Correlations

Overview

The primary references for the correlation was Mayne (2007) and Lunne et al. (1997). Many of the correlations listed in this section use constants within a formula. Users can set the constants in the following tables. The tables are listed in order of priority.

  1. CPT_POINT_MATERIAL_PROPERTIES (split screen child of CPT_POINT_CORRELATION_PARAMETERS)
  2. CPT_POINT_PARAMETERS or CPT_POINT_CORRELATION_PARAMETERS
  3. CPT_PROJECT_CORRELATION_PARAMETERS or CPT_PROJECT_PARAMETERS

For example, if the Relative_Density_1_C0 field on CPT_POINT_ CORRELATION_PARAMETERS has a value it will be used in preference to the value, if any, on the CPT_PROJECT_CORRELATION_PARAMETERS table.The fields in the CPT_POINT_MATERIAL_PROPERTIES table allow the constants to be defined for depth ranges for a particular PointID. A top and bottom depth must be specified when using the CPT_POINT_MATERIAL_PROPERTIES table, and the depth ranges must not overlap.

Undrained Shear Strength and Consistency Term

Undrained Shear Strength 1

Undrained Shear Strength 1 (s_u) in Undrained_Shear_Strength_1 is defined as:

When qt has data,

s_u = \frac {(q_t - \sigma_{v0})}{N_{kt}}

Otherwise,

s_u = \frac {(q_c - \sigma_{v0})}{N_{k}}

NCHRP Synthesis 368 p 39

N_kNk and N_{kt} are defined on the CPT_POINT_MATERIAL_PROPERTIESCPT_POINT_CORRELATION_PARAMETERS and CPT_PROJECT_CORRELATION_PARAMETERS tables. Different values for N_k and N_{kt} can be defined for when q_c or q_t is either greater than or equal to, or less than a defined break point. Each of these tables have six fields from which the N_k and N_{kt} values, and the q_c and qt break point values are stored and retrieved for the calculation of s_u .

Field NameDescription
Undrained_Shear_Strength_1_Nk_qc_BP

Break point used to determine which N_k to use in the s_u calculation

Undrained_Shear_Strength_1_Nk_qc_LT_BP

Used as the N_k in the s_u calculation, where q_t does not have data, and q_c is less than the break point.

Undrained_Shear_Strength_1_Nk_qc_GTE_BP

Used as the N_k in the s_u calculation, where qt does not have data, and q_c is greater than or equal to the break point.

Undrained_Shear_Strength_1_Nkt_qt_BP

Break point used to determine which N_{kt} to use in the s_u calculation

Undrained_Shear_Strength_1_Nkt_qt_LT_BP

Used as the N_{kt} in the s_u calculation, where q_t has data, and q_t is less than the break point.

Undrained_Shear_Strength_1_Nkt_qt_GTE_BP

Used as the N_{kt} in the s_u calculation, where q_t has data, and q_t is greater than or equal to the break point.

The fields in the CPT_POINT_MATERIAL_PROPERTIES table allow the N_k and N_{kt} to be defined for depth ranges for a particular PointID. A top and bottom depth must be specified when using the CPT_POINT_MATERIAL_PROPERTIES table, and the depth ranges must not overlap.

If the CPT_POINT_MATERIAL_PROPERTIES table is populated for the calculated PointID, the N_k or N_{kt} that lies within the depth range of the current depth of the row in the CPT_DATA table is used to calculate s_u. If a matching depth range for the current depth is not found, or N_k or N_{kt}  is missing, then the value is taken from the CPT_POINT_CORRELATION_PARAMETERS or the CPT_PROJECT_CORRELATION_PARAMETERS tables.

Undrained Shear Strength 1 Term

The Undrained_Shear_Strength_Term_1 is defined based on the value of the Undrained_Shear_Strength_1 field and the values in the DG_LOG_CONSISTENCY_DENSITY library table.

Undrained Shear Strength 2

Undrained Shear Strength 2 (s_u) in Undrained_Shear_Strength_2 is defined as:

When q_t has data,

s_u = \frac {(q_t)}{N_{kt}}

Otherwise,

s_u = \frac {(q_c - \sigma_{v0})}{N_{kt}}

Where:

     N_{kt} is stored in the Undrained_Shear_Strength_2_Nkt field.

     N_k is stored in the Undrained_Shear_Strength_2_Nk field.

The variables are stored on CPT_POINT_MATERIAL_PROPERTIESCPT_POINT_CORRELATION_PARAMETERS and CPT_PROJECT_CORRELATION_PARAMETERS tables.

The fields in the CPT_POINT_MATERIAL_PROPERTIES table allow the N_k and N_{kt} to be defined for depth ranges for a particular PointID. A top and bottom depth must be specified when using the CPT_POINT_MATERIAL_PROPERTIES table, and the depth ranges must not overlap.

If the CPT_POINT_MATERIAL_PROPERTIES table is populated for the calculated PointID, the N_k or N_{kt} that lies within the depth range of the current depth of the row in the CPT_DATA table is used to calculate s_u. If a matching depth range for the current depth is not found, or N_k or N_{kt} is missing, then the value is taken from the CPT_POINT_CORRELATION_PARAMETERS or the CPT_PROJECT_CORRELATION_PARAMETERS tables.

Undrained Shear Strength 2 Term

The Undrained_Shear_Strength_Term_2 is defined based on the value of the Undrained_Shear_Strength_2 field and the values in the DG_LOG_CONSISTENCY_DENSITY library table.

Undrained Shear Strength 3

Undrained Shear Strength 3 (s_u) based on CSSM in Undrained_Shear_Strength_3 is defined as:

When q_t has data,

s_u = 0.5 \cdot \sin \Phi' \cdot OCR ^\Lambda \cdot \sigma'_{v0}\\

Wroth (1984), NCHRP Synthesis 368 p 39

Where:

     \Phi'  is taken from the first of these fields with data: Friction_Angle_3 and Friction_Angle_1 
    OCR is taken from Overconsolidation_Ratio_1
     \Lambda = 1 - \frac{C_s}{C_c}\\ , typically low to medium sensitivity clays are  0.7 \leq \Lambda \leq0.8 , and sensitive and structured clays are  0.9 \leq \Lambda \leq1.0and is stored in the Undrained_Shear_Strength_3_Lambda field.

