Experimental Investigation on Anisotropy of Rocks Using Digital Drilling Technology

Abstract

Accurate determination of rock anisotropy is of great significance for analyzing the safety and stability of engineering rock mass. In this paper, uniaxial compression tests are carried out on four kinds of rocks: slate, gneiss, sandstone and shale, to obtain the uniaxial compressive strength of each rock in the different directions. Digital drilling tests are carried out on four kinds of rocks to study the anisotropy of drilling parameters. According to the working principle of the drill bit, its force balance analysis model is established, and the concept of cutting strength ratio is proposed. Using the drilling parameters (drilling depth, drilling time, torque and thrust, etc.) in the different directions for each rock, the interrelationships between them are analyzed. The anisotropy index of rock is defined according to the ratio of cutting strength in different directions of drill parameters, and a new method for judging rock anisotropy is proposed. The results show that the thrust and torque in all directions of the rock increase with the drilling depth. The torque in all directions of the rock has a positive linear relationship with the thrust. The ranking of the anisotropy degree for the four types of rocks is as follows: gneiss > slate > shale > sandstone. The anisotropy results have been validated by an alternative method utilizing uniaxial compressive strength. The determination results are verified by the uniaxial compressive strength of the rocks, and the degree of anisotropy of the four rocks is consistent with the determination results. This method can help engineers analyze the anisotropy of rock, and provide a new idea for studying the integrity and stability of rock mass.

1. Introduction

Particles that make up the rock exhibit shape characteristics such as layers, flakes and blocks during the rock formation process. The difference in particle size and the specific arrangements among the particles cause the mechanical anisotropy in rocks. This phenomenon becomes evident through the varying elastic modulus acquired from identical rock samples when subjected to different loading directions [1]. The anisotropy of rock materials complicates the determination of mechanical properties complex in practical engineering, which places urgent demands for design and construction [2,3,4,5,6]. Many scholars have studied the anisotropy of rock according to the rock strength characteristics. Zhao [7] derived rock strength from diverse orientations using uniaxial compression, triaxial compression and Brazilian splitting tests. A large number of experimental investigations have found that the overall change of strength with the included angle is to first decrease and then increase [7,8,9,10]. There is a lowest value of uniaxial compressive strength when the angle between the lamination and the loading direction is around 30° [7,9,10,11,12,13,14,15]. Moreover, other scholars have also proposed anisotropy coefficients through a dynamic test for measuring longitudinal waves velocity to describe the anisotropy of rock [16,17]

The mechanical anisotropy of rock based on strength parameters is widely accepted by many scholars. However, the determination of mechanical parameters in rocks usually requires time-costing and expensive preparation. The processes of coring, cutting and grinding from rock boreholes to standard specimen are complex and time-consuming, according to the testing requirement from ISRM (2007). Such laboratory methods provide limited rock in situ information and cannot reflect the engineering properties of rock masses [18,19].

Digital drilling technology have been used as an effective method to determine the mechanical parameters of rocks for nearly 50 years [18,20,21,22]. This in situ method has the characteristics of continuous measurement, no sampling and simple operation [19]. Technicians can predict the strength of rock masses from the drilling parameters recorded by the sensor. Researchers have established several analytical models based on the force and energy balance of the drilling process in recent years, aiming to improve the accuracy of digital drilling method in predicting rock mechanical parameters. Nakajima and Kinoshita [23] have derived the functional relationship of drilling data by considering the fracture zone [24] based on the force balance between the drill bit and the rock. Kalantari [25] has developed an analytical model for estimating rock strength parameters using T-shaped drag bits. Munoz [20,26] obtained a fitted relationship between the rock brittleness and the uniaxial compressive strength based on the energy balance from the cutting tests [22]. Based on digital drilling technology, an analytical model of the relationship between rock internal friction angle and drilling parameters was developed by He et al. [27]. Correspondingly, a method for predicting rockburst proneness in advance is proposed. Wang [28] carried out the digital drilling test to deduce the relationship between the cutting energy and the drilling parameters by referring to the energy analysis method. Using the results of digital drilling tests, DP-_c model is developed by Jiang [18] to accurately obtain the uniaxial compressive strength of rock. Nishimatsu [29] believed that no plastic phenomenon would occur in the cutting process of rock, and its cutting breakage was brittle failure. Based on Mohr–Coulomb failure criterion, he established the shear model of rock cutting. Warren [30] proposed a drilling model based on theoretical concepts and experimental data to show the relationship between various parameters to control the mechanical speed. Hareland [31] obtained the compressive strength of the rock through this drilling model. Hareland and Hoberock [32] built a modified model based on this model, but the model parameters were not easy to determine. Moreover, a large number of experimental and numerical results confirmed that drilling performances are closely related to rock mechanical properties [32,33,34]. Through the in situ evaluation of mechanical properties of rock mass, digital drilling method has shown a practical application for determining engineering properties of rock mass, such as identification of structural planes, reinforcement of potential sliding face and stable analysis of tunneling excavation [8,34]. The above scholars have done detailed research on drilling parameters and have new understanding for the changes of drilling parameters, which provide substantial reference for engineering construction. At present, most of the research combined with digital drilling technology mainly focuses on the field of rock mechanics parameter determination or rock burst tendency prediction. However, the anisotropy of rock has a significant impact on the construction safety. It is also important to reflect the anisotropy of rock by studying the change in the drilling parameters. Some scholars have been committed to the theoretical analysis and research of anisotropy of rock drill-ability in mining engineering for a long time and have made some achievements [35,36,37].

