolation should be 1.70 times greater than that applied to the two constituents propagating together. The results of a numerical model of the tides in Gulf St Vincent, Australia (where equal M₂ and S₂ tides occur) are consistent with this prediction. A general result of this work is that the drag coefficients predicted by harmonic analysis of the friction force give the correct rate of energy dissipation for any number of tidal constituents, equal or not.     

支座摩擦系数对摩擦摆基础隔震结构地震反应的影响

对不同地震烈度作用下的摩擦摆基础隔震结构进行了地震反应分析,分析了支座摩擦系数对支座位移、楼层加速度和楼层剪力的影响。结果表明随着摩擦摆支座摩擦系数的增大,支座位移逐渐减小,而结构的加速度和楼层剪力逐渐增大;随着地震作用强度的提高,摩擦系数对支座位移的影响逐渐增大,而摩擦系数对结构加速度和楼层剪力的影响逐渐减小。     

断层摩擦的过山车现象

在地震中,摩擦对断层行为的生成、传播和消减过程起到了关键性控制作用.实验室测试了多种滑动速率下的摩擦行为.结果表明,摩擦在地震中的演化比我们假想的要复杂得多.     

Experimental evidence for flexibility of a building foundation supported by concrete friction piles

This article explores the possibility to measure deformations of building foundations from measurements of ambient noise and strong motion recordings. The case under study is a seven-storey hotel building in Van Nuys, California. It has been instrumented by strong motion accelerographs, and has recorded several earthquakes, including the 1971 San Fernando (M_L=6.6, R=22 km), 1987 Whittier–Narrows (M_L=5.9, R=41 km), 1992 Landers (M_L=7.5, R=186 km), 1992 Big Bear (M_L=6.5, R=149 km), and 1994 Northridge (M_L=6.4, R=1.5 km) earthquake and its aftershocks (20 March: M_L=5.2, R=1.2 km; 6 December, 1994: M_L=4.3, R=11 km). It suffered minor structural damage in 1971 earthquake and extensive damage in 1994. Two detailed ambient vibration tests were performed following the Northridge earthquake, one before and the other one after the 20 March aftershock. These included measurements at a grid of points on the ground floor and in the parking lot surrounding the building, presented and analyzed in this article. The analysis shows that the foundation system, consisting of grade beams on friction piles, does not act as a “rigid body” but deforms during the passage of microtremor and therefore earthquake waves. For this geometrically and by design essentially symmetric building, the center of stiffness of the foundation system appears to have large eccentricity (this is seen both from the microtremor measurements and from the earthquake recordings). This eccentricity may have contributed to strong coupling of transverse and torsional responses, and to larger than expected torsional response, contributing to damage during the 1994 Northridge, earthquake.     

Bidirectional shaking table tests of a low-cost friction sliding system with flat-inclined surfaces

A novel low-cost friction sliding system for bidirectional excitation is developed to improve the seismic performance of reinforced concrete (RC) bridge piers. The sliding system is a spherical prototype developed by combining a central flat surface with an inclined spherical segment, characterized by stable oscillation and a large reduction in response accelerations on the flat surface. The inclined part provides a restoring force that limits the residual displacements of the system. Conventional steel and concrete are employed to construct a flat-inclined spherical surface atop an RC pier. The seismic forces are dissipated through the frictions generated during the sliding movements; hence, the seismic resilience of bridges can be ensured with a low-cost design solution. The proposed system is fabricated utilizing a mold created by a three-dimensional printer, which facilitates the use of conventional concrete to construct spherical shapes. The concrete surface is lubricated with a resin material to prevent abrasion from multiple input ground motions. To demonstrate the effectiveness of the system, bidirectional shaking table tests are conducted in the longitudinal and transverse directions of a scaled bridge model. The effect of the inclination angle and the flat surface size is investigated. The results demonstrate a large decrease in response acceleration when the system exhibits circular sliding displacement. Furthermore, the inclination angle that generates the smallest residual displacement is identified experimentally.     

Tidal friction for semidiurnal tides

The quadratic law of bottom friction demands an increased frictional coefficient for the S₂ and N₂ tides with respect to a dominant M₂ tidal signal. A numerical model of the semidiurnal tides in the northeast Atlantic gives an increase in friction of ∼35% for the N₂, S₂ and K₂ tides with respect to the M₂ tide and this value is close to a theoretically derived estimate for the region, providing confirmation of the general widescale applicability of the quadratic friction law. Small differences in friction also occur for the N₂, S₂ and K₂ tides and this is attributed to the interaction of the L₂ and μ₂ tides with the M₂ tide in the presence of quadratic friction. Energy dissipation relationships, anomalous K₂/S₂ amplitude ratios and the role of quadratic friction on 18.6 year variations of semidiurnal forcing are examined.     

Dynamic faulting under rate-dependent friction

We discuss the effects of rate-dependent friction on the propagation of seismic rupture on active faults. Several physicists using Burridge and Knopoff's box and spring model of faulting have proposed that fault complexity may arise from the spontaneous development of a self-similar stress distribution on the fault plane. If this model proves to be correct, it has important consequences for the origin of the complexity of seismic sources. In order to test these ideas on a more realistic earthquake model, we developed a new boundary integral equation method for studying rupture propagation along an antiplane fault in the presence of nonlinear rate-dependent friction. We study rupture dynamics of models with single and twin asperities. In our models, asperities are places on the fault with a higher value of prestress. Othewise all fault parameters are homogeneous. We show that for models with such asperities, a slip velocity weakening friction leads to the propagation of supersonic healing phases and to the spontaneous arrest of fracture if the prestress outside the asperities is low enough. For models with asperities, we can also observe narrow slip velocity pulses, qualitatively similar to the so-called Heaton pulses observed in some earthquake accelerograms. We also observe a complex distribution of stress after the rupture that depends on details of the initial distribution of asperities and on the details of the friction law.