Study on Discrete Fracture Network Model and Rock Mass Quality Evaluation of Tunnel Surrounding Rock

Abstract

In order to fully explore the development degree and distribution law of the structural plane of a tunnel surrounding rock in three-dimensional space, this paper studies the geometric characteristic parameters of a structural plane in the study area through field investigation, data acquisition and statistical analysis. The structural plane is divided into three dominant groups by using DIPS. v5. 103 software. The probability distribution model of occurrence, trace length, diameter and spacing of the structural plane is established. This paper focuses on the error correction of structural plane occurrence and the estimation of average trace length based on the rectangular window method. The discrete fracture network model is generated by using MATLAB R2021b software, and the discrete fracture network model is verified from three aspects: structural plane occurrence, average trace length and area density. The verification results are compared with the measured data, and the simulation results are in line with the actual situation on site. Based on the discrete fracture network model, the volume joint number of rock mass is calculated. Based on the JSR index, BQ classification method and RQD classification, the development degree of fractures and surrounding rock classification in this area are evaluated. A method of surrounding rock classification based on three evaluation indexes is discussed to comprehensively and accurately classify the quality of rock mass in this area.

1. Introduction

The structural model of rock mass is the basis of studying the mechanical parameters of rock mass. In the field observation, it is difficult to see the spatial distribution of the rock mass structure plane, and the statistical discrete fracture network (DFN) simulation is the most effective method for a comprehensive and systematic understanding of the structure plane. Kulatilake and Wu [1] proposed the window method to measure structural plane parameters. By counting the number of different structural plane types in the field outcrop window, estimated values of structural plane trace length and center point density were obtained, and statistical methods were used to obtain the probability distribution of structural plane geometric parameters. Robertson [2] proposed the probability distribution form of a statistical structural plane by line method. Ross-Brown et al. [3] put forward the method of photogrammetry earlier and obtained images of jointed rock mass by taking on-site photos. Fan et al. [4] adopted digital photogrammetry to acquire images of jointed rock mass and used Projoint 1.0 software to interpret the jointed rock mass images. Because digital photogrammetry is affected by the environment of tunnels and other underground engineering, such as insufficient light and dust, the measurement data is incomplete, and the accuracy is poor. Other methods, such as three-dimensional laser scanning, have disadvantages such as high cost, difficult interpretation and “point with surface”, which makes it difficult to be applied to large-scale projects such as tunnels. Therefore, the traditional direct measurement method is still the main method for obtaining the geometric parameters of the structural plane.

Uncertainty in geometric configurations of fracture network systems poses challenges to the accurate and efficient simulation of fractured rock masses, which results from the limitations of geological survey techniques. Usually, fractures are observed and mapped in outcrops and excavation walls only as traces. The outcrop data, including the orientation, length and location of fractures, are statistically analyzed based on some assumed distributions. Previous studies show that the fracture length varies widely and can be described by a power-law or lognormal distribution [5,6]. The orientation of fracture sets follows a Fisher distribution [7,8], while the location of fracture centers can be represented by a multiplicative cascade [9] or Poisson process [10].

In order to more intuitively reflect the spatial distribution of the structural plane and the position relationship between the dominant groups, Kulatilake [11] estimated the distribution law of the three-dimensional spatial structural plane by using the geometric parameters of the structural plane collected from the two-dimensional outcrop surface and verified the estimated three-dimensional spatial structural plane distribution twice before and after tunnel excavation. Lei [12] made statistics on the geometric feature parameters of large-scale structural planes in the Beishan region, used VC++ and OpenGL technology to generate the distribution of structural planes in 3D network space based on the analysis results of the original data, and tested the 3D network simulation from the perspective of the occurrence of structural planes. With Songta Hydropower Station as the engineering background, Zhan [13] built a discrete fracture network model based on statistics and probability theory to comprehensively characterize the discrete network in rock mass. Wu [14] programmed a program in Visual Basic to automatically generate a 3D crack network model in AutoCAD according to the given parameters and verified it. Tan [15] uses a non-contact measurement system to measure and analyze parameters of rock mass and establishes a three-dimensional fracture network model to provide a basis for determining the REV of rock mass. Based on the three-dimensional fracture network model, Li [16] proposed an improved projection method to calculate the three-dimensional joint continuity of rock mass by replacing the disk model with the polygon model. Han [17] used empirical probability distribution to describe the geometric features of the structural plane and proposed a simulation method for constructing a three-dimensional fracture network based on a small sample rock mass. Nie [18] focuses on the calculation of crack diameter, adopts a new method to deduce the crack disk diameter in three-dimensional space, establishes a three-dimensional crack network model based on this method and verifies its rationality.

