# Axial Clay Methods¶

There are various methods available that can be used to calculate the axial capacity of a pile, either for generation of axial capacity, TZ & QZ curves or in ALLCAP.

 Method Soil Parameter Input in Main Table Additional Parameters 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 CLAYAPI X X Clay residual CLAYAPICOMM X X Clay residual CLAYNGI X X X X Clay residual CLAYKOLK X X Clay residual CLAYEXP X X Clay residual, Clay Exp 1 & 2 CLAYME X X X X Clay residual, Clayme parameters CLAYF05 X X Clay residual CLAYICP X X X X X X Clay residual, ICP base condition CLAYUWA2013 $$X^{(1)}$$ $$X^{(1)}$$ X Clay residual, ICP base condition CLAYALPHA X X Clay residual, Clay alpha CLAYUSER X X Clay residual
$$X^{(1)}$$ The corrected cone tip resistance $$q_t$$ is required instead of the cone tip resistance $$q_c$$.

List of soil parameters used in the axial methods:

No. Symbol Unit Soil Parameter
1 $$f_{u}$$ (kPa) ultimate skin friction
2 $$q_{u}$$ (kPa) ultimate end bearing
3 $$s_{u,top}$$ (kPa) undrained shear strength at the top of the layer
4 $$s_{u,bottom}$$ (kPa) undrained shear strength at the bottom of the layer
5 $$PL$$ (%) plastic limit
6 $$LL$$ (%) liquid limit
7 $$w$$ (%) water content
8 $$\Delta I_{vy}$$ (-) relative void index at yield
9 $$YSR / OCR$$ (-) yield stress ratio / overconsolidation ratio
10 $$\Delta I_{v0}$$ (-) relative void index
11 $$q_{c,top}$$ (kPa) CPT cone resistance at the top of the layer
12 $$q_{c,bottom}$$ (kPa) CPT cone resistance at the bottom of the layer
13 $$\delta _{f}$$ (deg) ultimate interface friction angle (ring shear test)
14 $$\delta _{API}$$ (deg) interface friction angle
15 $$N_{q}$$ (-) bearing capacity factor
16 $$d_{mean}$$ (mm) mean particle size for sand
17 $$f_{user}$$ (kPa) user defined ultimate shaft friction
18 $$q_{user}$$ (kPa) user defined ultimate end bearing

Note

Where possible the notation used in the explanation of each method is the same as used in the original source paper, rather than translate many different methods and styles of notation to a common one to be used in OPILE. Thus the notation used within OPILE is not necessarily consistent across methods. It is always advised to consult the original reference sources of these methods if the user is not familiar with the implementation of a particular method, although the references cited within the OPILE documentation are by no means exhaustive. Note that easy unit conversions can be made when inputting data such as dimensions and shear strengths, see units convention section for details.

## CLAYAPI¶

### Skin Friction¶

According to API WSD (2000) , for pipe piles in cohesive soils, the shaft friction f in kPa at any point along the pile may be calculated using the equation:

$f = \alpha \cdot c$

Where:

 $$\alpha$$ is a dimensionless factor calculated: $$\alpha = 0.5 \cdot \Psi^{-0.25} \qquad \Psi > 1.0$$ $$\alpha = 0.5 \cdot \Psi^{-0.5} \qquad \Psi < 1.0$$ With the constraint that $$\alpha$$ must not be greater than 1.0. $$\Psi$$ is $$\Large\frac{c}{p_0}$$ for the point in question $$p_0$$ is the effective overburden pressure [kPa] at the depth in question. $$c$$ is the undrained shear strength at the current depth.

### End Bearing¶

The end bearing pressure in kPa for CLAYAPI is calculated using:

$q = 9 \cdot c$

The calculation to determine whether the pile behaves in a plugged or unplugged manner at a specific penetration is outlined in the axial capacity section.

The clay residual affects the shape of the TZ curve beyond the peak and is discussed in the TZ_&_QZ_Curves_ section.

