# 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 \[Reese and Van Impe, 2011\]](https://openbrim.atlassian.net/wiki/download/attachments/3049652248/SoftClayMatlock.jpg?api=v2)

***

\[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.


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