Experimental research into the drilling cutting method of rockburst-prone coal under water-rich conditions

Abstract

The drilling cuttings weight index fails to reflect coal’s stress conditions under water-rich environments, potentially undermining the drilling cutting method’s reliability for monitoring and early warning of rockburst risks. We integrated theoretical analysis with triaxial drilling tests to investigate the mechanical evolution, the spatio-temporal dynamics of absolute energy, and the failure modes during the drilling of water-bearing coal specimens. Moreover, we established the critical drilling cuttings weight index for these specimens by analyzing test outcomes and associated weakening coefficients. Results show that: (1) as the moisture content increases, the damage and rupture mode of coal changes from punctate frictional damage between microstructures to interlayer slip, dislocation, and friction of weak structural planes; macroscopically, it is shown as the increasing number of cracks in the horizontal and vertical directions in specimens; (2) The dynamic response frequency of rockburst-prone coal has a positive correlation with the moisture content. The elastic energy storage capacity of water-bearing coal is reduced, dynamic events develop in a shorter period while their frequency increases. In addition, the level of single energy release decreases; (3) With increasing moisture content, damage to boreholes in coal can be divided into two stages: convergence and crack initiation; (4) The deformation and damage range of boreholes is positively correlated with the moisture content. When the moisture contents are 1.4%, 2.3%, and 3.7%, the damage radii of specimens along the center of the boreholes are 2.03, 2.98, and 3.36 times the drilling radius; (5) The weight of drilling cuttings for coal with the moisture content of 3.70% is 2.78–3.48 times that of natural coal; for coal containing 5.60% of water, the weight of drilling cuttings is 1.50–3.20 times that of natural coal. The research conclusions provide reference for optimization of the index for the weight of drilling cuttings and effective rockburst monitoring of rockburst-prone coal under water-rich conditions.

Article highlights

• (1) Propose a formula for calculating the weight of drill cuttings under water-bearing conditions.

• (2) To carry out the moisture content of different coal sample triaxial loading drilling test.

• (3) Optimizing the critical index of drilling cuttings method under the condition of coal water content.

1 Introduction

A rockburst represents a typical dynamic disaster in coal mining, characterized by sudden and violent rock or coal ejections and indicative of unique stratal behaviors in mines. Currently, two primary methods are employed for the monitoring and early warning of rockbursts (Dou et al. 2014; Wang et al. 2022; Li et al. 2020; Pan et al. 2022; Xu et al. 2022). The first method encompasses typical rock mechanics techniques, which involve direct testing of coal and rocks using various devices to determine their physico-mechanical properties. The risk of rockbursts in monitored areas is then evaluated based on the collected data and compared with relevant indices, employing approaches such as the drilling cutting method and stress measurement. The second category includes geophysical methods that gather seismic waves, energy, and radiation emitted by coal and rocks during deformation and rupture. This information, captured through specific detection devices, is analyzed using post-processing algorithms, culminating in the assessment of rockburst risk by comparing the findings with established indices. This category encompasses methods such as microseismic monitoring, electromagnetic radiation detection, and thermal infrared remote sensing.

Among various monitoring and warning strategies, the drilling cutting method is notably effective in assessing impact risk by integrating mining stress, coal quality, outburst environment, and other indicators. Originating from a German scholar's proposal, this method assesses rockburst risk based on the weight of drilling cuttings discharged and the borehole’s boring effect during drilling in coal seams with diameters ranging from 42 to 50 mm (Dou and He 2001). Primarily, it is used to identify zones of high stress concentration significantly influenced by mining activities and local discontinuities over small ranges. Drawing upon the quantitative relationship between the weight of drilled coal cuttings and coal stress (Hatherly et al. 2015), the method calculates the degree of stress concentration, peak stress, and the specific location based on the weight of the coal cuttings discharged.

Building on its theoretical foundation, researchers worldwide have advanced the drilling cutting technique. Petukhov (1980) devised strain solutions for circular holes in infinite media planes and formulas to link the weight of drilling cuttings with the surrounding rock pressure, considering rock’s elastoplastic behavior and the deformation zone around boreholes. Brona (1983) expanded the theory by classifying drilling cuttings into two categories: those from cylindrical coal matching the borehole diameter and those resulting from stress redistribution and borehole wall movement. These theories have provided a solid basis for the drilling cutting method's application in practical scenarios.

Subsequent studies have continued to refine the drilling cutting method’s theoretical underpinnings. Li and Pan (2005) utilized the coal damage model and concepts of extreme point instability to study borehole wall collapse, identifying critical loads for failure, which is essential for practical rockburst prediction. Chen et al. (2013) used these theories to ascertain a critical drilling cuttings weight index for rockburst states, contributing to the efficacy of pressure-relief boreholes and enhancing rockburst risk detection.

