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Rock physical and mechanical properties 61

2.5.1 Static Young’s modulus
The static axial Young’s modulus (E s ) in the laboratory core test is defined
as the ratio of the axial stress change (Ds) to the axial strain change (Dε)
produced by the stress change, i.e.,
Ds
E s ¼ (2.48)
Dε
If an axial stress and axial strain curve before reaching the ultimate
strength of the rock takes approximately a linear form (Fig. 2.19), the slope
of this stressestrain curve is the static Young’s modulus or elastic modulus.
ISRM (1979) suggested the following three methods for calculating
Young’s modulus from the stressestrain curve in uniaxial compression of a
rock specimen of regular geometry:
(1) Tangent Young’s modulus is measured at a stress level, which is some
fixed percentage of the ultimate strength. It is generally taken at a stress
level equal to 50% of the ultimate uniaxial compressive strength.
(2) Average Young’s modulus is determined from the average slopes of the
more-or-less straight line portion of the axial stresseaxial strain curve
(Fig. 2.19).
(3) Secant Young’s modulus is usually measured from zero stress to some
fixed percentage of the ultimate strength, generally at 50%.
Young’s modulus describes the capacity of rock deformation, or the
stiffness of a rock. A rock with a high Young’s modulus is less deformable

4000

Axial stress (psi) 3000 Δσ

2000

1000 Δε
E = Δ σ
Δ ε
0.01 0.02 0.03
Axial Strain
Figure 2.19 Average Young’s modulus (E) from the uniaxial stressestrain curve in a
shale sample cored at the depth of 25,000 ft TVD ss (from the sea level) in the Gulf of
Mexico. TVD, true vertical depth