# Exploration on Formation Mechanism of Core Discing Based on Energy Analysis

Authors: Siqi Ye; Jianan Li; Jing Xie; Bengao Yang; Haichun Hao; Fei Li
Journal: Geofluids
 (2022)

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## Abstract

The basic premise of deep in situ fluidized mining is to study the in situ stress state of deep rocks, and coring is one of the basic physical means. However, core discing often occurs in the process of coring. And core discing is one of the symbols of high in situ stress in deep engineering area, and revealing the mechanical response of core stub under different conditions is an important premise to explore the formation mechanism of core discing. Therefore, the effects of in situ stress combination condition, core diameter, and drilling depth on the maximum tensile stress after core stub unloading are discussed by PFC2D discrete element numerical simulation method, and the formation mechanism of core discing is preliminarily explored based on strain energy and dissipated energy. Research shows that in situ stress combination is the most dominant factor of core discing. When the hydrostatic stress increases from 40 MPa to 80 MPa, the maximum tensile stress at the core stub increases by 98.42%. When the horizontal stress is 60 MPa and the axial stress increases from 40 MPa to 100 MPa, the maximum tensile stress at the core stub increases by 53.33%. However, when the axial stress is 60 MPa and the horizontal stress increases from 40 MPa to 80 MPa, the maximum tensile stress at the core stub first increases and then decreases, and there is an inflection point when the horizontal stress is 75 MPa. When the core diameter increases from 8.00 mm to 13.00 mm, the maximum tensile stress at the core stub increases by 1.58 times. When the drilling depth increases from 3.00 cm to 4.00 cm, the maximum tensile stress at the core stub increases by 4.01 times; that is, small diameter cores and cores with large drilling depth are more prone to core discing. The total energy of the system increases with the increase of in situ stress. When the hydrostatic pressure is 80 MPa, the dissipated energy of the system is 2.80 times greater than that when the hydrostatic pressure is 40 MPa. More energy must be dissipated when the core discing occurs under higher in situ stress conditions. It is preliminarily proved that the formation mechanism of core discing is that the tensile cracks extend and penetrate at the core stub, and the core is pulled off to form a core disc, which is reciprocating to produce core discing. The research results are expected to provide a certain reference for understanding the formation mechanism of core discing and provide useful ideas for the related research of discing phenomenon.


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## Body

## 1. Introduction

With the vigorous development of industrial economy all over the world, major social problems such as the depletion of shallow resources and the lack of ground space have made the development and utilization of deep resources and space of the earth become the scientific commanding elevation for all countries in the world to explore first [1–3]. The geological environment of the deep engineering area is far different from the shallow geological environment. Its in situ occurrence environment of “high in situ stress, high temperature, and high seepage pressure” leads to the complexity and variability of the basic mechanical properties and engineering response of the rock [4, 5]. In addition, in deep in situ fluidized mining, the basic premise is to study the in situ occurrence environment of deep rocks [6], and the common physical means is borehole coring. However, core discing often occurs in the process of coring, which is the phenomenon that the core is cracked into discs during deep drilling and coring under the condition of high in situ stress [7]; whether it occurs or not can be the main basis for judging whether the engineering area is a high in situ stress area from the macro level. Therefore, it is necessary to reveal the formation mechanism of deep core discing and explore the factors affecting the phenomenon of core discing, so as to deepen the understanding of deep in situ stress mechanism and provide some reference for the prediction of in situ stress field in deep engineering area.Domestic and foreign scholars have deeply explored the formation mechanism of core discing through theoretical research, engineering-scale in situ experiment, laboratory-scale model experiment, and numerical simulation. In terms of theoretical research, Liu et al. [8] analyzed the fracture expansion mechanism of core discing failure by using the theory of fracture mechanics, indicating that the in situ stress is one of the main factors for the fracture expansion of cracks. Through theoretical analysis, Li et al. concluded that the core discing is mainly controlled by the average value of in situ stress [9]. Matsuki et al. [10] proposed a linear criterion for core discing suitable for cores of any length. In engineering-scale in situ experiment, Zhong et al. [11] conducted in situ tests on the failure mechanism of marble core discs in 2400 m deep underground cavern by drilling cores with different diameters. Zhou [12] studied the occurrence conditions of core discing and the evolution law of core discing with the borehole depth and core diameter. Zheng et al. [13] designed a novel drill bit with an inner conical crown and applied it to the field experiment. The experiment shows that the core discing rate of inner conical crown drill bit is reduced by 41.3% compared with that of rectangular crown drill bit. Kang et al. [14] put forward a method to estimate core stress by using core discing of CCBO method. At the laboratory-scale model test level, Yan et al. [15] compared the damage range and degree of borehole sampling under different stress levels through uniaxial compression test and acoustic emission test. Li et al. [16] obtained the microfracture mechanism of core discing of discs with different diameters by using fracture electron microscope scanning experiment. In terms of numerical simulation, Hu et al. [17] used ABAQUS to analyze the relationship between internal tensile stress of core and in situ stress, drilling depth, and core diameter during drilling process and revealed the core discing mechanism. Corthésy and Leite [18] used FLAC2D to carry out numerical simulation of core discing under different in situ stress combinations. The results show that core discing may involve only tensile failure, only shear failure, and the combination of tensile failure and shear failure. Some scholars [19] studied the influence of different in situ stresses on the unit safety of core potential failure surface through numerical simulation. Jiang and Zeng [20] studied the influence of original stress on core discing by numerical simulation and obtained the characteristics of core discs.In summary, scholars have discussed the formation mechanism of core discing from the aspects of theoretical research, engineering-scale in situ experiment, laboratory-scale model experiment, and numerical simulation and achieved fruitful results. However, few scholars combine energy with core discing in the existing research. In this paper, PFC2D is used to simulate the phenomenon of core discing, the effects of different in situ stress combinations, core diameter, and drilling depth on core discing are discussed, and the changes of maximum tensile stress at core stub after unloading are analyzed; then, the formation mechanism of core discing is preliminarily explored based on energy, hoping to provide a useful reference for the related research of core discing.


