# Estimating RQD for Rock Masses Based on a Comprehensive Approach
## 1 Introduction
[27] examined the fractal dimensions of discontinuity spacing measurements in a fractured rock mass and observed that the RQD tends to increase with a decrease in the fractal dimension for a given scanline length. [PERSON] et al. [28] used discontinuity parameters and a non-linear prediction model to derive the RQD. [PERSON] et al. [29] estimated the RQD distribution along the planned tunnel using the kriging method in geostatistics. [PERSON] et al. [30] comparatively studied the applicability of four common machine learning methods in predicting the RQD status along the entire tunnel route. Theoretical calculations of the RQD are able to provide the suggested RQD value in a timely and cost-effective way but suffer from several limitations. For instance, during formula derivation, it is assumed that the joints are parallel, which contradicts the actual joint distribution. Furthermore, prediction models are highly dependent on calculation data. As an example, when noise or extrema are present in the dataset, kriging results are easily affected, producing inaccurate estimates. Simulation modeling of the RQD utilizes stochastic simulation technology to model the fracture network due to the ease of obtaining RQD samples in given directions. Specifically, careful field mapping leads to the successful capture of the probability distribution of fracture geometry. Such probability distribution input allows the generation of random numbers for the space coordinates, orientations and radius using the Monte Carlo simulation method. With these random numbers, individual fractures are assembled, and the fracture network composed of individual fractures is then modeled. Virtual boreholes are placed in the model, and thus RQD samples may be obtained. The fracture network simulation, which accounts for a range of factors affecting the RQD, provides a realistic depiction of the rock mass state. The ability to select the placement, quantity and length of virtual boreholes renders this simulation technology a reference tool for studying the anisotropy and size effect of the RQD. [PERSON] et al. [31] researched the relationship between the RQD and the rockburst intensity of surrounding layered joints under varying inclination angles and spacing changes using simulation technology. Additionally, a discrete fracture network stochastic model was utilized by [PERSON] et al. [32] for a discrete element simulation study on the size effect of shale. Previously, [PERSON] et al. [27] analyzed the connection between fractal dimensions and the RQD using two-dimensional fracture network modeling technology. Also, based on this technology, [PERSON] et al. [33] investigated the anisotropy and size effect of the RQD. In recent years, the fracture network model has been extended from two dimensions to three dimensions. Several researchers [34; 35; 36] have investigated the spatial effect of the RQD in the model by varying the length and orientation of the virtual borehole. Compared to other techniques, fracture network simulation technology considers various influencing factors of the RQD as input parameters, reflecting the distribution of fractures within the rock mass in a reasonable way. Although the RQD has been widely used in rock classification systems such as RMR, Q, GSI and MRMR, it still exhibits limitations [37; 38]. For instance, traditional RQDs use 10 cm as a threshold, posing challenges in defining the jointing degree of a rock mass with extremely closely spaced joints or joints with wide to extremely wide spacing. The definition of RQD may vary across different countries or even deviate from its original approach. In certain classification systems like RMR and MRMR, estimating the RQD based on exposure introduces subjective bias, potentially leading to inaccuracies. In light of the research presented in this article, the following considerations warrant attention. First, the number of virtual boreholes is mostly determined intuitively, and this may yield differential RQD estimates.