Theoretical and numerical studies of crack initiation and propagation in rock masses under freezing pressure and far-field stress

Water-bearing rocks exposed to freezing temperature can be subjected to freeze–thaw cycles leading to crack initiation and propagation, which are the main causes of frost damage to rocks. Based on the Griffith theory of brittle fracture mechanics, the crack initiation criterion, propagation direction, and crack length under freezing pressure and far-field stress are analyzed. Furthermore, a calculation method is proposed for the stress intensity factor (SIF) of the crack tip under non-uniformly distributed freezing pressure. The formulae for the crack/fracture propagation direction and length of the wing crack under freezing pressure are obtained, and the mechanism for coalescence of adjacent cracks is investigated. In addition, the necessary conditions for different coalescence modes of cracks are studied. Using the topology theory, a new algorithm for frost crack propagation is proposed, which has the capability to define the crack growth path and identify and update the cracked elements. A model that incorporates multiple cracks is built by ANSYS and then imported into FLAC3D. The SIFs are then calculated using a FISH procedure, and the growth path of the freezing cracks after several calculation steps is demonstrated using the new algorithm. The proposed method can be applied to rocks containing fillings such as detritus and slurry.