Question

A plug dam is to be constructed in a mine gallery of size 3.5 m \(\times\) 2.5 m. The interfacial shear strength between the surrounding rock and plug dam is 1.0 MPa. The minimum thickness of the dam, in m, to withstand a water pressure of 10.0 MPa, is . (rounded off to two decimal places)

Hint:

Balance the total water force on the dam face against the shear resistance developed around its perimeter.

Answer 1

Correct Answer: 7.29

The same result can be reached by thinking in terms of forces per meter of dam perimeter instead of total forces, which is how a mine engineer would size the plug on site.

Step 1: Work out the water pressure force per meter of perimeter. The gallery face is 3.5 m by 2.5 m, so its area is 8.75 m2 and its perimeter is $2(3.5+2.5) = 12$ m. The total water force is $P \times A = 10.0 \times 8.75 = 87.5$ MN, spread around a perimeter of 12 m. So the force each meter of perimeter must resist is $87.5/12 = 7.29$ MN per meter.

Step 2: Work out how much resisting force one meter of thickness supplies per meter of perimeter. The interface shear strength is $\tau = 1.0$ MPa $= 1.0$ MN/m2. For a 1 m strip of perimeter and thickness $t$, the contact area is $1 \times t$ m2, so the resisting force it supplies is $1.0 \times t$ MN, meaning each meter of thickness gives 1.0 MN/m of resistance.

Step 3: Match supply to demand. Each meter of thickness gives 1.0 MN/m of resistance, and we need 7.29 MN/m to balance the water. So the required thickness is $t = 7.29/1.0 = 7.29$ m.

Let's summarize:

• The water load per meter of gallery perimeter is 7.29 MN/m.
• Each meter of dam thickness supplies 1.0 MN/m of shear resistance at this interface strength.
• Matching the two gives a minimum thickness of 7.29 m.

So the minimum thickness of the plug dam is 7.29 m.