Rock Mechanics and Rock Engineering
https://doi.org/10.1007/s00603-025-04527-3
ORIGINAL PAPER
Experimental Investigation on the Influence Mechanism of the Dip
Angle of the Stiff Structural Planes with Strong Cementation
on Double‑Face Unloading Rockburst
Fuqiang Ren2,3,4 · Jinze Gu4 · Chun Zhu2,5 · Xiaoshuang Li1 · Dongqiao Liu3 · Bingbing Chen6 · Jun Lu2
Received: 13 October 2024 / Accepted: 10 March 2025
© The Author(s), under exclusive licence to Springer-Verlag GmbH Austria, part of Springer Nature 2025
Abstract
The role of structural planes (SPs) in inducing rockburst is crucial, but the precise mechanism of how the stiff SPs influence
rockburst remains unclear. To address this, triaxial loading and double-face unloading rockburst tests were performed on
sandstone specimens with stiff SPs exhibiting strong cementation (by epoxy resin) and five different dip angles (β = 0°, 30°,
45°, 60°, 90°). The rockburst stress, energy consumption, failure mode, and acoustic emission (AE) characteristics were
analyzed to assess the impact of β on rockburst. In particular, the stress release characteristics were evaluated based on the
spatial distribution of b-values from the AE events. The results reveal that the rockburst stress initially decreases and then
increases as β increases, with β = 45° representing an inflection point. The maximum principal stress drop rate and fragments’
ejection velocity (0–3.4 m/s) exhibit a similar evolution pattern: they first decrease as β increases and then increase. Among
the specimens with different β angles, those with β = 0° and 60° display the greatest and weakest rockburst intensities, respectively. The main failure patterns include splitting, buckling, and shear fractures, with specimens having β = 45° exhibiting
the least failure degree (slight splitting). Additionally, the SPs affect stress release characteristics: microcracks with weak
stress release are present in the upper SPs rock for β angles less than 45°, whereas stress release in the rock below the SP
(including the free face) are weakest for β = 60°. Finally, a model based on the K-Nearest Neighbors method was developed
using AE entropy (an AE parameter based on Shannon’s entropy) to predict the rockburst stress. The model performs well,
especially for predicting stress before the peak (including peak).
Highlights
•
•
•
•
The double-face rockburst tests of sandstone with strong cementation stiff structural planes were conducted.
The influence of structural planes on double-face rockburst characteristics was revealed.
The stress relief features of rockburst were evaluated based on the spatial distribution of b-values.
A rockburst stress model was established based on the KNN method using AE entropy.
Keywords Rockburst · Stiff structural planes · Dip angle · b-value distribution · Stress prediction
* Xiaoshuang Li
xsli2011@cczu.edu.cn
3
* Dongqiao Liu
liudongqiao@yeah.net
State Key Laboratory for Tunnel Engineering,
Beijing 100083, China
4
School of Civil Engineering, University of Science
and Technology LiaoNing, Anshan 114051, China
5
School of Earth Sciences and Engineering, Hohai University,
Nanjing 210098, China
6
Faculty of Science and Engineering, Swansea University,
Swansea SA1 8EN, UK
1
School of Urban Construction, Changzhou University,
Changzhou 213164, China
2
State Key Laboratory of Intelligent Construction and Healthy
Operation and Maintenance of Deep Underground
Engineering, Shenzhen University, Shenzhen 518000, China
Vol.:(0123456789)
F. Ren et al.
1 Introduction
The structural planes (SPs) are a common discontinuity in
rock masses, and stiff SPs are widely distributed (Fig. 1) in
deep-buried hard rock tunnels, making them a crucial factor affecting tunnel stability (Han et al. 2023). Additionally,
stiff SPs significantly affect rockburst occurrence in highstress tunnels (Feng et al. 2017; Feng et al. 2019). Existing
rockburst cases demonstrate that the orientation, location,
geometric parameters, filling type, and whether the SPs are
filled or not can affect rockburst characteristics (He et al.
2023, 2018; Hu et al. 2020; Naji et al. 2018; Cheng et al.
2021). When the SPs intersect the tunnel axis at a large angle
or intersect with the tangential stress at a small angle, the
rockburst intensity is slight (see Table 1). An SP located on
the tunnel side wall can easily induce buckling rockburst,
while one located in the spandrel can easily induce fault-slip
rockburst. Iron or calcium cement can increase rockburst
intensity to some extent.
Regarding the action mechanism of SPs, Manouchehrian
and Cai (2018) established a two-dimensional numerical
model of rockbursts to analyze the effects of weak SPs inclination, spacing, and length on rockburst characteristics. Wu
et al. (2022) conducted physical model tests to investigate
the effects of SPs number and distribution on the stress distribution and failure mode of tunnel surrounding rock during
rockburst evolution. Their results indicate that tunnels with
multiple groups of SPs are more susceptible to large-scale
collapse, while those with a single SP tend to induce smallscale rockburst. Zhou et al. (2015) provide a summary of
the types of rockbursts influenced by the SPs during the
construction of the Jinping-II hydropower station, including
fault-slip, shear rupture, and buckling bursts. Additionally,
Wang et al. (2021) describe the impact of SPs inclination
on the spatial distribution characteristics of rockbursts in
deep-buried tunnels. On-site microseismic (MS) monitoring results show that MS activity increases when large-scale
joints appear and disappear, and that the intersection of two
sets of joints increases the risk of rockbursts. When the
angle is between 70 and 80°, the likelihood of rockbursts
increases. Moreover, the disclosure form, orientation, and
quantity of small-scale SPs in the surrounding rock of underground chambers affect the evolution of rockbursts. Finally,
the characteristics of AE and microcracks energy release
accompanying rockbursts are also quite distinct (Su et al.
2023).
There are different variations in the rockburst mechanism induced by different types of SPs (Cheng et al. 2023).
