Dams and spillways

In short

A dam is a barrier across a river that stores water and raises its level; a spillway is the controlled outlet that passes surplus flood water safely downstream so the dam is never overtopped. Dam engineering combines structural stability (forces, stresses, factors of safety), seepage control and open-channel hydraulics at the spillway and its energy dissipator. India has over 6,000 large dams — the third-largest number in the world — operating under the Dam Safety Act, 2021, so the subject matters for design, inspection and rehabilitation work alike. It is examined in GATE Civil (Water Resources), university Water Resources/Irrigation Engineering papers, and in technical rounds for CWC, state irrigation departments, NHPC, NTPC, SJVN, WAPCOS and consultancies such as AFCONS, L&T and Tata Projects.

Explained

Classification of dams and selection of type

• By function: storage (conservation), detention (flood moderation), diversion (barrage/weir, raises level without large storage), coffer dam (temporary).
• By material and structural action:
  • Gravity dam — resists water thrust by its own weight; masonry or concrete; needs sound rock foundation. Bhakra (226 m, concrete gravity), Nagarjuna Sagar (masonry).
  • Embankment (earthfill/rockfill) dam — resists by mass and friction; flexible, accepts weaker foundations; cannot be overtopped. Tehri (260.5 m, earth-and-rockfill — India's tallest), Hirakud (longest, composite).
  • Arch dam — transfers thrust to abutments by arch action; needs a narrow gorge with strong rock; thin and economical in concrete. Idukki (double-curvature arch, Kerala).
  • Buttress dam — thin deck (flat slab or multiple arches) supported on buttresses; saves concrete, more formwork and steel.
• Selection factors: topography of the valley, foundation geology, availability of construction material, spillway location and size, seismicity (IS 1893 Part 1 zones), diversion during construction, cost and construction time.
• Classification by height (IS/CWC "large dam"): height above lowest foundation > 15 m, or 10–15 m with crest length > 500 m, storage > 1 Mm³ or flood discharge > 2,000 m³/s.

Forces on a gravity dam and stability requirements

• Forces considered: self-weight W (through the centroid of each part), water pressure on upstream (and tailwater on downstream) face, uplift (pore) pressure at the base, silt pressure, wave pressure, ice pressure (not for India), earthquake forces (inertia of dam + hydrodynamic pressure of reservoir), and earth/temperature effects.
• Water pressure: triangular, resultant P = ½ γ H² per metre length acting at H/3 above the base, where γ = 9.81 kN/m³.
• Uplift: reduces effective weight. Assumed 100% of reservoir head at the heel and tailwater head at the toe, varying linearly, but a line of drainage holes / drainage gallery near the upstream face reduces intensity there to tailwater + (1/3)(headwater − tailwater) in Indian and USBR practice.
• Earthquake (seismic coefficient method): horizontal inertia force = αh W acting at the centroid; vertical force = αv W (reduces effective weight when acting upward). Hydrodynamic pressure from Zangar's / Westergaard's formula, pe = Cm αh γ h.
• Modes of failure: (1) overturning about the toe, (2) sliding (shear) on the base or a weak seam, (3) crushing/compression failure (stress exceeding allowable), (4) tension development in concrete or masonry, (5) foundation failure or piping.
• Requirements (IS 6512: criteria for design of solid gravity dams):
  • Factor of safety against overturning = ΣM(resisting)/ΣM(overturning) ≥ 1.5 (normal loading); ≥ 1.2 with earthquake.
  • Sliding factor = ΣH/ΣV ≤ coefficient of friction μ; the better shear friction factor SFF = (μΣV + c·B)/ΣH ≥ 4–5 normal, ≥ 1.5–2.5 for extreme loads.
  • No tension at the heel under reservoir full and at the toe under reservoir empty — eccentricity e ≤ B/6, i.e. resultant must pass within the middle third of the base.
  • Maximum compressive stress ≤ allowable (concrete about 3–4 MPa in old masonry dams, higher in modern concrete), with allowance for the principal and shear stress at the toe.
• Base stress: combined direct and bending stress, pmax/min = (ΣV/B)(1 ± 6e/B) — pmin < 0 means tension.

