All soil types

groundhog.siteinvestigation.correlations.general.acousticimpedance_bulkunitweight_chen(bulkunitweight, specific_gravity=2.65, saturation=1.0, gamma_w=10.0, calibration_factor_4=0.0001315, calibration_factor_3=-0.03776, calibration_factor_2=4.201, calibration_factor_1=-245.0, calibration_factor_0=8603.0, **kwargs)

Several authors have researched the correlation between porosity and acoustic impedance. Chen et al compiled available measurements for sand and clay and supplemented them with deepwater measurements with the multi-sensor core logger.

Since porosity is not a parameter which is commonly used, the user can enter bulk unit weight instead which is then converted to porosity for a saturated soil.

The correlation shows a tight relation between acoustic impedance and porosity. However, soils with in-situ excess pore pressure are not included in this dataset.

Parameters:

• bulkunitweight – Bulk (total) unit weight (\(\gamma\)) [\(kN/m3\)] - Suggested range: 12.0 <= bulkunitweight <= 22.0

• specific_gravity – Specific gravity of the soil (\(G_s\)) [\(-\)] - Suggested range: 1.0 <= specific_gravity <= 3.0 (optional, default= 2.65)

• saturation – Saturation of the soil (fully saturated for offshore soils) (\(S\)) [\(-\)] - Suggested range: 0.0 <= saturation <= 1.0 (optional, default= 1.0)

• gamma_w – Unit weight of water (\(\gamma_w\)) [\(kN/m3\)] - Suggested range: 9.5 <= gamma_w <= 10.5 (optional, default= 10.0)

• calibration_factor_4 – Calibration factor on the fourth order term (:math:``) [\(-\)] (optional, default= 0.0001315)

• calibration_factor_3 – Calibration factor on the third order term (:math:``) [\(-\)] (optional, default= -0.03776)

• calibration_factor_2 – Calibration factor on the second order term (:math:``) [\(-\)] (optional, default= 4.201)

• calibration_factor_1 – Calibration factor on the first order term (:math:``) [\(-\)] (optional, default= -245.0)

• calibration_factor_0 – Calibration factor on the zero order term (:math:``) [\(-\)] (optional, default= 8603.0)

\[ \begin{align}\begin{aligned}I =1.315 \cdot 10^{-4} \cdot n^4 - 3.776 \cdot 10^{-2} \cdot n^3 + 4.201 \cdot n^2 - 2.450 \cdot 10^2 \cdot n + 8.603 \cdot 10^3\\e = \frac{\gamma_w G_s - \gamma}{\gamma - S \gamma_w}\\w = \frac{S e}{G_s}\\n = \frac{e}{e+1}\end{aligned}\end{align} \]

Returns:

Dictionary with the following keys:

• ’e [-]’: Void ratio (\(e\)) [\(-\)]

• ’we [-]’: Water content (\(w\)) [\(-\)]

• ’n [-]’: Porosity (\(n\)) [\(-\)]

• ’I [(m/s).(g/cm3)]’: Acoustic impedance (\(I\)) [\((m/s).(g/cm3)\)]

Compiled data from Chen et al

Reference - Chen et al (2021). Machine Learning Based Digital Integration of Geotechnical and Ultra-High Frequency Geophysical Data for Offshore Site Characterizations. Journal of Geotechnical and Geoenvironmental Engineering.

groundhog.siteinvestigation.correlations.general.k0_frictionangle_mesri(phi_cs, ocr=1, **kwargs)

Calculates the coefficient of lateral earthpressure at rest for normally and overconsolidated sand and clay. Mesri and Hayat (1993) showed that the equation by Jaky (1944) only applied for sedimented, normally consolidated young clays and sands. The effect of overconsolidation was captured by multiplying the value for normally consolidated soil with the OCR raised to an exponent. This exponent is independent of the soil’s initial density and thus needs to be related to the critical state friction angle, rather than the peak friction angle of the soil. By adjusting for the effect of overconsolidation, reasonable predictions are obtained for overconsolidated and pre-sheared soils.

