Influence of Tunnel Axis Stress on Strainburst: An Experimental Study

Abstract

This paper investigates the influence of tunnel axis stress on strainburst. An experimental study of strainburst was conducted using a true-triaxial rockburst system. During the test process, a loading path that maintained one face free and applied loading along three axial directions on the other five faces was used to simulate the change of stresses of a representative rock element near the excavated boundary during strainburst process. Different X direction stresses were applied on rectangular prismatic granite specimens to simulate different tunnel axial stresses acting on rocks. High-speed cameras were used to monitor the rock failure process. The kinetic energy of the ejected fragments was quantitatively estimated by analyzing the recorded videos. The experimental results indicate that the tunnel axis stress has a significant influence on the strainburst characteristics. With increasing X direction stress, the strength of rock specimens increases continually and subsequently decreases gradually after reaching a peak, whereas the volume of the rockburst pits and the kinetic energy of the ejected fragments first increase continually, subsequently decrease gradually and finally increase drastically.

1 Introduction

Rockburst is a typical geological disaster that occurs during deep underground excavations and is frequently accompanied by rock fragment ejection at high speed. Such a dynamic failure poses a significant threat to workers and construction equipment. Considerable efforts have been devoted to investigation of the rockburst (Cook 1965; Ortlepp and Stacey 1994; Kaiser et al. 1996; He et al. 2010; Zhu et al. 2010; Feng et al. 2015). However, the rockburst mechanism is still unclear and should be further explored. Generally speaking, rockburst is classified into three major types: strainburst, fault-slip-burst and pillar-burst. Strainburst is the most common rockburst and is caused by strain energy release of the rock mass near the free boundary after excavation. Thus, gaining deeper insight into strainburst is important for safe construction and operation of deep underground excavations.

Strainburst frequently occurs in rock masses near the excavated boundary. Thus, strainburst is closely related to the stress state of the rock masses near the excavated boundary. As shown in Fig. 1, before excavation, the rock masses at depth exist in a true-triaxial equilibrium state (σ ₁ > σ ₂ > σ ₃). An open of free boundary changes the stress state of the rock masses near the excavated boundary. The tangential stress σ _θ increases gradually, the radial stress σ _r decreases rapidly, and the axis stress σ _a varies slightly. After excavation, as a result of the Poisson effect caused by increasing tangential stress, the radial stress is slightly elevated again and shows a gradient variation. The radial stress on the free face is relieved completely. With the increase in the distance away from free face, the radial stress increases. In addition, because of the constraint of the surrounding rock elements, shear stresses act on the surface of the representative rock element. As discussed above, the representative rock element near the excavated boundary exists in a special stress state, namely, “one face freed and the other five faces stressed”. Once the tangential stress increases to the strength of the representative rock element, strainburst may occur.

Fig. 1

Stress state of a representative rock specimen before and after excavation (σ ₁, σ ₂ and σ ₃ are initial stresses, and σ ₁ > σ ₂ > σ ₃; σ _θ , σ _a and σ _r are stresses acting on representative rock element, and σ _θ  > σ _a  > σ _r )

In previous studies, rock masses near the excavated boundary were usually considered in a uniaxial or biaxial state and the corresponding rockburst was studied using uniaxial compression tests (Cook 1963; Singh 1987, 1989; Li et al. 2004; Cho et al. 2005; Okubo et al. 2006; Jiang et al. 2015) or biaxial compression tests (Cai 2008; Zhao et al. 2014). However, both the uniaxial tests and biaxial tests fail to describe the stress state of the rock mass where strainburst occurs. Experimental study under true-triaxial condition is needed. In recent years, true-triaxial rockburst tests have been used to simulate the stress change and boundary of rock masses after excavation. This approach has gradually replaced the uniaxial, biaxial, conventional triaxial and true-triaxial tests and has become the preferred method in investigation of rockburst. For example, He et al. (2007, 2012a, b, 2014) conducted a true-triaxial rapid unloading test on granite using a developed true-triaxial machine and successfully simulated the strainburst process during the underground excavation. After performing the true-triaxial unloading test, Zhao and Cai (2014) discussed the influence of width and height on strainburst, and Gong et al. (2015) analyzed the crack angle of rockburst faulting planes. During these studies, unloading tests were conducted to simulate the strainburst under the high initial ground stress condition after excavation. However, the rockburst recorded in tunnel construction, such as in the Jinping II Hydropower Station in China, shows that most instant strainbursts occurred 2–5 h after excavation (Feng et al. 2003), indicating that the tangential stress concentration is a progressive process. Tangential stress concentration should be considered. Therefore, loading tests under true-triaxial condition are needed to investigate the rock failure characteristics during strainburst.

