Soft Clay (Matlock) [Matlock, 1970]

Static Loading Condition

$$\tag{1} p = 0.5p_{ult}(\frac{y}{y_{50}})^{1/3}$$

where,

$p$ = horizontal soft clay resistance per unit length $p_{ult}$ = horizontal ultimate soft clay resistance per unit length of pile $y$ = horizontal displacement $y_{50}$ = displacement at one-half of the ultimate soft clay resistance $p_{ult}$ calculated using the lesser of the values given by the equations below,

$$\tag{2} p_{ult} = \Bigl[3+\frac{\gamma'}{c_u}z+\frac{J}{b}z\Bigl]c_ub$$

$$\tag{3} p_{ult} = 9c_ub$$

where,

$b$ = diameter of the pile $z$ = depth below ground surface $γ′$ = effective unit weight $J$ = constant; based on experiments, factor determined experimentally Matlock [Matlock, 1970] recommends J = 0.5 for soft clay and J = 0.25 for medium clay. The default value 0.5 is used.

$y_{50}$ can be obtained from following equation,

$$\tag{4} y_{50} = 2.5\varepsilon_{50}b$$

where,

$ε_{50}$ = the strain corresponding to one-half the maximum principal stress difference

The value of p remains constant beyond $y = 8y_{50}$.

Cyclic Loading Condition

The transition depth is defined as,

$$\tag{5} z_r = \frac{6cb}{\gamma'b+Jc}$$

For depths greater than or equal to $z_r$, then $p$ is equal to $0.72p_u$ for $y>3y_{50}$.

For depths less than $z_{r}$, the value of $p$ reduces from $0.72p_u$ at $y=3y_{50}$ to the value given by the following equation at, $y=15y_{50}$. The value of the $p$ remains constant beyond $y=15y_{50}$,

$$\tag{6} p = 0.72p_{u}\frac{z}{z_r}$$

p − y curves for soft clay (a) static loading; (b) cyclic loading [Reese and Van Impe, 2011]

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[Matlock, 1970] Matlock, H. (1970). Correlation for design of laterally loaded piles in soft clay. In Offshore technology conference, pages OTC–1204. OTC.

[Reese and Van Impe, 2011] Reese, L. C. and Van Impe, W. F. (2011). Single piles and pile groups under lateral loading. CRC Press/Balkema.