Fig. 1 Rockburst phenomena affected by structural planes, a, b extremely intense and moderate rockbursts at Jinping-II hydropower station
(Feng et al. 2017, 2019), c, d the intense and moderate rockburst at a deep tunnel in southwest China (Wang et al. 2021)
Experimental Investigation on the Influence Mechanism of the Dip Angle of the Stiff Structural…
Table 1 The rockburst characteristics affected by the structural planes
Reference
Features of structural planes
Rockburst characteristics
Features
Filling
Intensity
Failure features
Hu et al. (2020)
Closed or slightly open
None
Slight, moderate
Feng et al. (2019)
Rigid, dip angle larger than 60°
Intense
Naji et al. (2018)
Iron or
calcium
cement
None
V-shape burst pit
Prone on the side of the wall
Many rock block ejections
(1) A large angle with the tangential stress
and the tunnel axis
(2) A large angle with the tunnel axis and
a slight angle with the tangential stress
(3) Parallel to the tunnel axis
(4) A slight angle with the tunnel axis near
the tunnel boundary
–
(1) In the tunnel spandrel
(2) In the tunnel sidewall
(3) Intersecting with tunnel
(1) Intense
(2) Slight–moderate
(3) Intense
(4) Extremely intense
(1) Deep burst pit
(2) Medium-depth burst pit
(3) Steep ridges and deep burst pit
(4) Deep burst pit
–
(1) Fault-sliding rockburst
(2) Buckling rockburst
(3) Shear-fracture rockburst
Cheng et al. (2021)
Generally, stress concentration occurs near the SPs, altering
the cracking initiation and propagation process of cracks
and ultimately influencing the intensity and extent of the
rockburst. Additionally, the presence of SPs undermines the
integrity of the rock mass, which mitigates the rockburst
intensity to some extent. When the SPs slip and fail, secondary rockbursts are induced. Zhang et al. (2022) analyzed the
source mechanism of MS events resulting from fault-slip
rockburst in a deep-buried tunnel. The dislocation of the
SPs generates a large number of tensile fractures before a
rockburst occurs. Zhang et al. (2023) established a rockburst
risk evaluation criterion based on the energy release rate
and used numerical models to examine the effects of SPs
on rockburst risk level: the SP increases rockburst intensity,
delays its occurrence time, and affects the rockburst location.
Yao et al. (2023) confirmed, through biaxial shear tests with
smooth joint specimens, that stick–slip is the primary cause
of seismic events in smooth joints, and stress paths influence
the intensity and sliding pattern of the events.
In addition to exploring rockburst mechanisms under the
influence of SPs, some studies focus on predicting and providing early warning of rockburst. Meng et al. (2016) studied
the fault-slip rockburst induced by the shear failure of the SP
through direct shear testing of jointed granite, pointing out
that the unstable stick–slip of the SP causes rockburst. The
b-value of AE can be used as an early warning indicator of
rockbursts, with a specific threshold provided. Whether in
laboratory tests or actual engineering, the general approach
for predicting and warning of rockbursts is to use one or
more monitoring methods (e.g., AE, MS) and determine
early warning indicators (single or multiple) based on the
dynamic variation of monitoring parameters (Li et al. 2021;
Ma et al. 2021). The warning threshold is then determined
based on changes in parameters during rockbursts. Different rockburst types may have different warning thresholds
(Feng et al. 2022), and therefore, understanding the influence
of SPs on the microcracking mechanism during rockburst
evolution can aid in predicting and warning SPs-induced
rockbursts.
In summary, rockburst events are often accompanied by
a violent energy release, which varies in intensity and can
result in different degrees of damage. The presence of SPs
can alter the stress state and cracking behavior of the surrounding rock, leading to different failure modes and energy
release mechanisms (Weng et al. 2017; Yao et al. 2022).
While the impact of stiff SPs on rockburst has been qualitatively understood, the specific influence mechanism remains
largely unrevealed. Moreover, the unloading boundary conditions of the surrounding rock before and after excavation
are also important factors affecting the stress and energy
release of rock masses with SPs. In current studies, little
attention has been given to analyzing the influence of SPs
on stress release characteristics, especially for double-face
rockburst events.
Based on this, five groups of through-SPs sandstone samples with different dip angles (β) were prepared, with the
epoxy resin used as the filler to form a firmly cemented stiff
SP. Afterwards, double-face rockburst experiments were
performed using true triaxial loading and one-direction
double-face. During the test, the AE monitoring system and
high-speed cameras captured the microcracking and ejection failure process of the rockburst. The analysis included
rockburst stress, failure patterns, AE parameters, and AE
event clustering. The influence of the SPs on stress relief
characteristics was evaluated based on the spatial distribution of b-values from the AE events. Finally, a rockburst
F. Ren et al.
stress prediction model with AE entropy (an AE parameter
based on Shannon’s entropy) as the input was established
based on the K-Nearest Neighbors (KNN) algorithm.
2 Material and Methods
2.1 Samples
The rockburst samples with SPs used in this paper were
made of fine-grained red sandstone. First, a cube block
was cut at a preset angle, and then the cross-section was
bonded with epoxy resin to form a cube specimen with a
side length of 150 mm. The inclination angle β of the SPs
was defined as the angle between the normal outside the SPs
and the maximum principal stress (σ1) axis. As illustrated in
Figs. 2a, b, the rockburst samples were divided into 5 groups
of different β angles (0°, 30°, 45°, 60°, and 90°), and each
group contained three specimens that were tested in repetition. The red sandstone used is composed mainly of quartz
(58.0%), potash feldspar (13.4%), and clay minerals (12.1%),
with the specific mineral composition and relative content
shown in Fig. 2c. The microstructure of the red sandstone
is illustrated in Fig. 2d, with the blue filling area indicating the pores, which are primarily intergranular and range
in size from 0.06 mm to 0.25 mm. The uniaxial compressive strength, elastic modulus, and Poisson’s ratio of the red
sandstone were 51.9 MPa, 6.15 GPa, and 0.26, respectively.
The P-wave velocity of the samples was measured before
and after cutting. As shown in Fig. 2e, the P-wave velocity
of the samples with a firmly cemented stiff SP decreased by
less than 7% compared to the complete specimen.
2.2 Experimental Setup
The rockburst tests were conducted using a true triaxial
rockburst experiment system, as depicted in Fig. 3a. This
system allows for independent loading in three perpendicular
directions, with a maximum vertical (Z-direction) load of
up to 5000 kN and a maximum horizontal (X and Y) load of
2000 kN. During the rockburst test, microcracking evolution
and ejection failure process were captured by the AE monitoring and high-speed image recording. The AE equipment
used was a Micro-II system with a maximum signal amplitude of 100 dB and a maximum sampling rate of 40 M/s.
The probe utilized Nano-30-type sensors with a frequency
response range of 100–400 kHz. All eight channels were set
to a sample rate of 5 M/s, with a sample length of 4 k (4096
points). The preamplifier gain was set to 40 dB (100 × amplification), and the threshold was set to 40 dB.
The arrangement of the AE sensors is indicated in Fig. 3b.
All sensors were positioned on the exterior surface of the
loading plate using a simple device, namely a resin housing
fitted with magnets. Moreover, a spring was inserted into the
resin housing to guarantee that the sensor remained in close
contact with the loading plate. The specific arrangement of
the AE sensors is elaborated in Fig. 3c. Probes No. 1 and No.
