The fracture behavior of concrete can be described by an R-curve, which represents the ability of concrete to resist crack propagation. In this study, the R-curve is defined as the envelope of the energy release rates in the critical state and is constructed on the basis of the boundary effect model. Two fracture parameters are introduced for constructing the R-curve, namely, the fracture energy G_f and the equivalent crack extension c_f in an infinitely large specimen, and these two vital parameters can be obtained from testing specimens of different sizes. One of the greatest features of the proposed R-curve is that the influence of concrete aggregate is explicitly manifested in the R-curve expression in terms of the maximum aggregate size. The theoretically derived ascending branch of the R-curve is fitted using a unified function for three-point bending specimens with varying values of the initial crack length relative to the specimen depth (between 0.2 and 0.9). The developed R-curve approach is applied to the tested three-point bending notched concrete beams, and the predicted load-displacement responses are found to agree with the experimental curves. It is also shown that the results are not sensitive to the choice of the discrete number β, which is included in the R-curve expression to address the linkage between the fictitious crack growth and coarse aggregate structures of concrete.

混凝土的断裂行为可以用R曲线来描述，它代表了混凝土抵抗裂纹扩展的能力。在这项研究中，R曲线定义为临界状态下能量释放速率的包络，并基于边界效应模型构建。引入两个断裂参数来构造R曲线，即无限大试样中的断裂能G _f和等效裂纹扩展c _f，这两个重要参数可以从不同尺寸的试样中获得。建议的R的最大特点之一-曲线是混凝土骨料的影响明确地以最大骨料尺寸显示在R曲线表达式中。R曲线的理论导出的上升分支使用统一函数拟合三点弯曲样本，该样本的初始裂纹长度相对于样本深度（在0.2和0.9之间）有所变化。将已开发的R曲线方法应用于已测试的三点弯曲槽形混凝土梁，发现预测的载荷-位移响应与实验曲线一致。还表明结果对R中包括的离散数β的选择不敏感曲线表达以解决虚拟裂纹扩展与混凝土粗骨料结构之间的联系。