Eqn.1The Barton-Bandis failure criterion is an empirical relationship widely used to model the shear strength of rock discontinuities (e.g. joints). It is very useful for fitting a strength model to field or laboratory shear test data of discontinuities. The Barton-Bandis criterion is non-linear, and relates the shear strength to the normal stress using the equations described below.
The original Barton equation for the shear strength of a rock joint is given by Eqn.1:
Eqn.1
where 
is the basic
friction angle of the failure surface, JRC is the joint roughness coefficient,
and JCS is the joint wall compressive strength [Barton,
1973, 1976]. On the basis of direct shear test results for 130 samples
of variably weathered rock joints, Barton and Choubey revised this to
Eqn.2:
Eqn.2
where 
is the residual
friction angle of the failure surface [Barton
and Choubey, 1977]. Barton and Choubey suggest that can be estimated from Eqn.3:
Eqn.3
where r is the Schmidt hammer rebound number on wet and weathered fracture surfaces and R is the Schmidt rebound number on dry unweathered sawn surfaces. Equations 2 and 3 have become part of the Barton-Bandis criterion for rock joint strength and deformability [Barton and Bandis, 1990].
For further information on the shear strength of discontinuities, including a discussion of the Barton-Bandis failure criterion parameters, see Practical Rock Engineering (Chapter 4 - Shear Strength of Discontinuities) on the Rocscience website.