Geomechanics & Ground Control

Geotechnical Properties of Rocks

Porosity, void ratio and the point-load estimate of strength — the index properties that classify a rock for design.

PART 1

Topic Breakdown & Traps

A rock's mechanical behaviour is summarised by index properties. Porosity

n

is the fraction of the total volume that is voids; the void ratio

e

relates voids to solids and is recovered from porosity by

e = n / (1 - n)

. Strength is quickly estimated in the field by the point-load test, whose index

I_{s (50)}

correlates with uniaxial compressive strength through a multiplier of roughly 22–24.

Porosity:

n = \frac{V _{v}}{V}

(void volume / total volume).

Void ratio:

e = \frac{V _{v}}{V _{s}} = \frac{n}{1 - n}

.

UCS from point load:

σ_{c} \approx 22 I_{s (50)}

⚠
Porosity and void ratio are different. $n$ is per *total* volume; $e$ is per *solids* — convert with $e = n / (1 - n)$ .
⚠
Point-load index gives an *estimate* of UCS, not the UCS itself; apply the ~22 multiplier.
⚠
**Keep $n$ as a fraction in the $e$ formula.** Using 20 instead of 0.2 wrecks the ratio.

PART 2

Q1BASIC1 Mark · MCQ

A rock sample of total volume

0.5 m^{3}

contains

0.1 m^{3}

of voids. Its porosity is:

Q2MEDIUM2 Marks · NAT

For a rock of porosity

20%

, the void ratio is ______. (Round off to two decimal places.)

Q3HARD2 Marks · NAT

A point-load test gives

I_{s (50)} = 4 MPa

. Using

σ_{c} \approx 22 I_{s (50)}

, the estimated uniaxial compressive strength is ______ MPa. (Round off to two decimal places.)

MPa