Kiyohiko Yamamoto

Constitutive relations between dynamic physical parameters near a tip of the propagating slip zone during stick-slip shear failure

Abstract Constitutive relations between physical parameters in the cohesive zone during stick-slip shear failure are experimentally investigated. Stick-slip was generated along a 40 cm long precut fault in Tsukuba granite samples using a servocontrolled biaxial loading apparatus. Dynamic behavior during local breakdown processes near a tip of the slipping zone is revealed; the slip velocity and acceleration are given as a function of the slip displacement and the cohesive (or breakdown) shear stress as a function of the slip velocity. A cycle of the breakdown and restrengthening process of stick-slip is composed of five phases characterized in terms of the cohesive strength and the slip velocity. The cohesive strength can degrade regardless of the slip velocity during slip instabilities. The maximum slip acceleration u max and the maximum slip velocity u max are obtained experimentally as: u max = 2 u c u max 2 and u max = Δτ b G v where u c is the critical displacement, Δτ b the breakdown stress drop, G the rigidity and v the rupture velocity. These relations are consistent with Idas theoretical estimation based on the cohesive zone model. The above formula gives good estimates for the maximum slip acceleration of actual earthquakes. The cutoff frequency ƒ max of the power spectral density of the slip acceleration increases with increasing normal stress; in particular, ƒ max is found to be directly proportional to the normal stress σ n within the normal stress range less than 17 MPa as: ƒ max (kHz) = 4.0σ n (MPa) σ n ƒ max increase with an increase in u max or u max . All these results lead to the conclusion that u max , u max and ƒ max increase with increasing normal stress. This is consistent with a previous observation that τ b increases with increasing normal stress. The above empirical linear relation between ƒ max and σ n can be explained by a linear dependence of Δτ b on σ n . The size-scale dependence of physical parameters is discussed, and such size-scale dependent parameters as u max and apparent fracture energy are scaled to the breakdown zone size regarded as a characteristic length, to extend the results obtained in the laboratory to an earthquake failure in the earth.

Strain-rate effect on frictional strength and the slip nucleation process

Abstract Kato, N., Yamamoto, K., Yamamoto, H. and Hirasawa, T., 1992. Strain-rate effect on frictional strength and the slip nucleation process. In: T. Mikumo, K. Aki, M. Ohnaka, L.J. Ruff and P.K.P. Spudich (Editors), Earthquake Source Physics and Earthquake Precursors. Tectonophysics, 211: 269–282. The strain-rate dependence of frictional strength is investigated in relation to sliding behaviour by biaxial compression tests of large-scale granite samples. Frictional sliding is generated by increasing shear strain at a constant rate under a constant normal stress on the fault. The ram displacement is held constant for a prescribed time interval between two successive sliding events so as to have the same time effect of stationary contact between sliding surfaces. We obtained the following results. As the strain rate increases: (1) sliding becomes more unstable; (2) the nucleation zone size of stick-slip decreases; and (3) frictional strength logarithmically increases. Result (3) is consistent with the previous study by Dieterich (1979a), and (1) and (3) are similar to the strain-rate effects on failure characteristics of intact rocks reported in the literature. Result (3) can be explained by a rate- and state-dependent friction law. Our results suggest that the strain-rate dependence of the fault strength plays an important role in controlling the nucleation process of faulting.

Microfracture processes in the breakdown zone during dynamic shear rupture inferred from laboratory observation of near-fault high-frequency strong motion

High-frequency velocities are measured during stick-slip motion in the immediate vicinity of a fault in a granite sample to reveal the microscopic process taking place in the breakdown zone defined in the slip-weakening model. It is found that 1) the onset time of the observed strong motion approximately coincides with the local rupture onset time, 2) the observed near-fault high-frequency strong-motion duration is approximately proportional to the local breakdown time, and 3) the power spectra of strong motions exhibit significant amplitudes at frequencies above the value offmax, wherefmax is a cut-off frequency relevant to rupturing the breakdown zone. These observations suggest that the high-frequency motion would be due to the incoherent brittle microfracture whose characteristic scale is much shorter than the breakdown zone size. We present a stochastic fault model to synthesize the near-fault high-frequency velocity waveforms. In the model, a number of small circular subfaults are distributed randomly on the fault and the rupture onset time of an individual subfault is assumed to be random. The main features of the observed velocity waveforms are well explained by this numerical modeling. It is concluded that approximately half of the total energy of high-frequency elastic waves observed at a point is radiated from the propagating breakdown zone. We emphasize the importance of the observation of near-fault high-frequency strong motions for large shallow earthquakes.

