Drilling Process Monitoring for Predicting Mechanical Properties of Jointed Rock Mass: A Review

Abstract

Reliably assessing the quality and mechanical properties of rock masses is crucial in underground engineering. However, existing methods have significant limitations in terms of applicability and accuracy. Therefore, a field measurement method that meets the real-time monitoring and safety requirements for the quality of engineering rock masses is needed. Firstly, the research findings of domestic and international scholars on the application of drilling process monitoring technology are comprehensively analyzed. Rotary cutting penetration tests are conducted on tuff rock masses containing fractures and joints. Various rock mass classification and evaluation standards are integrated with rotary penetration tests. Rotary cutting penetration tests are used to determine the residual strength of rock, based on this review. The rationality of the calculated m_i parameter values is validated. The peak strength, residual strength, and errors of the rock are obtained based on the penetration method. The rock quality index rock quality designation from drilling (RQD_d) is redefined, based on the drilling process monitoring apparatus (DPMA). Rock mass classification is conducted, based on the correlation between the standard deviation of rotary drilling energy and the rock quality designation (RQD). Additionally, a new relational formula is introduced to determine the RQD from variations in drilling energy, based on discontinuity frequency. This field measurement method undoubtedly provides a crucial scientific basis for rock design and construction, ensuring long-term safety in engineering applications.

1. Introduction

The swift and reliable evaluation of rock mass quality and mechanical properties is crucial for underground engineering projects. It is especially crucial in the design and construction of subway systems and tunnel excavation [1,2,3]. As an efficient reference, the RQD has been regarded as the worldwide standard to determine the quality of engineering rock masses [4]. Some complex issues are considered during construction, such as fractured surrounding rock, fault fracture zones, and extremely soft rock. Various methods for evaluating the quality of engineering rock masses have been developed [5]. A series of emerging technologies have been introduced, including core drilling technology [6,7], sonic detection technology [8], laser scanning technology [9] and digital imaging technology [10]. Sonic detection results in relatively large wave velocity measurements obtained during field surveys, due to disparities in wave velocities between intact rock masses and jointed rock masses [11]. The integrity of the rock mass can be effectively determined through digital imaging. The risk of rock burst is avoided. However, the technology is time-consuming and costly, necessitating its integration with core drilling techniques [12]. In addition, the elasticity and brittleness indices of rock formations are influenced by various mineral compositions, rock shapes, and failure modes [13]. So, the core is damaged during drilling in hard rock formations. The mechanical performance is affected [14]. The physical and mechanical properties during rock excavation have been analyzed by numerous scholars and applied for many years. Examples include the characterization of cutting energy for rock brittleness assessment [15], the transition from ductile to brittle failure during rock drilling [15], analysis of rock’s lateral anisotropy [16], and the tendency analysis of rock burst occurrences [11].

Field sampling and laboratory testing methods are a good choice [1] to avoid unnecessary biases, such as those arising from the hardness and discontinuities of jointed rock masses in field conditions. Certain issues are overlooked as a result of this consideration [17]. These include mechanical grinding during rock sample preparation [18] and rock sample damage caused by drilling and blasting [19]. Engineering projects often face complex geological conditions, such as high stress, extremely soft rock masses, and fault fracture zones [20]. The reliance on geological surveys for preliminary design and subsequent reinforcement cannot be mitigated, due to the concealed nature of large rock masses. Collapse and roof collapses are prone to occur, due to the loosening and fracturing of surrounding rock after blasting. Anchoring and grouting reinforcement is a commonly used method for addressing the aforementioned issues [21]. The increase in surrounding rock strength after anchoring and grouting is a key indicator for quantitatively evaluating the effectiveness of the grouting process. The anchoring effect of the surrounding rock and the effective spread range of grouting are indirectly assessed with the anchor bolt tension test method [18], which measures the rate of increase in tension of the anchor bolt after grouting. The supporting system and reinforced surrounding rock are affected when this method requires destructive testing [22]. Therefore, a field measurement method is required to meet the safety requirements for the real-time monitoring of engineering rock mass quality.

In this paper, the research conducted by domestic and foreign scholars using this technique is analyzed, including: (1) Providing an overview of the parameter m_i in the Hoek–Brown (H-B) criterion, concerning the determination of residual strength and peak strength from drilling data. (2) Training an improved H-B criterion, using a deep convolutional neural network (DCNN). (3) Analyzing the evaluation of rock mass quality RQD_d through rotary drilling, based on the unique response of the intermittent frequency to drilling energy. (4) Enhancing the prediction of the deformation modulus and uniaxial compressive strength (UCS), based on the rock mass quality of jointed rock masses assessed by RQD_d. The advantages and limitations of drilling process monitoring technology and rock mass quality RQD_d are comprehensively considered. The future development direction of this technology is envisaged.

2. Drilling Equipment

2.1. The Limitation of Q-System, RQD, RMR

The Q-value method is significantly influenced by adverse underground construction conditions and inadequate equipment, as observed through on-site investigations. The fluctuation in rock mass quality grading is caused by to the extensive computational space of rock mass integrity grading parameters (RQD and J_n) in the Q-value method [23].

The RQD serves as a crucial indicator of rock mass quality, bearing significant importance in assessing engineering rock mass integrity and analyzing rock mass characteristics. A quantitative measure of rock mass quality is provided by the RQD. The accuracy of geological assessments is improved [24]. Understanding of rock properties is obtained through core samples collected during the drilling process [25]. The RQD is combined with drilling energy data. The correlation between drilling parameters and rock characteristics is identified, enabling precise rock mass classification. Real-time monitoring provides immediate data for decision-making, enhancing safety, and optimizing construction processes. The risk of unforeseen geological conditions and potential costs are reduced during the drilling process [26]. However, significant differences in rock mass quality within the same area exist, due to long-term geological processes and the impact of other engineering activities. Therefore, extensive drilling and geological surveys are required before mining development and during the production process. Important foundations for rock design and construction are provided through the extraction and systematic analysis of drilling data. The core data volume that needs to be processed is typically large [27]. Traditional RQD manual measurement and calculation methods are inefficient and susceptible to the influence of subjective factors from the survey personnel. Therefore, designing an efficient and automated RQD calculation method has practical engineering significance [28].

