Study on in situ stress testing method based on Kaiser effect of acoustic emission and COMSOL simulation

Abstract

In situ stress testing can improve the safety and efficiency of coal mining. Identifying the Kaiser effect point is vital for in situ stress calculations; however, the in situ stress calculation is limited by the rock sampling angle. Here, the Kaiser effect point identification theory is established and applied to the Xuyong Coal Mine. Uniaxial compression and acoustic emission experiments were carried out on sandstone with 6 sampling directions. Furthermore, COMSOL simulation is applied to study the in situ stress distribution in the coal mine to verify the calculation accuracy. The results are as follows. 1) The failure mode of non-bedded and vertical-bedded rocks is primarily tensile shear failure with obvious brittleness in mechanical and acoustic emission characteristics. Shear slip along the bedding plane is the primary failure mode of inclined-bedded rock. Additional take-off points exist in the AE count curve. 2) The Kaiser point identification method based on the variation of AE count curve parameters \mathrm{\Delta }{t}_i and {\tau }_i can effectively calculate the in situ stress. According to the numerical value of Kaiser point and sampling direction, the in situ stress of the conveyor roadway in the Xuyong Coal Mine was calculated as {\sigma }_1=22.81\mathrm{M}\mathrm{P}\mathrm{a}, {\sigma }_2=10.87\mathrm{M} \mathrm{P}\mathrm{a} and {\sigma }_3=6.14\mathrm{M} \mathrm{P}\mathrm{a}. 3) By the COMSOL simulation study, it was found that a stress concentration zone of 16.13 MPa exists near the two sides roadway. Compared with the Kaiser effect method, the deviation rates of the three-direction principal stress calculated by COMSOL were all less than 5%. This verifies that the in situ stress calculation by Kaiser effect in this study can be applied to the Xuyong Coal Mine.

Graphical abstract

Keywords

Kaiser effect point / in-situ stress calculation / Xuyong Coal Mine / uniaxial compression / acoustic emission / COMSOL simulation

1 Introduction

In situ stress is also called initial rock stress, which is the fundamental factor leading to the deformation and failure of engineering rock mass (Liu et al., 2017; Radwan et al., 2021). In situ stress calculation is crucial to the study of rock engineering design. In recent years, underground rock engineering (Yin et al., 2015), water conservancy and hydropower engineering (Yin et al., 2012), civil engineering (Jiang et al., 2010), and other production activities are constantly expanding scale and developing toward greater depths (Ye et al., 2021). The equilibrium state of ground stress is likely to be disturbed during any of these activities, thus, causing instability collapse, reservoir earthquake, rock burst, roof collapse, floor water inrush, and other geological disasters (Xie et al., 2019; Yu and Mao, 2020). It is critical to accurately measure the in situ rock mass stress and consider the influence of geological conditions or engineering excavation on natural stress to solve various engineering and geological problems.

Currently, various in situ stress testing methods are being widely used, such as hydraulic fracturing (HF) (Subrahmanyam, 2019), strain recovery (Zhao et al., 2015), stress relief (Krietsch et al., 2019), and acoustic emission (AE) (Wu et al., 2019). The HF method can more accurately measure the rock stress in the deeper area than the others, but it is only suitable for the stress test of relatively intact rock masses (Lai et al., 2019). The measurement accuracy of the strain recovery method is greatly affected by rock strain factors (such as temperature, rock anisotropy, etc.), and the measurement accuracy is low (Liu et al., 2015). The stress relief method is suitable for open spaces where technicians can enter and perform construction measurements. In the AE method, the in situ stress can be estimated only by obtaining the core of the corresponding measuring point for the AE test (Heimisson et al., 2015). The AE method is widely used in underground engineering due to its advantages of easy operation and low price (Liu et al., 2018; Sause et al., 2019).

In recent years, the Kaiser effect of rock to determine the original rock stress has been widely used in engineering. When the rock stress exceeds the previous maximum stress, the AE activity increases significantly, accompanied by a sharp increase in cumulative AE counts (Tham et al., 2005; Nian et al., 2016). The stress at this time can be considered as the original rock stress. However, the Kaiser effect also has limitations. Because there are many abrupt points of cumulative AE counts during rock loading, the selection of Kaiser effect points is subjective (Ganne et al., 2007). Second, the Kaiser effect method to calculate the principal stress requires an exact angle of rock sampling. However, most construction sites, such as underground roadways, are manually sampled, and the sampling angle cannot be accurately controlled (Yokoyama et al., 2014), contributing to deviations in the calculation results of principal stress. Therefore, establishing a new Kaiser effect theory is necessary, which can effectively identify the Kaiser effect points and not be affected by rock sampling angle.

Current studies on in situ stress of AE test primarily focus on the effect of loading rates, temperature, water content, and other factors on the Kaiser effect point (Li et al., 2022). However, few studies have been conducted on effectively identifying Kaiser points and reducing the influence of sampling angle on the calculation accuracy of principal stress (Bai et al., 2018). Meng et al. (2019) performed tests on uniaxial cyclic loading and unloading of rocks and AE characteristics under different horizontal stresses and loading rates. They demonstrated that the horizontal stress affects the Kaiser effect more than the loading rate. Li et al. (2019a) studied the influence of loading rate on the AE of three rock types. The test results show that the loading rate significantly affects the Kaiser effect of brittle rock, but less affects the soft plastic rock. Chen et al. (2012) conducted uniaxial compression and AE on granite tests after heat treatment at 20°C−1200°C and collected AE signals. It was found that 300°C is the threshold value of rock Kaiser effect point stress reduction. The rock heat-treated at 600°C−1200°C has obvious brittle-plastic transition, which leads to the time delay of the Kaiser effect point. Xiao et al. (2021) analyzed the real-time total stress-strain-AE count curves of red sandstone in a temperature range of 20°C−900°C. The high-temperature thermal expansion effect contributes to the stone-rock void expansion and increases the abrupt change point of AE count.

