Question 1

What FoS is required for overturning?

Accepted Answer

USACE EM 1110-2-2200 requires FoS_overturning ≥ 1.5 for normal operating loads, ≥ 1.3 for unusual (flood) loads, and ≥ 1.1 for extreme (earthquake or PMF) loads. The factor is computed as the ratio of resisting moments to overturning moments about the downstream toe of the section.

Question 2

What FoS is required for sliding?

Accepted Answer

USACE uses the shear-friction approach: FoS_sliding = (μ·ΣV + c·A) / ΣH, where c is foundation cohesion and A is base contact area. For friction-only screening (c = 0), FoS_sliding = μ·ΣV/ΣH, with required FoS ≥ 2.0 normal, ≥ 1.7 unusual, ≥ 1.3 extreme. Typical concrete-on-rock μ = 0.7–0.8 if foundation is sound; lower if foliated or weathered.

Question 3

What is uplift and why does it matter so much?

Accepted Answer

Uplift is the upward water pressure under the dam from reservoir water leaking through the foundation contact and pore-water pressure in the rock. Without drainage, uplift varies linearly from γw·h_w at the heel to γw·h_t at the toe — total uplift force is large, often 30–50% of dam weight, and acts at B/3 from the heel, creating significant overturning moment. Drainage galleries with foundation drains reduce uplift at the line of drains to typically 25–50% of intercepted head.

Question 4

What does 'no tension at the heel' mean?

Accepted Answer

For the resultant of all forces to fall within the middle third of the base (the 'kern'), eccentricity e ≤ B/6. When e exceeds B/6, the upstream heel of the dam goes into tension — concrete-rock contact opens up, water enters the open joint, uplift increases dramatically along the cracked length, and the dam can fail catastrophically. USACE requires σ_min ≥ 0 at the heel for normal load combinations and allows tension only for extreme loads.

Question 5

What concrete unit weight should I use?

Accepted Answer

For mass concrete in gravity dams, γc = 150 lb/ft³ (2,400 kg/m³) is the typical design value. RCC (roller-compacted concrete) is similar to slightly lower at 145 lb/ft³. Heavy-aggregate concrete with magnetite or barite reaches 200+ lb/ft³ but is rare. Verify with mix design test data for the specific project.

Question 6

What loads aren't included in this calculator?

Accepted Answer

This screening calc handles dead load, hydrostatic pressure, and base uplift. NOT included: ice loads (typically 5–10 kips/lin ft for cold climates), silt pressure (small for most projects but matters for sediment-laden reservoirs), seismic inertia (USACE EM 1110-2-6053 pseudostatic or response spectrum), wave loads (small but additive), and post-tensioned anchor loads (resisting). Apply each per the relevant USACE EM after passing this screening check.

Load case	FoS overturning	FoS sliding	Base stress (heel)
Normal (usual) operating	≥ 1.5	≥ 2.0	No tension
Flood (unusual)	≥ 1.3	≥ 1.7	No tension
Extreme (earthquake, PMF)	≥ 1.1	≥ 1.3	Limited tension allowed

Concrete Gravity Dam Stability Calculator

Forces (per unit length perpendicular to flow)

Stability checks

USACE required factors of safety

Worked example

Example — 100-ft concrete gravity dam at normal pool

Related tools