# Research on the Large Deformation Prediction Model and Supporting Measures of Soft Rock Tunnel

Authors: Junying Rao; Yonghu Tao; Peng Xiong; Chongxin Nie; Hao Peng; Yanghao Xue; Zuowei Xi
Journal: Advances in Civil Engineering
 (2020)

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## Abstract

The weak surrounding rock has the characteristics of easy softening, poor integrity, low mechanical strength, etc., which makes it easy to induce different degrees of deformation and damage under excavation disturbance and then seriously affects the stability of the tunnel. Carrying out soft rock tunnel deformation prediction research and designing the supporting structure according to the predicted value is of great significance to engineering construction and design. Based on the grey theory, the large deformation of the vault, shoulder, and waist of the soft rock tunnel are predicted, and then the specific bolt support is designed in the maximum predicted value (Smax·R) area. The control effects of different bolts, spacing (d), length (L) on the maximum displacement (Smax·M), and maximum stress (σmax·M) the surrounding rock are analyzed by numerical simulation. Results show that the gray model has high prediction accuracy, the best prediction time is one week, and the maximum error is only 2.99%; with the decrease in d, resin bolt support has a significant supporting effect compared with mortar bolt support, with Smax.M and σmax·M reduced by 64.38% and 10.35%, respectively; as the L of bolt increases, compared with the mortar bolt support, the resin bolt support has a more obvious restraining effect on the surrounding rock deformation, and Smax·M and σmax·M are reduced by 28.20% and 10.00%, respectively; when 4.5 m < L < 6.0 m and 0.6 m < d < 0.7 m, resin bolt support should be adopted; in other ranges, mortar bolt support or resin bolt support has a less significant difference in controlling surrounding rock deformation.


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## Body

## 1. Introduction

Large deformation of soft rock tunnels is a common disease in the tunnel field, which not only affects the safety of tunnel construction but also endangers its service life. For engineering, it is crucially important to predict deformation and propose countermeasures. At present, the study of tunnel deformation prediction methods has been mentioned in many documents [1, 2], but gray theory is applied to deformation prediction and few studies on the design of support at the maximum deformation [3–5]. Therefore, it is still necessary to research whether the gray theory prediction method is carried out in-depth.In terms of gray theory and the feasibility study of bolting and shotcrete supports, many scholars at home and abroad have elaborated on it in many aspects; researches such as Szpak and Tchórzewska-Cieślak found that the gray theory was widely used in domestic water, infrastructure construction, economic development, etc. [6–8]; Lu believed that the gray theory could predict mine water inflow with high reliability and applicability [9]; Harding et al. found that bolt support could effectively control surrounding rock deformation, and its support effect was related to bolt parameters [10–12]; Forrestde and Liu convinced that the gray theory prediction could grasp real-time problems in tunnel deformation, slope collapse, and surface settlement [13]; Zhou believed that the gray theory could predict the stress change and unknown deformation of tunnel lining [14]; Huo et al. believed that the gray prediction was an effective means of predicting tunnel deformation, which could be used as a theoretical support for tunnel construction, design, and support to improve operation efficiency [15–18].Scholars have made many discussions on the research of gray prediction accuracy. Chen et al. believed that the gray prediction model could monitor the deformation characteristics of the surrounding rock of the tunnel entrance in real time, the difference between the predicted value and the monitored value was small, and the accuracy was higher [19, 20]; Hu et al. believed that the gray model predicted tunnel deformation more accurately [21–23]; Ning, Li, and others believed that the use of gray prediction model to monitor large tunnel deformation has high prediction accuracy and small absolute error [24].In the combined application of the gray theory and numerical simulation, industry experts have carried out many studies; Pan et al. found that the combination of gray theory and numerical simulation can effectively evaluate the deformation of foundation pit excavation and can make real-time prediction [25, 26]; Zhang found that the accuracy of numerical simulation was related to the continuity of the gray sequence [27]; Bi et al. found that the application of gray prediction and simulation technology could effectively improve model accuracy [28]; Hu et al. believed that finite element software analysis of tunnel surrounding rock deformation, combined with gray theory prediction and its mechanical behavior, could effectively change the modeling conditions and accuracy [29, 30].In summary, it was found that the gray prediction model could solve many problems in engineering fields, and its prediction accuracy was higher, which could provide an important reference for the safe construction of the project. However, in their research studies, scholars mainly considered the engineering application of the gray prediction model and analyzing its error between the prediction value and the monitoring value, there was little research on the combination of the prediction model and support design. Therefore, in order to well grasp the tunnel deformation and design support in real time, this article relies on the tunnel of Tong Province, establishes a prediction model based on the gray principle, uses related programming software to draw its prediction curve, and analyzes the rationality of the prediction results. The design support of the dangerous point (Smax·R) is selected, the maximum displacement (Smax) and the maximum stress (σmax) of the surrounding rock under the support conditions are calculated by numerical simulation, and the optimal support proposal is finally given.


