Critical state of a two-dimensional elastic continuum containing elliptical voids

Mallick, Kaushik; Krajčinović, Dušan; Sumarac, Dragoslav; Vujosevic, Milena

doi:10.1016/0013-7944(93)90162-l

Cited by 9 publications

(8 citation statements)

References 21 publications

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“…Porosity is a convenient intermediate as it is normally measured in the field and in the laboratory. The number density G = f/W of tabular cracks (where f is porosity and W is the long/short aspect ratio of cracks) is a more fundamental parameter [Krajcinovic, 1993;Mallick et al, 1993]. The relationship between state and S-wave velocity obtained using porosity as an intermediate proxy parameter for number density thus may be more accurate than relationships of porosity to state and porosity to S-wave velocity.…”

Section: Discussionmentioning

confidence: 99%

Seismically damaged regolith as self-organized fragile geological feature

Sleep

2011

Geochem. Geophys. Geosyst.

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[1] The S-wave velocity in the shallow subsurface within seismically active regions self-organizes so that typical strong dynamic shear stresses marginally exceed the Coulomb elastic limit. The dynamic velocity from major strike-slip faults yields simple dimensional relations. The near-field velocity pulse is essentially a Love wave. The dynamic shear strain is the ratio of the measured particle velocity over the deep S-wave velocity. The shallow dynamic shear stress is this quantity times the local shear modulus. The dynamic shear traction on fault parallel vertical planes is finite at the free surface. Coulomb failure occurs on favorably oriented fractures and internally in intact rock. I obtain the equilibrium shear modulus by starting a sequence of earthquakes with intact stiff rock extending all the way to the surface. The imposed dynamic shear strain in stiff rock causes Coulomb failure at shallow depths and leaves cracks in it wake. Cracked rock is more compliant than the original intact rock. Cracked rock is also weaker in friction, but shear modulus changes have a larger effect. Each subsequent event causes additional shallow cracking until the rock becomes compliant enough that it just reaches Coulomb failure over a shallow depth range of tens to hundreds of meters. Further events maintain the material at the shear modulus as a function where it just fails. The formalism provided in the paper yields reasonable representation of the S-wave velocity in exhumed sediments near Cajon Pass and the San Fernando Valley of California. A general conclusion is that shallow rocks in seismically active areas just become nonlinear during typical shaking. This process causes transient changes in S-wave velocity, but not strong nonlinear attenuation of seismic waves. Wave amplitudes significantly larger than typical ones would strongly attenuate and strongly damage the rock.Components: 8800 words, 12 figures.

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Section: Discussionmentioning

confidence: 99%

Seismically damaged regolith as self-organized fragile geological feature

Sleep

2011

Geochem. Geophys. Geosyst.

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“…Near the limit where an intact network ceases to exist, transport and elastic constants depend on the difference between the number of intact sites s and the critical number of intact sites Sc below which the network is not intact. The expression may be written in terms of crack porosity in a continuum material [Krajcinovic, 1993;Mallick et al, 1993]…”

Section: Friction As a Thermally Activated Creep Processmentioning

confidence: 99%

Application of a unified rate and state friction theory to the mechanics of fault zones with strain localization

Sleep¹

1997

J. Geophys. Res.

151

177

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is •n Cn(O)/AP•Cn(AT). The theoryis complete in the sense that the complete earthquake cycle is represented and that there are no unmeasurable state parameters. The theory was applied to investigate earthquake quenching by fluid pressure decreases associated with frictional dilatancy and the related topic of strain localization and delocalization within fault zones. It was found that strain localization will occur when b > a. Such strain localization tends to destabilize sliding within drained faults by reducing the effective value of the critical displacement. Fault zones that are hydraulically sealed from the country rock but internally hydraulically connected are also destabilized because strain localization reduces the fluid pressure decrease from frictional dilatancy. Two mechanisms that delocalize strain once sliding is well underway were investigated. Strain rate strengthening at high-strain rates leads to a high strain zone that gradually broadens throughout an earthquake. An increase in the coefficient of friction with temperature leads to a high strain rate zone that moves through the fault zone from hot regions created by frictional heating to cold regions.

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“…We do not need to explicitly consider porosity if we only want to obtain failure properties from S wave velocity including the dependence of strength or porosity in . The number density of tabular cracks is a more fundamental parameter that provides this relationship [ Krajcinovic , 1993; Mallick et al , 1993]. It is Γ = f /Ω, where Ω is the short/long aspect ratio of the cracks.…”

Section: Porosity Percolation Theory and Failurementioning

confidence: 99%

Nonlinear attenuation and rock damage during strong seismic ground motions

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Hagin

2008

Geochem Geophys Geosyst

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[1] Strong seismic waves cause nonlinear behavior in the shallow subsurface in fractured rocks. Seismologists use low-amplitude signals from small repeating earthquakes to measure S wave velocity decrease after strong motion. The 2004 Parkfield, California, earthquake provides examples of such velocity changes in fractured sandstone with an S wave velocity of $300 m s À1 . This nonlinear behavior occurred around the wave number depth of the incident waves, $30 m, for the $10 s À1 dominant angular frequency on a velocity seismogram. The low-amplitude S wave velocity gradually recovered with the logarithm of time. The attenuation of strong waves in general depends nonlinearly on their amplitude. High dynamic stress triggered small, very shallow earthquakes, at sites including Parkfield. The theoretical frictional behavior of a fractured medium with heterogeneous prestress relates these phenomena. Failure occurs in the highly prestressed domains causing small earthquakes and opening-mode cracks. The energy to dilate the cracks dissipates a significant fraction of the incoming seismic energy. The local high-porosity domains close with the logarithm of time, as expected from the aging law of rate and state friction, increasing the S wave velocity. The domain model indicates that nonlinear effects increase gradually over a range of dynamic Coulomb stresses as observed and as included in the widely used Masing rules. The Linker and Dieterich (1992) relationship provides the maximum sustainable dynamic coefficient of friction needed to utilize the Masing rules. This parameter is the coefficient of friction at a laboratory normal traction plus a constant $0.15 times the logarithm of the ratio of field normal traction to the laboratory normal traction. It is helpful to relate S wave velocity to starting frictional strength, as coefficient of friction near the quarter-wavelength depth determines nonlinear behavior. Then the dynamic coefficient of friction and equivalently the maximum sustainable acceleration at the dominant frequency depend weakly on S wave velocity. For example, the coefficient of friction at an angular frequency of 10 s À1 is less than 1.5 for rocks ranging from Parkfield sandstone to intact granite. Keywords: nonlinear seismology; engineering seismology; Parkfield earthquake; strong ground motions; tribology.Index Terms: 7212 Seismology: Earthquake ground motions and engineering seismology; 4455 Nonlinear Geophysics: Nonlinear waves, shock waves, solitons (0689, 2487, 3280, 3285, 4275, 6934, 7851, 7852).

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Critical state of a two-dimensional elastic continuum containing elliptical voids

Cited by 9 publications

References 21 publications

Seismically damaged regolith as self-organized fragile geological feature

Seismically damaged regolith as self-organized fragile geological feature

Application of a unified rate and state friction theory to the mechanics of fault zones with strain localization

Nonlinear attenuation and rock damage during strong seismic ground motions

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