This article discusses the scale dependence of the mode \(\mathrm {I}\) fracture toughness of rocks measured via the semi-circular bend (SCB) test. An extensive set of experiments is conducted to scrutinise the fracture toughness variations with size for three distinct rock types with radii ranging from 25 to 300 mm. The lengths of the fracture process zone (FPZ) for different sample sizes are measured using the digital image correlation (DIC) technique. A theoretical model is also established that relates the value of fracture toughness to the sample size. This theorem is based on the strip-yield model to estimate the length of FPZ, and the energy release rate concept to relate the FPZ length to the fracture toughness. This theoretical model does not rely on any experimental-based curve-fitting parameter, but only on the tensile strength of the rock type as well as the fracture toughness at a specific sample size. The size effects predicted by the theoretical model is in a good agreement with the experimental data on both fracture toughness and the FPZ length. Finally, theoretical correction factors are introduced for various geometrical configurations of the SCB specimen, using which a scale-independent mode \(\mathrm {I}\) fracture toughness of the rock material can be estimated from the results of experiments performed on small samples.

本文讨论模式\（\ mathrm {I} \）的比例依赖通过半圆弯曲（SCB）测试来测量岩石的断裂韧性。进行了广泛的实验，以检查半径在25到300毫米范围内的三种不同岩石类型的断裂韧性随尺寸的变化。使用数字图像相关（DIC）技术测量不同样本大小的断裂过程区（FPZ）的长度。还建立了理论模型，该模型将断裂韧性的值与样品大小相关联。该定理基于带材屈服模型来估计FPZ的长度，并且基于能量释放速率概念将FPZ的长度与断裂韧性相关联。该理论模型不依赖于任何基于实验的曲线拟合参数，而仅依赖于岩石类型的拉伸强度以及特定样本大小下的断裂韧性。理论模型预测的尺寸效应与断裂韧性和FPZ长度的实验数据非常吻合。最后，针对SCB标本的各种几何构造引入了理论校正因子，使用该校正因子可以实现与比例无关的模式\（\ mathrm {I} \）上的小样品进行的岩石材料的断裂韧性可以从实验的结果估计的。