Overview

Liquefaction related correlations are defined in this section.

Soil Behaviour Type Index 1

Soil behaviour type index 1, Ic, in CPT_DATA_LIQUEFACTION.Soil_Behaviour_Type_Index_1 is defined based on the method by Robertson and Wride (1998) as:

Where:

The stress exponent $//<![CDATA[ \begin{array}{l}n\end{array} //]]>$ in Stress_Exponent calculated from $//<![CDATA[ \begin{array}{l}I_c\end{array} //]]>$, so iterations are done to find the final value.

Stress Exponent n

Stress exponent $//<![CDATA[ \begin{array}{l}n\end{array} //]]>$ is calculated from either method by Robertson (2009) or NCEER 2001 method based on the method selected on point/parameters table:

Robertson (2009):

     Where $//<![CDATA[ \begin{array}{l}I_c\end{array} //]]>$ is from CPT_DATA_LIQUEFACTION.Soil_Behaviour_Type_Index_1 and depends on n, so iterations are done to find the final value.

NCEER 2001: Initially $//<![CDATA[ \begin{array}{l}n=1\end{array} //]]>$, if the corresponding $//<![CDATA[ \begin{array}{l}I_c\end{array} //]]>$ is smaller than $//<![CDATA[ \begin{array}{l}I_{\text{c_Break}}\end{array} //]]>$ then try $//<![CDATA[ \begin{array}{l}n=0.5\end{array} //]]>$, if the calculated $//<![CDATA[ \begin{array}{l}I_c\end{array} //]]>$ is larger than $//<![CDATA[ \begin{array}{l}I_{\text{c_Break}}\end{array} //]]>$ then $//<![CDATA[ \begin{array}{l}n=0.7\end{array} //]]>$.

Layer Thickness

The adjacent layers with similar Ic value compared to reference value $//<![CDATA[ \begin{array}{l}I_{\text{c_Break}}\end{array} //]]>$ ($//<![CDATA[ \begin{array}{l}I_c > I_{\text{c_Break}}\end{array} //]]>$: fine grained, $//<![CDATA[ \begin{array}{l}I_c \leq I_{\text{c_Break}}\end{array} //]]>$: coarse grained) are grouped to either fine or coarse layer and the thickness of the overall layer is calculated.

Thin Layer Correction Factor (K_H)

Thin layer correction factor is calculated for thin stiff layers lying within softer strata based on lower bound of the field curve suggested by NCEER 2001:

The soft and stiff layers are recognised based on the Ic value compared to reference value Ic Break.

     $//<![CDATA[ \begin{array}{l}H≤1000 \quad mm\end{array} //]]>$, and is calculated and stored in Transitional_Layer_Thickness on CPT_DATA_LIQUEFACTION 
     $//<![CDATA[ \begin{array}{l}d_c\end{array} //]]>$ is Cone Diameter, and is stored in the Cone_Diameter on CPT_CONE_INFORMATION.
     $//<![CDATA[ \begin{array}{l}I_c\end{array} //]]>$ is soil behaviour type index 1, NCEER, and is stored in the Soil_Behaviour_Type_Index_1_NCEER on CPT_DATA_LIQUEFACTION.
     $//<![CDATA[ \begin{array}{l}I_{\text{c_Break}}\end{array} //]]>$ Break is soil behaviour type index break point that separates sand-like behaviour from clay-like behaviour, and is stored in the Ic_Break_Point on CPT_LIQ_PROJECT_PARAMETERS and/or CPT_LIQ_POINT_PARAMETERS.

This is an indicative value and won't be used automatically to correct cone penetration resistance readings. If correction is required, user needs to do it manually as

Coefficient of Lateral Earth Pressure 1

Coefficient of lateral earth pressure in Coefficient_Lateral_Earth_Pressure_1 is taken either from Coefficient_of_Lateral_Earth_Pressure field on CPT_LIQ_PROJECT_PARAMETERS and/or CPT_LIQ_POINT_PARAMETERS or from Coefficient_Lateral_Earth_Pressure_1 / Coefficient_Lateral_Earth_Pressure_3 on CPT DATA table.

State Parameter

State parameter 1

Based on the method by Been et al. (1987), the state parameter method 1, $//<![CDATA[ \begin{array}{l}\Psi\end{array} //]]>$1, in State_Parameter_1 is calculated from:

Soil liquefaction, a critical state approach, pp. 191-193

In which:
     $//<![CDATA[ \begin{array}{l}Q_p=\left( \frac{3Q_t} {1+2K_0}\right)\end{array} //]]>$
     $//<![CDATA[ \begin{array}{l}Q_t\end{array} //]]>$  is the normalised cone resistance, and is stored in Normalised_Cone_Resistance on CPT_DATA 
      $//<![CDATA[ \begin{array}{l}K_0\end{array} //]]>$ is the coefficient of lateral earth pressure, and is stored in Coefficient_Lateral_Earth_Pressure_1 on CPT_DATA_LIQUEFACTION 
     $//<![CDATA[ \begin{array}{l}k\end{array} //]]>$  is stored in Soil_and_Rigidity_Coefficient_k 
     $//<![CDATA[ \begin{array}{l}m\end{array} //]]>$  is stored in Soil_and_Rigidity_Coefficient_m

State parameter 2

Based on the method by Shuttle and Jefferies (1998), the state parameter 2, $//<![CDATA[ \begin{array}{l}\Psi\end{array} //]]>$2, in State_Parameter_2 with constant rigidity index is calculated from:

In which:

Where:

     $//<![CDATA[ \begin{array}{l}Q_t\end{array} //]]>$  is the normalised cone resistance, and is stored in the Normalised_Cone_Resistance in CPT_DATA Table.
     $//<![CDATA[ \begin{array}{l}I_r\end{array} //]]>$  is rigidity index and is stored in Rigidity_Index field
     $//<![CDATA[ \begin{array}{l}K_0\end{array} //]]>$  is the coefficient of lateral earth pressure, and is stored in Coefficient_Lateral_Earth_Pressure_1 on CPT_DATA_LIQUEFACTION
     $//<![CDATA[ \begin{array}{l}M\end{array} //]]>$  is critical state ratio and is stored in Critical_State_Ratio field
     $//<![CDATA[ \begin{array}{l}N\end{array} //]]>$  is dilation parameter and is stored in Dilation_Parameter field
     $//<![CDATA[ \begin{array}{l}H\end{array} //]]>$  is plastic hardening modulus and is stored in Plastic_Hardening_Modulus field
     $//<![CDATA[ \begin{array}{l}\lambda\end{array} //]]>$ is slope of CSL line and is stored in Lambda field

State parameter 3

The state parameter 3, $//<![CDATA[ \begin{array}{l}\Psi\end{array} //]]>$3, in State_Parameter_3 with varying rigidity index is similar to state parameter 2 except for the rigidity index that is calculated from:

     
     $//<![CDATA[ \begin{array}{l}I_{r100}\end{array} //]]>$ is rigidity index in reference pressure and is stored in Rigidity_Index field
     $//<![CDATA[ \begin{array}{l}K_0\end{array} //]]>$ is the coefficient of lateral earth pressure, and is stored in Coefficient_Lateral_Earth_Pressure_1 on CPT_DATA_LIQUEFACTION
     $//<![CDATA[ \begin{array}{l}P_a\end{array} //]]>$ is the reference pressure (100 kPa).
     $//<![CDATA[ \begin{array}{l}\sigma'_{v0}\end{array} //]]>$ is effective vertical overburden stress in Effective_Stress on CPT_DATA Table

State parameter 4

The state parameter 4, $//<![CDATA[ \begin{array}{l}\Psi\end{array} //]]>$4, in State_Parameter_4 is defined based on the method by Plewes (1992) as:

Soil liquefaction, a critical state approach, pp. 202-204

Where:

     $//<![CDATA[ \begin{array}{l}Q_t\end{array} //]]>$  is the normalised cone resistance, and is stored in the Normalised_Cone_Resistance in CPT_DATA Table
     $//<![CDATA[ \begin{array}{l}B_q\end{array} //]]>$  is pore pressure ratio and is stored in Pore_Pressure_Ratio on CPT_DATA Table
     $//<![CDATA[ \begin{array}{l}K_0\end{array} //]]>$ is the coefficient of lateral earth pressure, and is stored in Coefficient_Lateral_Earth_Pressure_1 on CPT_DATA_LIQUEFACTION
     $//<![CDATA[ \begin{array}{l}F_r\end{array} //]]>$ is normalised friction ratio and is stored in Normalised_Friction_Ratio on CPT_DATA Table
     $//<![CDATA[ \begin{array}{l}M\end{array} //]]>$ is critical state ration and is stored in Critical_State_Ratio field

State parameter 5

The state parameter 5, $//<![CDATA[ \begin{array}{l}\Psi\end{array} //]]>$5, in State_Parameter_5 is defined based on the method by Been and Jefferies (1992) as:

Soil liquefaction, a critical state approach, pp. 202-204
Where:

     $//<![CDATA[ \begin{array}{l}Q_t\end{array} //]]>$ is the normalised cone resistance, and is stored in the Normalised_Cone_Resistance on CPT_DATA   
     $//<![CDATA[ \begin{array}{l}B_q\end{array} //]]>$  is pore pressure ratio and is stored in Pore_Pressure_Ratio on CPT_DATA Table   
     $//<![CDATA[ \begin{array}{l}K_0\end{array} //]]>$ is the coefficient of lateral earth pressure, and is stored in the Coefficient_of_Lateral_Earth_Pressure field.
     $//<![CDATA[ \begin{array}{l}I_c\end{array} //]]>$ is soil behaviour type index (method 4, Been and Jefferies 1992) and is stored in Soil_Behaviour_Type_Index_4 on CPT_DATA Table
     $//<![CDATA[ \begin{array}{l}M\end{array} //]]>$ is critical state ration and is stored in Critical_State_Ratio

Fines Content (FC)

Correlations calculated values may be overridden by a user defined profile defined in Fines_Content on CPT_POINT_MATERIAL_PROPERTIES.

Fines Content 1

Fines content 1, in Fines_Content_1 is based on the method by Robertson and Wride 1998:

     $//<![CDATA[ \begin{array}{l}I_c\end{array} //]]>$ is soil behaviour type index 1, NCEER, and is stored in the Soil_Behaviour_Type_Index_1_NCEER on CPT_DATA_LIQUEFACTION.

Fines Content 2

Fines content 2, in Fines_Content_2 is based on the method by Suzuki et al. 1998:

Soil liquefaction during earthquakes, p. 79

$//<![CDATA[ \begin{array}{l}I_c\end{array} //]]>$ is soil behaviour type index 1, NCEER, and is stored in Soil_Behaviour_Type_Index_1_NCEER on CPT_DATA_LIQUEFACTION.

Fines Content 3

Fines content 3, in Fines_Content_3 is based on the method by Boulanger and Idriss 2014:

Boulanger and Idriss (2014), CPT and SPT Based Liquefaction Triggering Procedures, p. 21

     $//<![CDATA[ \begin{array}{l}I_c\end{array} //]]>$ is soil behaviour type index 1, NCEER, and is stored in Soil_Behaviour_Type_Index_1_NCEER on CPT_DATA_LIQUEFACTION.
     $//<![CDATA[ \begin{array}{l}C_{FC}\end{array} //]]>$ is a fitting parameter that can be adjusted based on site specific data and is stored in Fines_Content_Fitting_Parameter on CPT_LIQ_POINT_PARAMETERS / CPT_LIQ_PROJECT_PARAMETERS.
     $//<![CDATA[ \begin{array}{l}C_{FC}\end{array} //]]>$ is varied between -0.29 and +0.29 with $//<![CDATA[ \begin{array}{l}C_{FC}\end{array} //]]>$=0.07 approximates the Robinson et al. (2013) relationship for liquefiable soil along the Avon river in Christchurch, New Zealand.

Bulk Unit Weight (Earthquake)

Unit Weight may be defined in two locations and are used in the order listed:

1. CPT_POINT_MATERIAL_PROPERTIES table (Point Parameters – Bottom half). This allows you to enter a depth profile. If a depth range is missing a value, then the CPT_PROJECT_PARAMETERS table is used.
2. CPT_PROJECT_PARAMETERS table. A saturated and unsaturated unit weight must be defined, the former is applied bellow the water table and the later above the water table. Water table is from either design groundwater table for earthquake from CPT_LIQ_PROJECT_PARAMETERS / CPT_LIQ_POINT_PARAMETERS or ground water depth from CPT_POINT_PARAMETERS/ CPT_PROJECT_PARAMETERS.

In-Situ Pore Pressure (Earthquake)

In-Situ Pore Pressure may be defined in two methods and are used in the order listed:

1. CPT_POINT_MATERIAL_PROPERTIES table (Point Parameters – Bottom half). This allows you to enter a depth profile.
2. The in-situ pore pressure for earthquake is calculated based on the position of design groundwater table for earthquake from CPT_LIQ_PROJECT_PARAMETERS or CPT_LIQ_POINT_PARAMETERS.

Total Stress (Earthquake)

The total stress for earthquake is calculated using bulk unit weight (earthquake). In case of a fill existence, the weight of the fill has been considered in calculation of the total stress. The total stress (earthquake) is used for calculation of cyclic stress ratio.

Effective Stress (Earthquake)

The effective stress for earthquake is calculated from total stress (earthquake) and pore pressure (earthquake). The effective stress (earthquake) is used for calculation of cyclic stress ratio.

