Seepage Exit Gradient Calculator
Critical hydraulic gradient from soil properties, exit gradient from flow-net (or FEM seepage) data, and the factor of safety against heave at the exit face — the toe-of-dam, levee landside, or excavation-bottom check. Pair with the embankment seepage tool for the flow quantity and the filter criteria tool for piping protection.
The assessment flags FoS < 3 as deficient and 3–4 as marginal against the commonly specified 3–5 range — the governing agency's criterion controls. A passing heave FoS does not demonstrate safety against backward-erosion piping in internally unstable or unfiltered soils; check filter criteria separately. In unit-weight mode, γ′ = γsat − γw with γw = 62.4 pcf (9.81 kN/m³).
Critical gradient for common soils
| Soil state | e | ic |
|---|---|---|
| Dense sand | 0.45 | 1.14–1.17 |
| Medium sand | 0.60 | 1.03–1.06 |
| Loose sand | 0.85 | 0.89–0.92 |
| Silty sand | 0.65–0.90 | 0.87–1.03 |
The rule of thumb ic ≈ 1.0 holds across most granular soils — which is why exit gradients above ~0.3 already draw attention at FoS-of-3 criteria.
Worked example
Example — levee landside toe during high water
References: Terzaghi, K. & Peck, R.B. (1967). Soil Mechanics in Engineering Practice, 2nd ed. USACE EM 1110-2-1901 (1993). Seepage Analysis and Control for Dams. Cedergren, H.R. (1989). Seepage, Drainage, and Flow Nets, 3rd ed. Das, B.M., Principles of Geotechnical Engineering.
Common mistakes
- Taking the average gradient across the whole foundation. Heave happens where the gradient is highest, usually right at the toe or the exit face. Use the local exit gradient from a flow net or seepage model.
- Using total unit weight instead of buoyant unit weight. The critical gradient comes from the submerged weight of the soil. Total unit weight overstates it by about a factor of two.
- Treating a passing factor of safety as protection against piping. Backward-erosion piping can start at gradients well below the heave value in fine, uniform sands. Filter protection at the exit is the main defense.
- Ignoring a thin blanket. Where a clay blanket covers the sand, the check becomes uplift on the blanket, which compares the blanket’s weight with the pressure beneath it.
When this calculator doesn’t apply
The calculation is a one-dimensional heave check for granular soil at a free exit face. Layered foundations, confined aquifers under a blanket and three-dimensional flow concentrations at corners and conduits need a seepage model. Levees and dams should be evaluated with the governing agency’s methods, such as USACE EM 1110-2-1913 for levee underseepage.
Related tools
- Embankment seepage — phreatic surface and seepage quantity
- Filter criteria — piping protection at the exit face
- Slope stability FoS — the companion toe-stability check
- Lateral earth pressure — Rankine coefficients for retaining analyses
- Gravity dam stability — uplift in the rigid-structure case
- Soil permeability k