Log In

Come Join Us!

Are you an
Engineering professional?
Join Eng-Tips Forums!
  • Talk With Other Members
  • Be Notified Of Responses
    To Your Posts
  • Keyword Search
  • One-Click Access To Your
    Favorite Forums
  • Automated Signatures
    On Your Posts
  • Best Of All, It's Free!
  • Students Click Here

*Eng-Tips's functionality depends on members receiving e-mail. By joining you are opting in to receive e-mail.

Posting Guidelines

Promoting, selling, recruiting, coursework and thesis posting is forbidden.

Students Click Here


CD test formula vs Kp

CD test formula vs Kp

CD test formula vs Kp

For the triaxial CD test, (σ_1^')/(σ_3^' )= (1+sin⁡〖∅'〗)/(1-sin⁡〖∅'〗 )
The term on the right side of the equaition resembles the Kp lateral earth pressure coefficient.
I want to understand why is this so. Is it because Kp relates the vertical force to horizontal force, and here at the triaxial test the vertical vs horizontal forces are related in the same way, and taht is why the formula is the same?

RE: CD test formula vs Kp

Good observation - it's no coincidence. It looks like that because, in one of the original slope-stability methods, W.J.M. Rankine assumed essentially that same condition: that the soil was in a state of yield, with Sigma1 vertical and Sigma3 horizontal for active pressure, and the reverse of that for passive pressure. Easiest way to look at it is a Mohr circle touching the MC strength line. It was later extended to the case of a wall with friction, in which case Sigma1 and Sigma3 aren't exactly horizontal and vertical.

For the special case with a vertical frictionless wall, Coulomb's Ka and Kp work out to be the same.


RE: CD test formula vs Kp

sorry i didnt understand. are you able to expand your explanation a little further, or this is as simple as it gets? if so thanks so much anyway and I will keep checking

RE: CD test formula vs Kp

First off, when I said "slope-stability method," that was wrong. I should have said "active and passive pressure method." Slope stability on the brain today.

Draw a Mohr circle representing failure in a Tx test. It will go from (Sigma3,0) to (Sigma1,0) and touch the strength envelope, which has slope tan phi. Now, assume that the whole mass of soil behind the wall is in yield/failure like the Tx specimen, as the fill pushes the wall away, so that the Mohr circle for any particular point is just barely touching the strength envelope, with Sigma1 being the vertical stress at that point. If the wall is frictionless and vertical, the pressure the soil exerts upon it is Sigma3 (the minor principal stress, no shear stress). You can now solve for Sigma3 as a function of Sigma1 and phi, and the ratio Sigma3/Sigma1 is Ka. For Kp, just reverse 1 and 3, so that Sigma1 will be the wall pressure and Sigma3 is the vertical.

Or, just think of the soil behind the wall as being a big triaxial test (or plane-strain compression test, more correctly). Sigma3 is the vertical stress at a particular point. Then start pushing the wall against the fill until the fill yields; the stress the wall has to apply to yield the soil is analogous to stress on the Tx load platen, Sigma1; that's the passive pressure.

For active pressure, let the fill push the wall/platen away, like a reduced triaxial extension test. The vertical stress in this case is sigma1. It remains constant while sigma3 is reduced and the diameter of the circle increases until it hits the strength envelope and the fill yields.


Red Flag This Post

Please let us know here why this post is inappropriate. Reasons such as off-topic, duplicates, flames, illegal, vulgar, or students posting their homework.

Red Flag Submitted

Thank you for helping keep Eng-Tips Forums free from inappropriate posts.
The Eng-Tips staff will check this out and take appropriate action.

Reply To This Thread

Posting in the Eng-Tips forums is a member-only feature.

Click Here to join Eng-Tips and talk with other members!


White Paper - The State of Product Development and Hardware Design 2019
The most successful companies are usually the ones that never rest. They are always striving to get better, to deliver more innovative products and get them to market faster. Onshape surveyed 850 product design and manufacturing pros to learn what techniques and strategies they’ve employed to keep ahead of their competition and in this white paper their answers are distilled. Download Now
Research Report - Mass Customization Placing Design in the Customers Hands
Products come in all shapes and sizes, and customers demand solutions tailored to their needs. With mass customization software, these two facts can be reconciled in an automated, customer-facing experience called a product configurator. In this engineering.com research report, we examine the different levels of mass customization with the pyramid of product configurators. Taking a look at real-world case studies, we discover how the highest level of the pyramid can enable true engineering automation, saving time and increasing customer satisfaction. Download Now
Research Report - Test and Simulation Survey
We at engineering.com continually hear how engineers and designers will be doing simulation, such as FEA and CFD, and that they will be doing it early in the design cycle. Is this wishful thinking? We found out what it is really like in industry. Read more now. Download Now

Close Box

Join Eng-Tips® Today!

Join your peers on the Internet's largest technical engineering professional community.
It's easy to join and it's free.

Here's Why Members Love Eng-Tips Forums:

Register now while it's still free!

Already a member? Close this window and log in.

Join Us             Close