The Rock Mass Rating (RMR) method has been widely applied since the 1980s. Significant success has been achieved in the assessment of rock mass quality, particularly in shallow-depth and hard rock formations [29]. However, the following problems arise when applying the RMR method, as resource extraction gradually extends to deeper regions and faces the complex geological environment of deep rock masses [30]:

(1)

The influence of high in-situ stress on rock strength has not been taken into account.

(2)

The influence of different combinations of joint sets has been overlooked. The impact of intersecting joint sets on rock mass quality remains significant, although the RMR method currently incorporates joint sets as evaluation criteria.

(3)

The influence of deep-seated, high-temperature effects has been overlooked. The strength of rocks undergoes changes in high-temperature environments.

(4)

The influence of deep-seated high pore pressure has been overlooked. The strength of rocks has been diminished by the high permeability pressure.

2.2. The Advantages of RQD_d

RQD_d is the developed rock quality designation from drilling. A new method was proposed by He et al. [28] for predicting the RQD using borehole data. Rock mass classification was proposed, based on the correlation between the standard deviation of rotary drilling energy and the RQD. Rock quality can be predicted solely using drill core data with the RQD_d [31]. The RQD method was introduced by Azimian et al. [32] and has found widespread application in engineering geology due to its simplicity and cost-effectiveness. It has been widely applied in engineering geology, due to its simplicity and cost-effectiveness. The rock mass quality can be rapidly assessed with just statistical analysis of core lengths obtained from drilling. Yasrebi et al. [29] demonstrated that reliable assessments of rock mass quality can be provided by the RQD through standardized calculations and statistical methods. It is beneficial for engineering design and risk assessment. RQD data were introduced by Lin et al. [30], obtained through the conventional core drilling process [33]. The complexity of rock mass quality assessment has been simplified. The time and cost of on-site data collection have been reduced. Hasan et al. [8] noted that the RQD method has been widely applied and validated in various engineering projects. These include tunnel construction, mining operations, and hydraulic engineering [34]. Therefore, the new method for predicting the RQD possesses advantages such as simplicity, reliability, and ease of data acquisition, all achieved through the utilization of borehole data. These advantages give the RQD_d method significant practical value and broad applicability in rock mass quality assessment.

2.3. Drilling Process Monitoring Apparatus

The XCY-1 drilling process monitoring apparatus (DPMA) is shown in Figure 1 [35,36]. The apparatus is a tracked device, adaptable to most on-site environments. The mechanical parameters of the rock mass are estimated using a reference rotary drilling method. The DPMA is composed of the following six parts: an electrical control system, a hydraulic system, an oil pump transmission system, a real-time monitoring and data acquisition control system, and a diamond drill bit. The technical parameters of the equipment are shown in

Table 1. Main technical parameters of the XCY-1 DPMA.

Technical Parameters
Maximum stroke of power head (mm) [20]	1700	Drilling depth (m) [20]	50
Rated lifting power (kN) [20]	40	Drill diameter (mm) [20]	42/50
Maximum pressure (kN) [20]	18	Motor power (kW) [20]	90
Drilling speed (m/min) [20]	0~28	Maximum torque (N·m) [20]	2458
Drilling angle (°) [20]	0~90	Rotating speed (r/min) [20]	0~1000

.

The operation of the DPMA can be divided into normal drilling and the parameter acquisition modes. The DPMA in normal drilling mode drives at a relatively fast rate for pre-drilling before the test depth. The apparatus works for the precise acquisition of the rotary cutting penetration parameters in parameter acquisition mode. The robotic arm is capable of rotating, with a drilling angle ranging from 0 to 90 degrees. The DPMA operates automatically as a drive control indicator, facilitated by the coordination of various systems. Real-time parameters at different testing depths are recorded. These include drilling force F, torque M, speed ω, and drilling speed ν, etc. Finally, the measurement data are saved in an Excel 2019 version file at a rate of 500 points per second.

The loading system has as a power source the maximum thrust of 18 kN from the Rexroth hydraulic pump. The torsion system has a torque of 2458 N·m with the torque servo motor, as shown in Figure 2. The power system has two working statuses of constant current and voltage. The transmission is stable and accurate, with low noise during operation. The torque system consists of a drive motor and a gearbox. The drive gearbox is divided into first, second, third, and neutral, respectively corresponding to the different surrounding rock conditions, as shown in

Table 2. Relationship between drive gear transmission and rock.

Gear	Neutral	First	Second	Third
Rotating speed (r/mm)	0	0~300	300~600	600~1000
Surrounding rock type	-	IV, V	II, III	I, II

.

The monitoring system plays a key role in the drilling process, and consists of two S12 speed sensors, two composite sensors, and two high-precision displacement sensors. The S12 speed sensor is fixed on the front of the drill bit and connected with the gearbox. The rotational speed of the drill bit and the drilling speed are detected. The composite sensor is mounted above the control console, with a maximum reception frequency of 500 Hz. It is equipped with an advanced digital wireless transmitter device from the UK. Pressure and torque are concurrently monitored. The displacement sensor is used to control and record real-time drilling depth. The parameter data collected are transmitted from the data acquisition control system to the recorder. The recorder is connected to the display via a controller area network (CAN) communication module. The console and display with the system framework are shown in Figure 3. The variation trends of speed, drilling speed, drilling pressure, torque, and time can be observed through the display. The system pressure, drilling distance, and controller I/O status are monitored simultaneously. The equipped touch keyboard controls the feed cylinder to drive the drill bit through the programmable control system (PLC system). The integration of drilling control, data acquisition and storage, and real-time display has been achieved.

