The image above represents horizontal strain.

To compute for horizontal strain, five essential parameters are needed and these parameters are **Principal Horizontal Stress Component 1 (σ**_{H1}), Principal Horizontal Stress Component 2 (σ_{H2}), Poisson’s Ratio (v), **Vertical Stress (σ**_{v}) and **Young’s Modulus (E).**

The formula for calculating the horizontal strain:

ε_{H} = ^{(σH1 – vσH2 – vσv)} / _{E}

Where:

ε_{H} = Horizontal Strain

σ_{H1} = Principal Horizontal Stress Component 1

σ_{H2} = Principal Horizontal Stress Component 2

v = Poisson’s Ratio

σ_{v} = Vertical Stress

E = Young’s Modulus

Let’s solve an example;

Find the horizontal strain when the principal horizontal stress component 1 is 7, the principal horizontal component 2 is 9, the Poisson’s ratio is 11, the vertical stress is 21 and young’s modulus is 27.

This implies that;

σ_{H1} = Principal Horizontal Stress Component 1 = 7

σ_{H2} = Principal Horizontal Stress Component 2 = 9

v = Poisson’s Ratio = 11

σ_{v} = Vertical Stress = 21

E = Young’s Modulus = 27

ε_{H} = ^{(σH1 – vσH2 – vσv)} / _{E}

ε_{H} = ^{(7 – 11(9) – 11(21))} / _{27}

ε_{H} = ^{(7 – 99 – 231)} / _{27}

ε_{H} = ^{-323} / _{27}

ε_{H} = -11.96

Therefore, the **horizontal strain **is **-11.96.**

**Calculating the Principal Horizontal Stress Component 1 when the Horizontal Stress, Principal Horizontal Stress Component 2, Poisson’s Ratio, Vertical Stress and Young’s Modulus is Given.**

σ_{H1} = (ε_{H} x E) + vσ_{H2} + vσ_{v}

Where;

σ_{H1} = Principal Horizontal Stress Component 1

ε_{H} = Horizontal Strain

σ_{H2} = Principal Horizontal Stress Component 2

v = Poisson’s Ratio

σ_{v} = Vertical Stress

E = Young’s Modulus

Let’s solve an example;

Find the principal horizontal stress component 1 when the horizontal strain is 22, the principal horizontal component 2 is 10, the Poisson’s ratio is 7, the vertical stress is 12 and young’s modulus is 3.

This implies that;

ε_{H} = Horizontal Strain = 22

σ_{H2} = Principal Horizontal Stress Component 2 = 10

v = Poisson’s Ratio = 7

σ_{v} = Vertical Stress = 12

E = Young’s Modulus = 3

σ_{H1} = (ε_{H} x E) + vσ_{H2} + vσ_{v}

σ_{H1} = (22 x 3) + 7(10) + 7(12)

σ_{H1} = 66 + 70 + 84

σ_{H1} = 220

Therefore, the **principal horizontal stress component 1 **is **220.**

**Calculating the Principal Horizontal Stress Component 2 when the Horizontal Stress, Principal Horizontal Stress Component 1, Poisson’s Ratio, Vertical Stress and Young’s Modulus is Given.**

σ_{H2} = -(^{(εH x E) – σH1 + vσv} / _{v})

Where;

σ_{H2} = Principal Horizontal Stress Component 2

ε_{H} = Horizontal Strain

σ_{H1} = Principal Horizontal Stress Component 1

v = Poisson’s Ratio

σ_{v} = Vertical Stress

E = Young’s Modulus

Let’s solve an example;

Find the principal horizontal stress component 2 when the horizontal strain is 28, the principal horizontal component 1 is 14, the Poisson’s ratio is 5, the vertical stress is 17 and young’s modulus is 7.

This implies that;

ε_{H} = Horizontal Strain =28

σ_{H1} = Principal Horizontal Stress Component 1 = 14

v = Poisson’s Ratio = 5

σ_{v} = Vertical Stress = 17

E = Young’s Modulus = 7

σ_{H2} = -(^{(εH x E) – σH1 + vσv} / _{v})

σ_{H2} = -(^{(28 x 7) – 14 + 5(17)} / _{5})

σ_{H2} = -(^{196 – 14 + 85} / _{5})

σ_{H2} = -(^{182 + 85} / _{5})

σ_{H2} = -(^{267} / _{5})

σ_{H2} = -(53.4)

σ_{H2} = -53.4

Therefore, the** principal horizontal stress component 2 **is **-53.4.**

Continue reading How to Calculate and Solve for Horizontal Strain | Rock Mechanics