Crack Extension Resistance Curve And Effect Of Aggregate Gradation On Fracture Parameters Based On Boundary Effect Model

Various models have been introduced to account for the nonlinearity of concrete in fractures,and among them,the boundary effect model（BEM）has gained increasing attention in recent years.BEM attributes the size effect of the strength of cracked concrete structures to the interaction between the fracture process zone（FPZ）and the structure boundary.By using the simple linear relationship between the ultimate load P_maxand the equivalent area,the tensile strength and fracture toughness of the material can be determined.However,as a model in the development process,the influence of aggregate gradation on the dispersion coefficientβhas not been studied yet.At the same time,the corresponding crack extension resistance curve has not been developed.This paper analyzes and discusses BEM through experimental research and theoretical derivation.The main research contents and conclusions are as follows:（1）Three kinds of coarse aggregates with different particle size distributions were used to pour concrete specimens of two strength levels,and a series of material and fracture tests were carried out.The results show that the porosity,elastic modulus E_c,cube compressive strength f_cuand crack initiation load P_iniof concrete are not sensitive to aggregate gradation;For C30 mix proportion,the splitting tensile strength f_tsand flexural strength f_rincrease gradually with the decrease of average aggregate size,The tensile strength of C60 mix ratio is less affected by the aggregate gradation;The fracture test shows that the ultimate load P_maxincreases with the decrease of average aggregate size when the crack-depth ratio is the same.（2）The fracture parameters of each group of specimens are calculated by the double-K fracture model and analytical method,and the influence law of aggregate gradation is analyzed.The results show that the fracture toughness calculated by the two models are relatively close,and both show an increasing trend with the decrease of the average aggregate particle size,but the range of change is limited;the equivalent crack extension decreases with the decrease of the average aggregate size,the equivalent crack extension calculated by the double-K fracture model is generally larger than the analytical method results,and the difference between them is about 2mm.（3）For C30 and C60 mixs,when using BEM to fit the fracture toughness of double-K fracture model and analytical method,βdecreases with the decrease of average aggregate size,but aggregate gradation has a great influence on C30 mixs,while C60 mixs has little change,which can be ignored.When using the unifiedβ=0.8 to analyze all the specimens,the fracture toughness fitted by each group of specimens is more consistent with the results of other models,and the corresponding tensile strength is close to the bending strength determined by the test.（4）Based on the boundary effect model,the expressions of fracture energy G_fand limit equivalent crack extension c_fof the infinite specimen are derived.The crack extension resistance curve was constructed according to the conditions of crack instability,and the proposed R curve was verified by using literature data.The results show that the proposed R-curve considers the effect of aggregate on the fracture performance of concrete,which is composed of rising convex curve and horizontal straight line.βmainly affects the resistance value of crack propagation before 0.6c_f.The P-CMOD curves predicted by differentβare basically the same,which are in good agreement with the experimental data.