3 are positioned on the opposite diagonal of plate 4#, while
probes No. 2 and No. 4 are situated diagonally across plate
2#. Probes No. 7 and No. 8 are installed on the top plate 5#.
The distance between the edge of the loading plate and the
center of the six aforementioned probes is 10 mm. Meanwhile, probes No. 5 and No. 6 are located on the diagonal of
plate 6#, with their centers being 10 mm and 25 mm away
from the two edges, respectively.
After installing the specimen and probe, the composite
wave velocity propagating through the specimen and plate
was measured to be 2899 m/s using the wave velocity measurement function included in the AE system. For the calibration tests of the probe, a lead break test was conducted. The
average deviation within the plane of the loading plate was
7.8 mm, and the deviation in the direction of the thickness
of the loading plate reached 14.2 mm. The maximum deviation of about 9.5% was considered acceptable. The high-speed
acquisition system consists of two AcutEye cameras, whose
relative positions are depicted in Fig. 3d. The angle between
the line of sight of the camera and the intermediate principal
stress axis was 40°. The system’s sampling rate was 1000
f/s, and the resolution was 1024 × 1024 pixels. Both cameras
were linked to the same memory through a synchronization
controller to achieve high-precision synchronous (within 1 μs)
shooting.
2.3 Experimental Scheme
In high-stress areas, deep-buried tunnels are often constructed with a parallel adit, connected to the main tunnel through cross channels. To expedite the construction
progress, the main tunnel employs two-direction excavation, as illustrated in Fig. 4a, resulting in a doubleface unloading state at the tunnel face. The double-face
unloading rockburst test simulates the rockburst failure in
one direction (He et al. 2021). The loading path, depicted
in Fig. 4b, involves applying three-direction principal
stresses at an initial loading rate of 2 kN/s, followed by
instantaneous unloading of σ3 (unloading rate 40 MPa/s)
to expose the two free faces of the specimen. Finally, σ1 is
loaded at the same rate (2 kN/s) until a rockburst occurs.
The initial principal stress values (σ1o/σ2o/σ3o) were calculated using the in-situ stress formula in North China. The
initial stress state at a depth of 1000 m is σH = 30.7 MPa,
σV = 25.7 MPa, and σh = 19.0 MPa, for σ1o, σ2o, and σ 3o,
respectively. Furthermore, the inclinations of the SPs are
parallel to the axis of the σ3.
Experimental Investigation on the Influence Mechanism of the Dip Angle of the Stiff Structural…
Fig. 2 Rockburst test samples, a photographs of red sandstone specimens with the structural plane, b diagram of sample size and dip
angle of the structural plane, c mineral composition and relative con-
tent, d microstructure of red sandstone, and e P-wave velocities of
intact and structural plane sandstones
2.4 Data Analysis Methods
vice versa. Therefore, the spatial distribution characteristics
of the b-value of AE localization events can be utilized to
describe the stress relief in the local area during the rockburst experiment. The degree of stress release is weak in the
area with a large b-value, while the area with a small b-value
corresponds to intense stress release. Figure 5 shows that
the YoZ coordinate plane of 150 mm × 150 mm is initially
divided into square grids with a side length of 10 mm. Then
2.4.1 Stress Relief Based on the b‑Value
The b-value of the AE events serves as a strain gauge, and
the magnitude of the b-value is inversely proportional to
the stress difference (Scholz 2015). This means that the
larger the b-value, the smaller the stress difference, and
F. Ren et al.
Fig. 3 a Ture triaxial rockburst experimental system (He et al. 2021), b, c photograph and diagram of the arrangement of AE sensors respectively, and d schematic of the position of high-speed cameras (He et al. 2021)
Experimental Investigation on the Influence Mechanism of the Dip Angle of the Stiff Structural…
the b-value (Liu et al. 2020) of each area is calculated using
Eq. (1). Finally, the distribution contour of the b-value is
evaluated to determine the impact of β on stress relief.
( )
A
Log10 N AdB = a − b dB
20
(1)
where AdB is the AE event amplitude and is measured in
decibels (dB), N(AdB) represents the total number of events
with an amplitude greater than AdB, parameter a is an empirical constant, and parameter b is defined as the AE b-value.
2.4.2 Rockburst Stress Prediction Using AE Entropy
Fig. 4 a Force diagram of typical rock element in cross-section of the
tunnels, and b rockburst loading path
Fig. 5 Diagram of the subregional calculation of b-value
The entropy of AE can quantify the degree of chaos
in microcracking: higher entropy values correspond to
higher degrees of chaos (Caesarendra et al. 2016; Kong
et al. 2019). Microcrack initiation and propagation inside
rocks can increase entropy values, indicating stress redistribution. The change in stress distribution is affected by
the macroscopic stress state, and the relationship between
external load changes and entropy values is highly nonlinear. Machine learning techniques can establish a correlation model between AE entropy and stress during rockburst
tests. The model can be continuously trained with measured
F. Ren et al.
Fig. 6 a The typical stage division of the stress–strain curve in the maximum principal stress direction, b the stress–strain curves for different
samples, variation of c rockburst stresses, and d stress drop rates with β
data to predict rockburst stress based on AE entropy values.
In this study, K-Nearest Neighbors (KNN) (Młynarczuk
et al. 2013) was used as a regression prediction model with
AE entropy as input and σ1 as output. KNN is a supervised
learning algorithm that calculates the similarity between
samples based on distance and makes predictions based on
the nearest neighbor data labels. The K value is an important
parameter in the KNN algorithm, with smaller values being
more susceptible to noise and overfitting, while larger values can lead to underfitting. Cross-validation determined the
K value as two in this study. The entropy value (Karimian
et al. 2020) of a random sequence X = {x1, x2, …, xn}, can
be calculated using Eq. (2).
H=
n
∑
( )
p xj ∗ log(p(xj ))
(2)
i=1
n
∑
( )
p xj = 1
i=1
(3)
where H is the entropy, p(xj ) is the probability of the value xj
in the sequence X. To segment the AE time series of amplitude, the sliding window method was used with a window
length and step size of 200 and 30 AE hits, respectively.
3 Results
3.1 Rockburst Stress
Figure 6a shows the stress–strain curves of specimen F90-1.
Combined with the loading path, the stress–strain curve in
the direction of the σ1 can be divided into 5 typical stages.
Stage I is the initial stress loading, where σ1, σ2, and σ3 are
loaded to their initial in-situ stress levels. Stage II is the
unloading stage, where rapid unloading of σ3, σ1, and σ2
occurs with minor fluctuations. Stage III is the stress concentration stage, where σ1 continues to increase and simulates
the tangential stress concentration caused by excavation.