## 2. Introduction of the Core Discing and Model Construction

### 2.1. Summary of Core Discing Characteristics

Core discing is a common rock failure phenomenon in deep and high in situ stress areas. Core discing has occurred to varying degrees in Forsmark nuclear power plant in Sweden and Ertan, Yingxiuwan, Jinping, Baihetan, Laxiwa, and other hydropower projects in China, as well as Jinchuan, Huize, and other mining areas [16, 21, 22], as shown in Figure 1. Because the geometric shape of fracture surface of rock discs is mainly affected by different in situ stress conditions, drilling tool shapes, and geological conditions, it tends to be diversified, including lamp shape, saddle shape, and petal shape. According to the stress state, it can be divided into three shapes [23–25]. In normal fault stress regime SV>SH>Sh, the geometry of fracture surface of rock discs tends to petal shape. In thrust fault stress regime SH>Sh>SV, the geometry of fracture surface of rock discs tends to be flat section or saddle shape. In strike-slip fault stress regime SH>SV>Sh, the geometry of fracture surface of rock discs tends to petal-centerline shape.Figure 1
Typical core discs of Jinping marble at different depths. (a) Depth 1400 m. (b) Depth 1800 m. (c) Depth 2400 m.
(a)(b)(c)Many studies [17, 18, 22, 26] have shown that the core discing is mainly due to the maximum tensile stress generated during unloading, exceeding the tensile strength; that is, tensile failure is the main mechanism of core discing, and it is considered that the study of the stress mechanism of the residual core stub after drilling and coring is of great significance to the study of core discing. Gao et al. [27] concluded that under the excavation disturbance in the hydrostatic state, the extreme value of the maximum tensile stress at the core stub presents a saddle distribution. Matsuki et al. and Zhang et al. [10, 22] showed that only when the direction of tensile stress generated at the core stub is parallel to its axis after stress relief, and the tensile stress is greater than its own tensile strength, can the phenomenon of core discing occur. Hu et al. [17] and Liu et al. [8] focused on the stress mechanism of the core stub after drilling and coring, indicating that the maximum tensile stress always appears at the core stub. Lu et al. [7] used numerical simulation to explore the location where tensile failure may occur at the core stub under different in situ stress combinations and obtained the conclusion that tensile failure may expand from the edge of the core stub. Therefore, the core stub is taken as the research object to monitor the change of the maximum tensile stress after borehole coring unloading and the energy change of the process of drilling core, in order to explore the formation mechanism of core discing.


### 2.2. Model Establishment and Parameter Selection

PFC2D is a discrete element simulation software based on Cundall’s definition, also known as particle flow method. The software can accurately predict the mechanical response of the model system under various load excitations. At present, it is mainly used in the field of geotechnical engineering. A two-dimensional numerical model of 10cm×10cm×10cm was established by PFC2D, as shown in Figure 2. PFC2D is used to set different in situ stress conditions in the x and y directions of the model as stress boundary conditions. And the parallel bonding model is adopted as the particle constitutive model in PFC2D, which can reflect the mechanical properties of rock. The basic macroparameters of rock refer to the borehole core of 1# adit of Jinping underground laboratory phase II project in Reference [7]. The rock meso- and micromechanical parameters calibrated by PFC2D are shown in Table 1. In Figure 2, a is the side length of the square model, d is the cutting seam width of drilling tool, D is the core diameter, and h is the drilling depth. The drilling coring simulation is carried out by deleting particles step by step to further study the mechanical response of the core stub under different drilling coring conditions.Figure 2
Geometric model of drilling core.Table 1
Micromechanical parameters of PFC2D calculation model.
ParametersValueMinimum particle radius (m)2.5×10−4Maximum particle radius (m)3.75×10−4Elastic modulus (GPa)22.00Particle stiffness ratio (kn/ks)2.5Particle friction coefficient0.5Parallel bond elastic modulus (GPa)22.00Parallel bond stiffness ratio (kn∗/ks∗)2.5Parallel bond tensile strength (MPa)58.50Parallel bond cohesion (MPa)90.00Parallel bond friction angle30.00Particle density (kg/m3)2750