In view of the promising application of digital drilling technology in the field of rock mechanics, authors and members of the research team used a newly developed indoor digital drilling test system for rock digital drilling to carry out a rock digital drilling test, aiming to use digital drilling technology to analyze rock anisotropy. First, four different types of rock were selected and drilled in different directions. By analyzing the characteristics and differences of drilling parameters in different directions (drilling depth, drilling time, torque and thrust, etc.), it is preliminarily determined that there is a response relationship between rock anisotropy and drilling parameters during a drilling test. Secondly, according to the working principle of drill bit, the balance analysis model of the drill bit is established, and the concept of cutting strength ratio of rock is proposed. A new method to determine the anisotropy of rock is proposed by defining the anisotropy index by the cutting intensity ratio of rock. Finally, uniaxial compression test is carried out to verify the reliability of rock anisotropy index by using uniaxial compression strength. This paper uses digital technology to study the anisotropy of rock from the angle of cutting strength ratio, which provides insight for the research and development of rock mechanics.

2. Analytical Model

Generally, the rock drilling process is divided into cutting and friction phase, according to the difference in footage per revolution [8]. Both of these stages require the execution of the drilling process. The axial movement of the drill bit needs to maintain the cutting depth and feed rate, while the rotational movement perpendicular to the indentation motion is necessary for rock cutting. These two stages are continuous and rapid processes that need to be considered simultaneously. The entire drilling process is uniform and stable. The force relationships remain constant during this process. Therefore, we assume that the entire motion process can be treated as a static process. In the cutting phase, the torque perpendicular to the axial movement governs the rock failure. In the friction phase, the thrust force causes rock failure in drilling process, since the rock cuttings do not wash away efficiently [38]. Meanwhile, rock failure is mainly manifested by the extrusion and crushing [39,40]. On this basis, the analytical model for drilling force analysis is modified from Kalantari [27], as shown in Figure 1. There are two drilling forces provided from the rig machine: thrust force and torque acting on the rock continuously, which play an important role for rock breaking during drilling. According to the two independent phases, the thrust force F_n and torque F_t have two components with superscript with c and w denoting cutting and friction, respectively:

$$F_n=F_n^c+F_n^w$$

(1)

$$F_t=F_t^c+F_t^w$$

(2)

where $F_n^c$ and $F_n^w$ are the cutting and friction components of the thrust force, and $F_t^c$ and $F_t^w$ are the cutting and friction components of the torque, respectively.

The relationship between these parameters can be expressed:

$$F_n^c=F_t^c\tan \left(\alpha +\theta \right)$$

(3)

$$F_t^w=F_n^w\tan \theta$$

(4)

$${\tau }_o={\sigma }_o\tan {\phi }^{\prime }$$

(5)

where θ is the contact friction angle between the cutting surface of the drill bit and the rock contact surface, φ’ is the friction angle between the compression zone and the intact rock, σ_o is the normal stress in the crushed zone and τ_o is the shear stress acting on the fracture surface from the crushed zone.

When the drilling bit initially intrudes the rock, a crushed zone quickly forms. As the drilling bit continues to penetrate, the original crushed zone is squeezed into small fragments. Meanwhile, the contact area between the rock and the bit breaks along the potential fracture surface to generate rock chips. Friction occurs between the crushed zone and the chip to transfer the drilling load. Then, a new fracture zones is created. By considering the crushed zone, the cutting components of thrust force and torque are calculated [25]:

$$F_n=A{\sigma }_o\left(\tan \alpha +\tan {\phi }^{\prime }\right)$$

(6)

$$F_t=A{\sigma }_o\left(1+\tan \alpha \tan {\phi }^{\prime }\right)$$

(7)

where A is the vertical cross-sectional area and a is the geometric parameter of the drill bit. According to Equations (6) and (7), σ_o and τ_o are respectively:

$${\sigma }_o=\frac{F_t^c-\tan a{F}_n^c}{A-A{\tan }^2\alpha }$$

(8)

$${\tau }_o=\frac{F_n^c-\tan a{F}_t^c}{A-A{\tan }^2\alpha }$$

(9)

At the contact surface between the broken zone and the intact part of the rock, the normal stress σ and shear stress τ in the broken zone can be calculated:

$$\sigma ={\sigma }_o{\sin }^2\psi -{\tau }_o\cos \psi \sin \psi$$

(10)

$$\tau ={\tau }_o{\sin }^2\psi +{\sigma }_o\cos \psi \sin \psi$$

(11)

where Ψ is the rock fracture angle.