Stage IV is the yield stage, where σ1 exhibits an evident
Experimental Investigation on the Influence Mechanism of the Dip Angle of the Stiff Structural…
yield plateau. Finally, stage V is the rockburst stage, where
σ1 undergoes a significant stress drop, while σ2 produces
a relatively small increase. For specimens with different β
values, the stress–strain curves in the σ1 direction are shown
in Fig. 6b. When β is 30°, 60°, and 90°, the specimens show
plastic hardening features after reaching the yield stress,
with the 60° specimen exhibiting the highest increase in
plastic strain. On the other hand, when β is 0° and 45°, the
specimens remain unchanged after the yield point until
the rockburst, with very minimal ultimate strain after the
rockburst.
The yield stress, peak stress, and residual stress in the
σ1 direction for all samples are presented in Table 2. The
change in peak stress with β is illustrated in Fig. 6c. The
average peak stress initially decreases and then increases
with an increase in β. The minimum and maximum peak
stresses are observed when β is 45° and 90°, respectively.
Additionally, the stress drop rate during the rockburst was
calculated to assess the intensity of the rockburst, with a
higher rate indicating a more violent rockburst. The relationship between stress drop rate and β is shown in Fig. 6d. The
average stress drop rate initially decreases and then increases
with an increase in β, with the minimum and maximum values observed when β is 60° and 0°, respectively. Therefore,
an increase in β reduces the difficulty of rockburst occurrence to some extent, but when β is greater than 45°, the
difficulty of rockburst generation increases. For specimens
with β values of 0° and 60°, the difficulties of rockburst
are moderate, but the rockburst intensities are the greatest
and weakest, respectively. Thus, from a rockburst control
Table 2 Summary of the
rockburst test results
No
F0-1
F0-2
F0-3
F30-1
F30-2
F30-3
F45-1
F45-2
F45-3
F60-1
F60-2
F60-3
F90-1
F90-2
F90-3
σ1 of yield (MPa)
79.5
88.6
90.8
92.2
75.7
68.1
76.1
70.5
83.4
75.3
88.4
78.4
103.7
97.6
116.3
perspective, a β value of 60° is more beneficial for engineering safety.
3.2 Energy Consumption
According to the stress–strain curve of the specimen in
Fig. 7a, the input energy can be divided into four parts: prepeak dissipative energy (Ud1), elastic strain energy (Ue),
post-peak dissipative energy (Ud2) and residual strain energy
(Ur). The elastic modulus of the linear elastic stage is the
hypotenuse slope of the Ue and Ur triangles. The releasable
elastic strain energy is Ue-Ur, which will be partially converted into fragments’ kinetic energy. The energy distribution of specimens with different β is shown in Fig. 7b and
summarized in Table 3. The Ur of all specimens is less than
7%. The average proportion of Ud1 for specimens with β of
0°, 45°, and 60° is 16.3%, 16.7%, and 29.7%, respectively,
which is much higher than specimens with β of 30° and 90°
(less than 5%). Most specimens’ energy is distributed in Ue
or Ud2, where the average value of Ue ranges from 30 to
42%. The Ue of most specimens has a small proportion gap,
except for the specimen with β of 30°. The proportion of Ud2
is consistent with the stress drop rate trend with β. When β
is 0°, 45° and 60°, the proportion of Ud2 is close to ~ 45%,
and when β is 30°, Ud2 accounts for the largest proportion
(66%), which is 2.3 times the proportion of the specimen
with β of 60°.
As depicted in Fig. 7c, the total post-peak input energy
(S CDFG) of the specimen varies with the value of β. If
σ1max (MPa)
79.7
89.5
92.3
94.0
78.5
68.7
76.5
72.4
84.1
81.8
92.3
83.2
105.0
98.4
117.1
Residual
Stress drop rate
stress (MPa) of σ1 (MPa/s)
25.9
26.2
26.7
16.5
14.7
13.7
16.0
14.8
12.5
25.1
25.6
22.3
26.4
26.3
26.5
468.1
543.1
498.6
688.7
678.9
609.3
542.1
573.1
501.2
529.6
497.6
460.2
598.8
535.7
578.9
Increment rate
of σ2 (MPa/s)
35.1
13.5
29.6
71.3
65.8
83.2
109.1
112.4
96.8
110.2
123.4
103.7
5.7
15.9
12.9
Ejection
­velocitya
(m/s)
V–y
Vy
1.6
2.3
2.4
1.8
1.4
0.9
0.3
0.5
0.8
0.3
0.4
0.6
2.3
2.5
3.1
1.8
3.4
3.0
1.2
1.5
1.3
3.4
0.3
0.5
0.0
0.2
0.5
1.7
2.9
1.9
a
The ejection velocity is the horizontal initial ejection velocity, and the Vy and V–y, respectively, for the two
free faces; y means the direction
F. Ren et al.
Fig. 7 a The schematic of strain energy calculations, b distribution of
four parts strain energy for samples with different β, c the diagram
of the pre-peak accumulation releasable elastic strain energy and total
Table 3 The calculation results
of strain energy
No
post-peak input energy, and d the variation of the ratios of SCDFG/
(SBCDE + SCDFG) with β
Percentage of parts to total strain energy (%)
SCDFG/(SBCDE + SCDFG)
Ue
Ud1
Ud2
Ur
F0-1
F0-2
F0-3
F30-1
F30-2
F30-3
F45-1
F45-2
F45-3
F60-1
F60-2
F60-3
F90-1
F90-2
38.06
44.21
35.08
26.71
33.12
29.63
45.14
39.87
36.57
35.49
40.33
34.67
45.32
38.88
19.68
11.74
16.87
4.22
2.59
3.08
20.37
16.54
12.52
39.63
20.33
28.72
3.88
4.77
38.21
39.46
44.07
68.27
63.26
66.06
32.65
40.05
46.6
21.51
34.67
30.07
47.95
53.14
4.05
4.59
3.98
0.8
1.03
1.23
1.84
3.54
4.31
3.37
4.67
6.54
2.85
3.21
0.55
0.53
0.61
0.73
0.67
0.70
0.44
0.55
0.61
0.44
0.52
0.57
0.54
0.61
F90-3
43.11
2.98
48.59
5.32
0.59
Experimental Investigation on the Influence Mechanism of the Dip Angle of the Stiff Structural…
Fig. 8 The ejection failure process of sandstone with structure plane, a–e respectively for the samples F0-1, F30-1, F45-1, F60-1, F90-1
SCDFG equals 0, the specimen is considered an ideal brittle
material, and the larger the S CDFG, the weaker the brittle nature of the sample after the peak. The ratio S CDFG/
(SCDFG + SBCDE) is used to characterize the brittle features
of the rockburst process, and the closer the value is to
0, the more prominent the brittle nature. Overall, S CDFG/
F. Ren et al.
Fig. 8 (continued)
(SCDFG + SBCDE) increases first, then decreases, and then
increases again with the increase in β. For specimens with
β of 30°, despite a larger rockburst intensity, the specimen
exhibits weak brittle features from an energy point of view.