3. Calculation for Intact Rock Mechanical Parameters Using DPMA

3.1. Intact Rock Strength Characteristics

3.1.1. Digital Penetration into Response Mechanisms

Drilling monitoring technology has gradually developed into a mature method for on-site assessment of rock mass quality over the past half century [38]. The current research primarily consists of several analytical models established based on laboratory experiments. The primary models encompass the indentation model [39], shear model [40], and bit model [33,34,35]. However, techniques for analyzing rock strength are seldom explored in conjunction with drilling monitoring. The tip stress of a “T”-shaped drag bit was used to estimate rock mass strength, based on the limit equilibrium from a stress perspective [41]. The energy distribution characteristics in a penetration process was described by Hu et al. [34], by providing a specific drilling energy e.

The drilling process in rock is carried out in a helical motion, simultaneously involving continuous drilling and cutting. The cutting process is crucial for drilling, owing to the cutting force acting as a dominant force [42]. Debris poses resistance to drilling speed, generated by the friction between the cutting and crushing zones. The drilling response is significantly affected when the device rotates to cut through the rock [43]. The intersection of the two kinds forces is located at the cutting point, which experiences a combination of cutting and friction processes (shown in Figure 4 from Dagrain et al. [44]).

A theoretical model relating rock strength to the drill bit is derived [44], and this drilling principle is taken into account:

$$\frac{F_t}{F_n}=\frac{cos\left({\phi }^{\prime }-\phi \right)cos\left(a+\phi \right)+cos\phi \left(2tan\theta -cosa\right)\left[cos\left({\phi }^{\prime }-\phi \right)-sin{}^2\left({\phi }^{\prime }-\phi \right)+sin\left({\phi }^{\prime }-\phi \right)\right]}{cos\left({\phi }^{\prime }-\phi \right)cos\left(a+\phi \right)+3cos\phi sina\left[cos\left({\phi }^{\prime }-\phi \right)-sin{}^2\left({\phi }^{\prime }-\phi \right)+sin\left({\phi }^{\prime }-\phi \right)\right]}$$

(1)

where F_n is the normal thrust. F_t is the rotating cutting force. a is the rake angle of the blade. φ is the internal friction angle of the complete rock. φ is the friction angle of the complete rock and the cutting zone. θ is the contact friction at the blade side.

The ratio of F_t to F_n can be simplified as a constant value named H, which is dependent on the four inherent drill bit parameters a, φ, φ′, and θ′, according to Equation (1). a and θ′ are the rake angle of the diamond blade and the contact friction angle of the cutting face of the diamond blade. In addition, the value of the θ′ is approximately equal to θ. Equation (1) can be simplified as [41,45]:

$$\frac{F_t}{F_n}=\frac{1}{tan\left(a+{\theta }^{\prime }\right)}=H$$

(2)

3.1.2. Determination of Rock Strength Parameters

The rake angle value cannot be accurately obtained under high-thrust conditions (F_n > F_t at the cutting point), due to the large degree of diamond blade material grain deformation [46]. The unknown value of a can be assumed to estimate the rock strength parameter through the following five steps:

(1)

According to the ratio H of F_t to F_n at low-thrust conditions (F_n > F_t at the cutting point), substitute H into Equation (2) to calculate the value of a + θ′.

(2)

Substitute H under high-thrust conditions to obtain a and θ′. The cutting debris generated as the thrust increases accordingly. Thus, the friction angle φ′ between the zone and the intact rock is calculated as [44]:

$${\phi }^{\prime }=arctan\frac{tan\left(a+{\theta }^{\prime }\right)-tana}{1-tan\left(a+{\theta }^{\prime }\right)tana}$$

(3)

where φ′ is the frictional angle between the zone and the intact rock. a and θ′ are the rake angle of diamond blade and the contact friction angle of the cutting face of the diamond blade.

(3)

Gerbaud [41] found that φ′ has the following relationship with the intact rock friction angle φ:

$$\phi ={tan}^{-1}\left(\frac{2}{\pi }tan{\phi }^{\prime }\right)$$

(4)

where φ is the internal friction angle of the complete rock.

(4)

The four DPMA parameters can be substituted into Equation (5) to obtain the C as [40]:

$$F_t=\frac{2Ccos\left({\phi }^{\prime }-\phi \right)\left(1+tana\cdot tan{\phi }^{\prime }\right)}{\left[cos\left({\phi }^{\prime }-\phi \right)-{sin}^2\left({\phi }^{\prime }-\phi \right)+sin\left({\phi }^{\prime }-\phi \right)\right]}$$

(5)

where F_t is the rotating cutting force.

(5)

C and φ substituting the UCS of rock can be calculated as [44], according to the M-C criterion:

$$q_c=\frac{2Ccos\phi }{1-sin\phi }$$

(6)

where q_c is the UCS of the intact rock. C and φ are the cohesion and internal friction angle of the rock, respectively. The uniaxial compressive strength values are refined and enhanced. A statistical relationship exists between drilling speed V_DPM and rock uniaxial compressive strength R_c, according to the study by Azimian et al. [32]:

$$R_c=a{\mathrm{e}}^{-b{V}_{\mathrm{DPM}}}$$

(7)

where R_c is the uniaxial compressive strength. V_DPM is the drilling speed, and a and b are statistical constants. These constants vary with the type and efficiency of the drilling machine and the size and sharpness of the drill bit. The drilling speed is utilized to estimate the uniaxial compressive strength of the rock blocks. Alternatively, depending on the geological conditions of the actual engineering site, the drilling speed and uniaxial compressive strength of several different rock blocks can be measured [47]. A new relational formula between the drilling speed and uniaxial compressive strength is established, applicable to this specific drilling machine and drill bit. The same drilling machine and drill bit are used. The drilling speed is measured from different directions into the rock block, yielding either similar or varying speeds. The isotropy or anisotropy of the rock block is quickly determined [48]. Therefore, several different drilling speeds of rock blocks at the engineering site are measured, using DPM data from exploration and construction drilling. The uniaxial compressive strength and underground spatial distribution are obtained. Meanwhile, relationships can be established between the rock block drilling speed and parameters such as the elastic modulus, porosity, water content, permeability coefficient, internal friction angle, and cohesion [49].

