SPT corrections and correlations

groundhog.siteinvestigation.insitutests.spt_correlations.frictionangle_spt_PHT(N1_60, intercept=27.1, multiplier=0.3, multiplier_quadratic=0.00054, **kwargs)

Correlation proposed by Peck, Hanson and Thornburn (1974) and mentioned by Wolff (1989)

Parameters:

• N1_60 – Corrected SPT N value (\(\left( N_1 \right)_{60}\)) [-] - Suggested range: 0.0 <= N1_60 <= 60.0

• intercept – Intercept at N=0 (\(-\)) [deg] - Suggested range: 23.0 <= intercept <= 35.0 (optional, default= 27.1)

• multiplier – Multiplier on linear term (\(-\)) [deg/blow] - Suggested range: 0.1 <= multiplier <= 0.7 (optional, default= 0.3)

• multiplier_quadratic – Multiplier on the quadratic term (\(-\)) [deg/blow^2] - Suggested range: 0.0001 <= multiplier_quadratic <= 0.001 (optional, default= 0.00054)

\[\varphi^{\prime} = 27.1 + 0.3 \cdot \left( N_1 \right)_{60} - 0.00054 \cdot \left( N_1 \right)_{60}^2\]

Returns:

Dictionary with the following keys:

• ’Phi [deg]’: Friction angle derived from SPT (\(\varphi^{\prime}\)) [deg]

Reference - Peck, Hanson and Thornburn (1974). Foundation Engineering.

groundhog.siteinvestigation.insitutests.spt_correlations.frictionangle_spt_kulhawymayne(N, sigma_vo_eff, atmospheric_pressure=100.0, coefficient_1=12.2, coefficient_2=20.3, coefficient_3=0.34, **kwargs)

Kulhawy and Mayne approximated the chart for friction angle selection from SPT using the formula given below. The friction angle depends on the effective overburden stress and SPT N number.

Parameters:

• N – SPT N number (\(N\)) [\(-\)] - Suggested range: 0.0 <= N <= 60.0

• sigma_vo_eff – Vertical effective stress (\(\sigma_{vo}^{\prime}\)) [\(kPa\)] - Suggested range: 0.0 <= sigma_vo_eff <= 1000.0

• atmospheric_pressure – Atmospheric pressure (\(P_a\)) [\(kPa\)] - Suggested range: 90.0 <= atmospheric_pressure <= 110.0 (optional, default= 100.0)

• coefficient_1 – First calibration coefficient (:math:``) [\(-\)] (optional, default= 12.2)

• coefficient_2 – Second calibration coefficient (:math:``) [\(-\)] (optional, default= 20.3)

• coefficient_3 – Third calibration coefficient (:math:``) [\(-\)] (optional, default= 0.34)

\[\phi = \tan^{-1} \left[ \frac{N}{12.2 +20.3 \cdot \left( \frac{\sigma_{v0}^{\prime}}{P_a} \right)} \right]^{0.34}\]

Returns:

Dictionary with the following keys:

• ’Phi [deg]’: Effective internal friction angle of the soil (\(\phi\)) [\(deg\)]

Reference - Kulhawy FH, Mayne PW (1990) Manual on estimating soil properties for foundation design. Electric Power Research Institute, Palo Alto

groundhog.siteinvestigation.insitutests.spt_correlations.overburdencorrection_spt_ISO(N, sigma_vo_eff, granular=True, **kwargs)

Corrects the SPT N number or corrected N number (\(N_{60}\)) for the effect of overburden pressure in granular soils. The multiplier \(C_N\) is calculated and applied to N or \(N_{60}\). Note that \(C_N\) should be limited to 2 and preferably be kept below 1.5. In the function, a lower limit on the vertical effective stress of 25kPa is used in the validation to achieve this.

Parameters:

• N – Uncorrected or corrected SPT N number (\(N or N_{60}\)) [-] - Suggested range: 0.0 <= N <= 60.0

• sigma_vo_eff – Vertical effective stress (\(\sigma_{v0}^{\prime}\)) [kPa] - Suggested range: 25.0 <= sigma_vo_eff <= 400.0

• granular – Boolean defining whether the soil is granular or not. If the soil is not granular, the correction factor is taken equal to 1

\[C_N = \sqrt{\frac{98}{\sigma_{v0}^{\prime}}}\]

Returns:

Dictionary with the following keys:

• ’CN [-]’: Multiplier on SPT N number (\(C_N\)) [-]

• ’N1 [-]’: Corrected N number (\(N_1 or \left( N_1 \right)_{60}\)) [-]

Reference - BS EN ISO 22476-3

groundhog.siteinvestigation.insitutests.spt_correlations.overburdencorrection_spt_liaowhitman(N, sigma_vo_eff, granular=True, atmospheric_pressure=100.0, **kwargs)

Applies a correction to the SPT N value to account for the effect of effective overburden pressure in granular soils. The relation given by Liao and Whitman (1986) is one of the most commonly used. Increasing overburden pressure will lead to less penetration at deeper depths for the same soil type. By applying the correction, the field value of N is corrected to a standard effective overburden pressure of 100kPa.