## 2. Establishment of Gray Forecasting Model

The tunnel deformation monitoring data generally have no regularity, after the probability and statistics analysis; the gray theory can be used to generate the sequence number with time as the axis to construct the prediction model such as constructing the original sequence number of time [31, 32]:(1)k0=k01,k02,…,k0b−1,k0b.In equation (1), k(0)(j) is the jth original sequence number corresponding to the sequence number j.In order to make the data of equation (1) into a regular sequence, the data are accumulated and processed to obtain the following:(2)k1m=∑b=1mk0b.In equation (2), k(1)(j) is the jth time new sequence number generated by the accumulation of j original sequence numbers.Construct a new time series number as follows:(3)k1=k11,k12,…,k1b−1,k1b.Thus, the original sequence and the new sequence of tunnel deformation monitoring values can be obtained as follows:(4)S0=S01,S02,…,S0b−1,S0b,S1=S11,S12,…,S1b−1,S1b.In equation (4), F0·(j) is the jth original tunnel deformation monitoring value sequence number corresponding to the sequence number j and F1·(j) is the new sequence number generated by the accumulation of j original sequence numbers.Knowing from the gray principle, equation (4) obeys the exponential distribution, constructing a linear differential equation between the monitoring value S and the time K, and integrates it to obtain the following.Differential equation:(5)dSdk+RS=H.Integrating both sides of equation (5), we get(6)Sk=C⋅EXPR−Rk+HR−1.In equation (6), R and H are gray parameters and C is the integral constant.Whenk = 1, S (K) = S (1); substituting it into equation (6), we get the following equation:(7)C=S1−HR−1.Substituting equation (7) into equation (6), the differential equation of S and K can be obtained as(8)SK=S1−HR−1⋅EXPR−Rk+HR−1.According to the definition of the derivative of the function, we get(9)dSdk=limΔk⟶0Sk+Δk−SkΔk,dSdk=limΔk⟶1Sk+Δk−SkΔk.Knowing from the function continuity, when Δk is smaller, the fluctuation of the function value is small. In order to reasonably represent the deformation monitoring value, replacing S with the average value of S (k) and S (k + 1), and substituting the average value into equation (6), we get(10)S0k+1=H−0.5RS1k+S1k+1.Based on the above derivations, substitutingk = 1, 2, …, b − 1, b in equation (10), we get(11)S02=H−0.5RS11+S12,S03=H−0.5RS12+S13,⋮S0b−1=H−0.5RS1b−2+S1b−1,S0b=H−0.5RS1b−1+S1b.To solve equation (11), it can be written in matrix form as follows:(12)S02S03⋮S0b−1S0b=H−0.5RS11+S12H−0.5RS12+S13⋮H−0.5RS1b−2+S1b−1H−0.5RS1b−1+S1b.Simplifying equation (12), it can be obtained as follows:(13)S02S03⋮S0b−1S0b=H−0.5RS11+S12F12+S13⋮S1b−2+S1b−1S1b−1+S1b.Making(14)S∗=1−12S11+S121−12S12+S13⋮⋮1−12S1b−2+S1b−11−12S1b−1+S1b,S=S02S03⋮S0a−1S0a,N=HR,equation (13) can be written as(15)S=S∗×N.From equation (15), we get(16)N=S∗−1S.Equation (16) is expressed by the least square method as follows:(17)N=HRT=S∗T⋅S∗−1S∗TS.Equation (17) is the calculation formula of gray parameters.Summarizing equations (8)–(17), the prediction model of large deformation of soft rock in a tunnel can be obtained as follows:(18)S^1j+1=S01−HR−1⋅EXP−Rk1j+1−k11+HR−1.In equation (18), S^1j+1 is the predicted value corresponding to sequence j, where j = 1, 2, …, b – 1, b.


### 2.1. Model Analysis

The prediction accuracy and error of equation (18) are not known for the establishment of the prediction model. This section will analyze in detail from the following aspects and study its accuracy.


#### 2.1.1. Error Analysis

The mean and variance of the original data of tunnel deformation monitoring valueF are as follows:(19)S¯0=1b∑j=1bS0j,(20)βS2=1b∑j=1bS0j−S¯02.In equations (19) and (20), S¯0 is the average value of the original monitoring data and βS2 is the variance of the original monitoring data.The establishment of the gray forecasting model takes the time series as the axis, and the residual analysis needs to use the sample series.The residual sequenceω0 (j) is as follows:(21)ω0j=S0j−S^0j.Average value ofω0 (j) is as follows:(22)ω¯0j=1b∑j=1bω0j,The variance value ofω0 (j) is as follows:(23)βω02=1b∑j=1bω0j−ω¯0j2,(24)ν=βω0βS,(25)P=Pω0j−ω¯0j<0.6745⋅βS.In equations (24) and (25), ν is the variance ratio, P is the error probability, βS is the variance value of the original data of the tunnel deformation and settlement monitoring value S, and βω0 is the mean square error of the residual sequence ω0 (j).


#### 2.1.2. Relevance Analysis

Correlation analysis is mainly to establish the mutual influence relationship between the predicted value and the monitored value and calculate the accuracy of the model through the correlation calculation. The calculation is as follows.From equation (18), we get(26)S^0j=S^01,S^02,…,S^0b−1,S^0b,S0j=S01,S02,…,S0b−1,S0b.Relevance calculation is as follows:(27)ξj=minS0j−S0j+χmaxS0j−S0jS0j−S0j+χmaxS0j−S0j,j>0,1,j=0.In equation (27), ξ(j) is the correlation coefficient, S^0j−S0j is the absolute error value, minS^0j−S0J is the minimum absolute error, maxS^0j−S0j is the maximum absolute error, and χ is the error accuracy coefficient, generally 0.5.Solving equation (27), the correlation degree can be obtained as(28)G=b−1∑j=1bξj,j>0,1,j=0.Equation (18) is the calculation formula for the degree of relevance. Equation (28) is obtained by combining equations (26) and (27). Therefore, the G value is uniquely determined, and the R value represents the prediction accuracy; the larger the value, the much higher the precision.


## 2.1. Model Analysis

The prediction accuracy and error of equation (18) are not known for the establishment of the prediction model. This section will analyze in detail from the following aspects and study its accuracy.


### 2.1.1. Error Analysis

The mean and variance of the original data of tunnel deformation monitoring valueF are as follows:(19)S¯0=1b∑j=1bS0j,(20)βS2=1b∑j=1bS0j−S¯02.In equations (19) and (20), S¯0 is the average value of the original monitoring data and βS2 is the variance of the original monitoring data.The establishment of the gray forecasting model takes the time series as the axis, and the residual analysis needs to use the sample series.The residual sequenceω0 (j) is as follows:(21)ω0j=S0j−S^0j.Average value ofω0 (j) is as follows:(22)ω¯0j=1b∑j=1bω0j,The variance value ofω0 (j) is as follows:(23)βω02=1b∑j=1bω0j−ω¯0j2,(24)ν=βω0βS,(25)P=Pω0j−ω¯0j<0.6745⋅βS.In equations (24) and (25), ν is the variance ratio, P is the error probability, βS is the variance value of the original data of the tunnel deformation and settlement monitoring value S, and βω0 is the mean square error of the residual sequence ω0 (j).