### 2.3. Selection of Drilling Simulation Conditions

The drilling simulation conditions taken were as follows:(1)
Working conditions of different in situ stress combinations. In situ stress environment is one of the important factors causing core discing. It is necessary to explore the in situ stress combination that may produce core discing. According to the research statistics, the average stress is in the range of 8.9~48.7 MPa [9], and the core discing may occur at the dam site of Laxiwa Hydropower Station. As early as the in situ stress measured at the Forsmark nuclear power plant was σ1=65.9MPa and σ2=29.57MPa and at the Ertan Hydropower Station was σ1=29.57MPa and σ2=16.81MPa, the core discing appeared [28]. Therefore, a variety of complex in situ stress combination environments are tried to be selected, combined with PFC2D particle flow software to preliminarily reveal the mechanical mechanism of core discing. Five hydrostatic pressure conditions (conditions 1~5), five kinds of fixed horizontal stress and different axial stress working conditions (conditions 6~10), and five fixed axial stresses and different horizontal stress working conditions (conditions 11~15) (Table 2) are used as the stress boundary conditions of the model(2)
Working conditions of different core diameters. In order to study the influence of core diameter on core discing, PFC2D was used to simulate the effects of core diameters of 8.00 mm, 9.00 mm, 10.00 mm, 11.00 mm, 12.00 mm, and 13.00 mm on core discing. The in situ stress combination is the most conducive to the core discing among the different in situ stress conditions, which is σV=σH=80MPa. The drilling depth and cut width are shown in Table 2(3)
Working conditions of different drilling depths. In order to study the influence of drilling depth on core discing, PFC2D was used to simulate the influence of drilling depths of 3.00 cm, 3.20 cm, 3.40 cm, 3.60 cm, 3.80 cm, and 4.00 cm. The in situ stress combination is the most conducive to the core discing among the different in situ stress conditions, which is σV=σH=80MPa. The core diameter and kerf width are shown in Table 2Table 2
Different in situ stress combination conditions.
ConditionsAxial stressσV (MPa)Horizontal stressσH (MPa)Core diameterD (mm)Drilling depthh (cm)Kerf widthd (cm)1404010.005.000.402505010.005.000.403606010.005.000.404707010.005.000.405808010.005.000.406406010.005.000.407506010.005.000.408606010.005.000.409706010.005.000.4010806010.005.000.4011604010.005.000.4012605010.005.000.4013606010.005.000.4014607010.005.000.4015608010.005.000.4016609010.005.000.40176010010.005.000.40


## 2.1. Summary of Core Discing Characteristics

Core discing is a common rock failure phenomenon in deep and high in situ stress areas. Core discing has occurred to varying degrees in Forsmark nuclear power plant in Sweden and Ertan, Yingxiuwan, Jinping, Baihetan, Laxiwa, and other hydropower projects in China, as well as Jinchuan, Huize, and other mining areas [16, 21, 22], as shown in Figure 1. Because the geometric shape of fracture surface of rock discs is mainly affected by different in situ stress conditions, drilling tool shapes, and geological conditions, it tends to be diversified, including lamp shape, saddle shape, and petal shape. According to the stress state, it can be divided into three shapes [23–25]. In normal fault stress regime SV>SH>Sh, the geometry of fracture surface of rock discs tends to petal shape. In thrust fault stress regime SH>Sh>SV, the geometry of fracture surface of rock discs tends to be flat section or saddle shape. In strike-slip fault stress regime SH>SV>Sh, the geometry of fracture surface of rock discs tends to petal-centerline shape.Figure 1
Typical core discs of Jinping marble at different depths. (a) Depth 1400 m. (b) Depth 1800 m. (c) Depth 2400 m.
(a)(b)(c)Many studies [17, 18, 22, 26] have shown that the core discing is mainly due to the maximum tensile stress generated during unloading, exceeding the tensile strength; that is, tensile failure is the main mechanism of core discing, and it is considered that the study of the stress mechanism of the residual core stub after drilling and coring is of great significance to the study of core discing. Gao et al. [27] concluded that under the excavation disturbance in the hydrostatic state, the extreme value of the maximum tensile stress at the core stub presents a saddle distribution. Matsuki et al. and Zhang et al. [10, 22] showed that only when the direction of tensile stress generated at the core stub is parallel to its axis after stress relief, and the tensile stress is greater than its own tensile strength, can the phenomenon of core discing occur. Hu et al. [17] and Liu et al. [8] focused on the stress mechanism of the core stub after drilling and coring, indicating that the maximum tensile stress always appears at the core stub. Lu et al. [7] used numerical simulation to explore the location where tensile failure may occur at the core stub under different in situ stress combinations and obtained the conclusion that tensile failure may expand from the edge of the core stub. Therefore, the core stub is taken as the research object to monitor the change of the maximum tensile stress after borehole coring unloading and the energy change of the process of drilling core, in order to explore the formation mechanism of core discing.


