Based on the design relation value of the variation dispersion coefficient $\beta$ at the notch tip in concrete specimens at the peak load $P_{\mathit{max}}$, a Weibull distribution method was employed to analyze the experimental data for different loading methods (3 PB, 4 PB, WS). The dispersion coefficient $\beta$, which complies with the Weibull distribution for notched specimens, leads to a Weibull distribution of the tensile strength $f_t$ and fracture toughness $K_{\mathit{IC}}$. Furthermore, when the characteristic crack of concrete is ${\alpha }_{\mathit{ch}}^{\ast }=1.0d_{\mathit{max}}$ (or $1.5d_{\mathit{max}}$), the coefficient of variation for the Weibull distribution is the smallest in most cases. By adopting the simple relation ${\alpha }_{\mathit{ch}}^{\ast }=1.0d_{\mathit{max}}$ (or $1.5d_{\mathit{max}}$) and the fictitious crack growth, $\mathrm{\Delta }{\alpha }_f=\beta d_{\mathit{max}}$, the fracture properties of concrete specimens with$W/d_{\mathit{max}}$ = 4–50 under different loading conditions (3 PB, 4 PB, WS) were investigated. Because of the scatter in the peak load $P_{\mathit{max}}$ of the notched specimens and the variation in the fictitious crack growth $\mathrm{\Delta }{\alpha }_{\mathit{fici}}$, a new statistical approach using the solution of the boundary effect model (BEM) was employed. The curves between the peak load $P_{\mathit{max}}$ and specimen height $W$ were predicted. The critical values of the peak load $P_{\mathit{max}}$ and specimen height $W$ were obtained, in which the notched specimen failure was controlled by the fracture toughness $K_{\mathit{IC}}$.

基于变异分散系数的设计关系值 $\beta$ 在峰值载荷下混凝土试件的缺口尖端 ${磷}_{\mathit{最大限度}}$，采用威布尔分布方法来分析不同加载方法（3 PB、4 PB、WS）的实验数据。色散系数$\beta$，符合缺口试样的威布尔分布，导致抗拉强度的威布尔分布 $F_{吨}$ 和断裂韧性 ${钾}_{\mathit{我知道了}}$. 此外，当混凝土的特征裂缝为${\alpha }_{\mathit{ch}}^{＊}=1.0d_{\mathit{最大限度}}$ （或者 $1.5d_{\mathit{最大限度}}$)，Weibull 分布的变异系数在大多数情况下最小。通过采用简单的关系${\alpha }_{\mathit{ch}}^{＊}=1.0d_{\mathit{最大限度}}$ （或者 $1.5d_{\mathit{最大限度}}$) 和虚构的裂纹扩展， $\mathrm{\Delta }{\alpha }_F=\beta d_{\mathit{最大限度}}$, 混凝土试件的断裂特性$宽/d_{\mathit{最大限度}}$ = 4-50 在不同负载条件下（3 PB、4 PB、WS）进行了研究。由于峰值负载的分散${磷}_{\mathit{最大限度}}$ 缺口试样和假想裂纹扩展的变化 $\mathrm{\Delta }{\alpha }_{\mathit{金融机构}}$，采用了一种使用边界效应模型 (BEM) 解法的新统计方法。峰值负载之间的曲线${磷}_{\mathit{最大限度}}$ 和试样高度 $宽$被预测。峰值负载的临界值${磷}_{\mathit{最大限度}}$ 和试样高度 $宽$ 得到，其中缺口试样的破坏由断裂韧性控制 ${钾}_{\mathit{我知道了}}$.