### 2.1.2. Relevance Analysis

Correlation analysis is mainly to establish the mutual influence relationship between the predicted value and the monitored value and calculate the accuracy of the model through the correlation calculation. The calculation is as follows.From equation (18), we get(26)S^0j=S^01,S^02,…,S^0b−1,S^0b,S0j=S01,S02,…,S0b−1,S0b.Relevance calculation is as follows:(27)ξj=minS0j−S0j+χmaxS0j−S0jS0j−S0j+χmaxS0j−S0j,j>0,1,j=0.In equation (27), ξ(j) is the correlation coefficient, S^0j−S0j is the absolute error value, minS^0j−S0J is the minimum absolute error, maxS^0j−S0j is the maximum absolute error, and χ is the error accuracy coefficient, generally 0.5.Solving equation (27), the correlation degree can be obtained as(28)G=b−1∑j=1bξj,j>0,1,j=0.Equation (18) is the calculation formula for the degree of relevance. Equation (28) is obtained by combining equations (26) and (27). Therefore, the G value is uniquely determined, and the R value represents the prediction accuracy; the larger the value, the much higher the precision.


## 2.1.1. Error Analysis

The mean and variance of the original data of tunnel deformation monitoring valueF are as follows:(19)S¯0=1b∑j=1bS0j,(20)βS2=1b∑j=1bS0j−S¯02.In equations (19) and (20), S¯0 is the average value of the original monitoring data and βS2 is the variance of the original monitoring data.The establishment of the gray forecasting model takes the time series as the axis, and the residual analysis needs to use the sample series.The residual sequenceω0 (j) is as follows:(21)ω0j=S0j−S^0j.Average value ofω0 (j) is as follows:(22)ω¯0j=1b∑j=1bω0j,The variance value ofω0 (j) is as follows:(23)βω02=1b∑j=1bω0j−ω¯0j2,(24)ν=βω0βS,(25)P=Pω0j−ω¯0j<0.6745⋅βS.In equations (24) and (25), ν is the variance ratio, P is the error probability, βS is the variance value of the original data of the tunnel deformation and settlement monitoring value S, and βω0 is the mean square error of the residual sequence ω0 (j).


## 2.1.2. Relevance Analysis

Correlation analysis is mainly to establish the mutual influence relationship between the predicted value and the monitored value and calculate the accuracy of the model through the correlation calculation. The calculation is as follows.From equation (18), we get(26)S^0j=S^01,S^02,…,S^0b−1,S^0b,S0j=S01,S02,…,S0b−1,S0b.Relevance calculation is as follows:(27)ξj=minS0j−S0j+χmaxS0j−S0jS0j−S0j+χmaxS0j−S0j,j>0,1,j=0.In equation (27), ξ(j) is the correlation coefficient, S^0j−S0j is the absolute error value, minS^0j−S0J is the minimum absolute error, maxS^0j−S0j is the maximum absolute error, and χ is the error accuracy coefficient, generally 0.5.Solving equation (27), the correlation degree can be obtained as(28)G=b−1∑j=1bξj,j>0,1,j=0.Equation (18) is the calculation formula for the degree of relevance. Equation (28) is obtained by combining equations (26) and (27). Therefore, the G value is uniquely determined, and the R value represents the prediction accuracy; the larger the value, the much higher the precision.


## 3. Typical Case Analysis and Support Design

### 3.1. Analysis of Typical Cases

This paper relies on the Duimenzhai Tunnel on the left line, the ground elevation of the project is 1310 m∼1390 m, the relative elevation difference is 80 m, and the mileage is ZK190 + 780∼ZK191 + 275. The geological structure is complex, with well-developed rock folds, joints, and cracks, active faults fractures are developed, and the rock mass is relatively broken. The surrounding rock is prone to instability and failure. And the deformation of the tunnel increases with time. The geological longitudinal section is shown in Figure1, and the layout of monitoring and measuring points is shown in Figure 2. The gray model is used to predict the tunnel deformation, and the results are shown in Table 1.Figure 1
Schematic map of geological profile design (unit: m).Figure 2
Schematic diagram of measuring point layout (unit: cm).Table 1
Tunnel deformation monitoring data.
Time (d)S1 (left)S1 (right)S2 (left)S2 (right)DomeMonitoring value (m)Predictive value (m)Monitoring value (m)Predictive value (m)Monitoring value (m)Predictive value (m)Monitoring value (m)Predictive value (m)Monitoring value (m)Predictive value (m)15050.034545.06121121.349595.394444.0526062.256560.30188190.36123125.465555.08399110.389599.02189193.56151153.477981.004150153.42101103.40236240.63153154.65111113.025197200.96127129.36251256.37161163.45131134.056240243.50146147.56256259.78167168.94145149.697279283.00160164.30258265.96168172.99150154.878281285.30184190.36259266.97178184.74153156.409307312.50185195.39262269.35179189.92155159.90In order to more intuitively study the relationship between the tunnel deformation monitoring value and the predicted value, programming drawing software is used to draw the predicted values ofS1 (left), S1 (right), S2 (left), S2 (right), and the vault, respectively. The monitoring value trend chart is shown in Figure 3.Figure 3
Schematic diagram of comparative analysis of tunnel deformation prediction value and monitoring value: (a)S1 (left); (b) S1 (right); (c) S2 (left); (d) S2 (right); (e) dome.
(a)(b)(c)(d)(e)


#### 3.1.1. Forecast Duration Analysis

The data in Figure3 show that, at S1 (left), the inflection point occurs on the 7th day (8 d), the error probabilities PH1 = 0.42 and PH2 = 0.43, and the correlation coefficients RH1 = 0.68 and RH2 = 0.67; at S1 (right), the inflection point occurs on the 7th day, the error probability PF = 0.41, and the correlation coefficient RF = 0.69; at S2 (left), the inflection point occurs on the 6 d, the error probability PE = 0.42, and the correlation coefficient RE = 0.72; at S2 (right), the inflection point occurs on the 6th day, the error probability PJ = 0.38, and the correlation coefficient RJ = 0.71; and at the vault, the inflection point occurs on the 6th day, the error probability PA = 0.41, and the correlation coefficient RA = 0.67.AtS1 (left) and S1 (right), the error inflection points occurred on the 7th day of prediction, and the prediction error inflection points at S2 (left), S2 (right), and the tunnel vault all occurred on the 6th day of prediction; at S1 (left), S1 (right), S2 (left), S2 (right), and the vault, P and R are closer; comprehensive analysis and gray prediction belongs to a short-term prediction model; the prediction time is about 6 days; beyond this range, the prediction error and correlation coefficient are all great changes that have occurred, so it is recommended that if the gray model is used to predict tunnel deformation, the prediction duration should be controlled.


