A simple method for determining the material constants of rock (e.g., fracture toughness K_IC and tensile strength f_t) using normal distribution with respect to average grain size g_av is proposed as an alternative to the commonly used of curve fitting using rock test data. Supposing different characteristic crack $a_{\infty }^{\ast }$ and considering different fictitious crack growth length Δa_fic at peak load P_max for different relative size W/g_av, the normal distribution histograms of K_IC and f_t with the smallest discrete coefficient are statistically obtained. The Δa_fic of rock specimens with different size are quantitatively studied, and the corresponding design relations of Δa_fic for rock specimens with different W/g_av are statistically derived. The full fracture curves of rock with different W/g_av are constructed using the designed relation. The simple closed-form solutions for different notched rock specimens (e.g., three-point bending and compact tension) are proposed. The experimental P_max using normal distribution methodology with 95% reliability and simple closed-form solutions with upper and lower limits are reliably predicted. K_IC, f_t, and P_max of real rock structures with W/g_av = 1000 are reliably obtained using the simple closed-form solutions.

提出了一种使用相对于平均晶粒度g _av的正态分布确定岩石材料常数（例如，断裂韧性K _IC和抗拉强度f _t）的简单方法，以代替通常使用岩石测试数据进行曲线拟合的方法。 。假设不同的特征裂纹${\mathrm{一种}}_{\infty }^{\ast }$并考虑不同的虚拟裂缝生长长度Δ一个_FIC在峰值负载P_最大为不同相对尺寸w ^ /克_AV，正常分布直方图的ķ _IC和˚F_吨进行统计获得具有最小的离散系数。所述Δ一个_FIC岩石标本不同尺寸的定量研究，Δ的相应的设计关系一个_FIC用于岩石样品具有不同W¯¯ /克_AV进行统计的。不同岩石的全断裂曲线W / g _av使用设计的关系构造。提出了针对不同缺口岩石样本的简单封闭形式解（例如，三点弯曲和紧凑张力）。可靠地预测了使用具有95％可靠性的正态分布方法和上限和下限的简单闭式解的实验P _max。 使用简单的封闭形式解可以可靠地获得W / g _av = 1000的真实岩石结构的K _IC，f _t和P _max。