Parameters:

• phi_cs – Critical state friction angle (\(\varphi_{cs}^{\prime}\)) [\(deg\)] - Suggested range: 0.01 <= grain_size <= 2.0

• ocr – Overconsolidation ratio (\(\text{OCR}\)) [\(-\)] (optional, default= 1, suggested range: 1 <= OCR < 30)

\[K_0 = \left( 1 - \sin \varphi_{cv}^{\prime} \right) \text{OCR}^{\sin \varphi_{cv}^{\prime}}\]

Returns:

Dictionary with the following keys:

• ’K0 [-]’: Coefficient of lateral earth pressure at rest (\(K_0\)) [\(-\)]

Reference - Mesri and Hayat (1993) The coefficient of earth pressure at rest. Canadian Geotechnical Journal. 30(4), 647-666

groundhog.siteinvestigation.correlations.general.shearwavevelocity_compressionindex_cha(Cc, sigma_eff_particle_motion, sigma_eff_wave_propagation, alpha=nan, beta=nan, calibration_factor_alpha_1=13.5, calibration_factor_alpha_2=-0.63, calibration_factor_beta_1=0.17, calibration_factor_beta_2=0.43, **kwargs)

Shear wave velocity is dependent on the stiffness of the soil skeleton which is in turn affected by the compression index \(C_c\). Cha et al (2014) reported a series of oedometer tests with bender elements to establish the coefficients of a power law equation. Note that \(C_c\) itself is also stress-dependent and requires the selection of appropriate points in \(e-\log p^{\prime}\) space.

The relations proposed by Cha et al (2014) are used here by default, but the user can also enter custom values for \(\alpha\) and \(\beta\) Since porosity is not a parameter which is commonly used, the user can enter bulk unit weight instead which is then converted to porosity for a saturated soil.

For application to field cases, the effective stress in the direction of particle motion and wave propagation needs to be estimated. This usually involves estimation of the coefficient of lateral earth pressure.

Parameters:

• Cc – Compression index (\(C_c\)) [\(-\)] - Suggested range: 0.005 <= Cc <= 1.2

• sigma_eff_particle_motion – Effective stress in the direction of particle motion (\(\sigma_{\perp}^{\prime}\)) [\(kPa\)] - Suggested range: 10 <= sigma_eff_particle_motion <= 1200

• sigma_eff_wave_propagation – Effective stress in the direction of wave propagation (\(\sigma_{\parallel}^{\prime}\)) [\(kPa\)] - Suggested range: 10 <= sigma_eff_wave_propagation <= 1200

• alpha – Custom alpha-factor in the power law (\(\alpha\)) [\(-\)] - Suggested range: 5 <= alpha <= 1000 (optional, default=``np.nan``)

• beta – Custom beta-factor in the power law (\(\beta\)) [\(-\)] - Suggested range: 0.0 <= beta <= 0.6 (optional, default= ´´np.nan´´)

• calibration_factor_alpha_1 – First calibration factor for alpha [\(-\)] (optional, default= 13.5)

• calibration_factor_alpha_2 – Second calibration factor for alpha [\(-\)] (optional, default= 0.63)

• calibration_factor_beta_1 – First calibration factor for beta [\(-\)] (optional, default= 0.17)

• calibration_factor_beta_2 – First calibration factor for alpha [\(-\)] (optional, default= 0.43)

\[ \begin{align}\begin{aligned}V_s = \sqrt{\frac{G}{\rho}} = \alpha \left( \frac{\sigma_{\perp}^{\prime} + \sigma_{\parallel}^{\prime}}{2 \ \text{kPa}} \right)^{\beta}\\\alpha = 13.5 (\text{m/s}) \cdot C_c^{-0.63}\\\beta = 0.17 \log_{10} C_c + 0.43\end{aligned}\end{align} \]

Returns:

Dictionary with the following keys:

• ’Vs [m/s]’: Shear wave velocity (\(V_s\)) [\(\text{m/s}\)]

• ’alpha [-]’: Alpha-factor (multiplier) (\(\alpha\)) [\(-\)]

• ’beta [-]’: Beta-factor (exponent) (\(\beta\)) [\(-\)]

Compiled data from Cha et al

Reference - Cha et al (2014). Small-Strain Stiffness, Shear-Wave Velocity and Soil Compressibilitys. Journal of Geotechnical and Geoenvironmental Engineering.