Naoto Yoshioka

A review of the micromechanical approach to the physics of contacting surfaces

Abstract The recent advance in the micromechanical approach to the physics of fractures, joints and faults (contacting surfaces) is reviewed. Although the methods and techniques of this approach have originally been developed mainly in engineering tribology, they have been successfully applied to various problems in geophysics, such as the behaviors of joints under normal loads, and under mixed normal and shear loads. The approach has also been applied to investigate the physics of the characteristic displacement appearing in the slip-rate-dependent friction that was observed in experiments made by others. The results obtained by this approach not only predict the experimental observations well, but also reveal the underlying mechanism of various phenomena of contacting surfaces. Since the behavior of contacting surfaces is determined by the micromechanics of asperity contacts, it is recognized to be important, for further progress of this approach, to investigate the detailed mechanism of asperity interactions that includes time-dependent and velocity-dependent deformation processes.

The characteristic displacement in rate and state-dependent friction from a micromechanical point of view

The physical meaning of the characteristic displacement that has been observed in velocity-stepping friction experiments was investigated based on the micromechanics of asperity contact. It has been empirically found for bare rock surfaces that the magnitude of the characteristic displacement is dependent only on surface roughness and insensitive to both slip velocity and normal stress. Thus the characteristic displacement has been interpreted as the displacement required to change the population of contact points completely. Here arises a question about the physical mechanism by which the contact population changes. Because individual asperity contacts form, grow and are eliminated with displacement, there are at least two possible interpretations for the characteristic displacement: (1) it is the distance over which the contacts existing at the moment of the velocity change all fade away, being replaced by new asperity contacts, or (2) it is the distance required for a complete replacement in the real contact area that existed at the moment of the velocity change. In order to test these possibilities, theoretical models were developed based on the statistics of distributed asperity summits. A computer simulation was also performed to check the validity of the theoretical models using three-dimensional surface topography data with various surface roughnesses. The deformation was assumed to be elastic at each asperity contact. The results of both the simulation and the theoretical models show that the characteristic displacement in (1) is about three times longer than that in (2). Comparison of the results with the experimental observations obtained by others indicates that the possibility (2) is the correct interpretation. This means that the “state” in the rate and state variable friction law is memorized in a very confined area of real contact. Further, our results explain why the characteristic displacement is insensitive to normal stress: this comes from the fact that the microscopic properties such as the mean contact diameter are insensitive to normal stress. The approach based on the micromechanics of asperity contact is useful to investigate the underlying mechanism of various phenomena in rock friction.

Dynamic process of Vickers indentation made on glass surfaces

Dynamic processes of Vickers indentation on glass surfaces were observed with a newly developed apparatus. It enables us to take successive picture images of a growing indentation from behind a transparent specimen with a CCD camera through an optical microscope with a minimum time interval of 16.7 ms. Growing rates of indentations were measured under several conditions of loading weight and collision velocity of the indenter with the sample surface. An indentation rapidly grows at the initial stage, followed by decrease in growing rate, finally approaching a value specified with the loading weight and the hardness of glass. This behavior can be described by a Voigt model, indicating that ‘‘visco‐elastic’’ nature in a microscopic sense is involved in the indentation process of glass. It is also found that the initial growing rate highly depends on the collision velocity; that is, the larger the collision velocity is, the higher the initial growing rate is. The result suggests that local temperature rise i...

A sandpile experiment and its implications for self-organized criticality and characteristic earthquake

We have performed an experiment in which a conical sandpile was built by slowly dropping sand onto a circular disk through a funnel with a small outlet. Avalanches (sand dropping off the disk) occurred, the size and the number of which were observed. It was seen that the behavior of avalanches (frequency-size distribution) was determined solely by the ratio of grain size to disk size, which is consistent with earlier studies. We categorize the behavior into three types: (1) the self-organized criticality (SOC) type (obeying Gutenberg-Richter’s law), (2) the characteristic earthquake (CE) type where only large avalanches are almost periodically generated, and (3) the transition type. The transition from SOC to CE type drastically occurs when the ratio of grain diameter to disk radius is reduced to about 0.02. The underlying mechanism to cause the transition is considered. Results of simulation by cellular automaton models, an experimental result showing that a conical pile has a stress dip near its center, and a two-dimensional simulation building up a conical pile, all suggest that the transition occurs due to a change in stress profile inside and near the surface of the pile. Although we are unfortunately not able to understand the detailed mechanism at the present stage, it seems very important to further investigate the underlying physics of the transition because it presumably provides us a clue to understand the mechanism of the periodicity of large characteristic earthquakes and may open a way for earthquake prediction.

Visco‐elastic response of joints to transmission waves

Experiments of wave transmission across a joint were carried out to investigate the visco-elastic response of the joint. Two models for wave transmission were examined with the experimental data. The results show that the velocity discontinuity model which includes the effect of viscosity is in better agreement with the experimental observations for both P- and S-waves under dry conditions than the displacement discontinuity model. This suggests that at the real asperity contacts, the solid material behaves visco-elastically to transmission waves in the high frequency range. A possible mechanism for the visco-elastic behavior is plastic flow at the asperities caused by high local pressure.

