Continuing the experiments on the double-edge notched pecimens on which the mode Ⅱ fracture toughness KIIc of concrete was measured, a practical testing approach to determine mode Ⅱ fracture energy GIIF is studied using the same geometry.

Based on the complete fracture process in concrete, the crack extension resistance associated with the cohesive force on the fictitious crack is investigated in detail for standard three-point bending notched beams. Five concrete materials are speci

Assuming the weakest link concept. A probalilistic model of fracure in concrete structures has been developed in terms of the critical stress intensity factors. The probabilistic model, wodel, which is expressed in the form of the Weiball distribution, has been compared with arange of experimental results in the literature. The results predicted by the formula are in good agreement with the values reported in the literature for four test secimen geometries-compact tension spectimens, notched three-point bend specinens, wedge splitting spectimens and compact compression specimens. The results presented in the paper have been applied to predict the fracture in large concrete dams and the results compare favourably with observed craking.

A simplified method for determining the double-K fracture parameters Kini Ic and Kun Ic for three-point bending tests is proposed. Two empirical formulae are used to describe the crack mouth opening displacement CMOD and the stress intensity factor Kc I caused by the cohesive force σ(x) on the fictitious crack zone for threepoint bending beams. It has been found that the two empirical formulae are accurate for a large practical region of a/D. Experiments carried out by many researchers showed that the new formula of CMOD for three-point bending beams can be directly used to predict the initial crack length for precracked beams, the notch depth and the critical effective crack length, as well as the crack length in the post-critical situation with a satisfactory accuracy. Further verification is demonstrated to determine the double-K parameters Kini Ic and Kun Ic. They are very close to those determined by the method proposed in our previous work. Using the simplified procedure, the experiments can be performed even without a closed-loop testing facility and the calculation can be carried out on a pocket calculator.

The crack extension resistance and fracture properties are studied in detail for quasi-brittle materials like concrete with a softening traction-separation law by investigating the complete fracture process. The computed samples are the three-point bending notched beams of concrete with different sizes tested by other researchers. The softening traction-separation law which was proposed by Reinhardt et al. based on direct tension tests for normal concrete materials was chosen in the computations. Different distribution shapes of the cohesive force on the fictitious crack zone were considered for the corresponding loading states. The computations were mainly based on the analytic solutions for this problem using Gauss-Chebyshev quadrature to achieve the integration which is singular at the integral boundary. The crack extension resistance curves in terms of stress intensity (KRcurves) were determined by combining the crack initiation toughness Kini Ic that is the inherent toughness of the material needed to resist the crack initiation in the case that is in the lack of an extension of the main crack with the contribution due to the cohesive force along the fictitious crack zone during the complete processes of fracture. The situation of crack propagation can be judged by comparing KR-curves of crack extension resistance with the stress intensity factor curves which were calculated using the lengths of the extending crack and the corresponding loads at each loading states, e.g., when the crack extension resistance curve (KR-curve) is higher than the stress intensity factor curve, the crack propagation is stable; otherwise, it is unstable. In the computation, the obtained relationship between the crack tip opening displacement CTOD and the amount of crack extension for the complete fracture process is in agreement with the testing results of other researchers.