Per the discussion above, the representative rock element near the excavated boundary exists in a special true-triaxial stress state. Except for the tangential stress and radial stress, the tunnel axis stress is also a significant factor that affects rock failure under a true-triaxial state. Because the tunnel axis stress is lower than the tangential stress but higher than the radial stress after excavation, the tunnel axis stress is usually referred to as the intermediate principal stress in previous research. The influence of the intermediate principal stress on rock failure is commonly acknowledged, and it was first verified that, under constant minimal principal stress σ ₃ condition, the rock strength in the conventional triaxial extension test (σ ₁ = σ ₂ > σ ₃) was higher than that in the conventional triaxial compression test (σ ₁ > σ ₂ = σ ₃) (Murrell 1963; Handin et al. 1967). Subsequently, Mogi (1967, 1971, 1972) reported an outstanding contribution to the study of the effect of intermediate principal stress on rock failure by fabricating a high-pressure true-triaxial stress machine to test hard rock under three independently applied principal stresses. For better understanding of the influence of the intermediate principal stress on the rock deformation failure, improved true-triaxial testing machines were developed (Takahashi and Koide 1989; Haimson and Chang 2000; Li et al. 2015; Feng et al. 2016). In addition, advanced numerical methods have provided a deeper insight into the influence of intermediate principal stress on rock failure (Cai 2008; Shi and Li 2009; Pan et al. 2012). For example, a combined FEM/DEM numerical tool was used to investigate the impact of intermediate principal stress on rock fracturing and strength near the excavation boundary (Cai 2008). Based on EPCA3D software, the mechanism of the intermediate principal stress effect on rock failure behavior was studied; the end effect and material homogeneity are thought to be the two main reasons for the influence of the intermediate principal stress on rock failure (Pan et al. 2012). These aforementioned studies have enhanced the understanding of the influence of intermediate principal stress on rock failure, and strength criteria that consider the intermediate principal stress have also been proposed (Mogi 1971; Colmenares and Zoback 2002; Mogi 2007; You 2009; Chang and Haimson 2012). As mentioned above, significant achievements were reported that revealed the influence of the intermediate principal stress on the static failure of rocks without fragment ejection. However, the influence of the intermediate principal stress corresponding to tunnel axis stress on rockburst has not yet been studied systemically.

This paper presents an experimental study on the influence of tunnel axis stress on strainburst. One free face loading tests under true-triaxial condition were performed to simulate the strainburst using a true-triaxial rockburst testing apparatus. The strainburst process was monitored using two high-speed cameras, a stress–strain recording system and a voice recorder. As detailed in the following sections, the true-triaxial rockburst testing apparatus, testing plan and granite specimen are introduced first. Second, the experimental results are presented. Finally, the influence of the tunnel axis stress on the rock strength and the kinetic energy of the ejected fragments are discussed systematically.

2 Test

2.1 True-Triaxial Rockburst Testing Machine

The used true-triaxial rockburst testing machine is developed at Guangxi University, Nanning, China, as shown in Fig. 2. The testing machine is highly rigid with a stiffness of 9000 kN/mm in the vertical direction and 5000 kN/mm in the horizontal direction, and it can load/unload along three mutually orthogonal directions, which allows application of 5000 kN of vertical force and 3500 kN of lateral force via a servo-control system. A significant function of the testing apparatus is the two mutually independent loading systems along the Y direction, by which the loading along the Y direction on one face of the tested specimen can be unloaded, while the loading on the opposite face is held constant. In addition, the loading on the opposite side of the free face can still be increased. Thus, the loading path of “maintaining one free face and loading on the other free faces” can be used to simulate the tangential stress concentration and radial stress distribution of rock masses near the excavated boundary, as shown in Fig. 3. During the test, the stresses are directly applied on the surface of the specimens using a rigid loading bar. In such a situation, shear stress occurs between the surface of the specimen and the end of the rigid platen. “End effect” should be reduced in a conventional true-triaxial test. However, the object of the current study is rock failure in a certain region in the initial stress space rather than in the principal stress space, and shear stress on the representative rock element caused by the surrounding rock element is allowable. This shear stress can be mimicked by friction acting between the surface of the specimen and the rigid platen.