Elementary profile and practical gravity-dam section

• Elementary profile: a triangle with zero width at the top and base width B at the bottom — the theoretical minimum section that satisfies no-tension and no-sliding.
  • No tension (with uplift factor c): B = H/√(Sc − c), reducing to H/√(Sc) when uplift is neglected, where Sc = specific gravity of dam material (≈ 2.4).
  • No sliding: B = H/[μ(Sc − c)].
  • The larger of the two governs. Limiting height: beyond H = f/[γ(Sc + 1)] (f = allowable stress) the stress limit governs and the dam is called a high dam, needing a non-elementary profile.
• Practical profile differs from the triangle: a finite top width (3–8 m, for a roadway, typically 14% of H), freeboard above the maximum water level, a slight upstream batter near the base, and a fillet at the heel. Added top weight introduces tension at the toe when the reservoir is empty, corrected by the upstream batter.
• Galleries: foundation/drainage gallery (collects seepage, houses grout and drainage holes), inspection galleries, instrumentation for uplift, deflection, pore pressure and seismic response.
• Joints: transverse contraction joints divide the dam into monoliths (15–20 m) with water stops (seals); longitudinal joints in very wide blocks; grout curtain near the heel reduces seepage and uplift.
• Temperature control: low-heat cement, pozzolana/fly ash, pre-cooling aggregates, post-cooling by embedded pipes; RCC (roller-compacted concrete) dams allow thin layers and rapid placement (used at Ghatghar, Maharashtra).

Embankment dams: seepage, stability and filters

• Zones: impervious core (clay) controlling seepage; pervious shells (sand, gravel, rock) giving stability; filters and transition zones preventing migration of fines; riprap on the upstream slope against waves; cut-off trench or diaphragm into rock; chimney and horizontal blanket drains; toe drain.
• Seepage line (phreatic line): approximately a base parabola (Casagrande) with focus at the downstream toe of the drain; discharge through the body per metre length q = k·s (Casagrande), where s = focal distance.
• Seepage quantity by flow net: q = k H (Nf/Nd), with Nf flow channels and Nd equipotential drops.
• Piping and internal erosion: failure when the exit gradient exceeds the critical value, or fines wash through. Controlled by filter design (Terzaghi criteria: D15(filter) ≥ 4–5 D15(base) for permeability, ≤ 4–5 D85(base) for retention) and by IS 9429 drainage provisions.
• Slope stability: analysed by the Swedish slip-circle / Bishop's method for (a) end of construction, (b) steady seepage with reservoir full (downstream slope critical), (c) sudden drawdown (upstream slope critical, pore pressures trapped), each with and without earthquake. Minimum FOS typically 1.5 (steady seepage), 1.3 (construction and drawdown), 1.0–1.2 with seismic loading, per IS 7894.
• Causes of failure (statistically): hydraulic — overtopping and wave erosion (about one-third of failures); seepage — piping, sloughing, conduit leakage; structural — slope slides, settlement, foundation spreading.

Spillways: types, design discharge and gates

• Purpose: pass the design flood safely, with adequate freeboard, without damage to the dam, its foundation or the downstream channel. Spillway capacity is fixed by flood routing of the inflow design flood through the reservoir (IS 11223 for inflow design flood).
• Inflow design flood (IS 11223 / CWC practice): small dams — 100-year flood; intermediate — Standard Project Flood (SPF); large dams — Probable Maximum Flood (PMF). Classification by gross storage and hydraulic head.
• Types:
  • Ogee (overflow) spillway — crest shaped to the lower nappe of a freely falling jet, so the flow has near-atmospheric pressure at design head; the commonest type on gravity dams.
  • Chute (open channel/trough) spillway — flow carried in a steep lined channel away from the dam; common for earthfill dams (Ukai, Hirakud auxiliary).
  • Side-channel spillway — crest along one side of a channel running roughly parallel to it; used in narrow gorges.
  • Shaft (morning-glory) spillway — circular crest leading to a vertical shaft and tunnel; capacity "drowns out" at high heads, so it needs care. Used at Tehri; Hungry Horse (USA) is the classic morning-glory.
  • Siphon spillway — primes automatically and runs under full siphonic head, giving high discharge at small head rise; risk of air locking and sudden surges.
  • Duckbill, labyrinth and fuse-plug (emergency) spillways — increase crest length or act as a sacrificial washout section.
• Crest shape (ogee): downstream profile xⁿ = K Hdⁿ⁻¹ y (USBR/WES form, for vertical upstream face n ≈ 1.85, K ≈ 2.0); upstream quadrant made of compound circular arcs.
• Gates: radial (Tainter) gates — most common on Indian barrages and spillways; vertical lift gates; drum and flap gates; stop logs for maintenance. Gated spillways store water up to the gate top, so operation schedules and rule curves become a dam-safety issue (Kerala 2018 and Chennai 2015 floods).
• Cavitation and aeration: at high velocities (> about 15–20 m/s) negative pressures pit the concrete; prevented by smooth profiles, a well-shaped crest and aerators (air slots) on chute and tunnel spillways.

