The size distribution of rock chips can fully reflect the performance of shield machine, and existing size distribution indicators suffer from low efficiency and poor accuracy. Therefore, the aim is to find an accurate and rapid quantitative indicator to characterize the rock chips size distribution and address the engineering issues of shield machine rock-breaking efficiency analysis and tunneling parameter optimization. In this study, five groups of rock chips with different quality components and eight shooting heights were designed to explore the performance and applicability of the image fractal dimension (D), a quantitative indicator of rock chip size distribution based on the Sandbox fractal method, and also to compare it with the traditional Box-counting method. Additionally, an analysis of 136 groups of rock chips data from different surrounding rock grades was conducted to investigate the correlation between image fractal dimension and common shield performance indexes, such as the average single cutter thrust force (Fn), and penetration depth (Prev). The results indicate that the experimental platform constructed in this study, with image data acquired at a shooting height of 120 cm, is well-suited for calculating image fractal dimension. Compared to the traditional Box-counting method, the Sandbox method demonstrates higher sensitivity to changes in the particle size distribution of rock chips and does not impose restrictions on input image size, making it more appropriate for quantitative analysis. The image fractal dimension decreases as the proportion of large-sized rock chips increases. Under the same surrounding rock conditions, the image fractal dimension of rock chips is positively correlated with the logarithm of specific energy (SE) and negatively correlated with the logarithm of coarseness index (CI), effectively reflecting shield rock-breaking efficiency. Based on the correlation between image fractal dimension and SE, the optimal ranges of Fn and S/Prev under grade II, III, IV, and V surrounding rock conditions can be determined, thereby enabling the optimization of tunneling performance.

中文翻译：

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基于 Sandbox 方法的岩屑图像分形特征提取及盾构掘进性能分析

岩屑的粒度分布可以充分反映盾构机的性能，现有的粒度分布指标存在效率低、精度差等问题。因此，旨在找到一种准确、快速的定量指标来表征岩屑粒度分布，解决盾构机破岩效率分析和隧道参数优化的工程问题。本研究设计了 5 组不同质量成分的岩片和 8 个拍摄高度，探究基于 Sandbox 分形法的岩屑粒径分布定量指标图像分形维数 （D） 的性能和适用性，并与传统的计盒法进行了比较。此外，对来自不同围岩等级的 136 组岩屑数据进行了分析，以研究图像分形维数与常见盾构性能指标之间的相关性，例如平均单刀推力 （Fn） 和穿透深度 （Prev）。结果表明，本研究构建的实验平台，在 120 cm 拍摄高度处获取图像数据，非常适合计算图像分形维数。与传统的 Box-counting 方法相比，Sandbox 方法对岩屑粒度分布的变化表现出更高的灵敏度，并且对输入图像大小没有限制，使其更适合定量分析。图像分形维数随着大型岩屑比例的增加而减小。 在相同围岩条件下，岩屑图像分形维数与比能对数（SE）呈正相关，与粗度指数（CI）对数呈负相关，有效反映了盾构破岩效率。基于影像分形维数与 SE 的相关性，可以确定 II、III、IV、V 级围岩条件下 Fn 和 S/Prev 的最佳范围，从而优化隧道掘进性能。