Sample Problem Help, Peak & Yield Stress

[Stewie8]

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