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Algebraic error propagation of flow laws

Source: R/error_propagation.R
creep_quartz_analytic.Rd

Uses 1st order Taylor expansion (linearization) of the natural log-space flow law

Usage

creep_quartz_analytic(
  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")
)

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)

Value

list.

"e_best"

Strain rate (1/s)

"sd_e_range"

Range of 1s standard deviation (1/s)

"var_log_e_total"

Variance in natural log-space

"sd_log_e_total

Standard deviation in natural log-space

"var_log_e"

Individual variance components in natural log-space

See also

creep_quartz()

Examples

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

creep_quartz_analytic(
  stress = stress, temperature = temperature, fugacity = fugacity, pressure = pressure,
  model = "Hirth2001"
)
#> $e_best
#> 1.165839e-14 [1/s]
#> 
#> $sd_e_range
#> Units: [1/s]
#> [1] 1.834746e-16 7.408012e-13
#> 
#> $var_log_e_total
#> [1] 17.23666
#> 
#> $sd_log_e_total
#> [1] 4.151706
#> 
#> $var_log_e
#>          prefactor    stress_exponent  fugacity_exponent grainsize_exponent 
#>        1.908683320       15.322485539        0.000000000        0.000000000 
#>             stress           fugacity          grainsize        temperature 
#>        0.000000000        0.000000000        0.000000000        0.000000000 
#>           enthalpy 
#>        0.005491873 
#> 

creep_quartz_analytic(
  stress = stress, temperature = temperature, fugacity = fugacity, pressure = pressure,
  model = "Lusk2021_LP"
)
#> $e_best
#> 4.17758e-13 [1/s]
#> 
#> $sd_e_range
#> Units: [1/s]
#> [1] 4.982208e-14 3.502899e-12
#> 
#> $var_log_e_total
#> [1] 4.521764
#> 
#> $sd_log_e_total
#> [1] 2.126444
#> 
#> $var_log_e
#>          prefactor    stress_exponent  fugacity_exponent grainsize_exponent 
#>          2.3095068          0.8483037          0.2207950          0.0000000 
#>             stress           fugacity          grainsize        temperature 
#>          0.0000000          0.0000000          0.0000000          0.0000000 
#>           enthalpy 
#>          1.1431584 
#> 

creep_quartz_analytic(
  stress = stress, temperature = temperature, fugacity = fugacity, pressure = pressure,
  model = "Kronenberg1984"
)
#> $e_best
#> 6.264269e-07 [1/s]
#> 
#> $sd_e_range
#> Units: [1/s]
#> [1] 5.288804e-07 7.419650e-07
#> 
#> $var_log_e_total
#> [1] 0.02865229
#> 
#> $sd_log_e_total
#> [1] 0.1692699
#> 
#> $var_log_e
#>          prefactor    stress_exponent  fugacity_exponent grainsize_exponent 
#>        0.000000000        0.001192927        0.000000000        0.000000000 
#>             stress           fugacity          grainsize        temperature 
#>        0.000000000        0.000000000        0.000000000        0.000000000 
#>           enthalpy 
#>        0.027459365 
#>