2002/09/05 by Renaud Toussaint, Steven R. Pride · 2 citations
Earth and Planetary Sciences · Engineering · Physics and Astronomy · #Geotechnical and Geomechanical Engineering #High-pressure geophysics and materials #Rock Mechanics and Modeling #cond-mat.dis-nn #cond-mat.mtrl-sci #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.66.036137
published as Phys. Rev. E 66, art. 036137 (2002) · 11 pages, 3 figures
arxiv created 2002/09/05 · openalex publication_date 2002/09/27 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The properties of the Hamiltonian developed in Paper II are studied showing that at a particular strain level a "localization" phase transition occurs characterized by the emergence of conjugate bands of coherently oriented cracks. The functional integration that yields the partition function is then performed analytically using an approximation that employs only a subset of states in the functional neighborhood surrounding the most probable states. Such integration establishes the free energy of the system, and upon taking the derivatives of the free energy, the localization transition is shown to be continuous and to be distinct from peak stress. When the bulk modulus of the grain material is large, localization always occurs in the softening regime following peak stress, while for sufficiently small bulk moduli and at sufficiently low confining pressure, the localization occurs in the hardening regime prior to peak stress. In the approach to localization, the stress-strain relation for the whole rock remains analytic, as is observed both in experimental data and in simpler models. The correlation function of the crack fields is also obtained. It has a correlation length characterizing the aspect ratio of the crack clusters that diverges as xi approximately ( epsilon (c)- epsilon )(-2) at localization.