Similarly, for specimens with β of 60°, the brittle features
are the strongest, but the corresponding rockburst intensity
is the weakest. This phenomenon is related to inaccurate
post-peak stress measurements.
3.3 Failure Characteristics
3.3.1 Ejection Failure Process
Fig. 9 The variation of initial horizontal ejection velocities of fragments with β, Vy, and V–y corresponding to two opposite free faces,
respectively
The failure process of rockburst ejection in specimens with
different β is presented in Fig. 8, where distinct failure phenomena and occurrence times of the two opposite free faces
are observed. Typical failure phenomena such as particle
ejection, cracking, spalling, splitting, bending, and bursting
Experimental Investigation on the Influence Mechanism of the Dip Angle of the Stiff Structural…
Fig. 10 a The failure patterns of sandstone after rockburst, and b the sketch maps of macro-cracks on the face of specimen in intermediate principal stress direction
F. Ren et al.
are observed. While the specimen with β of 45° did not
form a significant burst pit after the rockburst, the rest of the
specimens had at least one free face that formed a depression-shaped pit. Moreover, the intensity of the rockburst for
the two free faces differed (one strong and one weak), and
the burst occurrence was related to the evolution of microcracks inside the specimen. For β of 0°, the SP limits the
propagation of surface cracks to a certain extent (Hu et al.
2020), and the burst of one of the free faces only occurs
below the SP, while the SP of the ejection block of the other
free face also separates. For specimens with β of 30°, 60°,
and 90°, spalling and splitting features are prominent, but
the specimen of 0° also exhibits ejection of debris after the
detachment of the splitting block. For β of 45°, fragments are
ejected at two outlet positions on the SP. Despite the ejection
of fragments, the overall degree of specimen failure is low.
Figure 9 shows the relationship between the initial ejection velocity and β, based on the principle of the particle
image velocity method (Wang et al. 2015). The ejection
velocities Vy and V–y (ranging from 0 to 3.4 m/s, see Table 2
for specific values) are measured for the double-free faces
of the specimens. The variation of Vy and V–y with β is consistent with the law of stress drop rate, indicating that the
change in rockburst intensity from velocity is consistent with
the conclusions based on stress drop rate. Specifically, the
slowest ejection velocity (0.23 m/s) corresponds to specimens with a β of 60°. The velocities of specimens with β
of 0° and 90° are larger (2.7 m/s) and have similar values.
3.3.2 Failure Patterns
The failure photographs of the specimen after the rockburst
are presented in Fig. 10a, illustrating that the orientation of
the SPs had a significant impact on the distribution and failure mode of the macroscopic cracks of the specimen (Cheng
et al. 2023). When β was less than or equal to 30°, the shear
cracks passed through the SPs, and the macroscopic cracks
were dense. In contrast, when β was 45°, there were hardly
any cracks on the surface of the specimen. For β values of
60° and 90°, the SPs altered the propagation path of the
macroscopic crack, particularly for the specimen with β of
90°, where the shear crack deflected as it approached the
SP. Concerning the overall failure degree of the sample, the
integrity of the specimen was highest when β was 45°, while
the free face of the specimen with the other dip angles had
varying degrees of failure.
Based on the crack sketch of the specimen in the direction of σ2 after the rockburst (see Fig. 10b), it can be seen
that the distribution of shear, buckling, and splitting cracks
followed a hierarchical pattern. When β is less than or equal
to 30°, many splitting cracks are approximately parallel to
σ1 and are distributed near the free face. The SPs have a
noticeable limiting effect on the penetration of the splitting
cracks. Buckling and shear cracks are orderly near the middle of the specimen. Therefore, from the perspective of macroscopic crack distribution, as β increases from 0° to 30°,
it weakens the buckling deformation of the specimen and
strengthens the splitting failure. When β increases from 30°
to 45°, the control effect of the SP on macroscopic failure is
significantly strengthened. For β increasing from 45° to 60°,
the specimen’s buckling deformation and splitting features
gradually become significant. Finally, if β is between 60°
and 90°, the specimens gradually exhibit the macroscopic
shear fracture plane. For specimens with SPs (β = 0°, 30°,
and 90°), the fracture angles (angle between the shear plane
and the σ1 axis) of the shear plane after a double-face rockburst have only a slight difference. Therefore, regarding the
failure patterns, the rockburst had the least impact when β
was 45°, followed by 60°.
3.4 Characteristics of AE
3.4.1 AE Hits Rate and Damage
The AE hits rate is an index used to evaluate the activity of
AE, which was calculated using the sliding window method
with a length and moving step of 100 and 20 AE hits, respectively. Figure 11 presents the hit rate evolution process of
different β samples, and the time is normalized and defined
as the time ratio. Figure 11 also shows the evolution of the
damage, where the damage is the normalized cumulative
released AE energy (shown in logarithmic coordinates)
(Akdag et al. 2018). It can be observed from Fig. 11 that AE
activity is intermittent, and instantaneous unloading of σ3
enhances it. The AE signals with high hit rates are primarily
concentrated in the stress concentration and rockburst stages.
There is an apparent ‘quiet period’ (Li et al. 2016) phenomenon before the rockburst for the samples with different
β. The maximum AE hit rates in the rockburst stage are
around 1200 per/s, except for the specimen with a β of 90°.
The β mainly affected the AE activity before the rockburst
(Feng et al. 2019), with AE activity gradually decreasing
as β increased from 0° to 45°, increasing and then decreasing as β increased to 60° and 90°, respectively. The damage
evolution curve showed a stepwise distribution, with sudden
increases in damage at the initial loading, unloading, and
rockburst moments. Samples with a larger β (60° and 90°)
had the most significant damage increments corresponding
to the rockburst, with damage due to unloading reaching
0.26 and 0.24, respectively, much larger than the specimen
with a small β.