\Lambda  is stored on CPT_POINT_CORRELATION_PARAMETERS and CPT_PROJECT_CORRELATION_PARAMETERS tables.

Undrained Shear Strength 3 Term

The Undrained_Shear_Strength_Term_3 is defined based on the value of the Undrained_Shear_Strength_3 field and the values similar to that in DG_LOG_CONSISTENCY_DENSITY library table.

Undrained Shear Strength 4

Undrained Shear Strength 4 (s_u) in Undrained_Shear_Strength_4 is defined as:

s_u = {C_1} \cdot {\sigma'_p}


Trak et al. (1980), Terzaghi et al. (1996), NCHRP Synthesis 368 p 40

Where:

      \sigma'_p  is taken from Preconsolidation_Stress_1
      C_1  is 0.22 in the published formula, and is stored in the Undrained_Shear_Strength_4_C1 field.
      C_1  is stored on CPT_POINT_CORRELATION_PARAMETERS and CPT_PROJECT_CORRELATION_PARAMETERS tables.

Undrained Shear Strength 4 Term

The Undrained_Shear_Strength_Term_4 is defined based on the value of the Undrained_Shear_Strength_4 field and the values similar to that in DG_LOG_CONSISTENCY_DENSITY library table.

Undrained Shear Strength 5

Undrained Shear Strength 5 (s_u) in Undrained_Shear_Strength_5 is defined as:

s_u = \frac {\Delta u}{N_{\Delta u}}

Robertson (2009), pp 28-29

Where:

      \Delta u  is taken from Excess_Pore_Pressure field
      {N_{\Delta u}}  is taken from Undrained_Shear_Strength_5_N field
      {N_{\Delta u}}  is stored on CPT_POINT_CORRELATION_PARAMETERS and CPT_PROJECT_CORRELATION_PARAMETERS tables.

Undrained Shear Strength 5 Term

The Undrained_Shear_Strength_Term_5 is defined based on the value of the Undrained_Shear_Strength_5 field and the values similar to that in DG_LOG_CONSISTENCY_DENSITY library table.

Relative Density and Relative Density Term

Relative Density 1

Relative density (D_r) in Relative_Density_1 is defined as:

Dr= \frac{1}{C_2}\cdot ln\left(\frac{q_c \cdot W_{ehr}}{C_0 \cdot(\sigma'_{v0})^{C_1}}\right)\cdot100

Baldi et al. (1986) and Al-Homoud and Wehr (2006), CPT in Geotechnical Practice p 83

Where:
     q_c and \sigma'_{v0} are in kPa
     C_0 is stored in the Relative_Density_1_C0 field. Published value for normally consolidated 157, over consolidated 181
     C_1 is stored in the Relative_Density_1_C1 field. Published value is 0.55
     C_2 is stored in the Relative_Density_1_C2 field. Published value for normally consolidated 2.41, over consolidated 2.46
     W_{ehr} is the Wehr Correction for Calcareous Soils, this constant is defined in the Relative_Density_1_Wehr_Correction field and was suggested in Al-Homoud and Wehr (2006). If the field is empty the default is 1.The constants are stored on CPT_POINT_CORRELATION_PARAMETERS and CPT_PROJECT_CORRELATION_PARAMETERS tables.

Relative Density Term 1

Relative density term in Relative_Density_Term_1 is defined based on Relative_Density_1 on the CPT_DATA table and the values in the DG_LOG_CONSISTENCY_DENSITY library table.

Relative Density 2

Relative density (D_r) in Relative_Density_2 is defined as:

D_r= 100 \cdot \left[C_1 \cdot ln(\frac{q_t / \sigma_{atm}}{\sqrt{\sigma'_{vo}/\sigma_{atm}} })+C_2\right]


Jamiolkowski et al. (2001), NCHRP Synthesis 368 pp 41-42

Where:
     C_1 is stored in the Relative_Density_2_C1 field. Published value is 0.268 for all sands
     C_2is stored in the Relative_Density_2_C2 field. For average compressibility: C_2=-0.675, for high compressibility and sands of carbonate or calcareous composition: C_2 \leq 1.0, for low compressibility: C_2 \geq 2.0.

The constants are stored on CPT_POINT_CORRELATION_PARAMETERS and CPT_PROJECT_CORRELATION_PARAMETERS tables.

Relative Density Term 2

Relative density term in Relative_Density_Term_2 is defined based on Relative_Density_2 on the CPT_DATA table and the values in the DG_LOG_CONSISTENCY_DENSITY library table.

Relative Density 3

Relative density (D_r) in Relative_Density_3 is defined as:

D_r = \left[\frac{q_{c1}}{305\cdot C_1\cdot OCR^{0.18}\cdot(12+0.5\cdot log(t/100))}\right]^{0.5} \cdot 100\\

Kulhawy and Mayne (1990), CPT in Geotechnical Practice p 84

Where:
     q_{c1}=\frac{q_c}{\sqrt{\sigma'_{v0}\cdot \sigma_{atm}}}
     C_1 is stored in the Relative_Density_3_C1 field. Published values range from 0.91 for low compressibility, 1.0 for medium compressible sands, to 1.09 for highly compressible
     t is time in years and stored in the Relative_Density_3_t field.

The constants are stored on CPT_POINT_CORRELATION_PARAMETERS and CPT_PROJECT_CORRELATION_PARAMETERS tables.

Relative Density Term 3

Relative density term in Relative_Density_Term_3 is defined based on Relative_Density_3 on the CPT_DATA table and the values in the DG_LOG_CONSISTENCY_DENSITY library table.