Cyclic Stress Ratio (CSR)

Cyclic Stress Ratio 1

Cyclic stress ratio 1, in Cyclic_Stress_Ratio_1 is defined based on the relation proposed by Seed and Idriss (1971) as:

NCEER 2001, p818

Where:
     $//<![CDATA[ \begin{array}{l}PGA\end{array} //]]>$ is peak horizontal acceleration at the ground surface generated by earthquake, and is stored in Peak_Ground_Acceleration     
     $//<![CDATA[ \begin{array}{l}\sigma_{v0}\end{array} //]]>$ is total vertical overburden stress in Total_Stress on CPT_DATA_LIQUEFACTION  
     $//<![CDATA[ \begin{array}{l}\sigma'_{v0}\end{array} //]]>$ is effective vertical overburden stress calculated from design groundwater depth for earthquake, bulk and saturated unit weights, and stored in Effective_Stress on CPT_DATA_LIQUEFACTION Table
     $//<![CDATA[ \begin{array}{l}r_d\end{array} //]]>$ is the stress reduction coefficient. T. F. Blake (1996) approximated the mean values of $//<![CDATA[ \begin{array}{l}r_d\end{array} //]]>$ as:

     $//<![CDATA[ \begin{array}{l}z\end{array} //]]>$=depth below ground surface+fill height

Cyclic Stress Ratio 2

Cyclic stress ratio method 2, in Cyclic_Stress_Ratio_2 is defined based on the relation proposed by Idriss and Boulanger (2008) as:

Soil liquefaction during earthquakes, p. 68

Where:
     $//<![CDATA[ \begin{array}{l}PGA\end{array} //]]>$ is peak horizontal acceleration at the ground surface generated by earthquake, and is stored in Peak_Ground_Acceleration
     $//<![CDATA[ \begin{array}{l}\sigma_{v0}\end{array} //]]>$ is total vertical overburden stress in Total_Stress on CPT_DATA_LIQUEFACTION
     $//<![CDATA[ \begin{array}{l}\sigma'_{v0}\end{array} //]]>$ is effective vertical overburden stress calculated from design groundwater depth for earthquake, bulk and saturated unit weights, and stored in Effective_Stress on CPT_DATA_LIQUEFACTION Table

     $//<![CDATA[ \begin{array}{l}M\end{array} //]]>$ is the Earthquake magnitude and is stored in Earthquake_Magnitude
     $//<![CDATA[ \begin{array}{l}z\end{array} //]]>$=depth below ground surface+fill height

Cyclic Stress Ratio 3

Cyclic stress ratio method 3 is calculated from normalised shear wave velocity as

Moss et al. (2006)

Where: 

     $//<![CDATA[ \begin{array}{l}PGA\end{array} //]]>$ is peak horizontal acceleration at the ground surface generated by earthquake, and is stored in Peak_Ground_Acceleration 
     $//<![CDATA[ \begin{array}{l}\sigma_{v0}\end{array} //]]>$ is total vertical overburden stress in Total_Stress on CPT_DATA_LIQUEFACTION 
     $//<![CDATA[ \begin{array}{l}\sigma'_{v0}\end{array} //]]>$ is effective vertical overburden stress calculated from design groundwater depth for earthquake, bulk and saturated unit weights, and stored in Effective_Stress on CPT_DATA_LIQUEFACTION Table

     $//<![CDATA[ \begin{array}{l}M\end{array} //]]>$ is the Earthquake magnitude and is stored in Earthquake_Magnitude
     $//<![CDATA[ \begin{array}{l}z\end{array} //]]>$=depth below ground surface+fill height

Cyclic Stress Ratio 4

Cyclic stress ratio method 4 is calculated from normalised shear wave velocity as

Kayen et al (2013), p. 411

Where:

     $//<![CDATA[ \begin{array}{l}PGA\end{array} //]]>$ is peak horizontal acceleration at the ground surface generated by earthquake, and is stored in Peak_Ground_Acceleration 
     $//<![CDATA[ \begin{array}{l}\sigma_{v0}\end{array} //]]>$ is total vertical overburden stress in Total_Stress on CPT_DATA_LIQUEFACTION 
     $//<![CDATA[ \begin{array}{l}\sigma'_{v0}\end{array} //]]>$ is effective vertical overburden stress calculated from design groundwater depth for earthquake, bulk and saturated unit weights, and stored in Effective_Stress on CPT_DATA_LIQUEFACTION Table
     $//<![CDATA[ \begin{array}{l}M\end{array} //]]>$ is the Earthquake magnitude and is stored in Earthquake_Magnitude
     $//<![CDATA[ \begin{array}{l}z\end{array} //]]>$=depth below ground surface+fill height
     $//<![CDATA[ \begin{array}{l}V^*_{s,12m}\end{array} //]]>$ is the average shear wave velocity in the upper 12.2m (40 ft) of the soil column
     $//<![CDATA[ \begin{array}{l}z\end{array} //]]>$=depth below ground surface+fill height

Overburden Correction Factor

Overburden Correction Factor 1 ($//<![CDATA[ \begin{array}{l}C_q\end{array} //]]>$)

Overburden correction factor 1 is calculated from method by Robertson and Wride (1998)/NCEER (2001) as:

     $//<![CDATA[ \begin{array}{l}n\end{array} //]]>$ is Stress Exponent and is stored in Stress_Exponent on CPT_DATA_LIQUEFACTION.

Overburden Correction Factor 2 ($//<![CDATA[ \begin{array}{l}C_N\end{array} //]]>$)

Overburden correction factor 2 is calculated from method by Idriss and Boulanger (2008) as:

Four iterations are carried out. The first iteration assumes $//<![CDATA[ \begin{array}{l}C_N=\left(\frac{P_a}{\sigma'_{v0}}\right )^m\end{array} //]]>$ and m is taken as 0.5.
Soil liquefaction during earthquakes, p. 87.

Overburden Correction Factor 3 ($//<![CDATA[ \begin{array}{l}C_q\end{array} //]]>$)

Overburden correction factor 3 is calculated from method by Moss et al. (2006) as:

     $//<![CDATA[ \begin{array}{l}q_c\end{array} //]]>$ is normalised tip resistance $//<![CDATA[ \begin{array}{l}q_{c1}=C_q q_c\end{array} //]]>$. Three iterations are carried out.

Overburden Correction Factor 4 (Cvs)

Overburden correction factor 4 is calculated from method by Kayen et al. (2013) as:

Normalised Cone Resistance, (q_c1N)

Normalised Cone Resistance 1

$//<![CDATA[ \begin{array}{l}q_{c1N}\end{array} //]]>$ is calculated as:

NCEER 2001, p. 301

Normalised Cone Resistance 2

$//<![CDATA[ \begin{array}{l}q_{c1N}\end{array} //]]>$ is calculated from $//<![CDATA[ \begin{array}{l}C_N\end{array} //]]>$ as:

Four Iterations has been carried out between $//<![CDATA[ \begin{array}{l}q_{c1N}\end{array} //]]>$ and $//<![CDATA[ \begin{array}{l}C_N\end{array} //]]>$ to find final solution.
Soil liquefaction during earthquakes, p. 85, 88

Normalised Cone Resistance 3 ($//<![CDATA[ \begin{array}{l}q_{c1}\end{array} //]]>$)

$//<![CDATA[ \begin{array}{l}q_{c1N}\end{array} //]]>$ is calculated as:

Moss et al. (2006)

Normalised Shear Wave Velocity (V_s1)

Normalised shear wave velocity method 1 is calculated from shear wave velocity as:

Kayen et al. (2013), p. 411

$//<![CDATA[ \begin{array}{l}V_s\end{array} //]]>$ is referenced from CPT_DATA.Shear_Wave_Velocity_Extrapolated

