Abstract
Rocks and other geomaterials are heterogeneous materials, with a well-recognized hierarchy of defects from micro-heterogeneities on the grain level to a large-scale network of cracks and layering structures. Their nature create a challenge for determining macroscopic properties, particularly for properties that are scale dependent, complicating both the property measurement and its appropriate application in modeling. This paper discusses the concept of a “representative volume”, which is commonly used in modeling microheterogeneous but statistically homogeneous material by an effective homogeneous continuum. The foundation of this concept is presented, along with its limitations in dealing with properties like strength and fracture toughness that exhibit a scale effect. This limitation is illustrated with a study of brittle fracture of a concrete where it is considered a model for statistically homogeneous rock. The study includes determining a scaling rule for the scale effect in fracture toughness, and shows that the fracture of brittle materials like rocks and concrete appears in the form of highly tortuous, stochastic paths. This reflects a complex interaction between a crack and pre-existing as well as newly formed micro-defects controlled by chance, and results in a large scatter of all fracture-related parameters. This behavior suggests a synthesis of fracture mechanics with probability and statistics, and so a brief exposition of statistical fracture mechanics (SFM) that addresses the statistical aspects of fracture is also presented. SFM is a formalism that combines fracture mechanics methods with probability theory and serves as the basis for an adequate modeling of brittle fracture.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.