The difficulty of judging Kaiser effect points has increased. Zhang and Chen (2010) compared the AE properties of uniaxial compression of sandstones with three water contents. As the water content increases, the AE activity also becomes denser, and the Kaiser point appears earlier in the time domain. Miao et al. (2016) conducted cyclic loading and unloading experiments on granite with different water contents. The increased water content develops the rock lithology from brittleness to ductility, which makes the rock enter the stage of damage acceleration transition earlier. Accordingly, the number of Kaiser suspected points is reduced and appear earlier.

The in situ stress calculation method is improved in this study, aimed at the abovementioned problems. First, based on the influence law of internal rock structure on Kaiser effect point discrimination, a comprehensive discrimination theory of Kaiser effect points is established. The theory is competent in identifying Kaiser effect points for rocks at any sampling angle and free from interference from take-off points of other AE counts curves. Then, based on the elastic rock mechanics principle, a new calculation method of the principal stress in three directions of rock is established. After that, sandstone was collected from a mining roadway of the Xuyong Coal Mine in south-eastern Sichuan Province. Uniaxial compression and AE tests were conducted to analyze the mechanical failure mechanism and acoustic emission characteristics of the samples. Finally, in situ stress in the geological field was calculated by COMSOL simulation, and the accuracy of the in situ stress calculation results was verified by combining it with the laboratory test results.

2 Improved in situ measurement principles

2.1 Kaiser effect identification theory

When rock is under a load, the AE count may have multiple sudden increases to varying degrees (Jin et al., 2009). Thus, there may be multiple suspected Kaiser effect points (Fig.1). Therefore, the effective identification of Keiser effect points is the key to in situ stress measurements. The study deduces a new method for Kaiser points identification. Rocks are elastoplastic materials, and reloading produces AE signals after stress relief (Damani et al., 2018). Only minor AE signals are generated when the rock load does not reach the maximum value in the geological history. If the maximum load is reached, many acoustic emission signals begin to generate (He et al., 2019). Then there is a sudden increase point with a large slope on the time-AE count curve, the take-off point. Based on the above information, the time-cumulative AE count curve in the rock failure process can be processed as follows:

(1)\{\begin{array}{c}\mathrm{\Delta }{t}_i=t_i-t_{i-1}\\ k_i=A_i/\mathrm{\Delta }{t}_i\\ {\tau }_i=\mathrm{a}\mathrm{r}\mathrm{c}\mathrm{t}\mathrm{a}\mathrm{n}{k}_i\end{array},

where t_i is a point in time of the time-cumulative AE count curve; A_i is the ring count of the curve at time t_i; k_i is the inclination angle of the curve; {\tau }_i is the inclination of AE curve (° ); \mathrm{\Delta }{t}_i is the time difference of AE ringing count, s.

\mathrm{\Delta }{t}_i represents the AE signal time characteristics during the rock compression process. The smaller the \mathrm{\Delta }{t}_i value, the smaller the fluctuation range, indicating that the AE in the corresponding time range is more frequent. {\tau }_i can represent the tilt of the time-cumulative AE count curve. If {\tau }_i is close to 90°, it indicates a sharp increase in AE count at the corresponding time, as shown in Fig.1.

Therefore, if the curve \mathrm{\Delta }{t}_i is small and the {\tau }_i is close to 90° at t_i, the AE frequency is high and the AE count increases significantly at this time. It fits the definition of a Kaiser point. Note that if {\tau }_i is large (say 80°) but has a significant deviation from 90°, it cannot be regarded as a Kaiser point. Because when a Kaiser point occurs, the AE count increases. The slope of the AE count curve is also close to 90°.

Therefore, the location of Kaiser point can be found according to \mathrm{\Delta }{t}_i and {\tau }_i. The specific steps are as follows.

1) The Kaiser effect point time interval is roughly determined over the time-cumulative AE count curve obtained in the uniaxial compression test.

2) The \mathrm{\Delta }{t}_i and {\tau }_i are obtained by processing the AE real-time count over Eq. (1).

3) According to the curve of \mathrm{\Delta }{t}_i–{\tau }_i–stress-time, Kaiser effect point can be found within the time interval determined in the first step.

2.2 Principal stress calculation of in situ stress

In the three-dimensional stress field, the six components of in situ stress ({\sigma }_x, {\sigma }_y, {\sigma }_z, {\tau }_{xy}, {\tau }_{xz}, {\tau }_{yz}) act at infinity (Lavrov, 2003). The direction and magnitude of the in situ stress can be calculated from its 6 components. The Kaiser effect can calculate the maximum historical stress of a rock specimen (Alkan et al., 2007). However, the in situ stress calculation by the Kaiser effect requires rock sampling from 6 specific angles. Due to the complex construction site conditions, such as coal mines and roadways, angle deviations inevitably occur, resulting in increased errors in the calculation results (Li et al., 2019b). Based on this, this study proposes an improved in situ stress calculation method based on the Kaiser effect. This method can calculate the in situ stress under any rock sampling angle to avoid the in situ stress calculation errors caused by sampling angle deviation.