Clean-Sand Equivalent Normalised Cone Resistance (q_c1N)_cs

Clean-Sand Equivalent Normalised Cone Resistance 1

The clean-sand equivalent normalised cone resistance 1, in qc1N_cs_1 is calculated by the following equation:

Robertson and Wride (1998), NCEER 2001 pp. 822-823

Where, 
     For $//<![CDATA[ \begin{array}{l}I_c\leq1.64, \quad K_c=1.0\end{array} //]]>$
     For $//<![CDATA[ \begin{array}{l}I_c>1.64, \quad K_c=-0.403I_c^4+5.581I_c^3-21.63I_c^2+33.75I_c-17.88\end{array} //]]>$
     If $//<![CDATA[ \begin{array}{l}1.64< I_c< 2.36\end{array} //]]>$ and $//<![CDATA[ \begin{array}{l}F_r\leq0.5, \quad K_c=1.0\end{array} //]]>$
     $//<![CDATA[ \begin{array}{l}q_{c1N}\end{array} //]]>$ is normalised cone resistance in qc1N_1 on CPT_DATA_ LIQUEFACTION

The stress exponent $//<![CDATA[ \begin{array}{l}n\end{array} //]]>$ in Stress_Exponent and $//<![CDATA[ \begin{array}{l}P_a\end{array} //]]>$ is a reference pressure (100 kPa).

Clean-Sand Equivalent Normalised Cone Resistance 2

The clean-sand equivalent normalised cone resistance 2, in qc1N_cs_2 based on method by Idriss and Boulanger (2008) is defined as:

Soil liquefaction during earthquakes, pp. 84-89 and 111

Where:
     $//<![CDATA[ \begin{array}{l}q_{c1N}\end{array} //]]>$ is normalised cone resistance in qc1N_2 on CPT_DATA_ LIQUEFACTION
     $//<![CDATA[ \begin{array}{l}FC\end{array} //]]>$ is the fine content 2 in Fines_Content_2 on CPT_DATA_LIQUEFACTION

Clean-Sand Equivalent Normalised Cone Resistance 3

The clean-sand equivalent normalised cone resistance 3, in qc1N_cs_3, is similar to clean-sand equivalent normalised cone resistance 2, with the fines content from Fines_Content_1 (Robertson and Wride, 1998).

Clean-Sand Equivalent Normalised Cone Resistance 4

The clean-sand equivalent normalised cone resistance 4, in qc1N_cs_4, based on method by Idriss and Boulanger (2008), using the corrections recommended by Seed 1987, is defined as:

The Corrections due to fines content are as per below table:

Soil liquefaction during earthquakes, p. 131

Where:
     $//<![CDATA[ \begin{array}{l}q_{c1N}\end{array} //]]>$ is normalised cone resistance in qc1N_2 on CPT_DATA_ LIQUEFACTION 
     $//<![CDATA[ \begin{array}{l}FC\end{array} //]]>$ is the fines content 2 in Fines_Content_2 on CPT_DATA_LIQUEFACTION

Clean-Sand Equivalent Normalised Cone Resistance 5

The clean-sand equivalent normalised cone resistance 5, in qc1N_cs_5 based on method by Boulanger and Idriss (2014) is defined as:

Boulanger and Idriss (2014), CPT and SPT Based Liquefaction Triggering Procedures, p. 15

Where:
     $//<![CDATA[ \begin{array}{l}q_{c1N}\end{array} //]]>$ is normalised cone resistance in qc1N_2 on CPT_DATA_ LIQUEFACTION 
     $//<![CDATA[ \begin{array}{l}FC\end{array} //]]>$ is the fine content 3 in Fines_Content_3 on CPT_DATA_LIQUEFACTION

Modified Normalised CPT Cone Resistance (q_c1-mod)

Modified normalised CPT tip resistance for the frictoinal effects of apparent fines, (method by Moss et al., 2006), 

Ciclicic Resistance Ratio (CRR)

Cyclic Resistance Ratio 1

The clean-sand based cyclic resistance ratio method 1, in Cyclic_Resistance_Ratio_1 method by Robertson and Wride (1998), for sand-like behaviour (Ic≤Ic Break) for standard earthquake of magnitude 7.5 is calculated by:

Robertson and Wride (1998), NCEER 2001 pp. 822-823
Idriss & Boulanger 2008, Soil liquefaction during earthquakes, pp. 199

Where:
     $//<![CDATA[ \begin{array}{l}(q_{c1N})_{CS}\end{array} //]]>$ is the clean-sand equivalent normalised cone resistance 1, in qc1N_cs_1 on CPT_DATA_LIQUEFACTION 
     $//<![CDATA[ \begin{array}{l}I_c\end{array} //]]>$ is soil behaviour type index 1, NCEER, and is stored in Soil_Behaviour_Type_Index_1_NCEER on CPT_DATA_LIQUEFACTION.
     $//<![CDATA[ \begin{array}{l}I_{cBreak}\end{array} //]]>$ is soil behaviour type index break point that separates sand-like behaviour from clay-like behaviour, and is stored in Ic_Break_Point on CPT_LIQ_PROJECT_PARAMETERS and/or CPT_LIQ_POINT_PARAMETERS.

Cyclic Resistance Ratio 2

Cyclic resistance ratio 2, in Cyclic_Resistance_Ratio_2 for standard earthquake of magnitude 7.5, is based on critical state approach for sand-like behaviour ($//<![CDATA[ \begin{array}{l}I_c\leq I_{cBreak}\end{array} //]]>$) and calculated from:

Jefferies & Been 2006, Soil liquefaction, a critical state approach, p 395

Idriss & Boulanger 2008, Soil liquefaction during earthquakes, pp. 199

Where:
     $//<![CDATA[ \begin{array}{l}\Psi\end{array} //]]>$ is state parameter and is by default is set to method 1 which is stored in State_Parameter_1 in CPT_DATA_LIQUEFACTION Table. The default method is in Cyclic_Resistance_Ratio_2_Y_Method in LIQUIFACTION_PROJECT_PARAMETERS table
     $//<![CDATA[ \begin{array}{l}a\end{array} //]]>$ is 0.03 and stored in Cyclic_Resistance_Ratio_2_a in LIQUIFACTION_PROJECT_PARAMETERS table
     $//<![CDATA[ \begin{array}{l}b\end{array} //]]>$ is -11 and stored in Cyclic_Resistance_Ratio_2_b in LIQUIFACTION_PROJECT_PARAMETERS table
     $//<![CDATA[ \begin{array}{l}I_c\end{array} //]]>$ is soil behaviour type index 1, NCEER, and is stored in the Soil_Behaviour_Type_Index_1_NCEER on CPT_DATA_LIQUEFACTION.
     $//<![CDATA[ \begin{array}{l}I_{cBreak}\end{array} //]]>$ is soil behaviour type index break point that separates sand-like behaviour from clay-like behaviour, and is stored in the Ic_Break_Point on CPT_LIQ_PROJECT_PARAMETERS and/or CPT_LIQ_POINT_PARAMETERS.