Effect of fault bend on the rupture propagation process of stick-slip

Abstract An experimental study of stick-slip is performed to examine the effect of a fault bend on the dynamic rupture propagation process. A granite sample used in the experiment has a pre-cut fault that is artificially bent by an angle of 5.6° at the center of the fault along strike, and accordingly the fault consists of two fault segments. The rupture propagation process during stick-slip instability is investigated by analyzing the records of shear strain and relative displacement measured with strain gauge sensors together with the hypocenters of AE (acoustic emission) events detected with piezoelectric transducers. The observed rupture propagation process of typical stick-slip events is as follows. (1) The dynamic rupture started on a fault segment is stopped near the fault bend. (2) The rupture propagation is restarted near the bend on the other fault segment 10.8 ms to 3.5 s after the stop of the first rupture. The delay time of the second rupture decreases with an increase in the slip amount of the first rupture or a decrease in the normal stress acting on the fault segment where the second rupture started. (3) The restarted rupture is not arrested by the presence of a fault bend, and slip occurs over the entire fault. We theoretically analyze the stress concentration near the fault bend to find that the normal stress produced by the preceding slip near the fault bend plays an important part in controlling the rupture propagation. A numerical simulation based on a rate- and state-dependent friction law is performed to interpret physically the retarded rupture in the experiment. The observed time interval of 10.8 ms to 3.5 s between the first rupture and the second is explained by the numerical simulation, suggesting that the rate- and state-dependence of rock friction is a possible mechanism for the retarded rupture on the fault.

In situ stress state from walkaround VSP anisotropy in the Kumano basin southeast of the Kii Peninsula, Japan

To reveal the stress state within the Kumano basin, which overlies the Nankai accretionary prism, we estimated seismic anisotropy from walkaround vertical seismic profiling (VSP) data recorded at Site C0009 during Integrated Ocean Drilling Program (IODP) Expedition 319. We obtained the following anisotropic parameters: (1) P wave velocity anisotropy derived from azimuthal normal moveout (NMO) velocity analysis, (2) P wave amplitude variation with azimuth, and (3) axes of symmetry of S wave splitting. Azimuthal variations of P wave velocity by ellipsoidal fitting analysis showed that P wave velocity anisotropy within sediments of the Kumano basin was ∼5%. Both the directions of fast P wave velocity and strong amplitude are aligned with the convergence vector of the Philippine Sea plate. Furthermore, S wave splitting analysis indicated that S wave polarization axes were parallel to and normal to the direction of plate subduction. These results indicate that the maximum horizontal stress at Site C0009 in the Kumano basin is in the direction of plate subduction. The horizontal differential stress estimated from the P wave velocity anisotropy (2.7∼5.5 MPa) indicates that the maximum horizontal stress is similar in magnitude to (or a little higher than) the vertical stress.

A theory of rock core-based methods for in-situ stress measurement

The behavior of the inelastic strain of rocks under the loading of compression reflects the history of stresses applied to the rocks. A number of methods based on this rock property of stress memory have been proposed for measuring in-situ stress. The magnitudes of in-situ stress can be determined from drilled core samples by deformation rate analysis (DRA); in other words, rocks do have the property of in-situ stress memory. In general, the inelastic strain of rocks increases with an increase in applied stress difference. The Keiser effect observed in laboratory experiments is explained as the behavior of the inelastic strain of this well-known mode. However, this effect cannot be the mechanism of the in-situ stress memory because the effect does not potentially allow us to determine the magnitudes of previously applied stress. Here, I theoretically show that rocks exhibit another mode of inelastic strain under axial loading of compression—if locally concentrated stresses in rocks relax to some extent under in-situ stress at depth. The magnitudes of in-situ stress can be determined from the behavior of this mode of inelastic strain under axial loading. The results of DRA suggest that this hypothesis is actually valid and that it is not only valid for the DRA, but also for the other rock core-based methods used for measuring in-situ stress.

Elastic property of damaged zone inferred from in-situ stresses and its role on the shear strength of faults

The Nojima fault in Hyogo prefecture, Japan, ruptured during the 1995 Hyogo-ken Nanbu earthquake (MJMA = 7.3). The stress measurements at sites close to this fault have revealed that the direction of the largest horizontal stress is almost perpendicular to the strike of this sub-vertical fault and that, in the zone within about 100 m from the fault core axis, the ratio of the largest shear stress to the normal stress is significantly small compared with that of the outside. It is thus the logical consequence that the principal stress outside the zone tends to direct perpendicularly to the fault plane. A model called the fracture process model is introduced for the relationship between fracture strength and elastic property of rocks. Making use of this model on the assumption that the observed shear stress equilibrates to the shear strength of damaged zone, it is found that the elastic wave velocities estimated from the stress well explain the observed velocities of damaged zone. This model suggests further that the friction coefficient of fault can be smaller than 0.15 due to the characteristic deformation of damaged zone and that the pressurized fluid is not essential for the formation of weak faults.

A stress-corrosion model for strain-rate dependence of the frictional strength of rocks

This Technical Note presents a simple model of the time-dependent fracture of asperities on sliding surfaces to explain the experimental results obtained for the strain-rate dependence of friction strength. A model is derived taking into account brittle fracture of asperities in two dimensions with an infinite periodic array of cracks. Kato et al. had examined the strain- rate dependence of maximum frictional strength prior to unstable slip by biaxially compressing a large-scale granite sample with a 40cm long precut fault. The results from this work are presented and compared with the theoretical equation. Predictions that the friction strength is proportional to the 1/(n+1)th power of the strain-rate, where n is the stress corrosion index, are borne out. The experimental values of the power index however are a third to a half that of the theoretical ones. Reasons for this are put forward and areas for future research suggested.