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Strain Rates for Creep in Quartz

Source: R/strainrate.R
disl_creep_quartz.Rd

Calculates strain rates of deforming quartz from stress, temperature, and grain size from experimentally determined creep law parameters. Monte Carlo sampling is used for propagating parameter uncertainties in to creep estimate.

Usage

disl_creep_quartz(
  stress,
  temperature,
  fugacity = NULL,
  grainsize = NULL,
  pressure = NULL,
  model = c("Hirth2001", "Paterson1990", "Kronenberg1984", "Luan1992", "Gleason1995",
    "Gleason1995_melt", "Rutter2004", "Fukuda2018_LT", "Fukuda2018_HT", "Richter2018",
    "Lu2019", "Tokle2019_LT", "Tokle2019_HT", "Lusk2021_LP", "Lusk2021_HP"),
  propagate_err = TRUE,
  sim = 1e+06
)

Arguments

stress

Differential stress in MPa or units object

temperature

Temperature in Kelvin or units object

fugacity

Water fugacity in MPa or units object

grainsize

Grain size in \(\mu\)m or units object

pressure

Pressure in MPa or units object

model

character specifying the flow law to be used:

"Hirth2001"

Hirth and Tullis (2001), dislocation creep

"Paterson1990"

Paterson and Luan (1990): dislocation creep; axial compression

"Kronenberg1984"

Kronenberg and Tullis (1984): deformation mechanism: dislocation creep and grain-size sensitive creep; strain geometry: axial compression

"Luan1992"

Luan and Paterson (1990): dislocation creep; axial compression

"Gleason1995"

Gleason and Tullis (1995): dislocation creep; axial compression

"Gleason1995_melt"

Gleason and Tullis (1995): dislocation creep; axial compression; 1–2% melt

"Rutter2004"

Rutter and Brodie (2004b): dislocation creep; axial compression

"Fukuda2018_LT"

Fukada et al. (2018): dislocation creep; axial compression; low temperatures (600–750 °C)

"Fukuda2018_HT"

Fukada et al. (2018): dislocation creep and grain-size sensitive creep; axial compression; high temperatures (800–950 °C)

"Richter2018"

Richter et al. (2018): dislocation creep and grain-size sensitive creep; general shear; 800–1000 °C

"Lu2019"

Lu and Jiang (2019): dislocation creep

"Tokle2019_HT"

Tokle et al. (2019): dislocation creep and grain-size sensitive creep; high temperatures/low stress

"Tokle2019_LT"

Tokle et al. (2019): dislocation creep and grain-size sensitive creep; low temperature/high stress

"Lusk2021_LP"

Lusk et al. (2021): dislocation-dominated creep in wet quartz, for low pressures (≤560 MPa)

"Lusk2021_HP"

Lusk et al. (2021): dislocation-dominated creep in wet quartz, for high pressures (700–1600 MPa)

propagate_err

logical. Whether errors of the flow law parameters should be propagated. TRUE by default.

sim

non-negative number. Number of Monte Carlo simulations

Value

list. Strain rate in 1/s. If Monte Carlo Simulation was used, and object of class "MCS" is returned (see summary() for detailed description of output). The flow laws produce log-normal distributed estimates considering the uncertainties in the parameter. Hence it is recommended to report the median (or geometric mean), and the interpercentile range.

Details

General flow law giving the strain rate is $$\dot{\epsilon} = A \sigma^n d^m f_{H_2O}^r \, e^{\left({\frac{-H}{RT}}\right)}$$

where \(\sigma\) is the differential stress, \(d\) is the grain size, \(f_{H_2O}\) is the water fugacity, \(T\) is the temperature, \(H\) is the enthalpy, and \(R\) is the ideal gas constant. The flow parameters are the prefactor \(A\), and the exponents \(n\), \(m\), and \(r\).

To propagate the uncertainties of the flow parameters Monte Carlo simulation is used here.