2.2.1 Shear stress distribution of the tetrahedral element

The stress distribution on each surface of tetrahedral OABC is shown in Fig.2 according to the elastic mechanical principle (Zhang et al., 2018; Zhu et al., 2018). The area of plane ABC is S, the principal stress is T^{\left(n\right)}, and the direction vectors of the outer normal line n are {\alpha }_x, {\alpha }_y, and {\alpha }_{\mathit{\text{z}}}, respectively. The areas of plane OBC, OAC, and OAB are S{\alpha }_x, S{\alpha }_y, and S {\alpha }_{\mathit{\text{z}}}, respectively, and the corresponding stresses are {-T}^{\left(1\right)}, -T^{\left(2\right)}, and {-T}^{\left(3\right)}, respectively.

At the in situ stress test point, the balance equation of partial stress and principal stress of the micro-element is

(2)T^{\left(n\right)}S- \left(T^{\left(1\right)}{S}_1+T^{\left(2\right)}{S}_2+T^{\left(3\right)}{S}_3\right)+f\cdot Sh/3=0,

where h is the vertical distance from point O to surface ABC; f is the volume force of tetrahedral element OABC; Sh/3 indicates the volume of the tetrahedral unit OABC. The f\cdot Sh/3 can be ignored when the tetrahedron OABC is an infinitesimal base unit. Eq. (2) can be transformed into:

(3)T^{\left(n\right)}=T^{\left(1\right)}{\alpha }_x+ T^{\left(2\right)}{\alpha }_y+ T^{\left(3\right)}{\alpha }_z.

The plane ABC stress vector can be decomposed into stress components along three coordinate axes:

(4)\{\begin{array}{c}{T}^{\left(1\right)}={\sigma }_x{e}_x+{\tau }_{yx}{e}_y+{\tau }_{zx}{e}_z\\ T^{\left(2\right)}={\tau }_{xy}{e}_x+{\sigma }_y{e}_y+{\tau }_{zy}{e}_z\\ T^{\left(3\right)}={\tau }_{xz}{e}_x+{\tau }_{yz}{e}_y+{\sigma }_z{e}_z\end{array}.

Substituting Eq. (4) into Eq. (3), gives

(5)T^{\left(n\right)}=T^{\left(1\right)}{e}_x+ T^{\left(2\right)}{e}_y+ T^{\left(3\right)}{e}_z,

where

(6)\{\begin{array}{c}{T}^{\left(1\right)}={\sigma }_x{\alpha }_x+{\tau }_{yx}{\alpha }_y+{\tau }_{zx}{\alpha }_z\\ T^{\left(2\right)}={\tau }_{xy}{\alpha }_x+{\sigma }_y{\alpha }_y+{\tau }_{zy}{\alpha }_z\\ T^{\left(3\right)}={\tau }_{xz}{\alpha }_x+{\tau }_{yz}{\alpha }_y+{\sigma }_z{\alpha }_z\end{array},

where matrix \left[\begin{array}{ccc}{\sigma }_x& {\tau }_{yx}& {\tau }_{zx}\\ {\tau }_{xy}& {\sigma }_y& {\tau }_{zy}\\ {\tau }_{xz}& {\tau }_{yz}& {\sigma }_z\end{array}\right] is the stress component of tetrahedral element OABC.

Substituting Eq. (6) into Eq. (5), gives

(7)\begin{array}{rl}{T}^{\left(n\right)}=& {\sigma }_x{{\alpha }_x}^2+{\sigma }_y{{\alpha }_y}^2+{\sigma }_z{{\alpha }_z}^2+\left({\tau }_{xy}+{\tau }_{yx}\right){\alpha }_x{\alpha }_y\\ & +\left({\tau }_{xz}+{\tau }_{zx}\right){\alpha }_x{\alpha }_z+\left({\tau }_{yz}+{\tau }_{zy}\right){\alpha }_y{\alpha }_z.\end{array}

According to Eq. (7), if the stress component matrix of OABC is known, the normal stress on the oblique section of ABC can be calculated. If the rock mass is considered as an elastic medium with a continuous mean, then {\tau }_{xy}={\tau }_{yx}, {\tau }_{yz} ={\tau }_{yz}, and {\tau }_{xz}={\tau }_{zx}. The shear stress values can be obtained by calculating the stress component matrix. The OXY plane stress distribution is taken as an example, as shown in Fig.3, to show how to obtain the shear stress values on the OYZ, OXZ, and OXY planes.

Assuming that the angle between principal stress {\sigma }_{x\theta y} and X axis is \theta, the relation between principal stress and shear stress {\tau }_{xy} on plane XOY is as follows:

(8){\sigma }_{x\theta y}={\sigma }_x{\mathrm{c}\mathrm{o}\mathrm{s}}^2\theta +{\sigma }_y{\mathrm{s}\mathrm{i}\mathrm{n}}^2\theta +{\tau }_{xy} \mathrm{s}\mathrm{i}\mathrm{n}2\theta .