3.1.3. Strength Determination Considering Different Failure Criteria

The obtained specimens were selected from the homogeneous rocks (the same below) due to the negative dependence of the rock discontinuities on the rock’s mechanical properties using drilling logging data. All the drilling tests were performed five times, to avoid the impact of surrounding influences (humidity and temperature) on the results. The limestone, granite, marble, and sandstone were tested in a laboratory and rotary cutting penetration test. The cohesive force c obtained from the rotary penetration test is reduced by 5.8%, 7.5%, 8.6%, and +0.88% −11%, respectively, compared with the laboratory-measured value (as shown in

Table 3. Obtained strength parameters for rocks from drilling tests [40].

Rock Type	ρ	φ′ (°)	θ (°)	φ (°)	C (MPa)		qc (MPa)
					Drilling Value	Standard Value	Drilling Value	Standard Value
Sandstone	2.31	49.6	11.31	38.7	5.16	5.46	22.39	21.58
Limestone	2.52	71.5	16.7	60.7	10.08	10.84	72.28	63.89
Marble	2.47	70.3	14.04	62.3	8.79	9.54	71.26	65.42
Granite	2.78	75.02	14.6	67.2	15.82	17.56	157.04	172.27

). This is due to the greater plastic deformation of the rock caused by the drilling process, especially for soft rock. The UCS errors of limestone, granite, marble, and sandstone are 3.6%, 11.6%, 8.2%, and −9.7%, respectively. The prediction of the compressive strength of hard rock is too large, so the overall error range is controlled within 12%. The predictive results are accurate. In summary, the practical application of this practical method in rock engineering is very meaningful.

Scholars have also proposed several analytical models, based on standard tests for estimating the peak and residual strength of intact rocks. These include the Mohr–Coulomb (M-C) model [41], Joseph–Barron (J-B) model [50], geological strength index (GSI) softening model [51], cohesion loss model [25], and Hoek–Brown (H-B) model [52]. The M-C model can accurately adopt the peak strength envelope of the rock [46]; it cannot describe the non-linear characteristics of the strength. The J-B model proposed by Joseph can determine the non-linear rock residual strength, but it is greatly affected by the large value of the confining pressure. The GSI model is widely used to describe the residual strength characteristics of rocks. However, the residual strength of most brittle rocks can hardly be determined by the corresponding GSI_r value. The true extent of damage in brittle rocks cannot be reflected.

The H-B rock strength criterion is widely used in both intact and jointed engineering rock, according to the Griffith brittle fracture theory [53]. The H-B criterion is shown in Equation (8):

$${\sigma }_1={\sigma }_3+{\left(\frac{m_i{\sigma }_3}{UCS}+1\right)}^{0.5}$$

(8)

where σ₁ and σ₃ are the maximum and the minimum principal stress, respectively. UCS is the uniaxial compressive strength of the intact rock. m_i is the rock material parameter, and its physical significance remains to be explored [54]. Sari [47] determined the m_i through regression analysis on a triaxial test. The discovery of errors is attributed to the use of different regression functions in the estimation of constants, so the influence of the confining pressure cannot be avoided effectively. Zuo et al. [50] demonstrated that the constant m_i can also be derived from the microdamage phenomenon of brittle rocks and the principle of linear elastic fracture mechanics [55]. The H-B criterion has been extended to the fracture damage strength criterion by introducing the fracture coefficient κ:

$${\sigma }_1={\sigma }_3+UCS{\left[\left(\frac{\mu UCS}{\kappa \left|{\sigma }_t\right|}\frac{{\sigma }_3}{UCS}+1\right)\right]}^{0.5}$$

(9)

where μ is the coefficient of friction (μ = tanφ, φ is the friction angle of the crack surface). κ is the mixed fracture coefficient. The parameter m_i cannot be effectively obtained, due to the difficulty of measuring the friction angle of the crack surface [56].

Zuo et al. [48] found that the parameter m_i is related to the rock strength characteristics. A method for determining the residual strength of rocks has been proposed using rotary cutting penetration tests, referencing a large amount of rock strength data. The regression analysis of H is carried out with the parameter m_i, the residual strength and cohesion of various rocks under the condition of low confining pressure (≤60 MPa), according to the peak. The blade rake angle á is selected as 5°, 10°, 15° and 20°. The internal friction angle φ of the complete rock is used to calculate the H value in the analysis function. A linear relationship exists between 1/H and the parameter m_i (as shown in Figure 5), which can be approximated as [57,58]:

$$m_i=\gamma H^{-1}+b$$

(10)

where constants γ and b are taken as 20.1 and −18, respectively.

The cohesive strength decreases continuously due to the cumulative damage caused by microcracks when the rock undergoes residual deformation. The following three conditions should be followed when estimating the residual strength of rocks:

(1)

The model parameters are simple and clear with an easily obtained physical meaning;

(2)

The rock residual strength envelope has an obvious nonlinearity;

(3)

The residual strength curve should pass through the coordinate origin of the principal stress space, for brittle rocks.

The residual strength characteristics of the rock are described using the cohesive loss model (C-L) proposed by Dagrain et al. [44]:

$${\sigma }_r={\sigma }_3+{\left(\lambda {\sigma }_{3}UCS+1\right)}^{0.5}$$

(11)

where λ is a dimensionless parameter. The C-L nonlinear rock residual strength model is similar to the constant m_i in the H-B model, including an easily obtained parameter λ.

