Abstract Chaotic geological bodies composed of rock inclusions of different lithology and size enclosed in a weaker matrix are often referred to as bimrocks (block-in-matrix rocks). When dealing with these challenging and widespread geomaterials, a major concern for geopractitioners is the estimation of block content, which has been demonstrated to strongly affect the overall mechanical behaviour of bimrocks. Since the estimation of this parameter is not a simple matter, stereological principles are generally applied to infer 3D block contents from 1D or 2D measurements. However, they are often fraught with a high magnitude of error. In this study, a statistical approach was developed to determine the uncertainties associated with estimates of the 3D block proportions from 2D measurements. A Matlab code was implemented to generate heterogeneous models with a size distribution typical of bimrocks. An uncertainty factor is provided related to the size of the outcrop area investigated and the 2D block content to adjust the initial 2D estimates. It was found that a larger investigation area increases the reliability of the 2D measurements and as actual volumetric block proportion increases, the uncertainty decreases. The results obtained through this procedure were subsequently compared with previous findings from the literature concerning the uncertainty in estimates of the VBP from 1D measurements. The outcome of this comparison highlights the strength of the procedure described in this paper.

中文翻译：

---

从 2D 测量值中识别 bimrocks 体积比例估计中的不确定性

摘要 由不同岩性和大小的岩石包裹体包裹在较弱的基质中组成的混沌地质体通常被称为bimrocks（block-in-matrix rock）。在处理这些具有挑战性和广泛分布的地质材料时，地质从业人员主要关注的是块体含量的估计，这已被证明会强烈影响 bimrocks 的整体力学行为。由于此参数的估计不是一件简单的事情，因此通常应用立体学原理从 1D 或 2D 测量中推断 3D 块内容。然而，它们通常充满了很大的误差。在这项研究中，开发了一种统计方法来确定与 2D 测量的 3D 块比例估计相关的不确定性。实现了 Matlab 代码以生成具有典型 bimrocks 尺寸分布的异构模型。提供了与所调查的露头区域的大小和 2D 区块内容相关的不确定因素，以调整初始 2D 估计。发现更大的调查区域会增加 2D 测量的可靠性，并且随着实际体积块比例的增加，不确定性会降低。随后将通过此程序获得的结果与文献中关于从一维测量估计 VBP 的不确定性的先前发现进行比较。这种比较的结果突出了本文中描述的程序的优势。提供了与所调查的露头区域的大小和 2D 区块内容相关的不确定因素，以调整初始 2D 估计。发现更大的调查区域会增加 2D 测量的可靠性，并且随着实际体积块比例的增加，不确定性会降低。随后将通过此程序获得的结果与文献中关于从一维测量估计 VBP 的不确定性的先前发现进行比较。这种比较的结果突出了本文中描述的程序的优势。提供了与所调查的露头区域的大小和 2D 区块内容相关的不确定因素，以调整初始 2D 估计。发现更大的调查区域会增加 2D 测量的可靠性，并且随着实际体积块比例的增加，不确定性会降低。随后将通过此程序获得的结果与文献中关于从一维测量估计 VBP 的不确定性的先前发现进行比较。这种比较的结果突出了本文中描述的程序的优势。随后将通过此程序获得的结果与文献中关于从一维测量估计 VBP 的不确定性的先前发现进行比较。这种比较的结果突出了本文中描述的程序的优势。随后将通过此程序获得的结果与之前文献中的发现进行比较，这些发现涉及从一维测量中估计 VBP 的不确定性。这种比较的结果突出了本文中描述的程序的优势。