Abstract
Quasi-static stepwise propagation of a hydraulic fracture in rock with a regular structure in the absence of filtration is considered. It is proposed to use a brittle fracture diagram taking into account the hydraulic fracturing fluid pressure and the confining pressure. Fracture curves describing the brittle rock fracture where the hydraulic fracturing fluid partially fills the fracture are constructed and used to predicted the possibility of stepwise propagation of hydraulic fracturing in the case where the fluid gradually flows into the fracturing crack. The regularity of the structure of the brittle rocks fracture is estimated from the results of two full-scale experiments: the critical stress intensity factor and the tensile strength limit of the rock. Experiments on pulsed loading of polymethylmethacrylate samples with stepwise crack propagation along concentric circular arcs were performed. The results of the experiments are consistent with theoretical predictions.
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References
M. G. Mack and N. R. Warpinski, “Mechanics of Hydraulic Fracturing,” in Reservoir Stimulation (John Wiley and Sons, Chichester-Toronto, 2000), p. 6-1–6-49.
Yu. P. Zheltov and S. A. Khristianovich, “On Hydraulic Fracturing of Oil Reservoirs,” Izv. Akad. Nauk SSSR, Otd. Tekh. Nauk, No. 5, 3–41 (1955).
T. K. Perkins and L. R. Kern “Widths of Hydraulic Fractures,” J. Petrol. Technol. 13(9), 937–949 (1961).
B. Carrier and S. Granet, “Numerical Modeling of Hydraulic Fracture Problem in Permeable Medium using Cohesive Zone Model,” Eng. Fracture Mech. 79, 312–328 (2012).
G. Neuber, Kerbspannunglehre: Grunglagen fur Genaue Spannungsrechnung (Springer-Verlag, Berlin, 1937).
V. V. Novozhilov, “Necessary and Sufficient Criterion of Brittle Fracture,” Prikl. Mat. Mekh. 33(2), 212–222 (1969).
I. M. Kershteyn, V. D. Klyushnikov, E. V. Lomakin, and S. A. Shesterikov, Basis of Experimental Fracture Mechanics (Izd. Mosk. Univ., Moscow, 1989) [in Russian].
M. P. Savruk, “Stress Intensity Factors in Bodies with Cracks,” in Fracture Mechanics and Strength of Materials, Vol. 2 (Naukova Dumka, Kiev, 1988) [in Russian].
Stress Intensity Factors, Ed. by Yu. Murakami (Pergamon Press, Oxford, 1986), Vol. 1.
S. E. Kovchik and E. M. Morozov, Characteristics of Short-Term Crack Resistance of Materials and Methods for Their Determination (Naukova Dumka, Kiev, 1988). (Fracture Mechanics and Strength of Materials, Vol. 3.)
N. F. Morozov, Yu. V. Petrov, and V. I. Smirnov, Limiting Equilibrium of Brittle Bodies with Stress Concentrators: Structural Approach: Textbook (St. Petersburg Univ., St. Petersburg, 2011).
V. M. Kornev, “Quasibrittle Fracture Diagrams of Bodies with a Hierarchy of Structures under Low-Cycle Loading,” Fiz. Mezomekh. 14(5), 31–45 (2011).
V. M. Kornev, “Quasibrittle Fracture Diagrams in Fatigue (Two-Frequency Loading),” Fiz. Mezomekh. 15(6), 45–58 (2012).
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Original Russian Text © V.M. Kornev, A.G. Demeshkin.
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 55, No. 3, pp. 164–173, May–June, 2014.
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Kornev, V.M., Demeshkin, A.G. Model of stepwise propagation of the tip of a hydraulic fracture in the absence of filtration. J Appl Mech Tech Phy 55, 515–523 (2014). https://doi.org/10.1134/S0021894414030146
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DOI: https://doi.org/10.1134/S0021894414030146