The H-B model and the C-L model should be used when calculating the triaxial compressive strength (TCS) and the residual strength σ_r. The H-B model based on the parameters of the rotary cutting penetration test can be obtained [58], substituting Equation (10) into Equation (8):

$${\sigma }_1={\sigma }_3+UCS{\left(\frac{\left(\gamma H^{-1}+b\right){\sigma }_3}{UCS}+1\right)}^{0.5}$$

(12)

The essence of rock deformation and failure is a combination of enhancement of frictional strength and reduction in cohesive strength [59]. The parameters m_i and s represent the frictional strength and the cohesive strength components, respectively, in the H-B model. The parameter “s” corresponds in heavily damaged rocks to the minimum response (value is 0). The H-B criterion has been refined, and upon substitution into Equation (10) becomes:

$${\sigma }_r={\sigma }_3+UCS{\left(\frac{\eta \left(\gamma H^{-1}+b\right){\sigma }_3}{UCS}\right)}^{0.5}$$

(13)

where η, γ, and b are constants. η is determined by the collected test data.

The parameter η has an exponential relationship with 1/H, as shown in Figure 6a. The specific relationship is:

$$\eta =\frac{1.5}{4H^{-1}-2}$$

(14)

The correlation coefficient R² is greater than 0.90. Substituting Equation (14) into Equations (12) and (13), the σ₁ and σ_r are obtained, respectively [59]:

$${\sigma }_1={\sigma }_3+UCS{\left(\frac{\left(20.1H^{-1}-18\right){\sigma }_3}{UCS}+1\right)}^{0.5}$$

(15)

$${\sigma }_r={\sigma }_3+UCS{\left(\frac{\left(30.2H^{-1}-27\right){\sigma }_3}{UCS\left(4H^{-1}-2\right)}\right)}^{0.5}$$

(16)

The value of λ in the C-L model can be expressed as above (Figure 6b) [59], comparing Equation (11) with Equation (16):

$$\lambda =\frac{30.2H^{-1}-27}{4H^{-1}-2}$$

(17)

The validity of the calculated parameter m_i is confirmed through comparison of the fitting values between the H-B and C-L models (as shown in Figure 7) [51]. The m_i values of slate, granite, limestone, and sandstone (in the C-L model) are 13.30, 18.03, 12.98, and 8.83, respectively. The m_i values (in the H-B model) are 13.45, 19.99, 11.34, and 8.92, respectively. The m_i derived in this model is less than the value of the original H-B model for granite, slate, and sandstone. The m_i obtained in this study is basically the same as the H-B value for limestone.

Residual strength and error obtained by the penetration method (as shown in Figure 8), based on the peak strength of the four types of rock [51]. The maximum error of the four types of rock is controlled within 15%. Among them, the residual strength of granite and slate is less than the measured value. The model proposed in this paper can directly and easily estimate the residual strength of rocks.

3.2. Applications for AI-Based Rock Strength Parameter Determination

The convolutional neural network (CNN) has been successfully transplanted into engineering analysis; it is an artificial intelligence (AI) technique that was proposed in the late 1980s [60]. It has applications such as rock mass classification [61], crack damage detection [61], landslide analysis [62], and rock burst prevention [63]. The objective of the established computational framework is to train the proposed CNN model for reliable estimations, in order to reliably and swiftly estimate the strength parameters of intact rock. The computational framework has five steps, including: (a) collecting intact rock, (b) establishing a database of strength parameters by performing laboratory tests, (c) collecting data during drilling work using a DPMA, (d) training the proposed CNN model by using the database, and (e) predicting the cohesion, internal friction angle, and UCS of intact rock (as shown in Figure 9).

The DCNN architecture of the rotary cutting penetration technique is used to train the strength algorithm, in order to enhance the algorithm’s generalization capability [37]. The drilling performance parameters for each type of rock are represented by a two-dimensional (2D) matrix of size 4 × 75, which cannot be used directly for the proposed CNN model. The training data for the CNN model must be an n × n matrix. Drilling performance parameters are converted into 76 × 76 pixel images. The details of the drilling performance parameters are retained, increasing the dimensions of the training data. The following steps are required to obtain the 76 × 76 pixel image, as shown in Figure 10 [63]. The feature elements are selected by the DCNN model and multi-classification problems are avoided in the calculation figure, due to the random pooling method and L-soft max loss. The verification of DCNN training in rock strength prediction can be performed as follows: (1) Orderly put the 18 different 2D matrices of the DPMA parameters into a 4 × 76 matrix. (2) Repeatedly nest the matrix18 times to expand it into a 76 × 76 matrix (seen in Figure 10b). (3) Then, use gray theory to normalize the 76 × 76 matrix, and then convert it into a gray value of the corresponding image (seen in Figure 10c). (4) Assign the gray values to 76 × 76 pixel images using MATLAB R2018a software (see Figure 10d). (5) Finally, obtain the gray-based rock strength database (seen in Figure 10d) [63].

The practical training technique has shown huge potential for field engineering application in the Hanjiang-to-Weihe River Project of China. The drilling tests of several rock types were performed to present the odds from the DCNN in the Daheba Water Conservancy Project. A comparison between the strength parameters (cohesion c, internal friction angel φ, and UCS) of sandstone, limestone, shale, and marble from laboratory measurements and trained model calculations is shown in Figure 11a,b [37]. The calculation error can be controlled within 10%, especially in medium-hard rocks. The results demonstrate that CNN predictions of rock strength exhibit high accuracy. The obtained values of c and φ from the laboratory and DCNN were substituted into the M-C criterion to calculate the UCS, in order to further verify the superiority of the DCNN. Another comparison of UCS between the DCNN, M-C, and DCNN~M-C is shown in Figure 11c [37]. The variance in predictive UCS from the DCNN~M-C is significantly lower than that from the M-C, as shown specifically in

Table 4. R² scores and MSE to evaluate the predicted results [37].