Cyclic Resistance Ratio 3

The cyclic resistance ratio method 3, in Cyclic_Resistance_Ratio_3 for standard earthquake of magnitude 7.5 is calculated by:

Idriss & Boulanger 2008, Soil liquefaction during earthquakes, pp. 95, 100 and 199

Where:
     $//<![CDATA[ \begin{array}{l}(q_{c1N})_{CS}\end{array} //]]>$ is the clean-sand equivalent normalised cone resistance 2 and is stored in qc1N_cs_2 on CPT_DATA_LIQUEFACTION. 
     _{$//<![CDATA[ \begin{array}{l}OCR\end{array} //]]>$}  is taken from Overconsolidation_Ratio_1 or Overconsolidation_Ratio_5 
     $//<![CDATA[ \begin{array}{l}I_c\end{array} //]]>$ is soil behaviour type index 1, NCEER, and is stored in the Soil_Behaviour_Type_Index_1_NCEER on CPT_DATA_LIQUEFACTION.
     $//<![CDATA[ \begin{array}{l}I_{cBreak}\end{array} //]]>$ is soil behaviour type index break point that separates sand-like behaviour from clay-like behaviour, and is stored in the Ic_Break_Point on CPT_LIQ_PROJECT_PARAMETERS and/or CPT_LIQ_POINT_PARAMETERS.

Cyclic Resistance Ratio 4

The cyclic resistance ratio method 4 in Cyclic_Resistance_Ratio_4 is similar to cyclic resistance ratio method 3 with $//<![CDATA[ \begin{array}{l}(q_{c1N})_{CS}\end{array} //]]>$ from qc1N_cs_3 on CPT_DATA_LIQUEFACTION.

Cyclic Resistance Ratio 5

Cyclic resistance ratio method 5 is calculated from normalised shear wave velocity as:

Moss et al. (2006),

Where:
     $//<![CDATA[ \begin{array}{l}\Phi\end{array} //]]>$ is the cumulative normal distribution
     $//<![CDATA[ \begin{array}{l}P_L\end{array} //]]>$=15% is the probability of liquefaction
     $//<![CDATA[ \begin{array}{l}\Phi^{-1}(P_L)=\Phi^{-1}(0.15)=-1.036433732\end{array} //]]>$

Cyclic Resistance Ratio 6

Cyclic resistance ratio method 6 is calculated from normalised shear wave velocity as:

Kayen et al. (2013), p. 413

Where:
     $//<![CDATA[ \begin{array}{l}\Phi\end{array} //]]>$ is the cumulative normal distribution
     $//<![CDATA[ \begin{array}{l}P_L\end{array} //]]>$=15% is the probability of liquefaction
     $//<![CDATA[ \begin{array}{l}\Phi^{-1}(P_L)=\Phi^{-1}(0.15)=-1.036433732\end{array} //]]>$

Cyclic Resistance Ratio 7

The cyclic resistance ratio method 7, in Cyclic_Resistance_Ratio_7 for standard earthquake of magnitude 7.5 is calculated by:

Boulanger and Idriss (2014), CPT and SPT Based Liquefaction Triggering Procedures, p. 17

Where:
     $//<![CDATA[ \begin{array}{l}(q_{c1N})_{CS}\end{array} //]]>$ is the clean-sand equivalent normalised cone resistance 5 and is stored in qc1N_cs_5 on CPT_DATA_LIQUEFACTION. 
     $//<![CDATA[ \begin{array}{l}OCR\end{array} //]]>$ is taken from Overconsolidation_Ratio_1 or Overconsolidation_Ratio_5 
     $//<![CDATA[ \begin{array}{l}I_c\end{array} //]]>$ is soil behaviour type index 1, NCEER, and is stored in the Soil_Behaviour_Type_Index_1_NCEER on CPT_DATA_LIQUEFACTION.
     $//<![CDATA[ \begin{array}{l}I_{cBreak}\end{array} //]]>$ is soil behaviour type index break point that separates sand-like behaviour from clay-like behaviour, and is stored in the Ic_Break_Point on CPT_LIQ_PROJECT_PARAMETERS and/or CPT_LIQ_POINT_PARAMETERS.

Factor of Safety (FoS)

Factor of Safety 1

The factor of safety method 1, in Factor_of_Safety_1 for depths greater than design ground water depth is defined as:
For sand like behaviour ($//<![CDATA[ \begin{array}{l}I_c\leq I_{cBreak}\end{array} //]]>$)

NCEER 2001, p 828

Where:

For clay like behaviour ($//<![CDATA[ \begin{array}{l}I_c>I_{cBreak}\end{array} //]]>$)

Soil liquefaction during earthquakes, pp. 193, 199-200
     $//<![CDATA[ \begin{array}{l}CRR\end{array} //]]>$ is the cyclic resistance ratio method 1 and is stored in Cyclic_Resistance_Ratio_1 
     $//<![CDATA[ \begin{array}{l}CSR\end{array} //]]>$ is the cyclic stress ratio 1 and is stored in Cyclic_Stress_Ratio_1 
     $//<![CDATA[ \begin{array}{l}\sigma'_{v0}\end{array} //]]>$ is the effective vertical overburden stress in Effective_Stress on CPT_DATA 
     $//<![CDATA[ \begin{array}{l}P_a\end{array} //]]>$ is the reference pressure (100 kPa)
     $//<![CDATA[ \begin{array}{l}f\end{array} //]]>$ is the overburden correction factor exponent, a function of site conditions, including relative density, stress history, aging, and overconsolidation ratio. For relative densities between 40 and 60%, $//<![CDATA[ \begin{array}{l}f\end{array} //]]>$ = 0.7 - 0.8; for relative densities between 60% and 80%, $//<![CDATA[ \begin{array}{l}f\end{array} //]]>$ = 0.6 - 0.7 
     $//<![CDATA[ \begin{array}{l}M\end{array} //]]>$ is the earthquake magnitude and is stored in Earthquake_Magnitude 
     $//<![CDATA[ \begin{array}{l}K_{\alpha}\end{array} //]]>$ is the correction factor for sloping ground and is stored in Correction_Factor_for_Sloping_Ground 

For thin fine/coarse layers, layers with thickness less than Minimum_Layer_Thickness on CPT_Liq_ Point Parameters/CPT_Liq Project _Parameter table, the FOS of first upper thick layer is used.