The derivative of Equations (3)–(17) can obtain the minimum value of σ_o, and the value of Ψ can be calculated:

$$\frac{\partial {\sigma }_o}{\partial \psi }=0$$

(12)

$$\psi =\frac{\pi }{4}-\frac{{\phi }^{\prime }+\phi }{2}$$

(13)

According to Equations (8) and (9), normal stress σ_o is critical to establish the analytical model. The stress state in the crushed zone is assumed to satisfy the M-C criterion. Thus, σ_o is calculated:

$${\sigma }_o=\frac{2C\cos \left({\phi }^{\prime }-\phi \right)}{1-\tan \left({\phi }^{\prime }-\phi \right)\left(1-\sin \left({\phi }^{\prime }-\phi \right)\right)}\times \frac{1}{1+\tan \phi \tan {\phi }^{\prime }}$$

(14)

where C is the cohesion of the rock and φ is the internal friction angle of the intact rock. The friction angle φ’ in crushed zone can be calculated [25]:

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

(15)

After some mathematical calculation, the relationship between $F_n^c$ and F^c is simplified:

$$F^c=\frac{F_n^c}{\sin (a+\theta )}$$

(16)

Substituting Equations (3)–(15) into Equation (16), the cutting force F^c is obtained:

$$F^c=\frac{2C}{1-\tan \left({\phi }^{\prime }-\phi \right)\left(1-\sin \left({\phi }^{\prime }-\phi \right)\right)}\times \frac{A\left(\tan a+\tan {\phi }^{\prime }\right)}{\left(1+\tan \phi \tan {\phi }^{\prime }\right)\sin \left(a+\theta \right)}$$

(17)

The rock failure is caused by the cutting force during the drilling process. An indicator for describing the cutting strength of rock is defined:

$$S_c=F^c/A=\frac{2C}{1-\tan \left({\phi }^{\prime }-\phi \right)\left(1-\sin \left({\phi }^{\prime }-\phi \right)\right)}\times \frac{\left(\tan a+\tan {\phi }^{\prime }\right)}{\left(1+\tan \phi \tan {\phi }^{\prime }\right)\sin \left(a+\theta \right)}$$

(18)

Based on the Mohr–Coulomb criterion, the unconfined compressive strength (UCS) of the rock is calculated:

$${\sigma }_c=\frac{2C\cos \phi }{1-\sin \phi }$$

(19)

where σ_c denotes the UCS of rock. By giving the geometric parameter a of the drill bit, a = 5° in this paper. The ratio of rock UCS to cutting strength can be calculated:

$$\frac{{\sigma }_c}{S_c}=\frac{1-\tan \left({\phi }^{\prime }-\phi \right)\left(1-\sin \left({\phi }^{\prime }-\phi \right)\right)}{\left(\tan a+\tan {\phi }^{\prime }\right)\left(1-\sin \phi \right)}\times \cos \phi \left(1+\tan \phi \tan {\phi }^{\prime }\right)\sin \left(a+\theta \right)$$

(20)

Combining equations of thrust force and torque, there is a linear correlation between thrust and torque. The F_t/F_n ratio mainly depends on the contact angle θ and the geometric parameter a [25], which is calculated as

$$\frac{F_t}{F_n}=\frac{1}{\tan (a+\theta )}$$

(21)

The relationship between φ and φ’ is introduced [5,17]:

$$\tan \phi =\frac{2}{\pi }\tan {\phi }^{\prime }$$

(22)

By substituting Equation (15) into Equation (22), the rock internal friction angle is calculated:

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

(23)

3. Test Samples and Test Methods

3.1. Test Sample

Four types of rock are selected in this research, slate, gneiss, sandstone and shale (Figure 2). Slate comes from the eastern section of the fold belt of Qinling Mountain. It is cemented by sedimentary grains such as clay and chalk sand, having the characteristics of compactness and low permeability. The sandstone comes from the road project. The main grains in the sandstone are mainly potassium feldspar, and the rock chips are mainly volcanic and volcanic clastic rocks. Its grain shape is sub-circular, with 86% grain content and 14% interstitial content. The shale is taken from the mineralized zone of Qijiang, Chongqing City. Its composition is dominated by clay minerals (kaolinite, hydromica, etc.) and has a distinct thin laminated structure. The gneiss is taken from the Fengxiangling mine in Tongcheng City, Anhui Province, and is characterized by a flow structure with dark and light colored minerals in a metamorphic structure. Its main constituent minerals are quartz, feldspar, hornblende and mica. The scanning electron microscope results of the sample are shown in Figure 3.

To ensure the natural state of cored samples, the sampling area is located at the homogeneous formation above the groundwater table. Weathered sections and rock discontinuity are excluded to minimize the effect of defects on the experimental results. In view of the randomness of strata stratification, the author collected geological data of sampling area under the guidance of engineers and technicians. Through field exploration, exposed rock mass with the same stratification trend and level is selected as the sampling point. In order to ensure the consistency of structural bedding of rock samples in digital drilling test and uniaxial compression test, rocks used in the two kinds of tests in this paper are obtained from rock material in the same area and at the same groundwater level. In order to reduce the difference of mechanical properties of the same kind of rock samples, the samples with cracks and uneven particles are screened out. As shown in Figure 2a, rock samples are obtained in the X, Y and Z directions. A digital drilling test and compressive test are carried out on the same three directions.

The processing of the specimens used for compression test strictly follows the precautions suggested by the ISRM (2007). The cored samples are cut and polished into cylinders of 100 mm in height and 50 mm in diameter (Figure 2b). The specimens used for digital drilling test are machined into cubes with a side length of 50 mm. In order to ensure a uniform contact between the sample and drilling bit, the error of non-parallelism on each end face should not exceed 0.05 mm.

