How to Calculate and Solve for Horizontal Stress | Rock Mechanics

September 25, 2019March 8, 2024 Loveth Idoko

Last Updated on March 8, 2024

The image above represents horizontal stress. To calculate horizontal stress, two essential parameters are needed, and these parameters are Poisson’s ratio (v) and vertical stress (σ_v).

The formula for calculating the horizontal stress:

σ_H = ^vσ_v / _{1 – v}

Where;

σ_H = Horizontal Stress
v = Poisson’s Ratio
σ_v = 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
σ_v = Vertical Stress = 28

σ_H = ^vσ_v / _{1 – v}
So, σ_H = ²⁴⁽²⁸⁾ / _{(1 – 24)}
σ_H = 672 / _-23
σ_H = -29.217

Therefore, the horizontal stress is 29.217.

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

v = ^σ_H / _{σ_v + σ_H}

Where;

v = Poisson’s Ratio
σ_H = Horizontal Stress
σ_v = 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;

σ_H = Horizontal Stress = 12
σ_v = Vertical Stress = 16

v = ^σ_H / _{σ_v + σ_H}
v = ¹² / _{16 + 12}
Then, v = ¹² / ₂₈
v = ¹² / ₂₈
v = 0.428

Therefore, the Poisson’s ratio is 0.428.

Calculating the Vertical Stress when the Horizontal Stress and the Poisson’s Ratio are Given

σ_v = ^{σ_H (1 – v)} / _v

Where;

σ_v = vertical stress
σ_H = Horizontal Stress
v = Poisson’s ratio

Let’s solve an example;
Find the vertical stress when the horizontal stress is 14 and the Poisson’s ratio is 8.

This implies that;

σ_H = Horizontal Stress = 14
v = Poisson’s ratio = 8

σ_v = ^{σ_H (1 – v)} / _v
σ_v = ^{14 (1 – 8)} / ₈
That is, σ_v = ^{14 (- 7)} / ₈
σ_v = ^{– 98} / ₈
σ_v = – 12.25

Therefore, the vertical stress is – 12.25.

How to Calculate Horizontal Stress Using Nickzom Calculator

Nickzom Calculator – The Calculator Encyclopedia is capable of calculating horizontal stress.

To get the answer and workings of the horizontal stress using the Nickzom Calculator – The Calculator Encyclopedia. First, you need to obtain the app.

You can get this app via any of these means:

Web – https://www.nickzom.org/calculator-plus

To get access to the professional version via web, you need to register and subscribe for NGN 1,500 per annum to have utter access to all functionalities.
You can also try the demo version via https://www.nickzom.org/calculator

Android (Paid) – https://play.google.com/store/apps/details?id=org.nickzom.nickzomcalculator
Android (Free) – https://play.google.com/store/apps/details?id=com.nickzom.nickzomcalculator
Apple (Paid) – https://itunes.apple.com/us/app/nickzom-calculator/id1331162702?mt=8
Once, you have obtained the calculator encyclopedia app, proceed to the Calculator Map, then click on Geology under Add-on.

Now, Click on Rock Mechanics under Geology

Now, Click on Horizontal Stress under Rock Mechanics

The screenshot below displays the page or activity to enter your values, to get the answer for the lateral strain according to the respective parameters which are the Poisson ratio (v) and vertical stress (σ_v).

Now, enter the values appropriately and accordingly for the parameters as required by the Poisson ratio (v) is 24 and vertical stress (σ_v) is 28.

Finally, Click on Calculate

As you can see from the screenshot above, Nickzom Calculator– The Calculator Encyclopedia solves for the horizontal stress and presents the formula, workings and steps too.