###### Abstract  
This paper provides research that shows that the scale and quantification of the degree of fracturing in a rock mass should and can be considered when estimating geological strength index (GSI) ratings for rock mass strength and deformability estimates. In support of this notion, a brief review is provided to demonstrate why it is imperative that scale is considered when using GSI in engineering design. The impact of scale and scale effects on the engineering response of a rock mass typically requires a definition of fracture intensity relative to the volume or size of rock mass under consideration and the relative scale of the project being built. In this research three volume scales are considered: the volume of a structural domain, a representative elemental REV, and unit volume. A theoretical framework is established that links these three volume scales together, how they are estimated, and how they relate to parameters used to estimate engineering behaviour. Analysis of data from several examples and case histories for real rock masses is presented that compares and validates the use of a new and innovative but practical method (a sphere of unit volume) to estimate fracture intensity parameters VFC or P30 (\(\mathrm{fractures/m^{3}}\)) and P32 (\(\mathrm{fracture\ area}{\mathrm{area}}\)\(\mathrm{-m^{2}/m^{3}}\)) that is included on the vertical axis of the volumetric V-GSI chart. The research demonstrates that the unit volume approach to calculating VFC and P32 used in the V-GSI system compares well with other methods of estimating these two parameters (e.g., discrete fracture network (DFN) modelling). The research also demonstrates the reliability of the VFC-correlated rating scale included on the vertical axis of the V-GSI chart for use in estimating first-order strength and deformability estimates for rock masses. This quantification does not negate or detract from geological logic implicit in the original graphical GSI chart.  
2025158219920  
Recent publications by [PERSON] and [PERSON] (2022 [1], 2023 [2]) critique the quantification attempts of GSI, claiming that \"attempts to quantify GSI rely upon parameters that are themselves not a quantity, and therefore it is not possible to quantify them. As a result, there cannot exist a quantified GSI or quantified GSI chart.\" [1]. The authors also state \"there is no need to quantify the original GSI table... since there is no apparent advantage in terms of design analysis of using any of the proposed quantification methods\".  
The critique by [1,2] provided the impetus for additional research presented in this paper to show that the quantification of the degree of fracturing based on real measurements can and should be included on the vertical axis of the GSI chart.  
The first part of this paper provides a reminder that the validity of the use of the Hoek-Brown (H-B) equations and relationships and the use of GSI is scale- and failure mechanism-controlled. The following are briefly reviewed in this regard:  
* The historical development of scale effects in rock mechanics and why it is critical to the understanding of rock mass behaviour.
* The concept of a representative elementary volume (REV) and its relationship to the engineering behaviour of a given rock mass.
* Guidance provided in the literature that the use of GSI and the H-B strength criteria is scale- and failure mechanism-dependent.
* The development of quantified GSI charts with a focus on the volumetric GSI (V-GSI) chart proposed in [PERSON] and [PERSON] (2018) [3].
* The quantification of the vertical axis on the V-GSI chart using true joint spacing on the vertical axis.
* The limitations and challenges of quantifying the horizontal axis of the V-GSI chart.  
The second part of this paper presents research undertaken using data from three real rock engineering projects that provides validation that VFC (P30) and P32 parameters used in the V-GSI chart are based on measured data and the vertical axis is in fact quantifiable.