## Info

Hence the total characteristic resistance is now:

7.7.5 Stability of weir against hydraulic failure

Example 7.5 considers the design of the weir shown in Figure 7.15 against hydraulic failure at its toe when water emerges with too large an exit gradient.

In order to assess the exit hydraulic gradient at the toe of the weir, we have chosen to use an analytical solution, rather than carry out a flow net or numerical solution. This has the advantage of enabling the solution of a range of problems without drawing a flow net for each change in geometry.

### Notes on Example 7.5

O The exit gradient can be determined in a number of ways (for example, by drawing a flow net) - this equation has the advantage of providing a convenient analytical solution.12

© The exit gradient is calculated by substituting the values of B, hw, and d into Khosla's equation O.

© For limit state HYD, partial factors are given in EN 1997-1 Annex A5.

0© Eurocode 7 provides two expressions, 2.9(a) and 2.9(b), for verifying HYD. The former compares the design destabilizing pore water pressure to the design stabilizing vertical stress; the latter compares the design destabilizing seepage force to the design stabilizing submerged weight. Both equations are applied at the base of the column of soil under consideration.

Example 7.5 Stability of weir against hydraulic failure Verification of stability against piping (HYD)

### Design situation

Consider a weir of width B = 15m which is retaining free water of height hw = 5m. A cut-off wall of depth d = 3.2m helps to reduce the hydraulic gradient at the downstream end of the weir (the 'exit' gradient). The weir is founded on a permeable stratum of characteristic weight density kN

Yk = 19.5-. An impermeable stratum is located at depth D = <x>. The m kN

characteristic weight density of water is Yw = 9.81-.

Calculation model

For the situation where D = <x>, the exit gradient can be calculated from Khosla's equation:©

0 0