Due to the requirements of engineering rock mass and on-site workload, the above scholars often ignore the structural plane with a trace length of less than 1 m. From the perspective of overall stability, the structural plane with a smaller trace length has little influence, but it has a greater impact on the strength and deformation properties of the tunnel surrounding rock. In order to comprehensively explore the development degree and distribution law of the rock mass structural plane around the tunnel in three-dimensional space, a discrete fracture network model is established by systematic method, and the fracture development degree is evaluated based on the JSR index, BQ classification method and RQD classification. Based on the tunnel project of Qingdao Metro Line 6, the window method is used to directly measure the geometric parameters of the site structural plane and establish the probability distribution model. The Monte Carlo method is used to randomly generate the discrete fracture network, which provides the research basis for determining the characteristics and mechanical parameters of rock mass.

2. Engineering Background

The tunnel project of Qingdao Metro Line 6 is located in the Huangdao District of Qingdao City. The surrounding rock of the tunnel is breezed and is medium-weathered granite with high hardness, mainly non-penetrating joints and cracks, and the basic quality grade of the rock is III~IV. Lingshanwei fault intersects the tunnel line twice. The fault strike is 40°~55° to the northeast, the inclination is mainly to the north and west, the inclination is generally about 70°~88°, and the fault width is about 3 m. Affected by the secondary fracture of the Lingshanwei fault, the surrounding rock is broken obviously, which will lead to a change of stress conditions. The tunnel section of the Shishan section of the Metro Line 6 tunnel project was selected to investigate and study the spatial distribution of the structural plane. With the advance of the working face, five excavated sections were selected as samples of the surrounding rock outcrop surface to obtain the geometric parameters of the structural plane. The location of the selected section is shown in Figure 1.

The selected location is mainly located in the level III₂ surrounding rock and level IV₁ area, and the location is similar, which can be used as the same homogeneous area to measure the spatial distribution of the structural plane. The main methods for measuring structural plane parameters are the line method and the window method. The size of the window is 100 cm × 200 cm and 200 cm × 400 cm. The outcrop of the palm surface was photographed (Figure 2a) and the occurrence of the structural plane was measured with the geological compass (Figure 2b). Combined with the field measured data, outcrop photos and sketch drawings (Figure 3), the geometric feature parameters of the structural plane were obtained.

3. Geometric Parameters Were Measured by Probabilistic Statistical Methods

For the structural plane in a certain geological environment, its geometric distribution characteristics usually have some regularity, and mathematical statistics and probability analysis are the most effective ways to obtain this regularity. Using the structural plane analysis software DIPS. v5. 103 and the method of probability statistical analysis, the geometric parameter probability distribution model of the regional structural plane is obtained. The statistical results are shown in Figure 4 and

Table 1. Mean values and probability distributions of the fracture geometric parameters.

Parameter	Dominant Group			Probability Distribution
	I	II	III
Dip direction∠Dip angle/°	141∠69	190∠16	296∠76	Bivariate normal distribution
Trace length/m	0.48	0.46	0.51	Gamma distribution
Diameter/m	0.60	0.59	0.64	Gamma distribution
Spacing/m	0.43	0.72	0.66	Negative exponential distribution
Fracture density/m−3	9	5	7	N/A

. The fracture orientation (dip direction/dip angle) has been modeled using a bivariate normal distribution. The fracture trace length has followed a gamma distribution. The fracture spacing has followed a negative exponential distribution. Robertson [2] found that the length of the structural plane in the strike and dip directions is roughly the same. Based on that, an equivalent circular thin disk model is used to simplify the fracture shape in simulating the fractures in 3D. The fracture diameter was estimated from the fracture trace length using the procedure given by Kulatilake and Wu [19]. The estimated fracture diameter followed a gamma distribution. The steps of probabilistic statistical analysis are described as follows:

(1) Determine the maximum value a and minimum value b of the structural plane parameters of each dominant group; that is, all structural planes falling within the interval $\left[a,b\right]$ belong to this dominant group. The total number of structural planes in the interval $\left[a,b\right]$ is N.

