- mechanics_functions.friction_angle_funcs.calc_Alabatal_friction_angle(relative_density, unit_weight, max_depth, atmospheric_pressure=101.325)¶
Calculate the friction angle (phi) using the modified Duncan correlation coefficients from Albatal.
This function acts as a wrapper for the Duncan friction angle equation, using the specific coefficients provided by Albatal. The coefficients and methodology are adapted from Albatal et al. (2020).
Albatal et al. (2020) DOI: 10.1139/cgj-2018-0267
- Parameters:
relative_density (float) – Relative density of the soil.
unit_weight (float) – Unit weight of the soil (assumed to be 1120 kg/m^3 for the calculation).
max_depth (float) – Max penetration depth of the FFP.
atmospheric_pressure (float, optional) – Atmospheric pressure in kPa (default is 101.325 kPa).
- Returns:
Calculated friction angle (phi).
- Return type:
float
Notes
This function utilizes the Duncan friction angle equation with coefficients from Albatal et al. (2020):
- \[\phi' = A^{*} + B^{*}(D_{r}) - [C^{*} + D^{*}(D_{r})] \log(\sigma'_{n} / P_{a})\]
- where:
\(A^{*}\) is a constant with a value of 34.
\(B^{*}\) is a constant with a value of 10.
\(C^{*}\) is a constant with a value of 2.
\(D^{*}\) is a constant with a value of 5.
\(D_{r}\) is the relative density.
\(\sigma_{n}\) is the normal stress (assumed to be the vertical normal stress).
\(P_{a}\) is the atmospheric pressure (used to make the stress dimensionless).
Note: The coefficients are specific to Albatal’s fit and may differ from other versions of the Duncan correlation.
- mechanics_functions.friction_angle_funcs.calc_Duncan_friction_angle(relative_density, unit_weight, max_depth, coeff=[34, 10, 3, 2], atmospheric_pressure=101.325)¶
Calculate the friction angle (phi) using the Duncan correlation.
This function computes the friction angle of soil based on the Duncan correlation, as noted in Albatal et al. (2020) DOI: 10.1139/cgj-2018-0267. The original source of the equation should be verified as the Duncan et al. (2014) reference. I couldn’t find this equation in there.
- Parameters:
relative_density (float) – Relative density of the soil.
unit_weight (float) – Unit weight of the soil (assumed to be 1120 kg/m^3 for the calculation).
max_depth (float) – Max penetration depth of the FFP.
coeff (list of float, optional) – Coefficients [A, B, C, D] from the Duncan correlation (default is [34, 10, 3, 2]).
atmospheric_pressure (float, optional) – Atmospheric pressure in kPa (default is 101.325 kPa).
- Returns:
Calculated friction angle (phi).
- Return type:
float
Notes
The friction angle is calculated using the following equation:
\[\phi' = A^{*} + B^{*}(D_{r}) - [C^{*} + D^{*}(D_{r})] \log(\sigma'_{n} / P_{a})\]- where:
\(A^{*}\) is a constant with a value of 34.
\(B^{*}\) is a constant with a value of 10.
\(C^{*}\) is a constant with a value of 3.
\(D^{*}\) is a constant with a value of 2.
\(D_{r}\) is the relative density.
\(\sigma_{n}\) is the normal stress (assumed to be the vertical normal stress).
\(P_{a}\) is the atmospheric pressure (used to make the stress dimensionless).
Note: If alternate values for the equation coefficients are available, they can be passed into this function.