Fig. 2

True-triaxial rockburst experimental system

Fig. 3

Rock specimen under the one free face true-triaxial loading condition: a front view; b back view

High-speed cameras, linear variable differential transformer (LVDT) deformation sensors, and a decibel meter are used to monitor the rockburst process.

2.2 Testing Plan

In the present tests, the X direction stress σ _x , the Y direction stress σ _y and the Z direction stress σ _z correspond to the in situ tunnel axis stress σ _a , radial stress σ _r and tangential stress σ _θ , respectively.

A commonly admitted loading path, maintaining loading after unloading, is usually used to simulate the stress change of the rock masses near the free boundary after excavation, as shown in Fig. 4a. This loading path is described as follows. Stresses on the surfaces of the specimens are simultaneously increased to predefined values to simulate the initial ground stress state. Subsequently, one of the Y direction stresses σ _y1 is suddenly unloaded using an abrupt unloading device, i.e., two swing links, to emulate excavation in underground construction. The other Y direction stress σ _y2 on the opposite of the free face is rapidly decreased to zero, then, and is subsequently increased to a given value to describe the change process of the radial stress on the rock masses near the excavated boundary. The X direction stress σ _x is held constant. Finally, the vertical stress is continuously increased until the rock specimen fails.

Fig. 4

Loading path in the rockburst test: a initial loading path; b improved loading path

According to our testing trial, the process of “suddenly unload σ _y1 and rapidly decrease σ _y2 to zero” can be neglected. Therefore, the improved loading path shown in Fig. 4b is used and can be described as follows: maintain one free face and increase the stress on other five surfaces to specific values at the same time, hold σ _x and σ _y constant on the opposite of the free face, and continue to increase σ _z until the rock specimen fails. It can be found that when the initial ground stress is far less than the rock strength, the experimental result using the improved loading path is consistent with that using the initial loading path. Furthermore, because the unloading process is neglected, the tests using the improved loading path is highly efficient compared with the tests using the initial loading path. Thus, the improved loading path was used.

The testing plan is shown in Table 1. Based on experience, σ _y is set to 1 MPa. To reveal the influence of tunnel axis stress on rockburst, different σ _x values are considered. The testing processes are described in detail as follows. First, the specimen was loaded at 0.002 mm/s up to 20 kN along the vertical direction and 10 kN along the horizontal direction, and one surface of the tested specimen was free. The σ _x and σ _y were increased to specific values and held constant, while σ _z was increased with a loading rate of 0.5 MPa/s until the specimen failed.

Table 1 Testing plan

2.3 Rock Specimen

The aim of previous experimental tests under the true-triaxial condition was to investigate the mechanical behavior of a point or a microelement. In general, rockburst is a failure of rock masses in a spatial scope near the excavated boundary. The radial stress of the representative rock element near the excavated boundary shows a gradient variation. To simulate the gradient-varied radial stress, a rectangular prismatic rock specimen with dimensions of 100 mm (length along the X axis) × 100 mm (thickness along the Y axis) × 200 mm (height along the Z axis) was used in our tests, dimensions that are larger than those (150 mm × 60 mm × 30 mm) used in the true-triaxial strainburst tests in previous research (He et al. 2007, 2012a, b, 2014). The specimens are red coarse granite from Guangxi province in China. The intact granite is a typical brittle-hard rock material, and its major minerals are quartz, feldspar and mica. The specimens have a uniaxial compression strength of 114 MPa and a density of 2570 kg/m³. The P-wave velocities of these specimens are nearly 5240 m/s. Based on the wave velocity results, it is reckoned that the specimens contain similar initial damage. Considering the discreteness of rock mechanical test, three samples were prepared for each test with a given σ _x .

3 Testing Results

To facilitate observation of the failure process of the tested specimens, the free face of tested specimens was divided into 18 sub-regions marked with A-R. Selected still images captured from video recorded by high-speed camera are presented to describe the failure characteristics of the tested specimens. As shown in Fig. 5, all of the tested specimens show strainburst failure behavior. The strainburst process can be divided into grain ejection, splitting of rock into plates, rock plate bending, and fragment ejection at the instant when the rock plates break off.

