ORIGINAL PAPER Coalescence of Fractures Under Uni-axial Compression and Fatigue Loading Y. L. Chen • J. Ni • W. Shao • Y. C. Zhou • A. Javadi • R. Azzam Received: 23 November 2010 / Accepted: 12 September 2011 / Published online: 30 September 2011 Ó Springer-Verlag 2011 Abstract In this paper, white Portland cement was used as an experimental material. Prismatic specimens with pre- existing flaws at different angles of inclination (a) varying through 0°, 30°, 45°, 60°, 75° to 90° and cylindrical specimens with different numbers of pre-existing flaws (n) varying through 0, 1, 2 to 3 were tested under uni-axial compression tests. Crack initiation, propagation, coales- cence, and failure were observed. The corresponding ana- lytical expression for the stress intensity factor under uni- axial compression was derived, the coefficient of friction and the stress intensity factor of the specimens on the surfaces of the crack were analysed, and the corrective coefficient for the stress intensity factor was introduced. Fatigue tests with a loading frequency of f = 100 Hz were carried out on cylindrical specimens with constant ampli- tude of the cyclic load which is a proportion of the com- pressive load at failure (F f ) obtained from the uni-axial compression tests. The fatigue property of the specimens was analysed and the relationship (S max - lg N f ) between the maximum stress and the number of loading cycles at failure for specimens with pre-existing flaws was proposed. The effect of pre-existing flaws on the fatigue life (N f ) and dynamic load (S D ) which can be applied was investigated. Keywords Pre-existing flaws  High frequency cyclic loading  Stress intensity factor  Coefficient of friction  Crack propagation List of Symbols a Half the flaw length (mm) a 0 Initial half the flaw length (mm) b Vertical space (mm) f Cyclic loading frequency (Hz) F f Load at failure (kN) F N Corrective coefficient of the stress intensity factor h Horizontal space (mm) k II Stress intensity factor for type II pure shear flaw MPa ffiffiffiffiffiffiffiffi mm p ð Þ n Number of pre-existing flaws N f Number of loading cycles at failure S D Dynamic load (kN) S DS Static load (kN) S max Maximum load (kN) T Test period (min) w Width of the specimen (mm) Greek symbols a Inclination angle of the flaw (°) Y. L. Chen  J. Ni (&)  W. Shao  Y. C. Zhou Department of Civil Engineering, University of Shanghai for Science and Technology, 516 Jungong Road, Shanghai 200093, People’s Republic of China e-mail: wendy_1943@163.com Y. L. Chen e-mail: chenyouliang2001@yahoo.com.cn W. Shao e-mail: shaowei2775@163.com Y. C. Zhou e-mail: zyc_scu@126.com A. Javadi Department of Engineering, University of Exeter, North Park Road, Exeter EX4 4QF, UK e-mail: a.a.javadi@ex.ac.uk R. Azzam Department of Engineering Geology and Hydrogeology, RWTH Aachen University, Lochnerstr. 4-20, 52064 Aachen, Germany e-mail: azzam@lih.rwth-aachen.de 123 Rock Mech Rock Eng (2012) 45:241–249 DOI 10.1007/s00603-011-0186-x