(2) The interval is divided into n equal spacing between cells, the length of the interval is $\Delta =\left(a-b\right)/n$, the number of structural noodles in each cell is counted, which is called frequency $f_i$, and the frequency $f_i/N$ and histogram height $f_i/N\Delta$ are calculated.

(3) The statistical histogram of structural plane parameters is made based on statistical data, and the probability density function of the structural plane parameters can be obtained by fitting it so as to establish the structural plane probability distribution model.

Due to the sampling deviation, the relative frequency of occurrence of each group of a structural plane should be corrected, and the trace length of a structural plane should be estimated when studying the geometric characteristics of a structural plane.

The correction of the occurrence of a structural plane takes into account the probability of intersecting the survey line with the disk of the structural plane, the intersection angle between the direction of the survey line and each structural plane, the length of the survey line and the size of the structural plane and other influencing factors [20]. The calculation expression is as follows:

$$CR{F}_{\mathrm{i}}={\displaystyle \frac{W_i}{{\displaystyle \sum _{i=1}^N{W}_i}}}$$

(1)

$$W_i={\displaystyle \frac{1}{V_i}}={\displaystyle \frac{1}{\pi {\left(r_j\right)}_i^2\cos {\alpha }_{i}L}}$$

(2)

where (r_j)_i is the radius of the disk of the structural plane of i. α_i is the angle between the structural plane of i and the measurement line. N is the total number of structural planes. L is the length of the measuring line.

The relative frequencies obtained by the calculation are compared with the relative frequencies of the occurrence of structural planes before and after correction by using the dip direction of 10° or 20° and the dip angle of 5° as the group distance. The sampling deviation correction is significant in group I and group II, while the relative frequency change of group III before and after correction is small. Figure 5 shows the influence of sampling deviation on the occurrence of the three groups of structural planes.

Kulatilake [1] proposed an average trace length estimation method based on rectangular windows, and Wu [14] improved and simplified the method. The expression for the improved mean trace length µ is as follows:

$$\mu ={\displaystyle \frac{wh}{wE\left(\sin \phi \right)+hE\left(\left|\cos \phi \right|\right)}}\times {\displaystyle \frac{N_t+N_0-N_2}{N_t-N_0+N_2}}$$

(3)

where w and h represent the width and height of the rectangular window, respectively; N_t is the number of traces in the window. $N_0$ is the number of traces invisible at both ends. $N_2$ is the number of traces visible at both ends. $\phi$ is the apparent angle of structural plane. $E\left(x\right)$ represents the mathematical expectation of variable x.

Rectangular windows of two sizes (1 m × 2 m, 2 m × 4 m) are arranged at five different positions on the tunnel’s face. The average trace length of the three groups of structural plane data samples collected from the five windows is estimated by using the above formula. The estimated average trace length and the estimated error are shown in

Table 2. Estimation value and estimation error of average trace length of each window structural plane.

Position	Estimated Value (m)			True Value (m)			Estimation Error (%)
	I	II	III	I	II	III	I	II	III
1#	0.405	——	0.250	0.461	——	0.537	12.1	——	53.4
2#	0.300	0.222	0.186	0.338	0.342	0.473	11.2	35.1	60.7
3#	0.429	0.262	0.693	0.525	0.367	0.584	18.3	28.6	−18.7
4#	0.370	0.463	0.609	0.406	0.491	0.399	8.9	5.7	−52.6
5#	0.484	0.550	0.533	0.537	0.531	0.599	9.9	−3.6	11.0

.

As can be seen from Table 2, the error between the real value and the estimated value of the average trace length is basically about 20%. The difference between the estimated value and the real value of the first group of the structural plane is small, and the error range is only 8.9~18.3%. The error range of the second group is −3.6~35.1%. The error range of the third group of the structural plane is −52.6~60.7%. There are several reasons for the error: (1) The size of the window leads to the change of the type of the structural plane; (2) the location of window selection has particularity; (3) the number of structural planes is small, and the chance is large.

4. Visualization and Validation of Discrete Fracture Network Models

4.1. Visualization of Discrete Fracture Network Model

According to the method of calculating the volume density proposed by Yang [21] and Kulatilake [22], the volume density required for the discrete fracture network model can be calculated as follows: the density of group I is 9/m³, the density of group II is 5/m³ and the density of group III is 7/m³.

