U-curve global inversion

Estimates Coulomb parameters for intact rock and its weakness planes from triaxial strength at multiple orientations.

MATLAB code and digitized data accompanying the paper "The U-curve: expressing the effect of discontinuity orientation and comments on Mohr theory" by O.A. AlDajani and H.H. Einstein.

The script estimates four Coulomb parameters: the intact friction coefficient and cohesion, and the weakness-plane friction coefficient and cohesion, for each of three lithologies by global least-squares inversion. A single parameter set per lithology is fitted simultaneously to all bedding orientations and all confining pressures, using a confinement-balanced objective and multi-start Nelder-Mead optimization. Running the script reproduces Figures 22 and 23 of the paper.

The strength data are digitized from the published figures of McLamore and Gray (1967), "The mechanical behavior of anisotropic sedimentary rocks," Journal of Engineering for Industry 89(1), 62-73, for two Green River oil shales and one slate. They are embedded in the script and also supplied as a CSV recording the full chain from the raw digitized values to the peak axial stresses used in the inversion.

The script is self-contained, requires no toolboxes beyond base MATLAB, and is seeded for exact reproducibility.

Archived version of record: https://doi.org/10.5281/zenodo.22090249