Fig. 5

Failure processes of typical tested specimens under different σ _x conditions: a σ _x  = 10 MPa, b σ _x  = 20 MPa, c σ _x  = 30 MPa, d σ _x  = 40 MPa, e σ _x  = 50 MPa, f σ _x  = 60 MPa, g σ _x  = 70 MPa, h σ _x  = 80 MPa, i σ _x  = 90 MPa, j σ _x  = 100 MPa and k σ _x  = 110 MPa. The numbers at the bottom-left corner of the pictures indicate the time in h:m:s

The maximum decibel values of the sound monitored during the rockburst process of typical tested specimens under different σ _x conditions are shown in Fig. 6. It can be observed that with an increase in σ _x , the maximum decibel value of the sound first increases, subsequently decreases and finally increases. Because sound can be used to classify the intensity of the rockburst (Russenes 1974), we inferred that the intensity of the strainburst first increases, subsequently decreases, and finally increases with the increase in σ _x .

Fig. 6

The maximum decibel values of the monitored sound of the typical tested specimens under different σ _x conditions

3.1 Influence of σ _x on Failure Form of Rock Specimen

Figure 7 presents the failure forms of the typical tested specimens under different σ _x conditions. When σ _x is less than 90 MPa, the failure form of the tested specimens is known as the zoning failure form, i.e., rockburst pits on and near the free face and shearing cracks away from the free face. When σ _x is 100 MPa or 110 MPa, the tested specimens were broken into several rock pieces. The failure forms in present study obviously vary with the single shear failure (Haimson and Chang 2000) or single tensile failure (Haimson and Chang 2002) in conventional true-triaxial tests in previous research.

Fig. 7

Failure forms of the typical tested specimens under different σ _x conditions: a σ _x  = 10 MPa, b σ _x  = 20 MPa, c σ _x  = 30 MPa, d σ _x  = 40 MPa, e σ _x  = 50 MPa, f σ _x  = 60 MPa, g σ _x  = 70 MPa, h σ _x  = 80 MPa, i σ _x  = 90 MPa, j σ _x  = 100 MPa and k σ _x  = 110 MPa

Figure 8 presents the volume of the rockburst pits of typical tested specimens under different σ _x conditions. It can be observed that with increasing σ _x , the volume of the rockburst pits increases, subsequently deceases and finally increases. The variation in the volume of the rockburst pits is consistent with that of the intensity of the rockburst. Thus, the volume of the rockburst pits is closely related to rockburst intensity.

Fig. 8

Volume of rockburst pits of the typical tested specimens with rockburst failure behavior under different σ _x conditions

3.2 Influence of σ _x on Rock Strength

Figure 9 shows Z direction stress–strain curves of the typical tested specimens under different σ _x conditions. An obvious yield point can be observed on each stress–strain curve in the pre-peak area. Furthermore, a yield platform, namely, obvious plastic deformation between the yield point and peak point, can be noted on each stress–strain curve. The yield platform corresponds to the pre-peak energy dissipation. This pre-peak energy dissipation is caused by the rock elements near free face being split into rock plates, rock plate bending, and the rock elements behind the rock plates breaking into pieces.

Fig. 9

Z direction stress–strain curves of the typical tested specimens under different σ _x conditions

Figure 10 shows the rock strength under different σ _x conditions. As σ _x increase in the range from 10 to 80 MPa, the strength increases and its increase rate (ratio of the change of rock strength with respect to the increment of σ _x ) decreases. When σ _x increase in the value range from 80 to 110 MPa, the strength decreases and its decrease rate increases. The highest rock strength of the typical stressed specimen under a σ _x of 80 MPa is 260 MPa, which is 24% larger than 210 MPa under a σ _x of 10 MPa and 4% larger than 250 MPa under a σ _x of 110 MPa condition. Thus, with an increase in σ _x , the rock strength first increases and subsequently decreases after reaching a peak.

Fig. 10

Strength of the tested specimens under different σ _x conditions

3.3 Influence of σ _x on Kinetic Energy of Strainburst

The kinetic energy of the ejected fragments can be taken as important indicators for quantitative assessment of the intensity of the rockburst.

Generally speaking, the kinetic energy of an ejected fragment during strainburst is described by

$$ E_{\text{k}} = \frac{1}{2}mv^{2} $$

(1)

where m is the mass of the ejected fragment, and v is the speed of the ejected fragment. The mass can be weighed directly, and measurement of speed of the ejected fragments is described in details as following.

