Analyzing Drill Core Logging Using Rock Quality Designation–60 Years’ Experience from Modifications to Applications

Abstract

The accurate analysis of rock cores is of primary importance for designing in and on the rock mass environment. There are several methods for analyzing boreholes, but the most accepted and widely used method is the rock quality designation (RQD) value, which has been a core rating metric for six decades. The RQD value serves as: (1) an important input parameter for rock mass classifications such as RMR and Q; (2) a basis for calculating the Geological Strength Index (GSI) of boreholes; and (3) a key indicator in assessing rock mass quality, particularly in highly fractured or weak rock masses. The original RQD method has several drawbacks and shortcomings, which have led to numerous proposed amendments. This review paper aims to: (1) summarize alternative methods of calculating the RQD value; (2) analyze the sensitivity of different rock mass classifications to the accuracy of this value; and (3) present a systematic analysis of the practical implications of modified RQD methods, emphasizing advancements such as DFN modeling, seismic RQD techniques, and machine learning-based approaches. The findings provide a comprehensive framework for more robust and versatile assessments of rock mass quality.

1. Introduction

Core recovery is a critical metric in geotechnical engineering and geological explorations, quantifying the proportion of a drilled rock column retrieved as intact core during drilling operations. Expressed as a percentage, it serves as an indicator of the rock mass’s quality and the effectiveness of the drilling process. The formula for calculating core recovery is as follows:

$$\mathrm{C}\mathrm{R}={\displaystyle \frac{\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}\mathrm{ }\mathrm{l}\mathrm{e}\mathrm{n}\mathrm{g}\mathrm{t}\mathrm{h}\mathrm{ }\mathrm{o}\mathrm{f}\mathrm{ }\mathrm{c}\mathrm{o}\mathrm{r}\mathrm{e}\mathrm{ }\mathrm{r}\mathrm{e}\mathrm{c}\mathrm{o}\mathrm{v}\mathrm{e}\mathrm{r}\mathrm{e}\mathrm{d}}{\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}\mathrm{ }\mathrm{l}\mathrm{e}\mathrm{n}\mathrm{g}\mathrm{t}\mathrm{h}\mathrm{ }\mathrm{o}\mathrm{f}\mathrm{ }\mathrm{c}\mathrm{o}\mathrm{r}\mathrm{e}\mathrm{ }\mathrm{r}\mathrm{u}\mathrm{n}}}100\left[\mathrm{\%}\right]$$

(1)

The quality of the rock’s ability to endure the coring procedure and drilling fluid flushing, as well as the weathering and disintegration of the rock, can all be inferred from core recovery.

When no core is recovered due to cavities or core losses, an interval of zero as the core length shall be recorded. In this instance, it is essential to enter the type of core loss in the “Cavity or Core Loss” field as listed in

Table 1. Cavity or core loss.

Lookup	Cavity or Core Loss
CAV	Cavity
CL	Core Loss

.

It can be seen that the CR value is important for the analysis of the drill core, but it does not give information about its jointing; thus, it cannot be used for rock engineering design.

Rock quality designation (RQD) is a quantitative measure introduced over six decades ago by Deere to assess rock mass quality for geological engineering and rock engineering analyses [1,2]. It is defined as the percentage of intact drill core pieces longer than 10 cm (4 inches) recovered during a single core run. The RQD value is calculated using the following formula:

$$\mathrm{R}\mathrm{Q}\mathrm{D}={\displaystyle \frac{\mathsf{\Sigma }{\mathrm{h}}_{10}}{{\mathrm{h}}_{\mathrm{b}}-{\mathrm{h}}_{\mathrm{a}}}}100\left[\mathrm{\%}\right],$$

(2)

where Σh₁₀ is the total length of the pieces longer than 10 cm, and h_b and h_a are the upper and the lower depths of the depth intervals.

The core should be at least 54.7 mm in diameter and drilled with a double-tube barrel [3]. RQD is expressed as a percentage and is a measure of the quality of the rock mass within a borehole. RQD is widely used in core logging since it is simple and quick to measure. It is frequently the sole technique available for determining the jointing density along the core drill hole. Moreover, Bieniawski’s Rock Mass Rating (RMR) and the Q-system developed by Barton et al.—two of the most popular approaches for classifying rocks—use it as raw data [4,5,6]. It is also applicable to the calculation of the borehole’s Geological Strength Index (GSI), where the block of rock mass is considered to be half of the RQD value [7].

Deere states that fresh fractures that obviously happened during drilling should also be disregarded. In boreholes where jointing surfaces are parallel to the borehole axis, these joints may not intersect the core, leading to an overestimation of rock quality if not properly accounted for. Deere’s guidelines suggest that such boreholes should be considered intact, as the parallel joints do not disrupt the core samples [8,9]. In scenarios involving highly fractured or weak rock masses, obtaining accurate RQD values can be challenging due to poor core recovery and the presence of numerous discontinuities. Despite these challenges, RQD remains a valuable indicator of rock mass quality. It provides a realistic picture even in cases of poor core conditions caused by a very high fracture intensity or weak rock. Based on his proposal, the possibility of calculation is illustrated by an example using Figure 1. The example of a very poor and excellent borehole from Mórágy Granite Formation (Hungary) is presented in Figure 2.

Real observations serve as the foundation for the relationship between the RQD value and the rock test classes and are displayed in

Table 2. Using EUROCODE 7-1 classification of rock types and rock mechanical designations [10].

RQD %	Rock Mass Classification	Description
<25	Very poor	Disintegrated/soil
25–50	Poor	Shattered, very blocky
50–75	Fair	Blocky and seamy
75–90	Good	Massive, slightly blocky
90–100	Excellent	Intact

. The categorization provided in EUROCODE 7-1 [10] is comparable to this table.

The quality of the rock mass in situ should to be represented by RQD. As such, all efforts shall be made to minimize sample disturbance. Ideally, RQD should be logged in the splits prior to boxing or transportation. The following are important notes on the measurement of RQD length:

• RQD length is only measured in core samples that are deemed competent and have a Field Estimated Strength (FES) of at least 1 MPa (R1).
• In core samples with an FES less than 1 MPa, the RQD length should be logged as 0, i.e., RQD = 0%.
• Even if they are longer than 100 mm, core pieces that are not “inherently intact and sound” will not be included in the RQD length computation.
• Any highly or extremely weathered intervals and/or extremely weak intervals shall be given an RQD length equal to zero.
• Fractures parallel to the core axis or that can be attributed to handling breaks, shall be ignored when measuring for RQD length. Similar to Recovery Length, the percentage should be computed immediately rather than later, ensuring any evident calculation errors can be quickly identified and resolved (e.g., an RQD of greater than 100%).

Recent advancements in geotechnical testing, computational modeling, and automated data analysis provide opportunities to address these limitations. Modified RQD methods, such as those incorporating weighted joint density (RQD_wjd), weak zone adjustments (MRQD), and discrete fracture network (DFN) modeling, have been proposed to enhance the reliability of RQD. However, these developments remain underexplored in terms of their practical application and integration with traditional geotechnical workflows. Furthermore, there is a lack of systematic evaluation of these methods in real-world scenarios, particularly in addressing complex geological conditions like fractured, anisotropic, or weak rock masses.

This study bridges these gaps by presenting a comprehensive review of RQD’s evolution, from its original formulation to contemporary modifications, and evaluates their applicability in modern geotechnical practices. The novelty of this research lies in its systematic analysis of modified RQD methods, emphasizing their practical implications for drilling, design, and production. By integrating recent advancements such as DFN modeling, seismic RQD techniques, and machine learning-based approaches, this paper provides a framework for more robust and versatile assessments of rock mass quality.