3.4.2 Entropy
Figure 12 displays the entropy evolution process of five
groups of different β samples, and it shows that the evolution
Experimental Investigation on the Influence Mechanism of the Dip Angle of the Stiff Structural…
Fig. 11 The evolutions of AE hit rates and damage during rockburst of sandstones with the structural plane, a–e respectively for the samples
F0-1, F30-1, F45-1, F60-1, and F90-1
law of entropy value is relatively unaffected by β. During the initial loading stage, the entropy value fluctuates
upward, and unloading σ3 causes the entropy value to suddenly increase and then maintain a low-level fluctuation
for an extended period. The fluctuation amplitude gradually increases as it approaches the peak stress, reaches the
maximum just before the rockburst, and decreases after the
rockburst. When β increases from 0° to 90°, the average
F. Ren et al.
Fig. 12 a The evolution of entropy of sandstone with loading curve, b the local amplification of rockburst stage, c the average maximum entropy
at different β
maximum entropy values before the rockburst are 1.52, 1.48,
1.44, 1.32, and 1.55, respectively. The effect of β on the
chaotic degree of microcracks is consistent with the law of
rockburst intensity. However, when β is 60°, the entropy
value is small, and the variation characteristics of entropy
are not obvious from the perspective of rockburst early
Experimental Investigation on the Influence Mechanism of the Dip Angle of the Stiff Structural…
Fig. 13 The Gaussian mixture clustering results of AE locations, a–e respectively, for the F0-1, F30-1, F45-1, F60-1, and F90-1
F. Ren et al.
Fig. 14 The cloud map of b-values and the corresponding failure photographs in the yoz section
warning. This feature increases the difficulty of identifying
precursors and is not conducive to successful early warning.
3.5 Cluster of AE Events
To cluster the AE events, the Gaussian mixed clustering
algorithm (Ju et al. 2022) was used, and Fig. 13 shows
the clustering results obtained after multiple attempts to
determine the number of groups of clusters. Based on
the spatial distribution of AE events, the 3D confidence
ellipsoid for each cluster group was determined using the
Hotelling T2 distribution (Worley et al. 2013). Moreover,
the source amplitude of AE events was distinguished by
the volume of the ball: the larger the volume of the ball,
the larger the amplitude, and the greater the energy of the
corresponding signal. Notably, when β is 60°, the number of AE events is significantly less than that of other
specimens. While each cluster group of microcracks corresponds to the macroscopic failure area, the nucleation
characteristics of microcracks are weak overall.
When β is 0°, the horizontal SP plays a specific role in
dividing the distribution of AE events. There are fewer
events near the SP, and most high-amplitude AE events
occur close to the surface. Cluster 4 has a deeper corresponding burst pit depth and denser events, while Cluster
5 has fewer events. When β is 30°, the high-amplitude
signals near the free face in the positive direction of
the y-axis are concentrated in the upper part of the SP,
whereas those near the free face in the negative direction
of the y-axis are concentrated in the lower part of the
SP. The minor axis of the Cluster 5 ellipsoid is parallel
to the SP. When β increases to 45°, high-amplitude AE
events are concentrated at the upper and lower ends of the
specimen, and there are fewer high-amplitude events at
the two shear outlet positions of the SP. When the SP is
perpendicular (β = 90°), many high-amplitude AE events
are gathered near the SP.
Therefore, the distribution characteristics of microcracks change to varying degrees as β increases from 0°
to 90°. The specimen with a horizontal SP exhibits an
approximately uniform distribution type, which transitions to a discrete distribution type for specimens with
β values of 30° and 45°, then to a weakened distribution
type for β is 60°, and finally to a concentrated distribution
type for the specimen with a vertical SP.
3.6 Distribution Characteristic of b‑Value
The variations in the b-value reflect the stress difference
distribution within the specimen, influenced by structural characteristics, loading conditions, and microcrack
propagation behavior. The b-value is a measure inversely
proportional to the stress difference. A higher b-value
indicates a smaller stress difference in the corresponding area, which means that the stress relief characteristics during microcrack propagation become more evident. Figure 14 presents the b-value distribution in the
yoz section for specimens with different β, which ranges
from 3 to 7. Generally, β affects the stress release during
rockburst pregnancy in the specimens (Su et al. 2023; Wu
Experimental Investigation on the Influence Mechanism of the Dip Angle of the Stiff Structural…
Fig. 15 The prediction σ1 and the corresponding errors by the KNN model using the entropy values as input, a–e respectively for the samples
F0-1, F30-1, F45-1, F60-1, F90-1, f the performance of the prediction model for the samples with different β of structural plane
et al. 2022). All samples have a local region with a small
b-value, particularly when β is 60°. This leads to a highstress difference at the bottom of the specimen, making it
difficult for the stress to release.
When β is 0°, the area with a larger b-value is near the
free face and located in the lower half of the specimen,
corresponding to the burst pit position of the free face after
the rockburst. For specimens with β values of 30°, 45°, and
60°, the b-value distribution shows clear differences in the
two-part areas divided by the SPs, and the difference in the
b-value magnitude increases with β. At 30° and 45°, the
overall b-values in the area above the SPs are smaller, while
F. Ren et al.
Fig. 16 Schematic of the failure mechanism of sandstone with different β of structural plane
at 60°, the area below the SP has a smaller b-value. When β
is 90°, the b-value distribution in the regions on both sides
of the SP is asymmetrical, and the regions with a larger
b-value are close to the two free faces and the upper end of
the specimen.
As β increases from 0° to 45°, microcracks with larger
stress differences (weak stress release) accumulate inside
the rock in the upper SP. However, when β increases to 60°,
the rock below the SP (including the free face) develops
microcracks with larger stress differences, making the stress
release characteristic in the rockburst area of the specimen
at an inclination of 60° the weakest. Therefore, from the
perspective of the SP’s influence on the stress release characteristics, the SP’s presence changes the stress release pattern
during the rockburst evolution.
3.7 Rockburst Stress Prediction
The stress prediction results obtained by applying the KNN
model are presented in Figs. 15a–e, using the AE amplitude
entropy values as input, along with the corresponding prediction error. The model’s predicted stress before the peak
stress (including peak stress) shows a good agreement with
the experimental values, with a prediction error of less than
0.5 MPa. However, the post-peak stress prediction error
is relatively high, particularly for specimens with a β of
90°, where the error can be as high as 25 MPa, while for
the remaining inclination specimens, the error is less than
7 MPa. The KNN model appears to have relatively poor
performance in predicting stress mutation, as shown by the
histograms of mean absolute error (MAE) and mean absolute percentage error (MAPE) for samples with different
β (Fig. 15f). Overall, the model’s overall performance is
acceptable for all specimens, although there is a significant
prediction error for individual specimens at the stress drop
moment.
4 Discussion
4.1 Influence Mechanism of the Structural Planes
on Rockburst
For intact rocks undergoing a double-face unloading
rockburst, slabbing, buckling, and shear zones are distributed from the free face to the inside. This failure process
experiences slabbing cracking, buckling deformation, and
macroscopic shear fracture penetration (Hu et al. 2021).