The ejection speed of the fragments was measured by analyzing the video of rock fragment ejection using the dynamic image analysis software Image Pro Plus 7.0 (Fig. 11). The layout of the high-speed camera system is shown in Fig. 12. It should be noted that an angle exists between the ejection direction of the fragment and the recording direction of the high-speed camera, which means that the measured speed is different from the actual speed. According to the layout of the high-speed cameras, the relationship between the measured speed v′ and actual speed v can be described as v = v′/cosα, where α is the angle between the measured speed and actual speed. Using this relationship, the actual speed can be obtained. In addition, because the direction of the ejected fragments was approximately perpendicular to the free face of tested specimen during rock failure process in one free face true-triaxial test. The angle α is 30° for high-speed camera #1 and 15° for high-speed camera #2.

Fig. 11

Speed measurement interface of Image Pro Plus 7.0

Fig. 12

Layout of high-speed camera system

To facilitate analysis, the rock fragments were divided into several groups according to three different particles size (as shown in Fig. 13, taking the fragments of tested specimen under σ _x of 10 MPa condition as an example), including coarse fragments with diameter larger than 9.50 mm (the size of these fragments is relative large and can be directly measured), medium size fragments with diameter between 4.75 and 9.50 mm (these fragments were still countable, while size of these fragments was hard to be measured), fine size fragments with diameter less than 4.75 mm (the number and size of these fragments cannot be obtained).

Fig. 13

Ejected fragments of the typical tested specimen under σ _x of 10 MPa condition

Then, identification of the fragments in the video, i.e., corresponding the ejected fragments in the video with the actual fragments, was conducted, according to the marks, dimension and characteristics of the fragments. The marks and characteristics of the fragments can be directly observed. The dimensions of the fragments in the video were measured via the following method. First, the actual dimension of the length of rock specimens is obtained using a measuring tool, and the video-measured dimension of the length of rock specimens is measured via an analysis software. Subsequently, an actual dimension to video-measured dimension ratio can be calculated, and the actual particle size of specific fragments in the video can be determined using the video-measured particle size and the ratio.

For fragments with diameters beyond 9.50 mm, the ejection speed of each fragment can be directly measured, which was the average of speeds of several feature points on a fragment. For the fragments with particle size between 4.75 and 9.50 mm, the ejection speeds of fragments were measured and the average value was taken as the ejection speed. For the fragments with particle size less than 4.75 mm, the speeds of fragments in different locations were measured, and the average value was viewed as the ejection speed.

After obtaining the speed and mass of the ejected fragments, the total kinetic energy of the ejected fragments can be calculated according to the following formula:

$$ E_{k} = \sum\limits_{i = 1}^{n} {\frac{1}{2}m_{1i} \bar{v}_{1i}^{2} + \frac{1}{2}M_{2} \bar{v}_{2}^{2} + } \frac{1}{2}M_{3} \bar{v}_{3}^{2} $$

(2)

where n is the number of coarse fragments, m _1i is the mass of the ith coarse fragment, M ₂ is the total mass of the medium size fragments, M ₃ is the total mass of the fine size fragments, $\bar{v}_{1i}$ is the speed of the centroid point of the ith coarse fragment, $\bar{v}_{2}$ is the average speed of the medium size fragments, and $\bar{v}_{3}$ is the average speed of fine size fragments.

The kinetic energy of the ejected fragments under different σ _x conditions is plotted in Fig. 14. For constant σ _y , the kinetic energy of the ejected fragments increases continually, subsequently decreases gradually and finally increases rapidly as a function of σ _x . For the typical tested specimens, when σ _x varies in the low value range (10–60 MPa), the kinetic energy of the ejected fragments increases, the increases rate (ratio of the change of kinetic energy of ejected fragments with respect to the increment of σ _x ) declines, and the average increase rate is 0.09 J/MPa; As σ _x increases in a relatively high value range (60–90 MPa), the kinetic energy of the ejected fragments decreases, the decreases rate increases, the average decreasing rate is 0.16 J/MPa; For σ _x increasing in a high value range from 90 to 110 MPa, the kinetic energy of the ejected fragments increases, the increasing rate increases, and the average increasing rate is 0.43 J/MPa. It is indicated that the effect of σ _x on the kinetic energy of ejected fragments under high σ _x conditions is more significant than that under low σ _x conditions.

