Geomechanics & Ground Control

Design of Supports

Support pressure from the loosened rock height, the roof load it implies, and the number of rock bolts to carry it safely.

PART 1

Topic Breakdown & Traps

The Engineering Principle

An excavation's roof must carry a loosened (loading) height

H_{p}

of rock above it. The support pressure is the weight of that column per unit area,

γ H_{p}

. Multiplied by the roof area it gives the total roof load, which the support system — here rock bolts — must hold with an adequate factor of safety. The number of bolts is the factored load divided by the capacity of one bolt.

The Core Formula Matrix

Support pressure:

p = γ H_{p}

(

γ

= rock unit weight,

H_{p}

= loosened height).

Roof load:

F = p \times A

(

A

= roof area supported).

Number of bolts:

N = \frac{F \times F S}{capacity per bolt}

The ‘IIT Traps’

⚠
**Support pressure is $γ H_{p}$ **, the weight of the loosened column — not the full overburden stress.
⚠
Apply the factor of safety to the load before dividing by bolt capacity.
⚠
Round bolt numbers up. A fractional bolt still means installing a whole one.

PART 2

Progressive 3-Tier Question Suite

Q1BASIC1 Mark · MCQ

A loosened rock height of

2 m

(unit weight

25 kN/m^{3}

) bears on the roof. The support pressure is:

Q2MEDIUM2 Marks · NAT

A support pressure of

50 kPa

acts over a roof area of

12 m^{2}

. The total roof load is ______ kN. (Round off to the nearest whole number.)

Q3HARD2 Marks · NAT

The

600 kN

roof load is to be held by rock bolts of capacity

100 kN

each, with a factor of safety of

2

. The number of bolts required is ______. (Round off to the nearest whole number.)