Factor of Safety 2

The factor of safety method 2, in Factor_of_Safety_2 for depths greater than design ground water depth is defined as:
For sand like behaviour ($//<![CDATA[ \begin{array}{l}I_c\leq I_{cBreak}\end{array} //]]>$)

NCEER 2001, p 828

Where:

For clay like behaviour ($//<![CDATA[ \begin{array}{l}I_c>I_{cBreak}\end{array} //]]>$)

Soil liquefaction during earthquakes, pp. 193, 199-200

     $//<![CDATA[ \begin{array}{l}CRR\end{array} //]]>$ is the cyclic resistance ratio method 2 and is stored in Cyclic_Resistance_Ratio_2 
     $//<![CDATA[ \begin{array}{l}CSR\end{array} //]]>$ is the cyclic stress ratio 1 and is stored in Cyclic_Stress_Ratio_1 
     $//<![CDATA[ \begin{array}{l}\sigma'_{v0}\end{array} //]]>$ is the effective vertical overburden stress in Effective_Stress on CPT_DATA 
     $//<![CDATA[ \begin{array}{l}P_a\end{array} //]]>$ is the reference pressure (100 kPa)
     $//<![CDATA[ \begin{array}{l}f\end{array} //]]>$ is the overburden correction factor exponent, a function of site conditions, including relative density, stress history, aging, and overconsolidation ratio. For relative densities between 40 and 60%, $//<![CDATA[ \begin{array}{l}f\end{array} //]]>$ = 0.7 - 0.8; for relative densities between 60% and 80%, $//<![CDATA[ \begin{array}{l}f\end{array} //]]>$ = 0.6 - 0.7 
     $//<![CDATA[ \begin{array}{l}M\end{array} //]]>$ is the earthquake magnitude and is stored in Earthquake_Magnitude 
     $//<![CDATA[ \begin{array}{l}K_{\alpha}\end{array} //]]>$ is the correction factor for sloping ground and is stored in Correction_Factor_for_Sloping_Ground 

For thin fine/coarse layers, layers with thickness less than Minimum_Layer_Thickness on CPT_Liq_ Point Parameters/CPT_Liq Project _Parameter table, the FOS of first upper thick layer is used.

Factor of Safety 3

The factor of safety method 3, in Factor_of_Safety_3 is defined as:
For sand like behaviour ($//<![CDATA[ \begin{array}{l}I_c\leq I_{cBreak}\end{array} //]]>$)

Soil liquefaction during earthquakes, pp. 93-102
For clay like behaviour ($//<![CDATA[ \begin{array}{l}I_c>I_{cBreak}\end{array} //]]>$)

Soil liquefaction during earthquakes, pp. 193, 199-200

Where:
     $//<![CDATA[ \begin{array}{l}CRR\end{array} //]]>$ is the cyclic resistance ratio method 3, and is stored in Cyclic_Resistance_Ratio_3 
     $//<![CDATA[ \begin{array}{l}CSR\end{array} //]]>$ is the cyclic stress ratio method 2 and is stored in Cyclic_Stress_Ratio_2 
     $//<![CDATA[ \begin{array}{l}M\end{array} //]]>$ is the earthquake magnitude and is stored in Earthquake_Magnitude 
     $//<![CDATA[ \begin{array}{l}K_{\alpha}\end{array} //]]>$ is the correction factor for sloping ground and is stored in Correction_Factor_for_Sloping_Ground
     $//<![CDATA[ \begin{array}{l}\sigma'_{v0}\end{array} //]]>$ is effective vertical overburden stress in Effective_Stress on CPT_DATA 

For thin fine/coarse layers, layers with thickness less than Minimum_Layer_Thickness on CPT_Liq_ Point _Parameters / CPT_Liq_ Project _Parameters tables, the FOS of first upper thick layer is used.

Factor of Safety 4

The factor of safety method 4, in Factor_of_Safety_4 is similar to factor of safety method 3 with CRR from Cyclic_Resistance_Ratio_4. This follows the procedure defined by New Zealand Department of Building and Housing, Interim guidance for repairing and rebuilding foundations in Technical Category 3, Appendix C to the Guidance Document: Revised guidance on repairing and rebuilding houses affected by the Canterbury earthquake sequence (November 2011).

Factor of Safety 5

Factor of safety method 5 is calculated from CRR 5 and CSR 3 as

Moss et al. (2006)

For thin fine/coarse layers, layers with thickness less than Minimum_Layer_Thickness on CPT_Liq_ Point Parameters/CPT_Liq Project _Parameter table, the FOS of first upper thick layer is used.

Factor of Safety 6

Factor of safety method 6 is calculated from CRR 6 and CSR 4 based on shear wave velocity assessment as

Kayen et al. (2013), p. 414

For thin fine/coarse layers, layers with thickness less than Minimum_Layer_Thickness on CPT_Liq_ Point Parameters/CPT_Liq Project _Parameter table, the FOS of first upper thick layer is used.

Factor of Safety 7

The factor of safety method 7, in Factor_of_Safety_7 is defined as:
For sand like behaviour ($//<![CDATA[ \begin{array}{l}I_c\leq I_{cBreak}\end{array} //]]>$)

Soil liquefaction during earthquakes, pp. 93-102

For clay like behaviour ($//<![CDATA[ \begin{array}{l}I_c>I_{cBreak}\end{array} //]]>$)

Boulanger and Idriss (2014), CPT and SPT Based Liquefaction Triggering Procedures, pp. 11-14

Where:

     $//<![CDATA[ \begin{array}{l}CRR\end{array} //]]>$ is the cyclic resistance ratio method 7, and is stored in Cyclic_Resistance_Ratio_7 
    $//<![CDATA[ \begin{array}{l}CSR\end{array} //]]>$ is the cyclic stress ratio method 2 and is stored in Cyclic_Stress_Ratio_2 
    $//<![CDATA[ \begin{array}{l}(q_{c1N})_{CS}\end{array} //]]>$ is the clean-sand equivalent normalised cone resistance 5 and is stored in qc1N_cs_5 on CPT_DATA_LIQUEFACTION. 
    $//<![CDATA[ \begin{array}{l}M\end{array} //]]>$ is the earthquake magnitude and is stored in Earthquake_Magnitude 
    $//<![CDATA[ \begin{array}{l}K_{\alpha}\end{array} //]]>$ is the correction factor for sloping ground and is stored in Correction_Factor_for_Sloping_Ground
    $//<![CDATA[ \begin{array}{l}\sigma'_{v0}\end{array} //]]>$ is effective vertical overburden stress in Effective_Stress on CPT_DATA  

For thin fine/coarse layers, layers with thickness less than Minimum_Layer_Thickness on CPT_Liq_ Point Parameters/CPT_Liq Project _Parameter table, the FOS of first upper thick layer is used.

Liquefaction Potential Index (LPI)

Liquefaction Potential Index 1

Liquefaction potential index method 1 which predicts the potential of liquefaction to cause foundation damage at a site is calculated from factor of safety 1 as:

Toprak and Holzer (2003).

Liquefaction Potential Index 2

Liquefaction potential index method 2 is similarly calculated from factor of safety 3.