#### 3.1.2. Error Analysis

Figure3 shows that the predicted value is close to the monitored value, and the maximum error is only 2.99%. If the forecast time becomes longer, the error reaches 5.67% on the 9th day. Although the error is within the allowable range, the error increases with time.


#### 3.1.3. Correlation Analysis

The data in Figure3 show that, at S1 (left), there is an associated area from 7 d to 8 d. In this area, P and R are close, PH1 = 0.42, PH2 = 0.43, RH1 = 0.68, and RH2 = 0.67; at S1 (right), there is an associated area from 3 d to 4 d, PG1 = 0.41, PG2 = 0.40, RG1 = 0.65, and RG2 = 0.67; at S2 (left), there is an associated area from 2 d to 3 d, PM1 = 0.38, PG2 = 0.37, RM1 = 0.71, and RM2 = 0.70; at S2 (right), there is an associated area from 3 d to 4 d, PK1 = 0.39, PK2 = 0.40, RK1 = 0.69, and RK2 = 0.70; and there is no associated area at the vault.Associated areas appear atS1 (left), S1 (right), S2 (left), and S2 (right), indicating that the tunnel deformation in this area is in a gentle state, and the deformation hardly increases with time. It is relatively safe to carry out tunnel construction at this moment; Figure 3(e) shows that the deformation of the vault increases with time, and after the 6th day, its deformation is relatively slower; comprehensive analysis shows that the design of the support at the maximum deformation in the associated area is very important for the safe construction of the tunnel, and it can prevent large settlement of the vault.The proposed tunnel is located in a soft rock area, and the surrounding rock grade is Grade V. Figure3 shows that the deformation of the tunnel increases with time, and the maximum predicted value reaches Smax·R = 312.50 mm. If effective treatment measures are not taken, the safety of tunnel construction will be endangered. In the following part, the author will design the support measures at Smax·R using numerical simulation to compare and analyze Smax·M and σmax·M generated by the surrounding rock under different support conditions and giving optimal support recommendations.


### 3.2. Design of Support Measures atSmax·R

#### 3.2.1. Selection of Support Methods

The mechanical mechanism of the conventional mortar bolt and the resin bolt support is the same [33], but the force transmission effect of the resin bolt is slightly weaker than that of the mortar bolt, and the pulling force is smaller, as shown in Figure 4. However, resin bolts also have some advantages as a means of tunnel support:Figure 4
Displacement curves of resin anchor and mortar anchor.(1)
In terms of anchoring force, the anchoring force of resin anchors is equivalent to that of mortar anchors of the same specification. For example, the anchoring force ofφ15 mm resin anchors can reach 50 kN∼75 kN, which can provide sufficient anchoring force to effectively control the surrounding rock deformation.(2)
In terms of processability, the resin anchor rod is a composite material composed of unsaturated polyester resin as the matrix material and glass fiber as the reinforcing material; it has high tensile strength, but low shear resistance and good cutting performance, and no spark. Ordinary mortar anchor rods are prone to damage the processing machinery (such as being involved in the drum to damage the pick) during the cutting and processing of the support site, and sparks are prone to occur during the cutting and processing of the construction site, which poses safety hazards such as fire and explosion in special geological sections.(3)
In terms of dead weight, the density of resin anchor rods is generally about 2.0 g/cm3, which is equivalent to 1/4 of conventional metal anchor rods. Therefore, resin anchor rods are lighter in handling, less difficult to transport, and faster, achieving the purpose of timely construction, improving construction efficiency and construction schedule.For these reasons, in the design of supporting measures below, we plan to compare the control effects of resin bolts and mortar bolts on surrounding rock deformation to determine whether resin bolts can be used as one of the options for controlling large deformation of soft rock tunnels, so as to give reasonable support recommendations.


#### 3.2.2. Supporting Parameters

The supporting project was originally designed for spray-anchor support; the circumferential arrangement of anchor rods is 1.0 m apart, after the small pipes are grouted and consolidated; the upper, middle, and lower step method is used for weak blasting excavation or mechanical excavation. Physical and mechanical parameters of related materials are shown in Table2. As shown in Figure 3(a), when the original design support is adopted, the tunnel deformation is large, according to the gray model prediction, and the maximum predicted value Smax·R = 312.50 mm. For Smax·R, the following bolt supports are designed:Table 2
Physical and mechanical parameters of rock mass.
Surrounding rock categoryLayer thickness (m)Weight (kN m−3)Elastic modulus (GPa)Poisson’s ratioCohesion (MPa)Internal friction angle (°)Powder clay1420.40.0420.251.4646Sand stone2717.30.0140.320.02630Argillaceous rock1916.50.0060.350.04337Ordinary mortar bolt—81.32000.30——Resin anchor—76.62800.28——(1)
Design resin bolts with the same parameters as the original mortar bolts and analyze the effect of the resin bolts and mortar bolts on controlling surrounding rock deformation through numerical simulation. The supporting parameters are shown in Table3.(2)
Change theL and d of the mortar bolt and the resin bolt, study the Smax·M and Smax·M produced by the surrounding rock based on the numerical method, and give the optimal support recommendations. The support parameters can be seen in Tables 4 and 5.Table 3
Bolt support parameters.
Anchor typesLength (m)Ring distance (m)Longitudinal distance (m)Diameter (mm)Mortar bolt4.51.01.0φ22Resin anchor4.51.01.0φ22Table 4
Encrypted bolt support parameters.
Anchor typesLength (m)Ring distance (m)Longitudinal distance (m)Diameter (mm)Mortar bolt4.50.70.7φ22Resin anchor4.50.70.7φ22Mortar bolt4.50.40.4φ22Resin anchor4.50.40.4φ22Table 5
Parameters of lengthened bolt support.
Anchor typesLength (m)Ring distance (m)Longitudinal distance (m)Diameter (mm)Mortar bolt7.51.01.0φ22Resin anchor7.51.01.0φ22Mortar bolt6.01.01.0φ22Resin anchor6.01.01.0φ22


