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# Understanding Principal Stresses In Soil Mechanics

## Understanding Principal Stresses In Soil Mechanics

(OP)
Hello all

I was wondering if someone could help with the following:-

I am trying to understand the concept of principal stresses in terms of soil mechanics.

I have a soil element that is being loaded by 25kN. I am trying to draw all of the stresses the soil element experiences.

I have attached a drawing of my soil element, the bit I cannot get my head round is the last cube which I got from an online source which shows the Principal stresses 1 3, would it be correct to say that:-

Sigma1 = 25kN worth of stress acting downwards & upwards

Sigma3 = ?????? No idea where this comes from?

Any ideas?

Thank you.

https://files.engineering.com/getfile.aspx?folder=...

### RE: Understanding Principal Stresses In Soil Mechanics

I recommend you get yourself a good soil mechanics book which explains all these concepts.

#### Quote (MatthewMansfield)

Sigma1 = 25kN

Sigma 1 is not 25 kN it is 25 kN multiplied by the height.
Sigma 3 is the horizontal confining stress usually associated with a Ko value which associates the vertical to horizontal stress.

### RE: Understanding Principal Stresses In Soil Mechanics

Your unit confuses me, isn't kN is the unit for force? You should review "Principal Stresses" and "Mohr's Circle for Plan Stresses" in any engineering/soil mechanics textbook.

### RE: Understanding Principal Stresses In Soil Mechanics

(OP)
Hi GeoEnvGuy

I am trying to build a picture in my head of the soil element by imagining a Wall that exerts 25kN of force on the ground.

I want to know the stresses that the soil is experiencing as result of this wall exerting 25kN onto it.

So i take a square portion of the soil directly under the wall and cut it at some angle theta.

I know that a portion of the 25kN of force of the wall creates stresses that act Normal to my cutting face (green and blue arrows) and shear stresses parallel to my cutting face (Pink & black).

When i put all this together so it fits the soil element picture at the bottom of my attachment i dont understand what Sigma 1 and Sigma 3 is of where it comes from?

I thought Sigma 1 acting downwards came from the 25kN of force from the wall divided by the cross sectional area of the soil element to give a stress and Sigma 1 acting upwards was the reaction force from the 25kN from the wall which is divided by the cross sectional area of the soil element to give a stress - Is this correct?

I have no idea where Sigma 3 comes from?????

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