## 1 Introduction  
One of the most difficult tasks in rock engineering is the proper characterization of the fracturing present in a rock mass for the purpose of engineering analysis [1]. Research on the rock foundations of the Kates Arch Dam in Lesotho, southern Africa, in the 1990s led to the development of a bias-free volumetric fracture count parameter (_VFC_--fractures/m3) that advanced the understanding and quantification of fracturing in rock [2]. Subsequently, [PERSON] and [PERSON] [1] integrated the _VFC_ parameter into a new and unified volumetric-based Geological Strength Index (V-GSI) chart. The chart provides a new approach and tool for rock engineers to calculate bias-free volumetric fracture counts and associated GSI ratings required to determine strength and deformability estimates for rock masses using the Hoek-Brown failure criteria equation [1]. The V-GSI system builds on the work of many researchers (references [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20], to name a few). For those not familiar with the development of the Geological Strength Index (GSI) chart, the following is offered as background information. The 1980s Hoek-Brown failure criterion was expanded on in the 1990s and 2000s to aid in designing underground excavations and slopes in rock [3, 4, 5, 6, 7, 8, 9, 10]. The criterion and associated equations, which provide a means of estimating the strength and deformability, and hence the mechanical behaviour of rock masses encountered in tunnels, slopes, and foundations, have continued to evolve over the last 40 years. A key part of the system includes the Geological Strength Index (GSI) chart, which was introduced by [PERSON] and [PERSON] in the 1990s and 2000s [3; 6]. In the early versions of their GSI chart, the degree of fracturing (or structure) in a rock mass needed to be matched to schematic caricatures of jointing and descriptors in a series of horizontal rows in the chart [3]. The observed surface condition of joints or fractures in the rock mass also needed to be matched to descriptors provided in vertical columns of their chart. The graphical chart has increasingly come under criticism [1; 2; 9; 10; 11; 12; 13; 14; 15; 16] because of the lack of scale on the vertical axis of the chart. Many researchers have attempted to quantify the vertical axis of the chart for this reason, but none of these approaches have gained traction in industry [1; 13; 14]. [PERSON] et al. [12] published a fully quantified chart using rock quality designation (RQD) [21] as a measure of fracturing on the vertical axis. This 2013 chart [12], too, has not gained widespread traction [1]. This is related to the well-known issues that RQD suffers from, i.e., scale and orientation bias, thus making it a less ideal parameter for inclusion in the chart [1; 2; 11; 13; 14; 15; 16]. The Hoek-Brown failure criterion may still be valid despite the limitations introduced with the use of RQD on the vertical axis of the 2013 chart [1]. If, for example, the dimensions of an excavation or slope on large projects in good quality rock are many times larger than the widely spaced joint sets, the Hoek-Brown failure criteria can still be applicable despite RQD being static at 100%, and therefore an insensitive scale or blockiness parameter [1; 2; 13; 14; 18]. Moreover, depending on the orientation of measurement of RQD, the results can be close to 100% in one direction but 0% in another direction for the same rock mass, even if the spacing of joints are within the sensitivity range of RQD (typically \(<\) 0.3 m) [1; 14; 18]. If scale and orientation biases related to RQD are not understood or considered, this can result in unreliable rock mass strength estimates if RQD alone is used in the 2013 chart. With the inclusion of the bias-free _VFC_ parameter in the V-GSI chart (Figure 1), this overcomes many of the issues related to the use of RQD described above. The _VFC_ parameter does not suffer from scale or orientation bias, and readers interested in more details are referred to [PERSON] et al.