Soil Behaviour Type Index

Soil Behaviour Type Index 1

The soil behaviour type index (I_c) in Soil_Behaviour_Type_Index_1 is defined as:

I_c=((C_1 - log_{10} Q_t)^2 + (log_{10}F_r+C_2)^2)^{0.5}\\ \ \\ Q_t=\frac{q_c-\sigma_{v0}} {P_a} \left(\frac{P_a} {\sigma'_{v0}}\right)^n\\ \ \\ \left(\frac{P_a}{\sigma'_{v0}}\right) \leq 1.7 \\ \ \\ F_r=\frac{f_s}{q_t-\sigma_{v0}}\times 100 \text {%}

     I_c is calculated using n=1, if I_c> I_{\text{c break}}, then it's been accepted, otherwise it's calculated using n=0.5. If I_c< I_{\text{c break}} break then it's accepted, otherwise it's calculated using n=0.7.

Robertson and Wride (1998)

Where:

     C_1 is 3.47 in the published formula, and is stored in the Soil_Behaviour_Type_Index_1_C1 field. 
     C_2is 1.22 in the published formula, and is stored in the Soil_Behaviour_Type_Index_1_C2 field.

The constants are stored on CPT_POINT_CORRELATION_PARAMETERS and CPT_PROJECT_CORRELATION_PARAMETERS tables.

Transition zones

A Trasition Zone in Soil_Behaviour_Type_Index_Transition_1 for a certain depth is considered when:
     2.3<I_c<2.9;
     The rate of I_c change is rapid (slope of I_c vs. depth above and below of the current depth > 5) 
     and crosses the I_c=2.6 line.

Soil Behaviour Type Index 2

The soil behaviour type index (I_c) in Soil_Behaviour_Type_Index_2 is defined as:

I_c=\sqrt {[C_1-log_{10}Q_t(1-B_q)]^2+[C_2+C_3 \cdot log_{10}F_r]^2}

Jefferies and Davies (1993), NCHRP Synthesis 368 p 27

Where:
     C_1 is 3 in the published formula, and is stored in the Soil_Behaviour_Type_Index_2_C1 field. 
     C_2 is 1.5 in the published formula, and is stored in the Soil_Behaviour_Type_Index_2_C2 field. 
     C_3 is 1.3 in the published formula, and is stored in the Soil_Behaviour_Type_Index_2_C3 field.

The constants are stored on CPT_POINT_CORRELATION_PARAMETERS and CPT_PROJECT_CORRELATION_PARAMETERS tables.

Soil Behaviour Type Index 3

The non-normalised Soil Behaviour Type Index (I_{SBT}) in Soil_Behaviour_Type_Index_3 is defined as:

I_{SBT}= \left(\left(C_1-log \left( \frac{(q_c)}{p_a}\right)\right)^2+(log(R_f)+C_2)^2\right )^{0.5}

Robertson (2010), CPT 10, paper 2-56 (http://www.cpt10.com/PDF_Files/2-56RobSBT.pdf)

Where:
     C_1 is 3.47 in the published formula and is stored in the Soil_Behaviour_Type_Index_3_C1 field.
     q_t is taken from the Total_Cone_Resistance field on the CPT_DATA table.
     q_c is taken from the Cone_Resistance field on the CPT_DATA table.
     p_a is the Atmospheric pressure, 101.4 kPa, and is set in the Formula Tool.
     R_f is taken from the Friction_Ratio field on the CPT_DATA table.
     C_2 is 1.22 in the published formula and is stored in the Soil_Behaviour_Type_Index_3_C2 field.

The constants are stored on CPT_POINT_CORRELATION_PARAMETERS and CPT_PROJECT_CORRELATION_PARAMETERS tables.

Soil Behaviour Type Index 4

The soil behaviour type index (I_c) in Soil_Behaviour_Type_Index_4 is defined as:

I_c=\sqrt {[C_1-log_{10}Q_t(1-B_q)+1]^2+[C_2+C_3 \cdot log_{10}F_r]^2}

Been and Jefferies (1992), Soil liquefaction, a critical state approach, pp. 206-207

Where:
     C_1 is 3 in the published formula, and is stored in the Soil_Behaviour_Type_Index_4_C1 field. 
     C_2 is 1.5 in the published formula, and is stored in the Soil_Behaviour_Type_Index_4_C2 field. 
     C_3 is 1.3 in the published formula, and is stored in the Soil_Behaviour_Type_Index_4_C3 field.

The constants are stored on CPT_POINT_CORRELATION_PARAMETERS and CPT_PROJECT_CORRELATION_PARAMETERS tables.

SPT N60 Value

SPT N60 Value 1

The SPT N_{60} in SPT_N60_1 is defined as:

N_{60}=\frac{q_c}{C_1 \cdot p_a(1-\frac{I_c}{C_2}})

Robertson and Wride (1998), CPT in Geotechnical Practice p 151

Where:
     C_1 is 8.5 in the published formula, and is stored in the SPT_N60_1_C1 field.
     C_2 is 4.6 in the published formula, and is stored in the SPT_N60_1_C2 field.
     p_a is the Atmospheric pressure, 100 kPa, and cannot be changed in the CPT Tool.
     I_c is stored in the Soil_Behaviour_Type_Index_1 field.

The constants are stored on CPT_POINT_CORRELATION_PARAMETERS and CPT_PROJECT_CORRELATION_PARAMETERS tables.

SPT N60 Value 2

The SPT N_{60} in SPT_N60_2 is defined as:

N_{60}=\frac{q_c}{C_1 \cdot (1- \frac{I_c}{C_2})}

Jefferies and Davies (1993)

Where:
     C_1 is 0.85 in the published formula, and is stored in the SPT_N60_2_C1 field.
     C_2 is 4.75 in the published formula, and is stored in the SPT_N60_2_C2 field.
     I_c is stored in the Soil_Behaviour_Type_Index_2 field.

The constants are stored on CPT_POINT_CORRELATION_PARAMETERS and CPT_PROJECT_CORRELATION_PARAMETERS tables.

SPT Average N60 Value

The SPT average N60 value is a stepped average of SPT N60 values in the SPT_N60_1 or SPT_N60_2 fields in the CPT_DATA table for each defined depth interval step.

The average of the N60 values is calculated for each depth interval step, and the result is recorded in the SPT_ Average_N60_1 or SPT_Average_N60_2 fields in the CPT_DATA table for each row in that interval step.

The depth interval distance is defined on the SPT_N60_Average_Interval field on CPT_POINT_CORRELATION_PARAMETERS and CPT_PROJECT_CORRELATION_PARAMETERS tables, and is in metres.

