Choked Drainage Gallery in a Gravity Dam: Uplift Turns Compression into Tension
A 30 m high concrete gravity dam has a vertical upstream face, a 4 m crest and a 22 m base; concrete weighs 24 kN/m³ and the foundation rock has a friction coefficient of 0.70. The reservoir is at full supply level. The original design assumed a linear uplift diagram from full reservoir head at the heel to zero at the toe, and required no tension anywhere at the base. The drainage gallery is shown on the drawings, but its relief wells and weep holes are choked with calcium carbonate. The inspection note records seepage emerging at the toe and a continuous hairline crack along the upstream edge of the base, 0.3 mm wide. The safety committee must decide whether the reservoir may be retained at full supply level through the coming monsoon.
1. Check the dam as it stands for base stresses and sliding, showing all steps.
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Step 1 - Self weight and its line of action (per metre length). Section is a right trapezoid: area = (4 + 22)/2 x 30 = 390 m²; W = 390 x 24 = 9360 kN. Centroid from heel: x̄ = (1/A)∫(b(y)²/2)dy with b(y) = 22 − 0.6y gives x̄ = 7.54 m from the heel.
Step 2 - Uplift (full, as the drains are choked). U = 0.5 x 9.81 x 30 x 22 = 3237 kN, acting at 2/3 x 22 = 14.67 m from the heel.
Step 3 - Resultant vertical force and its eccentricity. ΣV = 9360 − 3237 = 6123 kN. Moment about heel: 9360 x 7.54 − 3237 x 14.67 = 70 570 − 47 490 = 23 080 kN·m. x̄R = 23 080/6123 = 3.77 m from the heel, so from the centreline e = 11 − 3.77 = 7.23 m, against B/6 = 3.67 m.
Step 4 - Base stresses. σ = ΣV/B (1 ± 6e/B) = 278.3 x (1 ± 1.973) σ_toe = 827 kPa (compression); σ_heel = −270 kPa (tension).
Step 5 - Sliding. Water thrust P = 0.5 x 9.81 x 30² = 4414.5 kN. F = μΣV/P = 0.70 x 6123/4414.5 = 0.97 < 1.0.
Judgement. The dam fails on two counts: the resultant falls outside the middle third, producing 270 kPa tension at the heel, and the sliding factor is below unity. The hairline crack at the upstream edge is the direct physical confirmation - the heel has already been prised apart by uplift, and once a crack opens the full reservoir head acts over the whole base, making the figures above optimistic rather than conservative. The reservoir should not be retained at full supply level until the drains are restored.
2. Quantify the effect of restoring the drainage gallery, taking it 2 m from the heel and assuming it relieves the head effectively.
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Step 1 - Uplift with working drainage. With effective relief wells at 2 m from the heel, the head falls from the full reservoir head at the heel to near zero at the gallery, and is effectively zero downstream of it. The uplift diagram is a narrow triangle over 2 m only: U = 0.5 x 9.81 x 30 x 2 = 294 kN, acting at (2/3) x 2 = 1.33 m from the heel.
Step 2 - Resultant and eccentricity. ΣV = 9360 − 294 = 9066 kN. Moment about heel = 70 570 − 294 x 1.33 = 70 180 kN·m. x̄R = 70 180/9066 = 7.74 m; e = 11 − 7.74 = 3.26 m < B/6 = 3.67 m.
Step 3 - Base stresses. σ = 9066/22 x (1 ± 6 x 3.26/22) = 412 x (1 ± 0.889) σ_toe = 778 kPa; σ_heel = 46 kPa compression - no tension.
Step 4 - Sliding. F = 0.70 x 9066/4414.5 = 1.44, comfortably above unity (though still below the 1.5 usually sought for the friction-only case).
Judgement. Cleaning the drains converts a 270 kPa heel tension into 46 kPa compression and lifts the sliding factor from 0.97 to 1.44. This single maintenance action does more than any structural measure, and it costs a fraction of one. Note what it does not fix: the friction-only factor of 1.44 is still short of 1.5, so the committee should require either a shear key, a downstream apron with drains and a nominal cut-off, or acceptance of the value with documented justification based on the rock-concrete bond and cohesion being mobilised. The uplift assumed here is best-case; a piezometer reading is needed to confirm it, because the heel zone upstream of the gallery still carries the full head over 2 m and a poorly sealed gallery will not give the assumed relief.
3. Set out the decision and the monitoring you would require before and during the monsoon.
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Decision. Full supply level may be retained only after the drainage gallery has been physically cleaned, its relief wells proved flowing and clear, and the heel piezometric head measured and shown to match the design assumption. Until then, the reservoir should be held at least 5 m below full supply level - the reduction cuts the uplift and the water thrust roughly by (25/30)² = 0.69, which alone brings the resultant back towards the middle third - and the decision reviewed weekly.
Priority of remedial actions.
- Drainage first. De-choke the weep holes and relief wells by high-pressure water jetting and mechanical cleaning, and where calcium carbonate scaling is chronic, treat it as a water-chemistry problem: investigate the seepage water for carbonate hardness and consider a grout curtain to reduce the flow that carries the scale.
- Seal the heel crack. Grout the upstream crack with a compatible cementitious or epoxy grout after the drains are working, since grouting first would trap water under the base.
- Sliding. Add a shear key or a weighted downstream apron if the friction factor cannot be raised to the required value; record the justification if reliance is placed on cohesion.
Monitoring to be installed and read.
- Standpipe piezometers in the gallery and in the foundation downstream, read weekly during the monsoon; the target is that the gallery piezometric level stays close to the gallery floor.
- Uplift pressure cells or additional weep-hole flow measurement, recorded against reservoir level.
- Precise survey points on the crest and a plumb-line or inverted pendulum reading, to detect tilt; a 0.3 mm heel crack should not be allowed to widen.
- Visual inspection of the toe seepage for turbidity - muddy seepage means internal erosion of the foundation, which is a different and more urgent emergency from uplift.
- A written operating rule for the reservoir level, and a defined trigger for lowering it if any piezometer or tilt reading exceeds the design envelope.