Short note: Safety against piping and uplift

Seepage under a hydraulic structure (weir or barrage) can fail it in two ways: uplift pressure on the floor and piping (undermining) of the foundation sand.

Uplift

Water seeping under the floor exerts an upward pressure on its underside. If it exceeds the weight of the floor, the floor cracks or lifts.

• Pressure head at a point is the residual head $h$ left after losses along the creep path.
• Required floor thickness: $t = \dfrac{h}{G-1}$ (Khosla), or $t = \dfrac{4}{3}\dfrac{h}{G-1}$ (Bligh), where $G$ is the specific gravity of the floor material (about 2.24 for concrete).
• Safety measures: thicker floor at the point of highest pressure, longer upstream floor, upstream cut-off piles, and weep holes with an inverted filter.

Piping

At the downstream end, seepage water rises vertically. When the exit gradient exceeds the critical gradient the surface soil grains are lifted, a channel forms (piping), and the structure is undermined.

• Critical gradient: $i_c = \dfrac{G_s - 1}{1 + e} \approx 1.0$ (soil with $G_s = 2.65$, $e = 0.65$).
• Exit gradient (Khosla): $G_E = \dfrac{H}{d}\cdot\dfrac{1}{\pi\sqrt{\lambda}}$ with $\lambda = \dfrac{1+\sqrt{1+\alpha^2}}{2}$, $\alpha = b/d$.
• Safe exit gradient is about 1/4 to 1/5 for shingle, 1/5 to 1/6 for coarse sand and 1/6 to 1/7 for fine sand.

  H.F.L ~~~~~~~~~~~~~~
   upstream  |=== floor ===|  downstream
   cut-off   |             |  d/s pile (d)
             |  seepage    |      ^ exit gradient
             +---<---------+------|

Safety against piping

1. Provide a deep downstream pile (cut-off), the most effective measure.
2. Provide sufficient floor length (Bligh: $L = CH$; Lane's weighted creep).
3. Provide an inverted filter and loaded concrete blocks with gaps beyond the floor.
4. Keep exit gradient below the safe value for the soil.