#### 3.2.3. Model Establishment

Using FLAC3D finite element software, a two-dimensional numerical model of the Duimenzhai Tunnel is established. After considering the excavation of an underground tunnel, only the rock mass within the excavation range of 5 times the size of the tunnel has a disturbing effect, and the tunnel height of this project is 11.58 m, and the width is 10.60 m. Therefore, the height × width of the proposed model is 60 m × 60 m, and the model size and grid division are shown in Figures5 and 6.Figure 5
Model size diagram.Figure 6
Mesh division.


#### 3.2.4. Analysis of Surrounding Rock Stress and Displacement

Figure7 shows that when the mortar bolt is used to support the tunnel, Smax·M = 0.487 cm and σmax·M = 681.92 kN/m2; when the resin bolt is used to support the tunnel, Smax·M = 0.398 cm and σmax·M = 228.55 kN/m2.Figure 7
Original parameter mortar bolt and resin bolt support: (a)Smax of dangerous point; (b) σmax of dangerous point.
(a)(b)The results show that compared with the tunnel supported by mortar bolts,Smax·M is reduced by 22.36% and σmax·M is reduced by 66.48% for resin bolts. The supporting effect of resin bolts is significant.Figure8 shows that when the mortar bolts are used to support the tunnel, Smax·M = 0.320 m and σmax·M = 220.55 kN/m2; when the resin bolts are used to support the tunnel, Smax·M = 0.177 m and σmax·M = 183.65 kN/m2.Figure 8
The distance between mortar bolt and resin bolt support is reduced to 0.7 m: (a)Smax of dangerous point; (b) σmax of dangerous point.
(a)(b)The results show that compared with mortar bolts support,Smax·M is reduced by 32.46% and σmax·M is reduced by 47.08%, and its supporting effect is significant.Figure9 shows that when the mortar bolts are used to support the tunnel, Smax·M. = 0.114 m and σmax·M = 243.38 kN/m2; when the resin bolts are used to support the tunnel, Smax·M = 0.077 m and σmax·M = 128.80 kN/m2.Figure 9
The distance between mortar bolt and resin bolt support is reduced to 0.4 m: (a)Smax of dangerous point; (b) σmax of dangerous point.
(a)(b)The results show that compared with mortar bolt support, resin bolts have a reduction ofSmax·M by 44.68% and a reduction of σmax·M by 16.73%. The supporting effect is significant.Figure10 shows that when the mortar bolts are used to support the tunnel, Smax·M = 0.078 m and σmax·M = 165.38 kN/m2; when the resin bolt is used to support the tunnel, Smax·M = 0.036 m and σmax·M = 87.99 kN/m2.The results show that compared with mortar bolts support, Smax·M is reduced by 53.85% and σmax·M is reduced by 46.80%, and its supporting effect is significant.Figure 10
The length of mortar bolt and resin bolt support is 6.0 m: (a)Smax of dangerous point; (b) σmax of dangerous point.
(a)(b)Figure11 shows that when the mortar bolts are used to support the tunnel, Smax·M = 0.056 m and σmax·M = 148.55 kN/m2; when the resin bolts are used to support the tunnel, Smax·M = 0.032 m and σmax·M = 95.65 kN/m2.Figure 11
The length of mortar bolt support and bolt support is 7.5 m: (a)Smax of dangerous point; (b) σmax of dangerous point.
(a)(b)The results show that compared with the tunnel supported by mortar bolts, theSmax·M is reduced by 42.85% and the σmax·M is reduced by 35.61%, and the supporting effect is significantly improved.From the comparative analysis of Figures5–9, when mortar bolts are used for support, Smax·M and σmax·M are approximately 1.6 times and 3 times than that of resin bolts support; Figures 6 and 7 are compared with Figure 5, the surrounding rock deformation decreases with the reduction of the bolt spacing, and when it is reduced to 0.4 m～0.7 m, the resin bolt support has a significant effect on controlling the surrounding rock deformation; Figures 8 and 9 are compared with Figure 5; when the length of the bolt is 4.5 m～6 m, the effect of using resin bolt support to control surrounding rock deformation is significant, but with the increase in the length of the bolt, the mortar bolts or the resin anchor effect of rod support in controlling the deformation of surrounding rock is small.


## 3.1. Analysis of Typical Cases

This paper relies on the Duimenzhai Tunnel on the left line, the ground elevation of the project is 1310 m∼1390 m, the relative elevation difference is 80 m, and the mileage is ZK190 + 780∼ZK191 + 275. The geological structure is complex, with well-developed rock folds, joints, and cracks, active faults fractures are developed, and the rock mass is relatively broken. The surrounding rock is prone to instability and failure. And the deformation of the tunnel increases with time. The geological longitudinal section is shown in Figure1, and the layout of monitoring and measuring points is shown in Figure 2. The gray model is used to predict the tunnel deformation, and the results are shown in Table 1.Figure 1
Schematic map of geological profile design (unit: m).Figure 2
Schematic diagram of measuring point layout (unit: cm).Table 1
Tunnel deformation monitoring data.
Time (d)S1 (left)S1 (right)S2 (left)S2 (right)DomeMonitoring value (m)Predictive value (m)Monitoring value (m)Predictive value (m)Monitoring value (m)Predictive value (m)Monitoring value (m)Predictive value (m)Monitoring value (m)Predictive value (m)15050.034545.06121121.349595.394444.0526062.256560.30188190.36123125.465555.08399110.389599.02189193.56151153.477981.004150153.42101103.40236240.63153154.65111113.025197200.96127129.36251256.37161163.45131134.056240243.50146147.56256259.78167168.94145149.697279283.00160164.30258265.96168172.99150154.878281285.30184190.36259266.97178184.74153156.409307312.50185195.39262269.35179189.92155159.90In order to more intuitively study the relationship between the tunnel deformation monitoring value and the predicted value, programming drawing software is used to draw the predicted values ofS1 (left), S1 (right), S2 (left), S2 (right), and the vault, respectively. The monitoring value trend chart is shown in Figure 3.Figure 3
Schematic diagram of comparative analysis of tunnel deformation prediction value and monitoring value: (a)S1 (left); (b) S1 (right); (c) S2 (left); (d) S2 (right); (e) dome.
(a)(b)(c)(d)(e)