Shear Wave Velocity

Shear Wave Velocity 1 (All Soils)

Shear Wave velocity 1 (V_s ) in Shear_Wave_Velocity_1 is defined as:

V_S

V_s=C_1 \cdot log(f_s)+C_2

Mayne (2006), NCHRP Synthesis 368 p 30

Where:
     f_s is in kPa.
     C_1 is 118.8 in the published formula, and is stored in the Shear_Wave_Velocity_1_C1 field.
     C_2is 18.5 in the published formula, and is stored in the Shear_Wave_Velocity_1_C2 field.

The constants are stored on CPT_POINT_CORRELATION_PARAMETERS and CPT_PROJECT_CORRELATION_PARAMETERS tables.

Shear Wave Velocity 2 (All Soils)

Shear Wave velocity 2 (V_s ) in Shear_Wave_Velocity_2 is defined as:

V_s=(C_1 \cdot log(q_t)-C_2)^{C_3} \cdot \left( \frac{f_s}{q_t} \cdot100 \right)^{C_4}

Hegazy and Mayne (1995), NCHRP Synthesis 368 p 30

Where:
     q_t and f_s are in kPa.
     C_1 is 10.1 in the published formula, and is stored in the Shear_Wave_Velocity_2_C1 field.
     C_2 is 11.4 in the published formula, and is stored in the Shear_Wave_Velocity_2_C2 field.
     C_3 is 1.67 in the published formula, and is stored in the Shear_Wave_Velocity_2_C3 field.
     C_4 is 0.3 in the published formula, and is stored in the Shear_Wave_Velocity_2_C4 field.

The constants are stored on CPT_POINT_CORRELATION_PARAMETERS and CPT_PROJECT_CORRELATION_PARAMETERS tables.

This correlation of V_s  is calculated when the Soil_Type_1 field value on the CPT_DATA table has any value for that row.

Shear Wave Velocity 3 (Clays)

Shear Wave velocity 3 (V_s ) in Shear_Wave_Velocity_3 is defined as:

V_s=C_1 \cdot(q_t)^{C_2}

Mayne and Rix (1995), NCHRP Synthesis 368 p 30

Where:
     q_t and f_s are in kPa
     C_1 is 1.75 in the published formula, and is stored in the Shear_Wave_Velocity_3_C1 field.
     C_2 is 0.627 in the published formula, and is stored in the Shear_Wave_Velocity_3_C2 field.


The constants are stored on CPT_POINT_CORRELATION_PARAMETERS and CPT_PROJECT_CORRELATION_PARAMETERS tables.

This correlation of Vs is calculated only when the Soil_Type_1 field value on the CPT_DATA table is Fine or Mixed for that row.

Shear Wave Velocity 4 (Sands)

Shear Wave velocity 4 (V_s ) in Shear_Wave_Velocity_4 is defined as:

V_s=C_1 \cdot q_t^{C_2} \cdot (\sigma'_{v0})^{C_3}

Baldi et al. (1989), NCHRP Synthesis 368 p 30

Where:
     q_t and \sigma'_{v0} are in MPa.
     C_1 is 277 in the published formula, and is stored in the Shear_Wave_Velocity_4_C1 field.
     C_2  is 0.13 in the published formula, and is stored in the Shear_Wave_Velocity_4_C2 field.
     C_3 is 0.27 in the published formula, and is stored in the Shear_Wave_Velocity_4_C3 field.

The constants are stored on CPT_POINT_CORRELATION_PARAMETERS and CPT_PROJECT_CORRELATION_PARAMETERS tables.

This correlation of Vs is calculated only when the Soil_Type_1 field value on the CPT_DATA table is Coarse or Mixed for that row.

Unit Weight

Dry Unit Weight 1 (Sands)

Dry Unit Weight 1 (\gamma_{dry}) in Dry_Unit_Weight_1 is defined as:

\gamma_{dry}=C_1 \cdot log(q_{t1})+C_2

Mayne (2007), NCHRP Synthesis 368 p 31

Where:
     C_1 is 1.89 in the published formula, and is stored in the Dry_Unit_Weight_1_C1 field.
     C_2 is 11.8 in the published formula, and is stored in the Dry_Unit_Weight_1_C2 field.

The constants are stored on CPT_POINT_CORRELATION_PARAMETERS and CPT_PROJECT_CORRELATION_PARAMETERS tables.

This correlation of V_S is calculated only when the Soil_Type_1 field value on the CPT_DATA table is Coarse or Mixed for that row.

Saturated Unit Weight 1

Saturated Unit Weight 1 (\gamma_{sat}) in Saturated_Unit_Weight_1 is defined as:

\gamma_{sat}=C_1 \cdot log(V_s)-C_2 \cdot log (z)

Mayne (2007), NCHRP Synthesis 368 p 31

Where:
     V_s is in m/s and z is in m
     C_1 is 8.32 in the published formula, and is stored in the Saturated_Unit_Weight_1_C1 field
     C_2 is 1.61 in the published formula, and is stored in the Saturated_Unit_Weight_1_C2 field
     z is Depth 
     V_S is taken from the first of these fields with data: Shear_Wave_Velocity_Extrapolated or Shear_Wave_Velocity_1

The constants are stored on CPT_POINT_CORRELATION_PARAMETERS and CPT_PROJECT_CORRELATION_PARAMETERS tables.

This correlation is applicable to all soil types.

Saturated Unit Weight 2

Saturated Unit Weight 2 (\gamma_{sat}) in Saturated_Unit_Weight_2 is defined as:

\gamma_{sat}=C_1 \cdot log(f_s)+C_2 \cdot G_s-C_3

Mayne (2007), NCHRP Synthesis 368 p 32

Where:
     f_s is in kPa.
     C_1 is 2.6 in the published formula, and is stored in the Saturated_Unit_Weight_2_C1 field.
     C_2 is 15 in the published formula, and is stored in the Saturated_Unit_Weight_2_C2 field.
     C_3 is 26.5 in the published formula, and is stored in the Saturated_Unit_Weight_2_C3 field.
     G_s is Specific Gravity of Solids, typically 2.4 to 2.9, and is stored in the Specific_Gravity_of_Solids field on CPT_PROJECT_CORRELATION_PARAMETERS.