Energy dissipation below spillways

• Need: the jet arrives with large kinetic energy; unchecked, it erodes the river bed and undermines the dam.
• Hydraulic jump based (stilling basin): the standing wave converts supercritical to subcritical flow. Choice between Type I–IV (USBR) and Indian IS 4997 designs depends on the Froude number F1 at the jump:
  • F1 < 1.7 — no appreciable jump; F1 = 1.7–2.5 weak jump; 2.5–4.5 oscillating jump (avoid — waves travel downstream, USBR Type IV / wave suppressor); 4.5–9 steady jump (Type III basin with chute blocks, baffle blocks, end sill); > 9 strong jump (Type II with chute blocks and dentated sill, long basin).
  • Appurtenances: chute blocks (split and aerate the incoming jet), baffle blocks (dissipate energy, not used above about 15 m/s to avoid cavitation), end sill (deflects residual flow upward).
• Tailwater considerations: compare the jump rating curve (y2) with the tailwater rating curve (TWC):
  • TWC lies above y2 — jump is drowned; use a sloping apron or a roller/ski-jump bucket.
  • TWC lies below y2 — jump sweeps out; depress the apron or provide a baffle/end sill to force the jump.
• Other dissipators: solid roller bucket (low tailwater variation), slotted roller bucket, ski-jump / flip bucket with trajectory and plunge pool (used widely on Indian high dams — Srisailam, Nagarjuna Sagar), plunge pool / free fall for arch dams, impact and USBR Type VI basins for conduit outlets.
• Downstream protection: launching apron, cut-off walls, inverted filter and toe walls; scour depth estimated from Lacey's regime scour (R = 1.35 (q²/f)^1/3) for alluvial rivers.

Indian codes, law and dam safety practice

• IS 6512 — design of solid gravity dams; IS 11223 — selection of inflow design flood; IS 7894 — stability of earth dams; IS 8826 / IS 9429 — rockfill and drainage; IS 4997 — hydraulic jump type stilling basins; IS 7365 — bucket type energy dissipators (roller and ski-jump); IS 5186 — chute and side channel spillways; IS 10137 — selection of spillways and energy dissipators; IS 4623 — radial gates; IS 1893 (Part 1) — seismic zoning; IS 7894 / IS 12169 for small embankment dams.
• Dam Safety Act, 2021 — created the National Dam Safety Authority (NDSA), National Committee on Dam Safety (NCDS), and state-level SDSO/SCDS; mandates pre- and post-monsoon inspections, comprehensive safety evaluation, emergency action plans (EAP), instrumentation and hazard classification for "specified dams" (height > 15 m, or 10–15 m with specified features).
• DRIP (Dam Rehabilitation and Improvement Project) — World Bank/CWC-funded rehabilitation of existing dams (Phase II/III ongoing); National Register of Large Dams (NRLD) maintained by CWC.
• Environmental and R&R: clearance under the Environment (Protection) Act, 1986 and EIA Notification 2006, Forest (Conservation) Act, 1980, and the LARR Act, 2013 for land acquisition and resettlement; Water (Prevention and Control of Pollution) Act, 1974 for downstream quality.
• Instrumentation: piezometers, inclinometers, settlement gauges, uplift pressure cells, strong-motion accelerographs, seepage measuring weirs — monitoring data is the basis of safety review.