### 3.1.1. Forecast Duration Analysis

The data in Figure3 show that, at S1 (left), the inflection point occurs on the 7th day (8 d), the error probabilities PH1 = 0.42 and PH2 = 0.43, and the correlation coefficients RH1 = 0.68 and RH2 = 0.67; at S1 (right), the inflection point occurs on the 7th day, the error probability PF = 0.41, and the correlation coefficient RF = 0.69; at S2 (left), the inflection point occurs on the 6 d, the error probability PE = 0.42, and the correlation coefficient RE = 0.72; at S2 (right), the inflection point occurs on the 6th day, the error probability PJ = 0.38, and the correlation coefficient RJ = 0.71; and at the vault, the inflection point occurs on the 6th day, the error probability PA = 0.41, and the correlation coefficient RA = 0.67.AtS1 (left) and S1 (right), the error inflection points occurred on the 7th day of prediction, and the prediction error inflection points at S2 (left), S2 (right), and the tunnel vault all occurred on the 6th day of prediction; at S1 (left), S1 (right), S2 (left), S2 (right), and the vault, P and R are closer; comprehensive analysis and gray prediction belongs to a short-term prediction model; the prediction time is about 6 days; beyond this range, the prediction error and correlation coefficient are all great changes that have occurred, so it is recommended that if the gray model is used to predict tunnel deformation, the prediction duration should be controlled.


### 3.1.2. Error Analysis

Figure3 shows that the predicted value is close to the monitored value, and the maximum error is only 2.99%. If the forecast time becomes longer, the error reaches 5.67% on the 9th day. Although the error is within the allowable range, the error increases with time.


### 3.1.3. Correlation Analysis

The data in Figure3 show that, at S1 (left), there is an associated area from 7 d to 8 d. In this area, P and R are close, PH1 = 0.42, PH2 = 0.43, RH1 = 0.68, and RH2 = 0.67; at S1 (right), there is an associated area from 3 d to 4 d, PG1 = 0.41, PG2 = 0.40, RG1 = 0.65, and RG2 = 0.67; at S2 (left), there is an associated area from 2 d to 3 d, PM1 = 0.38, PG2 = 0.37, RM1 = 0.71, and RM2 = 0.70; at S2 (right), there is an associated area from 3 d to 4 d, PK1 = 0.39, PK2 = 0.40, RK1 = 0.69, and RK2 = 0.70; and there is no associated area at the vault.Associated areas appear atS1 (left), S1 (right), S2 (left), and S2 (right), indicating that the tunnel deformation in this area is in a gentle state, and the deformation hardly increases with time. It is relatively safe to carry out tunnel construction at this moment; Figure 3(e) shows that the deformation of the vault increases with time, and after the 6th day, its deformation is relatively slower; comprehensive analysis shows that the design of the support at the maximum deformation in the associated area is very important for the safe construction of the tunnel, and it can prevent large settlement of the vault.The proposed tunnel is located in a soft rock area, and the surrounding rock grade is Grade V. Figure3 shows that the deformation of the tunnel increases with time, and the maximum predicted value reaches Smax·R = 312.50 mm. If effective treatment measures are not taken, the safety of tunnel construction will be endangered. In the following part, the author will design the support measures at Smax·R using numerical simulation to compare and analyze Smax·M and σmax·M generated by the surrounding rock under different support conditions and giving optimal support recommendations.


## 3.1.1. Forecast Duration Analysis

The data in Figure3 show that, at S1 (left), the inflection point occurs on the 7th day (8 d), the error probabilities PH1 = 0.42 and PH2 = 0.43, and the correlation coefficients RH1 = 0.68 and RH2 = 0.67; at S1 (right), the inflection point occurs on the 7th day, the error probability PF = 0.41, and the correlation coefficient RF = 0.69; at S2 (left), the inflection point occurs on the 6 d, the error probability PE = 0.42, and the correlation coefficient RE = 0.72; at S2 (right), the inflection point occurs on the 6th day, the error probability PJ = 0.38, and the correlation coefficient RJ = 0.71; and at the vault, the inflection point occurs on the 6th day, the error probability PA = 0.41, and the correlation coefficient RA = 0.67.AtS1 (left) and S1 (right), the error inflection points occurred on the 7th day of prediction, and the prediction error inflection points at S2 (left), S2 (right), and the tunnel vault all occurred on the 6th day of prediction; at S1 (left), S1 (right), S2 (left), S2 (right), and the vault, P and R are closer; comprehensive analysis and gray prediction belongs to a short-term prediction model; the prediction time is about 6 days; beyond this range, the prediction error and correlation coefficient are all great changes that have occurred, so it is recommended that if the gray model is used to predict tunnel deformation, the prediction duration should be controlled.


## 3.1.2. Error Analysis

Figure3 shows that the predicted value is close to the monitored value, and the maximum error is only 2.99%. If the forecast time becomes longer, the error reaches 5.67% on the 9th day. Although the error is within the allowable range, the error increases with time.


