13th International Conference on Fracture June 16–21, 2013, Beijing, China -1- On the Formation of Regular Crack Networks around a Circular Hole under Uniform Compression Ilya Nickolaevich Dashevskiy A. Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, 119526, Russia dash@ipmnet.ru Abstract The energy approach is used to propose a model of arising of regular systems of cracks, emerging the surface of a circular cavity, being observed, for example, around oil and gas wells under uniform compression. The cracks are supposed to arise due to the accumulation of elastic compression energy in the system. The limit compression (the exhaustion of strength) being achieved, a network of cracks is formed in the most stressed layer adjacent to the interior of the body, thus utilizing the accumulated elastic energy of this layer. In this case, of all the possible grids the least energy-consuming one is formed, that is, the system with such a number n and length L of the cracks, that the energy needed for its creation is minimal. In the simplest scheme the number n of "petals"-wedges arising from the cracking turns out to be equal to 5 (which corresponds to 2n = 10 cracks) and (contrary to limit compression pressure magnitude) be independent on geometrical and physical-mechanical parameters of the problem. Keywords Crack Systems, Oil and Gas Wells 1. Introduction Around oil and gas wells under hydrostatic pressure [1, 2] (Fig. 1, 2) a pattern of regular cracks grids, emerging the surface of a circular cavity, is frequently observed. In the so-called «geoloosening» (directed layer unloading) method such systems are produced specially for increasing the rock fracturing and stimulation of oil input to the well [1, 2]. That is why it is important studying the structure of this crack networks, in particular, their number, length, etc. Regular systems of cracks are found in many structures and natural objects (examples and references see, eg, [3]). They may be initially due to both non-mechanical factors, such as thermal stress, the effect of aggressive media, phase transforms (drying, freezing [4]), etc., as well as have purely mechanical nature. Note that the problem of regular cracking of bark in technically elementary but quite substantial statement was considered in [5] already in 1952. Point also the paper [6], in which the formation of regular ordered crack systems was used to illustrate the capabilities of the variational principle of cracks mechanics there proposed. In [3] for the near-surface thermal cracks the formation of "nested doll" systems was studied, where a regular system of equal cracks turns into two analogous crack systems, each with its own size but double period with respect to the original system. Moreover, it was shown that, in some cases, the crack may develop by jumps, and in others, for subsurface cracks it turns out more profitable not to extend into the material, but curl and form spalling. In [7] issues of arising of ordered crack systems and/or crack-like defects under compression were briefly touched upon. In [8] development of regular systems of surface cracks under the thermal shock, and in [9] – multiple cracking of brittle coatings upon loaded solids was studied. In [10-12] an experimental study was performed, and a model was proposed on formation and evolution of cracks echelon in the vicinity of a main longitudinal shear elastic-brittle crack. In [13-16] distribution of fragments of glass after break by size and time was experimentally studied and theoretically treated using methods of the theory of fractals.
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