Experimental and analytical studies on the response of freestanding laboratory equipment to earthquake shaking

This paper presents results of a comprehensive experimental program on the seismic response of full‐scale freestanding laboratory equipment. First, quasi‐static experiments are conducted to examine the mechanical behavior of the contact interface between the laboratory equipment and floors. Based on the experimental results, the response analysis that follows adopts two idealized contact friction models: the elastoplastic model and the classical Coulomb friction model. Subsequently, the paper presents shake table test results of full‐scale freestanding equipment subjected to ground and floor motions of hazard levels with corresponding displacements that can be accommodated by the shake table at the UC Berkeley Earthquake Engineering Research Center. For the equipment tested, although some rocking is observed, sliding is the predominant mode of response, with sliding displacements reaching up to 60 cm. Numerical simulations with the proposed models are performed. Finally, the paper identifies a physically motivated intensity measure and the associated engineering demand parameter with the help of dimensional analysis and presents ready‐to‐use fragility curves. Copyright © 2008 John Wiley & Sons, Ltd.     

Direct observation of frictional contacts: New insights for state-dependent properties

Rocks and many other materials display a rather complicated, but characteristic, dependence of friction on sliding history. These effects are well-described by empirical rate- and state-dependent constitutive formulations which have been utilized for analysis of fault slip and earthquake processes. We present a procedure for direct quantitative microscopic observation of frictional contacts during slip. The observations reveal that frictional state dependence represents an increase of contact area with contact age. Transient changes of sliding resistance correlate with changes in contact area and arise from shifts of contact population age. Displacement-dependent replacement of contact populations is shown to cause the diagnostic evolution of friction over a characteristic sliding distance that occurs whenever slip begins or sliding conditions change.     

Micromechanics of the velocity and normal stress dependence of rock friction

Among the second-order effects on friction the most important are those of variable normal stress and of slip velocity. Velocity weakening, which is usually considered the source of the stick-slip instability in rock friction, has been observed in velocity stepping experiments with Westerly granite. The friction change, , was –0.01 to –0.008 for a tenfold velocity increase. Using normal closure measurements, we observed dilation upon each increase in sliding rate. We also observed, for the first time, time-dependent closure between surfaces during static loading. The dilation that occurred during the velocity stepping experiment was found to be that expected from the static time-dependent closure phenomenon. This change in closure was used to predict friction change with an elastic contact model. The calculated friction change which results from a change in contact area and asperity interlocking, is in good agreement with the observed velocity dependence of steady-state friction. Variable normal stress during sliding has two effects, first in creating new partial slip contacts and locking some existing fully sliding contacts and second in increasing interlocking, for instance when normal load is suddenly increased. As a result, a transient change in friction occurs upon a sudden change in normal load.     

Characterizing friction in sliding isolation bearings

The force–displacement behavior of the Friction Pendulum? (FP) bearing is a function of the coefficient of sliding friction, axial load on the bearing and effective radius of the sliding surface. The coefficient of friction varies during the course of an earthquake with sliding velocity, axial pressure and temperature at the sliding surface. The velocity and axial pressure on the bearing depend on the response of the superstructure to the earthquake shaking. The temperature at an instant in time during earthquake shaking is a function of the histories of the coefficient of friction, sliding velocity and axial pressure, and the travel path of the slider on the sliding surface. A unified framework accommodating the complex interdependence of the coefficient of friction, sliding velocity, axial pressure and temperature is presented for implementation in nonlinear response‐history analysis. Expressions to define the relationship between the coefficient of friction and sliding velocity, axial pressure, and temperature are proposed, based on available experimental data. Response‐history analyses are performed on FP bearings with a range of geometrical and liner mechanical properties and static axial pressure. Friction is described using five different models that consider the dependence of the coefficient of friction on axial pressure, sliding velocity and temperature. Frictional heating is the most important factor that influences the maximum displacement of the isolation system and floor spectral demands if the static axial pressure is high. Isolation system displacements are not significantly affected by considerations of the influence of axial pressure and velocity on the coefficient of friction. Copyright © 2014 John Wiley & Sons, Ltd.     