On the other hand, the geographical shift of coal mining to the water-abundant regions of Inner Mongolia, Shaanxi, and other areas has prompted scholars to thoroughly investigate the physical and mechanical properties of moist coal. Recognizing the prevalence of water-rich coal in these areas, Mao et al. (2001) experimentally determined a reverse relationship between rockburst susceptibility and the moisture content in coal seams, observing that moisture notably diminishes coal’s impact and elastic energy indices. Wang et al. (2018) scrutinized the interplay between mechanical properties and the moisture content in various coal types, delineating distinct failure modes under different moisture conditions. Vishal et al. (2015) performed acoustic emission (AE) tests on fluid-saturated coal, noting a reduction in compressive strength with increasing moisture and gas levels. Similarly, Yao et al. (2015) documented that peak strain and compressive strength of coal specimens are positively and negatively affected by moisture content, respectively, while the elastic modulus exhibits a negative exponential relationship with moisture.

In summary, extensive theoretical and experimental research has focused on two aspects: the drilling cutting method and the impact of moisture on coal’s physical and mechanical traits. However, rockburst monitoring in these moist coal regions via the drilling cutting method encounters challenges: the water can alter the cuttings, significantly reducing their yield and sometimes failing to meet the critical early warning index. Addressing this, we designed triaxial loading drilling tests and inverted the AE energy to discuss the mechanical response and the evolution of stress and energy during drilling in water-rich coal. Furthermore, the critical index for the weight of drilling cuttings for moist coal was refined based on test results and weakening coefficients, enhancing the methodology for rockburst prediction under such conditions.

2 Analytical expression of the weight of drilling cuttings under water-rich conditions

The objectives of both theoretical research and experimental simulations in drilling cutting methodology aim to define a functional relationship between the weight of drilling cuttings and the stress experienced by coal, allowing for a quantitative analysis of this relationship. Typically, this method presupposes that pre-drilled coal is isotropic and homogenous, akin to an elastomer in elastic mechanics, and approaches the drilling process as a plane strain problem with a circular hole. The Mohr–Coulomb criterion serves as the failure threshold for coal's inelastic deformation post-drilling, simplifying the load to an axisymmetric scenario under even pressure. Figure 1 illustrates this concept with an elastic mechanical model of a borehole.

Fig. 1

The elastic mechanical model of a borehole as a plane-strain problem

Accounting for coal’s softening post-ultimate strength achievement, indicating a strength decline concurrent with strain increase, Zhao et al. (1985) proposed a correlation between drilling cuttings weight and coal stress:

$$\begin{aligned} G & = \gamma \left( {\pi a^{2} + 2\pi Ru_{a} } \right) + \left( {\frac{n - 1}{2}} \right)\gamma \left( {R^{2} - a^{2} } \right) \\ & = \gamma \pi a^{2} \left[ {\left( {1 - \frac{n - 1}{{2\pi }}} \right) + \left( {\frac{1 + \mu }{E}\left( {\sigma_{c} + \frac{q - 1}{{q + 1}}\left( {2p - \sigma_{C} } \right)} \right) + \frac{n - 1}{{2\pi }}} \right)\left[ {1 + \frac{{\left( {2m + q - 1} \right)\left( {2p - \sigma_{c} } \right)}}{{\sigma_{c}^{1 - m} \left[ {\sigma_{c} + \left( {q - 1} \right)p} \right]^{m} \left( {q + 1} \right)}}} \right]^{{\frac{2}{2m + q - 1}}} } \right] \\ \end{aligned}$$

(1)

$$q = \frac{1 + \sin \varphi }{{1 - \sin \varphi }}$$

(2)

where a is the borehole radius, $\gamma$ is the coal’s unit weight, n is the coal’s volumetric expansion coefficient, $\mu$ is the Poisson’s ratio, E represents the elastic modulus, ${\sigma }_{c}$ is the uniaxial compressive strength (UCS), p is the applied stress, $\varphi$ is the internal friction angle, and m is the plastic softening coefficient of coal.

Water’s impact on coal’s physical and mechanical parameters, as per Perera et al. (2011), includes the degradation of the UCS and elastic modulus at varying moisture levels. The plastic softening and volumetric expansion coefficients significantly influence the weight of drilling cuttings, while Poisson's ratio and internal friction angle have lesser effects. The plastic softening coefficient is variably defined; Cai (2002) characterizes it as the strength ratio of water-saturated to dry specimens, multiplied by 100%. Six distinct weakening coefficients K_i (i = 1–6, 0 < K) encapsulate the weakening effect of water on six parameters: UCS ${\sigma }_{c}$, elastic modulus E, Poisson’s ratio $\mu$, internal friction angle $\varphi$, plastic softening coefficient m, and volumetric expansion coefficient n.

$${\sigma }_{c}^{*}={K}_{1}\times {\sigma }_{c}\left({0<K}_{1}\right)$$

(3)

$${E}^{*}={K}_{2}\times E\left({0<K}_{2}\right)$$

(4)

$${\mu }^{*}={K}_{3}\times \mu \left(0{<K}_{3}\right)$$

(5)

$${\varphi }^{*}={K}_{4}\times \varphi \left(0<{K}_{4}\right)$$

(6)

$${m}^{*}={K}_{5}\times m\left(0<{K}_{5}\right)$$

(7)

$${n}^{*}={K}_{6}\times n\left({0<K}_{6}\right)$$

(8)

where K₁, K₂, K₃, K₄, K₅ and K₆ separately represent the weakening coefficients of the UCS, elastic modulus, Poisson’s ratio, internal friction angle, weakening coefficient, plastic softening coefficient, and volumetric expansion coefficient; ${\sigma }_{c}^{*}$, ${E}^{*}$,${\mu }^{*}$, ${\varphi }^{*}$, ${m}^{*}$ and ${n}^{*}$ separately denote the weakening parameter of the UCS, elastic modulus, Poisson’s ratio, internal friction angle, plastic softening coefficient, and volumetric expansion coefficient.

