Chapter 8 of 10

Gravity Dams & Spillways

In the GATE Civil syllabus under Hydrology & Irrigation · 2 parts

Reservoirs & Dams · Spillways & Energy Dissipators

CIVILGYAN TEST SERIES · civilgyantests.com — free study notes for civil engineering exams

📑 Contents (16 sections)

Part 1 of 2

Reservoirs & Dams

Last reviewed 16 Sept 2026 · 13 min read

Reservoirs

A reservoir is a body of water impounded by a dam to store water for later use.

Type	Purpose
Storage (conservation) reservoir	Stores excess water in wet seasons for use in dry seasons (irrigation, water supply, hydropower)
Flood control reservoir	Stores flood water temporarily and releases it gradually: retarding basin (ungated outlets — automatic) or detention basin (gated outlets — controlled)
Distribution reservoir	Small storage within a water supply system to meet hourly fluctuations
Balancing reservoir	Downstream of a main reservoir to balance releases (e.g. from a power house)
Multipurpose reservoir	Serves several purposes

Storage zones and levels

Level / zone	Meaning
Dead storage	Below the minimum pool level / MDDL (minimum drawdown level) — not available by gravity; reserved for sediment
Live (useful) storage	Between MDDL and full reservoir level (FRL) / normal pool level
Surcharge storage	Between FRL and maximum water level (MWL) — uncontrolled, occurs during floods above the spillway crest
Bank storage	Water held in the permeable banks — released as the level falls
Valley storage	Natural storage in the river valley before the dam; net storage created = total − valley storage

Capacity

Area–elevation curve from contour surveys; capacity–elevation curve by integration using the trapezoidal formula $Δ V = \frac{h}{2} (A_{1} + A_{2})$ , the cone formula $Δ V = \frac{h}{3} (A_{1} + A_{2} + A_{1} A_{2})$ or the prismoidal formula.
Safe (firm) yield — maximum quantity that can be supplied during a critical dry period; secondary yield — water available in excess of safe yield in wet years.
Required storage for a given demand: mass curve (Rippl) method or sequent peak algorithm (see Runoff).

Reservoir sedimentation

Rivers carry sediment; when flow enters a reservoir, velocity falls and sediment settles — coarse near the head (forming deltas), fine near the dam; density currents can carry fine sediment right up to the dam.

Trap efficiency $η_{T}$ — percentage of incoming sediment retained; depends mainly on the capacity–inflow ratio (C/I); Brune's curves relate them — large storage reservoirs trap almost all sediment.
Life of a reservoir — the time until sediment fills a specified part of its capacity (e.g. dead storage filled, or live storage reduced to the point the reservoir no longer serves its purpose). Life is computed stepwise because trap efficiency falls as capacity falls.
Distribution of sediment with depth — empirical area reduction method.

Control of sedimentation:

Catchment treatment — afforestation, soil conservation, check dams (most effective long-term).
Proper selection of dam site (low sediment yield).
Sluicing / flushing — releasing sediment-laden flood water through low-level outlets before it settles; drawdown flushing.
Sediment bypass tunnels; venting density currents.
Dredging or excavation (costly).
Vegetal screens at the head of the reservoir; design with adequate dead storage.

Reservoir losses: evaporation (major in shallow, wide reservoirs), seepage, sedimentation.

Dams — classification

Basis	Types
Function	Storage dam; diversion dam (weir/barrage); detention dam; debris dam; coffer dam (temporary enclosure for construction in dry)
Hydraulic design	Overflow dam (water spills over the crest); non-overflow dam
Material / structural behaviour	Rigid — gravity (concrete/masonry), arch, buttress, steel, timber; non-rigid — earth, rockfill

Site selection

Sound foundation rock at reasonable depth; narrow valley opening into a wide basin upstream (small dam, large storage); suitable site for spillway; availability of construction materials; minimum submergence of valuable land, forests, habitations and mineral deposits; low sediment yield; accessibility; watertight reservoir basin; geological stability (no active faults, landslides).

Gravity dams

A gravity dam resists external forces by its own weight. It is the most durable type, requires little maintenance, suits almost any height, and can accommodate an overflow spillway section, but needs a strong rock foundation.