Key points

• Gravity dam - resists overturning and sliding by its own weight; requires sound rock foundation.
• Uplift pressure - pore pressure under the base that reduces effective weight; cut by a grout curtain and a line of drainage holes.
• Middle-third rule - resultant must pass within the middle third (e ≤ B/6) so no tension develops at the heel or toe.
• Shear friction factor - (μΣV + cB)/ΣH; stricter and more realistic than the plain sliding factor ΣH/ΣV ≤ μ.
• Elementary profile - triangle with B = H/√(Sc − c) from the no-tension criterion; compare with the sliding criterion and take the larger.
• Low vs high dam - a low dam's height is below the limiting height f/[γ(Sc + 1)]; above it, allowable stress governs the profile.
• Arch dam - carries load to abutments by arch compression; thinnest section but needs a narrow gorge and strong flanks.
• Earthfill dam - cannot tolerate overtopping; fails mainly by overtopping, piping and slope slides.
• Phreatic line - the top seepage surface in an embankment, drawn as Casagrande's base parabola; seepage q = k·s.
• Filter criteria - Terzaghi's grain-size ratios keep the drain pervious yet retain base soil, preventing piping.
• Critical loading cases (earth dam) - end of construction, steady seepage (downstream slope), sudden drawdown (upstream slope).
• Ogee crest - shaped to the lower nappe so pressures are near atmospheric at the design head; Cd ≈ 2.1–2.2 (SI).
• Inflow design flood - 100-year for small dams, SPF for intermediate, PMF for large dams (IS 11223).
• Froude number governs the stilling basin - F1 2.5–4.5 is the troublesome oscillating-jump range; 4.5–9 suits USBR Type III.
• Roller/ski-jump bucket - used where tailwater is deep or variable, throwing the jet clear of the structure.
• Cavitation - caused by negative pressures at velocities above roughly 15–20 m/s; controlled by aerators and smooth profiles.
• Dam Safety Act, 2021 - NDSA and state SDSOs, mandatory inspections, EAP and instrumentation for specified dams.
• Freeboard - vertical distance from the maximum water level to the dam top, covering wave run-up and settlement.

Formulas and examples

Example 1 — Stability of a gravity dam section. A concrete gravity dam, 60 m high, top width 6 m, base width 48 m, upstream face vertical, water up to 57 m. Concrete unit weight 24 kN/m³. Uplift neglected. Check e, base stresses and overturning (per metre length).

• Split the section: rectangle 6 m × 60 m and triangle (48 − 6) = 42 m × 60 m.
• W1 = 6 × 60 × 24 = 8,640 kN; lever arm from heel = 3 m → M1 = 25,920 kN·m.
• W2 = ½ × 42 × 60 × 24 = 30,240 kN; centroid at 6 + 42/3 = 20 m → M2 = 604,800 kN·m.
• ΣV = 38,880 kN; ΣM_resisting (about heel) = 630,720 kN·m.
• P = ½ × 9.81 × 57² = 15,936 kN, at 57/3 = 19 m → M_overturning = 302,790 kN·m.
• Resisting moment about the toe = W1(48 − 3) + W2(48 − 20) = 8,640 × 45 + 30,240 × 28 = 388,800 + 846,720 = 1,235,520 kN·m. (About the heel the thrust's moment *adds*, not subtracts: x̄ = (630,720 + 302,790)/38,880 = 24.01 m from the heel — the same point.)
• Overturning moment about toe = 302,790 kN·m → FOS = 1,235,520/302,790 = 4.08 > 1.5, safe.
• Distance of resultant from toe x = (1,235,520 − 302,790)/38,880 = 932,730/38,880 = 23.99 m; e = 24 − 23.99 ≈ 0.01 m ≪ B/6 = 8 m → no tension.
• p_max/min = (38,880/48)(1 ± 6 × 0.01/48) = 810 × (1 ± 0.00125) ≈ 811 kPa and 809 kPa — both compressive, well within concrete capacity.
• Sliding factor = 15,936/38,880 = 0.41; with μ = 0.7 this is safe. SFF with c_s = 1,400 kPa: (0.7 × 38,880 + 1,400 × 48)/15,936 = (27,216 + 67,200)/15,936 = 5.92 > 5, safe.

Example 2 — Effect of uplift. Same dam, now with full uplift varying from γH = 9.81 × 57 = 559.2 kPa at the heel to zero at the toe.

• U = ½ × 559.2 × 48 = 13,421 kN upward, acting at 48/3 = 16 m from the heel, i.e. 32 m from the toe.
• ΣV = 38,880 − 13,421 = 25,459 kN.
• Moment of U about the toe (de-stabilising) = 13,421 × 32 = 429,472 kN·m.
• FOS(overturning) = 1,235,520/(302,790 + 429,472) = 1,235,520/732,262 = 1.69 — still ≥ 1.5 but much reduced.
• x from toe = (1,235,520 − 732,262)/25,459 = 503,258/25,459 = 19.77 m; e = 24 − 19.77 = 4.23 m < 8 m, no tension.
• p_max (toe) = (25,459/48)(1 + 6 × 4.23/48) = 530.4 × 1.529 = 811 kPa; p_min (heel) = 530.4 × 0.471 = 250 kPa.
• Sliding factor = 15,936/25,459 = 0.63 — close to μ = 0.7. *Conclusion: uplift cuts the overturning FOS from 4.08 to 1.69 and raises the sliding ratio by half (0.41 → 0.63) — hence grout curtains and drainage galleries.*

Example 3 — Elementary profile. Find the base width of an elementary profile 70 m high, S_c = 2.4, μ = 0.75, (a) uplift neglected (c = 0), (b) full uplift (c = 1).