## CLAYAPICOMM¶

### Skin Friction¶

The CLAYAPICOMM method is the method for clays which is presented in the commentary of API WSD (2000). The skin friction f is given by:

$f = \alpha \cdot c$

And $$\alpha$$ is interpolated from the plot below:

This is implemented in OPILE using the equation:

$\alpha = 1 + \frac {c-24kPa}{72kPa - 24kPa} \cdot (0.5 - 1.0)$

Where $$0.5 <= \alpha <= 1.0$$

### End Bearing¶

For the CLAYAPICOMM method end bearing is calculated in the same way as the CLAYAPI method.

## CLAYNGI¶

### Skin Friction¶

For further information on the CLAYNGI method refer to Karlsrud et al (2005).

Skin friction is calculated according to:

$\begin{split}\tau_{Skin} = \left\| \begin{array} \alpha_{NC} \cdot s_{uRef} & \quad \text{if } \Psi < 0.25 \\ \alpha \cdot s_{uRef} \cdot F_{Tip} & \quad \text{if } \Psi > 1.0 \\ ( \alpha_{NC} + (0.5 - \alpha_{NC} ) \cdot \frac{\log(\Psi) - \log(0.25)}{\log(1) - \log(0.25)} ) \cdot s_{uRef} & \quad \text{otherwise } \end{array}\right.\end{split}$

If 0.25 < :math:Psi < 1.0 then the skin friction is interpolated between the values at those two limits.

Where:

 $$\Psi$$ $$\Psi = \Large\frac{s_u}{\sigma'_{v0}}$$ $$\sigma'_{v0}$$ is the effective overburden pressure [kPa] at the point in question. $$s_{u Ref}$$ is the undrained shear strength at the current depth. $$\alpha_{NC}$$ $$\alpha_{NC} = 0.32 \cdot (I_p - 10)^{0.3}$$ and $$0.2 < \alpha_{NC} < 1.0$$ $$\beta_{NC}$$ $$\beta_{NC} = 0.08 \cdot (I_p - 10)^{0.3}$$ subject to the constraint that $$\beta_{NC}$$ is a minimum of: $$\beta_{min} = 0.06 \cdot (I_p - 12)^{0.33}$$ $$I_{p}$$ is the plasticity index (in %). $$F_{Tip}$$ is taken as $$1.0$$ for piles driven open ended.

### End Bearing¶

For the CLAYNGI method end bearing is calculated in the same way as the CLAYAPI method.

## CLAYICP¶

### Skin Friction¶

The CLAYICP method has two submethods:

• CLAYICP1 and
• CLAYICP2.

These take account of the two slightly different variations of the CLAYICP method presented by Jardine et al. (2005).

OPILE will only calculate skin frictions and end bearings for open ended piles and does not include the closed ended methods which are also presented by Jardine et al. (2005). It is recommended that for further information on the use of these methods users should refer to this reference.

The skin friction is calculated by:

$\tau_f = K_{fOverK_c} \cdot \sigma'_{rc} \tan(\delta_f)$

Where:

 $$\sigma_{rc} = K_c \cdot \sigma_{v0}$$ $$K_c$$ For CLAYICP1: $$K_c = [(2.2+0.016 \cdot YSR - 0.870 \cdot \Delta I_{vy}) \cdot \textrm{YSR}^{0.42} \cdot (\frac{h}{R^{*}})^{-0.2}]$$ For CLAYICP2: $$K_c = (2-0.625 \cdot \Delta I_{v0}) \cdot YSR^{0.42} \cdot (\frac{h}{R^{*}})^{-0.2}]$$ A lower limit of $$\large\frac{h}{R^{*}} \geq 8$$ applies $$R^{*}$$ $$R^{*} = [R^2-(R-t)^2]^{0.5}$$ Where R is the pile radius and t is the wall thickness. $$h$$ $$h = L - z$$ Where $$L$$ is the pile penetration and $$z$$ is the current depth. $$\frac{K_f}{K_c}$$ is always 0.8. The loading factor is constant regardless of the loading direction or drainage conditions $$\textrm{YSR}$$ Yield stress ratio, or apparent OCR $$\Delta I_{vy}$$ Relative void index at yield. $$\Delta I_{v0}$$ Relative void index. $$\delta_{f}$$ Operational interface angle of friction at failure.

