Dynamic Fracture Mechanics in Rock Engineering: Outline of Challenges and Advances

Kamran Panaghi, Aliakbar Golshani, Shahaboddin Yasrobi

In the proceedings of: GeoRegina 2014: 67th Canadian Geotechnical Conference

Session: Engineering Geology and Rock Mechanics

ABSTRACT: acture Mechanics in Rock Engineering: Outline of Challenges and Advances Kamran Panaghi, Aliakbar Golshani, Shahaboddin Yasrobi Tarbiat Modares University, Tehran, Iran ABSTRACT The studies devoted to fracture mechanism in rock engineering are mainly focused on the development of static stress intensity factors. Different analytical, numerical, and experimental methods are developed or under study to obtain the required accuracy deemed to lower operative costs while meeting safety regulations. Another realm in the field is concentrated on the dynamic characteristics of the same parameters introduced in static analyses. Similarly, the stress intensity factors in dynamic state are described and methods are developed to account for their combination during the fracture process. Critical stress intensity factor, fracture toughness and failure criteria for dynamic loading are introduced and theories regarding crack initiation, crack velocity, branching and crack arrest are scrutinized. In this paper, a brief review of the dynamic fracture studies as well as the current state of our knowledge is presented. Finally, the necessity of such studies in deep excavations and relevant phenomena are expounded upon accordingly. RÉSUMÉ Des études consacrées au mécanisme de fracture dans le domaine de "rock engineering" sont principalement concentrées sur le développement des statiques des facteurs d'intensité de contrainte. Afin d'obtenir la précision requise qui estime des coûts opératoires inferieurs, tout en gardant des règlements de la sécurité, de différentes méthodes analytique, numérique et expérimentale sont développées ou sont à l'étude. Autre problématique de ce domaine vise aux caractéristiques des mêmes paramètres qui se présentent dans les analyses statistiques. De la même manière, des éléments de l'intensité de pression dans l'état dynamique sont décrits et les méthodes, quant à elles, sont développées. La critique des facteurs d'intensité de contrainte, la ténacité à la rupture et les critères d'échec sont représentés et les théories concernant l'amorce et la vitesse de la propagation des fissures, l'extension et l'arrêt de fissuration sont examinées minutieusement. Dans cet article, une brève révision à propos des études de la fracture dynamique est évoquée et de surcroît, la nécessité de telles études est expliquée. 1 INTRODUCTION The induced heterogeneity due to static and dynamic loads borne throughout the bulk of the rock mass is the main factor responsible for rock failures. This phenomenon results from the development of plastic zones around pre-existing cracks along with weak bonds approaching their yield strength. Consequently, cracks in the rock mass either join each other or initiate following the loading process. The dynamic behaviour of linear elastic materials is described based on the following governing equations: - Equilibrium - Strain-displacement relationship - Stress-strain law These along with the initial and boundary conditions define the phenomenon in continuous domains. In fracture mechanics problems, however, a consistency law is required to account for the defects to be modeled. There are different failure criteria some of which are based on thermodynamics principles. Nonetheless, the critical stress intensity factor or fracture toughness is still the most common criterion in handling brittle fracture as in rocks. Dynamic stress intensity factors are not only functions of geometry of the domain and loading conditions as for the static case, but are also dependent on the crack propagation velocity. The significance of kinetic energy term in energy approach formulations of dynamic fracture giving rise to inertia effects is the distinguishing factor from quasi-static problems. The first attempts for the calculation of crack propagation velocity were made by Mott (Gdoutos, 2005) who introduced a kinetic energy term into system's energy balance formulation in Griffith's theory. As the 2D investigations related to practical engineering problems in fracture modes I and II along with their simultaneous effects in mixed mode studies are diverse, few attention is turned to mode III fracture in engineering materials since it requires 3D numerical simulations while seldom beneficial. 2 DYNAMIC FRACTURE MECHANICS 2.1 Dynamic Fracture Toughness Jaine and Kanwal (1972) obtained the stress distribution around two parallel and coplanar Griffith cracks in an infinite, homogeneous, and isotropic elastic domain using a simple integral equation technique that introduced values for stress intensity factors, displacement field, stress tensor, and far-field amplitudes at the low frequency range. Before their pioneering work, research on dynamic crack problems was limited to single crack in infinite domains due to mathematical related drawbacks. They solved the elastic waves' diffraction problem of normally incident longitudinal and anti-plane shear waves and derived approximate solutions, the reliability of which for SH waves declined at the low frequency end of the frequency scale as the stress intensity factor did not tend to increase with the wave number. Itou (1980)

RÉSUMÉ: ic Fracture Mechanics in Rock Engineering: Outline of Challenges and Advances Kamran Panaghi, Aliakbar Golshani, Shahaboddin Yasrobi Tarbiat Modares University, Tehran, Iran ABSTRACT The studies devoted to fracture mechanism in rock engineering are mainly focused on the development of static stress intensity factors. Different analytical, numerical, and experimental methods are developed or under study to obtain the required accuracy deemed to lower operative costs while meeting safety regulations. Another realm in the field is concentrated on the dynamic characteristics of the same parameters introduced in static analyses. Similarly, the stress

Access this article:
Canadian Geotechnical Society members can access to this article, along with all other Canadian Geotechnical Conference proceedings, in the Member Area. Conference proceedings are also available in many libraries.

Cite this article:
Kamran Panaghi; Aliakbar Golshani; Shahaboddin Yasrobi (2014) Dynamic Fracture Mechanics in Rock Engineering: Outline of Challenges and Advances in GEO2014. Ottawa, Ontario: Canadian Geotechnical Society.

@article{GeoRegina14Paper317,author = Kamran Panaghi; Aliakbar Golshani; Shahaboddin Yasrobi,title = Dynamic Fracture Mechanics in Rock Engineering: Outline of Challenges and Advances,year = 2014}