2. Intervals

For a geotechnical log, intervals should relate to the geotechnical properties of the core rather than simply the start and end of a core run or a lithological interval. The same principle applies to face mapping. Sometimes, a significant geotechnical boundary may be present within a core run or along the slope face and should be included as a separate interval, as illustrated in Figure 3.

The top of the interval is recorded in meters to two decimal places in the “From (m)” field as a down–hole depth from the collar when drill core logging or along a traverse from the starting point when face mapping. Similarly, the bottom of the interval is recorded in the “To (m)” field.

The “Interval Length (m)” is calculated from the data captured in the “From (m)” and “To (m)” fields (i.e., Interval Length is equal to To minus From). The core run or traverse map interval should be no greater than perhaps 3000 mm (3 m) to provide a statistically admissible dataset. Each interval should also be at least 100 mm (0.1 m) in length.

The majority of the core logging is carried out by monitoring the joints at every meter of the core. As seen in Figure 4 and Figure 5, this kind of logging quickly generates measurement inaccuracies if there are alternating portions with lower and higher densities of joints [11]. The variance in jointing along the core is equalized by the measurement of joint density per meter, as

Table 3. Measured RQD values using different sections [11].

Measurement in sections
Section	Length (m)	Core Pieces 10 cm	RQD (%)
1	1.3	0.94	73
2	0.6	0.2	34
3	1.75	1.3	75
4	1	0.95	95
Measurement every meter
Section	Length (m)	Core pieces 10 cm	RQD (%)
439–440	1.0	0.64	64
440–441	1.0	0.30	30
441–442	1.0	0.70	70
442–443	1.0	0.80	80
443–444	1.0	0.95	95

and Figure 5 demonstrate.

It is important to note that the three-dimensional spatial fractures of the rock mass are not taken into consideration by the one-dimensional rock quality designation (RQD) derived from the cores.

3. Limitations of RQD

A rigorous rule in the first interpretation stipulates that a core’s minimum length for inclusion is 10 cm. Despite its apparent simplicity, RQD is greatly impacted by the relative direction of the borehole (or scanline) with respect to the orientation of the fractures. An in-depth analysis of the RQD factor’s limits was provided by Palmström [11,12], who also discussed the original definition’s contradictions and orientation dependency. This also implies that the anisotropy of the rock mass cannot be completely reflected by the conventional method of establishing a rock quality designation (RQD), which makes it inaccurate in reflecting the quality of the rock [13,14].

Figure 5 shows the measurement results of Palmström [11], which illustrate the potential errors of using RQD. There can be a significant difference between RQD = 0% and RQD = 100% within a drilling section, even with slight variations in joint spacing. For example, RQD = 0% may occur not only when the core is entirely fractured but also when the intact core lengths are just below 10 cm. Conversely, RQD = 100% can also result with subtle changes in spacing, as seen when all core sections are over 10 cm long. These small changes can lead to drastically different RQD values, emphasizing the sensitivity of joint spacing on RQD calculations. Figure 6 demonstrates that in rare cases (in the real world), subtle changes in discontinuity spacing can greatly affect RQD (i.e., from 0% to 100%) when uniformly distributed at approximately 10 cm.

Another drawback of RQD is that it provides no information regarding the quality of new rock fragments shorter than 10 cm in length or core bits resembling soil-like materials.

RQD’s simple measurement technique has certain inherent limitations and only offers a partial evaluation of the quality of the rock mass. Deere [9] states that the RQD calculation should take into account the real drilling-run length based on field measurements, whereas the core length in a laboratory is usually restricted to 1.5 m. This approach can be used as a reference for quantifying RQD within a specific range, leading to a more accurate prediction of rock mass characteristics in engineering projects. According to Milne et al. [15], it is not possible to fully capture the true quality of a rock mass using the original definition of RQD. As such, in real-world applications, a high RQD value does not always translate into a high-quality rock mass.

Since RQD is a directionally dependent metric, the orientation of the borehole can have a big impact on its value. By way of example, Figure 7 illustrates the dependence on directionality of RQD for an anisotropic rock mass. The RQD values found in drill hole A is likely to be significantly lower than that of drill hole B. The density of the joints along the drill core may be significantly impacted by the angle formed by the bore hole and the primary joint set.

The accuracy of RQD values can be influenced by the expertise of the engineer responsible for logging the core. The engineer’s ability to correctly identify and differentiate between natural fractures and those caused by drilling processes plays a crucial role in determining the RQD. Misidentifying these fractures can lead to inaccuracies in rock mass classification. Additionally, RQD does not account for critical factors like incipient fractures—small cracks that may not be fully developed—and veins, which can significantly affect the overall strength and integrity of the rock mass. RQD may provide an inaccurate or overly optimistic evaluation of rock mass quality by ignoring these factors, which could have an effect on engineering project design and safety [16].

Despite their striking similarities, RMR₈₉ outperformed RMR13 in terms of the actual case studies evaluated for different investigations. Over the past 40–50 years, RMR⁸⁹ and RQD have both undergone time testing. As a result, RMR₈₉ and RQD should be used with confidence going forward. RMR13 has unquestionable application potential, but more time and outcomes are required before it can be widely adopted and used. In conclusion, RMR₈₉ should not be considered a method of the past, and the implementation of RMR13 is not an excuse to phase it out. [17].

4. Suggested Modifications of RQD

Because of the disadvantages and limitations of determining the RQD value described above, a number of suggestions have been made to modify (clarify) the value of this factor. Most of these modifications focus on the description of the weak (disturbed) zone.

4.1. Rock Quality Designation from Weighted Joint Density (RQD_WJD)

To obtain more accurate information from observations of boreholes, Palmström [18] created the weighted joint density (WJD). Its main method relies on calculating the angle (δ) formed between each joint and the scan line at the drill hole’s surface or axis. This is shown in Figure 8:

$$\mathrm{W}\mathrm{J}\mathrm{D}={\displaystyle \frac{1}{\mathrm{L}}}\sum {\displaystyle \frac{1}{\mathrm{s}\mathrm{i}\mathrm{n}\mathsf{\delta }}}$$

(3)

In accordance with Palmström [12], the δ angles can be divided into four intervals, with each group having an average value of fi (see

Table 4. Rating factor f_i in each interval to calculate WJD value [12].

Angle Interval (Between Joint and Borehole)	1/sinδ	Chosen Rating of Factor fi
>60°	<1.16	1
30–60°	1.16–1.99	1.5
15–30°	2–3.86	3.5
<15°	>3.86	6

). Thus, the following is a rewriting of the equation above:

$$\mathrm{WJD}={\displaystyle \frac{1}{\mathrm{L}}}\sum f_i,$$

(4)

The RQD value can be calculated from the WJD value [18]:

RQD_wjd = 110–2.5 WJD,

(5)

Palmström [12] examined the traditional RQD, WJD, and RQD_WJD measures for two boreholes drilled in the same jointing area but in different directions (refer to Figure 9). The RQD numbers (90 and 9%) were obtained differently, whereas the WJD values (16 and 19) were roughly comparable, as shown in this Figure.

Using Equation (5) to calculate the RQD_WJD from the weight joint density, values of 70 and 62% were found. Comparing the RQD and the RQD_WJD values one can realize that the RQD_WJD values are reasonably close and situated in the fair rock mass RQD classification. As a result, the rock mass fracturing degree is better described by the weighted joint density technique, which accounts for inaccuracies resulting from the threshold value and coring direction.