In summary, the weakening coefficients K₁ through K₆, representing the physico-mechanical parameters of water-bearing coal, have been determined. These coefficients, once adjusted, can be applied to Eq. (1) to calculate the weight of drilling cuttings. This application yields the revised calculation, represented by Eq. (9), for determining the weight of drilling cuttings accurately.

$$G = \gamma \pi a^{2} \left[ {\left( {1 - \frac{{k_{6} n - 1}}{2\pi }} \right) + \left( {\frac{{1 + K_{3} \mu }}{{K_{2} E}}\left( {K_{1} \sigma_{c} + \frac{q - 1}{{q + 1}}\left( {2p - K_{1} \sigma_{C} } \right)} \right) + \frac{{k_{6} n - 1}}{2\pi }} \right)\left[ {1 + \frac{{\left( {2k_{5} m + q - 1} \right)\left( {2p - K_{1} \sigma_{c} } \right)}}{{\left( {K_{1} \sigma_{c} } \right)^{{1 - k_{5} m}} \left[ {K_{1} \sigma_{c} + \left( {q - 1} \right)p} \right]^{{k_{5} m}} \left( {q + 1} \right)}}} \right]^{{\frac{2}{{2k_{5} m + q - 1}}}} } \right]$$

(9)

$$q=\frac{1+\mathit{sin}{k}_{4}\varphi }{1-\mathit{sin}{k}_{4}\varphi }$$

(10)

3 Drilling tests during triaxial loading

3.1 Triaxial loading and drilling test system

The triaxial loading and drilling test system consists of four main components: a triaxial stress loading system, an axial stress and acoustic emission (AE) monitoring system, a drilling assembly, and a support platform with auxiliary clamps, as depicted in Figs. 2 and 3. This system is capable of replicating the three-dimensional stress field distribution experienced during the drilling cutting method under natural coal seam conditions. For testing, cubic specimens with dimensions of 100 mm × 100 mm × 100 mm are utilized.

Fig. 2

Schematic diagram for the triaxial loading and drilling test and monitoring system

Fig. 3

Schematic diagrams for the drilling platform and monitoring system

In the Y-direction, the triaxial stress loading system employs a testing machine to apply and release stress, simultaneously monitoring the Y-direction displacement and stress levels; in the X-direction, hydraulic jacks impose and relieve stress, with sensors in place to observe stress and displacement changes on the specimen. The X-direction stress is managed by rotating a driving nut fixed on the rear wall of the drilling platform, interacting with a torque multiplier linked to the front wall for load application and removal. The Z-direction load is applied and released through a hydraulic jack attached to the right side of the drilling platform, operated by a manual pressure pump that exerts force on the platform’s left side. The monitoring setup consists of two radial pressure sensors, a data acquisition system that includes a digital-to-analog converter, and a central computer to capture and process the X and Z-direction stresses.The AE monitoring system is equipped with six AE probes, each connected to its respective preamplifier and AE data collection system to record AE signals. The drilling component comprises an electric drill and variously sized drill bits to accommodate different drilling specifications.

3.2 Test schemes

The triaxial tests employed specific stress paths in the Y-direction, with loads in the X and Z-directions held constant. He et al. (2013) suggested that for static loading, the strain rate should be less than 10^–3 s⁻¹, hence the static loading and unloading rates were set to 1 mm/min. Zhu et al. (2018), indicated that coal specimens typically begin to fail when the overstress coefficient is around 3; therefore, the Y-direction stress was adjusted to 30–80 MPa, which is 3–8 times the uniaxial compressive strength (USC) of the specimens, while the X and Z-direction stresses were maintained at 5–15 MPa, as detailed in Table 1. The drilling rate was consistently maintained at 950 rpm for each specimen. The specific testing procedures were as follows:

• 1. Stress was applied to each specimen at a rate of 1 mm/min until reaching a predefined initial stress state.

• 2. The loads in the X, Y, and Z-directions were then held constant for 600 s. Drilling of boreholes, to a depth of 100 mm, was initiated 100 s after the start of the load-holding period.

• 3. Subsequent to drilling, the weight of the drilling cuttings was recorded for each specimen. The Y-direction stress was then incremented to the second-stage preset value at the same rate of 1 mm/min.

• 4. Upon reaching the second-stage stress, the Y-direction stress was gradually released at a rate of 1 mm/min.

Table 1 Moisture contents of specimens and stress loading

As depicted in Fig. 4, twelve coal specimens were prepared and organized into four groups. Group B1 consisted of three natural coal specimens, individually labeled B1-1, B1-2, and B1-3. The remaining nine specimens were distributed into three groups—B2, B3, and B4—with three specimens in each. Each specimen’s mass was recorded pre and post water immersion, following drying and soaking for 2 h, 5 h, and 20 h respectively, to achieve average moisture contents of 1.4%, 2.3%, and 3.7%. The weights and moisture content of the specimens before and after soaking, along with the applied stresses, are itemized in Table 1.