• (a) No tension: B = 70/√2.4 = 70/1.549 = 45.2 m. No sliding: B = 70/(0.75 × 2.4) = 70/1.8 = 38.9 m → governing 45.2 m.
• (b) No tension: B = H/√(S_c − c) = 70/√(2.4 − 1) = 70/1.183 = 59.2 m. No sliding: B = 70/[0.75(2.4 − 1)] = 70/1.05 = 66.7 m → governing 66.7 m.
• Full uplift increases the required base from about 45 m to about 67 m — a 48% increase in material.
• Limiting height for f = 3,000 kPa: H = 3,000/[9.81(2.4 + 1)] = 3,000/33.35 = 90 m; a 70 m dam is therefore a "low" dam by this criterion.

Example 4 — Spillway discharge and gated crest. An ogee spillway has 6 bays of 12 m clear width separated by 2 m piers, C = 2.2, design head H_e = 4.5 m, pier contraction coefficient K_p = 0.02 (5 piers, 2 ends with K_a = 0.1).

• L (clear) = 6 × 12 = 72 m. Effective length L_e = 72 − 2 × 4.5 × (5 × 0.02 + 0.1) = 72 − 9 × 0.2 = 72 − 1.8 = 70.2 m.
• Q = 2.2 × 70.2 × 4.5^1.5 = 2.2 × 70.2 × 9.545 = 1,474 m³/s.
• At half the design head (2.25 m): Q ≈ 2.2 × 71.0 × 2.25^1.5 = 2.2 × 71.0 × 3.375 = 527 m³/s — discharge falls as H^1.5, so a small head rise gives a large capacity gain.
• Discharge intensity q = 1,474/70.2 = 21.0 m³/s per m.

Example 5 — Stilling basin design. The above spillway discharges q = 21 m³/s/m at the toe with velocity V1 = 24 m/s.

• y1 = q/V1 = 21/24 = 0.875 m.
• F1 = 24/√(9.81 × 0.875) = 24/√8.584 = 24/2.930 = 8.19 → steady jump; USBR Type III basin (but check baffle blocks — inlet velocity 24 m/s exceeds the ~15–18 m/s limit, so a Type II basin with chute blocks and a dentated end sill is safer).
• y2 = 0.875/2 × [√(1 + 8 × 8.19²) − 1] = 0.4375 × [√(1 + 536.6) − 1] = 0.4375 × (23.19 − 1) = 0.4375 × 22.19 = 9.71 m.
• V2 = 21/9.71 = 2.16 m/s — subcritical, as required.
• Energy loss E_L = (9.71 − 0.875)³/(4 × 0.875 × 9.71) = (8.835)³/33.99 = 689.7/33.99 = 20.3 m of head — about 67% of the pre-jump specific energy E1 = 0.875 + 24²/(2 × 9.81) = 0.875 + 29.36 = 30.2 m.
• Basin length ≈ 4.3 y2 ≈ 42 m (Type II). If the tailwater depth is only 7.5 m (< 9.71 m), the apron must be depressed by about 2.2 m or an end sill added, otherwise the jump sweeps out.

Where it is used

• Design and consultancy: CWC, WAPCOS, Central Water & Power Research Station (CWPRS, Pune — physical and numerical spillway models), NHPC, SJVN, THDC, NEEPCO; design engineer roles do stability sheets, flood routing and gate sizing.
• Construction: L&T, AFCONS, HCC, Tata Projects, Megha Engineering on projects such as Polavaram (Andhra Pradesh), Subansiri Lower, Punatsangchhu and Pakal Dul; roles in RCC/mass-concrete placement, grouting and spillway gate erection.
• Operation and safety: state irrigation/WRD dam-safety cells, SDSOs under the Dam Safety Act — pre/post-monsoon inspection, instrumentation review, reservoir rule curves, EAP drills; DRIP rehabilitation packages (spillway re-profiling, gate refurbishment, filter upgrades).
• Hydropower: intake, penstock and spillway hydraulics for projects from micro-hydro to Tehri (1,000 MW) and Sardar Sarovar (gravity dam with the world's second-largest concrete volume, gated spillways of about 87,000 m³/s capacity).
• Flood management and irrigation: barrages and diversion weirs (Farakka, Hathnikund, Prakasam), tank rehabilitation in Tamil Nadu/Telangana, Krishna-Godavari and interlinking projects.
• Specialised services: geotechnical investigation and grouting contractors, instrumentation suppliers, hydraulic model testing labs (CWPRS, IIT hydraulics labs), and gate/hoist manufacturers (BHEL, Texmaco, Om Metals).