## 3.1.3. Correlation Analysis

The data in Figure3 show that, at S1 (left), there is an associated area from 7 d to 8 d. In this area, P and R are close, PH1 = 0.42, PH2 = 0.43, RH1 = 0.68, and RH2 = 0.67; at S1 (right), there is an associated area from 3 d to 4 d, PG1 = 0.41, PG2 = 0.40, RG1 = 0.65, and RG2 = 0.67; at S2 (left), there is an associated area from 2 d to 3 d, PM1 = 0.38, PG2 = 0.37, RM1 = 0.71, and RM2 = 0.70; at S2 (right), there is an associated area from 3 d to 4 d, PK1 = 0.39, PK2 = 0.40, RK1 = 0.69, and RK2 = 0.70; and there is no associated area at the vault.Associated areas appear atS1 (left), S1 (right), S2 (left), and S2 (right), indicating that the tunnel deformation in this area is in a gentle state, and the deformation hardly increases with time. It is relatively safe to carry out tunnel construction at this moment; Figure 3(e) shows that the deformation of the vault increases with time, and after the 6th day, its deformation is relatively slower; comprehensive analysis shows that the design of the support at the maximum deformation in the associated area is very important for the safe construction of the tunnel, and it can prevent large settlement of the vault.The proposed tunnel is located in a soft rock area, and the surrounding rock grade is Grade V. Figure3 shows that the deformation of the tunnel increases with time, and the maximum predicted value reaches Smax·R = 312.50 mm. If effective treatment measures are not taken, the safety of tunnel construction will be endangered. In the following part, the author will design the support measures at Smax·R using numerical simulation to compare and analyze Smax·M and σmax·M generated by the surrounding rock under different support conditions and giving optimal support recommendations.


## 3.2. Design of Support Measures atSmax·R

### 3.2.1. Selection of Support Methods

The mechanical mechanism of the conventional mortar bolt and the resin bolt support is the same [33], but the force transmission effect of the resin bolt is slightly weaker than that of the mortar bolt, and the pulling force is smaller, as shown in Figure 4. However, resin bolts also have some advantages as a means of tunnel support:Figure 4
Displacement curves of resin anchor and mortar anchor.(1)
In terms of anchoring force, the anchoring force of resin anchors is equivalent to that of mortar anchors of the same specification. For example, the anchoring force ofφ15 mm resin anchors can reach 50 kN∼75 kN, which can provide sufficient anchoring force to effectively control the surrounding rock deformation.(2)
In terms of processability, the resin anchor rod is a composite material composed of unsaturated polyester resin as the matrix material and glass fiber as the reinforcing material; it has high tensile strength, but low shear resistance and good cutting performance, and no spark. Ordinary mortar anchor rods are prone to damage the processing machinery (such as being involved in the drum to damage the pick) during the cutting and processing of the support site, and sparks are prone to occur during the cutting and processing of the construction site, which poses safety hazards such as fire and explosion in special geological sections.(3)
In terms of dead weight, the density of resin anchor rods is generally about 2.0 g/cm3, which is equivalent to 1/4 of conventional metal anchor rods. Therefore, resin anchor rods are lighter in handling, less difficult to transport, and faster, achieving the purpose of timely construction, improving construction efficiency and construction schedule.For these reasons, in the design of supporting measures below, we plan to compare the control effects of resin bolts and mortar bolts on surrounding rock deformation to determine whether resin bolts can be used as one of the options for controlling large deformation of soft rock tunnels, so as to give reasonable support recommendations.


### 3.2.2. Supporting Parameters

The supporting project was originally designed for spray-anchor support; the circumferential arrangement of anchor rods is 1.0 m apart, after the small pipes are grouted and consolidated; the upper, middle, and lower step method is used for weak blasting excavation or mechanical excavation. Physical and mechanical parameters of related materials are shown in Table2. As shown in Figure 3(a), when the original design support is adopted, the tunnel deformation is large, according to the gray model prediction, and the maximum predicted value Smax·R = 312.50 mm. For Smax·R, the following bolt supports are designed:Table 2
Physical and mechanical parameters of rock mass.
Surrounding rock categoryLayer thickness (m)Weight (kN m−3)Elastic modulus (GPa)Poisson’s ratioCohesion (MPa)Internal friction angle (°)Powder clay1420.40.0420.251.4646Sand stone2717.30.0140.320.02630Argillaceous rock1916.50.0060.350.04337Ordinary mortar bolt—81.32000.30——Resin anchor—76.62800.28——(1)
Design resin bolts with the same parameters as the original mortar bolts and analyze the effect of the resin bolts and mortar bolts on controlling surrounding rock deformation through numerical simulation. The supporting parameters are shown in Table3.(2)
Change theL and d of the mortar bolt and the resin bolt, study the Smax·M and Smax·M produced by the surrounding rock based on the numerical method, and give the optimal support recommendations. The support parameters can be seen in Tables 4 and 5.Table 3
Bolt support parameters.
Anchor typesLength (m)Ring distance (m)Longitudinal distance (m)Diameter (mm)Mortar bolt4.51.01.0φ22Resin anchor4.51.01.0φ22Table 4
Encrypted bolt support parameters.
Anchor typesLength (m)Ring distance (m)Longitudinal distance (m)Diameter (mm)Mortar bolt4.50.70.7φ22Resin anchor4.50.70.7φ22Mortar bolt4.50.40.4φ22Resin anchor4.50.40.4φ22Table 5
Parameters of lengthened bolt support.
Anchor typesLength (m)Ring distance (m)Longitudinal distance (m)Diameter (mm)Mortar bolt7.51.01.0φ22Resin anchor7.51.01.0φ22Mortar bolt6.01.01.0φ22Resin anchor6.01.01.0φ22


### 3.2.3. Model Establishment

Using FLAC3D finite element software, a two-dimensional numerical model of the Duimenzhai Tunnel is established. After considering the excavation of an underground tunnel, only the rock mass within the excavation range of 5 times the size of the tunnel has a disturbing effect, and the tunnel height of this project is 11.58 m, and the width is 10.60 m. Therefore, the height × width of the proposed model is 60 m × 60 m, and the model size and grid division are shown in Figures5 and 6.Figure 5
Model size diagram.Figure 6
Mesh division.