Therefore, the following relations can be obtained:

(9)\{\begin{array}{l}{\tau }_{xy}={\displaystyle \frac{{\sigma }_{x\theta y}-{\alpha }_x{\mathrm{c}\mathrm{o}\mathrm{s}}^2\theta -{\alpha }_y{\mathrm{s}\mathrm{i}\mathrm{n}}^2\theta }{2\mathrm{c}\mathrm{o}\mathrm{s}\theta \mathrm{s}\mathrm{i}\mathrm{n}\theta }}\\ {\tau }_{x\mathit{\text{z}}}={\displaystyle \frac{{\sigma }_{x\gamma \mathit{\text{z}}}-{\alpha }_x{\mathrm{c}\mathrm{o}\mathrm{s}}^2\gamma -{\alpha }_{\mathit{\text{z}}}{\mathrm{s}\mathrm{i}\mathrm{n}}^2\gamma }{2\mathrm{c}\mathrm{o}\mathrm{s}\gamma \mathrm{s}\mathrm{i}\mathrm{n}\gamma }}\\ {\tau }_{y\mathit{\text{z}}}={\displaystyle \frac{{\sigma }_{y\psi \mathit{\text{z}}}-{\alpha }_y{\mathrm{c}\mathrm{o}\mathrm{s}}^2\psi -{\alpha }_{\mathit{\text{z}}}{\mathrm{s}\mathrm{i}\mathrm{n}}^2\psi }{2\mathrm{c}\mathrm{o}\mathrm{s}\psi \mathrm{s}\mathrm{i}\mathrm{n}\psi }}\end{array},

where \gamma and \psi are the included angles between plane XOZ and Z axis, plane YOZ, and Y axis, respectively.

Therefore, when {\sigma }_{x\theta y}, {\sigma }_{x\gamma \mathit{\text{z}}}, {\sigma }_{y\psi \mathit{\text{z}}}, \theta, \gamma , and \psi are known, the shear stress of a certain point in rock space can be calculated.

2.2.2 Principal stress calculation method

According to the solid mechanic theory, the principal stress on the space microelement has the following characteristics. If the shear stress of a section on the micro-element body where the in situ stress measurement point O is located at zero, the stress vector T^{\left(n\right)} is in the same direction as the external normal line n. The stress vector can be called the principal stress of the microelement (Schubnel et al., 2007; Zhang and Yin, 2014). Theoretical studies show that there are three principal stresses perpendicular to each other. According to the magnitude, they are respectively called the maximum, intermediate, and minimum principal stress ({\sigma }_1, {\sigma }_2, and {\sigma }_3).

If the principal stress at the in situ stress test point is represented as σ, its direction cosine is represented as {\alpha }_1, {\alpha }_2, and {\alpha }_3, respectively. Then

(10)\{\begin{array}{l}{T}^{\left(1\right)}=\sigma {\alpha }_1\\ T^{\left(2\right)}=\sigma {\alpha }_2.\\ T^{\left(3\right)}=\sigma {\alpha }_3\end{array}

Substituting Eq. (10) into Eq. (6) gives

(11)\{\begin{array}{l}{\left({\sigma }_x-\sigma \right)\alpha }_1+{\tau }_{yx}{\alpha }_2+{\tau }_{zx}{\alpha }_3=0\\ {{\tau }_{xy}\alpha }_1+\left({\sigma }_y-\sigma \right){\alpha }_2+{\tau }_{zy}{\alpha }_3=0.\\ {{\tau }_{xz}\alpha }_1+{\tau }_{yz}{\alpha }_2+\left({\sigma }_z-\sigma \right){\alpha }_3=0\end{array}

Based on the calculation results of Eq. (11), the principal stress {\sigma }_{1,2,3}\ne 0. Furthermore, based on the principle of linear algebra, the principal and partial stress at the in situ stress test point satisfy the following requirements:

(12)\left|\begin{array}{ccc}{\sigma }_x-\sigma & {\tau }_{yx}& {\tau }_{zx}\\ {\tau }_{xy}& {\sigma }_y-\sigma & {\tau }_{zy}\\ {\tau }_{xz}& {\tau }_{yz}& {\sigma }_z-\sigma \end{array}\right|=0.

Expanding Eq. (12) gives

(13){\sigma }^3-I_1{\sigma }^2+I_2\sigma -I_3= 0,

where

(14)\{\begin{array}{c}{I}_1={\sigma }_x+{\sigma }_y+{\sigma }_z\\ I_2={\sigma }_x{\sigma }_y+{\sigma }_y{\sigma }_z+{\sigma }_z{\sigma }_x-{{\tau }_{xy}}^2-{{\tau }_{yz}}^2-{{\tau }_{xz}}^2\\ I_3={\sigma }_x{\sigma }_y{\sigma }_z+2{\tau }_{xy}{\tau }_{yz}{\tau }_{zx}-{{{\sigma }_z\tau }_{xy}}^2-{\sigma }_x{{\tau }_{yz}}^2-{{{\sigma }_y\tau }_{xz}}^2\end{array}.

The calculation equation of principal stress {\sigma }_i is as follows:

(15)\{\begin{array}{c}{\sigma }_1=2\sqrt{-{\displaystyle \frac{p}{3}}}\mathrm{c}\mathrm{o}\mathrm{s}{\displaystyle \frac{w}{3}}+{\displaystyle \frac{1}{3}}{I}_1\\ {\sigma }_2=2\sqrt{-{\displaystyle \frac{p}{3}}}\mathrm{c}\mathrm{o}\mathrm{s}{\displaystyle \frac{w+2\pi }{3}}+{\displaystyle \frac{1}{3}}{I}_2\\ {\sigma }_3=2\sqrt{-{\displaystyle \frac{p}{3}}}\mathrm{c}\mathrm{o}\mathrm{s}{\displaystyle \frac{w+4\pi }{3}}+{\displaystyle \frac{1}{3}}{I}_3\end{array},

where

(16)\{\begin{array}{c}w=\mathrm{a}\mathrm{r}\mathrm{c}\mathrm{c}\mathrm{o}\mathrm{s}\left[-Q/2\sqrt{-{\left(p/3\right)}^3}\right]\\ p=-{\displaystyle \frac{1}{3}}{I_1}^2+I_2\\ Q=-{\displaystyle \frac{2}{27}}{I_1}^3+{\displaystyle \frac{1}{3}}{I}_1{I}_2-I_3\end{array}.