## 2.2. Model Establishment and Parameter Selection

PFC2D is a discrete element simulation software based on Cundall’s definition, also known as particle flow method. The software can accurately predict the mechanical response of the model system under various load excitations. At present, it is mainly used in the field of geotechnical engineering. A two-dimensional numerical model of 10cm×10cm×10cm was established by PFC2D, as shown in Figure 2. PFC2D is used to set different in situ stress conditions in the x and y directions of the model as stress boundary conditions. And the parallel bonding model is adopted as the particle constitutive model in PFC2D, which can reflect the mechanical properties of rock. The basic macroparameters of rock refer to the borehole core of 1# adit of Jinping underground laboratory phase II project in Reference [7]. The rock meso- and micromechanical parameters calibrated by PFC2D are shown in Table 1. In Figure 2, a is the side length of the square model, d is the cutting seam width of drilling tool, D is the core diameter, and h is the drilling depth. The drilling coring simulation is carried out by deleting particles step by step to further study the mechanical response of the core stub under different drilling coring conditions.Figure 2
Geometric model of drilling core.Table 1
Micromechanical parameters of PFC2D calculation model.
ParametersValueMinimum particle radius (m)2.5×10−4Maximum particle radius (m)3.75×10−4Elastic modulus (GPa)22.00Particle stiffness ratio (kn/ks)2.5Particle friction coefficient0.5Parallel bond elastic modulus (GPa)22.00Parallel bond stiffness ratio (kn∗/ks∗)2.5Parallel bond tensile strength (MPa)58.50Parallel bond cohesion (MPa)90.00Parallel bond friction angle30.00Particle density (kg/m3)2750


## 2.3. Selection of Drilling Simulation Conditions

The drilling simulation conditions taken were as follows:(1)
Working conditions of different in situ stress combinations. In situ stress environment is one of the important factors causing core discing. It is necessary to explore the in situ stress combination that may produce core discing. According to the research statistics, the average stress is in the range of 8.9~48.7 MPa [9], and the core discing may occur at the dam site of Laxiwa Hydropower Station. As early as the in situ stress measured at the Forsmark nuclear power plant was σ1=65.9MPa and σ2=29.57MPa and at the Ertan Hydropower Station was σ1=29.57MPa and σ2=16.81MPa, the core discing appeared [28]. Therefore, a variety of complex in situ stress combination environments are tried to be selected, combined with PFC2D particle flow software to preliminarily reveal the mechanical mechanism of core discing. Five hydrostatic pressure conditions (conditions 1~5), five kinds of fixed horizontal stress and different axial stress working conditions (conditions 6~10), and five fixed axial stresses and different horizontal stress working conditions (conditions 11~15) (Table 2) are used as the stress boundary conditions of the model(2)
Working conditions of different core diameters. In order to study the influence of core diameter on core discing, PFC2D was used to simulate the effects of core diameters of 8.00 mm, 9.00 mm, 10.00 mm, 11.00 mm, 12.00 mm, and 13.00 mm on core discing. The in situ stress combination is the most conducive to the core discing among the different in situ stress conditions, which is σV=σH=80MPa. The drilling depth and cut width are shown in Table 2(3)
Working conditions of different drilling depths. In order to study the influence of drilling depth on core discing, PFC2D was used to simulate the influence of drilling depths of 3.00 cm, 3.20 cm, 3.40 cm, 3.60 cm, 3.80 cm, and 4.00 cm. The in situ stress combination is the most conducive to the core discing among the different in situ stress conditions, which is σV=σH=80MPa. The core diameter and kerf width are shown in Table 2Table 2
Different in situ stress combination conditions.
ConditionsAxial stressσV (MPa)Horizontal stressσH (MPa)Core diameterD (mm)Drilling depthh (cm)Kerf widthd (cm)1404010.005.000.402505010.005.000.403606010.005.000.404707010.005.000.405808010.005.000.406406010.005.000.407506010.005.000.408606010.005.000.409706010.005.000.4010806010.005.000.4011604010.005.000.4012605010.005.000.4013606010.005.000.4014607010.005.000.4015608010.005.000.4016609010.005.000.40176010010.005.000.40


