Numerical analysis of multiple cracks in concrete using the discrete approach

The discrete crack approach, which has been extensively used for analyzing single cracks, is extended for the numerical analysis of multiple cracks, based on the fictitious crack model and the crack-tip-controlled numerical algorithm. Assuming each crack as an effective crack while restraining the growth of others in turn, an explicit formulation of the mode I type crack propagation for multiple cracks is presented, and a minimum load criterion for crack extension is proposed for its numerical implementation. By eliminating invalid solutions to ensure proper crack behavior, this numerical model is capable of producing a variety of crack propagation patterns. Furthermore, a numerical technique based on the incremental stress analysis is introduced, which replaces the commonly adopted total strain approach for the discrete modeling of single cracks. The accuracy and effectiveness of this numerical method in analyzing multiple-crack problems are demonstrated through a series of parametric studies on four-point bending tests of simple plain concrete beams, as well as an experimental verification with fracture tests on real-size tunnel specimens.