Fig. 14

Kinetic energy of ejected fragments under different σ _x conditions

The highest kinetic energy of the typical strainburst under σ _x of 110 MPa is 11.2 J, which is 267% larger than 3.05 J under σ _x of 10 MPa, 48% larger than 7.55 J under σ _x of 60 MPa and 319% larger than 2.67 J under σ _x of 90 MPa.

4 Discussion

4.1 Influence of σ _x on Rock Strength

The experimental results indicate that under one free face true-triaxial loading condition the rock strength increases with increasing σ _x and subsequently decreases after reaching a peak (Fig. 9). The influence of σ _x on rock strength approximates those (see Fig. 15) reported in the conventional true-triaxial tests of previous studies (Mogi 1971; Haimson and Chang 2000).

Fig. 15

True-triaxial experimental results under different intermediate principal stress conditions from a Dunham dolomite (Mogi 1971) and b Westerly granite (Haimson and Chang 2000)

As mentioned above, one question is apparent: Why does the strength increase and subsequently decrease with an increase in the tunnel axis stress (intermediate principal stress)? In the past, scholars tried to explore the question from different viewpoints. Adopting an internal friction theory, Mogi (1967) attempted to explain that the strength of the rock increases with the intermediate principal stress under the conventional true-triaxial stress state. Before overall failure, many initial micro-cracks randomly occur in the rocks. At failure, the combination of micro-cracks leads to the formation of macro-cracks. These micro-cracks are situated subparallel to the direction of the crack surface. The orientations of the macro-cracks might slightly vary from the intermediate principal stress direction. The intermediate principal stress has a normal component in the cracks. Thus, with the increase in the intermediate principal stress, the friction resistance of the faulting increases, leading to the increase in the rock strength. However, the decrease in the rock strength with further increases in the intermediate principal stress was not mentioned by Mogi. Based on a numerical modeling system EPCA3D, Pan et al. (2012) discussed the reasons why the rock strength first increases and subsequently decreases with the increase in intermediate principal stress. The conclusion was that the moderate intermediate principal stress delays the onset of failure propagation of the rock element in the pre-peak region, which leads to the increase in the rock strength. When the intermediate principal stress exceeds a certain value, a large number of internal rock elements fail in the pre-peak region, and the strength of the rock tends to decrease.

The rock strength in the current study is the strength of the tested specimen under the one free face loading condition, which is different from the rock strength under conventional true-triaxial condition. The variation of the rock strength with increasing tunnel axis stress, especially the decrease of rock strength under high tunnel axis stress conditions, is explained as follows. To address this, constraint effect and Poisson effect are first introduced.

Generally speaking, when a rock mass is compressed in one direction, it usually tends to expand in the other two directions perpendicular to the direction of compression (Fig. 16a). This phenomenon is known as the Poisson effect. For the rock mass in a conventional true-triaxial compression state, expansion is usually significant along the minimal principal stress direction (Fig. 16b). In the current study, the rock specimen existed in a special stress state, namely, maintaining one face free and loading along three axial directions on other faces, and the expansion obviously occurred along the direction perpendicular to the free face (Fig. 16c). This Poisson effect (expansion) is caused by the combination of σ _x and σ _z , which results in that the rock elements on the free face are split into rock plates and the rock plates bend outward along Y direction.

Fig. 16

Deformation of rectangular specimen under different loading conditions: a uniaxial compression, b true-triaxial compression (σ _z  > σ _x  > σ _y ), c one free face true-triaxial compression. The dashed line is the boundary of the rectangular specimen after loading

The constraint effect is the lateral friction induced by σ _x in the tested specimens, as shown in Fig. 17. This constraint effect is described as follows. In our testing process, with increasing Z direction stress, the rock materials on the free face are split into rock plates, and the rock plates tend to bend outward. The bend of the rock plates along the Y direction is constrained by σ _x . The rock plates gradually break away from the lateral constraint of σ _x , dissipating a large amount of elastic strain energy. When the Z direction stress increases to the peak strength of the rock specimen, the rock plates shed the lateral constraint of σ _x completely and are ejected out. This constraint effect increases with increasing σ _x . It should be noted that the rock plates break off and the strainburst occurs only if the Poisson effect induced by σ _x and σ _z is superior to the constraint effect, and bend of rock plates is increased to its threshold.