The constants are stored on CPT_POINT_CORRELATION_PARAMETERS and CPT_PROJECT_CORRELATION_PARAMETERS tables.

This correlation is applicable to all soil types.

Small-Strain Shear Modulus

Small-Strain Shear Modulus 1 (Sands)

Small-Strain Shear Modulus 1 (G_0) of sand in Small_Strain_Shear_Modulus_1 is defined as:

G_0=C_1 \cdot \left( \frac{q_c}{\sqrt{\sigma'_{v0}}}\right)^{C_2} \cdot q_c

Rix and Stokoe (1992), CPT in Geotechnical Practice p 94

Where:
     q_c\sigma'_{v0} and G_0 are in kPa.
     C_1 is 1634 in the published formula, and is stored in the Small_Strain_Shear_Modulus_1_C1 field.
     C_2 is -0.75 in the published formula, and is stored in the Small_Strain_Shear_Modulus_1_C2 field.

The constants are stored on CPT_POINT_CORRELATION_PARAMETERS and CPT_PROJECT_CORRELATION_PARAMETERS tables.

This correlation of G_0 is calculated only when the Soil_Type_1 field value on the CPT_DATA table is Coarse or Mixed for that row.

Small-Strain Shear Modulus 2

Small-Strain Shear Modulus 2 (G_0) in Small_Strain_Shear_Modulus_2 is defined as:

G_0= \frac{\gamma_{bulk}}{g} \cdot V_s^2

Elastic theory, CPT in Geotechnical Practice p 74 and 94, NCHRP Synthesis 368 p 31

Where:
     V_s is taken from the first of these fields with data: Shear_Wave_Velocity_Extrapolated or Shear_Wave_Velocity_1
     \gamma_{bulk} is taken from Bulk_Unit_Weight

This correlation of G_0 is applicable to all soil types.

Young's Modulus

Young's Modulus 1

Small Strain Young's Modulus 1 (E_0) in Youngs_Modulus_1 is defined as:

E_0=2 \cdot(1+v) \cdot G_0

Elastic theory, CPT in Geotechnical Practice p 74 and 94, NCHRP Synthesis 368 p 32

Where:
     v = 0.2 is applied and can be varied in the Formula Tool. Published literature states: v'=0.2 applies for drained soils and v_u=0.5 applies for undrained soils .
     G_0 is taken from Small_Strain_Shear_Modulus_2.

This correlation of E_0 is applicable to all soil types.

Young's Modulus 2

Young's Modulus 2 (E_0) in Youngs_Modulus_2 is defined as:

E_0= \alpha q_c

CPT in Geotechnical Practice p 160, Figure 6.13

Where:
     \alpha is calculated from degree of loading, q_c, effective stress and reduction factor as given in the following plot.

Constrained Modulus

Constrained Modulus 1

The constrained modulus 1 (M) in Constrained_Modulus_1 is defined as:

M=C_1 \cdot(q_t-\sigma_{vo})

Kulhawy and Mayne (1990), NCHRP Synthesis 368 p 33, CPT in Geotechnical Practice p 72

Where:
     C_1 is 8.25 in CPT in Geotechnical Practice, and is stored in the Constrained_Modulus_1_C1 field. NCHRP Synthesis 368 suggest values ranging from 1 to 20, with normal soils approximately 5.

The constant is stored on CPT_POINT_CORRELATION_PARAMETERS and CPT_PROJECT_CORRELATION_PARAMETERS tables.

Constrained Modulus 2

The constrained modulus 2 (M) in Constrained_Modulus_2 is defined as:

M=C_1 \cdot G_0

Burns and Mayne (2002), NCHRP Synthesis 368 pp 33-34

Where:
     C_1 is 0.02 for organic plastic clays, up to 2 for over consolidated quartz sands in the published literature, and is stored in the Constrained_Modulus_2_C1 field.
     G_0 is taken from Small_Strain_Shear_Modulus_2.

The constant is stored on CPT_POINT_CORRELATION_PARAMETERS and CPT_PROJECT_CORRELATION_PARAMETERS tables.

This global approach to defining C_1 is potentially inaccurate, it would be better to define the constant based on soil type with depth.

Coefficient of Volume Change

The coefficient of volume change 1 (m_v) in Coefficent_Volume_Change_1 is defined as:

m_v=\frac{1}{M}

CPT in Geotechnical Practice p 71

Where:
     M the constrained modulus, and is taken from the Constrained_Modulus_1 field.

Compression Index

The Compression Index 1 (C_c) in Compression_Index_1 is defined as:

C_c=\frac{2.3(1+e)\cdot\sigma'_{v0}}{M}

CPT in Geotechnical Practice p 71

Where:
     e is the Void Ratio, and is stored in the Void_Ratio field.
     M is the constrained modulus, and is taken from the Constrained_Modulus_1 field.

The constant and e are stored on CPT_POINT_CORRELATION_PARAMETERS and CPT_PROJECT_CORRELATION_PARAMETERS tables.

Preconsolidation Stress and Overconsolidation Ratio

Preconsolidation Stress 1 and Overconsolidation Ratio 1

The Preconsolidation Stress 1 (\sigma_p') of clay in Preconsolidation_Stress_1 is defined as:

\sigma'_p=C_1\cdot (q_t-\sigma_{v0})

Mayne (1995), Demers and Leroueil (2002), NCHRP Synthesis 368 p 34

Where:
     C_1 is 0.33 in the published formula, and is stored in the Preconsolidation_Stress_1_C1 field.

The constant is stored on CPT_POINT_CORRELATION_PARAMETERS and CPT_PROJECT_CORRELATION_PARAMETERS tables.

The overconsolidation ratio 1 in Overconsolidation_Ratio_1 is defined as:

OCR=\frac{\sigma'_p}{\sigma'_{v0}}

     \sigma'_p is taken from Preconsolidation_Stress_1 field

Preconsolidation Stress 2 and Overconsolidation Ratio 2

The Preconsolidation Stress 2 (\sigma_p') of clay in Preconsolidation_Stress_2 is defined as:

\sigma'_{p}=C_1 \cdot \Delta u

Chen and Mayne (1996), NCHRP Synthesis 368 p 34

Where:
     C_1 is 0.53 in the published formula, and is stored in the Preconsolidation_Stress_2_C1 field.