Dynamic observation of indentation process: A possibility of local temperature rise

Abstract Indentation experiments so far performed show that in a dynamic indentation test the rate of growth of the indentation size is highly dependent on the collision velocity of the indenter. Larger collision velocities yield higher rates of initial increase in indentation depth. The overall growth curves of the indentation depth are well modelled by a viscoelastic Voigt system. This model indicates that the viscosity of the sample reduces more rapidly as the collision velocity increases, suggesting the possibility of local temperature rise. In order to check this possibility, the temperature rise was observed with an infrared radiation thermosensor using a barium fluroide sample that is transparent to the infrared rays. The temperature was observed to increase in a wide area after the indenter collided with the sample. The temperature rise observed was small (less than 1K). Taking the limitation in the resolution of the sensor into account, the observed temperature was interpreted as that of the surf...

Dynamic observation of indentation process

Indentation experiments were performed with a pyramidal Vickers indenter on glass samples to observe the dynamic process of indentation. Successive picture images of indentation were taken by a CCD camera through a microscope. The change in diagonal length of the indentation was measured as a function of time of the order of several tens of milliseconds. The results show that the initial process of indentation is highly dependent on the collision velocity of the indenter when it comes into contact with the sample. Higher collision velocities yield larger rates of initial increase in diagonal length. An empirical equation was obtained that is similar to a visco-elastic Voigt model. It is suggested that local heating due to friction between the indenter and the sample or adiabatic compression reduced the viscosity of the sample material. The dynamic effect observed may be a cause of the change in resistance that is seen in the rate-dependent rock friction.

An experimental trial to detect precursory slips by transmission waves across a fault

It is known that there is a slow stage of precursory slip prior to a dynamic rupture propagation. Thus it is expected that there should be some physical contrasts between before and after the precursory slip. To detect the contrasts, we performed an observatory experiment in which P- and S-waves were transmitted across a fault in a double direct shear apparatus. Two types of experiments were made: first, Normal Stress Holding Test (NSHT), in which we focused on the effect of stationary contact time on transmission waves. Second, Shear Stress Increasing Test (SSIT), in which we measured local shear stresses in addition to transmission waves. In NSHT we observed increases in amplitude of transmission waves with the logarithm of stationary contact time. The change was several percent after about 3 hours contact. In SSIT we observed a significant increase in amplitude with a shear stress application until a stick-slip occurred. It may be explained by a strengthening of asperity interlocking. However, the detailed mechanism of this phenomenon is uncertain. Further we found a little reduction of increasing rate of amplitude which corresponds to the local precursory slips. This reduction may be attributed to the reset of stationary contact time due to local slips and replacement of asperity contacts with smaller contact sizes.

Shear resistance reduction due to vibration in simulated fault gouge

In order to investigate the mechanisms of dynamic triggering for earthquakes or creep events on natural faults with gouge layers, the frictional behavior of granular materials and its sensitivity to vibrational disturbances were examined by means of a direct shear test with crushed quartz sand and precise measurement equipments. The disturbances were created by light tapping on the lower part of a shear box. No displacement was observed from the tapping without shear load. From a series of experiments we found an acceleration in the horizontal displacement just after small vibration under shear. The acceleration indicates reduced shear resistance in the gouge layer, by about 3 % of the resistance just before the small vibration. This reduction in shear resistance seemed to be recovered soon and did not affect the long-term behavior of the gouge layer. The response of the vertical displacement to the small vibration depends on the amount of accumulated dilatation of the gouge layer. The mechanisms of shear resistance reduction and the variable response of the vertical displacement due to the vibration can be explained by the intrinsic feature of pillar-like structure of a force chain network in the gouge layer. Our results indicate that there might be dynamic triggering of fault motion due to shear resistance reduction of a gouge layer in a natural fault zone.

Effects of Contact Geometry of Faults on Transmission Waves

Abstract — In order to clarify the effects of contact geometry of faults on transmission waves, we have performed a series of experiments in which P and S waves with known wavelength were transmitted through an artificial fault. A pair of piezo-electric transducers (PZT) with various resonant frequency were used for the transmitter and the receiver. Parallel grooves were cut on disk surfaces and two disks were placed face to face with the grooves on one disk being perpendicular to those on the other disk. This yields evenly spaced square contacts on the fault. We regard the square contacts as asperity contacts, the size and the height of which were controlled by changing the width and the depth of the grooves. We found that the transmissivity of the waves is solely determined by the ratio of the groove depth/width to wavelength. The shallower and the narrower the groove depth and width are, the larger the amplitude of first arrival is for both P and S waves. When the groove depth is shallower than a quarter of wavelength, the effect of groove depth is negligible; deeper grooves significantly reduce the amplitude. We have made a mathematical model based on the stiffness of fault. By comparing the model calculations with the observation we found that the model has a limit at which the prediction by the model deviates from the data. The deviation occurs when the ratio of the groove depth/width to wavelength becomes 0.25. We refer to the wavelength as the critical wavelength. When the wavelength is larger than the critical wavelength, the observed data can be well explained by the model. Above this threshold, the model no longer fits the data. In this range, the amplitude of transmitted waves is found to be proportional to the real contact area. Although it is a kind of paradox that the amplitude, not the energy, is proportional to the real contact area, it is possibly explained by taking a non-uniform distribution of stress on the surface of the receiver PZT into account.