Uplift on floors downstream of a weir crest: minimum floor thickness If the hydraulic gradient line is h metres above a floor of thickness t and the material of the floor has specific gravity G, what minimum thickness t is required downstream of the crest wall to resist uplift?

Introduction / Context:
Hydraulic structures on pervious foundations are subjected to upward seepage pressures. The floor thickness must be adequate so that its submerged weight can counter the uplift to prevent heave or failure.

Given Data / Assumptions:

• Hydraulic gradient line (HGL) lies h metres above the floor soffit.
• Floor material has specific gravity G (with respect to water).
• Objective: minimum floor thickness t to prevent uplift at that section.

Concept / Approach:
Upward water pressure per unit area at the floor = γ_w * h. Downward resisting force per unit area due to the floor = (γ_floor − γ_w) * t = γ_w * (G − 1) * t. For safety at the limiting case, set resisting pressure equal to uplift pressure and solve for t.

Step-by-Step Solution:
Uplift pressure = γ_w * h.Resisting pressure = γ_w * (G − 1) * t.Equate: γ_w * (G − 1) * t = γ_w * h ⇒ t = h / (G − 1).

Verification / Alternative check:
The relation is dimensionally correct (both sides have length units). Additional safety may be provided by factors of safety or by drains/relief wells that lower h, reducing t required.

Why Other Options Are Wrong:
t = h * (G − 1): Overestimates thickness; not derived from equilibrium.t = h / G or G / h: Do not reflect the buoyancy reduction (G − 1) term.

Common Pitfalls:

• Using total unit weight instead of submerged unit weight.
• Ignoring reduction in uplift due to floor drains or cutoffs (which would lower h).

Final Answer:
t = h / (G − 1)