Undrained Shear Strength and Consistency Term

Undrained Shear Strength 1

Undrained Shear Strength 1 ($//<![CDATA[ \begin{array}{l}s_u\end{array} //]]>$) in Undrained_Shear_Strength_1 is defined as:

When q_t has data,

$$//<![CDATA[ \begin{array}{l}\displaystyle s_u = \frac {(q_t - \sigma_{v0})}{N_{kt}}\end{array} //]]>$$

Otherwise,

$$//<![CDATA[ \begin{array}{l}\displaystyle s_u = \frac {(q_c - \sigma_{v0})}{N_{k}}\end{array} //]]>$$

NCHRP Synthesis 368 p 39

$//<![CDATA[ \begin{array}{l}N_k\end{array} //]]>$N_k and $//<![CDATA[ \begin{array}{l}N_{kt}\end{array} //]]>$ are defined on the CPT_POINT_MATERIAL_PROPERTIES, CPT_POINT_CORRELATION_PARAMETERS and CPT_PROJECT_CORRELATION_PARAMETERS tables. Different values for $//<![CDATA[ \begin{array}{l}N_k\end{array} //]]>$ and $//<![CDATA[ \begin{array}{l}N_{kt}\end{array} //]]>$ can be defined for when $//<![CDATA[ \begin{array}{l}q_c\end{array} //]]>$ or $//<![CDATA[ \begin{array}{l}q_t\end{array} //]]>$ is either greater than or equal to, or less than a defined break point. Each of these tables have six fields from which the $//<![CDATA[ \begin{array}{l}N_k\end{array} //]]>$ and $//<![CDATA[ \begin{array}{l}N_{kt}\end{array} //]]>$ values, and the $//<![CDATA[ \begin{array}{l}q_c\end{array} //]]>$ and qt break point values are stored and retrieved for the calculation of $//<![CDATA[ \begin{array}{l}s_u\end{array} //]]>$ _.

The fields in the CPT_POINT_MATERIAL_PROPERTIES table allow the $//<![CDATA[ \begin{array}{l}N_k\end{array} //]]>$ and $//<![CDATA[ \begin{array}{l}N_{kt}\end{array} //]]>$ 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 $//<![CDATA[ \begin{array}{l}N_k\end{array} //]]>$ or $//<![CDATA[ \begin{array}{l}N_{kt}\end{array} //]]>$ that lies within the depth range of the current depth of the row in the CPT_DATA table is used to calculate $//<![CDATA[ \begin{array}{l}s_u\end{array} //]]>$. If a matching depth range for the current depth is not found, or $//<![CDATA[ \begin{array}{l}N_k\end{array} //]]>$ or $//<![CDATA[ \begin{array}{l}N_{kt}\end{array} //]]>$  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 ($//<![CDATA[ \begin{array}{l}s_u\end{array} //]]>$) in Undrained_Shear_Strength_2 is defined as:

When $//<![CDATA[ \begin{array}{l}q_t\end{array} //]]>$ has data,

$$//<![CDATA[ \begin{array}{l}\displaystyle s_u = \frac {(q_t)}{N_{kt}}\end{array} //]]>$$

Otherwise,

$$//<![CDATA[ \begin{array}{l}\displaystyle s_u = \frac {(q_c - \sigma_{v0})}{N_{kt}}\end{array} //]]>$$

Where:

     $//<![CDATA[ \begin{array}{l}N_{kt}\end{array} //]]>$ is stored in the Undrained_Shear_Strength_2_Nkt field.

     $//<![CDATA[ \begin{array}{l}N_k\end{array} //]]>$ is stored in the Undrained_Shear_Strength_2_Nk field.

The variables are stored on CPT_POINT_MATERIAL_PROPERTIES, CPT_POINT_CORRELATION_PARAMETERS and CPT_PROJECT_CORRELATION_PARAMETERS tables.

The fields in the CPT_POINT_MATERIAL_PROPERTIES table allow the $//<![CDATA[ \begin{array}{l}N_k\end{array} //]]>$ and $//<![CDATA[ \begin{array}{l}N_{kt}\end{array} //]]>$ 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 $//<![CDATA[ \begin{array}{l}N_k\end{array} //]]>$ or $//<![CDATA[ \begin{array}{l}N_{kt}\end{array} //]]>$ that lies within the depth range of the current depth of the row in the CPT_DATA table is used to calculate $//<![CDATA[ \begin{array}{l}s_u\end{array} //]]>$. If a matching depth range for the current depth is not found, or $//<![CDATA[ \begin{array}{l}N_k\end{array} //]]>$ or $//<![CDATA[ \begin{array}{l}N_{kt}\end{array} //]]>$ 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 ($//<![CDATA[ \begin{array}{l}s_u\end{array} //]]>$) based on CSSM in Undrained_Shear_Strength_3 is defined as:

When $//<![CDATA[ \begin{array}{l}q_t\end{array} //]]>$ has data,

$$//<![CDATA[ \begin{array}{l}s_u = 0.5 \cdot \sin \Phi' \cdot OCR ^\Lambda \cdot \sigma'_{v0}\\\end{array} //]]>$$

Wroth (1984), NCHRP Synthesis 368 p 39

Where:

     _{$//<![CDATA[ \begin{array}{l}\Phi'\end{array} //]]>$}  is taken from the first of these fields with data: Friction_Angle_3 and Friction_Angle_1 
    $//<![CDATA[ \begin{array}{l}OCR\end{array} //]]>$ is taken from Overconsolidation_Ratio_1
    $//<![CDATA[ \begin{array}{l}\Lambda = 1 - \frac{C_s}{C_c}\\\end{array} //]]>$ , typically low to medium sensitivity clays are  $//<![CDATA[ \begin{array}{l}0.7 \leq \Lambda \leq0.8\end{array} //]]>$ , and sensitive and structured clays are  $//<![CDATA[ \begin{array}{l}0.9 \leq \Lambda \leq1.0\end{array} //]]>$, and is stored in the Undrained_Shear_Strength_3_Lambda field.

$//<![CDATA[ \begin{array}{l}\Lambda\end{array} //]]>$  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 ($//<![CDATA[ \begin{array}{l}s_u\end{array} //]]>$) in Undrained_Shear_Strength_4 is defined as:

$$//<![CDATA[ \begin{array}{l}\displaystyle s_u = {C_1} \cdot {\sigma'_p}\end{array} //]]>$$

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

Where:

      $//<![CDATA[ \begin{array}{l}\sigma'_p\end{array} //]]>$  is taken from Preconsolidation_Stress_1
      $//<![CDATA[ \begin{array}{l}C_1\end{array} //]]>$  is 0.22 in the published formula, and is stored in the Undrained_Shear_Strength_4_C1 field.
      $//<![CDATA[ \begin{array}{l}C_1\end{array} //]]>$  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 ($//<![CDATA[ \begin{array}{l}s_u\end{array} //]]>$) in Undrained_Shear_Strength_5 is defined as:

$$//<![CDATA[ \begin{array}{l}\displaystyle s_u = \frac {\Delta u}{N_{\Delta u}}\end{array} //]]>$$

Robertson (2009), pp 28-29

Where:

      $//<![CDATA[ \begin{array}{l}\Delta u\end{array} //]]>$  is taken from Excess_Pore_Pressure field
      $//<![CDATA[ \begin{array}{l}{N_{\Delta u}}\end{array} //]]>$  is taken from Undrained_Shear_Strength_5_N field
      $//<![CDATA[ \begin{array}{l}{N_{\Delta u}}\end{array} //]]>$  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.