Interview questions

• Q: Why must the resultant force pass through the middle third of a gravity dam's base? A: Because e ≤ B/6 keeps both base stresses compressive; outside it, tension develops at the heel (reservoir full), opening a crack that admits water and raises uplift.
• Q: How does a drainage gallery improve dam stability? A: It intercepts seepage through the body and foundation and relieves pore pressure, reducing the uplift intensity near the heel to roughly tailwater + one-third of the net head, which restores effective weight.
• Q: Why is the shear friction factor preferred to the sliding factor? A: The sliding factor ignores the cohesion/shear strength of the concrete-rock bond; the shear friction factor includes μΣV plus the shear resistance cB, which is how a real base actually fails.
• Q: When would you choose an earthfill dam over a gravity dam? A: When the foundation rock is weak or deep, the valley is wide, and suitable earth/rock borrow material is available locally; a separate chute or saddle spillway is then provided since the embankment cannot be overtopped.
• Q: Why is the ogee crest shaped to the lower nappe of a free jet? A: So that at the design head the flow follows the profile with pressures close to atmospheric — no separation, no sub-atmospheric zones and hence maximum discharge coefficient without cavitation.
• Q: What happens to an ogee spillway at heads above and below the design head? A: Below the design head the nappe presses on the crest (positive pressure, slightly reduced coefficient); above it, the flow springs clear and sub-atmospheric pressures develop, risking cavitation.
• Q: How do you decide which USBR stilling basin to use? A: From the Froude number of the incoming jet — Type IV or wave suppressors for F1 2.5–4.5, Type III with baffle blocks for 4.5–9 at moderate velocity, and Type II with chute blocks and a dentated sill for F1 above 9 or inlet velocity above about 15–18 m/s.
• Q: What do you do if the tailwater depth is less than the required y2? A: Force the jump by depressing the apron, adding an end sill or baffles, or widening the basin; otherwise the jump sweeps downstream and erodes the unprotected bed.
• Q: Which slope of an earth dam is critical under sudden drawdown, and why? A: The upstream slope — the reservoir water that supported it is removed while pore pressures inside remain high, so the effective stresses and the factor of safety drop.
• Q: What is the difference between SPF and PMF? A: SPF is the flood from the most severe storm reasonably characteristic of the region (no transposition maximisation); PMF is from the probable maximum precipitation, the physical upper limit, and is used for large dams.
• Q: Why are contraction joints and water stops provided in a concrete gravity dam? A: They let the monoliths shrink and move independently with temperature and foundation settlement without cracking, and the embedded seals stop water leaking through the joint.
• Q: What does the Dam Safety Act, 2021 require of a dam owner? A: Hazard classification, pre- and post-monsoon inspections, instrumentation and data reporting, periodic comprehensive safety evaluation and an emergency action plan, under the oversight of the state SDSO and the NDSA.

Common mistakes

• Taking moments about the heel and the toe inconsistently, or forgetting that uplift acts upward *and* has its own moment — this is the commonest source of wrong factors of safety.
• Neglecting uplift in stability checks, which flatters the design badly (Example 2 shows FOS falling from 4.08 to 1.69).
• Using the no-tension base width alone; the sliding criterion often governs, especially when uplift is included.
• Confusing the Froude number of the incoming (supercritical) flow with that after the jump, and reading the wrong basin type.
• Using y2 from the jump equation as the tailwater depth — they are independent; the design hinges on comparing the two rating curves.
• Mixing unit weight (kN/m³) with density (kg/m³), or using H^1.5 with the wrong coefficient set (C ≈ 2.2 in SI, 3.97 in FPS).
• Drawing the phreatic line ending at the downstream face instead of at the drain/toe filter, and then wrongly concluding the slope is unsafe.

Related topics

Hydrology · Flood control and river engineering · Open channel flow · Irrigation engineering · Groundwater hydraulics · Fluid properties and statics