R2			Variance
M-C	DCNN~M-C	DCNN	M-C	DCNN~M-C	DCNN
0.988	0.991	0.998	17.35	13.89	2.14

. The results have shown that the DCNN greatly improves the M-C criterion. However, a deviation in strength prediction occurs in the brittle failure of high-strength rock, due to the strong correlation between the plastic failure of weak rocks and the M-C criterion [64].

4. Prediction of Jointed Rock Mass Quality Using DPMA

4.1. Relationship between Drilling Specific Energy and Discontinuity

The discontinuity characteristics of drilling data have already been considered by many researchers in rock mechanics. This basic relationship was investigated by Li et al. [60]. The regular response of cutting parameters on discontinuity frequency was listed. The mechanism of how drilling systems interact with discontinuities in rock formations was summarized. The uncertainty is attributed to the variability in rock discontinuities arising from the fragile zones within the rock mass (including rock fragments, joints, and cracks). Drilling parameters did not change significantly with increasing borehole depth.

Research indicates that structural anomalies are difficult to be fully represented by core samples alone. The structural anomalies of jointed rock masses have been overlooked. This oversight has an impact on the fracturing and fragmentation processes of rocks, as joints may serve as the initiation points for rock layer fracturing. Several factors influence the mechanical properties of rocks. This includes the geometric shape, distribution of joints, and hydrological conditions [65].

The specific energy of drilling e was defined as a work combination of thrust F_n (N) and torque M (N·m) per unit volume. The discontinuities of jointed rock masses are described. The expression is shown as [17,18]:

$$e=\frac{F_n}{A}+\frac{2\pi M\omega }{A\upsilon }$$

(18)

where A is the contact area between the diamond bit and the rock mass, taking π(D12–D22). F_n is the thrust force. M is the bit torque. ω is the rotation speed. v is the drilling speed.

Calculation errors can be caused by minor variations in individual borehole depths. Errors are mitigated by using weighted averages. e is considered as the following Equation (9):

$$f=\frac{e-e_{min}}{e_{max}-e_{min}}$$

(19)

where f is the revised specific drilling energy. e is the specific drilling work at a single drilling depth. e_min and e_max are the minimum and maximum drilling specific energy at the depth.

The rotary cutting penetration test was performed on a tuff rock mass with a fracture and joint in order to study the response law of drilling specific energy (e or f) to fracture frequency λ [66]. A large number of invisible structural planes in jointed rock masses lead to significant deviations in drilling specific energy, as shown in Figure 12. The revised standard deviation s can be used to describe the response to the discontinuities when the e increases with the drilling depth. The intact and joint fracture sections can be distinguished in depth. s remains generally stable (with values consistently below 0.05), when drilling depth is at the intact rock section. The drilling standard deviation can rapidly increase (reaching s maximum value of 0.3) when the drilling depth reaches the structural planes of the rock mass. Therefore, the drilling specific energy standard deviation s = 0.05 can be considered as the critical value for the intact weak band length range.

4.2. Proposal of New Indicator RQD_d

The definition of the rock quality index RQD was proposed by Adoko et al. [55]. The quality of a rock mass was assessed through on-site surveys of granite. Palmstrom et al. [59] introduced the weighted joint density (WJD) to modify the evaluation of the RQD. The influence of weak areas such as joints, voids, and weathering zones was considered by Araghi et al. [67]. A modified rock quality index MRQD (modified rock quality designation) was proposed. However, the suggested index RQD from Xie et al. [46] has only been confirmed effective for complete rock masses. The introduced indices proposed by Palmstrom et al. [59] and Araghi et al. [67] show the weak correlation with drilling data. A strong correlation between traditional RQD and rotational penetration parameters was demonstrated through a comparison of traditional and improved RQD [68]. The definition of RQD was referenced. A new calculation method has been proposed, which takes into account both the accuracy and adaptability of the DPMA.

The lengths of f₁ and f₂ are considered as the effective values in the calculation of the RQD, taking into account the DPMA parameters. The lengths of f₁ and f₂ are relatively large, as shown in Figure 13. Thus, the RQD_d is related to the range from the starting point to the lengths of core and non-core in the drilling plane. The range is calculated by the suggested method that the sections f₁ and f₂ are modified as the intact sections f₃ and f₅ and joint section f₄, and its value is smaller than the RQD.

The quality evaluation of a rock mass with open and closed fractures is analyzed according to Abbas et al. [69] and He et al. [49], as shown in Figure 14. The RQD_d of tuff rock shows a strong correlation in the calculation length, which is similar to the traditional RQD. The RQD_d value fluctuates little with an increase in the borehole depth (which indicates the quality of the rock mass is better) when the length of a single drilling is 1~3 m.

The demands for rock mass quality assessment cannot be met in modern engineering, due to the limitations of the traditional RQD calculation method for length calculations. The rock quality index RQD_d [31] has been redefined, based on the DPMA, through an analysis of extensive penetration test data. A linear relationship between drilling specific energy and RQD_d (as shown in Figure 15) is obtained by the proposed method. The RQD_d is represented as:

$${\mathrm{RQD}}_d=-\mathrm{Ls}+100$$

(20)

where sis the standard deviation of drilling specific energy, inversely proportional to the integrity of the rock L. The fitting parameter L = 640, and the fitting coefficient R² is 0.964.

The influence of calculation length on the RQD_d has been eliminated by the introduction of s [70]. The new index can distinguish between primary fractures and those caused by damage, owing to the sensitivity of the “s” value to primary fractures in the rock mass [71]. Such rock masses include phyllite, schist and slate. The determination of fracture frequency λ has become the main difficulty in determining the RQD, due to the unclear anisotropy of rock mass mechanical properties [72]. A rotary drilling penetration test was conducted across various rock types, including sandstone, granite, and limestone. A rapid response to encountered fractures of the rock mass is exhibited by the standard deviation of drilling specific energy s during the drilling process (as shown in Figure 16a). The rock mass quality RQD_d obtained, based on the penetration method, needs more data verification. But the unique advantages of this method are unmatched by on-site sampling and indoor testing.

