To calculate the average total stress below the tunnel element, we need to consider two primary factors:

1. Weight of the tunnel element itself, which will exert stress due to its volumetric weight.
2. The water column above the tunnel element, which will contribute additional pressure based on the depth of the river.

Step-by-step Calculation:

1. Weight of the Tunnel Element

The tunnel element has:

• Width ($W$) = 45 m
• Height ($H$) = 8 m
• Volumetric weight of concrete = 25 kN/m²

We can calculate the weight of the tunnel element using the volumetric weight, which is expressed in terms of area but can be converted for volume by assuming a unit length (per meter depth):

$\text{Weight of tunnel per meter} = \text{width} \times \text{height} \times \text{volumetric weight}$

$\text{Weight of tunnel} = 45 \, \text{m} \times 8 \, \text{m} \times 25 \, \frac{kN}{m^2} = 9000 \, \text{kN/m}$

This is the force exerted by the tunnel per meter length.

2. Water Column Pressure

The depth of the river is 14 m, but the tunnel extends 2 m above the water surface. Therefore, the effective water depth on top of the tunnel element is:

$\text{Effective water depth} = 14 \, \text{m} - 2 \, \text{m} = 12 \, \text{m}$

The pressure exerted by the water column can be calculated using the equation for hydrostatic pressure:

$\text{Water pressure} = \rho \cdot g \cdot h$

Where:

• $\rho$ is the density of water (1000 kg/m³)
• $g$ is the gravitational acceleration (9.81 m/s²)
• $h$ is the depth of the water column (12 m)

In kilopascals (kPa), the water pressure is:

$\text{Water pressure} = 1000 \, \frac{kg}{m^3} \times 9.81 \, \frac{m}{s^2} \times 12 \, m = 117.72 \, \text{kPa}$

3. Total Stress

The total stress below the tunnel is the sum of the stress due to the weight of the tunnel element and the water column pressure:

$\text{Total stress} = \frac{\text{Weight of tunnel element}}{\text{Area}} + \text{Water pressure}$

The area of the base of the tunnel element is:

$\text{Area} = \text{Width} \times 1 \, \text{m (per unit depth)} = 45 \, m^2$

Now we can calculate the stress due to the weight of the tunnel element:

$\text{Stress from tunnel element} = \frac{9000 \, \text{kN/m}}{45 \, m^2} = 200 \, \text{kPa}$

Finally, the average total stress below the tunnel element is:

$\text{Total stress} = 200 \, \text{kPa} + 117.72 \, \text{kPa} = 317.72 \, \text{kPa}$

Final Answer:

The average total stress below the tunnel element is 317.72 kPa.

Would you like further clarification or details?

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Here are some related questions:

1. How does the volumetric weight of the concrete affect the total stress?
2. What would happen to the total stress if the tunnel element's width increased?
3. How does the water pressure change with depth?
4. What other factors could influence the stress on the riverbed under the tunnel?
5. How is stress distributed across different points below the tunnel?

Tip: Always check the units during calculations to ensure consistency, especially when dealing with different measures of weight and pressure.