3.2. Test Instruments and Test Method

The test instrument is a WDT-1500 multifunctional material testing machine, and its control system adopts DOLI full-digital servo controller imported from Germany. This test instrument was produced by Changchun city chaoyang test instrument Co., Ltd., Changchun, China. It consists of four systems: numerical control system, acoustic detection system, loading system and shearing system. The computer controls the experiment process by connecting four systems in series. The testing machine can carry out uniaxial and triaxial tests under dynamic and static load conditions. The axial bearing capacity of the testing machine is 1800 kN, the confining pressure is 80 MPa, the axial displacement is 100 mm, the lateral displacement is 5 mm and the loading displacement error is within 0.1%. The testing machine is a rigid dynamic mechanical equipment developed for high-strength materials such as rock and concrete. It has the characteristics of multi-function, high precision, good reliability and stability, which provide a technical guarantee for experimental research. This test is carried out entirely under computer control. Real-time data recording can be achieved by adopting advanced adaptive control methods and post-processing software test. At the same time, the system can directly display the stress–strain curve obtained from the test, accurately reflecting the change of the mechanical properties of the specimen. In this test, the displacement-controlled loading method is adopted, and the loading rate is 0.5 mm/min until the specimen was damaged. All of these experimental procedures were conducted following the guidelines set forth by the ISRM. Through the analysis of the stress–strain curve, the peak strength is taken as the uniaxial compressive strength of the rock in this direction.

Figure 4a shows the digital drilling system of rock mass mechanical parameters. This instrument was developed by the Geotechnical Institute of Xi’an University of Technology. The instrument is mainly composed of six parts: electrical control system, hydraulic system, oil pump transmission system, real-time monitoring system and data acquisition control system, as well as a diamond drill bit with an inner diameter of 16 mm and an outer diameter of 20 mm. Two modes of ordinary drilling and parameter acquisition can be adopted during the operation of the instrument. The normal drilling mode is suitable for the pre-drilling stage before the test depth. The parameter acquisition mode is suitable for the precise acquisition stage of digital drill parameters. The driving parameters are set according to the previous geological exploration report and the digital drilling system automatically operates according to the driving parameters. The loading system and the twisting system operate independently of each other. The source of axial power is manpower. According to the test and monitoring records, the axial loading system can induce a maximum down-pressure of 50 kN, and the axial pressure can be adjusted according to the rock softness and hardness during operation. The torque system consists of a drive motor, transmission gearbox and transmission, providing a maximum torque of 2000 N·m. The drive transmission is divided into 0–6 gears, corresponding to different surrounding rock conditions. Through the mutual cooperation between the various systems, the control in the drilling process is realized. As shown in Figure 4b, the digital drilling system drills the end faces of four kinds of rocks in three directions: x, y and z. During the drilling process, the loading servo motor and the twisting servo motor operate independently. The instrument can accurately measure thrust force F_n, torque F_t and drilling depth d through self-control. In the test, the system takes the rotational speed (w) and drilling speed (v) as the control parameters, and can get the thrust and torque as the drilling response at the same time. The values of thrust and torque change as the drilling depth increases. As the drilling depth increases, the system can automatically save job data in an Excel file. The device has a maximum acquisition capacity of 500 pieces of data per second, which enables it to accurately store hundreds of sets of data.

4. Experimental Results

4.1. Anisotropic Characteristics in Compression Test

Under normal temperature and pressure, the physical properties of four kinds of rocks were measured, and uniaxial compressive strength of each rock in x, y and z directions was obtained through uniaxial compression test. The results are shown in

Table 1. Physical test data and anisotropy index of four kinds of rocks.

Rocks	Direction	H (m)	ρ (g/cm3)	W (%)	V (%)	UCS (MPa)
Slate	X	5.20–5.50	2.83	2.82	2.94	39.1
	Y		2.70	3.67	4.97	24.4
	Z		2.80	3.23	2.28	39.9
Gneiss	X	88.4–88.6	2.94	3.28	1.75	48.9
	Y		2.80	0.47	0.25	146
	Z		2.77	0.29	0.12	205
Sandstone	X	6.30–6.50	2.64	3.02	2.57	32.8
	Y		2.63	3.28	2.17	43.1
	Z		2.71	3.36	3.54	28.5
Shale	X	24.7–24.9	2.66	3.45	2.12	37.7
	Y		2.73	2.57	1.72	51.1
	Z		2.68	2.33	1.06	54.8

.

In Table 1, H represents the sampling depth of rocks; ρ represents the natural rock density; W stands for natural water content of rock; V represents the natural porosity of the rock, UCS represents uniaxial compressive strength of rock.