Forces acting

FormulaForces on a gravity dam (per metre length)

Self-weight $W$ — acts through the centroid of the section; the main stabilising force.
Water pressure — horizontal $P = \frac{1}{2} γ_{w} H^{2}$ acting at $H /3$ above the base; plus the vertical weight of water on any upstream batter; tailwater on the downstream side.
Uplift — due to seepage through the foundation and dam body. Without drains: varies linearly from $γ_{w} H$ at the heel to $γ_{w} H^{'}$ (tailwater) at the toe. With a drainage gallery, uplift at the drain line is commonly taken as tailwater head plus one-third of the difference between reservoir and tailwater heads, varying linearly to the heel and toe; uplift assumed to act over the full base area.
Silt pressure — $P_{s} = \frac{1}{2} γ_{s u b} h_{s}^{2} K_{a}$ ( $K_{a} = \frac{1 - sin ϕ}{1 + sin ϕ}$ ).
Wave pressure — maximum $p = 2.4 γ_{w} h_{w}$ at about $h_{w} /8$ above still water; total $P_{w} = 2 γ_{w} h_{w}^{2}$ (kN/m) acting at $0.375 h_{w}$ above still water level.
Earthquake forces — horizontal and vertical inertia of the dam, and hydrodynamic pressure of water (Westergaard/Zanger approaches), as per IS 1893.
Ice pressure (cold regions) and wind pressure (minor).

Wave height (Molitor–Stevenson):

h_{w} = 0.032 V F + 0.763 - 0.271 F^{1/4} (F < 32 km); h_{w} = 0.032 V F (F > 32 km)

( $V$ = wind velocity in km/h, $F$ = fetch in km, $h_{w}$ in m.) Freeboard is commonly taken as about 1.5 $h_{w}$ above the maximum water level.

Load combinations

The dam is checked for combinations such as: construction condition (empty reservoir, with and without earthquake); normal operating condition (full reservoir, normal uplift, silt, ice); flood discharge condition (MWL, full uplift, tailwater); normal operating + earthquake; drains choked (extreme uplift). Permissible factors of safety are lower for extreme combinations.

Modes of failure

FormulaStability requirements

Overturning about the toe: $F S = \frac{\sum M _{R}}{\sum M _{O}}$ — commonly required 1.5 or more (without earthquake). In practice the no-tension condition usually governs before overturning.
Sliding:
- Sliding factor $= \frac{μ \sum V}{\sum H}$ (should exceed about 1.0)
- Shear friction factor $S F F = \frac{μ \sum V + B q}{\sum H}$ ( $q$ = shear strength of the joint/foundation) — commonly required 3 to 5 depending on load combination.
Compression (crushing): maximum stress at the toe must not exceed the permissible stress of concrete/masonry/foundation.
Tension: masonry and concrete dams should have no tension; the resultant must lie within the middle third of the base ( $e \leq B /6$ ).

Normal stresses at the base:

p = \frac{\sum V}{B} (1 \pm \frac{6 e}{B})

Principal stress at the toe (full reservoir): $σ_{1} = p_{v} sec^{2} α - (p^{'} + p_{e}) tan^{2} α$ (downstream face at angle $α$ to vertical).

Elementary profile

The theoretical profile of a gravity dam is a right-angled triangle with the vertical face upstream, height $H$ equal to the water depth and base $B$ .

FormulaElementary profile (reservoir full, water level at apex)

No tension (resultant at the middle-third point):
- Without uplift: $B = \frac{H}{S _{c}}$
- With full uplift ( $c$ = uplift intensity factor, 1 for full): $B = \frac{H}{S _{c} - c}$
No sliding (friction only): $B = \frac{H}{μ ( S _{c} - c )}$
$S_{c}$ = specific gravity of dam material (≈ 2.4 for concrete).

Limiting height (low vs high gravity dam):

H = \frac{f}{γ _{w} ( S _{c} + 1 )}

( $f$ = allowable compressive stress.) A dam taller than this is a high gravity dam — the downstream face is flattened near the base and the upstream face given a batter to keep stresses within limits.

The practical profile adds a top width (roadway, commonly about 14% of the height with a minimum), freeboard, and upstream/downstream batters near the base.

Galleries, joints and foundation treatment

Galleries — for drainage of seepage (drain holes), inspection, grouting and instrumentation.
Contraction joints (transverse) with shear keys and water stops; longitudinal joints in very large blocks.
Foundation treatment: excavation to sound rock; consolidation grouting (shallow, to strengthen the foundation); curtain grouting (deep, near the heel, to reduce seepage and uplift); drainage holes downstream of the curtain; treatment of faults and seams (dental concrete).