Fig. 17

Top view of the tested specimen under one free face true-triaxial loading condition

To summarize, the constraint effect hinders the bend of rock plates along Y direction, while the Poisson effect expedites this bend of rock plates. According to the constraint effect and the Poisson effect, the variation in the rock strength with increasing σ _x is described as follows.

• 1. When σ _x is in a low value range from 10 to 80 MPa, the σ _x -induced Poisson effect is small. The variation of the rock strength of the rock specimen is primarily affected by the σ _z -induced Poisson effect and constraint effect. During the testing process, the bend of rock plates is constrained by the constraint effect. With increasing σ _x , the constraint effect is greater. A greater σ _z -induced Poisson effect is needed to cause sufficient bend of rock plates corresponding to rock specimen failure. Consequently, the necessary σ _z , (i.e., the rock strength) increases. Therefore, the rock strength increases as σ _x increases from 10 to 80 MPa.

• 2. When σ _x is in a high value range from 80 to 110 MPa, the σ _x -induced Poisson effect is remarkable, and the corresponding σ _x -induced bend of rock plates is significant. As a result of the combination of the σ _x -induced Poisson effect and the σ _z -induced Poisson effect, the bend of rock plates can easily reach its threshold. The σ _x -induced constrain effect is favorable to the increase of rock strength. However, with increasing σ _x , the corresponding σ _z at the moment of rockburst decreases. This indicates that under a high σ _x conditions, the σ _x -induced Poisson effect on the rock strength is more significant than the σ _x -induced constraint effect on the rock strength. The variation of the strength of the rock specimen is primarily controlled by the σ _x -induced Poisson effect. Therefore, with the increasing σ _x in high value range, the contribution of the σ _x -induced Poisson effect to the bend of rock plate increases, and the contribution of the σ _z -induced Poisson effect to the bend of rock plate decreases, leading to the decrease in σ _z , i.e., the rock strength.

4.2 Influence of σ _x on Kinetic Energy of Strainburst

The kinetic energy of the ejected fragments can serve as a direct index for assessment of the intensity of the strainburst. The experimental results in the present study indicate that with the increase of σ _x , the kinetic energy of the ejected fragments increases continuously, subsequently decreases gradually and finally increases rapidly. This variation in the kinetic energy of the ejected fragments was not revealed in previous studies. In addition, the variation of the rockburst pit volume and the maximum decibel values of the sound with increasing tunnel axis stress are similar to that of the kinetic energy of the ejected fragments.

The kinetic energy of the ejected fragments is related to the accumulated elastic strain energy in the pre-peak. The accumulated elastic strain energy is dependent on the rock strength of the tested specimens. Hence, the variation of the kinetic energy of the ejected fragments should be consistent with that of the rock strength with the increase in σ _x . However, in this research, the kinetic energy variation of the ejected fragments is not in agreement with that of the rock strength of the tested specimens. For σ _x increasing from 10 to 60 MPa, both the kinetic energy of the ejected fragments and the rock strength of the tested specimens show an increasing variation. When σ _x increases from 60 to 80 MPa, the rock strength increases continually, while the kinetic energy of the ejected fragment decreases. With the increase of σ _x to greater than 80 MPa, the kinetic energy increases again, and the rock strength shows a decreasing variation. Thus, the variation in the kinetic energy of the ejected fragments cannot be explained according to the strength of the tested specimen.

In this work, we attempt to explain the variation using the completing between the constraint effect and the Poisson effect.

• 1. When σ _x is in a low value range from 10 to 60 MPa, the σ _x -induced constraint effect and the σ _x -induced Poisson effect are both small, and the pre-peak accumulated elastic energy (or rock strength) is the controlling factor for kinetic energy. Thus, the variation of the kinetic energy of the ejected fragments with increasing σ _x is consistent with that of the rock strength. With the increase of σ _x , the rock strength increases. Consequently, the kinetic energy of the ejected fragment, i.e., the intensity of the strainburst show increasing variation with increasing σ _x .