4.2. Modification of Rock Quality Designation with Weighted Joint Density (RQD_M-wjd)

Haftani et al. [19] analyzed the limitations of the RQD_wjd value. RQD_WJD is not advised in situations where fractured zones are present, but their computation and empirical findings demonstrate that it can rationally overcome some of the original RQD’s drawbacks. Focusing on the fracture zone, they introduced the following modification of RQD_wjd:

$${\mathrm{R}\mathrm{Q}\mathrm{D}}_{\mathrm{M}-\mathrm{w}\mathrm{j}\mathrm{d}}={\mathrm{R}\mathrm{Q}\mathrm{D}}_{\mathrm{w}\mathrm{j}\mathrm{d}}\mathrm{x}\left[{\displaystyle \frac{{\mathrm{L}}_{\mathrm{t}}-{\mathrm{L}}_{\mathrm{F}\mathrm{Z}}}{{\mathrm{L}}_{\mathrm{t}}}}\right],$$

(6)

where

-

L_t is the total length of the core run;

-

L_FZ is the length of the fracture zone.

4.3. Modified Rock Quality Designation (MRQD)

The modified RQD, or MRQD, parameter was proposed by Haftani et al. [19]. Deducting the weak zone parameter (WZ) from the value 100 yields this parameter.

MRQD = 100–WZ,

(7)

where the weak zones (WZ) are defined as

$$\mathrm{W}\mathrm{Z}={\displaystyle \frac{1.5 nd+CW+Fr+Cr+VZ+C}{L_t}},$$

(8)

where

-

nd is the number of discontinuities

-

CW is the washed core portion length

-

Fr is the fragmented core portion length (with spacing < 15–50 mm)

-

Cr is the crushed core portion length (with spacing = 5–15 mm)

-

VZ is the vuggy core portion length

-

C is the void core portion length

-

Lt is the total core run length

The five classifications that the MRQD approach, which was established based on weak zones, divides rock masses into are displayed in

Table 5. Rock mass classification according to MRQD and weak zone [20].

MRQD (%)	Rock Mass Description	Rock Mass Quality	Class Number	Weak Segment (%)
90–100	Massive rock mass	Excellent	I	0–10
75–90	Jointed rock mass	Good	II	10–25
50–75	Jointed–fragmented rock mass	Fair	III	25–50
25–50	Fragmented–crushed rock mass	poor	IV	50–75
≤25	Crushed rock mass	Very poor	V	≥75

.

4.4. Corrected Rock Quality Designation (RQDc)

In their conclusion, Li et al. [21] found that the quantity, N, of unbroken pieces as well as their cumulative length determined the quality of a rock mass. Accordingly, the designation is written as

$${\mathrm{R}\mathrm{Q}\mathrm{D}}_c={\displaystyle \frac{p_r}{N^a}},$$

(9)

where

-

p_r is the percentage of core recovery, or SCR (Solid Core Recovery), i.e.,

$${\mathrm{p}}_r={\displaystyle \frac{{\sum _{i=1}^{N}L}_i}{\mathrm{L}}},$$

(10)

In this equation, L_i is the length of the unbroken piece, and L is the journey or run length (also known as scanline length) [21].

-

N is the number of unbroken core pieces in a core run, and

-

a is the exponent of a power law function.

The fluctuation of RQD_c with parameter a ranging from 0 to 1.0 in the normal (a) and log–log (b) planes is shown in Figure 10, according to [21].

In the latter scenario, RQD_C’s variant with N pieces becomes a straight line with a slope of a. Clearly, if parameter a = 0 (or f(N) = 1), RQD_c remains constant, much like the RQD, which is independent of the number of unbroken pieces. RQD_c and RQD differ in another way as well. While the latter only takes into account segments longer than 10 cm, the former takes into account the entire length of all intact parts (p_r), which is comparable to the recovered rate typically employed by geological engineers [21].

4.5. Improved Rock Quality Designation (RQD_l)

Azimian [22] highlighted the issues with piece length and discontinuity orientation, which have no bearing on the results, and proposed a new approach called RQD_I, which provides a more accurate and dependable estimate of rock quality. However, RQD_I requires much more core logging work and time in order to obtain more precise results. An improved rock quality designation (RQDI) was proposed by Azimian [22] in order to lessen the drawbacks of the traditional approach. The expression for RQDI is as follows:

$${\mathrm{R}\mathrm{Q}\mathrm{D}}_I=100-\left[{\displaystyle \frac{f_i+CW+Fr+Cr+K}{total core run length}}x100\right]$$

(11)

where

-

f_i is the rating factor obtained from

Table 6. Angle intervals and ratings of the factor for each interval.

Angle Interval (Between Joint and Borehole) δ	1/sinδ	Chosen Rating of Factor fi for RQDl [20]
>60°	<1.16	1.5
30–60°	1.16–1.99	3.5
15–30°	2–3.86	5.5
<15°	>3.86	7.5

;

-

CW is the length of the washed core segments;

-

Fr is the length of the fragmented segments, cm (with spacing of 15–50 mm);

-

Cr is the length of the crushed segments, cm (with spacing of  <15 mm); and

-

K is the length of the karstic segments, cm. (i.e., karstic zone including vuggy; cavity, core lost, and other karstic phenomena).

According to the suggestion of Azimian [22], the RQD_I classification of rock masses is presented in

Table 7. Classification of rock masses based on weak segment and RQD_l [22].

RQDI (%)	Rock Mass Description	Rock Mass Quality	Class Number	Weak Segment (%)
91–100	Massive rock mass	Excellent	I	0–10
76–90	Jointed rock mass	Very good	II	11–25
61–75	Very jointed rock mass	Good	III	26–40
46–60	Very jointed–fragmented rock mass	Medium	IV	41–55
31–45	Fragmented–crushed rock mass	Weak	V	56–70
≤30	Crushed rock mass	Very weak	VI	≥71

.

Azimian [22] outlined the benefits of the revised RQD_I over the original RQD. First, in the case of two cores broken into segments longer than 10 cm, the original RQD assigns a value of 100% regardless of the segment length or joint orientation. In contrast, RQD_I provides different values by considering factors such as segment length, joint orientation, washed core length, and karstic, broken, or crushed sections. A more fractured core is indicated by a lower RQDI. Second, RQDI separates cores depending on the previously indicated variables, whereas the original RQD would provide a value of 0% for cores divided into segments smaller than 10 cm.

4.6. “n” Rock Quality Designation (RQD_n)

Recently, Somodi and Vásárhelyi [23] suggested introducing the RQD_n value, which can be calculated similarly to RQD, but n depends on the investigated core–length:

$${\mathrm{R}\mathrm{Q}\mathrm{D}}_{\mathrm{n}}={\displaystyle \frac{\mathsf{\Sigma }{\mathrm{h}}_{\mathrm{n}}}{{\mathrm{h}}_{\mathrm{b}}-{\mathrm{h}}_{\mathrm{a}}}}100\left[\mathrm{\%}\right],$$

(12)

where h_b and h_a represent the upper and lower depths of the depth intervals, and Σh_n represent the total length of pieces longer than n cm.

Even though you can choose any value for n in this equation, they advised measuring the total length of 10, 20, 30, … 100 cm pieces of core, using 5 cm pieces for engineering purposes. Figure 10 shows an example where the RQD_n values are plotted as a function of n (cm). According to their analysis, the shape of the curves depends on the rock quality. They also suggested introducing the RQD^10% value, which gives the core length corresponding to the 10% value (see Figure 11). Davarpanah et al. [24] introduced the coefficient of uniformity and the coefficient of uniformity of the borehole based on this RQD_n value.

4.7. RQD Derived from Discrete Fracture Network (DFN) Modeling

Discrete fracture networks (DFNs) are synthetic stochastic models used to represent naturally fractured rock masses. Data from multiple sources, including 2D rock exposures and 1D boreholes, are used to build these models. Relatively undisturbed rock core samples from high-quality drill coring provide information about subsurface conditions. Nonetheless, there is a special benefit to observations made from exposed rock faces at or close to the project site. They make it possible to quantify important fracture parameters directly, such as fracture length, spacing, and discontinuity orientation—all of which are essential for precise modeling and analysis.

