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# Yield Criteria for peak and ultimate strength

## Yield Criteria for peak and ultimate strength

(OP)
Hi everyone,

I'm new to the forum and hoping that someone can give me a hand with a sample problem I've been working on:

Samples of a typical rock joint were tested in a square shear box of 160 mm x 160 mm dimensions and the following data were collected:

Sample # Fn Fspeak FSult
#1 1.3 kN 2.5 kN 0.8 kN
#2 5.0 kN 8.2 kN 3.1 kN
#3 10 kN 13.6 kN 5.6 kN
#4 20 kN 20.5 kN 10.0 kN
#5 30 kN 25.1 Kn 13.6 kN
#6 40 kN 30.7 kN 16.9 Kn

Where: Fn = Normal Force
Fspeak = Peak Shear force
Fsult = Ultimate shear force

Question: Plot yield criteria for peak and ultimate strength on a Mohr diagram, noting that the values in the table above are given in terms of force. Assume a Patton bilinear model (two straight lines), and fit the two parts of the patton plot by hand, define the c' and Φ' of each part, and specify the approximate transition normal stress. Why does the ultimate yield criterion (in general) not show bilineraity?

I'm not familiar with the Patton model and am having a hard time getting anywhere with this problem

### RE: Yield Criteria for peak and ultimate strength

sounds like homework

### RE: Yield Criteria for peak and ultimate strength

(OP)
Not so much homework as professional development. My background is in Mechanical Engineering and I've always had an interest in rock mechanics. I've been doing a number of the questions from old PEO examinations and came across this one and its stumping me. I've discovered some information about the patton model but really can't seem to figure this one out. I was hoping that someone on here would be able to provide some insight.

### RE: Yield Criteria for peak and ultimate strength

This is no different than if you took a sample of large chunks of concrete which had a shearing value of 5,000 psi, but after shearing through the solid chunks your shearing value would be controlled by the angle of friction of fine gravel, not solid concrete. If your shearing plane happened to match the rock bedding planes then no need to shear solid stuff. Take your question to the Soil Mechanics room for comments from those that do a lot of shear testing.

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