Simulation of Frictional Strength and Steady Relaxation Using the Rate and State Dependent Friction Model

In this paper, frictional strength of hard solids, such as rock–rock sliding surfaces, is studied as a function of waiting time and shearing velocity. A one dimensional spring–mass sliding system is numerically simulated under the quasistatic condition using the rate and state dependent friction model. It is established that frictional strength varies linearly with the logarithm of waiting time (also known as time of stationary contact or relaxation time, etc.) as well as logarithm of shearing velocity. Analytical expression developed for frictional strength is found to be valid only in the case of high stiffness of the connecting spring. In the steady relaxation simulation, a steadily sliding mass is suddenly brought to zero velocity and relaxation of the interfacial stress and corresponding velocity at the sliding interface is studied as a function of relaxation time in the velocity strengthening regime of friction. A mathematical relation is derived between state variable and waiting time using the concept of steady relaxation. The relaxation model is also compared with the experimental data from the literature. Finally, the present study enables one to unify the slide–hold–slide friction experiments.     

A new friction law for sliding rigid blocks under cyclic loading

A rigid block sliding down an inclined plane under the action of gravity was monitored with accelerometers and an LVDT to investigate how the transition from static to kinetic friction develops. Once the transition patterns were identified, experiments were carried out to study the response of a dynamically excited rigid block sliding down the inclined plane of a shaking table. Harmonic time series were used as input motions. The laboratory results allowed the definition of a continuous friction law to model the continuous variation of the friction from its static to kinetic condition. This law was implemented into the commercial 3D distinct element code 3DEC to numerically reproduce the experiments carried out, thus validating the friction law. Afterwards, the friction law was used to evaluate the sliding due to the kinetics of the block. Three cases were analyzed: constant friction coefficient, Coulomb friction law and the proposed friction law. These computations were compared to laboratory measurements. It is found that permanent displacements computed by considering the new law are in better agreement with laboratory measurements.     

Impact of the equivalent center of mass separating from the sliding surface on the isolation performance of friction pendulum bearings

A new equivalent center of mass model of FPBs(friction pendulum bearings) is introduced, and based on this model, coefficient j of the equivalent center of mass separating from the sliding surface is defined. It is thought in theory that j has a significant impact on the isolation parameter of FPBs, since the equivalent post-yielding stiffness and friction coefficients are not simply determined by sliding radius and sliding friction pairs. The results of numerical simulation analysis using ABAQUS conducted on two groups of FPBs support this viewpoint. For FPBs with the same sliding radius and sliding friction pairs, the FPB modules of structural analysis software such as ETABS could only distinguish the equivalent transformation using j one by one. The seismic response data obtained in a base isolation calculation example of FPBs are very different, which reveals that j's impact on the isolation effectiveness of FPBs cannot be ignored. The introduction of j will help improve the classical structural theory of FPBs and the weak points of structural analysis software based on this theory, which is important in achieving more accurate analyses in structural design.     

Stick–Slip and the Transition to Steady Sliding in a 2D Granular Medium and a Fixed Particle Lattice

We report an experimental study of the stick–slip to steady sliding behavior of a solid object pulled, via a spring, across 2D granular substrates of photoelastic disks that are either fixed in a solid lattice (granular solid) or unconstrained, forming a granular bed. We observe a progression of friction regimes with increasing sliding speed, including single-slip, double-slip, and mixed stick–slip regimes, steady sliding, and inertial oscillations. For the case of the granular bed, we report a detailed analysis of frictional behavior for the low speed stick–slip regime, including spring and elastic energy dependencies during the stick and slip portions of the motion. For the case of the granular solid, we explore friction in the presence and absence of externally applied vibrations, and compare it with sliding on a granular bed, which is intrinsically disordered. We observe that external vibration reduces transition values for both the single-slip to double-slip transition and the stick–slip to steady sliding transition. Moreover, we observe that the effect of packing disorder on granular friction seems similar to the effect of vibration-induced disorder, a result that, to our knowledge, has not been reported previously in the experimental literature.     

Effects of vertical excitation on the seismic performance of a seismically isolated bridge with sliding friction bearings

A finite element model is constructed for a sliding friction bearing in a seismically isolated bridge under vertical excitation with contact/friction elements. The effects of vertical excitation on the seismic performance of a seismically isolated bridge with sliding friction bearings and different bearing friction coefficients and different stiffness levels (pier diameter) are discussed using example calculations, and the effects of excitation direction for vertical excitation on the analysis results are explored. The analysis results shows that vertical excitation has a relatively large impact on seismic performance for a seismically isolated bridge with sliding friction bearings, which should be considered when designing a seismically isolated bridge with sliding friction bearings where vertical excitation dominates.     