The ratio of the standard deviation of drilling specific energy s₁ to the discontinuity frequency λ is constant [28]. The relationship between λ and s₁can be expressed as follows:

$$\lambda =\zeta s_1$$

(21)

where λ is the discontinuity frequency, ξ is a constant, and s₁is the drilling specific energy. The RQD can be expressed as a function of λ, in accordance with the relationship between the RQD and the fracture frequency λ proposed by Wu et al. [73]:

$$\{\begin{array}{l}\mathrm{RQD}=100e^{-\lambda t}\left(\lambda \mathrm{t}+1\right)\\ \lambda ={\displaystyle \sum _{i=1}^N{\lambda }_{i}cos{\theta }_i}\end{array}$$

(22)

where t is the calculation length, λ_i is the discontinuity frequency normal to set i, θ_i is the angle according to the scanline, and N is the number of discontinuity sets. A further relationship can be obtained between the RQD and λ from Equations (21) and (22), as follows:

$$\mathrm{RQD}=100e^{-0.1\zeta s_1}\left(0.1\zeta s_1+1\right)$$

(23)

The relationship between the RQD and the standard deviation s₁ of the drilling specific energy (in Figure 16b) is estimated based on Equation (23) [48]. The RQD values all reach the value of 100 for granite, limestone, and sandstone when s₁approaches 0. The RQD of granite, limestone, and sandstone decreases by 48.8%, 73.3%, and 93.2%, respectively, when s₁ increases to 400.

5. Determination of Mechanical Parameters of Jointed Rock Mass Based on RQD_d

The mechanical properties of rocks are assessed by researchers, through various rock classification and evaluation criteria based on both field and laboratory measurements. These include the rock mass quality index RQD [74], the rock mass classification index RMR [69,75], the Q system [31,74], the rock mass quality grade RMQR [76], and the GSI [77]. Moreover, numerous empirical relationship models have been proposed to predict rock strength and modulus of deformation, which are related to the aforementioned rock classifications and assessments. A verification model has been proposed to assess the relationship between the modulus ratio of intact rock to rock mass, E_m/E_r, and the RQD [42]. The reduction factor a_E has been introduced to improve the model established by Shen et al. [10]. A linear relationship between E_m/E_r and the RQD, when the RQD > 57, has been well described by the model [42]. The value of a_E remains constant at 0.15 in the model, within an RQD range from 0 to 57. The model fails to encompass all rock types. Therefore, various rock mass classification and evaluation standards were combined with a rotary penetration test. Rock mechanical parameters can be conveniently and efficiently determined [78]. The modulus ratio (E_m/E_r) and RQD relationship model established by He et al. [49] was improved, using the expanded database. This is shown in the following Equation (24):

$$a_E=\frac{E_m}{E_r}={10}^{0.0186\mathrm{RQD}-1.91}$$

(24)

where a_E is reduction factor. E_m and E_r are the deformation modulus of the rock mass and the complete rock, respectively.

The relationship in Equation (21) is substituted into Equation (24) between the fracture frequency λ and the standard deviation s of drilling energy [28]. Equation (24) can be modified as follows:

$$a_E=\frac{E_m}{E_r}={10}^{\frac{\eta g\left(\zeta s_1\right)}{100}-\eta }$$

(25)

where E_m is the deformation modulus of rock mass, E_r is the modulus of elasticity of intact rock, and g(ξs₁) is the RQD function shown in Equation (23). s₁ is the standard deviation of drilling specific work. ζ is a parameter dependent on the rock type. η is a parameter related to e. ζ and E_r can be expressed as eζ/E_r.

Based on numerous rock mass classification systems, the predicted method for rock mass strength has become increasingly mature in recent years [79,80,81,82]. The UCS of the jointed rock mass σ_cm is about 0.33 times that of the complete rock σ_c when the RQD < 70. The σ_cm linearly increases from 0.33 σ_c to 0.8 σ_c, when 70 < RQD < 100. The relationship between σ_cm/σ and E_m/E_r has been studied by rock engineering researchers. The relationship between σ_cm/σ and the RQD was found to approximate the relationship between E_m/E_r and the RQD [28]:

$$\frac{{\sigma }_{cm}}{\sigma }=a_{\sigma }=\frac{E_m}{E_r}=a_E^q$$

(26)

where a_σ is the strength ratio q ∈ [0.61, 0.74].

Equation (25) is substituted into Equation (26), taking q = 0.7. σ_cm/σ can be expressed as:

$$\frac{{\sigma }_{cm}}{\sigma }=a_{\sigma }={10}^{\frac{0.7\eta g\left(\zeta s\right)}{100}-0.7\eta }$$

(27)

The three rock types of granite, limestone, and sandstone were subjected to a rotary penetration test, and the fitting relationship curve obtained is shown in Figure 17. The relationship between the deformation modulus ratio E_m/E_rand the drilling specific energy standard deviation is accurately described by the newly proposed method.

The relationship model covers the entire value range of the RQD between the RQD_d and the strength ratio σ_cm/σ, compared to other relational models [65,74]. The combined effect of changes is considered (as shown in Figure 18) in the specific energy of intact rock and rock boreholes on the strength ratios σ_cm/σ and modulus ratios E_m/E_r.

