mechanics_functions.general_geotech_funcs.calc_Jaky_at_rest(phi_prime)

Calculate at rest earth pressure coefficient (k_{0}) using Jaky relationship.

Parameters:

phi_prime (float) – Effective friction angle [degrees].

Returns:

Coefficient of At Rest Lateral Earth Pressure

Return type:

float

Notes

The coefficient of at rest lateral earth pressure is calculated using the equation:

\[\]
where:

  • \(k_{0}\) : Coefficient of At Rest Lateral Earth Pressure

  • :math:phi_prime` : Effective friction angle

mechanics_functions.general_geotech_funcs.calc_cambridge_mean_eff_stress(sigma_1, sigma_2, sigma_3)

Calculate the Cambridge mean effective stress (p’).

Parameters:

  • sigma_1 (float) – Effective stress 1.

  • sigma_2 (float) – Effective stress 2.

  • sigma_3 (float) – Effective stress 3.

Returns:

Cambridge mean effective stress (p’).

Return type:

float

Notes

The Cambridge mean effective stress is calculated using the equation:

\[p' = \frac{{\sigma'_{1} + \sigma'_{2} + \sigma'_{3}}}{{3}}\]
where:

  • \(p'\) : Cambridge mean effective stress.

  • \(\sigma'_{1}\) : Effective stress 1.

  • \(\sigma'_{3}\) : Effective stress 3.

  • \(\sigma'_{2}\) : Effective stress 2.

mechanics_functions.general_geotech_funcs.calc_consolidation_coeff(diameter, t_50, T_50=0.6)

Calculate the consolidation coefficient (c_h).

This function computes the consolidation coefficient based on the given diameter, time to 50% pore pressure dissipation, and a dimensionless time factor.

Parameters:

  • diameter (float) – Diameter of the penetrating object [m].

  • t_50 (float) – Time to 50% of pore pressure dissipation [s].

  • T_50 (float, optional) – Dimensionless time factor (default is 0.6).

Returns:

Consolidation coefficient [m^2/s].

Return type:

float

Notes

The consolidation coefficient is calculated using the following equation:

\[c_{h} = \frac{D^{2} T_{50}}{t_{50}}\]
where:

  • \(D\) is the diameter of the penetrating object.

  • \(t_{50}\) is the time to 50% of pore pressure dissipation.

  • \(T_{50}\) is the dimensionless time factor.

Reference

White, D. J., et al. “Free fall penetrometer tests in sand: Determining the equivalent static resistance.”

mechanics_functions.general_geotech_funcs.calc_dimensionless_velocity(v, D, coeff_consolidation)

Calculate the dimensionless velocity (V).

Parameters:

  • v (float) – Probe velocity [m/s].

  • D (float) – Diameter of the probe [m].

  • coeff_consolidation (float) – Consolidation coefficient (c_{h}).

Returns:

Dimensionless velocity (V).

Return type:

float

Notes

The dimensionless velocity is calculated using the equation:

\[V = \frac{v \cdot D}{c_{h}}\]

where:

  • \(V\) : Dimensionless velocity.

  • \(v\) : Probe velocity.

  • \(D\) : Diameter of the probe.

  • \(c_{h}\) : Consolidation coefficient.

mechanics_functions.general_geotech_funcs.calc_mohr_coulomb_su(failure_mean_eff_stress, phi_cv=32)

Calculate the undrained strength (s_{u}) assuming a Mohr-Coulomb failure envelope.

Parameters:

  • failure_mean_eff_stress (float) – Mean effective stress at failure [kPa].

  • phi_cv (float) – Friction angle at constant volume [degrees].

Returns:

Undrained strength (s_{u}) [kPa].

Return type:

float

Notes

The undrained strength is calculated using the equation:

\[s_{u} = \frac{1}{2} p'_{f} \frac{6 \sin(\phi_{cv})}{3 - \sin(\phi_{cv})}\]
where:

  • \(s_{u}\) : Undrained strength.

  • \(p'_{f}\) : Mean effective stress at failure.

  • :math:phi_{cv}` : Friction angle at constant volume (in degrees).

mechanics_functions.general_geotech_funcs.calc_white_failure_mean_eff_stress(relative_density, Q=10)

Calculate the mean effective stress at failure (p’_{f}).

Parameters:

  • Q (float) – Crushing strength parameter. Commonly taken as 10.

  • relative_density (float) – Relative density.

Returns:

Mean effective stress at failure (p’_{f}) [kPa].

Return type:

float

Notes

The mean effective stress at failure is calculated using the equation:

\[p'_{f} = e^{Q - \frac{1}{I_{D}}}\]
where:

  • \(p'_{f}\) : Mean effective stress at failure.

  • \(Q\) : Crushing strength parameter.

  • \(I_{D}\) : Relative density.

Note that the equation derivation assumes zero relative dilatancy (I_{R} = 0) at undrained failure.