The standard penetration number corrected for field condition (\(N_{60}\)) can also be used as an input in which case \(\left( N_1 \right)_{60}\) is obtained.

Parameters:

• N – Field value of SPT N number (\(N\)) or corrected value \(N_{60}\) [\(-\)] - Suggested range: N >= 0.0

• sigma_vo_eff – Effective overburden pressure (\(\sigma_{vo}^{\prime}\)) [\(kPa\)] - Suggested range: sigma_vo_eff >= 0.0

• granular – Boolean defining whether the soil behaves in a granular or not. If the behaviour is not granular, the correction factor is taken equal to 1.

• atmospheric_pressure – Atmospheric pressure (\(P_a\)) [\(kPa\)] (optional, default= 100.0)

\[ \begin{align}\begin{aligned}N_1 = C_N \cdot N\\C_N = \left[ \frac{1}{ \left( \frac{\sigma_{vo}^{\prime}}{P_a} \right) } \right]^{0.5}\end{aligned}\end{align} \]

Returns:

Dictionary with the following keys:

• ’CN [-]’: Correction factor (\(C_N\)) [\(-\)]

• ’N1 [-]’: Value of SPT N number corrected to an effective overburden pressure of 100kPa (\(N_1\) or \(\left( N_1 \right)_{60}\) in case \(N_{60}\) is used as input) [\(-\)]

Reference - Liao SSC, Whitman RV (1986) Overburden correction factors for SPT in sand. J Geotech Eng ASCE 112(3):373–377

groundhog.siteinvestigation.insitutests.spt_correlations.relativedensity_spt_kulhawymayne(N1_60, d_50, calibration_factor_1=60.0, calibration_factor_2=25.0, time_since_deposition=1.0, ocr=1.0, ca_override=nan, cocr_override=nan, **kwargs)

Estimates relative density from SPT test. Although initially proposed based on the results of tests on non-aged, normally consolidated sands, the correlation can account for the effect of ageing and overconsolidation through correction factors. The parameters for these correction factors are not always easy to estimate.

Note that stress and energy corrections need to be applied to the raw SPT data before applying the correlation.

Parameters:

• N1_60 – SPT number corrected for overburden stress and energy (\((N_1)_{60}\)) [\(-\)] - Suggested range: 0.0 <= N_1_60 <= 100.0

• d_50 – Median grain size (\(d_{50}\)) [\(mm\)] - Suggested range: 0.002 <= d_50 <= 20.0

• calibration_factor_1 – First calibration factor (:math:``) [\(-\)] (optional, default= 60.0)

• calibration_factor_2 – Second calibration factor (:math:``) [\(-\)] (optional, default= 25.0)

• time_since_deposition – Time since deposition (\(t\)) [\(years\)] - Suggested range: time_since_deposition >= 1.0 (optional, default= 1.0)

• ocr – Overconsolidation ratio (\(OCR\)) [\(-\)] - Suggested range: 1.0 <= ocr <= 50.0 (optional, default= 1.0)

• ca_override – Direct specification of factor CA (\(C_A\)) [\(-\)] - Suggested range: ca_override >= 1.0 (optional, default= np.nan)

• cocr_override – Direct specification of factor COCR (\(C_{OCR}\)) [\(-\)] - Suggested range: cocr_override >= 1.0 (optional, default= np.nan)

\[ \begin{align}\begin{aligned}\text{Unaged, normally consolidated sand}\\D_r = \sqrt{\frac{(N_1)_{60}}{60 + 25 \cdot \log_{10} ( d_{50} )}}\\\text{With corrections for overconsolidation and ageing}\\D_r = \sqrt{\frac{(N_1)_{60}}{\left( 60 + 25 \cdot \log d_{50} \right) \cdot C_A \cdot C_{OCR}}}\\C_A = 1.2 + 0.05 \cdot \log_{10} \left( \frac{t}{100} \right)\\C_{OCR} = (OCR)^{0.18}\end{aligned}\end{align} \]

Returns:

Dictionary with the following keys:

• ’Dr [-]’: Relative density (unitless) (\(D_r\)) [\(-\)]

• ’Dr [pct]’: Relative density (percent) (\(D_r\)) [\(pct\)]

• ’C_A [-]’: Correction factor for ageing (\(C_A\)) [\(-\)]

• ’C_OCR [-]’: Correction factor for overconsolidation (\(C_{OCR}\)) [\(-\)]

Reference - Kulhawy FH, Mayne PW (1990) Manual on estimating soil properties for foundation design. Electric Power Research Institute, Palo Alto

groundhog.siteinvestigation.insitutests.spt_correlations.relativedensityclass_spt_terzaghipeck(N, **kwargs)