When the shear fracture penetrates, the accumulated
strain energy partially converts into the ejection kinetic
energy of the fragment, forming an ejection zone in the
free face. Despite the high bonding strength of epoxy
resin, the shear strengths of the strongly cemented stiff
SPs are still lower than that of the rock matrix, and shearslip failure will occur when the inclination angles of the
SPs are large. Figure 16 shows that when β is 0°, the SP
only limits the penetration of tension cracks in the slabbing zone, and the overall failure mode is less affected.
The shear fracture plane still cuts through the SP. As β
increases, the shear-slip features along the SPs gradually
appear. When β is 30°, the shear slip deflects the macroscopic shear fracture plane, the buckling zone is closer
to the free face, and tension cracks appear perpendicular
to the SP.
When β is 45°, the specimen’s failure mode changes to
shear slip, and energy is released from both ends of the SP.
When β is 60°, the rocks in the SP distribution range remain
undamaged, and the slabbing and buckling zones are near
the two free faces. When β is 90°, the SP has less influence
on the failure patterns. The three failure zones mentioned
above are symmetrically distributed in the two rock parts
divided by the SP. Shear slip consumes the accumulated
energy during rock loading, resulting in lower rockburst
intensities for high inclination angles of the SPs (45° and
60°). Consequently, shear fracture causes stronger rockbursts
Experimental Investigation on the Influence Mechanism of the Dip Angle of the Stiff Structural…
than shear slip (Meng et al. 2016). The degree of buckling
also affects the rockburst intensity. From a rockburst control
perspective, weakening the surrounding rock is essential to
mitigate rockbursts. Measures such as pressure relief boreholes or inter cracks (Zhang et al. 2019) can release high
stress and reduce the integrity of the rock mass. Based on
the influence law of the angle between the SPs and σ1 axis in
the double-face unloading rockburst experiments, the cutting
crack control effect inside the rock mass is better for angles
between 45° and 60°.
4.2 Limitations and Future Work
The large error in post-peak stress prediction can be attributed to two reasons. Firstly, the stress sampling frequency is
much higher than that of the entropy, resulting in an unequal
number of AE entropy values and stress values. Despite
using downsampling and imputation techniques to preprocess the data, the effectiveness of these methods decreases
when the stress is rapidly dropping. Secondly, the AE sensor
fails to capture all the microcracks inside the rock during
the stress drop. This leads to inaccurate entropy calculations since the presence of pre-existing microcracks hinders
the propagation of elastic waves (Cartwright et al. 2020).
Although predicting the absolute value of the stress drop is
challenging, the peak stress can be accurately predicted from
the entropy value. In field applications, monitoring using
the microseismic (MS) method can also provide insight
into the evolution of microcracks inside the rock mass. The
corresponding entropy value of an MS event can still be
calculated, and the stress prediction method described in
this paper can be used to predict the stress of the rock mass.
However, to do so, the predicted model and stress value must
be trained and calibrated based on the measured data. Additionally, time series data based on entropy values should be
used in conjunction with time series prediction algorithms
to forecast the development trend. Finally, the stress can be
used to predict rockbursts.
(1) The rockburst stress decreases, followed by an increasing trend as β increases, with an inflection point at
β = 45° (77.7 MPa). This indicates that increasing β
from 0° to 45° reduces the difficulty of rockburst occurrence. At β = 90°, rockburst becomes less likely, as the
rockburst stress is approximately 1.38 times higher than
at β = 45°.
(2) The stress drop rate of σ1, the ejection velocity of fragments (0–3.4 m/s), and the chaotic degree of microcracks during rockburst all exhibit an initial decrease
followed by an increase with increasing β. Specimens
with β = 0° display the greatest rockburst intensities,
while those with β = 60° exhibit the weakest.
(3) As β increases from 0° to 30°, the buckling deformation
of the specimens weakens, while splitting failure intensifies. The dominant failure mode remains shear fracture. When β reaches 45°, a slight splitting macroscopic
failure is observed. With β increasing to 60°, buckling,
and splitting features become more pronounced, and
specimens gradually develop a macroscopic shear fracture plane at β = 90° (vertical SP).
(4) The SPs modify stress release characteristics. As β
increases from 0° to 45°, microcracks with significant stress differences accumulate, leading to weak
stress release in the upper SP rock. However, when β
increases to 60°, the stress release in the rock below the
SP (including the free face) becomes the weakest.
Acknowledgements Financial support from the National Natural Science Foundation of China (Grant No. 52409128), and the State Key
Laboratory of Intelligent Construction and Healthy Operation and
Maintenance of Deep Underground Engineering (SDGZK2425).
Fu n d i n g N a t i o n a l N a t u r a l S c i e n c e F o u n d a t i o n o f
China,52409128,Fuqiang Ren,State Key Laboratory of Intelligent
Construction and Healthy Operation and Maintenance of Deep Underground Engineering,SDGZK2425,Xiaoshuang Li
Data Availability Data used and analyzed in this study are available
from the corresponding author by request.
Declarations
5 Conclusion
To investigate the effect of the SPs dip angle on doubleface unloading rockburst characteristics, triaxial unloading
rockburst tests were performed on sandstones with a stiff SP
with strong cementation. The influence of β on rockburst
stress, failure pattern, and AE features was analyzed, and a
rockburst stress prediction model was established. Finally,
the influence mechanism of the SPs and the limitations of
this study were discussed. The specific conclusions are as
follows:
Conflict of Interest The authors declared that there is no conflict of
interest in this work.
References
Akdag S, Karakus M, Taheri A, Nguyen G, He MC (2018) Effects
of thermal damage on strain burst mechanism for brittle rocks
under true-triaxial loading conditions. Rock Mech Rock Eng
51:1657–1682
Caesarendra W, Kosasih B, Tieu AK, Zhu H, Moodie CA, Zhu Q
(2016) Acoustic emission-based condition monitoring methods:
F. Ren et al.
review and application for low speed slew bearing. Mech Syst
Signal Process 72:134–159
Cartwright-Taylor A, Main IG, Butler IB, Fusseis F, Flynn M, King
A (2020) Catastrophic failure: how and when? Insights from
4-D in situ x-ray microtomography. J Geophys Res Solid Earth
125(8):e2020JB019642
Cheng G, Zhang J, Gao Q, Liu C (2021) Experimental study on the
influence mechanism of the structural plane to rockbursts in
deeply buried hard rock tunnels. Shock Vib 2021:1–8
Cheng T, He M, Li H, Liu D, Qiao Y, Hu J (2023) Experimental investigation on the influence of a single structural plane on rockburst.
