Uplift pressure with Bligh's creep theory

Bligh's creep theory

Water seeping below the structure follows the contact between the base and the subsoil (the creep path). The length of creep $L$ is the sum of the horizontal creep (the horizontal lengths of the contact) and the vertical creep (the lengths of the cutoffs, each counted twice because the water goes down and up):

$$L = L_h + L_v$$

The head loss is assumed to be proportional to the creep length along the path (straight hydraulic gradient line).

   H ~~~~~~~~~|  ____________   ~~~~~~~ (d/s)
   u/s    |   |  |  floor   |  |
   ===+===|===+==+==========+==+====
     pile 1                 pile 2
   point A (start) ... point B (end of creep)
   HGL: straight line from H at A to 0 at B

Safety against piping

$$L \ge C\,H \quad \text{or} \quad \frac{H}{L} \le \frac{1}{C}$$

with Bligh's coefficient $C$ (e.g. 18 for light sand and mud, 15 for fine micaceous sand, 12 for coarse sand, 5-9 for sand mixed with boulders and gravel).

Pressure along the foundation

The head lost up to a point is proportional to the creep length up to it:

$$\text{Head lost up to point } x = H\,\frac{L_x}{L},\qquad h_x = H - H\frac{L_x}{L} = H\left(1 - \frac{L_x}{L}\right)$$

where $h_x$ is the residual (uplift) pressure head at the point and $L_x$ the creep length from the upstream end to it. The uplift pressure on the floor is $\gamma_w h_x$ (in kN/m²).

Safety against uplift

Let $t$ be the floor thickness and $G$ the specific gravity of the floor material. The floor is safe when its submerged weight balances the uplift:

$$\gamma_w (G-1)\,t \ge \gamma_w h_x \Rightarrow t = \frac{h_x}{G-1}$$

Usually 33% is added for safety, i.e. $t = \dfrac{4}{3}\dfrac{h_x}{G-1}$. If the thickness becomes excessive, lengthen the u/s floor or deepen the u/s pile to reduce $h_x$, or thicken the floor.