Normalised Residual Shear Strength (S_r/σ'_v0)

Normalised Residual Shear Strength 1

Residual shear strength 1 in Residual_Shear_Stregth_1 is defined as:

Soil liquefaction, a critical state approach, p 324

Where:
     $//<![CDATA[ \begin{array}{l}Q_t\end{array} //]]>$ is the normalised cone resistance, and is stored in the Normalised_Cone_Resistance on CPT_DATA 
     $//<![CDATA[ \begin{array}{l}\sigma'_{v0}\end{array} //]]>$ is effective vertical overburden stress in Effective_Stress on CPT_DATA 
     $//<![CDATA[ \begin{array}{l}a\end{array} //]]>$ and $//<![CDATA[ \begin{array}{l}b\end{array} //]]>$ are best fit constants equal to 0.03 and 0.1, respectively
     $//<![CDATA[ \begin{array}{l}I_r\end{array} //]]>$ is rigidity index and is stored in Rigidity_Index 
     $//<![CDATA[ \begin{array}{l}M\end{array} //]]>$ is critical state ration and is stored in Critical_State_Ratio 
     $//<![CDATA[ \begin{array}{l}N\end{array} //]]>$ is dilation parameter and is stored in Dilation_Parameter 
     $//<![CDATA[ \begin{array}{l}H\end{array} //]]>$ is plastic hardening modulus and is stored in Plastic_Hardening_Modulus 
     $//<![CDATA[ \begin{array}{l}\lambda\end{array} //]]>$ is slope of CSL line and is stored in Lambda

Normalised Residual Shear Strength 2

Residual shear strength 2 in Residual_Shear_Stregth_2, for negligible void redistribution effects, is defined as:

Soil liquefaction during earthquakes, p. 131

Where:
     $//<![CDATA[ \begin{array}{l}(q_{c1N})_{CS}\end{array} //]]>$ is the clean-sand equivalent normalised cone resistance 4, in qc1N_cs_4 on CPT_DATA_LIQUEFACTION 
     $//<![CDATA[ \begin{array}{l}\sigma'_{v0}\end{array} //]]>$ is effective vertical overburden stress in Effective_Stress on CPT_DATA 
     $//<![CDATA[ \begin{array}{l}\Phi'\end{array} //]]>$ taken from Residual_Friction_Angle on CPT_LIQ_PROJECT_PARAMETERS or CPT_LIQ_POINT_PARAMETERS

Normalised Residual Shear Strength 3

Residual shear strength 3 in Residual_Shear_Stregth_3, for significant void redistribution effects, is defined as:

Soil liquefaction during earthquakes, p. 132
Where:
     $//<![CDATA[ \begin{array}{l}(q_{c1N})_{CS}\end{array} //]]>$ is the clean-sand equivalent normalised cone resistance 4, in qc1N_cs_4 on CPT_DATA_LIQUEFACTION 
     $//<![CDATA[ \begin{array}{l}\sigma'_{v0}\end{array} //]]>$ is effective vertical overburden stress in Effective_Stress on CPT_DATA 
     $//<![CDATA[ \begin{array}{l}\Phi'\end{array} //]]>$ taken from Residual_Friction_Angle on CPT_LIQ_PROJECT_PARAMETERS or CPT_LIQ_POINT_PARAMETERS

Normalised Residual Shear Strength 4

Residual shear strength 4 in Residual_Shear_Stregth_4, method by Olson and Stark (2002) is defined as:

Where:
     $//<![CDATA[ \begin{array}{l}\sigma'_{v0}\end{array} //]]>$ is effective vertical overburden stress in Effective_Stress on CPT_DATA
     $//<![CDATA[ \begin{array}{l}P_a\end{array} //]]>$ is the reference pressure (100 kPa)

Relative Density, (D_r)

Relative density method by Tatsouka et al. (1990) to calculate maximum shear strain 2 is calculated as:

Zhang et al. (2004), p. 862

Where:
     $//<![CDATA[ \begin{array}{l}q_{c1N}\end{array} //]]>$ is normalised cone resistance method 1 on CPT_DATA_LIQ

Maximum Shear Strain, (γ_max)

Maximum Shear Strain 1

Maximum shear strain method 1 in Maximum_Shear_Strain_1, is calculated based on the method by Idriss and Boulanger (2008):

Soil liquefaction during earthquakes, pp. 141-142

Where:
     $//<![CDATA[ \begin{array}{l}FS_{liq}\end{array} //]]>$ is the factor of safety, and is stored in Factor_of_Safety_3 on CPT_DATA_LIQUEFACTION 
     $//<![CDATA[ \begin{array}{l}(q_{c1N})_{CS}\end{array} //]]>$ is the clean-sand equivalent normalised cone resistance 2, in qc1N_cs_2 on CPT_DATA_LIQUEFACTION

Maximum Shear Strain 2

Maximum shear strain method 2 in Maximum_Shear_Strain_2, is calculated based on the method by Zhang et al. (2004):

Where:

     $//<![CDATA[ \begin{array}{l}FoS\end{array} //]]>$FoS is the factor of safety method 1 in Factor_of_Safety_1 on CPT_DATA_LIQUEFACTION 
     $//<![CDATA[ \begin{array}{l}D_r\end{array} //]]>$ is the relative density method 1 in Relative_Density_1 on CPT_DATA_LIQUEFACTION

Lateral Displacement Index (LDI)

Lateral displacement index (LDI), is calculated by integrating maximum shear strains versus depth,

Soil liquefaction during earthquakes, p. 140 and 142

The maximum shear strain is in Maximum_Shear_Strain_2 and limited to 0.5 in calculating the LDI. (p. 142, 1^st paragraph)

Lateral Displacement (LD)

Lateral Displacement 1

The lateral displacement 1, in Lateral_Displacement_1, method by Youd et al (2002), for gently sloping ground conditions, is defined as,

Where:

     $//<![CDATA[ \begin{array}{l}M\end{array} //]]>$ is the earthquake magnitude ($//<![CDATA[ \begin{array}{l}6< M< 8\end{array} //]]>$) and is stored in Earthquake_Magnitude 
     $//<![CDATA[ \begin{array}{l}R\end{array} //]]>$ is the nearest horizontal or map distance from the site to the seismic energy source, in kilometres, and is stored in Hor_Dist_To_Earthquake_Source 
     $//<![CDATA[ \begin{array}{l}S\end{array} //]]>$ is the ground slope, in percent, ($//<![CDATA[ \begin{array}{l}0.1< S (\text %)< 6\end{array} //]]>$) and is stored in Ground_Slope 
     $//<![CDATA[ \begin{array}{l}T_{15}\end{array} //]]>$ is the cumulative thickness of saturated granular layers with corrected blow counts, $//<![CDATA[ \begin{array}{l}(N_1)_{60}\end{array} //]]>$, less than 15, ($//<![CDATA[ \begin{array}{l}1< T_{15}(m)< 15\end{array} //]]>$), and is stored in Cumulative_Thickness_SPTN_15 
     $//<![CDATA[ \begin{array}{l}F_{15}\end{array} //]]>$ is the average fines content for granular materials included within T15and is stored in Average_Fines_Content_SPTN_15 
     $//<![CDATA[ \begin{array}{l}D50_{15}\end{array} //]]>$ is the average mean grain size for granular materials within $//<![CDATA[ \begin{array}{l}T_{15}\end{array} //]]>$ and is stored in Average_Mean_Grain_Size

Lateral Displacement 2

The lateral displacement 2, in Lateral_Displacement_2, method by Youd et al (2002), for free face conditions, is defined as,

 Where:

     $//<![CDATA[ \begin{array}{l}M\end{array} //]]>$ is the earthquake magnitude ($//<![CDATA[ \begin{array}{l}6< M< 8\end{array} //]]>$) and is stored in Earthquake_Magnitude 
     $//<![CDATA[ \begin{array}{l}R\end{array} //]]>$ is the nearest horizontal or map distance from the site to the seismic energy source, in kilometres, and is stored in Hor_Dist_To_Earthquake_Source 
     $//<![CDATA[ \begin{array}{l}W\end{array} //]]>$ is the free-face ratio defined as the height of the free face devided by the distance ($//<![CDATA[ \begin{array}{l}1< W( \text %)< 20\end{array} //]]>$) and is stored in Free_Face_Ratio 
     $//<![CDATA[ \begin{array}{l}T_{15}\end{array} //]]>$ is the cumulative thickness of saturated granular layers with corrected blow counts, $//<![CDATA[ \begin{array}{l}(N_1)_{60}\end{array} //]]>$, less than 15, ($//<![CDATA[ \begin{array}{l}1< T_{15}(m)< 15\end{array} //]]>$) and is stored in Cumulative_Thickness_SPTN_15 
     $//<![CDATA[ \begin{array}{l}F_{15}\end{array} //]]>$ is the  average fines content for granular materials included within T15 and is stored in Average_Fines_Content_SPTN_15 
     $//<![CDATA[ \begin{array}{l}D50_{15}\end{array} //]]>$ is the average mean grain size for granular materials within $//<![CDATA[ \begin{array}{l}T_{15}\end{array} //]]>$ and is stored in Average_Mean_Grain_Size

Lateral Displacement 3

The lateral displacement 3, in Lateral_Displacement_3, method by Zhang et al (2004), for gently sloping ground conditions, is defined as,

Where:

     $//<![CDATA[ \begin{array}{l}S\end{array} //]]>$ is ground slope in Ground_Slope on CPT_LIQ_PROJECT_PARAMETERS or CPT_LIQ_POINT_PARAMETERS

Lateral Displacement 4

The lateral displacement 4, in Lateral_Displacement_4, method by Zhang et al (2004), for free face conditions, is defined as,

Where:

     $//<![CDATA[ \begin{array}{l}W\end{array} //]]>$ is the free-face ratio defined as the height of the free face divided by the distance and is stored in Free_Face_Ratio on CPT_LIQ_PROJECT_PARAMETERS or CPT_LIQ_POINT_PARAMETERS

Post Liquefaction Volumetric Strain, ε_v

Post Liquefaction Volumetric Strain 1

Post liquefaction volumetric strain 1, in Post_Liq_Volumetric_Strain_1, for saturated sands method by Yoshimine et al. (2006), is calculated as:

Soil liquefaction during earthquakes, p. 153

For dry sands, method by Pradel (1998) as:

Where:

     $//<![CDATA[ \begin{array}{l}K_0\end{array} //]]>$ is the coefficient of lateral earth pressure, and is stored in Coefficient_Lateral_Earth_Pressure_1 on CPT_DATA_LIQUEFACTION 
     $//<![CDATA[ \begin{array}{l}(q_{c1N})_{CS}\end{array} //]]>$ is the clean-sand equivalent normalised cone resistance 2, in qc1N_cs_2 on CPT_DATA_LIQUEFACTION 
     $//<![CDATA[ \begin{array}{l}N_1\end{array} //]]>$ is the corrected SPT N value normalised to an effective overburden of 100 kPa and to an effective energy of 60% of the free-fall energy, in SPT_N60_1 on CPT_DATA

Post Liquefaction Volumetric Strain 2

Post liquefaction volumetric strain 2, in Post_Liq_Volumetric_Strain_2, for saturated sands method by Zhang et al. (2002), is calculated as,

Can. Geotech. J. Vol. 39, 2002, p. 1180

For dry sands, similar to post liquefaction volumetric strain 1 based on method by Pradel (1998).
Where: 
     $//<![CDATA[ \begin{array}{l}FS\end{array} //]]>$ is the factor of safety, and is stored in Factor_of_Safety_4 on CPT_DATA_LIQUEFACTION 
     $//<![CDATA[ \begin{array}{l}q_{c1Ncs}\end{array} //]]>$is the clean-sand equivalent normalised cone resistance 3 in qc1N_cs_3 on CPT_DATA_LIQUEFACTION. For cases that qc1Ncs are less than 33, it was set to 33.

Post Liquefaction Volumetric Strain 3

To comply with the requirements of NZ DBH (Department of Building and Housing) the post liquefaction volumetric strain 3, in Post_Liq_Volumetric_Strain_3, for saturated sands is calculated using the method by Zhang et al. (2002) with factor of safety from Factor_of_Safety_4.

Post Liquefaction Reconsolidation Settlement, S

Post Liquefaction Reconsolidation Settlement 1

Post liquefaction reconsolidation settlement 1 in Post_Liq_Reconsolidation_Settlement_1 is calculated from post liquefaction volumetric strain 1:

Where:

     $//<![CDATA[ \begin{array}{l}\varepsilon_v\end{array} //]]>$ is the post liquefaction volumetric strain 1, and is stored in Post_Liq_Volumetric_Strain_1 on CPT_DATA_LIQUEFACTION

Post Liquefaction Reconsolidation Settlement 2

Post liquefaction reconsolidation settlement 2 in Post_Liq_Reconsolidation_Settlement_2 is calculated from post liquefaction volumetric strain 2:

Where:
     $//<![CDATA[ \begin{array}{l}\varepsilon_v\end{array} //]]>$ is the post liquefaction volumetric strain 2, and is stored in Post_Liq_Volumetric_Strain_2 on CPT_DATA_LIQUEFACTION

Post Liquefaction Reconsolidation Settlement 3

Post liquefaction reconsolidation settlement 3 in Post_Liq_Reconsolidation_Settlement_3 is calculated in a similar manner from post liquefaction volumetric strain 3.

Liquefaction Severity Number, LSN

Liquefaction Severity Number 1

The Liquefaction Severity Number LSN in Liquefaction_Severity_Number_1 is a new calculated parameter developed by Tonkin & Taylor (2013) to reflect the more damaging effects of shallow liquefaction on residential land and foundations, and is calculated for layers with triggering factor of safety reduces below 2 from:

Tonkin & Taylor (2013), "Liquefaction Vulnerability Study", pp. 24-25

Where:
     $//<![CDATA[ \begin{array}{l}\varepsilon_v\end{array} //]]>$ is the post liquefaction volumetric strain 1, and is stored in Post_Liq_Volumetric_Strain_1 on CPT_DATA_LIQUEFACTION 
     Triggering factor of safety is in Factor_of_Safety_4 on CPT_DATA_LIQUEFACTION

Liquefaction Severity Number 2

The Liquefaction Severity Number LSN in Liquefaction_Severity_Number_2 is calculated as:

Tonkin & Taylor (2013), "Liquefaction Vulnerability Study", pp. 24-25

Where:
     $//<![CDATA[ \begin{array}{l}\varepsilon_v\end{array} //]]>$ is the post liquefaction volumetric strain 2, and is stored in Post_Liq_Volumetric_Strain_2 on CPT_DATA_LIQUEFACTION 
     Triggering factor of safety is in Factor_of_Safety_4 on CPT_DATA_LIQUEFACTION