2.2.3 Principal stress direction calculation

The direction cosine of the principal stress vector with respect to axis Y and Z are m_i and n_i, respectively:

(17)\{\begin{array}{c}{m}_i=B/\sqrt{A^2+B^2+C^2}\\ n_i=C/\sqrt{A^2+B^2+C^2}\end{array},

where

(18)\{\begin{array}{c}A={\tau }_{xy}{\tau }_{yz}-\left({\sigma }_y-{\sigma }_i\right){\tau }_{zx}\\ B={\tau }_{xy}{\tau }_{zx}-\left({\sigma }_x-{\sigma }_i\right){\tau }_{yz}\\ C=\left({\sigma }_x-{\sigma }_i\right)\left({\sigma }_y-{\sigma }_i\right)-{{\tau }_{xy}}^2\end{array}i=1,2,3\dots

The azimuth angle {\beta }_i and inclination angle {\theta }_i of the principal stress {\sigma }_i can be calculated as follows:

(19)\{\begin{array}{c}{\theta }_i=\mathrm{a}\mathrm{r}\mathrm{c}\mathrm{s}\mathrm{i}\mathrm{n}{n}_i\\ {\beta }_i=\mathrm{a}\mathrm{r}\mathrm{c}\mathrm{s}\mathrm{i}\mathrm{n}\left(m_i/\sqrt{1-{n_i}^2}\right)\end{array} ,

where the principal stress inclination angle {\theta }_i represents the included angle between the principal stress {\sigma }_i and the horizontal plane XOY (elevation angle when {\theta }_i> 0, depression angle when ). The azimuth of the principal stress {\beta }_i represents the angle between the X axis and the principal stress {\sigma }_i projection on the horizontal plane (counterclockwise when and clockwise when {\beta }_i>0).

In summary, in the in situ stress test and calculation of Kaiser point, parameters of in situ stress measuring point should be obtained including {\sigma }_x, {\sigma }_y, {\sigma }_z, {\tau }_{xy}, {\tau }_{yz}, {\tau }_{zx}, \theta, \gamma , and \psi.

3 In situ stress testing experimental method

3.1 Sample preparation

Rock samples used in the test were taken from the conveyor roadway of Xuyong Coal Mine in Sichuan Province (Fig.4(a)). The depth of the roadway is 386 m, the azimuth is 150°, and the inclination angle is 10°−15°. The direction of the conveyor roadway (150° azimuth) is considered the X-axis. The direction perpendicular to the X-axis (240° azimuth) is considered the Y-axis. The XY plane normal direction is considered as the Z-axis (Fig.4(b)). Rock was drilled from 6 directions X, Y, Z, X \mathrm{\angle }{40}^{\circ }Y, X \mathrm{\angle }{30}^{\circ }Z, and Y\mathrm{\angle }{55}^{\circ }Z in the conveyor roadway (Fig.4(c)). The physical parameters of rock samples are shown in Table 1. The sampling angle does not limit the Kaiser effect point discrimination in this study, so the selection of the sampling angle is random. The rock was sent to the laboratory and processed into a standard cylindrical sample with a size of \phi 50 \times 100 \mathrm{m}\mathrm{m} (Fig.4(d)). Both faces of these rock samples were carefully polished to ensure the unevenness error was less than 0.05 mm.

3.2 Test equipment and methods

The test equipment contains an AE monitoring and uniaxial loading system (Fig.5). SHIMADZU AG-I250 servo material testing machine was the uniaxial loading system. The displacement control was used as a loading method with a loading speed of 0.01 mm/min. The AE monitoring system uses PCI-2 system with the AE signal acquisition threshold value of 40 dB. Before the experiment, rock samples were placed on the test table of the uniaxial loading system. Vaseline was applied on the surface of the acoustic emission probe as a coupling agent to avoid attenuation of the AE signal caused by air on the surface of the probe and specimen. Four acoustic emission probes were attached to the surface of the rock specimen. Before loading, a layer of butter was evenly spread on the upper and lower surfaces of the specimen to reduce the interference of the end effect on the AE signal. After setting the parameters of the AE monitoring and uniaxial loading system, start the experiment with both systems simultaneously. The AE monitoring and uniaxial loading system were shut down when rock fracture occurred, and the stress decreased significantly (Fig.6).

4 Analysis of tests results

4.1 Mechanical and AE characteristics analysis

A representative set of experimental results of uniaxial rock compression in six directions were chosen for characteristics analysis. The strain-stress curve of rock is shown in Fig.6. The strain-stress curves represent different mechanical properties of rock. It can be seen that the rocks in the six directions have obvious anisotropy. Among them, rocks in X and Y-axis directions are not bedding, Z-Axis is vertical bedding, X\mathrm{\angle }{40}^{\circ } Y, X\mathrm{\angle }{30}^{\circ } Z, and Y\mathrm{\angle }{55}^{\circ } Z are inclined bedding. The bedding structure of rock significantly influences its mechanical properties and energy dissipation process under compression (Panteleev et al., 2020). Therefore, this study analyzes the mechanical properties and acoustic emission variations of non-bedded and bedded rocks under uniaxial compression.

