What is the maximum vertical stresses at the tie and heel of the dam?

The maximum vertical stresses at the tie and heel of a dam are typically calculated using the formula:

σ = γh + q

Where:
σ = maximum vertical stress
γ = unit weight of water
h = depth of water above the tie or heel
q = any additional vertical load on the tie or heel

The maximum vertical stress at the tie and heel of the dam will depend on the specific design and loading conditions of the dam. It is important to consult with a structural engineer or dam design specialist to accurately determine the maximum vertical stresses at these locations.

Maximum Vertical Stress at the Tie

The maximum vertical stress at the tie (upstream face) of a gravity dam occurs at the base of the dam and is given by the formula:

```
σ<sub>max,tie</sub> = γH
```

where:

- σ_max,tie is the maximum vertical stress at the tie (kN/m²)
- γ is the unit weight of the dam material (kN/m³)
- H is the height of the dam (m)

Maximum Vertical Stress at the Heel

The maximum vertical stress at the heel (downstream face) of a gravity dam occurs slightly below the base of the dam and is given by the formula:

```
σ<sub>max,heel</sub> = γH(1 - c)
```

where:

- σ_max,heel is the maximum vertical stress at the heel (kN/m²)
- γ is the unit weight of the dam material (kN/m³)
- H is the height of the dam (m)
- c is the coefficient of friction between the dam and the foundation (dimensionless)