Advances in Civil Engineering

Volume 2019, Article ID 1340549, 11 pages

https://doi.org/10.1155/2019/1340549

## Selection of Optimal Threshold of Generalised Rock Quality Designation Based on Modified Blockiness Index

^{1}College of Resources, Environment and Materials, Guangxi University, Nanning, Guangxi 530004, China^{2}State Key Laboratory of Geomechanics and Geotechnical Engineering, Institute of Rock and Soil Mechanics, Chinese Academy of Sciences, Wuhan 430071, China^{3}School of Resources and Safety Engineering, Central South University, Changsha 410083, China

Correspondence should be addressed to Qingfa Chen; nc.ude.uxg@fqnehc

Received 15 October 2018; Accepted 11 December 2018; Published 10 January 2019

Academic Editor: Jian Ji

Copyright © 2019 Qingfa Chen et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Rock quality designation (RQD) is a critical index for quantifying the degree of rock mass jointing; it is widely used for evaluating the qualities and stabilities of engineering rock masses. However, the use of traditional RQD may yield inaccurate assessments because only core pieces longer than 100 mm are counted. To enhance the utility of RQD, generalised RQD was introduced. Based on the modified blockiness index (MB_{i}), the determination of the optimal threshold of generalised RQD was performed. In this work, 35 types of hypothetical three-dimensional joint network models were constructed, and their generalised RQD values (with different thresholds) and MB_{i} values were measured. The correlation between the standard ratings of MB_{i} and RQD was assessed; based on this correlation, the theoretical RQD values of the 35 models were derived. The reasonable thresholds of the generalised RQD were determined according to the theoretical RQD values, and the optimal threshold of generalised RQD was obtained using the variation coefficient and anisotropy index of the jointing degree. The discrepancy between the results produced using traditional and generalised RQDs was discussed. Finally, an actual case study was conducted, and the results indicate that the generalised RQD associated with the optimal threshold determined in this study can properly quantify the degree of jointing of a given rock mass.

#### 1. Introduction

A rock mass is a natural substance that is composed of different compositions and complex structures produced by geologic processes. It varies with the evolution of the geological environment. Owing to the complicacy and invisibility of the rock mass structure, engineers cannot deeply understand the mechanical behaviour of jointed rock mass. Rock mass is separated into blocks because of the presence of joints; therefore, the mechanical properties and stabilities of engineering rock masses are deteriorated significantly [1].

Rock quality designation (RQD) [2] is a critical index to quantify the degree of jointing and is typically applied in various rock engineering worldwide, including hydraulic engineering, underground and surface mining, and rock tunnel; furthermore, RQD has been used for over 50 years. RQD is defined as a percentage of the drill core in lengths of 100 mm or greater. Although the RQD is routinely used in practices, this concept has several inherent limitations; for example, the RQD index only considers core pieces longer than 100 mm and may result in a final RQD value that does not agree with the practice [3].

To improve the utility of the RQD, some investigations were undertaken; for example, Sen and Elssa [4] proposed the concept of volumetric RQD and evaluated the correlations between RQDs with different thresholds, volumetric joint count (*J*_{v}), and block size; they outlined that the relations between the RQD values with different thresholds and the *J*_{v} values should be nonlinear, and such relations vary with the shapes of the blocks. Harrison [5] reported that, with an optimal threshold, the variation in RQD values in different directions is maximal; that is, the anisotropy of the rock mass structure is highlighted maximally; additionally, through theoretical derivation, he provided a determination equation of the optimal threshold in conjunction with the maximum and minimum joint frequencies. Xu et al. [6] investigated the correlation between the fractal dimensions of joints and RQD values based on the discrete fracture network (DFN) technique. They also reported that when the rock masses are sparsely jointed, the use of traditional RQD cannot sufficiently differentiate the rock mass structures; however, when the slopes of the curve (fractal dimensions vs. RQDs with different thresholds) attain a maximum value, the associated threshold can be deemed an optimal value. Zhang et al. [7, 8] developed a determination method of the optimal RQD threshold based on a three-dimensional joint network model and setting virtual scanlines; they also claimed that the variation in RQD values can be maximised with an optimal threshold.

The reviewed literatures reported that when the RQD values are accompanied by an optimal threshold in a given rock mass, the anisotropy of the rock mass structure can be fully reflected; that is, the difference between the maximum RQD value (RQD_{max}) and the minimum RQD value (RQD_{min}) is maximised. However, from the perspective of engineering practicability, the RQD values accompanied by an optimal threshold should exactly quantify the degree of jointing to lay the groundwork for the subsequent tasks, e.g., rock mass quality classification and rock mass stability assessment.