## 3. Analysis on Stress Characteristics of Core Discing under Different Influencing Factors

### 3.1. Influence of Different In Situ Stress Combination Conditions on Core Discing

The variation of the maximum tensile stress at the unloading stage of the core stub with different stress combination conditions is shown in Figure3. The typical crack distribution diagrams of the model and typical stress cloud pictures under different in situ stress combination conditions are shown in Figures 4 and 5.Figure 3
Variation of the maximum tensile stressσtmax with different in situ stress combinations. (a) Different hydrostatic pressure combinations. (b) Different axial stress combinations. (c) Different horizontal stress combinations.
(a)(b)(c)Figure 4
Typical crack distribution diagrams of the model under different stress combinations. (a)σV=σH=50MPa. (b) σV=σH=70MPa. (c) σV=σH=80MPa. (d) σV=50MPa,σH=60MPa. (e) σV=70MPa,σH=60MPa. (f) σV=80MPa,σH=60MPa. (g) σV=60MPa,σH=70MPa. (h) σV=60MPa,σH=90MPa. (i) σV=60MPa,σH=100MPa.
(a)(b)(c)(d)(e)(f)(g)(h)(i)Figure 5
Typical stress cloud pictures of the model under different stress combinations. (a)σV=σH=60MPa. (b) σV=σH=80MPa. (c) σV=50MPa,σH=60MPa. (d) σV=80MPa,σH=60MPa. (e) σV=60MPa,σH=70MPa. (f) σV=60MPa,σH=90MPa.
(a)(b)(c)(d)(e)(f)From Figures3–5, it can be found that there is obvious stress concentration at the core stub. As the hydrostatic pressure increases, the maximum tensile stress at the core stub increases after unloading, and the tensile cracks generated at the core stub also increase. When the hydrostatic pressure increases from 40 MPa to 80 MPa; that is, after increasing 40 MPa, the maximum tensile stress generated at the core stub increases by 98.42%. When the horizontal stress remains unchanged, the maximum tensile stress generated at the core stub after unloading increases with the increase of axial stress, and when the axial stress increases from 40 MPa to 80 MPa, the maximum tensile stress generated at the core stub increases by 53.33%. In the working conditions of group 11~17, when the axial stress remains unchanged, with the increase of horizontal stress, the maximum tensile stress generated after unloading at the core stub first increases and then decreases. When σV=60MPa,σH=70MPa, there is an inflection point in the maximum tensile stress, and then when the horizontal stress continues to increase, the maximum tensile stress decreases, which may lead to the development of the core stub in a direction that is not conducive to the generation of core discing. Under different in situ stress combination conditions, tensile cracks are developed in the hole wall and core stub and mainly distributed in the core stub, which is tensile failure. With the increase of stress level, the tensile cracks at the core stub increase and gradually penetrate the core, resulting in core discing. Figure 4 shows that the tensile crack distribution at the core stub has a certain width, and Figure 4(i) shows that the tensile crack distribution at the core stub is concave, and the crack penetration makes it cup-shaped concave fracture.It can be seen that core drilling can release the stress of the core in the three-dimensional compression state instantaneously, and stress concentration often occurs at the core stub and produces tensile stress parallel to the axial direction, that is, consistent with the drilling direction. In the process of core drilling, instantaneous unloading makes the tensile stress in some parts of the core greater than the tensile strength and then leads to core discing. Through comprehensive analysis of the maximum tensile stress and tensile crack distribution at the core stub, it is found that the core is more prone to core discing under high in situ stress. Therefore, it is speculated that the corresponding core discing formation mechanism is that with the cyclic advancement of the core drilling process, a stress concentration area is formed at the core stub and an axial tensile stress pointing to the top of the core is generated. The tensile cracks extend and penetrate from the core stub, and the core is pulled off to form another core disc, so as to reciprocating, resulting in the core discing.


### 3.2. Influence of Different Core Diameters on Core Discing

The variation of the maximum tensile stress with core diameter in the unloading stage of core stub is shown in Figure6. The typical crack distribution diagrams of the model and typical stress cloud pictures are shown in Figures 7 and 8. By analyzing the maximum tensile stress state of core stub with different core diameters, it is found that the maximum tensile stress produced at core stub after unloading decreases with the increase of core diameter. Among them, when D=8.00mm, the maximum tensile stress is 9.86 MPa, which is 2.58 times that when the diameter is 13.00 mm. According to the analysis of Figures 7 and 8, it can be seen that stress concentration will also occur at the core stub, and the tensile cracks are mainly distributed at the core stub. With the decrease of core diameter, the tensile cracks at the core stub gradually increase until penetration. Therefore, for the same in situ stress field and the same lithology, the failure tensile stress of small-diameter core is greater, and the probability of core discing is greater. This conclusion is consistent with the conclusion in Reference [17].Figure 6
Variation of the maximum tensile stressσtmax with different core diameters.Figure 7
Typical crack distribution diagrams of the model under different core diameters. (a)D=8.00mm. (b) D=10.00mm. (c) D=13.00mm.
(a)(b)(c)Figure 8
Typical stress cloud pictures of the model under different core diameters. (a)D=9.00mm. (b) D=12.00mm.
(a)(b)


### 3.3. Influence of Different Drilling Depths on Core Discing

The variation of the maximum tensile stress with drilling depth in the unloading stage of core stub is shown in Figure9. The typical crack distribution diagrams of the model and typical stress cloud pictures are shown in Figures 10 and 11. Figures 9 and 11 show that no matter what the drilling depth is, there will be stress concentration at the core stub, and the maximum tensile stress generated at the core stub after unloading increases with the increase of drilling depth. When the drilling depth increases from 3.00 cm to 4.00 cm, the maximum tensile stress at the core stub increases by 4.01 times. It can be seen from the analysis of Figure 10 that the number of tensile cracks concentrated at the core stub increases with the increase of drilling depth, and it can be clearly seen from Figure 10 that the tensile cracks begin to expand from the outer edge of the core stub. With the deepening of drilling, the tensile cracks expand from the outer edge to the center of the core stub, resulting in the final core discing. Therefore, for the same in situ stress field and the same lithology, the core with larger drilling depth can achieve greater failure tensile stress, and the probability of core discing is greater. As shown in Figure 1, when the buried depth of Jinping marble increases from 1400 m to 2800 m, the thickness of core discs decreases significantly; that is, the greater the drilling depth, the more obvious the core discing. This conclusion is consistent with that in Reference [16].Figure 9
Variation of the maximum tensile stressσtmax with different drilling depths.Figure 10
Typical crack distribution diagrams of the model under different drilling depths. (a)h=3.40cm. (b) h=3.80cm. (c) h=4.00cm.
(a)(b)(c)Figure 11
Typical stress cloud pictures of the model under different drilling depths. (a)h=3.00cm. (b) h=4.00cm.
(a)(b)