### End Bearing¶

The calculation of end bearing for the CLAYICP method is the same regardless of whether CLAYICP1 or CLAYICP2 is selected.

The end bearing pressure is derived using the following logic:

$\begin{split}q_b = \left\|\begin{array} iif & PLUGGED & \quad \left\|\begin{array} \text{0.4} \cdot q_c \quad & \text{if Undrained} \\ 0.65 \cdot q_c \quad & \text{otherwise} \end{array}\right.\\ if & UNPLUGGED & \quad \left\|\begin{array} \text{q_c} \quad & \text{if Undrained} \\ 1.6 \cdot q_c \quad & \text{otherwise} \end{array}\right. \end{array}\right.\end{split}$

The pile plug condition is defined as:

$\begin{split}\left\|\begin{array} PPlugged \quad & \text{if } \quad \frac{D_{inner}}{D_{CPT}} + 0.45 \frac{q_c}{p_a} < 36 \\ \text{Unplugged} \quad & \text{otherwise} \end{array}\right.\end{split}$

Where:

 $$D_{inner}$$ inner diameter of the pile. $$D_{CPT}$$ diameter of the CPT used. $$q_c$$ cone tip resistance at the depth

## CLAYUWA2013¶

### Skin Friction¶

The CLAYUWA2013 method has two submethods for the calculation of the shaft friction:

• CLAYUWA2013a and
• CLAYUWA2013b.

These submethods represent the two best-fit expressions for the shaft friction presented in Lehane et al. (2013), namely equation (13) and equation (14) which includes the pile-soil friction angle as input, respectively.

With CLAYUWA2013a, the skin friction is calculated as:

$\tau_{Skin} = 0.055 \cdot q_t \left[\text{max}\left(\frac{h}{R^{*}},1 \right) \right]^{-0.2}$

With CLAYUWA2013b, the skin friction is calculated as:

$\tau_{Skin} = \frac{0.23 \cdot q_{t} \left[\text{max} \left(\frac{h}{R^{*}},1 \right) \right]^{-0.2}}{ \left(\frac{q_t}{\sigma'_{v}} \right)^{0.15}}\text{tan}(\delta_{f})$

Where:

 $$q_t$$ $$q_t = q_c + u(1-a)$$ CPT corrected cone tip resistance, where q_c is the cone tip resistance, u the pore pressure and a the cone area ratio. $$R^{*}$$ $$R^{*} = [R^2-(R-t)^2]^{0.5}$$ Where R is the pile radius and t is the wall thickness. $$h$$ $$h = L - z$$ $$h$$ is the distance to the pile tip, $$L$$ is the pile tip penetration and $$z$$ is the current depth. $$\delta_{f}$$ Operational interface angle of friction at failure.

### End Bearing¶

The end bearing resistance is calculated according to Jardine et al. (2005), as recommended in Lehane et al. (2005). Same as in the CLAYICP method, OPILE will only calculate skin frictions and end bearings for open ended piles and does not include the closed ended methods. It is recommended that for further information on the use of these methods users should refer to this reference.

It should be noted that the end bearing resistance is calculated from the corrected cone resistance q_t.

## CLAYF05¶

### Skin Friction¶

This method is referred to as the CLAYF05 method, although it was published in CUR (2001).

Skin friction for the CLAYF05 method is calculated using:

$f = 0.03 \cdot q_c$

Where:

 $$q_c$$ cone tip resistance

End Bearing

For the CLAYF05 method end bearing is calculated in the same way as the CLAYAPI method.

## CLAYALPHA¶

### Skin Friction¶

The CLAYALPHA method calculates the skin friction in clays by multiplying the undrained shear strength by a user specified alpha value.

### End Bearing¶

For the CLAYALPHA method end bearing is calculated in the same way as in the CLAYAPI method.

## CLAYKOLK¶

### Skin Friction¶

The CLAYKOLK method is taken from Kolk & Van de Velde (1996) and the equation used in OPILE includes a small correction, to that presented in the original paper.