Defines the relative density class for SPT measurements in cohesionless soils based on the uncorrected N-number

N (uncorrected)	Relative density category
<= 4	Very loose
4 < N <= 10	Loose
10 < N <= 30	Medium dense
30 < N <= 50	Dense
N <= 50	Very dense

Parameters:

N – Uncorrected SPT N number (\(N\)) [-] - Suggested range: 0.0 <= N <= 60.0

Returns:

Dictionary with the following keys:

• ’Dr class’: Relative density class (\(D_r\))

Reference - Terzaghi K, Peck RB (1967) Soil mechanics in engineering practice, 2nd edn. Wiley, New York

groundhog.siteinvestigation.insitutests.spt_correlations.spt_N60_correction(N, borehole_diameter, rod_length, country, hammertype, hammerrelease, samplertype='Standard sampler', eta_H=nan, eta_B=nan, eta_S=nan, eta_R=nan, **kwargs)

The performance of the SPT in a given soil type depends on the efficiency of energy transmission to the soil. It is common practice to correct the field value of SPT N number to an equivalent number of blows at an energy ratio of 60% (ratio of energy delivered to the sampler divided by the input energy). The hammer efficiency (\(\eta_H\)), borehole diameter (\(\eta_B\)), sampler type (\(\eta_S\)) and rod length (\(\eta_R\)) are corrected for.

The recommendations by Seed et al (1985) and Skempton (1986) as presented by Ameratunga et al (2016) are used by default. The user can specify overrides for each correction factor. If overrides are specified, they take precedence.

Country	Hammer type	Hammer release	\(\eta_H\) [pct]
Japan	Donut	Free fall	78
	Donut	Rope and pulley	67
United States	Safety	Rope and pulley	60
	Donut	Rope and pulley	45
Argentina	Donut	Rope and pulley	45
China	Donut	Free fall	60
	Donut	Rope and pulley	50

Diameter [mm]	\(\eta_B\) [-]
60-120	1
150	1.05
200	1.15

Sampler type	\(\eta_S\) [-]
Standard sampler	1.0
With liner for dense sand and clay	0.8
With liner for loose sand	0.9

Rod length [m]	\(\eta_R\) [-]
>10	1.0
6-10	0.95
4-6	0.85
0-4	0.75

Parameters:

• N – Field value of SPT N number (\(N\)) [\(-\)] - Suggested range: N >= 0.0

• borehole_diameter – Diameter of the borehole (\(D\)) [\(mm\)] - Suggested range: 60.0 <= borehole_diameter <= 200.0

• rod_length – Length of rods connecting hammer with sampler (\(L\)) [\(m\)] - Suggested range: rod_length >= 0.0

• country – Country where SPT test is executed - Options: (‘Japan’, ‘United States’, ‘Argentina’, ‘China’, ‘Other’). If ‘Other’ is chosen, an override for \(\eta_H\) should be specified

• hammertype – Type of hammer used - Options: (‘Donut’, ‘Safety’)

• hammerrelease – Release mechanism for the hammer - Options: (‘Free fall’, ‘Rope and pulley’)

• samplertype – Type of sampler used (optional, default= ‘Standard sampler’) - Options: (‘Standard sampler’, ‘With liner for dense sand and clay’, ‘With liner for loose sand’)

• eta_H – Correction factor for hammer efficiency (\(\eta_H\)) [\(pct\)] - Suggested range: 0.0 <= eta_H <= 100.0 (optional, default= np.nan)

• eta_B – Correction factor for borehole diameter (\(\eta_B\)) [\(-\)] - Suggested range: 1.0 <= eta_B <= 1.2 (optional, default= np.nan)

• eta_S – Correction factor for sampler type (\(\eta_S\)) [\(-\)] - Suggested range: 0.8 <= eta_S <= 1.0 (optional, default= np.nan)

• eta_R – Correction factor for rod length (\(\eta_R\)) [\(-\)] - Suggested range: 0.75 <= eta_R <= 1.0 (optional, default= np.nan)

\[N_{60} = \frac{N \cdot \eta_H \cdot \eta_B \cdot \eta_S \cdot \eta_R}{60}\]

Returns:

Dictionary with the following keys:

• ’N60 [-]’: SPT N number corrected to 60pct efficiency (\(N_{60}\)) [\(-\)]

• ’eta_H [%]’: Correction factor for hammer efficiency (\(\eta_H\)) [\(pct\)]

• ’eta_H [-]’: : Correction factor for hammer efficiency (\(\eta_H\)) [\(-\)]

• ’eta_B [-]’: Correction factor for borehole diameter (\(\eta_B\)) [\(-\)]

• ’eta_S [-]’: Correction factor for sampler type (\(\eta_S\)) [\(-\)]

• ’eta_R [-]’: Correction factor for rod length (\(\eta_R\)) [\(-\)]

Reference - J. Ameratunga et al., Correlations of Soil and Rock Properties in Geotechnical Engineering, Developments in Geotechnical Engineering, DOI 10.1007/978-81-322-2629-1_4

groundhog.siteinvestigation.insitutests.spt_correlations.undrainedshearstrength_spt_salgado(pi, N_60, atmospheric_pressure=100.0, alpha_prime_override=nan, **kwargs)

Calculates undrained shear strength based on plasticity index and SPT number (corrected to 60% energy ratio).

