Damage identification method using harmonic excitation force considering both modelling and measurement errors

A method of structural damage identification using harmonic excitation force is presented. It considers the effects of both measurement and modelling errors in the baseline finite element model. Damage that accompanies changes in structural parameters can be estimated for a damaged structure from the change between measured vibration responses and ones calculated from the analytical model of the intact structure. In practice, modelling errors exist in the analytical model due to material and geometric uncertainties and a reduction in the degrees of freedom as well as measurement errors, making identification difficult. To surmount these problems, bootstrap hypothesis testing, which enables statistical judgment without information about these errors, was introduced. The method was validated by numerical simulation using a three‐dimensional frame structure and real vibration data for a three‐storey steel frame structure. Copyright © 2005 John Wiley & Sons, Ltd.     

Earthquake rupture complexity due to dynamic nucleation and interaction of subsidiary faults

We numerically study the dynamic interaction of propagating cracks. It is assumed that propagating cracks can nucleate and drive subsidiary cracks because of shear strain enhancement near the propagating crack tips. The critical strain fracture criterion is assumed in the analysis. Intense interaction is expected to occur among the cracks. All the cracks are assumed to be parallel and antiplane strain deformation is assumed in the computation.In the interaction of two non-coplanar cracks, a strain shadow is formed in the neighborhood of each crack because of the strain release by the introduction of the crack. The growth of each crack is accelerated when the propagating tips of each crack are outside of the strain shadow of the other crack. In general, the crack tips enter the strain shadow, and the crack tips decelerate. The calculation shows that only one of the two cracks can continue to grow, and the other's growth is decelerated and arrested. If we can assume that the suite of cracks interact in a pairwise manner only, then this may suggest that only a limited number of cracks can continue to grow during the final stage of the rupture process. Hence the crack interaction causes complexity in dynamic earthquake faulting. The concepts of barrier and asperity have been employed by many researchers for the interpretation of complex seismic wave data. However, the physical realities of such concepts are obscure. Our calculations show that dynamic crack interactions can produce barriers and asperities in some cases; the crack tip deceleration or arrest due to the interactions among non-coplanar cracks can be interpreted as being due to a barrier. The dynamic coalescence among the coplanar cracks can be regarded as an asperity.Umeda found a localized area that strongly radiates high-frequency seismic waves in the epicentral areas of some large shallow earthquakes. He defined this as an earthquake bright spot. Our analysis implies that only a limited number of cracks continue to grow when many interactive cracks nucleate, and that all other cracks stop extending soon after nucleation. Hence, if the nucleation and termination of several cracks occur in a localized area, it will be observed seismologically as an earthquake bright spot. This is because it is theoretically known that the sudden termination of crack growth and dynamic crack coalescence efficiently emits high-frequency elastic waves.     

Scattering of elastic waves by a fracture zone containing randomly distributed cracks

We theoretically study the scattering ofP, SV andSH waves by a zonal distribution of cracks, which simulates a fault fracture zone. An investigation is conducted how the geometrical properties of the crack distribution and the frictional characteristics of the crack surface are reflected in the attenuation and dispersion of incident waves, as well as in the amplitudes of the transmitted and reflected waves from the zone. If the crack distribution within the fault zone changes temporally during the preparation process of the expected earthquake, it will be important for earthquake prediction to monitor it, utilizing the scattering-induced wave phenomena.We consider the two-dimensional problem. Aligned cracks with the same length are assumed to be randomly distributed in a zone with a finite width, on which elastic waves are assumed to be incident. The distribution of cracks is assumed to be homogeneous and sparse. The crack surface is assumed to be stress-free, or to undergo viscous friction; the latter case simulates fluid-filled cracks. The opening displacement of the crack is assumed to be negligibly small. The idea of the mean wave formalism is employed in the analysis, and Foldy's approximation is assumed.When the crack surface is stress-free, it is commonly observed for every wave mode (P, SV andSH) that the attenuation coefficientQ ^–1 peaks aroundka1, the phase velocity is almost independent ofk in the rangeka<1 and it increases monotonically withk in the rangeka>1, wherek is the intrinsicS wavenumber anda is the half length of the crack. The effect of the friction is to shift the peak ofQ ^–1 and the corner of the phase velocity curve to the low wavenumber range. The high wavenumber asymptote ofQ ^–1 is proportional tok ^–1 independently of model parameters and the wave modes. If the seismological observation thatQ ^–1 ofS waves has a peak at around 0.5 Hz in the earth's crust is combined with our results, the upper limit of crack size within the crust is estimated about 4 km. The information regarding the transmitted and reflected waves, such as the high wavenumber limit of the amplitude of the transmitted wave etc., allows estimation of the strength of the friction.     