The contribution of macroscopic heterogeneity to rock mass deformability was assessed [26] using the modified a-λ model (Figure 19). The model was evaluated for three types of rock, with standard deviations ranging from 65 to 150. The deformation moduli (drilling energy) were22.6 (397.4), 9.7 (292.2), and 2.3 GPa (108.3 N/mm²). Values ranging from 0.878 to 0.119 were obtained. The deformation capacity is primarily due to macroscopic fractures, rather than the intact rock blocks. For sandstone, limestone, and granite types, comparable levels of deformability would be expected from macroscopic heterogeneity (the standard deviation of 0 to +∞). The granite rock mass with a population of fracture with the same standard deviation, due to a higher deformation modulus, displayed much higher levels of a than sandstone and limestone of comparable macroscopic heterogeneity. The contribution of intact rock blocks is very prominent for the deformability of rock masses, in the case of complete macroscopic homogeneity (no fractures, standard deviation tends to zero, and the value of a approaches one). The contributions of macroscopic heterogeneity play a leading role in deformability, in the case that the standard deviation tends to +∞ (a value close to one). The deformation capacity of rock masses and individual rock blocks contributes significantly, correlating with the macroscopic heterogeneity induced by rock mass fracturing (standard deviation ranging from 0 to +∞). The macroscopic heterogeneity in fractured rock areas is enhanced, due to the relatively higher degree of rock fragmentation. Rock mass deformation is induced due to the exacerbation of high-level fault sliding, as facilitated by the movement of intact rock blocks along fracture surfaces. Rock mass deformation transitions from an intact block state to a fractured state induced by seismic activity, large-scale engineering excavations, and similar factors, under the influence of drilling energy. The shift from a macroscopically homogeneous state to a predominantly fractured state occurs [83].

The ratios of mechanical parameters based on DPMA data were compared with the classical correlations of the RMR [84], RMQR [85], Q [86], and GSI [87] to verify the accuracy of the proposed method in predicting the mechanical properties of rock masses (as shown in Figure 20). The values from the modified E_m/E_r versus RQD relation are essentially in the middle of those from the other empirical relations (as shown in Figure 20a). The values from the modified relation are essentially within the range of those from the different relations based on the Q, RMR, RMQR, GSI, and RQD, as shown in Figure 20b. The error can be disregarded [68]. The relationship between corrected E_m/E_r and σ_cm/σ_c with the RQD can provide a simple, easy, and rapid approach for estimating rock strength when the drilling energy method is used. Thus, the quality of rock masses can be effectively predicted, with practicality and accuracy being the advantages of the RQDd. The standard deviation data need to be considered for rotary drilling energy when evaluating the RQD_d in drilling methods. The correlation is not influenced by the type of rock [80]. It is an extremely practical tool for engineers working on rock engineering projects.

6. Conclusions and Prospect

The research findings of domestic and international scholars have been comprehensively analyzed through the application of drilling process monitoring technology. The quality and mechanical properties of rock masses have been effectively evaluated. The validity of the RQD_d method has been confirmed, based on drilling energy, through the comparison of fitting values from the H-B model and C-L model, as well as the application of rotary cutting penetration tests. This approach holds significant practical importance in rock engineering design and construction, providing a safeguard for long-term engineering applications.

6.1. Advantages

(1)

Accurate prediction of rock mass quality: The rock mass quality is predicted through drilling data of the rock, and the technique of rotary cutting penetration is used. This technique is practical and easy to measure. The speed, pressure, and direction can be precisely controlled, suitable for various types and hardness of rocks. Precise geological data are obtained.

(2)

New quality indicator (RQD_d): The classification of rock mass RQD_d is established, based on the correlation between standard deviation and the RQD_d. The rock quality index RQD_d is redefined based on the DPMA. The safety of rock engineering is enhanced, compared to the traditional RQD.

(3)

Improved prediction with DCNN: Rotary cutting penetration tests and standard testing are combined, improving the prediction of rock residual strength through the DCNN framework. The prediction error for rock strength decreased from 15% to 10%. The prediction error for UCS decreased to 3.2%. The primary limitations of traditional methods have been overcome.

(4)

Advanced experimental technique: rotary cutting penetration and a DCNN are combined. Comprehensive data acquisition and efficient feature extraction are achieved. The predictive accuracy of rock mechanical parameters is enhanced.

By integrating various rock classification and evaluation standards with rotary drilling penetration tests, the mechanical parameters of rock masses can be conveniently and efficiently determined. The innovative integration of these techniques has been emphasized to enhance the understanding and prediction of rock properties. A detailed discussion of the results has been conducted, emphasizing novelty.

6.2. Limitations

(1)

Structural identification issue: The variations in the rock mass structural features cannot be accurately identified through the drilling signals. The effectiveness of the rotary cutting monitoring technology is diminished.

(2)

Data processing challenges: The volume and complexity of data during drilling are significant. The precise inversion of rock mass parameters presents a formidable challenge. Solutions are established through artificial intelligence and machine learning techniques.

(3)

Calibration errors: The calibration process of rotary penetration technology may introduce errors. The prediction of mechanical parameters in the model is affected.

(4)

Environmental influences: The mechanical parameters of rocks are influenced by environmental factors. The decrease in prediction accuracy will be caused by the disparity between model training conditions and the actual application environment.

6.3. Outlook

(1)

Real-time monitoring of rock mass quality: A field measurement method will be developed based on rotary cutting penetration tests. Rock mass quality will be monitored in real time. Engineering safety and integrity will be enhanced.

(2)

Optimization of parameter calculation models: The calculation method for parameter m_i will be improved, and its validity will be verified. The Hoek–Brown and C-L models will be integrated to refine the method of estimating rock strength.

(3)

Integrating multiple technologies: Drilling monitoring, digital imaging, and acoustic wave detection technologies will be utilized to enhance the accuracy of rock classification and evaluation. This will enhance understanding of complex geological conditions.

(4)

Introducing automated and intelligent technologies: Artificial intelligence will be employed, such as deep convolutional neural networks (DCNNs). Methods for evaluating rock mass quality will be enhanced. Automation and intelligence will be realized.

(5)

Development of a multifunctional drilling monitoring device: The XCY-1 drilling monitoring apparatus is slated for enhancement, aimed at improving its adaptability and data acquisition capabilities. This will provide reliable technical support for underground engineering.