According to the data in Table 1, the UCS of slate in the X, Y and Z directions are 39.1, 24.4 and 39.9 MPa; the strengths of gneiss in the X, Y and Z directions are: 48.9, 146 and 205 MPa; The strengths of the sandstone in the X, Y and Z directions are: 32.8, 39.1 and 28.5 MPa; The strengths of the shale in the X, Y and Z directions are 37.7, 51.5 and 54.8 MPa, respectively. The results suggest that rock anisotropy exhibits in strength for different rock types. For most rock types, the strength in Z direction was greater than that in the X and Y directions, especially in gneiss. UCS in the Z direction is about 4.2 times and 1.4 times the UCS in the X and Y directions, respectively. Sandstone is an exception, which the directional difference in strength is less than 20%. This indicates an isotropy in sandstone UCS. The failure mode of sandstone in different loading directions has the similar splitting characteristics (see in Figure 5), confirming this phenomenon.

Figure 5 shows the failure mode of the four types of rock sample in X, Y and Z directions. An obvious increase in horizontal displacement is observed when loading directions is parallel to the bedding plane (X and Y direction). Tensile stresses between the bedding plane leads to a gradual expansion of the crack. Correspondingly, the specimen is divided into several independent compression bars, until the rock bar is fractured with the increasing tensile stress. This typical damage mode caused by splitting tension reflects the response of rock strength to direction of the bedding plane. When the compressive load is perpendicular to the bedding plane (Z direction), only one main shear crack penetrates the specimen, which is consistent with that of homogeneous rock material. This shows that the horizontally distributed bedding has little effect on the mechanical characteristics of rock.

Combined with the data in Table 1 and rock failure characteristics in Figure 5, it can be seen that rocks are distributed at different depths of rock layers, resulting in different geo-stress environments for each rock. Because of the different triaxial stress, the particle size and the degree of compaction of rocks in underground are different, which results in different kinds of rocks’ ability to resist failure. The sampling angles of the same lithology are different, and the mineral composition, density, water content, porosity and pore fluid of the rocks are also different. When there are micro-cracks in the bedding of rock, the strength of rock is greatly reduced. When the direction of the compressed rock is perpendicular to the direction of the bedding of the rock, the strength of the rock in this direction is usually greater. The compression direction of the test is parallel to the bedding direction, where the rock strength is usually relatively low.

Compared strength and failure mode of rock in different load directions, rock anisotropy is manifested obviously. When the load direction is perpendicular to the bedding plane, the anisotropy has the least effect on the strength of the rock. Moreover, the failure mode presents the similar anisotropic characteristics to the rock strength.

4.2. Digital Drilling Test Results

Digital drilling tests were carried out on four rocks. The drilling speed v, rotating speed w, drilling time t, depth h, thrust force F_n and torque F_t in the X, Y and Z directions are recorded, as shown in

Table 2. Digital drilling test parameters for four types of rock.

Rocks	Direction	t (s)	v (mm/s)	w (rpm)	h (mm)	Fn (kN)	Ft (kN)
Slate	X	53.9	0.33	42.5	17.8	17.3	16.7
	Y	50.3	0.33	42.5	16.6	17.6	21.0
	Z	55.8	0.33	42.5	18.4	19.4	19.1
Gneiss	X	66.7	0.33	42.5	22.0	32.5	29.5
	Y	58.2	0.33	42.5	19.2	22.2	12.1
	Z	59.4	0.33	42.5	19.0	44.3	19.5
Sandstone	X	60.6	0.33	42.5	20.4	7.38	8.40
	Y	54.5	0.33	42.5	18.1	12.2	11.2
	Z	51.5	0.33	42.5	17.0	9.44	10.1
Shale	X	57.6	0.33	42.5	19.2	12.1	12.4
	Y	60.6	0.33	42.5	20.0	14.3	12.3
	Z	66.1	0.33	42.5	21.8	18.3	13.4

.

The drilling time t for different rock types has a range from 30.3 to 66.1 s. The drilling depth h is from 19.0 to 21.8 mm. The thrust force and torque for four types of rock are different in three directions of X, Y and Z. For sandstone, the cementation among sand particles is weaker than that of other rock types with the thrust force of 7.38–12.2 kN and torque of 8.40–11.2 kN. This cemented characteristic in sandstone is easily broken by the cutter, which requires the small cutting forces. Gneiss has the largest UCS among four types of rock. It is formed by metamorphism of magmatic rocks and sedimentary rocks. The gneiss has a compacted metamorphic structure and a high degree of cementation, which requires large thrust force and torque to break rock. The thrust force arranges from 0 to 44.3 kN, and the torque is between 0 and 29.5 kN. The maximum thrust force in the three directions of slate is between 17.3 and 29.4 kN, and the maximum torque is between 16.7 and 21.0 kN. The maximum thrust in the three directions of shale is between 12.1 and 18.3 kN, and the maximum torque is between 12.3 and 13.4 kN.

The difference in drilling force in the X, Y and Z directions reflected its directional response. This directional characteristics of F_n and F_t are consistent with rock UCS. However, the F_n and F_t have different evolution trend along the borehole. The maximum value of F_n and F_t cannot describe the anisotropy degree. Thus, the drilling parameters are measured continuously in the drilling process. The anisotropy degree of rock in X, Y and Z directions is studied through the evolution of thrust and torque with the increasing drilling depth. The investigation focused on the degree of anisotropy in the X, Y and Z directions of the rock by observing the evolution of thrust and torque with increasing drilling depth.