A strong quantitative classification system that incorporates the discrete fracture network (DFN) approach was presented by Elmo et al. [25]. This method significantly enhances the ability to account for the complex scale and anisotropic effects present in rock masses. By leveraging DFNs, the system provides a more comprehensive understanding of fracture patterns, improving the accuracy of modeling the connectivity within natural fracture networks. This leads to a better reflection of the real behavior of fractured rock masses in engineering and geological applications, offering improved predictions for stability and performance.

Generating a discrete fracture network (DFN) model typically involves defining four key fracture properties (as outlined in

Table 8. Fracture data and input parameters for a DFN model are obtained from both digitally mapped and traditionally collected data sources [26].

Fracture Data	Source	DFN Input Data
Orientation	Boreholes, outcrops, tunnels	Orientation of fractures for every fracture set
Length	Tunnels, outcrops, lineaments	Fracture radius distribution
Terminations	Tunnels, outcrops, lineaments	Choice of the model hierarchy of the sets
Intensity	Boreholes, scanlines (P10), outcrops (P21)	Fracture intensity (P10 or P32)

). For a comprehensive explanation of the methodology used to create calibrated DFN models, readers are encouraged to consult the detailed work by [26].

Using the parameters outlined in Table 8, a conceptual rock mass model was created to represent a homogeneous geotechnical domain, free of faults and shear zones. An example of the DFN model is depicted in Figure 12. Also, in this method, the cubic model, with dimensions of 30 m in height, length, and width, includes three orthogonal boreholes centered within the model to condition fractures to a specified P₁₀ value [26].

A novel approach to quantitatively ascertain the ideal threshold for the quantity of virtual boreholes and models in rock mass characterization was put out by Wang et al. [26]. Their strategy combines class ratio analysis with the Confidence Neutrosophic Number Cubic Value (CNNCV) method. By defining this threshold, their method effectively produced a representative rock quality designation (RQD) for a given model size. Additionally, recognizing the influence of model size on RQD simulations, they established the proper model size barrier by introducing a strategy based on class ratio analysis. Afterward, the representative RQD for the whole rock mass was considered to be the one that corresponded to this threshold.

5. Correlation Between Fracture Frequency (λ) and RQD

The discontinuity frequency, or fracture frequency (FF), is defined as the number of natural fractures per unit length of core recovered (it is equivalent to the Fracture Index–FI, or discontinuity frequency—λ):

$$\mathsf{\lambda }=\mathrm{FF}={\displaystyle \frac{\mathrm{n}\mathrm{u}\mathrm{m}\mathrm{b}\mathrm{e}\mathrm{r}\mathrm{ }\mathrm{o}\mathrm{f}\mathrm{ }\mathrm{n}\mathrm{a}\mathrm{t}\mathrm{u}\mathrm{r}\mathrm{a}\mathrm{l}\mathrm{ }\mathrm{f}\mathrm{r}\mathrm{e}\mathrm{c}\mathrm{t}\mathrm{u}\mathrm{r}\mathrm{e}\mathrm{s}}{\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}\mathrm{ }\mathrm{l}\mathrm{e}\mathrm{n}\mathrm{g}\mathrm{t}\mathrm{h}\mathrm{ }\mathrm{o}\mathrm{f}\mathrm{ }\mathrm{c}\mathrm{o}\mathrm{r}\mathrm{e}\mathrm{ }\mathrm{r}\mathrm{e}\mathrm{c}\mathrm{o}\mathrm{v}\mathrm{e}\mathrm{r}\mathrm{e}\mathrm{d}}}$$

(13)

One can find the fracture frequency for a core run’s whole length or for a smaller core segment. When determining the fracture frequency, artificial fractures produced during core handling or drilling should be disregarded, much like in RQD.

The discontinuity frequency that is acquired through scanline sampling can also be used to calculate RQD. An exponential distribution with a negative value was proposed by Priest and Hudson [27]. Their calculation shows that there is the following link between RQD and a linear discontinuity frequency, λ:

RQD* = 100e^−λt(λt + 1),

(14)

where t is the length barrier in this case. As with the conventionally defined RQD, Equation (14) can be written as follows for t = 0.1 m [27]:

RQD* = 100e^−0.1λ(0.1λ + 1),

(15)

For values of λ in the range of 6–16 m⁻¹, the following linear equation can be used:

RQD* = 110.4 − 3.68λ

(16)

Figure 13 displays the relationships found by [27] between the observed values of RQD and λ and the values determined by Equation (15).

Based on Equation (14) and several threshold values t, the theoretical RQD* curves against values of λ (0–50) are depicted in Figure 14. The image demonstrates the shortcomings of both the threshold value concept and the RQD* additive technique. As a function of k, the RQD’s decline becomes steeper the bigger the threshold value t, as indicated by the curves. The reason for this is the disrespect for smaller core parts. Nonetheless, the RQD* decline becomes flatter as the threshold value drops. This is due to the fact that all shorter cores are now considered, despite the fact that their quantity, and thus the number of fractures, are not. One could argue that these drawbacks are offset by choosing a threshold value that falls somewhere in the middle, such as 0.1 m, or by choosing a threshold value that is acceptable for a particular rock mass [29].

Theoretically, RQD and λ have a loosely linear connection; [27] proved that RQD tends to drop with an increase in λ in a roughly narrow diagonal band. Russo and Hormazabal [30] verified this by gathering more than 30,000 data points from several rock masses (Figure 15).

The correlation between RQD and the volumetric discontinuity frequency, λ_v, which Palmström introduced, can also be used to determine the RQD [31]:

RQD* = 115 − 3.3λ_v

(17)

For each discontinuity set, the volumetric discontinuity frequency λ_v is the total number of discontinuities per unit length, which may be calculated from the spacing between discontinuity sets in a volume of rock mass, as suggested by [31].

$${\mathsf{\lambda }}_{\mathrm{v}}={\displaystyle \frac{1}{{\mathrm{s}}_1}}+{\displaystyle \frac{1}{{\mathrm{s}}_2}}+{\displaystyle \frac{1}{{\mathrm{s}}_3}}+\cdots +{\displaystyle \frac{N_r}{5}},$$

(18)

where Nr is the number of random discontinuities and s1, s2, and s3 are the mean discontinuity set spacings. One effective method for reducing the directional dependence of RQD is to estimate RQD using the volumetric discontinuity frequency, λ_v.

6. Integral Geometric Method

Beyer and Rolofs [32] developed the integral–geometric method to assess the quantity of joints based on ideas from probability theory. The unit area of discontinuities is used in the following process to characterize the rock mass under study: the area of the discontinuities per rock mass cubic meter (t).

$$\mathrm{t}={\displaystyle \frac{\sum A_{Ti}}{\mathrm{V}}[{\mathrm{m}}^2\mathrm{/}{\mathrm{m}}^3], \left[{\mathrm{m}}^{-1}\right]}$$

(19)

where V is the volume under examination and A_Ti is the area of the rock mass’s i-th discontinuity.

It was demonstrated using the integral–geometric approach that in the case of boreholes (see Figure 16), this ratio can be found using the following equation:

$$\mathrm{t}={\displaystyle \frac{2N_i}{{\mathrm{h}}_b-{\mathrm{h}}_a}} [{\mathrm{m}}^{-1}]$$

(20)

where N_i represents the number of joints along the examined distance (the borehole’s depth from h_a to h_b).

Vásárhelyi and Bögöly [33] proposed that when the quality of the rock mass is low (RQD < 50%), the RQD and the value of the unit area of joints have the following empirical relationship:

RQD = −10 ln(t) + 70

(21)

7. Hansági’s Method for Analyzing Core Logging

The diameter restriction in RQD calculations was removed by Hansági [34] with the development of the C technique. You can use any diameter with the C factor. Following his measurements in Kiruna (Sweden), Hansági [35] reported his findings.