Before the discrete fracture network model is generated, the center coordinates (x₀, y₀, z₀), diameter D, dip A₀ and dip B₀ of the fracture disk must be determined. These geometric parameters determine the position and shape of the fracture disk. Based on the probability density distribution of each parameter obtained by the above statistics, the Monte Carlo method was used to randomly generate the central point location, occurrence and diameter of three groups of fracture disks, and thus the waiting data for the generation of discrete fracture network model was obtained [23].

Based on six known geometric parameters, the analytical expression of a disk-like structural plane in three-dimensional space is established:

$$\begin{gathered} n_1=\sin (B_0)\left(-\cos \left(A_0\right)\right) \\ {n}_2=\sin \left(B_0\right)\sin \left(A_0\right) \\ {n}_3=\cos \left(B_0\right) \\ s=\arctan {\displaystyle \frac{-\left(n_1\cos \left(t\right)+n_2\sin \left(t\right)\right)}{n_3}} \\ x=x_0+{\displaystyle \frac{D}{2}}\cos \left(s\right)\cos \left(t\right) \\ y=y_0+{\displaystyle \frac{D}{2}}\cos \left(s\right)\sin \left(t\right) \\ z=z_0+{\displaystyle \frac{D}{2}}\sin \left(s\right) \end{gathered}$$

(4)

where (x₀, y₀, z₀) are the coordinates of the center point of the fracture disk, A₀ is the fracture inclination, B₀ is the fracture inclination, D is the disk diameter, and the value of t ranges from 0° to 360°.

Because MATLAB has the advantages of fast calculation speed and good visualization effect, the discrete fracture network model is established using MATLAB. By importing known data into MATLAB and calculating according to Equation (4), points (x, y, z) in three-dimensional space can be obtained. Using the linspace command, t can be uniformly valued within the range of 0°~360°, which can generate a large number of point coordinates. Then, the plot3 and fill3 commands can be used to connect these point coordinates and fill the colors so as to obtain the discrete fracture network model. The discrete fracture network model is cut with a plane-simulated outcrop surface, and the trace distribution map of the sectional structural plane is generated. The distribution of the discrete fracture network and structural plane trace is shown in Figure 6 (note: the software version used in this study is MATLAB R2021b).

4.2. Verification of Discrete Fracture Network Model

The verification of structural plane occurrence by window method is the distribution law of trace inclination and dip angle in the window of statistical model outcrop surface, and the comparison with the field measured results to see whether the mean and standard deviation of the two are consistent. It is impossible to calculate the inclination of the structural plane through the distribution of the trace of the two-dimensional structural plane. Therefore, it is necessary to label the fenced disk. The starting point of the trace corresponds to the fenced disk in the MATLAB program so as to obtain the information of the disk corresponding to the trace. The comparison between the statistical results of the three groups of fracture traces on the outcrop surface and the measured data are shown in

Table 3. Verification results of fracture network model occurrence based on measured data.

Group		Occurrence				Relative Error (%)
		Dip Direction (°)		Dip Angle (°)
		Mean Value	Deviation	Mean Value	Deviation	Dip Direction	Dip Angle
I	True	140.95	12.96	68.95	11.58	1.5	5.1
	Simulation	143.03	10.60	65.40	11.54
II	True	189.77	87.03	15.87	8.36	8.6	17
	Simulation	173.45	85.48	18.66	8.21
III	True	296.32	6.28	75.59	6.28	0.2	0.4
	Simulation	297.06	4.87	75.92	4.29

. The comparison results of trace length and surface density of structural plane are shown in

Table 4. Verification results of trace length and surface density based on measured data.

Group		Mean Track Length (m)	Surface Density (m−2)	Relative Error (%)
				Mean Track Length	Surface Density
I	True	0.48	4.05	4.2	21.9
	Simulation	0.50	4.94
II	True	0.46	1.85	17.4	11.9
	Simulation	0.54	2.07
III	True	0.51	2.90	21.6	15.2
	Simulation	0.62	3.34

.

