---
title: "Gravity dam concrete volume from hydrostatic thrust"
subject: "Hydropower Engineering"
chapter: 4
key: "semester_7/hydropower_engineering:gravity-dam-width-hydrostatic-thrust"
source: https://www.bctengineer.com/q/semester_7/hydropower_engineering/gravity-dam-width-hydrostatic-thrust
site: BCT Engineering
---

# Gravity dam concrete volume from hydrostatic thrust

Hydropower Engineering · Chapter 4: Headworks of Storage Plants

- Asked in: 2070 Ashad, 8 marks
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_7/hydropower_engineering/gravity-dam-width-hydrostatic-thrust
- Whole chapter: https://www.bctengineer.com/md/semester_7/hydropower_engineering/chapter-4

## Question

A concrete gravity dam on a rocky foundation is acted on by an upstream horizontal hydrostatic force of 4.50 million kN and by a downstream one of 0.50 million kN. Determine the volume of concrete works ($\gamma_{con}$ = 24 kN/m³), neglecting bond stress and uplift force, and taking a factor of safety on the horizontal thrust of 2.5 and a friction coefficient between the concrete and rock of 0.65.

## Short answer

Net horizontal thrust 4.0×10^6 kN. Required dam weight is (2.5×4.0×10^6)/0.65 = 15.38×10^6 kN. Required concrete volume = 15.38×10^6 / 24 ≈ 6.41×10^5 m³.

## Answer

#### Principle
With no bond stress and no uplift, sliding resistance comes only from friction between the concrete and the rock, $\mu\Sigma V$. The factor of safety on the horizontal thrust is

$$
FS=\frac{\mu\,\Sigma V}{\Sigma H}
$$

#### Net horizontal thrust
$$
\Sigma H=4.50\times10^6-0.50\times10^6=4.00\times10^6\ \text{kN}
$$

#### Required weight of the dam
$$
\Sigma V=\frac{FS\times\Sigma H}{\mu}=\frac{2.5\times4.00\times10^6}{0.65}=15,384,615\ \text{kN}=15.38\times10^6\ \text{kN}
$$

The vertical load is taken as the weight of the concrete (no uplift and no water weight).

#### Volume of concrete

$$
V=\frac{W}{\gamma_{con}}=\frac{15,384,615}{24}=641,026\ \text{m}^3\approx6.41\times10^5\ \text{m}^3
$$

**Answer: volume of concrete ≈ 641,026 m³ (about 6.41 × 10⁵ m³).**

## Check yourself

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

1. With no bond stress and no uplift, what provides the resistance to sliding?
   A. Friction between concrete and rock, mu x SumV
   B. The downstream water pressure only
   C. The shear strength of the rock
   D. The weight of the reservoir only
   Answer: A. The only resisting force is friction mu SumV, so FS = mu SumV / SumH. (Key point: Sliding resistance without bond)

2. What horizontal thrust is used in the factor of safety?
   A. 4.50 + 0.50 = 5.00 million kN
   B. 4.50 - 0.50 = 4.00 million kN
   C. 4.50 million kN only
   D. 0.50 million kN
   Answer: B. The downstream thrust opposes the upstream one, so the net thrust is 4.00 x 10^6 kN. (Key point: Net horizontal thrust)

3. How is the concrete volume obtained?
   A. W = 2.5 x 4e6 x 0.65, then V = W / 24
   B. W = FS x SumH / mu = 15.38e6 kN, then V = W / gamma_con = 641,026 m^3
   C. V = SumH / 24
   D. W = mu x SumH / FS, then V = W x 24
   Answer: B. Required weight = 2.5 x 4.0e6 / 0.65 = 15.38e6 kN; dividing by the concrete unit weight 24 kN/m^3 gives about 6.41e5 m^3. (Key point: Weight and volume of concrete)

## Related in Hydropower Engineering

- [Gravity dam section: shear stress near toe (2082)](https://www.bctengineer.com/question.md?key=semester_7%2Fhydropower_engineering%3Agravity-dam-stability-2082-baishakh) — Hydropower Engineering, chapter 4
- [Gravity dam stability and shear stress at toe (2081)](https://www.bctengineer.com/question.md?key=semester_7%2Fhydropower_engineering%3Agravity-dam-stability-2081-bhadra) — Hydropower Engineering, chapter 4
- [Gravity dam forces and stability checks (2081 Baishakh)](https://www.bctengineer.com/question.md?key=semester_7%2Fhydropower_engineering%3Agravity-dam-forces-stresses-2081-baishakh) — Hydropower Engineering, chapter 4
- [Gravity dam stresses, principal stress, FOS (2079)](https://www.bctengineer.com/question.md?key=semester_7%2Fhydropower_engineering%3Agravity-dam-stresses-2079-bhadra) — Hydropower Engineering, chapter 4
- [Gravity dam equilibrium and overtopping discharge coefficient](https://www.bctengineer.com/question.md?key=semester_7%2Fhydropower_engineering%3Agravity-dam-reservoir-capacity-curve-hrwl) — Hydropower Engineering, chapter 4
- [Gravity dam stability (SG 2.4, RL 0-70)](https://www.bctengineer.com/question.md?key=semester_7%2Fhydropower_engineering%3Agravity-dam-stability-2082-bhadra) — Hydropower Engineering, chapter 4

## Related in other subjects

- [Hydrostatic thrust and uplift with drainage gallery](https://www.bctengineer.com/question.md?key=semester_6%2Fhydro_power%3Adam-thrust-uplift-gallery) — 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
- [Sliding and overturning check of gravity dam](https://www.bctengineer.com/question.md?key=semester_6%2Fhydro_power%3Agravity-dam-sliding-overturning-figure) — Hydro Power, chapter 4
- [Horizontal shear stress variation, SF 50 kN](https://www.bctengineer.com/question.md?key=semester_3%2Fstrength_of_materials%3Ahorizontal-shear-stress-variation-t-section) — Strength of Materials, chapter 7