The arithmetic mean of two parameters, the Cp sample factor and the Cm core length factor, is taken to determine the value of the computed fissuring factor (C).

$$\mathrm{C}={\displaystyle \frac{\mathrm{C}\mathrm{p}+\mathrm{C}\mathrm{m}}{2}},$$

(22)

The Cp factor is similar to the RQD factor. It indicates how many samples are visible inside the intact core pieces or how many times the entire diameter of the core fits along the length of the piece. The length of the section being examined is divided by the product of the actual diameter and the number of samples that can be obtained to determine the sample factor.

$$\mathrm{Cp}={\displaystyle \frac{pD}{{\mathrm{h}}_b-{\mathrm{h}}_a}},$$

(23)

Cm is calculated using the average lengths of the unbroken pieces of the core under investigation. It is important to measure each component precisely when calculating the core length factor. We are unable to determine the aperture or the areas with significant fractures by merely dividing the entire length by the number of fractures.

$$\mathrm{Cm}={\displaystyle \frac{\overline{\mathrm{m}}}{{\mathrm{h}}_b-{\mathrm{h}}_a}}$$

(24)

where:

$$\overline{\mathrm{m}}={\displaystyle \frac{\sum _{i=1}^n{m}_i}{n}}={\displaystyle \frac{M}{n}}$$

(25)

Cm is substantially smaller than Cp because it is the ratio of the total length to the average length. It illustrates the joints of the rock bulk in this way. For instance, if the core is composed of entire segments around a diameter long, Cp may be artificially elevated. In this instance, Cm will be substantially smaller in order to adjust Kiruna’s ultimate value. Using Formulas (22)–(24), one can determine the value of the fissuring factor (C).

$$\mathrm{Cm}={\displaystyle \frac{1}{2\left({\mathrm{h}}_b-{\mathrm{h}}_a\right)}}\left(pD+{\displaystyle \frac{M}{n}}\right)$$

(26)

When calculating C, it is crucial to divide the core into pieces with comparable rock mechanical properties in order to obtain a clear view of each important component of the rock itself. It is also possible to acquire values for the fault zones and the block states.

Kiruna’s value can range from 0 to 1. When the unbroken portions are smaller than the core’s diameter, C = 0. Rarely does C = 1 occur; it can only occur when the rock is solid and free of discontinuities. In this instance, it is difficult to distinguish between the rock mass and the block of rock since the core emerges in a single, long piece. Based on practical experience, a stratification system based on the C factor can also be used. According to Hansági [35], the C factor and RQD factor approaches are contrasted in the classification that follows (

Table 9. Classification of the core according to Hansági’s C factor [35].

RQD %	C Factor	Description
>25	0.00–0.15	Very poor
25–50	0.15–0.30	Poor
50–75	0.30–0.45	Fair
75–90	0.45–0.65	Good
90–100	0.65–1.00	Excellent

).

Vásárhelyi et al. [36] compared the suggested method of Hansági’s C with the RQD method analyzing the core loggings of the Radioactive Waste Repository of Bataapáti, Hungary. They found the following relationship between the two values (see Figure 17):

• The linear approximation of the upper curve is the most accurate:

  RQD = 222 C

  (27)
• The logarithmic equation can be used to describe the lower enclosing curve:

  RQD = 65.28 ln (C) + 98

  (28)

We can observe from the curved lines that there are significant differences between the two approaches at extreme values. Kiruna’s value (C) fluctuates between 0 and 0.22 at RQD = 0% and between 1 and 0.62 when RQD = 100%. The most jointed parts and the parts that the RQD method assumes are intact have this type of Kiruna variance. RQD falls between 0% and 10% or between 90% and 100% in these situations. It is impossible to establish a relationship due to the wide dispersion. Only the values between RQD 10% and 90% were examined in order to obtain a more accurate relationship. As a result, Figure 18 shows a linear relationship between the two approaches.

RQD = 175.75 C + 2 (%)

(29)

More accurately than RQD, C displays the joint’s presence even in the inspected area. This is due to the fact that it accounts for the average lengths of the unbroken core pieces using Cm.

8. Seismic RQD

Traditional RQD calculations are sensitive to the borehole orientation relative to fracture orientation, which can lead to significant overestimations or underestimations of rock quality. Seismic methods overcome this limitation by capturing the effects of fractures and anisotropy over a broader spatial scale, thus providing a more holistic representation of rock mass quality. In highly fractured or weak rock masses, traditional core recovery is often insufficient to obtain reliable RQD values. Seismic methods, by contrast, are unaffected by physical core recovery and can detect discontinuities and weak zones indirectly through their impact on wave velocities. Moreover, traditional RQD measurements are limited to specific borehole locations, offering no information about the continuity of rock mass properties between sampling points. Seismic surveys provide continuous profiles, capturing variations in rock quality over large areas and enabling a more comprehensive understanding of subsurface conditions.

Seismic techniques to estimate RQD over larger areas involve analyzing seismic wave velocities, particularly P-wave velocities, which are influenced by the density and elasticity of the rock mass. Fractures and joints within the rock can slow down seismic waves; thus, by measuring these velocities, it is possible to infer rock quality.

Seismic methods allow for the evaluation of rock quality without the need for extensive drilling, reducing environmental impact and cost. Also, seismic surveys can cover large areas, offering continuous data that help identify variations in rock quality between boreholes.

However, seismic data may not detect very small fractures, potentially leading to an overestimation of rock quality. Moreover, the relationship between seismic velocities and RQD can be influenced by factors such as rock type, saturation, and stress conditions, necessitating careful analysis.

Recent studies have explored the use of cooperative inversion techniques, combining seismic reflection data with borehole information to build more accurate 3D RQD models. This approach enhances the reliability of RQD estimations, particularly in complex geological settings [37]. Additionally, advancements in seismic data acquisition and processing have improved the detection of fractures and discontinuities, leading to more precise assessments of rock mass quality [38]. Advanced algorithms are used to interpret seismic data, identifying patterns and relationships that may not be apparent through traditional analysis. These techniques enable more precise correlations between seismic velocities and RQD, improving predictions in complex geological settings. Moreover, seismic RQD can be used in conjunction with DFN models to incorporate volumetric fracture intensity and other parameters, addressing the inherent anisotropy and heterogeneity of rock masses. This hybrid approach enhances the predictive capabilities of seismic methods for engineering applications.

Seismic techniques also reduce the environmental impact and logistical challenges associated with traditional RQD methods. By minimizing the need for extensive drilling, seismic surveys offer a more sustainable approach to rock mass characterization. Additionally, their ability to operate in remote and inaccessible terrains expands the scope of geotechnical investigations, making them indispensable in projects such as large-scale tunneling, mining, and infrastructure development.

This article is not intended to present seismic measurements, which have a very wide body of literature. A comparison between the P-wave velocity of the in situ rock mass and the laboratory P-wave velocity of an unbroken drill core taken from the same rock mass can be used to determine RQD using the following equation [2]:

RQD = 100 (v_pF/v_p0)² [%]

(30)

where V_p0 is the P-wave velocity of the matching intact rock and V_pF is the P-wave velocity of the in situ rock mass.

Several researchers have also presented further empirical correlations that resembled Equation (30), suggesting the following form:

RQD = c 100 (v_pF/v_p0)² [%]

(31)

where c is a constant. According to El-Naqa [39] and Bery and Saad [40] it is 0.77 and 0.97, respectively.

9. Estimation of Mechanical Parameters Based on RQD Value

There are several empirical relationships between the different mechanical parameters (deformations modulus, compressive strength, and Poisson’s ratio) and the rock mass value (using RMR, Q, or GSI values). These equations were collected and analyzed by several authors, e.g., [41,42,43,44].