Tunn Undergr Space Technol 132:104914
Feng XT (2017) Rockburst: mechanisms, monitoring, warning, and
mitigation. Butterworth-Heinemann
Feng GL, Feng XT, Chen BR, Xiao YX, Zhao ZN (2019) Effects of
structural planes on the microseismicity associated with rockburst
development processes in deep tunnels of the Jinping-II Hydropower Station. China Tunn Undergr Space Technol 84:273–280
Feng GL, Chen BR, Xiao YX, Jiang Q, Li PX, Zheng H, Zhang W
(2022) Microseismic characteristics of rockburst development in
deep TBM tunnels with alternating soft–hard strata and application to rockburst warning: a case study of the Neelum-Jhelum
hydropower project. Tunn Undergr Space Technol 122:104398
Han ZY, Li JC, Wang HJ, Zhao J (2023) Initiation and propagation of
a single internal 3D crack in brittle material under dynamic loads.
Eng Frac Mech 285(6):109299
He MC, Ren FQ, Liu DQ (2018) Rockburst mechanism research and
its control. Int J Min Sci Tech 28(5):829–837
He M, Ren F, Liu D, Zhang S (2021) Experimental study on strain
burst characteristics of sandstone under true triaxial loading and
double faces unloading in one direction. Rock Mech Rock Eng
54:149–171
He MC, Cheng T, Qiao YF, Li HR (2023) A review of rockburst:
experiments, theories, and simulations. J Rock Mech Geotech Eng
15(5):1312–1353
Hu L, Feng XT, Xiao YX, Wang R, Feng GL, Yao ZB, Zhang W (2020)
Effects of structural planes on rockburst position with respect to
tunnel cross-sections: a case study involving a railway tunnel in
China. Bull Eng Geol Environ 79:1061–1081
Hu X, Su G, Li Z, Xu C, Yan X, Liu Y, Yan L (2021) Suppressing
rockburst by increasing the tensile strength of rock surface: an
experimental study. Tunn Undergr Space Technol 107:103645
Ju S, Li D, Jia J (2022) Machine-learning-based methods for crack
classification using acoustic emission technique. Mech Syst Signal
Process 178:109253
Karimian SF, Modarres M, Bruck HA (2020) A new method for detecting fatigue crack initiation in aluminum alloy using acoustic emission waveform information entropy. Eng Fract Mech 223:106771
Kong X, Wang E, Li S, Lin H, Xiao P, Zhang K (2019) Fractals and
chaos characteristics of acoustic emission energy about gas-bearing coal during loaded failure. Fractals 27(05):1950072
Li X, Wang E, Li Z, Liu Z, Song D, Qiu L (2016) Rock burst monitoring by integrated microseismic and electromagnetic radiation
methods. Rock Mech Rock Eng 49:4393–4406
Li X, Chen S, Wang E, Li Z (2021) Rockburst mechanism in coal rock
with structural surface and the microseismic (MS) and electromagnetic radiation (EMR) response. Eng Fail Anal 124:105396
Liu X, Han M, He W, Li X, Chen D (2020) A new b value estimation
method in rock acoustic emission testing. J Geophys Res Solid
Earth 125(12):e2020JB019658
Ma TH, Tang CA, Liu F, Zhang SC, Feng ZQ (2021) Microseismic
monitoring, analysis and early warning of rockburst. Geomatics
Nat Hazards Risk 12(1):2956–2983
Manouchehrian A, Cai M (2018) Numerical modeling of rockburst
near fault zones in deep tunnels. Tunn Undergr Space Technol
80:164–180
Meng F, Zhou H, Wang Z, Zhang L, Kong L, Li S, Zhang C (2016)
Experimental study on the prediction of rockburst hazards induced
by dynamic structural plane shearing in deeply buried hard rock
tunnels. Int J Rock Mech Min Sci 86:210–223
Młynarczuk M, Górszczyk A, Ślipek B (2013) The application of pattern recognition in the automatic classification of microscopic
rock images. Comput Geosci 60:126–133
Naji AM, Rehman H, Emad MZ, Yoo H (2018) Impact of shear zone
on rockburst in the deep neelum-jehlum hydropower tunnel: A
numerical modeling approach. Energies 11(8):1935
Scholz CH (2015) On the stress dependence of the earthquake b value.
Geophys Res Lett 42(5):1399–1402
Su G, Yan X, Zheng Z, Li C, Zhao X, Ren H (2023) Experimental
study on the influence of a small-scale single structural plane on
rockburst in deep tunnels. Rock Mech Rock Eng 56(1):669–701
Wang H, Liu DA, Gong W, Li L (2015) Dynamic analysis of granite rockburst based on the PIV technique. Int J Min Sci Technol
25(2):275–283
Wang J, Chen G, Xiao Y, Li S, Chen Y, Qiao Z (2021) Effect of structural planes on rockburst distribution: case study of a deep tunnel
in Southwest China. Eng Geol 292:106250
Weng L, Huang L, Taheri A, Li X (2017) Rockburst characteristics
and numerical simulation based on a strain energy density index:
a case study of a roadway in Linglong gold mine. China Tunn
Undergr Space Technol 69:223–232
Worley B, Halouska S, Powers R (2013) Utilities for quantifying separation in PCA/PLS-DA scores plots. Anal Biochem
433(2):102–104
Wu J, Zhang X, Yu L, Zhang L, Wu T (2022) Rockburst mechanism of
rock mass with structural planes in underground chamber excavation. Eng Fail Anal 139:106501
Yao Z, Fang Y, Yu T, Pu S, Luo H, Cui J, Wang J (2022) Dynamic
failure mechanism of tunnel under rapid unloading in jointed rockmass: a case study. Eng Fail Anal 141:106634
Yao Z, Fang Y, Zhang R, Pu S, Zhao G, Yu T, Ma C (2023) The mechanism of stick-slip as a rockburst source in jointed rockmass: an
experimental study. Rock Mech Rock Eng 56:1–21
Zhang S, Li Y, Shen B, Sun X, Gao L (2019) Effective evaluation of
pressure relief drilling for reducing rock bursts and its application
in underground coal mines. Int J Rock Mech Min Sci 114:7–16
Zhang W, Feng XT, Yao ZB, Hu L, Xiao YX, Feng GL, Zhang Y
(2022) Development and occurrence mechanisms of fault-slip
rockburst in a deep tunnel excavated by drilling and blasting: a
case study. Rock Mech Rock Eng 55(9):5599–5618
Zhang R, Liu Y, Hou S (2023) Evaluation of rockburst risk in deep
tunnels considering structural planes based on energy dissipation rate criterion and numerical simulation. Tunn Undergr Space
Technol 137:105128
Zhou H, Meng F, Zhang C, Hu D, Yang F, Lu J (2015) Analysis of
rockburst mechanisms induced by structural planes in deep tunnels. Bull Eng Geol Environ 74:1435–1451
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