Through uniaxial compression and acoustic emission experiments, the compressive stress data of rock specimens in 6 directions and AE data from four groups of AE sensors are measured. Finally, the time-stress-cumulative AE count curves were obtained (Fig.7). From Fig.8(a)−Fig.8(c), with time increases, the 4 cumulative AE count curves maintain similar variation rules, and the total AE numbers remain consistent. By analyzing the rock failure modes after the uniaxial compression test, the fracture angles of non-bedded and vertical-bedded rock specimens are larger. The main failure mode is longitudinal tensile shear failure. The strain-stress curve has an obvious stress drop phenomenon which shows brittle failure. The mechanical failure process is loading-complete failure.

The rock uniaxial compression process can be divided into four stages: elastic deformation, fracture initiation, fracture propagation, and stress failure. At the elastic deformation stage, the microcracks of rock specimens, including those between bedding layers, are compressed, and no new cracks appear or old cracks spread. Therefore, the cumulative AE count at this stage is small and grows slowly. At the fracture initiation stage, the rock appears to have plastic deformation. In the study, the rock sample is sandstone with high hardness. Therefore, at this stage, the expansion of rock micro-cracks releases more considerable strain energy, which accelerates the growth of AE count. When the stress value of rock reaches the maximum historical stress, the AE count take-off point, namely the Kaiser effect point, appears.

The cumulative AE count curve increases quickly with the fracture development acceleration at the fracture propagation stage. However, there are few AE count spikes like Kaiser point. This is because the development of fissures is accelerated but does not increase abruptly at this stage. Therefore, the release rate of strain energy is uniform. At the stress failure stage, the axial load gradually reaches its peak strength. Cumulative AE counts increase more rapidly and experiences unprecedented spikes at more than 99% of peak intensity. By analyzing the AE count variation process of non-bedded and vertical-bedded rock samples in the compression process, it can be concluded that the variation characteristic of cumulative AE count is ‘slow growth - uniform rapid growth - sharp growth’.

Fig.8(d)−Fig.8(f) shows the time-stress-cumulative AE count curve of inclined-bedded rock samples. The four AE counting curves of the same rock sample are close in variation trend but differ significantly in quantity. In the four stages of uniaxial compression, the variation trend of the AE count of rock with inclined bedding is similar to that of non-bedded and vertical-bedded rock. The cumulative AE count curve increases slowly at the elastic deformation stage, accelerates at the fracture initiation stage, further accelerates in the fracture propagation stage, and increases sharply in the stress failure stage. However, the cumulative AE count of inclined-bedded rock shows a step-like upward trend several times. This is due to the difference in internal damage mechanism between non-bedded, vertical-bedded, and inclined-bedded rock specimens under mechanical action.

The failure mode of inclined-bedded rock specimens is mostly slip-shear failure along the bedding plane. By analyzing the damage results of rock after loading, it is found that the rock mass after mechanical loading instability has two approximate parallel shear bands, and the shear plane is scratched. The failure process of rock specimens is loading - local slip shear failure - loading - shear zone instability, and rock specimen failure. During the fracture initiation and propagation stage, multiple local slip failures along the bedding plane occur with energy accumulation. Therefore, the strain energy of rock specimens is released numerous times, and the cumulative AE curve also has several sudden increases. Thus, the AE counting curve presents several step-like upward trends. The damage to the inclined-bedded rock is mainly concentrated in a shear zone parallel to the bedding plane. However, the longitudinal shear fracture plane of non-bedded and vertical-bedded rock runs throughout the specimen. Overall, the AE counts of the inclined-bedded rocks vary significantly in space.

4.2 Kaiser effect point discrimination

Determining the Kaiser effect point is key to in situ stress testing, which determines the accuracy of in situ stress calculation results. The determination of the Kaiser effect point is mainly based on the variation degree of AE characteristic parameters. However, this method is highly subjective, and significant errors can easily occur (Li et al., 2010). In recent years, in-depth research has been conducted on the phenomenon and proposed several Kaiser point discrimination methods. Zhao et al. (2018) constructed the relationship model between acoustic time difference and Kaiser stress point of rock samples. Sabanov (2018) proposed a method to determine the Kaiser point by correlating the dimension of the G-P algorithm. Chen et al. (2020) provided a genetic algorithm method to recognize the Kaiser effect point. The above research results contribute to the Kaiser point’s quantitative judgment. However, the algorithms used are complex, and the efficiency of discriminating the Kaiser point is low. Therefore, this study focuses on the Kaiser effect point discrimination method proposed in Section 2.1, where the Kaiser point is determined comprehensively based on AE count time difference {\tau }_i and time-cumulative AE count curve inclination angle \mathrm{\Delta }{t}_i. The accuracy of Kaiser effect point identification in Section 4.1 is determined by AE parameters

The time-\mathrm{\Delta }{t}_i-{\tau }_i-cumulative AE count curve of the whole mechanical failure process of rock specimens is calculated by Eq. (1) (Fig.8). To minimize the calculation error in space, the calculated data of rock specimens in each direction all come from AE sensor 3. The parameters \mathrm{\Delta }{t}_i and {\tau }_i fluctuate with the increase in axial loading time. The amplitude of fluctuation is closely related to the damage and AE number of the rock. With the continuous loading of the axial load, the amplitude of ∆ T_I wave decreases gradually, and the corresponding \mathrm{\Delta }{t}_i value of {\tau }_i wave time interval is closer to 90°. Therefore, the Kaiser point satisfies both the judgment conditions of \mathrm{\Delta }{t}_i is close to 0 and {\tau }_i is close to 90°.