The skin friction f is equal to:

$f = \alpha \cdot s_u$

Where:


 $$\alpha$$ $$\alpha = 0.9 \cdot \left(\frac{L-z}{D} \right)^{-0.2} \cdot \left(\frac{s_u}{p_0} \right)^{-0.3}$$ $$\alpha \text{ must satisfy: }(\alpha\leq 1.0)$$ $$p_0$$ is the effective overburden pressure [kPa] at the point in question. $$s_u$$ is the undrained shear strength at the current depth. L is the pile penetration. z is the current depth. D is the pile outer diameter.

The exponent “-0.2” was incorrectly presented in the original paper as “0.2”, communication with the authors confirmed it should be “-0.2” and indeed this is the case where the Kolk & Van de Velde method is presented in CUR (2001).

### End Bearing¶

For the CLAYKOLK method end bearing is calculated in the same way as in the CLAYAPI method.

## CLAYUSER¶

### Skin Friction & End Bearing¶

The CLAYUSER method allows the user to enter skin friction and end bearing pressures for use in the calculation of capacity and TZ and QZ curves.

The CLAYUSER method only differs from the SANDUSER method in the shape of the TZ curves that are generated. The QZ curves remain the same.

## CLAYEXP¶

### Skin Friction¶

The CLAYEXP method calculates the skin friction in clays by multiplying the undrained shear strength by a user specified alpha value.

It uses equations which have a similar form to those used in CLAYAPI:

$f = \alpha \cdot c$

Where:

 $$\alpha$$ $$\alpha = \textrm{min} \left[1 , 0.5 \cdot \left(\frac{c}{p_0} \right)^{EXP} \right]$$ $$\alpha$$ must satisfy: $$\alpha\leq 1.0$$ $$p_0$$ is the effective overburden pressure [kPa] at the point in question. $$c$$ is the undrained shear strength at the current depth. $$EXP$$ is an exponent selected by the user.

### End Bearing¶

For the CLAYEXP method end bearing is calculated in the same way as in the CLAYAPI method.

## CLAYME¶

### Skin Friction¶

The CLAYME method is a customisable method that calculates the skin friction in clays by multiplying the undrained shear strength by an alpha value that depends upon various inputs.

The skin friction is calculated by:

$f = \alpha \cdot s_u$

Where:

 $$\alpha$$ $$\alpha = 0.5 \cdot \Psi^{n}$$ $$\Psi$$ $$\Psi = \Large\frac{s_u}{p_0}$$ $$n$$ $$n = \left\|\begin{array}{c} \large\frac{I_p}{I_{pDivisor}} - \small I_{p Subtractor} & \text{if } \Psi<1.0 \\ n_A & \text{if otherwise} \end{array}\right.$$ $$I_p$$ the plasticity index is subject to the constraint that: $$I_{pLower} < I_p < I_{pUpper}$$ Where $$I_{pLower}$$ and $$I_{pUpper}$$ are the lower and upper bounds of the plasticity indexes custom defined in OPILE. They are given values of 10% and 25% respectively. $$I_{pDivisor}$$ $$I_{pDivisor}$$ is given a default value of 36. $$I_{pSubtractor}$$ $$I_{pSubtractor}$$ is given a default value of 0.22. $$n_A$$ $$n_A$$ is used if $$\Psi$$ is greater than 1.0. It is given a default value of 0.2. $$p_0$$ is the effective overburden pressure [kPa] at the depth in question. $$c$$ is the undrained shear strength at the current depth.

### End Bearing¶

For the CLAYME method end bearing is calculated in the same way as in the CLAYAPI method.

Note

The CLAYME method (also known as the Maersk 1996 method) has been used for pile design in the Arabian Gulf by Maersk Oil (Qatar). This method is included in OPILE although neither Cathie Associates nor Maersk Oil can accept any responsibility for its use. No further guidance on the input parameters (such as n and the I p limits) or the methods calibration can be provided. The default input parameters are the same as those used in the Maersk 1996 method.