Analytical And Experimental Study On Local Fracture Energy Distribution In Cementitious Materials And Reinforced Concrete

Fracture mechanics of concrete is a discipline developed in recent decades. With the development of testing method and analytical approach, the study on fracture properties of quasi brittle materials such as mortar and concrete has received wide attention. A lot of fracture models have been presented analyse the crack expansion process, and fracture energy is a very important parameter to determine the crack propagation. However, the previous results show that fracture energy has obvious size effect. When the specimen size is increased, the measured fracture energy also increases. Some researchers pointed out that size effect in fracture energy of cementitious materials is only related to the physical size of the specimens. But some researchers thought that size effect is main due to the uneven distribution of local fracture energy along the ligament of specimen, which is influenced by the specimen boundary. Therefore, the theory of boundary effect is adopted to analyse size effect on fracture energy. The local fracture energy reaches a maximum when the crack tip is far away from the boundary of specimen. The obtained fracture energy from the tests is the average value of the distributed local fracture energy along the ligament of specimen. Then the size effect on fracture energy can be explained. In this paper, the main work is to seek a simple and reasonable method to determine the distribution of fracture energy in cementitious materials, then analyze the boundary effect. At the same time, the boundary effect theroy is extended to reinforced concrete.In this paper, based on the fictitious crack model, the relationship between the maximum fracture load of three-point-bending notched beam and local fracture energy at the cohesive crack tip region has been built for mortar, plain concrete and reinforced concrete, respectively. Different height and initial crack-depth ratios are taken into account in tests. The variation of local fracture energy at the cohesive crack tip region is analyzed to determine the distribution of local fracture energy along the ligament by the comparision between the analytically predicted and experimentally determined results of the maximum fracture load of three-point-bending notched beam. It can lay a solid foundation for crack propagation law and size effect in fracture energy of cementitious materials. The main results are as follows:(1)Three-point-bending notched beam tests of mortar with different height and initial crack-depth ratios (a0/h=0.1～0.8) are carried out to get the maximum fracture load. Then the distribution of local fracture energy of mortar is determined based on the comparisons between the two extreme conditions with test results. Results show that when the crack tip approaches the front or back free boundary, the local fracture energy is reduced, reflecting the front or back free boundary effect of the specimens.(2) Three-point-bending notched beam tests of concrete with different height and initial crack-depth ratios (a0/h=0.1～0.8) are carried out to get the maximum fracture load. Then the distribution of local fracture energy of concrete is reconfirmed based on the comparisons between the two extreme conditions with test results. Results show that when the crack tip approaches the front or back free boundary, the local fracture energy is reduced, reflecting the front or back free boundary effect of the specimens. Only when the initial crack is long and the ligament height of specimen is large enough, fracture energy of cementitious materials by experiment has no size effect.(3) Three-point-bending notched beam tests of reinforced concrete with different height and initial crack-depth ratios (a0/h=0.1～0.8) are carried out to study the load changing rule of the whole loading process. Results show that two peaks will appear in the process of load change, and the first peak is closely ralated to the fracture energy of concrete. Then based on the deformation compatibility condition the first peak is calculated. The distribution of local fracture energy near the steel bar is determined by the comparison between the calculated and test results. Due to the boundary effect that steel bar can be a boundary, concrete crack propagation near the steel bar is restrained so that crack can not be fully expanded. And thus the value of fracture energy is low.