## 3.1. Influence of Different In Situ Stress Combination Conditions on Core Discing

The variation of the maximum tensile stress at the unloading stage of the core stub with different stress combination conditions is shown in Figure3. The typical crack distribution diagrams of the model and typical stress cloud pictures under different in situ stress combination conditions are shown in Figures 4 and 5.Figure 3
Variation of the maximum tensile stressσtmax with different in situ stress combinations. (a) Different hydrostatic pressure combinations. (b) Different axial stress combinations. (c) Different horizontal stress combinations.
(a)(b)(c)Figure 4
Typical crack distribution diagrams of the model under different stress combinations. (a)σV=σH=50MPa. (b) σV=σH=70MPa. (c) σV=σH=80MPa. (d) σV=50MPa,σH=60MPa. (e) σV=70MPa,σH=60MPa. (f) σV=80MPa,σH=60MPa. (g) σV=60MPa,σH=70MPa. (h) σV=60MPa,σH=90MPa. (i) σV=60MPa,σH=100MPa.
(a)(b)(c)(d)(e)(f)(g)(h)(i)Figure 5
Typical stress cloud pictures of the model under different stress combinations. (a)σV=σH=60MPa. (b) σV=σH=80MPa. (c) σV=50MPa,σH=60MPa. (d) σV=80MPa,σH=60MPa. (e) σV=60MPa,σH=70MPa. (f) σV=60MPa,σH=90MPa.
(a)(b)(c)(d)(e)(f)From Figures3–5, it can be found that there is obvious stress concentration at the core stub. As the hydrostatic pressure increases, the maximum tensile stress at the core stub increases after unloading, and the tensile cracks generated at the core stub also increase. When the hydrostatic pressure increases from 40 MPa to 80 MPa; that is, after increasing 40 MPa, the maximum tensile stress generated at the core stub increases by 98.42%. When the horizontal stress remains unchanged, the maximum tensile stress generated at the core stub after unloading increases with the increase of axial stress, and when the axial stress increases from 40 MPa to 80 MPa, the maximum tensile stress generated at the core stub increases by 53.33%. In the working conditions of group 11~17, when the axial stress remains unchanged, with the increase of horizontal stress, the maximum tensile stress generated after unloading at the core stub first increases and then decreases. When σV=60MPa,σH=70MPa, there is an inflection point in the maximum tensile stress, and then when the horizontal stress continues to increase, the maximum tensile stress decreases, which may lead to the development of the core stub in a direction that is not conducive to the generation of core discing. Under different in situ stress combination conditions, tensile cracks are developed in the hole wall and core stub and mainly distributed in the core stub, which is tensile failure. With the increase of stress level, the tensile cracks at the core stub increase and gradually penetrate the core, resulting in core discing. Figure 4 shows that the tensile crack distribution at the core stub has a certain width, and Figure 4(i) shows that the tensile crack distribution at the core stub is concave, and the crack penetration makes it cup-shaped concave fracture.It can be seen that core drilling can release the stress of the core in the three-dimensional compression state instantaneously, and stress concentration often occurs at the core stub and produces tensile stress parallel to the axial direction, that is, consistent with the drilling direction. In the process of core drilling, instantaneous unloading makes the tensile stress in some parts of the core greater than the tensile strength and then leads to core discing. Through comprehensive analysis of the maximum tensile stress and tensile crack distribution at the core stub, it is found that the core is more prone to core discing under high in situ stress. Therefore, it is speculated that the corresponding core discing formation mechanism is that with the cyclic advancement of the core drilling process, a stress concentration area is formed at the core stub and an axial tensile stress pointing to the top of the core is generated. The tensile cracks extend and penetrate from the core stub, and the core is pulled off to form another core disc, so as to reciprocating, resulting in the core discing.


## 3.2. Influence of Different Core Diameters on Core Discing

The variation of the maximum tensile stress with core diameter in the unloading stage of core stub is shown in Figure6. The typical crack distribution diagrams of the model and typical stress cloud pictures are shown in Figures 7 and 8. By analyzing the maximum tensile stress state of core stub with different core diameters, it is found that the maximum tensile stress produced at core stub after unloading decreases with the increase of core diameter. Among them, when D=8.00mm, the maximum tensile stress is 9.86 MPa, which is 2.58 times that when the diameter is 13.00 mm. According to the analysis of Figures 7 and 8, it can be seen that stress concentration will also occur at the core stub, and the tensile cracks are mainly distributed at the core stub. With the decrease of core diameter, the tensile cracks at the core stub gradually increase until penetration. Therefore, for the same in situ stress field and the same lithology, the failure tensile stress of small-diameter core is greater, and the probability of core discing is greater. This conclusion is consistent with the conclusion in Reference [17].Figure 6
Variation of the maximum tensile stressσtmax with different core diameters.Figure 7
Typical crack distribution diagrams of the model under different core diameters. (a)D=8.00mm. (b) D=10.00mm. (c) D=13.00mm.
(a)(b)(c)Figure 8
Typical stress cloud pictures of the model under different core diameters. (a)D=9.00mm. (b) D=12.00mm.
(a)(b)