Experimental assessment of sliding materials for seismic isolation systems

Novel self-lubricating materials are currently being proposed to be used in sliding isolation systems such as the curved surface sliding isolator system, or pendulum bearing system, for the protection of buildings and structures. The current codes for anti-seismic devices are focused on the evaluation of the performance of the whole isolation system; as a consequence, a reliable procedure for the pre-assessment of the material combinations of sliding interfaces is currently missing. Therefore in this paper, an experimental methodology is proposed for the characterization of self-lubricating materials through tests on small-scale specimens performed using customized equipment able to reproduce the operational conditions of real isolation systems as per contact pressure, sliding velocity, temperature and slide path. The testing sequence has been designed in order to evaluate the sliding properties of the material in terms of static and dynamic coefficient of friction and wear resistance. Examples are reported for the assessment of two self-lubricating materials with different sliding characteristics. In order to validate the method and to confirm the reliability of extrapolating the results to real working conditions, prototypes of pendulum isolation systems incorporating the assessed materials have been tested according to the AASHTO (Guide specifications for seismic isolation design, 2nd edn. American Association of State Highway and Transportation Officials, Washington, DC, 1999) specifications and the relevant dynamic properties assessed from the Horizontal Load—Displacement loops. The experimental outcomes confirmed that the frictional characteristics provided by the proposed procedure can be reliably used in the design of seismically isolated structures.     

Hysteretic models for sliding bearings with varying frictional force

The friction pendulum system is a sliding seismic isolator with self‐centering capabilities. Under severe earthquakes, the movement may be excessive enough to cause the pendulum to hit the side rim of the isolator, which is provided to restrain the sliding. The biaxial behavior of a single friction pendulum, in which the slider contacts the restrainer, is developed using a smooth hysteretic model with nonlinear kinematic hardening. This model is extended to simulate the biaxial response of double and triple friction pendulums with multiple sliding surfaces. The model of a triple friction pendulum is based on the interaction between four sliding interfaces, which in turn is dependent upon the force and displacement conditions prevailing at these interfaces. Each of these surfaces are modeled as nonlinear biaxial springs suitable for a single friction pendulum, using the yield surface, based on the principles of the classical theory of plasticity, and amended for varying frictional yield force, due to variation in vertical load and/or velocity‐dependent friction coefficient. The participation of the nonlinear springs is governed by stick‐slip conditions, dictated by equilibrium and kinematics. The model can simulate the overall force‐deformation behavior, track the displacements in individual sliding surfaces, and account for the ultimate condition when the sliders are in contact with their restrainers. The results of this model are verified by comparison to theoretical calculations and to experiments. The model has been implemented in programs IDARC2D and 3D‐BASIS, and the analytical results are compared with shake table experimental results. Copyright © 2013 John Wiley & Sons, Ltd.     

Seismic behaviour of above-ground oil pipelines

The dynamic behaviour of above-ground oil pipelines which are allowed to slide back and forth on intermediate supports during strong motion earthquakes is studied. This sliding is resisted by friction between the pipe and the top of the support. The main objective of the study is to determine the effect of this non-linear friction on both the static and dynamic stresses in the pipe. The study also considers the influence of other critical parameters such as: pipeline configuration, seismic wave velocity, initial temperature differential and internal pressure, and ground motion characteristics. Results show that the critical bending moments in the pipe occur during the static loading and that with seismic excitation, these moments tend to shake down as the pipe moves to a more stress free configuration. It is shown that the use of sliding friction can be an effective means of dissipating seismic energy and thereby damping the dynamic response of the pipeline even for low values of the coefficient of friction.     

海原断裂带断层泥摩擦特性的研究

用双剪法对海原断裂带5个点的13种断层泥的摩擦滑动特征进行的实验研究表明,海原断裂带的断层泥的存在有助于消除粘滑与增大摩擦强度,五个点断层泥的摩擦系数平均值分别是0.760(景泰),0.728(哈思山),0.669(大沟门),0.644(剌儿沟),0.684(蔡祥堡)。     

AN EXPERIMENTAL STUDY ON THE PROCESS OF INTERGRANULAR PRESSURE SOLUTION OF PLAGIOCLASE GOUGE UNDER HIGH TEMPERATURE AND PRESSURE: METHOD AND PRELIMINARY RESULTS

