Brittle Creep and Failure: A Reformulation of the Wing Crack Model. Issue 9 (15th September 2022)

• Record Type: Journal Article
• Authors: Bernabé, Yves; Pec, Matej
• Is Part Of: Journal of geophysical research. Volume 127:Issue 9(2022)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2022-09-15
• Subjects: brittle creep -- brittle failure -- wing cracks -- crack coalescence -- shear bands -- sub‐critical crack growth; Geomagnetism -- Periodicals; Geochemistry -- Periodicals; Geophysics -- Periodicals; Earth sciences -- Periodicals; 551.1
• DOI: 10.1029/2022JB024610
• Languages: English
• ISSNs: 2169-9313

Abstract

Abstract: We propose a reformulation of the wing crack model of brittle creep and failure. Experimental studies suggest that the mechanical interactions of sliding and tensile wing cracks are complex, involving formation, growth, and coalescence of multiple tensile, shear and mixed‐mode cracks. Inspired by studies of failure in granular media, we propose that these complex mechanical interactions lead to the formation of micro shear‐bands, which, in turn, develop longer wing cracks and interact with a wider volume of rock to produce larger shear bands. This process is assumed to indefinitely continue at greater scales. We assume that the original wing crack formalism is applicable to micro shear‐band formation, with the difference that the half‐length, a, of the characteristic micro shear band is allowed to increase with wing crack growth. In this approach, the functional relationship of a with the wing crack length l embodies the entire process of shear band formation, growth and interaction with other shear bands and flaws. We found that the function a ( l )/ a (0) = 1 + ( l / λ ) q, where λ and q are constant parameters, generated creep curves consistent with published creep data of rocks. Similar accord was also obtained with experimental brittle failure data. Furthermore, we found that the Mohr‐Coulomb behavior emerged from our model, allowing estimation of the cohesion and angle of internal friction in materials for which λ and q are independently known. Plain Language Summary: Rocks close to Earth's surface deform by fracturing. Fracturing can occur abruptly if the load the rocks bear increases rapidly. Fracturing can however also occur over much longer times without changes to the load during a process called brittle creep. Observations suggest that fracturing occurs due to growth and linkage of many small‐scale flaws present in the rock. The details of this growth and linkage process, however, are very complex which complicates our ability to assess when rocks will ultimately break. Here, we develop a model that simplifies the details of these small‐scale interactions between large populations of flaws into a simple functional form. We analyze a number of possible functional forms and find that the simplest power law form yields good agreement with experimental data. Our model reproduces the behavior observed in brittle creep experiments, where after a step increase in load, the initially rapid rate of deformation first slows down, reaches a transitory steady‐state and then accelerates until final failure occurs. Our model hence improves our ability to predict when failure will occur and presents a step toward mitigating the hazards associated with rock failure. Key Points: Sliding cracks and their wing cracks interact with nearby flaws to form shear bands, which coalesce to form shear bands at greater scales Formation, growth, and coalescence of shear bands are self‐similar over a range of length‐scales and are expressed by a power law function Our model returns experimentally measurable quantities and reproduces trimodal creep curves and failure stresses obeying the Mohr‐Coulomb criterion