Question

The support pressure of 20 kPa is required to stabilize the loose blocks of the Excavation Disturbed Zone (EDZ) at the crown of a circular tunnel with horizontal axis. The EDZ is to be stabilized by inserting rock bolts vertically into the roof. If the working capacity of a bolt is 160 kN, the area of the roof supported by a single bolt in m² is______ (in integer).

Hint:

Always convert kPa to kN/m\(^2\) directly, since \(1 \, \text{kPa} = 1 \, \text{kN/m}^2\). This helps in quickly balancing pressure–area–load relations.

Answer 1

Correct Answer: 8

Step 1: Write the given data - Support pressure required = \(20 \, \text{kPa} = 20 \, \text{kN/m}^2\)
- Capacity of one bolt = \(160 \, \text{kN}\) Step 2: Relationship between load, pressure, and area \[ \text{Load capacity of bolt} = \text{Support pressure} \times \text{Area supported} \] Step 3: Substitute the values \[ 160 = 20 \times A \] Step 4: Solve for \(A\) \[ A = \frac{160}{20} = 8 \, \text{m}^2 \] \[ \boxed{8 \, \text{m}^2} \]