Energy Scaling in Rock Cutting

在土木工程或采矿工程项目中，硬岩开挖机械化的运动使量化工具-岩石相互作用的力学的需要摆在了首位。一个相关的问题是对划痕测试的解释。这项实验技术最近引起了人们的兴趣，因为它似乎提供了一种简单而经济的方法来测量岩石、陶瓷和混凝土等准脆性材料的强度和断裂特性。然而，在这些实验中可以确定哪些参数以及如何从测试数据中解释这些参数仍然存在问题。因此，无论是预测切削力(平均值和波动值)以设计机械开挖设备、确定开挖进度和成本，还是在受控划痕实验中解释测量的切削力，都会产生相同的基本问题：切削力(I)与切割深度和刀具几何形状有关，(Ii)与岩石的强度和断裂特性有关。通过认识到岩石切割过程中会发生不同的破坏模式，因此不同的参数对切削力的影响取决于当时的模式，这项研究有可能开发出岩石切割的普遍尺度定律。此外，这项研究还有可能为我们理解混凝土或陶瓷等具有颗粒结构的工程材料的失效提供信息。由这些准脆性材料制成的结构的破坏以尺度效应和剪切和拉伸为主的破坏机制之间可能的转换为特征。然而，工程设计实践仍然植根于基于强度的方法，尽管它在处理准脆性材料时的适用范围有限。如果成功，这项研究将产生一种表征断裂特性的简单实验手段，从而将断裂力学--这一此类材料的基本概念--推广到工程实践中。这项研究的成果将纳入本科生和研究生的课堂教学，努力使下一代工程师掌握岩石力学、断裂力学和实验力学的基本知识。该项目解决了岩石切割中能量比例的基本问题，即比能量--每移出岩石体积所花费的能量--与切割深度和岩石性质的依赖关系。了解特定能量尺度(或切削力尺度如何)对于设计坚硬岩石的机械挖掘机以及解释划痕试验至关重要--划痕试验是一种评估准脆性材料特性的技术。这项研究是基于经验证据，表明在岩石切割中存在三种渐近机制。随着切割深度的增加(大于岩石的平均粒度)，确实可以观察到不同的破坏模式：(I)在浅切割深度处的延性区域，岩石在切割器前面被强烈剪切；(Ii)岩石破碎成碎片，这些碎片在很大的尺寸范围内按照幂定律分布；以及(Iii)脆性区域，宏观裂纹从刀具尖端开始并在刀具前方不稳定地扩展。这项研究建立在三个不同的经验定标定律上，分别基于现有的实验数据和来自数值模拟和定标分析的见解，在刀具至少与岩板厚度一样宽的情况下。这项研究的主要目的是通过理论和计算模型为这些经验标度律提供理论支持，并获得经验证据最薄弱的脆性区域的实验结果。

The drive to mechanize the excavation of hard rock in civil or mining engineering projects has brought to the forefront the need to quantify the mechanics of tool-rock interaction. A related issue is the interpretation of the scratch test. This experimental technique has garnered interest lately, because it appears to offer a simple and economical means to measure strength and fracture properties of quasi-brittle materials such as rock, ceramics, and concrete. However, there remain questions on which parameters can be determined in these experiments and how to interpret them from the test data. Therefore, whether predicting the cutting force (mean and fluctuations) to design mechanical excavation equipment and establish the excavation schedule and costs, or interpreting the measured force in controlled scratch experiments, the same fundamental question arises: what is the dependence of the cutting force (i) on the depth of cut and the cutter geometry, and (ii) on the strength and fracture properties of the rock. By recognizing that different regimes of failure take place in rock cutting and therefore that different parameters affect the cutting force depending on the prevailing regime, the research has the potential to develop universal scaling laws for rock cutting. Furthermore, this research has also the potential of informing our understanding of the failure of engineered materials with a grain structure, such as concrete or ceramics. Failure of structures made of these quasi-brittle materials is characterized by scale effects and possible transition between shear- and tensile-dominant failure mechanisms. However, engineering design practice is still rooted in the strength-based approach, despite its restricted range of applicability when dealing with quasi-brittle materials. If successful, the research will result in a simple experimental means for characterization of fracture properties, thus promoting fracture mechanics -- an essential concept for such materials -- to engineering practice. The findings of this research will be incorporated into classroom teaching at both undergraduate and graduate levels, in an effort to equip the next generation of engineers with fundamental knowledge of rock mechanics, fracture mechanics and experimental mechanics. The project addresses the fundamental question of energy scaling in rock cutting, i.e., the dependence of the specific energy - the energy spent per volume of rock removed, on the depth of cut and on the rock properties. Understanding how the specific energy scales (or alternatively how the cutting force scales) is critical for designing mechanical excavators for hard rocks, as well as for interpreting the scratch test - a technique to assess the properties of quasi-brittle materials. The research is grounded on empirical evidence that suggests the existence of three asymptotic regimes in rock cutting. With increasing depth of cut (larger than the rock mean grain size), different modes of failure can indeed be observed: namely, (i) a ductile regime at shallow depth of cut, with the rock intensely sheared in front of the cutter; (ii) a fragmentation regime with the rock breaking into fragments that are distributed according to a power law over a significant range of sizes, and (iii) brittle regime with macroscopic cracks initiating from the tool tip and propagating unstably ahead of the cutter. The research builds on three respective empirical scaling laws for these regimes, which are informed by the available experimental data and insights from numerical simulation and scaling analysis, for the case where the cutter is at least as wide as the rock slab thickness. The main objective of this research is to provide theoretical underpinnings to these empirical scaling laws using theoretical and computational models, as well as to obtain experimental results for the brittle regime, for which the empirical evidence is weakest.