Dynamic nucleation process of shallow earthquake faulting in a fault zone

Two distinct phases are commonly observed at the initial part of seismograms of large shallow earthquakes: low-frequency and low-amplitude waves following the onset of a P wave ( P ₁) are interrupted by the arrival of the second impulsive phase P₂ enriched with high-frequency components. This observation suggests that a large shallow earthquake involves two qualitatively different stages of rupture at its nucleation.
We propose a theoretical model that can naturally explain the above nucleation behaviour. The model is 2-D and the deformation is assumed to be anti-plane. A key clement in our model is the assumption of a zone in which numbers of pre-existing cracks are densely distributed; this cracked zone is a model for the fault zone. Dynamic crack growth nucleated in such a zone is intensely affected by the crack interactions, which exert two conflicting effects: one tends to accelerate the crack growth, and the other tends to decelerate it. The accelerating and decelerating effects are generally ascribable to coplanar and non-coplanar crack interactions, respectively. We rigorously treat the multiple interactions among the cracks, using the boundary integral equation method (BIEM), and assume the critical stress fracture criterion for the analysis of spontaneous crack propagation.
Our analysis shows that a dynamic rupture nucleated in the cracked zone begins to grow slowly due to the relative predominance of non-coplanar interactions. This process radiates the P₁ phase. If the crack continues to grow, coalescence with adjacent coplanar cracks occurs after a short time. Then, coplanar interactions suddenly begin to prevail and crack growth is accelerated; the P₂ phase is emitted in this process. It is interpreted that the two distinct phases appear in the process of the transition from non-coplanar to coplanar interaction predominance.     

Mineral composition variation in Alpine Schist, Southern Alps, New Zealand: Implications for recrystallization and exhumation

Abstract Compositional variation of silicates (plagioclase, K-feldspar, epidote, titanite, garnet, white mica, biotite, chlorite), ilmenite, carbonates (calcite, ankerite) and apatite, in quartzofeldspathic lithologies of the Alpine Schist, New Zealand, is discussed in terms of increasing metamorphic grade and possible isograd-producing reactions. The mineral data, in conjunction with geological considerations, are used to determine polychronous P-T arrays of an early high P/T event (c. 16°C/kb; 5°C/km) overprinted by a lower P/T event (c. 50°C/kb; 15°C/km) that provides an estimation of Mesozoic and Cenozoic exhumation of schist of 11 to 13 km and 19 to 22 km respectively. The effects of possible shear heating and recrystallization to form K-feldspar zone schist near the Alpine Fault is consistent with movement along a mid to lower crustal detachment surface during Cenozoic shortening, and near isothermal exhumation of the schists to form the Southern Alps.     

Electron microscopy studies of akermanites (Ca1−xSrx)2CoSi2O7 with modulated structure

Single crystals of akermanite (Ca_1–x Sr _x )₂Co-Si₂O₇ solid solution were grown in nitrogen by the floating zone method using a lamp-image furnace. The grown crystals were 6 mm in diameter by 50 mm in length. Microprobe analyses indicate uniform strontium content x except in the initially crystallized part. Synthetic crystals with x from 0.0 to 0.3 give, at room temperature, satellite reflections and circular diffuse scatterings in the electron diffraction pattern, which are related to an incommensurate phase and microdomains, respectively. With increasing Sr content the wavelength of a modulation increases and the intensity of satellites decreases, but the intensity of circular diffuse scattering increases up to x=0.15 and then decreases until eventually the satellites and the circular diffuse scatterings disappear at x = 0.3. The circular diffuse scattering is explained by the cluster model for the transition state, proposed by De Ridder et al. (1976).     

Simulation of seismicity due to fluid migration in a fault zone

Spatio-temporal variation of rupture activity is modelled assuming fluid migration in a narrow, porous fault zone formed along a vertical strike-slip fault in a semi-infinite elastic medium. The principle of the effective stress coupled to the Coulomb failure criterion introduces mechanical coupling between fault slip and the pore fluid. The fluid is assumed to flow out of a localized high-pressure fluid compartment in the fault at the onset of earthquake rupture. The duration of the earthquake sequence is assumed to be much shorter than the recurrence period of characteristic events on the fault. Both an earthquake swarm and a foreshock–main-shock sequence can be simulated by changing the relative magnitudes of the initial tectonic stress, pore fluid pressure, fracture strength and so on. When an inhomogeneity is introduced into the spatial distribution of fracture strength, high complexity is observed in the spatio-temporal variation of rupture activity. For example, the time interval between two successive events is highly irregular, and a relatively long quiescence of activity is sometimes observed in a foreshock–main-shock sequence. The quiescence is caused by the temporary arresting of rupture extension, due to an encounter with fault segments having locally high strengths. The frequency–magnitude statistics of intermediate-size events obey the Gutenberg–Richter relation. The calculations show the temporal variation of the b value during some foreshock sequences, and the degree of the change seems to depend on the statistical distribution of the fracture strength.