## 3.3. Influence of Different Drilling Depths on Core Discing

The variation of the maximum tensile stress with drilling depth in the unloading stage of core stub is shown in Figure9. The typical crack distribution diagrams of the model and typical stress cloud pictures are shown in Figures 10 and 11. Figures 9 and 11 show that no matter what the drilling depth is, there will be stress concentration at the core stub, and the maximum tensile stress generated at the core stub after unloading increases with the increase of drilling depth. When the drilling depth increases from 3.00 cm to 4.00 cm, the maximum tensile stress at the core stub increases by 4.01 times. It can be seen from the analysis of Figure 10 that the number of tensile cracks concentrated at the core stub increases with the increase of drilling depth, and it can be clearly seen from Figure 10 that the tensile cracks begin to expand from the outer edge of the core stub. With the deepening of drilling, the tensile cracks expand from the outer edge to the center of the core stub, resulting in the final core discing. Therefore, for the same in situ stress field and the same lithology, the core with larger drilling depth can achieve greater failure tensile stress, and the probability of core discing is greater. As shown in Figure 1, when the buried depth of Jinping marble increases from 1400 m to 2800 m, the thickness of core discs decreases significantly; that is, the greater the drilling depth, the more obvious the core discing. This conclusion is consistent with that in Reference [16].Figure 9
Variation of the maximum tensile stressσtmax with different drilling depths.Figure 10
Typical crack distribution diagrams of the model under different drilling depths. (a)h=3.40cm. (b) h=3.80cm. (c) h=4.00cm.
(a)(b)(c)Figure 11
Typical stress cloud pictures of the model under different drilling depths. (a)h=3.00cm. (b) h=4.00cm.
(a)(b)


## 4. Exploration on the Formation Mechanism of Core Discing Based on Energy

The calculation method of dissipated energy in rock mass proposed by Xie et al. [29] is shown in Equations (1) and (2). In PFC2D, the sum of the parallel bonding strain energy and the strain energy is defined as the total strain energy Ue [30]. At the same time, PFC2D is used to monitor the total energy U of the model, and the dissipated energy Ud of the model can be obtained from Equation (1). In Equations (1) and (2), U is the total energy input by external force to rock mass, Ud is the dissipated energy, Ue is the releasable strain energy, E¯ is the unloading modulus of elasticity, and ν¯ is the average of Poisson’s ratio. The energy variation diagrams of the model under various working conditions are shown in Figures 12–14, and the variation of dissipated energy under each working condition is shown in Figures 15–17.
(1)U=Ud+Ue,(2)Ue=12E¯σ12+σ22+σ32−2ν¯σ1σ2+σ2σ3+σ3σ1.Figure 12
Energy change diagrams under partial hydrostatic pressure combination conditions. (a)σV=σH=40MPa. (b) σV=σH=60MPa. (c) σV=σH=80MPa.
(a)(b)(c)Figure 13
Energy change diagrams under partial axial stress combination conditions. (a)σV=50MPa,σH=60MPa. (b) σV=70MPa,σH=60MPa. (c) σV=80MPa,σH=60MPa.
(a)(b)(c)Figure 14
Energy change diagrams under partial horizontal stress combination conditions. (a)σV=60MPa,σH=50MPa. (b) σV=60MPa,σH=80MPa. (c) σV=60MPa,σH=100MPa.
(a)(b)(c)Figure 15
Variation diagrams of dissipated energy under different stress combination conditions. (a) Different hydrostatic pressure combinations. (b) Different axial stress combinations. (c) Different horizontal stress combinations.
(a)(b)(c)Figure 16
Variation diagram of dissipated energy under different core diameter conditions.Figure 17
Variation diagram of dissipated energy under different drilling depth conditions.Figures12–14 show that before core drilling, the total energy and total strain energy increase during the stress process of the system. After core drilling, the energy accumulation is caused by stress concentration and the energy dissipation is caused by stress release [31], which indicates that the system is always carrying out energy exchange with the outside world during the whole process from the application of ground stress to the core drilling (unloading effect). It can be seen from Figures 12 and 15(a) that with the increase of hydrostatic pressure, the dissipated energy of the system increases. When σV=σH=40MPa, the dissipated energy of the system after unloading balance is 214.020 J, which is the minimum value of the dissipated energy under hydrostatic pressure conditions. When σV=σH=80MPa, the dissipated energy of the system after unloading balance is 812.622 J, which is 3.80 times that under hydrostatic pressure of 40 MPa. The total strain energy under each working condition is much greater than the dissipated energy. The total strain energy is released in a short time after instant unloading due to core drilling, and it often leads to new cracks in the rock sample. At this time, the equilibrium state of the system is broken. When the energy dissipation tends to be stable, the system is in a new equilibrium state again [32]. According to the analysis of Figures 15(b) and 15(c), with the increase of axial stress and horizontal stress, the dissipated energy of the system increases. But the variation range of dissipated energy under each axial stress condition in Figure 15(b) is small. In Figure 15(c), when the axial stress remains unchanged at 60 MPa and the horizontal stress increases from 40 MPa to 100 MPa, the dissipated energy increases by 6.17 times. It indicates that the influence of axial stress on the change of dissipated energy of the system is far less than that of horizontal stress. Combined with Section 3.1, under the same conditions, the total energy of the system increases with the increase of in situ stress, and at the same time, more energy must be dissipated when the core discing occurs [22]. According to the analysis of Figure 16, the dissipated energy of the system increases with the decrease of core diameter. But the change law of dissipated energy corresponding to each core diameter working condition and the dissipation energy value reached after equilibrium are basically the same, indicating that the influence of core diameter on the change of system dissipated energy is less than that of in situ stress. In Figure 17, the dissipated energy of system increases with the increase of drilling depth. When the drilling depth increases from 3.00 cm to 4.00 cm, the dissipated energy increases by 62.05%, indicating that the influence of drilling depth on dissipated energy of the system is greater than the core diameter.


