Apparent pressure diagrams for braced cuts

Peck's (1969) apparent pressure diagrams are envelopes of the measured strut loads in braced cuts, so they are used only to find the strut, wale and sheeting forces. $H$ is the depth of the cut.

1. Cuts in sand

Uniform (rectangular) pressure:

$$p_a = 0.65\,K_a\gamma H,\qquad K_a = \tan^2(45^\circ-\phi/2)$$

2. Cuts in firm (stiff) clay ($\gamma H/c \le 4$)

Trapezoid: the pressure rises from zero at the top to its maximum over $0.25H$, remains constant for $0.5H$, and then reduces to zero over the last $0.25H$.

$$p_a = 0.2\gamma H\ \text{to}\ 0.4\gamma H\quad(\text{average }0.3\gamma H)$$

3. Cuts in soft to medium clay ($\gamma H/c > 4$)

Trapezoid: the pressure rises over the top $0.25H$ and remains constant below.

$$p_a = \gamma H\left[1 - m\frac{4c}{\gamma H}\right]\ \ge 0.3\gamma H$$

with $m = 1$ in general ($m = 0.4$ for very soft clay below the cut).

 Pressure acts on the wall (left line) and is drawn to the right. Depth is downward.

 SAND                     FIRM (STIFF) CLAY            SOFT TO MEDIUM CLAY
 |--------------+         |                            |
 |              |         |\                           |\
 |              |         | \     0.25H                | \     0.25H
 |              |         |  \                         |  \
 |              |   H     |   |                        |   |
 |              |         |   |   0.5H                 |   |
 |              |         |   |                        |   |   0.75H
 |              |         |  /                         |   |
 |--------------+         | /     0.25H                |   |
                          |/                           |___|

 p = 0.65 Ka gamma H      p = 0.2 to 0.4 gamma H       p = gamma H (1 - 4mc / gamma H)
 (uniform)                (average 0.3 gamma H)        (not less than 0.3 gamma H)