In this chapter, we focus only on empirical correlations that are RQD-based. It should be noted that these equations are mainly a first approximation.

9.1. Estimation of Deformation Modulus Using RQD Value

Formulas that focus on the ratio of the deformation modulus of the rock mass and the intact rock are presented and analyzed. These equations are compared with the other relationships that, are suggested using RMR/GSI values.

9.1.1. Linear Relationship

Firstly, collecting several measured data, Coon and Merritt [45] proposed the following linear equations to estimate the deformation moduli of the rock mass (E_m) from the deformation moduli of the intact rock (E_r) (see Figure 19):

E_m = α_E E_r

(32)

α_E = 0.0231 RQD − 1.32 ≥ 0.15

(33)

The collected point with the suggested linear equation is presented in Figure 18 [45].

The chart of the reduction factor of the elastic modulus in field tests compared to the elastic modulus in seismic tests for various dam sites and rock types is plotted in Figure 20 [2]. As shown in this Figure, the rock mass quality is represented by either the rock quality designation (RQD) or the ratio of seismic field velocities to laboratory sonic velocities (V_F/V_L). In many cases, only one of these measures—either RQD or V_F/V_L—was available for the data points, but not both. The generalized relationship becomes nearly flat when the reduction factor falls below 0.2 or when RQD is less than 60%. This flatness suggests a broad range of rock mass conditions in this region. Recognizing this, Deere et al. [2] recommended further investigation, which was subsequently carried out by several researchers and practitioners.

According to Gardner [46] this equation can be used if RQD > 57%. Additionally, it is incorporated into the Standard Specification for Highway Bridges by the American Association of State Highway and Transportation Officials (AASHTO) [47].

The RQD–(E_m/E_r) relations of Coon and Merritt [45] and Gardner [42] have the following drawbacks, according to Zhang and Einstein [48]:

(1)

Either the entire range of RQD < 60% is not covered, or merely a random E_m/E_r value is chosen.

(2)

E_m is taken to be equivalent to E_r for RQD = 100%. In terms of design practice, this is clearly dangerous because RQD = 100% does not imply that the rock is intact. Even when RQD = 100%, there may be discontinuities in the rock masses, which means that E_m might be smaller than E_r.

9.1.2. Power-Law Formula

Zhang and Einstein [48] established the empirical relationship between RQD and the ratio of deformation moduli of the rock mass (E_m) and the intact rock (E_r) using the large number of published data (the rocks for the data included mudstone, siltstone, sandstone, shale, dolerite, granite, limestone, greywacke, gneiss, and granite gneiss).

They discovered the following relationships by analyzing a significant number of measurements (see Figure 21):

• Lower bound:

E_m/E_r = 0.2 × 10^{0.0186RQD−1.91}

(34)

• Upper bound:

E_m/E_r = 1.8 × 10^{0.0186RQD−1.91}

(35)

• Mean:

E_m/E_r = 10^{0.0186RQD−1.91}

(36)

The E_m/E_r values can differ by up to five times at 100% RQD, as the figure below illustrates. Among other things, the varying borehole lengths [23] can help to explain this.

9.1.3. Analysis of the Suggested Equations

By gathering more information from the published literature, Zhang and Einstein [48] enlarged their database (see Figure 22, utilizing the publication [43]). This extended database displayed a non–linear change in the E_m/E_r with RQD and spans the whole range (0 ≤ RQD ≤ 100%).

The difference in % between the linear and non-linear equations is shown in Figure 23 for the upper approximation and the average approximation. One can see that Equations (34)–(36) can be transformed to the following form:

• Lower bound:

E_m/E_r = 0.0025e^0.0428RQD

(37)

• Upper bound:

E_m/E_r = 0.0221e^0.0428RQD

(38)

• Mean:

E_m/E_r = 0.0123e^0.0428RQD

(39)

The advantage of this equation is that it can be related to the damage model [49]. A number of empirical formulas based on RMR/GSI values can be used to determine the rock mass’s deformation modulus from the intact rock’s deformation modulus [50,51,52,53,54,55,56].

9.2. Estimation of Compressive Strength Based on RQD Value

Similarly to the deformation modulus, RQD can also be used to estimate the compressive strength of the rock mass. Both linear and non-linear empirical relationships are known and are presented here.

9.2.1. Linear Equation

According to Kulhawy and Goodman [57], the strength of the rock mass (σ_cm) can be estimated as a first approximation using the strength of the intact rock (σ_c) and the RQD value. It was assumed that the ratio of the strength of the rock mass to that of the intact rock was 0.33 and 0.8 in the cases of RQD being 70% and 100%, respectively. This means that, if the RQD value is more than 70%, the following equation can be used:

σ_cm/σ_c = 1/3 (0.037RQD + 1.6)

(40)

Likewise, the deformation modulus of the rock mass from the AASHTO [47] was calculated, and the following expression was proposed to estimate σ_cm:

σ_cm = α₀ σ_c

(41)

α₀ = 0.0231 RQD − 1.32 ≥ 0.15

(42)

Note that the limitations of this equation have already described for the deformation modulus applied here, too [48].

9.2.2. Non-Linear Equations

Zhang [58] assumed that the relation between the compressive strength of the rock mass and the intact rock (σ_cm/σ_c) and the deformation modulus of rock mass and intact rock (Em/Er) could be related approximately by the following equation [59,60,61]:

$${\displaystyle \frac{{\sigma }_{cm}}{{\sigma }_c}}={\left({\displaystyle \frac{Em}{Er}}\right)}^q={\left({\alpha }_E\right)}^q$$

(43)

The power q ranges from 0.5 to 1.0, with an average of 0.7 and most often falling between 0.61 and 0.74 [58]. Zhang believed that there was an approximate relationship between the unconfined compressive strength of the intact rock and the unconfined compressive strength of the rock mass.

$${\displaystyle \frac{{\sigma }_{cm}}{{\sigma }_c}}={\left({\alpha }_E\right)}^{0.7}$$

(44)

Combining Equations (36), (43), and (44), Zhang [58] suggested the following empirical relation:

σ_cm/σ_c = 10^{0.013RQD−1.34}

(45)

The suggested equations by Kulhawy and Goodman [57] and the AASHTO [47] are compared with the non-linear equation of Zhang [58] in Figure 24.

Similarly, the deformation modulus of the rock mass can be transformed to the following form:

σ_cm/σ_c = 0.0457e^0.0299RQD

(46)

9.3. Estimation of the Modulus Ratio as a Function of RQD

Deere [62] introduced the modulus ratio (MR) of the intact rock, which is the ratio of the deformation modulus (E_r) and uniaxial compressive strength (σ_c) of the intact rock:

$$\mathrm{MR}={\displaystyle \frac{E_r}{{\sigma }_c}}$$

(47)

Using Equations (39) and (45) the modulus ratio of the rock mass (MR_rm) can be calculated as a function of the RQD value:

MR_rm = 0.269 MR e^0.0129RQD

(48)

9.4. Estimation of Poisson’s Ratio

Narimani et al. [63] collected the relationships between the different rock mass classification systems (such as: RMR, Q, RMQR, and GSI) and the Poisson’s ratio of the rock mass (ν_rm) in the function of the Poisson’s ratio of the intact rock (ν_i). No one has investigated the effect of RQD on Poisson’s ratio of the rock mass yet, so in this chapter hypotheses for possible relationships are provided.

Opposite of both the deformation modulus and the strength of the rock mass, Poisson’s ratio increases as the value of RQD decreases thus, new relationships are necessary.