## 5. Discussion on the Main Controlling Factors of the Formation Mechanism of Core Discing

Through numerical simulation, the effects of different in situ stress combination conditions, core diameter, and drilling depth on core discing are discussed. Combined with the change of system energy, the formation mechanism of core discing is preliminarily explored. It is found that different in situ stress combination conditions have the greatest impact on core discing and are the most dominant factor among the three influencing factors. For different hydrostatic pressure conditions, as shown in Figure15(a), when the hydrostatic pressure increases from 40 MPa to 80 MPa at intervals of 10 MPa, the dissipated energy of the system is 214.016 J, 324.958 J, 492.874 J, 666.141 J, and 812.622 J, and the variation range of dissipated energy is 51.84%, 51.67%, 35.15%, and 21.99%, respectively. For different core diameter conditions, with the change of core diameter, the variation range of dissipated energy of the system is very small (Figure 16). When the drilling depth increases from 3.00 cm to 4.00 cm, that is, when the drilling depth increases by 33.33%, the corresponding dissipated energy increases by 62.05%, while the hydrostatic pressure increases from 40 MPa to 80 MPa; that is, it only increases by 20%, and the corresponding dissipated energy increases by 51.84%. This phenomenon can prove that different in situ stress combination conditions are the most dominant factor among the three influencing factors. In the hydrostatic pressure conditions, when the hydrostatic pressure is 80 MPa, the dissipated energy of the system is the largest, which is 812.622 J, which is 2.80 times larger than that when the hydrostatic pressure is 40 MPa, indicating that under the condition of higher stress, the energy dissipated required for core discing is greater. And in the hydrostatic pressure conditions, when the hydrostatic pressure is 80 MPa, the maximum tensile stress generated at the core stub is 8.84 MPa, which is 1.98 times of the maximum tensile stress generated when the hydrostatic pressure is 40 MPa, indicating that when the hydrostatic pressure is 80 MPa, the core discing is most likely to occur in the hydrostatic pressure condition.


## 6. Conclusions

The geometric model of core drilling is established by using PFC2D, and the effects of different in situ stress combinations, core diameter, and borehole depth on core discing are discussed. Combined with energy, the formation mechanism of core discing is preliminarily explored, and the following conclusions are drawn.
(1)
When the hydrostatic stress increases from 40 MPa to 80 MPa, the maximum tensile stress at the core stub increases by 98.42%. When the horizontal stress is 60 MPa and the axial stress increases from 40 MPa to 80 MPa, the maximum tensile stress at the core stub increases by 53.33%. When the axial stress is 60 MPa and the horizontal stress increases from 40 MPa to 100 MPa, the maximum tensile stress at the core stub first increases and then decreases. When the horizontal stress is 70 MPa, there is an inflection point, and the tensile stress at the core stub reaches the maximum. Combined with the variation law of maximum tensile stress and tensile crack at the core stub after unloading, it shows that the greater the in situ stress is, the easier the core discing is to occur(2)
When the core diameter increases from 8.00 mm to 13.00 mm, the maximum tensile stress at the core stub increases by 1.58 times. When the drilling depth increases from 3.00 cm to 4.00 cm, the maximum tensile stress at the core stub increases by 4.01 times, indicating that small diameter cores and cores with large drilling depth are more prone to core discing(3)
Under the same conditions, the total energy of the system increases with the increase of in situ stress. The dissipated energy when the hydrostatic pressure is 80 MPa is 3.80 times higher than that when the hydrostatic pressure is 40 MPa, indicating that more energy must be dissipated when the core discing occurs under higher in situ stress(4)
Different in situ stress combination conditions have the greatest impact on the core discing, which is the most dominant factor among the three influencing factors. When the hydrostatic pressure increases from 40 MPa to 80 MPa, the dissipated energy of the model increases by 2.80 times. For the working conditions of different core diameter and drilling depth, with the change of core diameter and drilling depth, the change range of the dissipated energy of the system is less than that of the in situ stress, which proves that the working conditions of different in situ stress combinations are the most dominant factor(5)
It is speculated that the formation mechanism of core discing is that, with the cyclic advancement of core drilling process, a stress concentration area is formed at the core stub, resulting in axial tensile stress, the crack extends and penetrates from the core stub, and the core is pulled off to form another core disc, so as to reciprocating, resulting in core discing



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*Source: 9719509-2022-03-21.xml*