Fig. 4

Picture of test coal specimens

3.3 AE absolute energy release factor

Cao et al. (2017) identified that the micro-fracture process in coal and rocks under load typically coincides with energy discharge. Understanding the energy release characteristics during the fracture process under load is critical for studying the failure and rupture behaviour of the materials in question. Since acoustic emission (AE) absolute energy remains consistent irrespective of the preamplifier gain—unlike AE energy—it is a more direct comparative measure in physical terms. Consequently, this research adopted the absolute energy of AE events recorded by each probe as the analytical index. By correlating the coordinates, energy magnitude, and frequency of AE events, the study constructed a cumulative release index model for the absolute energy of the specimens. This model facilitates the examination of the spatio-temporal dynamics of energy release in specimens during the secondary loading phase post-triaxial loading and drilling. Furthermore, tomographic analysis was employed on the absolute energy release factor of specimens.

To compute this model, specimens were divided into 20 × 20 × 20 cubic elements, each with a side length of 5 mm, resulting in 9261 nodes for energy computation. Each node served as the center of a sphere, with algebraic operations performed on the absolute energy within the sphere’s volume for a given time interval. This energy was then accumulated at the respective nodes to represent the node’s absolute energy release index h_i. The search radius for node energy was set as half of the cube's body diagonal length.

Figure 5 illustrates the computational domain for node energy. To mitigate the impact of outlier AE events with exceptionally high or low energies on the accuracy of the energy release factor calculations, the energy release index h_i at each node underwent logarithmic transformation. Subsequently, a cumulative release coefficient c for absolute energy was formulated to evaluate energy dispersion in the specimens. The cumulative release coefficient for the absolute energy of the ith grid node during the nth inversion phase is represented by Eq. (9). This approach allows for a clear portrayal of the spatio-temporal progression of energy release in specimens during the loading process via tomographic imaging of the energy release factor c at each node:

$${c}_{i}=\sum_{1}^{n}\sum_{1}^{j}0.5ln\left(1+{h}_{j}\right)$$

(9)

where j is the jth AE event in the computational domain of the ith grid node in the nth inversion phase; h_i denotes the absolute energy of the jth AE event.

Fig. 5

Computational domain of nodal energy

4 Test results and analysis

4.1 Stress-time relationship in the test process

Figures 6 and 7 display the stress-time curves for both natural and water-bearing coal specimens under triaxial loading and drilling, alongside a comparison of the specimens’ appearances before and after the drilling process. To decipher the stress-time variations and dynamic events during testing, the process is dissected into six distinct phases according to Y-direction stress evolution: the initial loading stage (I), stress-adjustment stage (II), drilling stage (III), stress-stabilization stage (IV), second loading stage (V), and unloading stage (VI). This section elucidates the stress evolution characteristics at each stage, with a particular focus on natural coal and coal specimens with a moisture content of 3.7%. Unless noted otherwise, references to “stress” pertain to the stress applied in the Y-direction.

Fig. 6

Stress-time curves of natural coal at different load levels and comparison of damaged specimens

Fig. 7

Stress-time curves of water-bearing coal at different load levels and comparison of damaged specimens

• (1) Triaxial stress evolution characteristics across the stages:

  • ① I—Initial Loading Stage: This phase comprises the sample compaction and elastic deformation stages. Initially, stress increases slowly, signaling the sample compaction phase where open structural planes and micro-cracks close. As stress escalates rapidly, the specimen undergoes elastic deformation, correlating stress with strain in the specimen. Concurrently, micro-fractures develop progressively during this loading phase.

  • ② II—Stress-Adjustment Stage: When Y-direction stress attains the preset level, it typically decreases due to the transition from direct metal clamp application to servo-motor control, which initially stores some elastic deformation energy in the clamps. Upon halting continuous loading, this energy is released, possibly causing structural damage to the specimen and resulting in stress reduction. Stress drops also stem from specimen failure under stress, leading to ongoing damage, deformation, and unloading.

  • ③ III—Drilling Stage: Drilling disrupts specimen integrity, creating a fractured zone and a plastic zone extending from the borehole wall, diminishing the specimen's load-bearing capacity. Thus, triaxial stresses decrease after drilling. Natural coal, still in the elastic phase post-initial loading, demands significant drilling force due to its intact structure. Under higher stress, coal transitions to an elastic–plastic state, requiring less drilling force as plastic zones develop along the borehole walls. Released elastic energy from specimen zones enhances plastic flow towards the borehole, easing drilling and producing cuttings accompanied by acoustic emissions. In this stage, water-bearing coal exhibits greater stress drops, signifying stress-induced failure exacerbated by moisture, which also facilitates drilling due to increased plastic deformation capacity.

  • ④ IV—Stress-Stabilization Stage: Post-drilling, Y-direction stress reaches stability.

  • ⑤ V—Second Loading Stage: Y-direction stress steadily climbs until the preset level is achieved. Drilled boreholes, compromised under stress, contribute to varying stress drops in frequency and magnitude during the second loading, reflecting the diminished structural integrity of specimens, which then compact rapidly, resulting in continuous stress elevation. This phase is often marked by audible cracking sounds with each stress drop.