It can be seen from Table 3 and Table 4 that the average occurrence of the outcrop surface of the discrete fracture network model is very consistent with the field-measured results. The error range of structural plane inclination is less than 10%, and the error range of structural plane inclination is less than 20%. The maximum error of the average trace length and surface density of the three groups of structural planes is not more than 22%. In the discrete fracture network simulation, it is usually considered that the simulation results are consistent with the actual situation if the error is less than 30%. Therefore, the verification results show that the established discrete fracture network model is accurate.

5. Classification of Fractured Rock Mass

The development degree and distribution characteristics of rock mass cracks play an important role in controlling the long-term stability of underground engineering, so cracks occupy a certain weight in most rock mass quality evaluation systems [24,25,26]. The volume joint number $J_v$ of rock mass is an important parameter in the evaluation of rock mass fractures [27]. In general, the measurement of volume joint number $J_v$ adopts field measurement methods, such as the direct measurement method, spacing method and strip number method. These methods select the palm surface or the exposed part of the rock mass to make statistics on the two-dimensional fracture data in the field. However, due to the influence of the extension degree of the structural plane, the accuracy of the obtained volume joint number $J_v$ will be reduced, thus affecting the evaluation of the rock mass quality.

In this paper, based on the field measurement information, a discrete fracture network model is established to reproduce the fracture distribution in the rock mass, and the volume joint number $J_v$ in the rock mass can be determined by the fracture number in the statistical model. When calculating the volume joint number $J_v$, it is generally believed that the area of the fracture disk in the rock mass is greater than 1/2 the area of the fracture disk; that is, when the coordinate of the center point (x₀, y₀, z₀) of the fracture disk is located in the fracture network model, the fracture is included in the calculation sample of the volume joint number $J_v$. However, because there are three spatial positions between a rock mass of a certain size and cracks, namely, inclusion, intersection and penetration, when the spatial position relationship as shown in Figure 7 exists, the central point of the disk is located in the fracture network model, but the area of the fracture disk in the rock mass will be less than 1/2 the area of the fracture disk. As shown in Figure 7a, the area of the disk containing the slit can be calculated according to the length of the three intersecting incisor lines. As shown in Figure 7b, if the tangent plane trace length is less than the diameter of the structural plane, the fracture is considered to be included in the discrete fracture network model.

Based on the discrete fracture network model, the volume joint number is 15.3/m³. In this paper, the JSR index, BQ grade and RQD value are used to evaluate the development degree of crack and the grade of surrounding rock, and the evaluation index is related to volume joint number $J_v$. The midpoint surface density is an important parameter in the JSR index, which has a great correlation with volume joint number $J_v$, and can be calculated by volume joint number $J_v$. The BQ classification is related to the integrity coefficient $K_v$ of rock mass, but it is not easy to obtain $K_v$ by acoustic wave test in many projects, and the corresponding value is generally determined by volume joint number $J_v$. The RQD value is an important evaluation index. When there is no borehole and log record, the RQD value can be deduced by introducing the volume joint number $J_v$. The surrounding rock classification obtained by fracture distribution parameters is in good agreement with tunnel engineering classification, which can provide a new way for engineering rock mass classification quickly and effectively. The classification results of surrounding rock grades in the study area are shown in

Table 5. Surrounding rock classification results.

Method	Formula	Result	Class
JSR	$JSR=W_n{\overline{D}}_a\overline{L}$	159.6	III
BQ	$BQ=90+3R_c+250K_v$ $\left[BQ\right]=BQ-100\left(K_1+K_2\right)$	415.9	III
RQD	$RQD=115-3.3J_v$	64.5	III

.

6. Discussion

This paper focuses on mathematical statistics and probability analysis of geometric characteristic parameters of non-through fractured rock mass and establishes parameter models of each structural plane. In order to directly reflect the development degree and distribution law of each group of structural planes in three-dimensional space, a discrete fracture network model is generated in MATLAB using a systematic method. The accuracy of the discrete fracture network model is verified from three aspects: the occurrence, average trace length and surface density and the structural characteristics of the complex fractured rock mass are analyzed.