The constant is stored on CPT_POINT_CORRELATION_PARAMETERS and CPT_PROJECT_CORRELATION_PARAMETERS tables.

The overconsolidation ratio 2 in Overconsolidation_Ratio_2 is defined as:

OCR=\frac{\sigma'_p}{\sigma'_{v0}}

Where:

     \sigma'_p is taken from Preconsolidation_Stress_2 field

Preconsolidation Stress 3 and Overconsolidation Ratio 3

The Preconsolidation Stress 3 (\sigma_p') of clay in Preconsolidation_Stress_3 is defined as:

\sigma'_{p}=C_1 \cdot(q_t-u_2)

Mayne (2005), NCHRP Synthesis 368 p 35

Where:
     C_1 is 0.6 in the published formula, and is stored in the Preconsolidation_Stress_3_C1 field.

The constant is stored on CPT_POINT_CORRELATION_PARAMETERS and CPT_PROJECT_CORRELATION_PARAMETERS tables.

The overconsolidation ratio 3 in Overconsolidation_Ratio_3 is defined as:

OCR=\frac{\sigma'_p}{\sigma'_{v0}}

Where:

     \sigma'_p is taken from Preconsolidation_Stress_3 field

Preconsolidation Stress 4 and Overconsolidation Ratio 4

The Preconsolidation Stress 4 (\sigma_p') of clay in Preconsolidation_Stress_4 is defined as:

\sigma'_p=C_1 \cdot Q_t^{C_2}\cdot \sigma'_{v0}

Robertson (2009), Guide to CPT p 31

Where:
     C_1 is 0.25 in the published formula, and is stored in the Preconsolidation_Stress_4_C1 field
     C_2 is 1.25 in the published formula, and is stored in the Preconsolidation_Stress_4_C2 field

The constant is stored on CPT_POINT_CORRELATION_PARAMETERS and CPT_PROJECT_CORRELATION_PARAMETERS tables.

The overconsolidation ratio 4 in Overconsolidation_Ratio_4 is defined as:

OCR=\frac{\sigma'_p}{\sigma'_{v0}}

Where:

     \sigma'_p is taken from Preconsolidation_Stress_4 field

Preconsolidation Stress 5 and Overconsolidation Ratio 5

The Preconsolidation Stress 5 (\sigma_p') of sand in Preconsolidation_Stress_5 is defined as:

\sigma'_p=\left[ \frac{C_1 \cdot(q_t/\sigma_{atm})^{C_2}} {(1-sin\Phi')\cdot(\sigma'_{v0}/\sigma_{atm})^{C_3} }\right]^{\frac{1}{sin\Phi'-C_4}}\cdot\sigma'_{v0}

Mayne (2005), NCHRP Synthesis 368 p 35

Where:
     C_1 is 0.192 in the published formula, and is stored in the Preconsolidation_Stress_5_C1 field
     C_2 is 0.22 in the published formula, and is stored in the Preconsolidation_Stress_5_C2 field
     C_3 is 0.31 in the published formula, and is stored in the Preconsolidation_Stress_5_C3 field
     C_4 is 0.27 in the published formula, and is stored in the Preconsolidation_Stress_5_C4 field
     \Phi' is taken from Friction_Angle_3

The constants are stored on CPT_POINT_CORRELATION_PARAMETERS and CPT_PROJECT_CORRELATION_PARAMETERS tables.

The overconsolidation ratio 5 in Overconsolidation_Ratio_5 is defined as:

OCR=\frac{\sigma'_p}{\sigma'_{v0}}

Where:

     \sigma'_p is taken from Preconsolidation_Stress_5 field

Preconsolidation Stress 6 and Overconsolidation Ratio 6

The Preconsolidation Stress 6 (\sigma_p') of all soil types in Preconsolidation_Stress_6 is defined as:

\sigma'_p=C_1 \cdot \sigma_{atm}^{C_2} \cdot (G_0)^{C_3} \cdot \sigma_{v0}'^{C_4}

Mayne (2007), NCHRP Synthesis 368 pp 37

Where:
     \sigma'_p\sigma_{atm}G_0 and \sigma'_{v0} are in kPa
     C_1  is 0.101 in the published formula, and is stored in the Preconsolidation_Stress_6_C1 field
     C_2 is 0.102 in the published formula, and is stored in the Preconsolidation_Stress_6_C2 field
     C_3 is 0.478 in the published formula, and is stored in the Preconsolidation_Stress_6_C3 field
     C_4 is 0.420 in the published formula, and is stored in the Preconsolidation_Stress_6_C4 field
     G_0 is taken from Small_Strain_Shear_Modulus_2

The constants are stored on CPT_POINT_CORRELATION_PARAMETERS and CPT_PROJECT_CORRELATION_PARAMETERS tables.

The overconsolidation ratio 6 in Overconsolidation_Ratio_6 is defined as:

OCR=\frac{\sigma'_p}{\sigma'_{v0}}

Where:

     \sigma'_p is taken from Preconsolidation_Stress_6 field

Angle of Friction

Angle of Friction 1

The angle of internal friction of mixed soils (\Phi') in Friction_Angle_1 is defined as:

\Phi'=C_1º\cdot B_q^{C_2} \cdot [C_3+C_4 \cdot B_q+logQ_t]

Mayne and Campanella (2005), NCHRP Synthesis 368 pp 38-39

Where:
     C_1 is 29.5 in the published formula, and is stored in the Friction_Angle_1_C1 field.
     C_2 is 0.121 in the published formula, and is stored in the Friction_Angle_1_C2 field.
     C_3 is 0.256 in the published formula, and is stored in the Friction_Angle_1_C3 field.
     C_4 is 0.336 in the published formula, and is stored in the Friction_Angle_1_C4 field.

This correlation of \Phi' is only applicable for 0.1 < B_q<1.0 and hence will only be calculated if B_q in the Pore_Pressure_Ratio field on the same row lies within this range.