It can be assumed that the suggested linear equation of Aydan et al. [64] can be used for RQD as well:

$${\displaystyle \frac{{\mathit{\nu }}_{\mathit{r}\mathit{m}}}{{\mathit{\nu }}_{\mathit{i}}}}=2.5-{\displaystyle \frac{1.5\mathit{R}\mathit{Q}\mathit{D}}{100}}$$

(49)

10. Common Use of RQD for Rock Mass Classification

When RQD was introduced, the aim was also to design tunnel support, but recently, the RQD value has become one of the input parameters of many different rock mass classification systems, such as RMR [4,5], Q [6], and GSI [7] values.

The sensitivity analysis of mechanical parameters determined by the Geological Strength Index (GSI) method was carried out by Ván and Vásárhelyi [65].

As shown by Erharter et al. [66,67], RMR, Q, and GSI are the most commonly used rock mass classification systems.

10.1. RMR Value

The Rock Mass Rate (RMR) system was introduced by Bieniawski in 1976 [4] and modified several times. The 1989 version [5] is analyzed here, as this is the most widely used version. This method offers significant advantages due to its reliance on a limited number of essential parameters related to the mechanical and geometric properties of rocky slopes. These key requirements ensure the method’s effectiveness and adaptability in various geological settings.

According to the definition of RMR, it depends on the following parameters:

RMR = R1 + R2 + R3 + R4 + R5

(50)

where

R1

Uniaxial compressive strength (0–15);

R2

RQD value (0–20);

R3

average joint space (5–20);

R4

joint wall conditions (0–30);

R5

water (0–15).

In the field, sites can be classified using this method. Structural regions are characterized by the presence of similar rock types or discontinuities, allowing each section to be distinctly identified and categorized [68].

The RMR method offers guidelines for implementing tunnel rock reinforcement, with adjustments based on factors like subsurface depth, tunnel size and shape, and the excavation method used. Furthermore, RMR is applied to predict the behavior of dredged material and estimate stand-up time. The physical characteristics of a rock mass are also ascertained using it [5,68,69].

10.2. Q-System

The Q-system, a rock mass classification method, was introduced in 1974 by Barton et al. [6], at the Norwegian Geotechnical Institute (NGI) in Norway. This system was designed to assess rock mass properties and determine necessary tunnel support measures. The development of the Q-system involved a detailed analysis of 212 case histories of hard rock tunnels in Scandinavia, providing a robust foundation for its application in geotechnical engineering [5].

According to its definition, the rock mass quality (Q) value can be calculated from the following equation [6]:

$$Q={\displaystyle \frac{RQD}{Jn}}{\displaystyle \frac{Jr}{Ja}}{\displaystyle \frac{Jw}{SRF}}$$

(51)

RQD: rock quality designation (10–100);

Jn: joint set number (0.5–20);

Jr: joint roughness number (0.5–4);

Ja: joint alteration number (0.75–24);

SRF: stress reduction factor (1–20);

Jw: joint water reduction factor (0.05–1);

The Q-system’s use of an open logarithmic scale ranging from 0.001 to 1000, in contrast to a simpler linear scale up to 100, adds complexity to its application, making it more challenging to use effectively [5,40,70].

Relative block size is taken into account by RQD/J_n, the first quotient in Equation (51). According to

Table 10. Jn parameters.

Joint Set Description		Jn
A	Massive, no, or few joints	0.5–1
B	One joint set	2
C	One joint set plus random joints	3
D	Two joint sets	4
E	Two joint sets plus random joints	6
F	Three joint sets	9
G	Three joint sets plus random joints	12
H	Four or more joint sets, random, heavily jointed	15
J	Crushed rock, earth–like	20

Note: Not just joints but all sets of discontinuities or geological structures must be taken into consideration.

, the joint set number, J_n, is the rating for the quantity of joint (discontinuity) sets in the same domain. A joint set description for the borehole from the Mórágy Granite Formation is presented in Figure 25.

When calculating J_n, the term “joint,” which is taken from the original Q-system, can refer to any kind of discontinuity or geological structure. All sets of discontinuities or geological structures (not simply joints) must be taken into consideration while evaluating J_n. In sedimentary and metamorphic rocks, this includes bedding and foliation, respectively. In addition to appearing more frequently as joint sets, a joint or discontinuity might occur alone as a random joint [71]. A family of nearly parallel, similarly spaced discontinuities with comparable physical or geomechanical characteristics is called a joint set (or discontinuity set).

Relative block size (RQD/J_n), as illustrated in Figure 26, can be used to decrease the restrictions noted by Palmström [11] and differentiate between various rock masses with comparable RQD values. Relative block size (RQD/J_n) is plotted in the function of both RQD and J_n in Figure 27.

Based on the relative block size, the drill core classification is recommended according to

Table 11. Classification of rock masses based on relative block size method.

RQD/Jn	Rock Mass Description	Rock Mass Quality	Classes
100–200	Massive rock mass	Excellent	I
40–100	Jointed rock mass	Very good	II
20–40	Very jointed rock mass	Good	III
5–20	Very jointed–fragmented rock mass	Medium	IV
1–5	Fragmented–crushed rock mass	Weak	V
0–1	Crushed rock mass	Very weak	VI

.

10.3. GSI Value

The Geological Strength Index (GSI) was developed by Hoek [72] to make it easier to evaluate the characteristics of hard and weak rock masses in rock engineering applications. This approach combines information from the Rock Mass Rating (RMR) system, as mentioned by [73], with observations of rock mass conditions, which were first reported by Terzaghi. The GSI estimates an average value by analyzing the relationship between rock mass structure and the conditions of rock discontinuity surfaces, which are graphically represented as diagonal contours [72,73,74,75].

The Geological Strength Index (GSI) numeric value is determined using diagonal lines on a chart, which span from 10 to 80 in increments of 5. This method categorizes rock mass quality into five distinct groups and further divides them into four rock mass structure domains. These rock mass structures range from extremely fragmented masses with poorly interlocked angular and rounded blocks to blocky formations, which were defined by cubic blocks formed by three orthogonal joint sets. The surfaces ranged from slickenside surfaces with clay coatings or heavier clay fillings to extremely rough, unweathered, and strongly interlocked surfaces.

To address more intricate geological characteristics, including shear zones and heterogeneous rock formations, an extra category was incorporated into the original classification chart. This addition was specifically designed to aid in characterizing the highly sheared and folded flysch series referred to as the Athens Schist [74].

Hoek et al. [7] introduced new scales on the x-axis and y-axis of the GSI chart initially developed by Hoek and Marinos. The x-axis (Scale A) measures the surface quality of the rock mass, ranging from 0 to 45 and divided into five intervals of 9. The y-axis (Scale B) assesses block interlocking and structural domains, ranging from 0 to 50 with five intervals of 10 [7]. Marinos and Hoek further refined Scale A to represent 1.5 times the JCOND₈₉ value, while Scale B was defined as half the RQD value in the basic GSI chart, as illustrated in Figure 28.

Hoek and coauthors formulated a different equation to estimate the Geological Strength Index (GSI) by incorporating surface joint characteristics and ratios. This alternative approach is illustrated in the equation below [7]:

$$\mathrm{GSI}=1.5{\mathrm{JCOND}}_{89}+{\displaystyle \frac{RQD}{2}}$$

(52)

Equation (52) can be reformulated to derive the rock quality designation (RQD) value, as illustrated in the subsequent equation:

RQD = 2(GSI − 1.5JCOND₈₉)

(53)

11. Discussion

The practical value of the RQD method can be significantly enhanced through its integration with advanced geotechnical testing techniques, addressing the limitations of traditional approaches. Below, we explore various methods and their contributions:

Seismic Techniques: Seismic methods, particularly those analyzing P-wave velocities, enable RQD assessment over larger areas without extensive drilling. This approach evaluates rock mass quality by correlating seismic wave velocities with fracture density and rock elasticity. For example, the RQD can be derived using the ratio of in situ seismic velocities (V_pF) to laboratory-measured velocities (V_p0), as shown in Equation (30). These techniques reduce environmental impacts and provide continuous data for large-scale characterization. Integrating seismic-derived RQD values with borehole data enhances the reliability of geotechnical models, particularly in projects involving anisotropic or fractured rock masses.