The Kaiser effect points of rock specimens in the 6 directions were determined according to the above comprehensive judgment method. Noteworthy, the slip shear failure along the bedding plane can also contribute to a sharp increase in the AE curve, which causes improper identification of the Kaiser point. Because the Kaiser point occurs when the rock is under maximum historical stress, there is often no obvious fracture development in the rock at this time. However, when the number of AE increases sharply due to the shear slip of bedding, the development of rock cracks is accelerated, and even macroscopic cracks appear. Therefore, the first point that satisfies the criteria, which are \mathrm{\Delta }{t}_i is close to 0 and {\tau }_i, is close to 90°, and can be regarded as the Kaiser point.

The specimen in the X-axis direction in Fig.8(a) is used for illustration. When t = 164.27 s, the numerical point that conforms to the above criteria appears first. Simultaneously, \mathrm{\Delta }{t}_i= 0.16\mathrm{s} and {\tau }_i={87.41}^{\circ }. The stress value of the rock specimen is 17.0 MPa. This point is the Kaiser point along the X axis. After that, points meeting the above criteria appear in the fracture propagation and stress failure stage, called Kaiser suspected points. At this point, the fracture development degree of rock is large, and the cumulative AE counting curve appears to have multiple take-off points. Therefore, the Kaiser suspected points in these stages cannot be regarded as actual Kaiser effect points.

Similarly, Kaiser effect points of rock specimens in other directions can be obtained by using this determination method (Table 2). The Kaiser effect point discrimination result is identical to Fig.7, which proves the method’s effectiveness. Substituting Kaiser point calculation results into the calculation equations of in situ stress in Section 2.2, and the in situ stress calculation results by the Kaiser effect are obtained (Table 3). The maximum and minimum principal stresses are close to the horizontal direction, and the intermediate principal stress is close to the vertical direction. In engineering, the ratio of horizontal stress ({\sigma }_1) to vertical stress ({\sigma }_2) is regarded as the lateral pressure coefficient. In this study, the lateral pressure coefficient is 2.01, indicating that the original rock stress of this roadway is dominated by tectonic stress.

4.3 In situ stress calculation based on COMSOL

4.3.1 Calculation model establishment

To verify the accuracy of the calculated results of ground stress, this study simulated the in situ stress at the rock sampling points at the Xuyong Coal Mine. The COMSOL simulation can effectively analyze the stress distribution regularly near rock sampling points and provide the theoretical basis for road safety protection work. Numerous studies have been published on rock mechanics simulation, but there is a lack of research on the distribution law of ground stress. Cao et al. (2022) verified the statistical damage constitutive rock mass model by COMSOL and MATLAB software. They determined that the stress distribution of round holes surrounding rock is circular under the same in situ stress. Zhang et al. (2022) solved the rock state damage variable, displacement, and pressure in hydraulic fracturing by COMSOL simulation. A permeability anisotropy model was established to characterize hydraulic fracturing of a coal seam. Basirat et al. (2021) developed a fracture fluid flow model in a filling well in COMSOL. The change rule of fracture radius in different fracturing stages was obtained.

According to the geological conditions of rock sampling points (referring to the roadway information presented in Section 3.1), a 3D model of X × Y × Z = 80 m× 80 m× 80 m was established using COMSOL, including a conveyor roadway with an inclination angle of 10°. The model grid contained 110372 units (Fig.9(a)). The X-axis is the horizontal direction, ranging from −20−20 m; the Y axis is the horizontal direction perpendicular to the X axis, and with a 14° angle with the roadway, ranging from 0 to 40 m; the Z-axis is in the vertical direction ranging from −20 to 20 m.

As shown in Fig.9(b), the model top is subjected to the overlying rock stress. Usually, the vertical stress gradient of the rock is 25−30 KPa/m (Lu et al., 2020), and the burial depth of the conveyor roadway in the Xuyong Coal Mine is 386 m. Therefore, the overlying pressure boundary load value was set as 11.6 MPa. The model bottom was applied with fixed constraint boundary, and the roller support was adopted for the other four sides. The physical and mechanical parameters of rock after experimental tests are shown in Table 4. The Mohr-Coulomb model was applied to calculate in situ stress.

A monitoring surface and two monitoring lines were added to the geometric physical model to study the in situ stress distribution around the rock sampling point. The monitoring plane was XOZ located at Y = 20 m. In the monitoring plane, there was a monitoring line parallel to the X-axis and Z-axis. The intersection of the two lines is the rock sampling point of the Kaiser effect, namely the in situ stress test point. The test point was close to the right arch foot of the roadway, with a horizontal distance of 1 m and a vertical distance of 0.5 m.

4.3.2 In situ stress calculation results analysis

The principal stresses calculation results on the monitoring surface are shown in Fig.10. As the roadway trend in the calculation model is slightly inclined, the principal stress distribution presents weak asymmetry. The maximum, intermediate, and minimum principal stresses are in the shapes of ‘∞’, ‘+’, and square distribution, respectively. Three-directions principal stress is dominated by compressive stress. Small tensile stress exists in the shallow part of the roadway roof and floor. An obvious principal stress concentration exists at 1−5 m on both sides of the roadway. The test point is located in the main stress concentration area.