Angle of Friction 2

The angle of internal friction of sands (\Phi') in Friction_Angle_2 is defined as:

\Phi'=tan^{-1} \left (C_1+C_2 \cdot log \left( \frac{q_t}{\sigma'_{v0}} \right) \right)

Robertson and Campanella (1983), NCHRP Synthesis 368 p 38

Where:
     C_1 is 0.1 in the published formula, and is stored in the Friction_Angle_2_C1 field.
     C_2 is 0.38 in the published formula, and is stored in the Friction_Angle_2_C2 field.

This correlation of \Phi' is only applicable for Sands and hence will only be calculated if the Soil_Type_1 field value is coarse or mixed.

Angle of Friction 3

The angle of internal friction of sand (\Phi') in Friction_Angle_3 is defined as:

\Phi'=C_1+C_2 \cdot log(q_{t1})

Kulhawy and Mayne (1990), NCHRP Synthesis 368 p 38

Where:
     C_1 is 17.6° in the published formula, and is stored in the Friction_Angle_3_C1 field.
     C_2 is 11.0° in the published formula, and is stored in the Friction_Angle_3_C2 field.

This correlation of \Phi' is only applicable for Sands and hence will only be calculated if the Soil_Type_1 field value is coarse or mixed.

Effective Cohesion

Effective Cohesion 1

The cohesion (c') in Effective_Cohesion_1 is defined as:

c'=C_1 \cdot \sigma'_p


Mayne and Stewart (1988), Mesri and Abdel-Ghaffar (1993), NCHRP Synthesis 368 p 44

Where:
     C_1 is 0.02 in the published formula, and is stored in the Effective_Cohesion_1_C1 field.

     \sigma'_p is taken from Preconsolidation_Stress_1 field.

Sensitivity

Sensitivity 1

The Sensitivity (S_t) in Sensitivity_1 is defined as:

S_t= \frac{N_s}{R_f}

Schmertmann (1978), Rad and Lunne (1986), CPT in Geotechnical Practice p 68

Where:
     N_s is a value between 5 and 10 in the published formula, and is stored in the Sensitivity_1_Ns field.

The constant is stored on CPT_POINT_CORRELATION_PARAMETERS and CPT_PROJECT_CORRELATION_PARAMETERS tables.

Sensitivity 2

The Sensitivity (S_t) in Sensitivity_2 is defined as:

S_t= \frac{C_1 \cdot(q_t- \sigma_{v0})}{f_s}

Mayne (2007), NCHRP Synthesis 368 p 41

Where:
     C_1 is 0.073 in the published formula, and is stored in the Sensitivity_2_C1 field.

The constant is stored on CPT_POINT_CORRELATION_PARAMETERS and CPT_PROJECT_CORRELATION_PARAMETERS tables.

This correlation of St is based on the assumption of OCR<2s_u=0.22\cdot \sigma'_p and \sigma'_p=0.33(q_t- \sigma_{v0}). The value of S_t is recorded in the Sensitivity_2 field on the CPT_DATA table.

Coefficient of Lateral Earth Pressure

Coefficient of Lateral Earth Pressure 1

Coefficient of Lateral Earth Pressure 1 (K_0) for uncemented sands and well behaved clays in Coefficient_Lateral_Earth_Pressure_1 is defined as:

K_0=(1-sin\Phi') \cdot OCR^{sin \Phi'}\\ \ \\ Maximum \quad K_0=K_P=\frac{1+sin\Phi'}{1-sin\Phi'}

Mayne (2007), NCHRP Synthesis 368 p 42

Where:
     OCR is taken from the Overconsolidation_Ratio_1 field for fine material and the Overconsolidation_Ratio_5 for coarse material, on the CPT_DATA table. 
     \Phi' is taken from the Friction_Angle_3 and Friction_Angle_1 field on the CPT_DATA table. 

The constants are stored on CPT_POINT_CORRELATION_PARAMETERS and CPT_PROJECT_CORRELATION_PARAMETERS tables.

Coefficient of Lateral Earth Pressure 2

Coefficient of Lateral Earth Pressure 2 (K_0) for sand in Coefficient_Lateral_Earth_Pressure_2 is defined as:

K_0=C_1 \cdot \left( \frac {q_t} {\sigma_{atm}} \right)^{C_2} \cdot \left( \frac {\sigma_{atm}} {\sigma'_{v0}} \right)^{C_3} \cdot OCR^{C_4}

Mayne (2007), NCHRP Synthesis 368 p 43

Where:
OCR is taken from the Overconsolidation_Ratio_5 field on the CPT_DATA table. 
     C_1 is 0.192 in the published formula, and is stored in the Coefficient_Lateral_Earth_Pressure_2_C1 field.
     C_2 is 0.22 in the published formula, and is stored in the Coefficient_Lateral_Earth_Pressure_2_C2 field.
     C_3 is 0.31 in the published formula, and is stored in the Coefficient_Lateral_Earth_Pressure_2_C3 field.
     C_4 is 0.27 in the published formula, and is stored in the Coefficient_Lateral_Earth_Pressure_2_C3 field.

The constants are stored on CPT_POINT_CORRELATION_PARAMETERS and CPT_PROJECT_CORRELATION_PARAMETERS tables.

Coefficient of Lateral Earth Pressure 3

Coefficient of Lateral Earth Pressure 3 (K_0) for fine grained soils in Coefficient_Lateral_Earth_Pressure_3 is defined as:

K_0=C_1 \cdot \left( \frac{q_t-\sigma_{v0}}{\sigma'_{v0}} \right)

Kulhawy and Mayne (1990), CPT Guide p 32

Where:
     C_1 is 0.1 in the published formula, and is stored in the Coefficient_Lateral_Earth_Pressure_3_C1 field.

The constants are stored on CPT_POINT_CORRELATION_PARAMETERS and CPT_PROJECT_CORRELATION_PARAMETERS tables.