  • ⑥ VI—Unloading Stage: Stress in the Y-direction is methodically reduced by the servo-motor-controlled testing machine, followed by manual unloading of the X and Z-direction stresses.

• (2) Stress Evolution Characteristics of Natural Coal

The stress-time curves for natural coal specimens subjected to drilling at various loads (30–60, 45–70, and 60–80 MPa) are depicted in Fig. 6a–c. These curves exhibit a quasi-consistent behavior across different load levels. As the load increases, the specimens first show instability and unloading during the initial loading micro-fracture development stage. In the stress-adjustment stage, higher initial loads correspond to greater unloading due to specimen failure during the load-holding period. During the drilling stage, the stress drops for specimens B1-1, B1-2, and B1-3 post-drilling are 0.95, 2.60, and 5.84 MPa, respectively, indicating a positive correlation with the initial load. In the second loading stage, the stress-time curves transition from a nearly linear to a curved ascent, signifying more pronounced deformation and failure of the boreholes as the load increases.

Figure 6d compares the physical appearances of specimens before and after loading. At lower loads, specimen B1-1 retains its original form with no significant fractures, except for the drilling hole and some debris at the edges. For specimen B1-2, tested at an intermediate load level, the post-test appearance shows four macro-fractures running through the specimen, leading to rupture along these fractures. High load levels render specimen B1-3 incapable of being fully removed from the loading platform post-test, leaving behind a considerable amount of coal powder; the specimen breaks into blocks and strips, producing powdery debris that flakes off upon light contact, indicating complete structural compromise.

• (3) Stress Evolution Characteristics of Water-Bearing Coal (19 h).

Figure 7a–c present the stress-time curves for water-bearing coal specimens during triaxial loading and drilling at load levels of 30–60, 45–70, and 60–80 MPa. The stress-time curves of these specimens are quasi-consistent but exhibit distinct characteristics, particularly in the drilling stage (III), where stress drops before and after drilling increase with higher load levels. Also, the failure, deformation, and unloading are more pronounced with increased sustained load. In the second loading stage (V), the curves show smaller stress drops with larger loads. For instance, specimen B4-2 experiences a significant stress drop (3.75 MPa), and B4-3 demonstrates two stress drops (0.65 and 1.33 MPa), with a reduced slope in the stress-time curves compared to lower loads. This suggests that higher moisture content leads to deeper damage around the boreholes under stress and borehole failure, resulting in stress drops. Moreover, the lubricating and weakening effects of water on coal structural planes cause frictional slips, decreasing the slope of the stress-time curves.

Figure 7d illustrates that under different loads, the failure modes of water-bearing coal differ substantially from those of natural coal in two main aspects: the extent, quantity, and orientation of fractures under stress are significantly greater in water-bearing specimens, which feature numerous lamellar cracks. Additionally, the failure modes are characterized by interlayer friction and dislocation, with the specimens displaying interlayer slipping and fracturing, generating a considerable amount of powdery debris between lamellar fractures.

4.2 Comparison of stress evolution characteristics of coal specimens with different moisture contents

Figure 8 delineates the stress-time curves of natural coal and coal with varying moisture contents. Analysis of these curves and the dynamic behaviors and failure modes of coal specimens during the drilling process at different stress levels allows the following observations:

• (1) At the same applied load, higher moisture content corresponds to a flatter slope of the stress-time curve during the initial loading stage. This suggests an extended period to reach the preset stress state, indicating that increased moisture content leads to more micro-cracks within the coal, enlarging the surface area and volume of these cracks. The “compaction stage” duration is significantly prolonged as the coal mass and structural planes absorb more water, reducing both the coefficient of friction and the shear strength on these planes.

• (2) For a given load, the greater the moisture content, the larger the stress drop post-drilling in the coal. This indicates that with higher moisture content, the coal’s structural failure-induced stress diminishes more slowly, enhancing the deformation capacity of the drilled coal under stress. The observed stress drop is a dynamic consequence of damage evolution and deformation around the boreholes.

• (3) With identical loads, increased moisture content results in a higher frequency of dynamic responses during both the drilling and the second loading stages. As moisture content rises, the weakening effect of water on the coal’s structure intensifies, leading to easier damage and a reduced capacity for elastic energy storage. Consequently, dynamic events develop more rapidly, the response frequency increases, while the intensity of these events decreases.

• (4) At consistent load levels, higher moisture content makes the layering phenomenon in coal specimens more pronounced. This implies that as moisture content increases, the friction between particles on crack surfaces lessens, raising the likelihood of coal undergoing sliding failure. The active surface energy of coal is diminished, leading to a notable increase in the number of cracks during the loading process, enlarging the cracks' surface area and volume, and enhancing permeability. The overall structural integrity of the coal deteriorates, and the potential for interaction between structural planes weakens, resulting in evident sliding and dislocation at higher stress levels. Furthermore, the presence of drilling cuttings between layers, due to high-stress interactions like friction and slip, indicates that the structural planes themselves are thoroughly compromised.