To understand the mechanism of lower-crust earthquake and slow slips, it is necessary to study the frictional properties of mafic rocks and their major rock-forming minerals. Previous studies have performed a series of experimental researches on gabbro, basalt and their major constituents. According to the results of previous experiments, frictional sliding of plagioclase under hydrothermal conditions(100~600℃)shows a property of velocity weakening, and the experimental results show that both the direct rate effect parameter(a)and the healing effect parameter(b)increase with temperature, a typical feature for thermally-activated processes. Velocity weakening means property of a shear band that has a stronger friction healing effect than the direct rate effect in the rate and state friction constitutive framework, and the healing effect(b value)in constitutive relation mainly reflects the increase in contact area with time under hydrothermal conditions, with some minor effect of structural changes. Since the microphysical mechanism of feldspar minerals at the contacts is mainly brittle cataclasis for temperatures below 600℃, the significant frictional healing effect in this case can only be explained by the mechanism of pressure solution. In order to determine if the dissolution process of plagioclase actually occurs on the laboratory time scale, we conducted hydrostatic experiments on plagioclase powder samples under hydrothermal conditions whereby frequent contact switch between particles seen in frictional sliding experiments can be avoided, making the observation on the dissolution sites possible. Experimental temperatures were 400℃ and 500℃, with confining pressure of 90~150MPa, pore pressure of 30MPa, with 2mm initial thickness of fault gouge. The mechanical data show that a creep process occurred in the plagioclase fault gouge in the experimental temperature and pressure range; and the microstructures of the experiment show that precipitation of new grains is prevalent as the product of pressure solution process between plagioclase particles. At the same time, it is observed that the contact points have an appearance similar to fused, fuzzy structure as signatures of dissolution. The results of our experiments provide a definite experimental evidence for the healing mechanism in friction of plagioclase and for the theoretical relation between unstable slip and the pressure solution process. The results of the experiments are summarized as follows: (1)Drainage rate of pore water in plagioclase gouge was high in the first few hours of experiment, but gradually decreases over time for both temperature and pressure series of experiments slowing down to a steady state. This feature indicates that there is a creep process that evolves inside the plagioclase gouge. In the temperature-series experiments, the drainage rate of the pore water in the plagioclase gouge at 400℃ is relatively low than the cases for higher temperatures. Thus, the applied temperature is positively correlated with the creep of plagioclase gouge. (2)Scanning electron microscopy(SEM)observations of the experimentally deformed samples were performed on thin sections cut along the sample axis. Firstly, from the images of microstructure, it was found that the degree of particle fracture became more significant at a higher effective pressure, with smaller pore volume between particles. In the temperature-series experiments it was found that the degree of compaction of plagioclase gouge increased with increasing temperature. Precipitation of plagioclase grains in layered structures was generally observed in high-magnification images, indicating the presence of pressure solution processes. Contact points were also found to be in a state of ambiguity that seems to be a fused morphology, but the details of the structure remain to be determined by further observations. The above results indicate that the pressure solution process of plagioclase particles can occur on a typical laboratory time scale, and the results of this study provide robust experimental evidences for the theory that links between pressure solution and the mechanism of frictional healing and unstable slips for plagioclase.     

Experimental testing of a rocking timber shear wall with slip‐friction connectors

Allowing a structure to uplift and rock during an earthquake is one way in which activated forces can be capped and damage to the structure avoided or minimised. Slip‐friction connectors (also known as slotted‐bolt connectors) were originally developed for use in steel construction, but for this research have been adapted for use as hold‐downs in an experimental 2.4 m × 2.4 m rigid timber shear wall. A novel approach is used to achieve the desired sliding threshold in the connectors, and the wall uplifts when this threshold is reached. From a series of quasi‐static cyclic tests, it is shown that slip‐friction connectors can impart ductile and elasto‐plastic characteristics to what would otherwise be essentially brittle structures. Because forces on the wall were capped by the slip‐friction connectors to levels well below the design level, no damage to the wall was observed. Self‐centring potential was also found to be excellent. The slip‐friction connectors themselves are of a unique design and have proven to be robust and durable, adequately performing their duty even after almost 14 m of cumulative travel under high contact pressures. To resist base shear without unduly affecting rocking behaviour, a new type of shear‐key is proposed and implemented, and a procedure developed to quantify its influence on overall wall behaviour. Copyright © 2014 John Wiley & Sons, Ltd.     