4.2.1. Thrust Force versus Drilling Depth

The thrust force required for the borehole formation increases with the increasing drilling depth, as shown in Figure 6. This increasing trend is divided into three stages, according to the turning points. The turning points in the curve of thrust force versus drilling depth are related to the contact method between the rock and the bit. The thrust force increases sharply when the drill bit initially contacts the rock. The drilling bit is forced to make complete contact with the rock surface. After reaching the borehole depth of 4.00 mm, the cutter penetrates the rock, marking the beginning of the cutting stage. The thrust force maintains a slow increasing trend to overcome the friction resistance from the accumulation of rock cuttings. This also indicates the steady cutting efficiency. When the drilling depth reaches 16.0 mm, the drill bit completely penetrates the rock. The limitation of the rock sidewall on the rock-breaking effect is enhanced, and the resistance of the bit to break the rock increases. The thrust of the drill bit increases with the increase of the drilling depth, and the increase increases.

Moreover, the mechanical properties of the rock also relate to the thrust force evolution with the drilling depth. Due to the high strength of gneiss in the z-direction, the thrust of the drill bit increases significantly with the drilling depth (Figure 6b). The sand grains are tightly arranged in sandstone. The variation of thrust force with the drilling depth is less differentiated in different directions. There is no obvious turning point identified in the curves of the X and Z directions (Figure 6c).

It can be seen from Figure 6 that the difference in evolution process of thrust force along three directions shows rock anisotropy. The magnitude of the thrust force in the X, Y and Z directions of the four types of rocks is as follows: Slate: Z > X > Y; gneiss: Z > Y > X; sandstone: X > Z > Y; and shale: X > Y > Z. The results show that slate, gneiss and shale require large thrust force along the vertical bedding direction (Z direction). Affected by the bedding distribution, the thrust along the parallel bedding (X and Y directions) directions is discrete (seen in Figure 6a,b,d). The sandstone particles are fine and uniform, and the sample integrity is good. The thrust of the drill bit has nothing to do with the drilling direction of the drill bit but is related to the compactness of the sandstone particles (Figure 6c).

4.2.2. Torque versus Drilling Depth

As shown in Figure 7, the torque increases sharply with the increase of the drilling depth. When the drilling depth reaches similarly 4.00 mm, the front-end blade of the drill bit completely enters the rock. The cutting efficiency is improved. As the drill bit penetrates, the cooling water flow reduces the frictional resistance inside the borehole. The growth trend of the torque is slowed down, and the rock breaking effect is the stable. When the drilling depth reaches 16.0 mm, the drill bit completely penetrates into the rock. The bit is affected by the surrounding confining pressure, and the torque increases continuously. Because the drilling depth is too large, the water flow cannot lubricate the drill bit and the hole wall in time [41]. The rock-breaking resistance increases, and the torque increases with the drilling depth. Differences in rock strength and stiffness at different depths are due to the discrete nature of rock particle composition and internal structure. Therefore, the turning points of bit torque versus drilling depth are located near the region where the bit structure changes, rather than at the exact node [42].

As shown in Figure 7, there is anisotropy in the relationship between the torque in the x, y and z directions of the rock and the variation of the drilling depth. Under the same drilling depth, the overall magnitude of the torque of the four types of rock is as follows: Slate: X > Y > Z; gneiss: X > Y > Z; sandstone: X > Y > Z; and shale: Y > X > Z. The results show that when the drill bit is tested perpendicular to the rock bedding plane (z direction), the required torque is greatest. The torque in the X, Y and Z directions of the slate varies greatly with the drilling depth, and the turning points appear near the depths of 4.00 mm and 16.0 mm (Figure 7a). For the four rock types, gneiss required more torque from the drill bit to be tested (Figure 7b). Due to the uniform particle size of sandstone, when the drill bit breaks the rock, the torque increases steadily with the increase of depth. When the drill bit completely drilled into the rock, the inflection degree of the curve of torque and drilling depth was not obvious (Figure 7c). The torque in the X, Y and Z directions of the shale is the basically same along the entire drilling depth range (Figure 7d).

4.2.3. Thrust and Torque

The representative multi-group drilling parameters recorded by four kinds of rocks are selected to analyze and study the mathematical relationship between torque and thrust. As shown in Figure 8, torque is set as the y-axis and thrust as the x-axis, and a scatter plot of the relationship between the two is drawn. By performing linear fitting on thrust and torque, the fitting equations of the two are obtained (Table 2). The results show that the fitting degrees of the equations are all greater than 90%. The thrust and torque have a good positive linear correlation. Under the same thrust, there are differences in torque in the x, y and z directions of the rock. During the test, the torque subjected to the drill bit increases with the increase of thrust. The increasing trend of torque with thrust has nothing to do with rock lithology and drilling direction.

When the drill bit just intrudes into the rock, the torque and thrust are zero. Therefore, the intercept of the fitting equation corresponding to each rock can be ignored, and the slope of the fitting equation is considered to be the ratio of torque and thrust, namely F_t/F_n. As shown in Equation (11), F_t/F_n = 1/tan(α + θ). According to Equations (10)–(14), the geometric parameter of the drill bit is a = 5°. The rock cutting strength ratios σ_c/S_c in the x, y and z directions of the four kinds of rocks are obtained, as shown in

Table 3. Fitting equation between propulsion and torque and the ratio of cutting strength of four kinds of rocks.