Fig. 8

Stress-time curves of natural coal and coal with different moisture contents

4.3 Energy and fracture development characteristics of specimens

Figures 9, 10, 11 illustrate the distribution of the absolute energy release factor at the Z = 50 mm horizontal plane in natural coal and coal specimens containing 1.4%, 2.3%, and 3.7% water under stress levels of 30–60, 45–70, and 60–80 MPa, respectively. These figures shed light on how moisture content affects the distribution and concentration of released energy in coal specimens under triaxial stress, and consequently, their fracture and failure behavior.

Fig. 9

Distribution slices of the energy concentrated release factors (30–60 MPa)

Fig. 10

Distribution slices of the absolute energy release factors (45–70 MPa)

Fig. 11

Distribution slices of the absolute energy release factors (60–80 MPa)

For natural coal specimens:

• Figure 9a shows a zonal distribution of absolute energy release along a straight line from the top of the boreholes to the bottom of the specimens, indicating tension at the top of the boreholes under load, leading to energy release and cracking along this path.

• Figure 10a reveals a zonal distribution of absolute energy along a straight line diagonally from the upper left to the lower right corner of the boreholes, with a reduced energy release factor at the center, suggesting that specimens are prone to tensile and shear damage along this oblique line.

• Figure 11a presents a similar pattern of energy distribution, with the absolute energy being predominantly symmetrical along the diagonal line, and the specimen cracking along the borehole walls.

For water-bearing coal:

• Figure 9b demonstrates that at lower moisture contents, the specimens still show tendencies for cracking along the borehole walls with multiple oblique crack initiation paths.

• Figure 9c shows that with increased moisture, the maximum absolute energy release factor is at the borehole center, with energy release paths radiating outward in concentric circles. This X-shaped distribution is consistent with predictions from the twin-shear strength theory and extends over a long distance without significant energy concentration along the borehole walls.

• Figure 9d indicates that at even higher moisture contents, the pattern of energy release remains centered around the boreholes, but the energy distribution area and concentration at the center increase.

Comparative analysis of natural coal versus water-bearing coal:

• In natural coal, the damage and rupture tend to symmetrically crack along both sides of the borehole walls under stress.

• In water-bearing coal, damage first concentrates at the central wall of boreholes due to water weakening the structure. The damage then radiates outward in an X-shape, with borehole wall cracking occurring only when the damage extends well beyond the borehole radius, thus compromising the specimen structure more extensively.

Furthermore, the width of the energy concentration release band, which indicates the damage radius of the boreholes, is measured directly on the energy distribution slices. In water-bearing coal, the damage radius of boreholes remains consistent at lower stresses (30–60 MPa) regardless of moisture content, with values of 21.6, 28.8, and 35.4 mm. However, at higher stresses (45–70 MPa), the damage radii increase with moisture content, measuring 24.4, 35.8, and 40.4 mm, respectively. This suggests that as the moisture content rises, the coal's structure is increasingly compromised, leading to larger damage radii around the boreholes.

4.4 Spatio-temporal evolution characteristics of absolute energy

Figure 12 provides tomographic images that illustrate the distribution of absolute energy within natural coal specimens under various stress levels, depicted through longitudinal and transverse sections at 30–60, 45–70, and 60–80 MPa. These images showcase the stages of stress concentration, deformation, and energy release around the boreholes.

Fig. 12

Distribution sections of absolute energy in natural specimens: a 30–60 MPa, b 30–60 MPa, c 45–70 MPa, d 45–70 MPa, e 60–80 MPa, f 60–80 MPa

The evolution of borehole damage under stress in natural coal progresses as follows:

• Initially, stress concentrates along the borehole walls, causing them to deform towards the center.

• As stress increases, this concentration leads to the initiation of cracks along directions either parallel or at slight angles to the maximum principal stress, creating a symmetrical and focused zone of energy release around the borehole walls.

• At higher stress levels, the boreholes are subjected to overstress, resulting in fractures that traverse the entire specimen along the borehole walls.

This spatial damage evolution under stress can be categorized into three distinct stages:

• 1. Specimen convergence towards the borehole center with stress concentration on the walls.

• 2. Crack initiation from the borehole walls.

• 3. Specimen failure due to the propagation and coalescence of cracks along the walls.

Figure 13 exhibits tomograms of the absolute energy within specimens that contain a moisture content of 3.7%. These figures show the spatial distribution of absolute energy across both longitudinal and transverse sections at the same stress intervals as Fig. 12. The water-bearing coal specimens exhibit differences in their loading behavior compared to natural coal, specifically:

• 1. They only exhibit the first two stages of the spatial damage evolution observed in natural coal during loading.

• 2. The energy distribution forms connected clusters across each horizontal plane within the specimens throughout the loading process, as opposed to localized, unconnected regions.

Fig. 13

Distribution sections of absolute energy in water-bearing specimens: a 30–60 MPa, b 30–60 MPa, c 45–70 MPa, d 45–70 MPa, e 60–80 MPa, f 60–80 MPa

The reasons for these differences are:

• The presence of water weakens the physico-mechanical properties of the coal, enhancing the deformation capacity of the boreholes under stress. Consequently, symmetrical crack initiation along the borehole walls and through-running fractures do not occur.

• At lower moisture contents, friction and rupture of microscopic particles under stress are prevalent. As moisture content increases, the dominant failure mode transitions to friction, slip, and rupture along structural planes, with energy release manifesting as connected, layered clusters within the specimen horizons.