In order to analyze the structural characteristics of fractured rock mass, the JSR index, BQ classification method and RQD classification method are used to evaluate the development and distribution of fractures, and these classification methods take into account the influence of three structural plane parameters at most. However, the quality of complex fractured rock mass in rock mass engineering is often jointly affected by multiple factors [28]. Therefore, the above three classification methods are assigned a certain weight to the three indexes according to their impact on rock mass failure. The JSR index mainly evaluates the rock mass according to the surface density, trace length and number of joint groups, which basically includes all the basic parameters of the structural plane but does not reflect the more in-depth occurrence and other factors, so the JSR index is assigned a 30% weight. The BQ classification method evaluates the rock mass from the aspects of mechanical parameters such as hardness and integrity of rock mass, and the BQ value is modified from the perspective of occurrence of groundwater and structural plane. However, the structural plane in the study area is prone to form adverse combinations, which greatly promotes the destruction of rock mass. Therefore, the weight of the BQ value is assigned to 50%. The RQD classification mainly reflects the influence of structural plane spacing and assigns 20% weight to it. Based on the above conditions, this paper proposes A method for classifying rock mass by synthesizing three evaluation indexes, which is represented by A. The specific expression is as follows:

A = JSR × 30% + BQ × 50% + RQD × 20%

(5)

It is worth noting that the three indicators on the right of Equation (5) are not the sum of the values representing the physical meaning of their parameters but the sum of the scores of each indicator. See

Table 6. JSR, BQ and RQD scores.

JSR	BQ	RQD (%)	Score
0~24	>550	90~100	80~100
24~144	550~450	75~90	60~80
144~432	450~350	50~75	40~60
432~960	350~250	25~50	20~40
960~1500	<250	<25	<20

for the score of each indicator. The classification and description of the comprehensive rock mass classification index A are shown in

Table 7. Classification and description of comprehensive rock mass classification index A.

A	Rock Class	Development Degree	Rock Mass Integrity
80~100	I	Very slightly	Intact
60~80	II	Slightly	Relatively intact
40~60	III	Moderately	Relatively crush
20~40	IV	Developmentally	Crush
<20	V	Very developmentally	Very crush

.

Taking the rock mass in the study area as an example, the comprehensive rock mass grade classification index A is adopted to comprehensively and accurately evaluate and grade the rock mass quality from multiple angles, and the calculation results are shown in

Table 8. A index rock mass quality classification results.

JSR			BQ			RQD (%)			A	Class
Value	Score	Weight	Value	Score	Weight	Value	Score	Weight
159.6	59	30%	415.9	53	50%	64.5	52	20%	54.6	III

.

7. Conclusions

The discrete fracture network model is established by studying and analyzing the structural plane geometric parameters of fractured rock mass, and the accuracy of the discrete fracture network model is verified based on the field-measured data. At the same time, based on the discrete fracture network model, the fracture rock mass is evaluated by calculating the volume joint number, and the main conclusions are as follows.

(1) The rock mass structural plane in the study area is developed into three dominant groups, and the structural plane inclination and dip angle are normal distributions. The structural plane inclination is mainly steep (>60°), and a small part of the structural plane inclination is below 30°, which belongs to the low dip angle. The trace length, diameter and spacing of the structural plane all follow the negative exponential distribution. The rock mass in this region has high hardness and generally a small structural plane. The average diameter is in the range of 0.59~0.64 m, and the spacing of the structural plane is 0.43~0.72 m, which belongs to medium and wide spacing. Based on these data, the densities of three groups of structural are calculated as 9, 5 and 7/m³. These data provide the research basis for building the 3D network model of the structural plane and evaluating the quality of rock mass.

(2) Based on the probability distribution model of structural plane parameters, the 3D network model of fractured rock mass is simulated by the Monte Carlo method, and the 3D network visualization of rock mass structural plane is realized. The relative error of the occurrence, average trace length and density of the structural plane is about 20% by comparing the field-measured data with the distribution of the trace line of the model section. Therefore, the accuracy of the 3D structural plane network model is high.

(3) Based on the discrete fracture network model, the volume joint number of rock mass is calculated, and the development degree of rock mass structural plane is revealed from different angles by using the JSR index, BQ classification and RQD classification. Because the stability of rock mass is affected by many factors, a comprehensive rock mass classification index A combined with three methods is discussed. Compared with the traditional rock mass quality evaluation method, it has the advantages of being more comprehensive and accurate and is more in line with the actual situation of the rock mass structural plane. Taking the rock mass of this project as an example, the surrounding rock mass grade is calculated to be III.

The surrounding rock classification method proposed in this paper is based on the combination of quantitative and qualitative comprehensive indexes, which is suitable for most hard rock tunnels, but it needs further study for soft rock tunnels with high geostress.