• 2. When σ _x is in a relative high value range from 60 to 90 MPa, the σ _x -induced Poisson effect and the σ _x -induced constraint effect are relatively high. In the pre-peak, the constraint effect, or the friction on the surfaces of the tested specimen along the Y direction, is not sufficiently large to prevent the bend of rock plates on the free face (Fig. 18). During the rockburst process, the rock plates and fragments are prone to break away from the host rock and eject out, but the external friction forces in the rock specimen prevent the rock plates and fragments from ejecting. Thus, the friction forces apply the negative work along the ejection direction during ejection failure, leading to a large amount of dissipated energy. In this situation, ratio of the change in the elastic strain energy of the rock plates into kinetic energy is low, resulting in low kinetic energy. The kinetic energy of the ejected fragments is primarily influenced by the constraint effect. With increasing σ _x , the constraint effect increases, the energy dissipation during the rockburst increases, the ratio of energy change decreases, and the kinetic energy decreases.

  Fig. 18

  

  Expansion of a rock plate during loading process under σ _x of 80 MPa condition: a before excavation; b after excavation

• 3. When σ _x is in a high value range from 90 to 110 MPa, both the constraint effect and the σ _x -induced Poisson effect are significant. The rock element is subjected to high intermediate principal stress, the brittleness of the tested specimen is high (Mogi 1971) and the cracks along the X direction are promoted. Thus, in the pre-peak, the specimen is easily split into several parallel rock plates. In other words, when σ _x is larger than 90 MPa, the splitting failure migrates to the deeper rock element compared with that when σ _x is less than 90 MPa. In this situation, the influence of high σ _x on kinetic energy is described as follows. Before, the high constraint effect of σ _x is the controlling factor. The bend of the parallel rock plates is small, indicating that a large amount of elastic strain energy is accumulated in the rock plates in the pre-peak. During rockburst, the Poisson effect significantly affects the rock failure process, the rock plate bend and breaking off occur in a notably short time, subsequently followed by the rockburst. In other words, the accumulated elastic strain energy is released rapidly. The rate of change of elastic strain energy into kinetic energy is high. Moreover, the high σ _x -induced Poisson effect is favorable to the bend of rock plates on the eve of rockburst, the rock elements behind rock plate breaking away from the constraint of host rock, and rock plates ejection, leading to a large scale of rockburst. With increasing σ _x , the greater constraint effect leads to additional elastic strain energy accumulating in the rock plates, and a greater σ _x -induced Poisson effect results in a larger scale rockburst and a higher energy conversion ratio, leading to a rapid increase of kinetic energy.

Until now, the attention of engineers and researchers has primarily focused on the tangential stress of the rock masses near the excavated boundary, whereas the effect of tunnel axis stress is usually neglected in investigation of strainburst. The obtained results indicate that the tunnel axis stress has a significant influence on the intensity of the strainburst. Highly intensive strainburst is more likely to occur under high tunnel axis stress conditions. During excavation in a high ground stress region where the rock mass is prone to rockburst, ignorance of the effect of tunnel axis stress might lead to an inaccurate prediction of the intensity of rock burst, which might result in a serious catastrophe. Therefore, the experimental results in the present study provide a reference for the design and construction of deep underground excavation.

5 Conclusions

An experimental study on influence of tunnel axis stress on strainburst was conducted. A serials of one free face true-triaxial loading tests under different X direction stresses (corresponding to in situ tunnel axis stresses) were performed to investigate strainburst. A loading path was introduced, namely, maintaining one face free and loading along three axial directions on the other five faces. High-speed cameras were used to monitor the failure process of the tested specimens. The kinetic energy of the ejected fragments during the strainburst was quantitatively estimated according to the recorded videos. The failure form of the rock specimen, rock strength and the kinetic energy of strainburst under different σ _x conditions were investigated in detail. The effect of σ _x on the rock strength and the kinetic energy of the ejected fragments is discussed. The main observations and conclusions are as follows.

• 1. With increasing σ _x , the strength of the granite specimen under one free face true-triaxial condition first increases and subsequently decreases gradually after reaching a peak.

• 2. With increasing σ _x , the intensity of the strainburst of the granite specimen first increases, subsequently decreases and finally increases drastically. In detail, the kinetic energy of the ejected fragments, the maximum decibel values of the rockburst sound and the volume of rockburst pits first increase continually, subsequently decrease gradually and finally increase drastically with increasing σ _x .

The experimental results show that the tunnel axis stress significantly influence the strainburst. However, the present strainburst study is a laboratory investigation of the rock specimen with a small size, and the experimental results, to some content, vary with those of in situ rockbursts. Thus, it is necessary to strengthen the in situ rockburst test. Furthermore, the Y direction stress σ _y (corresponding to the in situ radial stress) was constant in the present tests, and the influence of radial stress on strainburst needs further study.