The principal stress difference of roadway surrounding rock presents a butterfly distribution (Fig.10(d)). The main stress difference relief zone is the shallow part of the roadway roof and floor. There is a prominent concentration area of principal stress difference within 5 m on the roadway on both sides. The deeper the surrounding rock extends, the smaller the principal stress difference—the more significant the difference in principal stress, the greater the possibility of rock failure. Therefore, the two sides of the roadway are more prone to collapse than the roof and floor. The safety protection work of the conveyor roadway in the Xuyong Coal Mine should focus on supporting the two sides.

To analyze the stress distribution in horizontal and vertical directions, the variation of principal stress and stress difference between the two monitoring lines and test point was studied (Fig.11). The −2.5−2.5 m range of the X monitoring line is the hollow area of the roadway, and no stress distribution exists. The stress and stress difference curves are humped. The stress increases within the 0−2 m range of the roadway᾽s two sides, and the maximum value of the principal stress difference appears near the detection point. As the surrounding rock depth increases, the principal stress and the principal stress difference decrease and tend to be stable. The {\sigma }_2 and {\sigma }_3 finally approach, and the principal stress difference is approximately 8.5 MPa.

The 0−5 m range of the Z monitoring line is in the same horizontal plane as the roadway, called the parallel area. It contains the extreme point of principal stress and stress differences. The {\sigma }_3 curve has a basin shape with a single peak. When Z = 0.5−3 m, the principal stress difference is approximately the maximum of 16 MPa. Similar to the X monitoring line, the principal stress and the principal stress difference gradually stabilize away from the roadway. At the test point, the {\sigma }_1, {\sigma }_2, and {\sigma }_3 are 22.01 MPa, 10.46 MPa, and 5.88 MPa, respectively.

The in situ stress results calculated by CMOSOL were compared with the Kaiser effect. Among them, the maximum principal stress of the deviation rate is: \left|{\sigma }_{1ae}-{\sigma }_{1re}\right|/{\sigma }_{1re}\times 100\mathrm{\%}=4.42\mathrm{\%}. Where {\sigma }_{1ae} is the maximum principal stress {\sigma }_1 calculated by the Kaiser effect, and {\sigma }_{1re} is {\sigma }_1 obtained by COMSOL. The deviation rates of the three principal stresses are 4.42%, 3.92%, and 3.63%, respectively, which are all less than 5%. Therefore, the in situ stress calculation results based on the Kaiser effect in this study are effective.

5 Conclusions

The discrimination of the Kaiser effect points and the rock sampling direction are always complex problems in in situ stress calculations. In this study, a Kaiser point discrimination method based on AE count curve parameters \mathrm{\Delta } t_i and {\tau }_i is established, free from inaccuracies caused by the rock sampling direction. Taking the sandstones of the Xuyong Coal Mine as the research object, uniaxial and acoustic emission tests were performed to calculate the in situ stress. The COMSOL simulation was used to verify the accuracy of in situ calculation results. The distribution law of the three-direction principal stresses near the roadway is also studied. The main conclusions of this study are summarized as follows.

1) Under uniaxial compression, non-bedded, vertical-bedded, and inclined-bedded rocks exhibit different mechanical and AE characteristics. The analysis shows that the root cause of the different rules lies in the difference in the damage process inside the rock. The failure mode of the former is mainly longitudinal tensile shear failure. The strain-stress curve has an apparent stress drop phenomenon. The failure mode of the latter is mainly slip shear failure along the bedding plane. As the damage of inclined-bedded rocks is mainly concentrated in shear zones of parallel bedding planes, numerous spatial differences exist in AE counts.

2) The Kaiser effect points can be effectively identified without interference from the other take-off points of AE count curves based on the two criteria of AE count curve time difference \mathrm{\Delta } t_i approaching 0 and inclination angle {\tau }_i approaching 90°. In fracture initiation and propagation stages, the Kaiser points of rock samples appear in six sampling directions. The values, azimuth, and inclination angles of the three-direction principal stress were calculated as {\sigma }_1= 22.81\mathrm{M} \mathrm{P}\mathrm{a}, {\sigma }_2=10.87 \mathrm{M}\mathrm{P}\mathrm{a}, and {\sigma }_3= 6.14\mathrm{M} \mathrm{P}\mathrm{a}. The lateral pressure coefficient of conveyor roadway in the Xuyong Coal Mine is 2.01, indicating that the original rock stress is dominated by tectonic stress.

3) The magnitude and distribution of in situ stress in roadway surrounding rock were studied by COMSOL simulation. The maximum, middle, and minimum principal stresses show ‘∞’, ‘+’, and square shape distribution, respectively. The principal stress difference of roadway surrounding rock shows butterfly shape distribution. The principal stress concentration is severe on the two sides of the roadway. Therefore, support needs to be provided to both sides of the roadway. Comparing the calculation results of COMSOL simulation with those of the Kaiser effect, the deviation rates of the three-direction principal stress {\sigma }_1, {\sigma }_2, and {\sigma }_3 are 4.42%, 3.92%, and 3.63%, respectively. This comparison verifies the accuracy of the calculation results of in situ stress based on the Kaiser effect in this study.

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