---
title: "Failure modes and stability criteria of gravity dams"
subject: "Hydro Power"
chapter: 4
key: "semester_6/hydro_power:gravity-dam-failure-modes"
source: https://www.bctengineer.com/q/semester_6/hydro_power/gravity-dam-failure-modes
site: BCT Engineering
---

# Failure modes and stability criteria of gravity dams

Hydro Power · Chapter 4: Dam Engineering

- Asked in: 2082 Kartik, 8 marks; 2081 Asoj, 8 marks (asked 2 times)
- Video: [Causes of Failure of Gravity DAM](https://www.youtube.com/watch?v=j1mAgf2HYnE) — BTU e-Learn (e-Learn)
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/hydro_power/gravity-dam-failure-modes
- Whole chapter: https://www.bctengineer.com/md/semester_6/hydro_power/chapter-4

## Question

Explain the failure modes and the structural stability criteria of gravity dams.

## Short answer

Gravity dams may fail by overturning (FSo ≥1.5), sliding (FSs ≥1, SFF ≥3-5), crushing (toe stress ≤ allowable), or tension cracking (resultant within middle third, e ≤ B/6). Design must satisfy these criteria under all loading conditions.

## Answer

A **gravity dam** resists the water thrust and other forces mainly by its own weight. It can fail in four ways; each one gives a stability criterion that the design must satisfy for all load combinations (empty reservoir, full reservoir, earthquake, flood).

```text
     |\           W = self weight
 P-> | \          P = water thrust
     |  \         U = uplift
 ~~~~|   \        R = resultant
     | W  \
     |  \  \
heel |___R__\ toe
     ^ U ^ ^ ^
```

#### 1. Overturning about the toe
- **Mode:** the horizontal forces (water pressure, silt, wave, earthquake) and uplift produce a moment that tends to rotate the dam about its toe.
- **Criterion:** factor of safety against overturning

$$
FS_o = \frac{\sum M_R}{\sum M_O} \geq 1.5\ (\text{usually } 2 \text{ to } 3)
$$

In practice, a dam that satisfies the no-tension and crushing criteria will not overturn.

#### 2. Sliding (shear failure)
- **Mode:** the dam slides along the base or along a weak joint/seam in the foundation when the horizontal force exceeds the frictional and shear resistance.
- **Criteria:**
  - Factor of safety against sliding (friction only): $FS_s = \dfrac{\mu \sum V}{\sum H} \geq 1$ (usually 1 to 1.5).
  - Shear friction factor (friction plus shear strength $q$ of the joint over base width $B$): $SFF = \dfrac{\mu \sum V + B q}{\sum H} \geq 3$ to 5.

#### 3. Compression or crushing
- **Mode:** the vertical stress at the toe (full reservoir) or heel (empty reservoir) exceeds the allowable compressive strength of concrete or rock.
- **Criterion:**

$$
p_{max} = \frac{\sum V}{B}\left(1 + \frac{6e}{B}\right) \leq \text{allowable stress}
$$

The principal stress at the toe, $\sigma_1 = p_v\sec^2\alpha - p'\tan^2\alpha$, must also be below the allowable value.

#### 4. Tension cracking
- **Mode:** if the resultant falls outside the middle third of the base ($e > B/6$), tension develops at the heel. Concrete is weak in tension, so a crack opens, uplift enters the crack, the effective base width reduces and stresses at the toe rise, which can lead to failure.
- **Criterion (middle-third rule):**

$$
e \leq \frac{B}{6} \quad\Rightarrow\quad p_{min} = \frac{\sum V}{B}\left(1 - \frac{6e}{B}\right) \geq 0
$$

A small tension (e.g. up to about 500 kN/m²) is sometimes allowed for extreme load cases such as earthquakes.

#### Summary of criteria

| Failure mode | Criterion |
|---|---|
| Overturning | $FS_o \geq 1.5$ |
| Sliding | $FS_s \geq 1$; $SFF \geq 3$–5 |
| Crushing | $p_{max} \leq$ allowable |
| Tension | Resultant in middle third ($e \leq B/6$) |

## Check yourself

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

1. Which are the four failure modes of a gravity dam?
   A. Overturning, sliding, crushing and tension cracking
   B. Seepage, piping, erosion and scour
   C. Buckling, torsion, bending and shear
   D. Cavitation, fatigue, creep and corrosion
   Answer: A. These four give the stability criteria. (Key point: Failure modes)

2. How is the factor of safety against sliding (friction only) written?
   A. FS = sum H / (mu sum V)
   B. FS = mu sum V / sum H, at least 1
   C. FS = sum M_R / sum M_O
   D. FS = B / e
   Answer: B. Friction resistance mu sum V divided by horizontal force; shear friction factor adds shear strength B q. (Key point: Sliding criteria)

3. What does the no-tension condition require?
   A. e at least B/2
   B. The resultant at the toe
   C. The resultant within the middle third of the base, e <= B/6
   D. Zero vertical load
   Answer: C. e <= B/6 makes p_min = (sum V/B)(1 - 6e/B) >= 0. (Key point: Middle-third rule)

4. About which point is overturning checked and what is the minimum FS?
   A. Heel; FS >= 0.5
   B. Toe; FS >= 1.5 (usually 2 to 3)
   C. Centre; FS >= 1
   D. Heel; FS >= 5
   Answer: B. FS_o = sum M_R / sum M_O about the toe, at least 1.5. (Key point: Overturning)

## Related in Hydro Power

- [Stability of trapezoidal gravity dam (RL 250 m)](https://www.bctengineer.com/question.md?key=semester_6%2Fhydro_power%3Atrapezoidal-dam-stability-250m) — Hydro Power, chapter 4
- [Stability of gravity dam (crest 1530 m)](https://www.bctengineer.com/question.md?key=semester_6%2Fhydro_power%3Agravity-dam-stability-1530) — Hydro Power, chapter 4
- [Forces on gravity dam and stability requirements](https://www.bctengineer.com/question.md?key=semester_6%2Fhydro_power%3Agravity-dam-forces-stability) — Hydro Power, chapter 4
- [Elementary profile and 40 m gravity dam stability](https://www.bctengineer.com/question.md?key=semester_6%2Fhydro_power%3Agravity-dam-elementary-40m) — Hydro Power, chapter 4
- [Dam types and forces on gravity dam](https://www.bctengineer.com/question.md?key=semester_6%2Fhydro_power%3Adam-types-forces) — Hydro Power, chapter 4

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