# Stiff Clay without Free Water (Welch and Reese) \[Welch and Reese, 1972]

Following *p-y* curve is recommended by \[Welch and Reese, 1972] for stiff clay under static loading.

$$
\tag{1}
p = 0.5p\_u(\frac{y}{y\_{50}})^{1/4}
$$

where,

$$p$$ = horizontal resistance per unit length $$p\_u$$ = horizontal ultimate resistance per unit length $$y$$ = horizontal displacement $$y\_{50}$$ = deflection at one-half the ultimate soil resistance

$$y\_{50}$$ is defined as:

$$
\tag{2}
y\_{50} = 2.5\varepsilon\_{50}b
$$

$$ε\_{50}$$ = the strain corresponding to one-half the maximum principal stress difference $$b$$ = pile diameter

Ultimate horizontal resistance $$p\_u$$ defined smaller of the values given below.

$$
\tag{3}
p\_u = \Bigg\[3+\frac{\gamma}{c}z+\frac{J}{b}z\Bigg]c\_ab
$$

$$
\tag{4}
p\_u = 9c\_ub
$$

where,

$$γ$$ = unit weight\
$$c\_u$$ = undrained shear strength $$c\_a$$ = average undrained shear strength over the depth z $$z$$ = depth $$J$$ = factor, taken as 0.5 by default

Beyond point where displacement, y, equals to $$16y\_{50}$$, $$p$$ is equal to $$p\_u$$ for all values of y.

***

\[Welch and Reese, 1972] Welch, R. and Reese, L. C. (1972). Laterally loaded behavior of drilled shafts. Technical Report 35-65-89, Center for Highway Research. University of Texas, Austin.


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