An Experimental and Numerical Study on the Influence of Filling Materials on Double-Crack Propagation
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ORIGINAL PAPER
An Experimental and Numerical Study on the Influence of Filling Materials on Double‑Crack Propagation Xiaoying Zhuang3,4 · Shuwei Zhou1,2 Received: 1 December 2019 / Accepted: 31 July 2020 © Springer-Verlag GmbH Austria, part of Springer Nature 2020
Abstract Filling materials such as clay or sand widely exist in natural rock joints and work as weak bonds between the joint surfaces. The fillings affect rock deformation and failure behavior, and show different influences in terms of single crack or multiple cracks. While most of the literature have focused on unfilled cracks in brittle materials, this study aims to investigate various filling materials on the crack behavior, e.g., initiation, secondary cracks and peak strength. In this paper, the crack propagation in rock-like specimens with double-filled and unfilled cracks are investigated experimentally and numerically. Uniaxial compression tests were conducted and the experimental observations indicate that the peak stress and first crack initiation stress of the specimens vary with different geometries and different filling materials, while the crack initiation location and the pattern of crack coalescence show similar behavior between filled and unfilled cracks. In parallel to the experimental tests, numerical simulations were carried out using a modified phase field model (PFM) to complement the experiments and provide a new perspective. The PFM is found to produce consistent stress–strain curve, strength, and crack patterns with those observed in the experimental tests for both unfilled and filled cracks. Keywords Filling material · Double-crack · Crack propagation · Phase field model · Stress parameter List of symbols 𝛼 Inclination angle of original crack b Body force E Young’s modulus 𝜺+ Tensile strain Gc Critical energy release rate GcII Critical energy release rate of mode II Hu Driving force of phase field 𝜆 First Lamé constant L1 Original crack length 𝜇 Shear modulus * Xiaoying Zhuang [email protected] 1
Institute of Advanced Studies, Department of Geotechnical Engineering, College of Civil Engineering, Tongji University, Shanghai 200092, People’s Republic of China
2
Chair of Computational Science and Simulation Technology, Department of Mathematics and Physics, Leibniz University Hannover, 30167 Hannover, Germany
3
Division of Computational Mechanics, Ton Duc Thang University, Ho Chi Minh City, Vietnam
4
Faculty of Civil Engineering, Ton Duc Thang University, Ho Chi Minh City, Vietnam
𝜙 Phase field 𝜓ts Energy contribution of tensile strains to mode II crack 𝜑 Internal friction angle u Displacement field 𝛽 Rock bridge angle c Cohesion 𝜺 Strain tensor 𝜺− Compressive strain GcI Critical energy release rate of mode I h Maximum element size k Stability parameter l0 Length scale parameter L2 Rock bridge length 𝜈 Poisson’s ratio 𝜓t Energy contribution due to positive volumetric strain 𝜓cs Energy contribution of compressive strains to mode II crack 𝝈 Stress tensor x Position vector
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