Geomechanics & Ground Control

Rock Bursts & Coal Bumps

The strain energy stored in highly stressed rock — the reservoir whose sudden release drives a rock burst.

PART 1

Topic Breakdown & Traps

The Engineering Principle

A rock burst (or coal bump) is the violent, sudden failure of highly stressed rock as stored elastic strain energy is released. The energy stored per unit volume under a uniaxial stress

σ

in a rock of Young's modulus

E

u = σ^{2} / (2 E)

. Stiff, strong, brittle rock at high stress stores the most — and is the most burst-prone. The total reservoir is this density times the stressed volume.

The Core Formula Matrix

Strain energy density:

u = \frac{σ ^{2}}{2 E} [J/m^{3}]

Total stored energy:

U = u \times V

(

V

= stressed volume).

σ

in Pa,

E

in Pa ⇒

u

in J/m³.

The ‘IIT Traps’

⚠
Stress is squared, modulus is in the denominator (×2). Higher stress ⇒ much more stored energy; stiffer rock ⇒ less per unit stress.
⚠
Keep units in Pa. $50 MPa = 50 \times 1 0^{6} Pa$ , $50 GPa = 50 \times 1 0^{9} Pa$ .
⚠
Energy *density* vs total energy. Multiply by the volume only for the total reservoir.

PART 2

Progressive 3-Tier Question Suite

Q1BASIC1 Mark · MCQ

Rock at a stress of

50 MPa

has

E = 50 GPa

. The stored strain energy density is:

Q2MEDIUM2 Marks · NAT

Rock at

σ = 80 MPa

with

E = 40 GPa

stores a strain energy density of ______ kJ/m³. (Round off to two decimal places.)

kJ/m³

Q3HARD2 Marks · NAT

If that rock (

u = 80 kJ/m^{3}

) occupies a stressed volume of

10 m^{3}

, the total stored strain energy is ______ kJ. (Round off to the nearest whole number.)