Research On Softening Relationship For Concrete From The Three-Point Bending Notched Beam Test

The mechanical behavior within the fracture process zone (FPZ) at the tip of crack in concrete can be well described by the fictitious cracking model (FCM) introduced by Hillerborg et al. The softening curve of concrete, reflecting the relationship of the residual intensity and crack width after its reach tensile strength, is a significant part of FCM. In this paper, a method to solve tension softening relationship of concrete obtained from three-point bending notched beams is presented. The method is based on the fictitious crack model, by fitting the theoretical calculated P-CMOD to the experimentally determined P-CMOD curves to obtain the tensile softening relationship. All inputted parameters used in the calculation were directly obtained from the three-point bending notched beam tests. The advantage of the present method is that the displacement-controlled bending test is much easier to carry out than the uni-axial tension test and the percentage of tests that can successfully carried out is higher than that by uni-axial tension.The method to obtain concrete softening relationship by inverse analysis also needs accurate experimental data. Because typical experimental data always contain measurement errors (outliers and noise) caused by environment, equipment and human error, meanwhile, for improving calculating efficiency, it is necessary to process data. Data processing is divided into three steps. Firstly, those non-positive and scattered far from the P-CMOD curve data are filtered. Secondly, for each group, a representative curve is obtained by averaging effective companion specimens with two hundreds data points, one hundred each for ascending and descending parts. Last, a total of twenty points including the peak and the end point (7 points in the ascending part, 13 points in the descending part) were extracted from the averaged load-CMOD curves to fit P-CMOD curves for inverse analysis.The fracture process of the concrete three-point bending notched beam is plane stress problem, and simulated by FORTRAN language. Softening parameters are optimized during the process. Considering its symmetry, only half of the specimen was modeled, in this way, the number of degrees of freedom is reduced significantly as compared to a two-dimension full model, meanwhile, the computational efficiency can be improved. The results of concrete fracture energy by inverse analysis and fracture work are dovetailed nicely with each other, tensile strength f tby inverse analysis are larger than that of uni-axial tests while frature energy is less than those of uni-axial tests.The maximum crack opening width wc and the fracture energy G_F increase with increase of coarse aggregate size. However, f_tdecrease after coarse aggregate size reach to some value and the trend is not apparent. f_t increases with increase of concrete compression strength and the wc and G_F decrease with increase of concrete compression strength. The influence of size of specimen on the tensile strength f_t is insignificant. Concrete fracuture energy exists size effect and its value increase with increase of specimen size and will not increase till some length. The first branch of softening curve is similar while wc increases with specimen size this may explain the size effect of fracture energy.