Rocks	Direction	Fitted Equation	R2	Ft/Fn	σc/Sc
Slate	X	y = 0.97x − 0.12	0.99	0.97	2.30
	Y	y = 1.21x + 1.34	0.97	1.21	1.83
	Z	y = 0.94x + 0.01	0.99	0.94	2.32
Gneiss	X	y = 0.95x − 4.27	0.92	0.95	2.61
	Y	y = 0.56x − 0.27	0.98	0.56	5.75
	Z	y = 0.46x − 1.57	0.98	0.46	7.62
Sandstone	X	y = 1.14x + 0.34	0.98	1.14	2.10
	Y	y = 0.97x − 0.09	0.98	0.97	2.43
	Z	y = 1.09x + 0.81	0.96	1.09	1.96
Shale	X	y = 1.02x + 0.02	0.99	1.02	2.25
	Y	y = 0.87x − 0.19	0.99	0.87	2.65
	Z	y = 0.88x − 1.82	0.87	0.88	2.61

.

As shown in Figure 9, the drill bit drilled into the rock from different directions, and the rock cutting strength ratios were different. The cutting strength ratio of slate is the smallest in the y direction, followed by the x direction, and the largest in the z direction. The cutting strength ratio of slate in three directions is between 1.92 and 2.43. The cutting strength ratio of gneiss is the smallest in the x-direction, followed by the y-direction, and the largest in the z-direction. The cutting strength ratio of gneiss in three directions is between 2.40 and 7.28. The cutting strength ratio of sandstone is the smallest in the z direction, followed by the x direction, and the largest in the y direction. The cutting strength ratio of sandstone in three directions is between 2.02 and 2.35. The cutting strength ratio of shale is the smallest in the x-direction, followed by the y-direction, and the largest in the z-direction. The cutting strength ratio of shale in three directions is between 2.23 and 2.65. This suggests that the anisotropy of the cutting strength ratio is largest for gneiss among the rocks. The cutting strength ratio presents the close value for slat, sandstone and shale in two directions, which is considered approximately as transversely isotropy.

5. Discussion

After the above analysis, the digital drilling test is carried out at the three directions of x, y and z. When the drilling depth is the same, there are differences in the thrust and the torque of the drill bit. The drilling parameters of the rock in different directions are different, reflecting the anisotropy of the rock. However, digital drill trials are performed in either direction of the rock. There are many drilling parameter data recorded by monitoring, and a single thrust or torque cannot represent the mechanical properties of the rock in this direction. Based on the linear correlation between torque and thrust, this paper proposes the concept of rock cutting strength ratio by using an analytical model. The test results show that the cutting strength ratio of rock in different directions is also different. Therefore, this paper attempts to analyze rock anisotropy with the rock cutting strength ratio as the criterion.

5.1. Calculation Method of Anisotropy Index

Rock strength at different angles along the bedding plane of the rock can often be used to study its anisotropy. Some scholars calculate the rock anisotropy index by the ratio of the maximum and minimum strength of the rock [43]. However, the mechanical properties of the rock are discrete, and the calculation method does not consider the strength data in all directions of the rock [44]. Other scholars put forward the expression of wave velocity anisotropy index based on the difference of the propagation velocity of shear wave and longitudinal wave in rock to measure the degree of anisotropy of rock [45]. However, calculation methods based on wave velocity are only suitable for measuring the degree of anisotropy in tight rocks. This study describes rock anisotropy as the difference in the ratio of cutting strengths in the three directions of rock x, y and z. In statistics, variance, range or ratio methods are commonly used to describe the dispersion degree of a set of data. Considering the limitation of test data, the ratio method is used to analyze the variation range of cutting intensity ratio in x, y and z directions. The anisotropy index of rock is defined by dividing the ratio of the maximum cutting intensity ratio to the middle value by the ratio of the middle value to the minimum value in three directions. This value represents the range of fluctuation of a set of data. The further the ratio is from 1, the greater the degree of dispersion; the closer the ratio is to 1, the smaller the dispersion [46]. The calculation equation of the anisotropy index is proposed:

$$B=\frac{{({\sigma }_c/S_c)}_{\max }\cdot {({\sigma }_c/S_c)}_{\min }}{{({\sigma }_c/S_c)}_{mid}\cdot {({\sigma }_c/S_c)}_{{}_{mid}}}$$

(24)

where B is the rock anisotropy index, ${({\sigma }_c/S_c)}_{\max }$ represents the maximum value of the cutting strength ratio in the three directions of x, y and z of the rock, ${({\sigma }_c/S_c)}_{mid}$ represents the intermediate value and ${({\sigma }_c/S_c)}_{\min }$ represents the minimum value. In order to check the reliability of the calculation equation of the anisotropy index, the uniaxial compressive strength of the rock in the three directions of x, y and z is substituted into Equation (24):

$$B^{\prime }=\frac{{\sigma }_{\max }\cdot {\sigma }_{\min }}{{\sigma }_{mid}\cdot {\sigma }_{mid}}$$

(25)

where B’ represents the anisotropy index calculated from the rock strength, σ_max represents the maximum value of the uniaxial compressive strength of the rock in the three directions of x, y and z, σ_mid represents the intermediate value and σ_min represents the minimum value.