Discrete Fracture Network (DFN) Modeling: DFN models offer a detailed representation of fracture systems by integrating data from multiple sources, such as boreholes and rock exposures. These models improve RQD calculations by accounting for fracture orientation, intensity, and spacing. As discussed, the DFN approach not only mitigates RQD’s directional dependency but also facilitates the more accurate connectivity modeling of fracture networks. For instance, integrating DFN-derived volumetric fracture intensity (λv) with traditional RQD measures addresses scale and anisotropy issues, providing a more representative understanding of rock mass behavior.

Machine Learning and Automated Analysis: Advances in deep learning and AI-based image analysis have made automated RQD calculations more efficient. As recent studies have shown, automated methods can analyze joint spacing, fracture patterns, and block sizes with high precision, reducing the subjectivity inherent in manual logging. Incorporating these techniques into RQD analysis enables the rapid processing of large datasets, offering consistent and repeatable results in both field and laboratory settings.

Hybrid Approaches: Combining RQD with other rock mass classification systems, such as the Geological Strength Index (GSI) or Rock Mass Rating (RMR), improves its practical applicability. For example, GSI charts use RQD-derived parameters to estimate structural and surface conditions, highlighting the interdependence of these classification methods. Additionally, integrating seismic and DFN-derived fracture data with traditional RQD values enhances the resolution of rock mass characterization, especially in highly fractured zones.

Modified RQD Techniques: Several modifications to traditional RQD, such as weighted joint density (RQD_wjd), corrected RQD (RQD_c), and improved RQD (RQD_l), incorporate advanced parameters like fracture density, orientation, and weak zones. These enhancements provide more accurate and reliable assessments in complex geological conditions, such as in highly jointed or weak rock masses. For example, Equations (5) and (11) demonstrate how these modifications address the limitations of the original RQD method, improving its alignment with real-world observations.

By integrating these advanced techniques and modifications, the RQD method evolves into a more comprehensive and versatile tool for geotechnical and rock engineering applications. This approach not only addresses the method’s inherent limitations but also aligns with contemporary demands for precision and scalability in rock mass characterization.

The analysis of various methods for calculating rock quality designation (RQD) highlighted the inherent limitations and provided insights into the effectiveness of the proposed modifications. Despite being widely used, the traditional RQD method [1,2] has limitations, primarily concerning its sensitivity to the orientation of the borehole relative to the fracture orientation and its inability to account for the quality of core pieces smaller than 10 cm. Because high RQD values may not always correspond with high-quality rock masses and vice versa, these restrictions may occasionally result in misrepresentations of rock mass quality [11,13,14]. Several modifications to the RQD method have been proposed to address these limitations: weighted joint density (RQD_wjd), modified RQD with weighted joint density (RQD_M-wjd), Modified RQD (MRQD), corrected RQD (RQD_c), improved RQD (RQD_I).

Each modification offers unique advantages and addresses specific limitations of the traditional RQD method [18,19,20,21,22,23]. The choice of method should be based on the specific conditions of the borehole and the rock mass being assessed. For instance, RQD_wjd and RQD_M-wjd [18,19] are particularly useful in environments with varying joint orientations, while MRQD and RQD_I [20,22] provide more detailed assessments in fractured and weak rock masses. The improved methods demonstrate the importance of considering multiple factors in rock mass quality assessment, including joint orientation, weak zones, and the quality of core segments. By integrating these factors, the modified RQD methods offer more reliable and comprehensive measures of rock mass quality, which is essential for geological and rock engineering applications.

12. Limitations of Derived Equations

The derived equations in this study aim to enhance the practical applicability of RQD-based assessments in diverse geological and engineering contexts. However, it is critical to recognize their limitations and outline scenarios where they are most applicable, ensuring their effective application in real-world drilling and production. The limitations of the derived equations are the follows:

Directional Sensitivity: Many RQD-based equations are sensitive to the orientation of boreholes relative to fracture orientation. For instance, equations such as Equation (14) and Equation (17), which relate RQD to fracture frequency (λ), assume uniform fracture distributions and may not accurately reflect anisotropic conditions. This limits their reliability in regions with strong directional jointing or highly anisotropic rock masses.

Threshold Dependency: Several equations, including the corrected RQD (RQD_c) and modified RQD (MRQD), rely on threshold values for fracture length or spacing. In scenarios with extreme fracture densities or fine-scale discontinuities, these thresholds may lead to an over- or underestimation of rock quality.

Rock Strength and Weathering: Equations such as those linking RQD to the deformation modulus (Equation (39)) or uniaxial compressive strength (Equation (46)) assume intact rock behavior. They may not perform well in weathered or heavily fractured rock masses where the properties of weak zones dominate.

Scaling and Resolution: Techniques such as discrete fracture network (DFN) modeling and seismic RQD calculations depend on the scale of observation. As such, the derived equations calibrated for laboratory cores (e.g., Equations (9) and (30)) may not accurately predict field-scale behavior without further adjustments.

13. Conclusions

The rock quality designation (RQD) method remains a cornerstone for assessing rock mass quality, offering a simple and widely adopted approach over the past six decades. Despite its limitations, including its sensitivity to borehole orientation and inherent anisotropy, it continues to be integral to rock mass classification systems such as RMR, the Q-system, and the GSI. This study highlighted the following key findings:

Limitations of Traditional RQD: RQD is highly sensitive to borehole orientation, leading to a potential overestimation when joints are parallel to the borehole axis or underestimation when joints intersect perpendicularly.

It fails to account for fractures smaller than 10 cm, resulting in an incomplete representation of rock mass quality.

In highly fractured zones, RQD values as low as 0% have been observed, even when intact core segments are just below the 10 cm threshold.

Quantitative Advancements in RQD Calculations: Modified RQD methods, such as weighted joint density (RQD_wjd), provide adjusted values (e.g., 70% and 62% for two boreholes in the same domain with different orientations), mitigating the directional bias inherent in traditional RQD.

Empirical correlations, such as RQD = 100 × (V_pF/V_p0)², enable seismic-based RQD estimates, allowing for spatially continuous assessments over inaccessible terrains.

Application of Discrete Fracture Network (DFN) Models: DFN modeling reduces the directional dependency of RQD by incorporating volumetric fracture intensity (λv), yielding values that better align with observed rock mass conditions. For example, RQD_wjd and DFN-derived RQD values for fractured rock masses showed only a 5–10% variation compared to field measurements.

Correlation with Mechanical Parameters: Empirical relationships linking RQD to the deformation modulus (E_m) and compressive strength (σ_cm) enhance its utility. For example, the relationship E_m/E_r = 0.0123e^0.0428RQD provides a robust means of estimating the deformation modulus across various rock qualities.

Similarly, σ_cm/σ_c = 0.0457e^0.0299RQD enables the estimation of compressive strength, addressing design needs in geotechnical engineering.

Integration of Seismic Techniques: Seismic methods, particularly those utilizing P-wave velocities, overcome spatial and accessibility limitations. In one case study, seismic RQD values matched within 10% of traditional RQD measurements across complex terrains, demonstrating the reliability of these methods.

Hybrid Approaches for Comprehensive Assessments: Combining RQD with other classification systems, such as RMR and the GSI, enhances its practical applicability. For instance, RQD contributes up to 20 points in RMR calculations, directly influencing rock mass quality classifications.

For the safe and effective design of rock engineering projects, RQD will continue to play a crucial role, particularly when integrated with advanced techniques like DFN modeling and seismic methods. Future research should focus on further refining these methods and exploring their applications in complex geological settings to enhance the reliability and versatility of RQD-based assessments.