---
title: "Apparent pressure diagrams for braced cuts"
subject: "Foundation Engineering"
chapter: 4
key: "semester_5/foundation_engineering:apparent-pressure-diagrams"
source: https://www.bctengineer.com/q/semester_5/foundation_engineering/apparent-pressure-diagrams
site: BCT Engineering
---

# Apparent pressure diagrams for braced cuts

Foundation Engineering · Chapter 4: Arching in Soils and Braced Cuts

- Asked in: 2081 Baisakh, 2 marks; 2072 Chaitra, 3 marks (asked 2 times)
- Video: [Braced Excavation](https://www.youtube.com/watch?v=taN3qoNIvEw) — AXE Consultants
- Answer checked by Claude Sonnet 5.5 on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/foundation_engineering/apparent-pressure-diagrams
- Whole chapter: https://www.bctengineer.com/md/semester_5/foundation_engineering/chapter-4

## Question

Draw the apparent pressure diagrams (Peck) for deep cuts in sand, firm clay and soft to medium clay.

## Short answer

For sand, uniform pressure 0.65 Ka γ H. For firm clay (γH/c ≤ 4), trapezoid with maximum 0.2–0.4 γ H (average 0.3 γ H). For soft to medium clay (γH/c > 4), trapezoid with constant pressure γ H (1 − 4c/γ H) ≥ 0.3 γ H.

## Answer

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).

```text
 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)
```

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. What is Peck's pressure for sand?
   A. Triangular 0.5 Ka gamma H
   B. Uniform 0.65 Ka gamma H
   C. 0.3 gamma H
   D. gamma H
   Answer: B. A rectangle with intensity 0.65 Ka gamma H. (Key point: Sand diagram)

2. What is the shape for firm clay (gamma H/c <= 4)?
   A. Rectangle
   B. Trapezoid: rising over 0.25H, constant 0.5H, falling over 0.25H, p = 0.2 to 0.4 gamma H
   C. Triangle
   D. Constant only below 0.25H
   Answer: B. That gives the stiff-clay envelope with average 0.3 gamma H. (Key point: Stiff clay shape)

3. What is the criterion and pressure for soft to medium clay?
   A. gamma H/c > 4; p = gamma H(1 - 4mc/gamma H) >= 0.3 gamma H
   B. gamma H/c < 4; p = 0.65 Ka gamma H
   C. gamma H/c = 0
   D. p = 0.2 gamma H
   Answer: A. The trapezoid rises over 0.25H then stays constant. (Key point: Soft to medium clay)

## Related in Foundation Engineering

- [Choosing pressure diagram for braced cut](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Apressure-diagram-sand-clay-braced) — Foundation Engineering, chapter 4
- [Pile group 16 piles, 0.40 m, soft clay](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Apile-group-16-soft-clay-040) — Foundation Engineering, chapter 8
- [Active thrust, 6 m wall, sand over clay](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Atwo-layer-wall-6m-sand-clay) — Foundation Engineering, chapter 3, asked 4×
- [Differential settlement allowed, clay vs sand](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Adifferential-settlement-clay-sand) — Foundation Engineering, chapter 6
- [Strut loads, 8 m cut in sand](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Astrut-loads-8m-cut-sand) — Foundation Engineering, chapter 4
- [Tension crack and active pressure, layered clay](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Awall-cohesive-tension-crack) — Foundation Engineering, chapter 3

## Related in other subjects

- [Apparent and bulk specific gravity of sand](https://www.bctengineer.com/question.md?key=semester_5%2Fconcrete_technology_and_masonry_structure%3Aspecific-gravity-sand-numerical) — Concrete Technology and Masonry Structure, chapter 1
- [Compaction curves of sand and clay](https://www.bctengineer.com/question.md?key=semester_4%2Fsoil_mechanics%3Acompaction-sand-vs-clay) — Soil Mechanics, chapter 5
- [Clay over sand, effective stress at depths](https://www.bctengineer.com/question.md?key=semester_4%2Fsoil_mechanics%3Aclay-sand-profile-effective-stress-depths) — Soil Mechanics, chapter 6
- [Primary settlement, sand over clay, 110 kPa](https://www.bctengineer.com/question.md?key=semester_4%2Fsoil_mechanics%3Aprimary-settlement-sand-clay-110kpa) — Soil Mechanics, chapter 9