How to Calculate and Solve for Horizontal Stress | Rock Mechanics

The image above represents horizontal stress.

To compute for horizontal stress, two essential parameters are needed and these parameters are Poisson’s ratio (v) and vertical stress (σv).

The formula for calculating the horizontal stress:

σH = v / 1 – v

Where;

σH = Horizontal Stress
v = Poisson’s Ratio
σv = Vertical Stress

Let’s solve an example;
Find the horizontal stress when the Poisson’s ratio is 24 and the vertical stress is 28.

This implies that;

v = Poisson’s Ratio = 24
σv = Vertical Stress = 28

σH = v / 1 – v
σH = 24(28) / (1 – 24)
σH = 672 / -23
σH = -29.217

Therefore, the horizontal stress is 29.217.

Calculating the Poisson’s Ratio when the Horizontal Stress and Vertical stress is Given.

v = σH / σv + σH

Where;

v = Poisson’s Ratio
σH = Horizontal Stress
σv = Vertical Stress

Let’s solve an example;
Find the Poisson’s ratio when the horizontal stress is 12 and the vertical stress is 16.

This implies that;

σH = Horizontal Stress = 12
σv = Vertical Stress = 16

v = σH / σv + σH
v = 12 / 16 + 12
v = 12 / 28
v = 12 / 28
v = 0.428

Therefore, the Poisson’s ratio is 0.428.

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