Part 2 of 2

Spillways & Energy Dissipators

Last reviewed 16 Sept 2026 · 9 min read

Spillways

A spillway passes surplus flood water from the reservoir to the river downstream safely, so that the reservoir never rises above the maximum water level and the dam is never overtopped.

Spillway capacity is fixed by the inflow design flood routed through the reservoir (surcharge storage reduces the peak outflow) — see Floods — Estimation & Flood Routing.
Spillway failure (inadequate capacity) is a major cause of dam failures, especially of earth dams.

Components

Entrance (approach) channel.
Control structure — crest (weir, orifice or gates) that regulates outflow.
Discharge channel (conveyance) — the face of the dam, a chute, tunnel or shaft.
Terminal structure — energy dissipator.
Outlet channel — returns water to the river.

Types of spillways

Type	Description	Suitable where
Free overfall (straight drop)	Water falls freely from the crest of a thin section; an apron/cushion pool downstream	Low arch dams, small bunds with rock foundation
Ogee (overflow) spillway	Crest shaped to the lower nappe of a sharp-crested weir; water glides over the downstream face; energy dissipator at the toe	Concrete and masonry gravity dams — most common
Chute (trough) spillway	Crest followed by a steep open channel (chute) conveying water to the river	Earth and rockfill dams; spillway in a saddle away from the dam
Side channel spillway	Crest parallel to the channel; water spills sideways into a trough and then turns 90° down a chute or tunnel	Narrow, steep valleys where a long frontal crest cannot fit
Shaft (morning glory / bell-mouth) spillway	Circular funnel-shaped crest leading to a vertical shaft and horizontal tunnel	Narrow valleys where a diversion tunnel exists; earth dams; small reservoirs with little debris
Siphon spillway	Closed conduit shaped as an inverted U; primes when water rises above the crest and passes large discharges with a small rise in level	Sites needing close control of reservoir level with limited space
Tunnel (conduit) spillway	Closed tunnel carries flow from an inlet structure to downstream	Narrow gorges, arch dams
Labyrinth spillway	Zigzag crest in plan — large crest length within a small width	Increasing capacity of existing spillways
Emergency spillway / fuse plug	Erodible embankment section designed to wash out when a rare flood exceeds service spillway capacity	Supplementary protection for extreme floods

Notes on special types

Shaft spillway — at low heads the flow is crest controlled ( $Q = C (2 π R) H^{3/2}$ ); at higher heads the flow becomes orifice/tube controlled and discharge increases very little with head. Needs debris protection and air vents; vortices must be prevented.
Siphon spillway — discharge $Q = C_{d} a 2 g H$ ; the crown (summit) pressure is negative, so the height of the crown above the downstream water is limited to avoid cavitation; an air vent (deprimer) at FRL stops siphon action when the water level falls; problems include clogging by debris, vibration, sudden surges and ice.

Ogee spillway

Crest profile

The downstream profile follows the lower surface of the nappe from a fully ventilated sharp-crested weir, so that pressures on the surface stay close to atmospheric.

FormulaWES standard ogee profile (vertical upstream face)

x^{1.85} = 2 H_{d}^{0.85} y

$H_{d}$ = design head (excluding velocity of approach head); origin at the crest apex; $y$ measured downward. The upstream crest is formed by compound circular curves; the profile joins the downstream face (slope of the dam) tangentially.

Discharge

FormulaOgee spillway discharge

Q = C L H_{e}^{3/2}

$C$ = coefficient of discharge (about 2.2 in SI units at the design head for a high overflow spillway, varying with head ratio and approach depth); $H_{e}$ = total head including approach velocity head.

Effective crest length with piers and abutments:

L = L^{'} - 2 (N K_{p} + K_{a}) H_{e}

$L^{'}$ = net clear length; $N$ = number of piers; $K_{p}$ = pier contraction coefficient (square-nosed ≈ 0.02, round-nosed ≈ 0.01, pointed ≈ 0); $K_{a}$ = abutment contraction coefficient (square abutment ≈ 0.20, rounded ≈ 0.10).

Head greater than design head — the nappe tends to leave the surface → negative pressures on the crest, higher discharge coefficient, but risk of cavitation and vibration.
Head less than design head — the nappe clings to the surface → positive pressures, lower discharge coefficient.
Design heads are therefore often chosen a little below the maximum head so that negative pressures at maximum flood remain within safe limits.

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