PI [%]	\(\alpha^{\prime}\) [-]
15	0.068
20	0.055
25	0.048
30	0.045
40	0.044
60	0.043

Parameters:

• pi – Plasticity index (difference between liquid and plastic limit) (\(PI\)) [\(pct\)] - Suggested range: 15.0 <= plasticity_index <= 60.0

• N_60 – SPT number corrected to 60% energy ratio (\(N_{60}\)) [\(-\)] - Suggested range: 0.0 <= N_60 <= 100.0

• atmospheric_pressure – Atmospheric pressure (\(P_a\)) [\(kPa\)] - Suggested range: 90.0 <= atmospheric_pressure <= 110.0 (optional, default= 100.0)

• alpha_prime_override – Override for direct specification of the alpha prime factor (\(\alpha^{\prime}\)) [\(-\)] - Suggested range: alpha_prime_override >= 0.0 (optional, default= np.nan)

\[\frac{S_u}{P_a} = \alpha^{\prime} \cdot N_{60}\]

Returns:

Dictionary with the following keys:

• ’alpha_prime [-]’: Factor based on plasticity index (\(\alpha^{\prime}\)) [\(-\)]

• ’Su [kPa]’: Undrained shear strength (\(S_u\)) [\(kPa\)]

Reference - Salgado R (2008) The engineering of foundations. McGraw-Hill, New York

groundhog.siteinvestigation.insitutests.spt_correlations.undrainedshearstrengthclass_spt_terzaghipeck(N, **kwargs)

Defines the relative density class for SPT measurements in cohesionless soils based on the uncorrected N-number

N (uncorrected)	Consistency	\(q_u\) [kPa]
<= 2	Very soft	< 25
2 < N <= 4	Soft	25 - 50
4 < N <= 8	Medium	50 - 100
8 < N <= 15	Stiff	100 - 200
15 < N <= 30	Very stiff	200 - 400
N > 30	Hard	> 400

Parameters:

N – Uncorrected SPT N number (\(N\)) [-] - Suggested range: 0.0 <= N <= 60.0

Returns:

Dictionary with the following keys:

• ’Consistency class’: Consistency class

• ’qu min [kPa]’: Minimum value for ultimate axial stress in a UCS test

• ’qu max [kPa]’: Maximum value for ultimate axial stress in a UCS test

Reference - Terzaghi K, Peck RB (1967) Soil mechanics in engineering practice, 2nd edn. Wiley, New York

groundhog.siteinvestigation.insitutests.spt_correlations.youngsmodulus_spt_AASHTO(N1_60, soiltype, multiplier_silts=0.4, multiplier_cleansand=0.7, multiplier_coarsesand=1.0, multiplier_gravel=1.1, **kwargs)

Calculates the Young’s modulus based on corrected SPT number for various soil types.

Soil type	Soil type (short name)	\(E_s\) [MPa]
Silts, sandy silts, slightly cohesive mixtures	Silts	\(0.4 ( N_1 )_{60}\)
Clean fine to medium sands and slightly silty sands	Clean sands	\(0.7 ( N_1 )_{60}\)
Coarse sands and sands with little gravel	Coarse sands	\(1.0 ( N_1 )_{60}\)
Sandy gravel and gravels	Gravels	\(1.1 ( N_1 )_{60}\)

Parameters:

• N1_60 – Corrected SPT N number (\(\left( N_1 \right)_{60}\)) [-] - Suggested range: 0.0 <= N1_60 <= 60.0

• soiltype – Soil type - Options: (“Silts”, “Clean sands”, “Coarse sands”, “Gravels”)

• multiplier_silts – Multiplier on the silty soils (\(-\)) [-] (optional, default= 0.4)

• multiplier_cleansand – Multiplier on the clean find sands (\(-\)) [-] (optional, default= 0.7)

• multiplier_coarsesand – Multiplier on the coarse sands (\(-\)) [-] (optional, default= 1.0)

• multiplier_gravel – Multiplier on the gravels (\(-\)) [-] (optional, default= 1.1)

Returns:

Dictionary with the following keys:

• ’Es [MPa]’: Young’s modulus (\(E_s\)) [MPa]

Reference - AASHTO 1997 - LRFD