Recently, the modified blockiness index (MB_{i}) [9, 10] was developed as a three-dimensional measurement for the degree of rock mass jointing; using this index, the implications of blocks of different sizes on the rock mass jointing can be considered. However, the typical practice in rock engineering applications is to use RQD to quantify the degree of jointing; meanwhile, knowing the RQD value is crucial in many rock mass quality classifications and stability assessment systems, such as the rock mass rating system [11], Q-system [12], and Q_{slope}-system [13, 14]; furthermore, the associated empirical relation with the determination of support schemes has been well developed. Therefore, we do not attempt to replace the RQD with MB_{i} but to enhance the utility of RQD. In this study, referring to the MB_{i}, the determination of the optimal threshold of RQD was investigated based on the three-dimensional joint network modelling suggested by Zhang et al. [8], which can avoid the high uncertainty of the determination of RQD values. The goal of this study is to obtain an RQD value with the optimal threshold to quantify the degree of jointing more properly. Additionally, this work may provide an appropriate reference for determining a proper RQD value in other rock engineering projects.

#### 2. Modified Blockiness Index (MB_{i})

The block percentage (*B*) [9] is defined as the ratio of the volume of blocks fully enclosed by joints to the total rock mass volume, which ranges from 0 to 100%, and can be expressed aswhere is the volume of block *i*, is the number of blocks, and is the total rock mass volume.

When the block percentage is used to quantify the degree of jointing, the effect of block size may be ignored. To address this problem, Chen et al. [10] developed the MB_{i}, in which the rock blocks are grouped into five categories according to block volume: 0–0.008 m^{3}, 0.008–0.03 m^{3}, 0.03–0.2 m^{3}, 0.2–1.0 m^{3}, and >1.0 m^{3}, and the percentages of blocks in different categories are assigned different weights, i.e., the coefficients of rock block scale effect [15, 16]. The MB_{i} value can be calculated bywhere , , , , and are the block percentages of the volumes in the five intervals (0–0.008 m^{3}, 0.008–0.03 m^{3}, 0.03–0.2 m^{3}, 0.2–1.0 m^{3}, and >1.0 m^{3}, respectively). Apparently, with an increase in the degree of jointing, the value increases and the number of small blocks inside the rock mass increases, and vice versa. The calculation of is based entirely on the three-dimensional joint network model, and this kind of model can be created by probabilistic and/or deterministic joints.

In this study, the block percentages and MB_{i} values were determined using the GeneralBlock program [9], in the following steps: (1) construct a three-dimensional joint network model, (2) calculate the volumes of the rock blocks that are separated by joints, and (3) determine the block percentages and MB_{i} values based on Eqs. (1) and (2).

#### 3. Traditional and Generalised RQDs

##### 3.1. Traditional RQD

Traditional RQD was pioneered by Deere in 1967 [2] and is defined by a percentage of the drill core in lengths of 100 mm or greater. The RQD concept is widely used worldwide; however, it suffers from critiques [17, 18], including the following: (i) the RQD value is anisotropic and orientation dependent and (ii) the RQD concept only considers core pieces longer than 100 mm; that is, the block scale effect is ignored.

##### 3.2. Generalised RQD

The concept of generalised RQD (RQD_{t}) was introduced in [7, 8]. Using this concept, the threshold can be varied. Far less work has been performed on investigating RQD_{t}; however, the RQD_{t} is important in the investigation of the anisotropy of the rock mass structure; that is, a specified threshold can enhance the variation in RQD_{t} values. When the joint density is extremely high, the calculated RQD_{t} values in all directions are always close to 100% if the selected threshold is small; if the threshold is large, the RQD_{t} values will be approximately 0% regardless of the directions of the scanlines. The RQD_{t} value is influenced by the threshold *t*, and the core pieces should be counted if their lengths are equal to or greater than *t*. The RQD_{t} can be calculated bywhere is the length of the core piece longer than *t* and is the total length of the scanline. Given various *t* values, a series of values can be obtained and subsequently used to describe the degree of jointing.

According to the recommendation from Zhang et al. [8], a calculation model of RQD_{t} termed “Model A-A-S” was employed, which can be expressed as follows:where and are the lengths of the core pieces at the start and end of the scanline, respectively, and is the total length of the inner core pieces that is greater than the given threshold *t*.

#### 4. Development of 35 Three-Dimensional Joint Network Models and Their MB_{i} and RQD Values

##### 4.1. Establishment of the Hypothetical Three-Dimensional Joint Network Models

According to the standard classification of rock joints suggested by the International Society for Rock Mechanics [19], five representative joint persistence values and seven representative joint spacing values were selected, as shown in Table 1. Additionally, the Baecher disc model [20] was applied to create the joints; it can be generated by the following parameters: the centre coordinate (, , ), diameter *d*, dip direction *α*, and dip angle *β* (Figure 1). A Baecher disc model can be represented as follows:where = sin *α* sin *β*, = sin *α* cos *β*, and = cos *α*. Therefore, the normal vector of the disc joint **n** is (*A*, *B*, *C*).