5 Optimization of the critical index of the weight of drilling cuttings for water-bearing coal

5.1 Optimization based on drilling tests

Combining the rockburst monitoring standards from the Chinese guidelines (2019) with the tomographic results from triaxial loading and drilling tests, the affected range around boreholes during drilling is identified by mapping the absolute energy release regions. This mapping allows for the calculation of the weight of drilling cuttings, facilitating the adjustment of the critical index for the weight of drilling cuttings according to different moisture contents, thereby achieving effective rockburst monitoring and early warning in water-rich conditions.

The absolute energy release distribution of specimens with varying moisture contents under different stress levels indicates that under low stress, natural specimens remain largely intact, as evidenced by the low concentration of absolute energy release regions along the boreholes. In contrast, at high stress levels, coal specimens tend to split directly. As a result, the concentrated energy release zones in natural specimens are not directly defined as the borehole-affected range but are rather estimated.

Figures 14 and 15 present the relationships between moisture content and the weight of drilling cuttings as determined by tomographic results and as measured in the tests, respectively. The tomographic weight of drilling cuttings refers to the calculated mass within a volume defined by the damage radius determined using the absolute energy release factor. In contrast, the damage radius in actual tests is typically the extremum value, and not all drilling cuttings are collected due to operational constraints of the drilling platform. Thus, at a moisture content of 3.7% under loads of 60–80 MPa, the tomographic analysis suggests a weight of 222.54 g, whereas field measurements indicate a mass of only 51.23 g—a substantial discrepancy.

Fig. 14

The relationship between the moisture content and weight of drilling cuttings (tomography)

Fig. 15

The relationship between the moisture content and weight of drilling cuttings (measurement)

To summarize, the drilling test results show that the weight of drilling cuttings for coal with a moisture content of 3.7% is 2.78 times that of natural coal. Tomographic analysis suggests a higher ratio, with water-bearing coal having 3.48 times the weight of drilling cuttings compared to natural coal. Although there is some variance between the two methods, the results are broadly consistent and provide a comparative basis for evaluating rockburst risk in water-rich conditions.

5.2 Optimization based on weakening coefficients

To calculate the weakening coefficients, which quantify the degree to which moisture affects the physico-mechanical properties of coal, researchers have conducted a meta-analysis of existing data on these properties and the associated weakening coefficients of water-bearing coal. Due to insufficient research data on the plastic softening coefficients K₅ and K₆ for water-bearing coal, the current calculations are based on the original drilling cuttings method, and the finalized data are collated in Table 2. This table lists the weakening coefficients for the physico-mechanical parameters of both natural coal and coal with a moisture content of 5.60%.

Table 2 Physico-mechanical parameters of natural coal and coal with a moisture content of 5.60% and their weakening coefficients

The weakening degrees for the six physico-mechanical parameters—the uniaxial compressive strength (UCS, ${\sigma }_{c}$), elastic modulus (E), Poisson’s ratio ($\mu$), internal friction angle ($\varphi$), plastic softening coefficient (m), and volumetric expansion coefficient (n)—are determined from the average values of the weakening coefficients K_i (where i ranges from 1 to 6, and K > 0). These coefficients reflect the extent to which water presence within the coal structure reduces its strength and stiffness.

By incorporating these coefficients into Eq. (8), researchers can calculate the expected weight of drilling cuttings for water-bearing coal under various confining pressures. Theoretically, it’s estimated that the weight of drilling cuttings from coal with a moisture content of 5.60% ranges from 1.50 to 3.20 times the weight from natural coal. This ratio provides an essential reference for adjusting the critical index for the weight of drilling cuttings, which is crucial for the effective monitoring and early warning of rockbursts in conditions where coal is saturated with water.

6 Discussion

6.1 Analytical expression of the weight of drilling cuttings

The exploration of the drilling cutting method in theoretical research is grounded in elastic mechanics, where the primary goal is to establish and analyze the relationship between the weight of drilling cuttings and the stress experienced by coal. Recent advancements have taken into account the strain softening of coal and the dilation of inelastic deformation zones to refine the quantitative functional relationship between coal stress and the weight of drilling cuttings. Despite these developments, a definitive theoretical calculation formula that accounts for the impact of water on the mass of drilling cuttings has yet to be quantitatively derived.

To address this gap, the current research has investigated the weakening effects of water on the physico-mechanical parameters of coal, leading to the introduction of six weakening coefficients, K_i (i = 1–6, 0 < K). These coefficients are employed to quantify the extent to which water presence diminishes the strength and deformation characteristics of coal, specifically affecting the uniaxial compressive strength UCS ${\sigma }_{c}$, elastic modulus E, Poisson’s ratio $\mu$, internal friction angle $\varphi$, plastic softening coefficient m, and volumetric expansion coefficient n.

Building upon these insights, the study proposes that by substituting the adjusted weakening coefficients into the existing formula for the weight of drilling cuttings, a new theoretical calculation model can be formulated. This model would accurately predict the weight of drilling cuttings in the presence of water, thereby enhancing the reliability of the drilling cutting method as a tool for monitoring and forecasting rockburst hazards in moist coal conditions. The development of this theoretical formula is significant as it provides a more comprehensive understanding of how water affects the mechanical behavior of coal, which is crucial for safe mining operations in water-rich environments.

