---
title: "Tension cracks in cohesive backfill"
subject: "Foundation Engineering"
chapter: 3
key: "semester_5/foundation_engineering:tension-cracks-cohesive"
source: https://www.bctengineer.com/q/semester_5/foundation_engineering/tension-cracks-cohesive
site: BCT Engineering
---

# Tension cracks in cohesive backfill

Foundation Engineering · Chapter 3: Lateral Earth Pressure Theories and Retaining Walls

- Asked in: 2074 Chaitra, 2 marks
- Video: [Practical applications of effect of lateral active earth pressure | formation of tension crack](https://www.youtube.com/watch?v=KkbwOCERf4A) — CIVIL FLEXURE : GATE IES & IRMS
- Answer checked by Claude Sonnet 5.5 on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/foundation_engineering/tension-cracks-cohesive
- Whole chapter: https://www.bctengineer.com/md/semester_5/foundation_engineering/chapter-3

## Question

How do tension cracks influence the distribution of active earth pressure in purely cohesive soils?

## Short answer

Tension cracks form to depth z0=2c/γ, eliminating tensile pressure. The active pressure acts only below z0 as a triangle with base γH-2c. The total thrust is Pa = ½(γH-2c)(H-z0), acting at (H-z0)/3 above the base. Cracks must be considered; water filling them adds hydrostatic pressure.

## Answer

In a purely cohesive soil ($\phi=0$) the active pressure at depth $z$ is $p_a = \gamma z - 2c$, which is **negative (tension)** near the surface.
- The tension zone extends to a depth $z_0 = \dfrac{2c}{\gamma}$ (zero pressure point). Soil cannot carry tension for long, so **tension cracks** form to this depth and the soil there gives no pressure on the wall.
- The pressure diagram is therefore a triangle from $z_0$ to the base, with maximum value $\gamma H - 2c$ at the bottom. Thus the active thrust is
$$
P_a = \tfrac12(\gamma H-2c)(H-z_0) = \tfrac12\gamma H^2 - 2cH + \frac{2c^2}{\gamma}
$$
and it acts at $(H-z_0)/3$ above the base.
- Neglecting the cracks (taking tension) would under-estimate the thrust. If the cracks fill with water, an extra hydrostatic thrust $\tfrac12\gamma_w z_0^2$ acts on the wall and increases pressure.

## Check yourself

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

1. In purely cohesive soil, tension cracks extend to a depth z0 =
   A. c/gamma
   B. 2c/gamma
   C. 4c/gamma
   D. gamma/2c
   Answer: B. Pressure gamma z - 2c is zero at z0 = 2c/gamma. (Key point: Depth of crack)

2. With tension cracks the pressure diagram is:
   A. A triangle from z0 to the base with maximum gamma H - 2c
   B. A rectangle over full height
   C. A triangle with tension included
   D. Zero throughout
   Answer: A. The tension zone gives no pressure, leaving a triangle of height (H - z0). (Key point: Pressure diagram)

3. If the cracks fill with water:
   A. Thrust decreases
   B. An extra hydrostatic thrust 1/2 gamma_w z0^2 acts and increases pressure
   C. No change
   D. The soil gains cohesion
   Answer: B. Water in the cracks adds hydrostatic thrust on the wall. (Key point: Effect of water in cracks)

## Related in Foundation Engineering

- [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
- [Active pressure on wall, cohesive soil](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Acohesive-wall-pressure-diagram) — Foundation Engineering, chapter 3
- [Active pressure, sloping backfill and water table](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Awall-sheet-pipe-sloping-backfill) — Foundation Engineering, chapter 3
- [Active pressure, 8 m wall, table of layers](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Awall-8m-two-layer-table) — Foundation Engineering, chapter 3
- [Why design for active pressure only](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Apassive-pressure-neglect) — Foundation Engineering, chapter 3, asked 4×
- [Active thrust, 7.5 m wall, 4.5 m sand](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Atwo-layer-wall-7-5m-4-5m-sand) — Foundation Engineering, chapter 3, asked 4×

## Related in other subjects

- [M-C envelopes for different soils](https://www.bctengineer.com/question.md?key=semester_4%2Fsoil_mechanics%3Amohr-coulomb-envelopes-soil-types) — Soil Mechanics, chapter 10