  • If the flow law parameters are given by a mean value and a marginal error (\(\mu \pm z\)), the Monte Carlo simulation assumes a normal distribution given by \(X = N\left(\mu, \sigma\right)\), where \(\mu\) is the mean and \(\sigma\) is the standard deviation of the mean (\(\sigma = \text{z}/1.96\)).

  • If the parameter is given by a range of possible values \(\left[x_\text{min}, x_\text{max}\right]\), the Monte Carlo simulation assumes an uniform distribution given by \(X = U\left(x_\text{min}, x_\text{max}\right)\).

References

Fukuda, J., Holyoke, C. W., & Kronenberg, A. K. (2018). Deformation of Fine‐Grained Quartz Aggregates by Mixed Diffusion and Dislocation Creep. Journal of Geophysical Research: Solid Earth, 123(6), 4676-4696. doi:10.1029/2017JB015133

Gleason, G. C., & Tullis, J. (1995). A flow law for dislocation creep of quartz aggregates determined with the molten salt cell. Tectonophysics, 247(1-4), 1-23. doi:10.1016/0040-1951(95)00011-B

Hirth, G., Teyssier, C., & Dunlap, W. J. (2001). An evaluation of quartzite flow laws based on comparisons between experimentally and naturally deformed rocks. International Journal of Earth Sciences, 90(1), 77-87. doi:10.1007/s005310000152

Kronenberg, A. K., & Tullis, J. (1984). Flow strengths of quartz aggregates: Grain size and pressure effects due to hydrolytic weakening. Journal of Geophysical Research: Solid Earth, 89(B6), 4281–4297. doi:10.1029/JB089iB06p04281

Lu, L. X., & Jiang, D. (2019). Quartz Flow Law Revisited: The Significance of Pressure Dependence of the Activation Enthalpy. Journal of Geophysical Research: Solid Earth, 124(1), 241–256. doi:10.1029/2018JB016226

Lusk, A. D. J., Platt, J. P., & Platt, J. A. (2021). Natural and Experimental Constraints on a Flow Law for Dislocation‐Dominated Creep in Wet Quartz. Journal of Geophysical Research: Solid Earth, 126(5), 1-25. doi:10.1029/2020JB021302

Paterson, M. S., & Luan, F. C. (1990). Quartzite rheology under geological conditions. Geological Society, London, Special Publications, 54(1), 299–307. doi:10.1144/GSL.SP.1990.054.01.26

Richter, B., Stünitz, H., & Heilbronner, R. (2018). The brittle-to-viscous transition in polycrystalline quartz: An experimental study. Journal of Structural Geology, 114(September 2017), 1-21. doi:10.1016/j.jsg.2018.06.005

Rutter, E. H., & Brodie, K. H. (2004a). Experimental grain size-sensitive flow of hot-pressed Brazilian quartz aggregates. Journal of Structural Geology, 26(11), 2011–2023. doi:10.1016/j.jsg.2004.04.006

Rutter, E. ., & Brodie, K. . (2004b). Experimental intracrystalline plastic flow in hot-pressed synthetic quartzite prepared from Brazilian quartz crystals. Journal of Structural Geology, 26(2), 259–270. doi:10.1016/S0191-8141(03)00096-8

Tokle, L., Hirth, G., & Behr, W. M. (2019). Flow laws and fabric transitions in wet quartzite. Earth and Planetary Science Letters, 505, 152-161. doi:10.1016/j.epsl.2018.10.017

See also

units::set_units() to set up units objects; summary.MCS_log() for statistical parameters of Monte Carlo samples

Examples

set.seed(20250411)
stress <- units::set_units(100, MPa)
temperature <- units::set_units(300, degC)
pressure <- units::set_units(400, MPa)
fugacity <- ps_fugacity(pressure, temperature)

disl_creep_quartz(
  stress = stress, temperature = temperature, fugacity = fugacity,
  model = "Hirth2001") |>
 summary()
#> Statistical summary of 1000000 Monte Carlo simulations
#> 
#> Median:                      1.2e-14 1 / s
#> 95% interpercentile range:   4.3e-19 - 3.1e-10 1 / s
#> Standard error in log-space: 0.00226041
#> Student's t-Test:            p<0.05