# Weak Rock (Reese) \[Reese, 1997]

Ultimate resistance of Rock determined by following equations

$$
\tag{1}
p\_{ur} = \alpha\_{r}q\_{ur}b(1+1.4\frac{x\_r}{b}) \quad for \quad 0 \leq x\_r \leq 3b
$$

$$
\tag{2}
p\_{ur} = 5.2\alpha\_{r}q\_{ur}b\quad for \quad x\_r > 3b
$$

where,

$$p\_{ur}$$ = ultimate rock resistance per unit length $$q\_{ur}$$ = unconfined compressive strength of rock $$α\_r$$ = strength reduction factor $$x\_r$$ = depth below rock surface $$b$$ = diameter of pile

The initial slope can be determined as,

$$
\tag{3}
K\_{ir} = k\_{ir}E\_{ir}
$$

where,

$$K\_{ir}$$ = initial slope of the *p-y* curve\
$$E\_{ir}$$ = initial modulus of rock\
$$k\_{ir}$$ = dimensionless constant

$$k\_{ir}$$ is calculated by;

$$
\tag{4}
k\_{ir} = (100+\frac{400x\_r}{3b})\quad for \quad 0 \leq x\_r \leq 3b
$$

$$
\tag{5}
k\_{ir} = 500\quad for \quad x\_r > 3b
$$

The relationship is divided into three portions: initial slope, transition, and ultimate resistance.

$$
\tag{6}
p = K\_{ir}y \quad for \quad y \leq y\_A
$$

$$
\tag{7}
p = \frac{p\_{ur}}{2}(\frac{y}{y\_m})^{0.25} \quad for \quad y \geq y\_A \quad and \quad p \leq p\_{ur}
$$

$$
\tag{8}
p = p\_{ur} \quad for \quad y \geq 16y\_m
$$

$$
\tag{9}
y\_m = k\_{rm}b
$$

where,

$$y$$ = horizontal displacement $$p$$ = horizontal rock resistance per unit length $$y\_A$$ = horizontal displacement end of linear portion $$k\_{rm}$$ = dimensionless constant, ranging from 0.0005 to 0.00005

The value of the $$y\_A$$ is found solving the following equation,

$$
\tag{10}
y\_A = \biggr\[\frac{p\_{ur}}{2(y\_m)^{0.25}K\_{ir}}\biggr]^{1.333}
$$

![p − y curve for weak rock (Reese) \[Reese, 1997\]](https://openbrim.atlassian.net/wiki/download/attachments/3052339223/WeakRock_Reese-20250402-093012.jpg?api=v2)

***

\[Reese, 1997] Reese, L. C. (1997). Analysis of laterally loaded piles in weak rock. *Journal of Geotechnical and Geoenvironmental engineering*, 123(11):1010–1017.


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