A model of triple friction pendulum bearing for general geometric and frictional parameters

Current models describing the behavior for the triple friction pendulum (TFP) bearing are based on the assumption that the resultant force of the contact pressure acts at the center of each sliding surface. Accordingly, these models only rely on equilibrium in the horizontal direction to arrive at the equations describing its behavior. This is sufficient for most practical applications where certain constraints on the friction coefficient values apply as a direct consequence of equilibrium. This paper presents a revised model of behavior of the TFP bearing in which no assumptions are made on the location of the resultant forces at each sliding surface and no constraints on the values of the coefficient of friction are required, provided that all sliding surfaces are in full contact. To accomplish this, the number of degrees of freedom describing the behavior of the bearing is increased to include the location of the resultant force at each sliding surface and equations of moment equilibrium are introduced to relate these degrees of freedom to forces. Moreover, the inertia effects of each of the moving parts of the bearing are accounted for in the derivation of the equations describing its behavior. The model explicitly calculates the motion of each of the components of friction pendulum bearings so that any dependence of the coefficient of friction on the sliding velocity and temperature can be explicitly accounted for and calculations of heat flux and temperature increase at each sliding surface can be made. This paper presents (a) the development of the revised TFP bearing model, (b) the analytic solution for the force–displacement relations of two configurations of the TFP bearing, (c) a model that incorporates inertia effects of the TFP bearing components and other effects that are useful in advanced response history analysis, and (d) examples of implementation of the features of the presented model. Copyright © 2016 John Wiley & Sons, Ltd.     

摩擦单摆支座等效摩擦系数数值仿真及试验研究

对摩擦单摆支座的主要参数等效摩擦系数进行了数值仿真及试验研究,为桥梁结构的减隔震设计提供了参考。数值仿真包括等效摩擦系数与滑动面和转动面的摩擦系数、竖向承载力及加载频率三者关系的研究,对比分析了模拟结果与试验结果。结果表明:当滑动面与转动面的摩擦系数为不同取值时,支座等效摩擦系数的模拟值略大于理论值,初步验证了支座等效摩擦系数理论公式的正确性;通过模拟结果与试验结果的对比分析,进一步验证了该理论公式的合理性。     

Investigation of the sliding behavior between steel and mortar for seismic applications in structures

The friction developed between a steel base plate and a mortar base contributes shear resistance to the building system during a seismic event. In order to investigate the possible sliding behavior between the base plate and the mortar, a shake table study is undertaken using a large rigid mass supported by steel contact elements which rest on mortar surfaces connected to the shake table. Horizontal input accelerations are considered at various magnitudes and frequencies. The results provide a constant friction coefficient during sliding with an average value of approximately 0.78. A theoretical formulation of the friction behavior is also undertaken. The theoretical equations show that the sliding behavior is dependent on the ratio of the friction force to the input force. The addition of vertical accelerations to the system further complicates the sliding behavior as a result of the varying normal force. This results in a variable friction resistance which is a function of the amplitude, phase, and frequency of the horizontal and vertical input motions. In general, this study showed a consistent and reliable sliding behavior between steel and mortar. Copyright © 2009 John Wiley & Sons, Ltd.     

On the stability of colonnade structural systems under static and dynamic loading conditions

The structural behavior of colonnade structural systems subjected to static and dynamic loading is investigated to identify the main factors affecting the stability and to improve our understanding of their behaviour. In particular, the discrete element method of analysis is utilised to study the static and dynamic behaviour of a typical section of the two storey colonnade of the Forum in Pompeii. Static analysis indicated that the failure of colonnade structures occur at higher friction angles as the weight above the structure decreases and so a sudden collapse can occur when parts of the monument are disassembled. For the dynamic analysis, the mechanical behavior of the colonnade was investigated for both harmonic and real seismic excitations. For excitations with relatively low dominant frequencies, the primary response is rocking; as the excitation frequency increases, the response becomes more complicated demonstrating both sliding and rocking movements. It was also shown that the construction methods used in ancient times, such as multi-block segmented trabeations and solid block beam, have quite significant impact on the mechanical response of the structures under static and dynamic loading.     

Frictional Behavior of Steel-PTFE Interfaces for Seismic Isolation

The widespread use of sliding bearings for the seismic isolation of structures requires detailed knowledge of their behavior and improved modeling capability under seismic conditions. The paper summarizes the results of a large experimental investigation on steel–PTFE interfaces, aimed at evaluating the effects of sliding velocity, contact pressure, air temperature and state of lubrication on the mechanical behavior of steel-PTFE sliding bearings. Based on the experimental outcomes, two different mathematical models have been calibrated, which are capable of accounting for the investigated parameters in the evaluation of the sliding friction coefficient. The first model is basically an extension of the model proposed by Constantinou et al. (1990)Journal of Earthquake Engineering, 116(2), 455–472, while the second model is derived from the one proposed by Changet al. (1990)Journal of Engineering Mechanics, 116, 2749–2763. Expressions of the model parameters as a function of bearing pressure and air temperature are presented for lubricated and non-lubricated sliding surfaces. Predicted and experimental results are finally compared.