6.2 Triaxial drilling tests

The conducted drilling tests across various stress levels on both natural and water-bearing coal specimens aimed to comprehensively understand the mechanical response, stress transmission, energy evolution, internal damage progression, and acoustic emission (AE) characteristics during drilling in water-rich conditions. The goal was to establish a theoretical foundation for the failure behavior and fracture development of water-bearing coal under stress. The specific areas of focus were:

• (1) Investigating the initial stress state’s stress and energy distribution characteristics in natural coal blocks, and examining the changes in these characteristics after drilling.

• (2) Exploring the stress and energy distribution in coal blocks with varying moisture contents under different stress states and after drilling, to understand how water content influences these distributions.

• (3) Developing a cumulative release index model for absolute energy based on the coordinates, energy levels, and frequencies of events during the drilling process. This model aimed to characterize the spatial and temporal evolution of energy release during the triaxial loading and drilling of specimens.

The research synthesized test results to analyze four key aspects:

• The stress-time relationship observed in coal specimens during the tests.

• The stress evolution characteristics of coal specimens with different moisture contents.

• The energy dynamics, stress evolution, and fracture development characteristics within the specimens.

• The spatial and temporal evolution characteristics of absolute energy release during the process.

From these analyses, insights into the stress transfer, energy dissipation, and damage evolution characteristics specific to water-bearing coal were gleaned. The research successfully identified the range of borehole damage in water-bearing coal and elucidated the deep-seated physical, mechanical, and structural factors that contribute to the susceptibility of rockbursts, particularly in regions with high moisture content. These findings are instrumental for devising more effective rockburst monitoring and early warning systems in coal mines where water presence is a significant factor.

6.3 Optimization of the critical index

The advancement of the drilling cutting method theory, which now includes elastic–plastic behavior assumptions, has led scholars to derive critical loads for predicting rockburst pressure, establish the critical state value of the drilling cuttings amount index through comparative analysis, and implement field practices for in-situ monitoring of coal stress and impact risk. This research further contributes to the method's evolution by employing two main approaches:

• 1. Tomography on absolute energy release factors: This technique was used in triaxial loading drilling tests to define the affected range around boreholes by mapping out regions of absolute energy release. This mapping allowed for the calculation of the weight of drilling cuttings, which is crucial for evaluating the rockburst potential.

• 2. Statistical analysis of weakening coefficients: By analyzing test data, six weakening coefficients K_i (i = 1–6, 0 < K) were determined. These coefficients represent the extent to which water presence affects the coal's physico-mechanical properties. Subsequently, these coefficients were integrated into the formula calculating the weight of drilling cuttings and stress on water-bearing coal, enabling a quantitative correction of the drilling cutting method's applicability in water-rich conditions.

This integrated approach provided a more nuanced understanding of rockburst mechanisms in wet environments and allowed for the optimization and correction of the critical index for the weight of drilling cuttings. It has refined the monitoring and early warning strategies for rockbursts, particularly addressing the needs of mines with complex hazards and high mining intensity, as often found in Western China.

Despite these advancements, there remains a gap in the recognition patterns for acoustic emission (AE) energy, which is pivotal for early detection of rockbursts. Additionally, the weakening coefficients K_i need further validation through weakening tests that measure the physico-mechanical parameters of coal in different mining contexts. These tests are essential to ensure the coefficients are accurately reflecting the conditions of specific coal mines, thus enhancing the predictive power and reliability of the drilling cutting method in diverse mining scenarios.

7 Conclusion

The prevalence of water-saturated coal bodies in regions such as Inner Mongolia and Shaanxi presents significant challenges to the application of the drilling cutting method for rockburst monitoring and warning. This research endeavors to test and adapt the drilling cutting method for such water-abundant conditions.

Theoretical analysis has indicated that coal with a moisture content of 5.60% yields 1.50–3.20 times the weight of drilling cuttings compared to natural coal. Triaxial drilling tests further revealed that, compared to natural coal, water-bearing coal primarily experiences interlayer slip, dislocation, and friction along weaker structural planes when it undergoes damage and rupture. Additionally, water-bearing coal exhibits a reduced capacity for elastic energy storage, with dynamic events developing more rapidly and frequently, albeit with less intensity per individual energy release event.

At moisture contents of 1.4%, 2.3%, and 3.7% and under stress levels of 45–70 MPa, the damage radii from the borehole centers were found to be 2.03, 2.98, and 3.36 times the radius of the drilling, respectively. The damage and rupture of boreholes in coal under stress unfold in two primary stages: convergence toward the borehole center and crack initiation along the walls due to stress concentration.

In practical drilling tests, coal with a moisture content of 3.7% produced drilling cuttings weighing 2.78 times that of natural coal, which aligns closely with tomographic results that suggest a ratio of 3.48 times. These findings underscore the necessity for modifying the existing index for the weight of drilling cuttings to improve the effectiveness of rockburst monitoring and early warning systems in mines with high water content. The research contributes valuable insights for addressing the complexities of rockburst phenomena in water-rich mining environments.