Application of rate‐and‐state friction laws to creep compaction of unconsolidated sand under hydrostatic loading conditions

Hagin, Paul; Sleep, Norman H.; Zoback, Mark D.

doi:10.1029/2006jb004286

Cited by 5 publications

(16 citation statements)

References 34 publications

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“…provides an estimate of the porosity change within failed domains. The rate and state parameter C ɛ was 0.0020 in an analysis of sandstones by Hagin et al [2007]. ( Sleep et al [2000] obtained 0.0034 for gouge.)…”

Section: Application Of Rate and State Frictionmentioning

confidence: 97%

“…We apply the aging law and as they apply in the laboratory to sandstones similar to those at the Parkfield sites [ Hagin et al , 2007]. (The slip law gives the inapplicable null result of no compaction and no seismic velocity change.)…”

Section: Application Of Rate and State Frictionmentioning

confidence: 99%

“…The main restriction is that this measurable parameter and the assumed critical porosity ϕ c = 19.23% should lead to failure in the porosity range at normal tractions relevant to the shallow subsurface. We let α have its measured value for sandstone 0.15 [ Hagin et al , 2007]; in another calculation, we assume its measured value for hard rock 0.21 [ Sleep , 1999].…”

Section: Porosity Percolation Theory and Failurementioning

confidence: 99%

“…We plot the true coefficient of friction and normal traction on the failure surface in Figure 17. The laboratory value of α = 0.15 [ Hagin et al , 2007] provides a good fit to the data.…”

Section: Porosity Percolation Theory and Failurementioning

confidence: 99%

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Nonlinear attenuation and rock damage during strong seismic ground motions

Sleep

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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Section: Application Of Rate and State Frictionmentioning

confidence: 97%

Section: Application Of Rate and State Frictionmentioning

confidence: 99%

Section: Porosity Percolation Theory and Failurementioning

confidence: 99%

“…We plot the true coefficient of friction and normal traction on the failure surface in Figure 17. The laboratory value of α = 0.15 [ Hagin et al , 2007] provides a good fit to the data.…”

Section: Porosity Percolation Theory and Failurementioning

confidence: 99%

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Nonlinear attenuation and rock damage during strong seismic ground motions

Sleep

Hagin

2008

Geochem Geophys Geosyst

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“…Real contacts are expected to evolve to very tabular aspect ratios for isotropic compaction. The laboratory value of α / b for sandstone is ∼10 implying Z / X is ∼10 for the traditional value of a [ Hagin et al , 2007; Sleep , 2010]. The value of α / b for mature gouge during holds is 16–32 [ Sleep et al , 2000], implying an aspect ratio of 6–3.…”

Section: Fractal Elastic Strain Energy and The Rate Parameter Amentioning

confidence: 99%

Microscopic elasticity and rate and state friction evolution laws

Sleep¹

2012

Geochem Geophys Geosyst

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[1] Rate and state friction formalism represents the dependence of macroscopic shear traction t M on sliding velocity V and the history of the sliding surface. In macroscopic terms,, where P N is normal traction, m 0 is the coefficient of friction, a ≈ b ≈ 0.01 are small dimensionless parameters, V ref is a reference velocity, y is the state variable that depends on history, and y norm represents the effect of changes in normal traction. This representation does not consider microscopic elasticity and is inadequate over very small times. The apparent value of a just after a small decrease in shear traction is a factor of a few larger than its traditional value of $0.01. Changes of microscopic elastic strain energy may cause this effect. Microscopic elasticity affects friction after changes in normal traction. Shear traction does not change instantly after a sudden change in normal traction because time is required for real contact area to change. A hybrid of the aging law (where y increases linearly with time during holds) and the slip law behavior (where the state variable does not change in the limit of zero sliding velocity) is necessary. Sliplaw behavior dominates near steady state and also applies to sudden initial sliding where the state variable and porosity are far from steady state. Porosity increases from its initial value toward the steady state value over slip scaling with the critical displacement D c . The ratio of dilatant to shear strain in low porosity material is a modest fraction of 1 and related to the construct of dilatancy angle in engineering.

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Sudden and gradual compaction of shallow brittle porous rocks

Sleep

2010

J. Geophys. Res.

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1] Porous brittle rocks fail in shear and compaction. Rate and state friction describes such failure on a planar surface, while end-cap failure describes the failure of a continuum. Both formalisms include Coulomb failure in shear at low normal tractions. Rate and state friction includes slow compaction of gouge by normal traction when shearing is not occurring. Rate and state friction also represents slow compaction of porous sandstone. End-cap failure includes both grain crushing and shear. Micromechanically, all these mechanisms involve exponential creep at stresses of a few gigapascals. Rate and state friction is modeled by tabular real contacts where shear and extrusion occur. The observed compaction rate depends on the normal traction to a modest power of ∼27 for gouge and ∼10 for sandstone. End-cap failure involves grain cracking in the neighborhood of the grain-grain contact. Its rate should depend on the normal traction raised to a power of ∼100. This strong rate dependence is not measurable in practice as a failure cascade commences once some grains crack. Materials with pointy contacts including unwelded tuff and "regolith" in the uppermost tens of meters that has repeatedly been damaged by strong seismic waves compact in this manner at dynamic stresses modestly above their ambient lithostatic stress. This failure produces significant nonlinear attenuation of compressional P waves with sustained dynamic accelerations that are a modest fraction of the ambient acceleration of gravity.

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Application of rate‐and‐state friction laws to creep compaction of unconsolidated sand under hydrostatic loading conditions

Cited by 5 publications

References 34 publications

Nonlinear attenuation and rock damage during strong seismic ground motions

Nonlinear attenuation and rock damage during strong seismic ground motions

Microscopic elasticity and rate and state friction evolution laws

Sudden and gradual compaction of shallow brittle porous rocks

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