Greetings
Patton (1966) described the effects of surface roughness on the shear strength measurement and this formula was found (τ = σ tan (φ + i)). I tried to get a reference with all the details but unfortunately, I could not. Please, if anyone can get the following reference, it would be beneficial.
Patton, F. D. (1966) Multiple modes of shear failure in rock. Proc. 1st. Int. Congress on Rock Mech., Lisbon, 1, 509–13.
If the whole mathematical derivation is available, it would also be a great help.
Thank you..