5.2. Analysis of Rock Anisotropy Degree

Anisotropy index can reflect the degree of anisotropy of rock. The closer the anisotropy index is to 1, the more isotropic the rock is. The farther the anisotropy index is from 1, the more anisotropic the rock tends to be. Substitute the cutting strength ratio and uniaxial compressive strength of slate, gneiss, sandstone and shale into Equation (24) and Equation (25), respectively, to obtain the anisotropy index of each rock.

Macroscopic mechanical properties of rock generally depend on the composition and structure characteristics of the rocks. For the intact rock material, its physical and mechanical properties of anisotropic performance mainly depend on its anisotropy microstructure. According to Figure 10, the anisotropy indices B of the four rocks obtained based on the cutting strength ratio are different. The degree of anisotropy of the rock can be calculated based on how far the anisotropy index of the rock is away from 1. Therefore, the degrees of anisotropy of slate, gneiss, sandstone and shale are 16.0%, 31.0%, 8.00% and 13.0%, respectively. After comparison, the degree of anisotropy of the four kinds of rocks is: gneiss > slate > shale > sandstone. There are also differences in the anisotropy indices $B^{\prime }$ obtained for the four rocks based on uniaxial compressive strength (Figure 10). The degree of anisotropy index away from 1 for slate, gneiss, sandstone and shale are 29.0%, 47.0%, 14.0% and 23.0%, respectively. Therefore, the degree of anisotropy of the four rocks is determined as: gneiss > slate > shale > sandstone. The characteristics of rock composition, sampling depth, water content and porosity are also important reasons for rock anisotropy [47]. The sampling depth of gneiss and slate in this paper is greater than that of shale and sandstone. From the point of view of water content and porosity, in descending order are sandstone, shale, slate and gneiss [46]. Therefore, from the point of view of density and dryness, the analysis from small to large is sandstone, shale, slate and gneiss in turn. Combined with the difference of uniaxial compressive strength on all sides of the four rocks, there are cracks in the gneiss and slate, resulting in greater anisotropy than the other two rocks (shale and sandstone). The results show that the anisotropy of the four rocks by the cutting strength ratio is consistent based on the uniaxial compressive strength of the rock. It is a new research method to analyze rock anisotropy using parameters while drilling. In future research, we intend to explore factors such as confining pressure, triaxial compression tests, moisture content, and elastic modulus concerning rock behavior. We will collect and sort out more rock parameters for demonstration, so as to improve the accuracy of the determination method. It is designed to provide practical assistance to engineers in analyzing the integrity and stability of rock masses.

Many researchers have conducted tests on the anisotropy of rocks using traditional acoustic emission methods. Liu et al. [48] studied the anisotropy of sandstone, while R. Fort et al. [49] conducted acoustic emission tests on rocks such as slate. The comparison of their results with the method proposed in this paper is shown in Figure 11. It can be observed that the trends are consistent with the test results presented in this paper, demonstrating the feasibility of the anisotropy calculation method defined in this study. In fact, the confining pressures have had a profound effect on the mechanical properties of rock including the anisotropy and digital properties of rocks [12]. The proposed method in this paper has a limitation on studying the effect of the confining pressures on the anisotropy of rock, which is going to be studied in the future work.

6. Conclusions

• The uniaxial compression test results show that the mechanical properties of rock are affected by factors such as particle composition, water content and fracture orientation. The direction of the test compression rock is perpendicular to the rock bedding direction, and the rock strength is relatively large. The compression direction is parallel to the bedding direction, and the rock strength is small. The compressive strength of slate in all directions is between 24.4 and 39.9 MPa. The compressive strength of gneiss is between 48.9 and 205 MPa. The compressive strength of sandstone is between 28.5 and 39.1 MPa. The compressive strength of shale is between 37.7 and 54.8 MPa. The strength values of rocks in X, Y and Z directions are different, which reflects the anisotropy of rocks.
• The relationship between drilling depth and bit torque, and between drilling depth and bit thrust was analyzed by digital drilling test. During the drilling process, the thrust and torque required by the drill bit increase with the increase of the drilling depth. At the same drilling depth, there are differences in the torque and thrust required by the drill bit in the x, y and z directions of the rock. The torque increases with the increase of thrust, and the two are linearly related. From the perspective of drilling parameters, it can be judged that the four kinds of rocks have anisotropy.
• According to the correlation between torque and thrust, the concept of cutting strength ratio is proposed by using the analytical model. Analysis of rock anisotropy based on cutting strength ratio. Based on the criterion of anisotropy index A, the anisotropy degree of slate, gneiss, sandstone and shale is 16.0%, 31.0%, 8.00% and 13.0%, respectively. The results show that the anisotropy degree of four kinds of rocks is gneiss > slate > shale > sandstone. The anisotropy index B defined by the uniaxial compressive strength of rocks is used for verification. The anisotropy degree of slate, gneiss, sandstone and shale is 29.0%, 47.0%, 14.0% and 23.0%, respectively. The ranking of anisotropy degree is consistent with the method defined in this paper. The method of analyzing anisotropy degree of rock based on cutting strength ratio is feasible.