Rigidity Index

Rigidity Index 1

Rigidity index 1 (I_r) for fine material is recorded in the Rigidity_Index_1 is defined as:

I_r=exp \left [ \left(\frac{C_1}{M}+C_2 \right) \cdot \left ( \frac{q_t- \sigma_{v0}} {q_t-u_2} \right) -C_3 \right]

Mayne (2001), NCHRP Synthesis 368 p 46

Where:
     C_1 is 1.5 in the published formula, and is stored in the Rigidity_Index_1_C1 field.
     C_2 is 2.925 in the published formula, and is stored in the Rigidity_Index_1_C2 field.
     C_3 is 2.925 in the published formula, and is stored in the Rigidity_Index_1_C3 field.
     M is the Cam clay constant, slope of the critical state line and is defined as:

M= \frac{6 \cdot sin \Phi'}{3- sin \Phi'}

     \Phi' for the calculation of the Cam clay constant M is taken from the  Friction_Angle_1  field on the  CPT_DATA  table. 

The constants are stored on CPT_POINT_CORRELATION_PARAMETERS and CPT_PROJECT_CORRELATION_PARAMETERS tables.

This correlation of I_r is calculated only when the Soil_Type_1 field value on the CPT_DATA table has a value of Fine for that row.

Rigidity Index 2

Rigidity index 2 (I_r) for fine material based on plasticity index and OCR is recorded in the Rigidity_Index_2 is defined as:

I_r= \frac{exp[C_1 \cdot(C_2-PI)]}{[1+ln\{1+C_3 \cdot(OCR-1)^{C_4}\}]^{C_5}}

Keaveny and Mitchel (1986), NCHRP Synthesis 368 p 46

Where:
     C_1 is 0.0435 in the published formula, and is stored in the Rigidity_Index_2_C1 field.
     C_2 is 137 in the published formula, and is stored in the Rigidity_Index_2_C2 field.
     C_3 is 0.385 in the published formula, and is stored in the Rigidity_Index_2_C3 field.
     C_4 is 3.2 in the published formula, and is stored in the Rigidity_Index_2_C4 field.
     C_5 is 0.8 in the published formula, and is stored in the Rigidity_Index_2_C5 field.
     PI is the Plasticity Index, and is stored in the Plasticity_Index field.
     OCR is taken from the Overconsolidation_Ratio_4 field on the CPT_DATA table.

The constants are stored on CPT_POINT_CORRELATION_PARAMETERS and CPT_PROJECT_CORRELATION_PARAMETERS tables.

This correlation of I_r is calculated only when the Soil_Type_1 field value on the CPT_DATA table has a value of Fine for that row.

Hydraulic Conductivity

Hydraulic Conductivity 1

The hydraulic conductivity (permeability) method 1 (K \quad1) in Hydraulic_Conductivity_1_Min and Hydraulic_Conductivity_1_Max are defined in the following table. Soil Behaviour Type Robertson et al. 1986 or Robertson et al. 1986 qc vs. Rf must be calculated for this correlation to be defined.

ZoneSoil Behaviour Type (SBT)Range of hydraulic conductivity (permeability) K (m/s)
1Sensitive fine grained3x10-9 to 3x10-8
2Organic soils1x10-8 to 1x10-6
3Clay1x10-10 to 1x10-9
4Silty clay to clay1x10-9 to 1x10-8
5Clayey silt to silty clay1x10-8 to 1x10-7
6Sandy silt to clayey silt1x10-7 to 1x10-6
7Silty sand to sandy silt1x10-5 to 1x10-6
8Sand to silty sand1x10-5 to 1x10-4
9Sand1x10-4 to 1x10-3
10Gravelly sand to dense sand1x10-3 to 1
11Very stiff fine-grained soil1x10-8 to 1x10-6
12Very stiff sand to clayey sand3x10-7 to 3x10-4

Robertson (2009), pp41, Table 6

Hydraulic Conductivity 2

The hydraulic conductivity (permeability) method 2 (K \quad2) in Hydraulic_Conductivity_2_Min and Hydraulic_Conductivity_2_Max are defined in the following table. Soil Behaviour Type Robertson 1990 or Robertson 1990 Extrapolated must be calculated for this correlation to be defined.

ZoneSoil Behaviour Type (SBTN)Range of hydraulic conductivity (permeability) K (m/s)
1Sensitive fine grained3x10-9 to 3x10-8
2Organic soils1x10-8 to 1x10-6
3Clay1x10-10 to 1x10-9
4Silt mixtures3x10-9 to 1x10-7
5Sand mixtures1x10-7 to 1x10-5
6Sands1x10-5 to 1x10-3
7Gravelly sands to dense sands1x10-3 to 1
8Very stiff sand to clayey sand1x10-8 to 1x10-6
9Very stiff fine-grained soil1x10-8 to 1x10-6

Robertson (2009), pp41, Table 7

Hydraulic Conductivity 3

The hydraulic conductivity (permeability) method 3 (K \quad3) in Hydraulic_Conductivity_3_Min and Hydraulic_Conductivity_3_Max are defined in the following table. I_c is from Soil_Behaviour_Type_Index_1

SBTnSoil Behaviour Type

K_{min}(m/s)

K_{max} (m/s)

I_c

1Sensitive fine grained3E-103E-08NA
2Organic soils-Clay1E-101E-08>3.6
3Clay1E-101E-092.95-3.6
4Silt mixtures3E-091E-072.6-2.95
5Sand mixtures1E-071E-052.05-2.60
6Sand1E-051E-031.31-2.05
7Sand to gravelly Sand1E-031E+00<1.31
8Very dense/ stiff soil1E-081E-03NA
9Very stiff fine grained1E-091E-07NA

Robertson (2010), paper 2-51

Hydraulic Conductivity 4

The hydraulic conductivity (permeability) method 4 (K \quad4) in Hydraulic_Conductivity_4 are defined in the following table. I_c is from Soil_Behaviour_Type_Index_1 Robertson (2010), paper 2-51

\text{When} \quad 1.0 < I_c \leq 3.27, \quad k=10^{(0.952 – 3.04\cdot I_c)} \quad (m/s)\\ \ \\ \text{When} \quad 3.27 < I_c < 4.0, \quad k=10^{(-4.52 – 1.37\cdot I_c)} \quad (m/s)

Robertson (2010), paper 2-51


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