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.

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[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.