1. The problem statement, all variables and given/known data I have been given the task of approximating Barton's Criteria of failure with rock mechanics to a linear function or proving that it cannot be done. Through reading some of Barton's papers - some which are 40 years old I have come to understand that the empirical relationship is not linear, but do not know why/how. All variables are independent and can be used with positive rational numbers. Any and all assistance is appreciated. 2. Relevant equations [tex]\tau = \sigma r * \tan(\phi c + JRC * \log (JCS/\sigma r))[/tex] 3. The attempt at a solution I spent some time considering disproving this through the subspace theorem considering I know that all variables are independent and that obviously it has to be within the rational numbers.