### 3.2.4. Analysis of Surrounding Rock Stress and Displacement

Figure7 shows that when the mortar bolt is used to support the tunnel, Smax·M = 0.487 cm and σmax·M = 681.92 kN/m2; when the resin bolt is used to support the tunnel, Smax·M = 0.398 cm and σmax·M = 228.55 kN/m2.Figure 7
Original parameter mortar bolt and resin bolt support: (a)Smax of dangerous point; (b) σmax of dangerous point.
(a)(b)The results show that compared with the tunnel supported by mortar bolts,Smax·M is reduced by 22.36% and σmax·M is reduced by 66.48% for resin bolts. The supporting effect of resin bolts is significant.Figure8 shows that when the mortar bolts are used to support the tunnel, Smax·M = 0.320 m and σmax·M = 220.55 kN/m2; when the resin bolts are used to support the tunnel, Smax·M = 0.177 m and σmax·M = 183.65 kN/m2.Figure 8
The distance between mortar bolt and resin bolt support is reduced to 0.7 m: (a)Smax of dangerous point; (b) σmax of dangerous point.
(a)(b)The results show that compared with mortar bolts support,Smax·M is reduced by 32.46% and σmax·M is reduced by 47.08%, and its supporting effect is significant.Figure9 shows that when the mortar bolts are used to support the tunnel, Smax·M. = 0.114 m and σmax·M = 243.38 kN/m2; when the resin bolts are used to support the tunnel, Smax·M = 0.077 m and σmax·M = 128.80 kN/m2.Figure 9
The distance between mortar bolt and resin bolt support is reduced to 0.4 m: (a)Smax of dangerous point; (b) σmax of dangerous point.
(a)(b)The results show that compared with mortar bolt support, resin bolts have a reduction ofSmax·M by 44.68% and a reduction of σmax·M by 16.73%. The supporting effect is significant.Figure10 shows that when the mortar bolts are used to support the tunnel, Smax·M = 0.078 m and σmax·M = 165.38 kN/m2; when the resin bolt is used to support the tunnel, Smax·M = 0.036 m and σmax·M = 87.99 kN/m2.The results show that compared with mortar bolts support, Smax·M is reduced by 53.85% and σmax·M is reduced by 46.80%, and its supporting effect is significant.Figure 10
The length of mortar bolt and resin bolt support is 6.0 m: (a)Smax of dangerous point; (b) σmax of dangerous point.
(a)(b)Figure11 shows that when the mortar bolts are used to support the tunnel, Smax·M = 0.056 m and σmax·M = 148.55 kN/m2; when the resin bolts are used to support the tunnel, Smax·M = 0.032 m and σmax·M = 95.65 kN/m2.Figure 11
The length of mortar bolt support and bolt support is 7.5 m: (a)Smax of dangerous point; (b) σmax of dangerous point.
(a)(b)The results show that compared with the tunnel supported by mortar bolts, theSmax·M is reduced by 42.85% and the σmax·M is reduced by 35.61%, and the supporting effect is significantly improved.From the comparative analysis of Figures5–9, when mortar bolts are used for support, Smax·M and σmax·M are approximately 1.6 times and 3 times than that of resin bolts support; Figures 6 and 7 are compared with Figure 5, the surrounding rock deformation decreases with the reduction of the bolt spacing, and when it is reduced to 0.4 m～0.7 m, the resin bolt support has a significant effect on controlling the surrounding rock deformation; Figures 8 and 9 are compared with Figure 5; when the length of the bolt is 4.5 m～6 m, the effect of using resin bolt support to control surrounding rock deformation is significant, but with the increase in the length of the bolt, the mortar bolts or the resin anchor effect of rod support in controlling the deformation of surrounding rock is small.


## 3.2.1. Selection of Support Methods

The mechanical mechanism of the conventional mortar bolt and the resin bolt support is the same [33], but the force transmission effect of the resin bolt is slightly weaker than that of the mortar bolt, and the pulling force is smaller, as shown in Figure 4. However, resin bolts also have some advantages as a means of tunnel support:Figure 4
Displacement curves of resin anchor and mortar anchor.(1)
In terms of anchoring force, the anchoring force of resin anchors is equivalent to that of mortar anchors of the same specification. For example, the anchoring force ofφ15 mm resin anchors can reach 50 kN∼75 kN, which can provide sufficient anchoring force to effectively control the surrounding rock deformation.(2)
In terms of processability, the resin anchor rod is a composite material composed of unsaturated polyester resin as the matrix material and glass fiber as the reinforcing material; it has high tensile strength, but low shear resistance and good cutting performance, and no spark. Ordinary mortar anchor rods are prone to damage the processing machinery (such as being involved in the drum to damage the pick) during the cutting and processing of the support site, and sparks are prone to occur during the cutting and processing of the construction site, which poses safety hazards such as fire and explosion in special geological sections.(3)
In terms of dead weight, the density of resin anchor rods is generally about 2.0 g/cm3, which is equivalent to 1/4 of conventional metal anchor rods. Therefore, resin anchor rods are lighter in handling, less difficult to transport, and faster, achieving the purpose of timely construction, improving construction efficiency and construction schedule.For these reasons, in the design of supporting measures below, we plan to compare the control effects of resin bolts and mortar bolts on surrounding rock deformation to determine whether resin bolts can be used as one of the options for controlling large deformation of soft rock tunnels, so as to give reasonable support recommendations.


## 3.2.2. Supporting Parameters

The supporting project was originally designed for spray-anchor support; the circumferential arrangement of anchor rods is 1.0 m apart, after the small pipes are grouted and consolidated; the upper, middle, and lower step method is used for weak blasting excavation or mechanical excavation. Physical and mechanical parameters of related materials are shown in Table2. As shown in Figure 3(a), when the original design support is adopted, the tunnel deformation is large, according to the gray model prediction, and the maximum predicted value Smax·R = 312.50 mm. For Smax·R, the following bolt supports are designed:Table 2
Physical and mechanical parameters of rock mass.
Surrounding rock categoryLayer thickness (m)Weight (kN m−3)Elastic modulus (GPa)Poisson’s ratioCohesion (MPa)Internal friction angle (°)Powder clay1420.40.0420.251.4646Sand stone2717.30.0140.320.02630Argillaceous rock1916.50.0060.350.04337Ordinary mortar bolt—81.32000.30——Resin anchor—76.62800.28——(1)
Design resin bolts with the same parameters as the original mortar bolts and analyze the effect of the resin bolts and mortar bolts on controlling surrounding rock deformation through numerical simulation. The supporting parameters are shown in Table3.(2)
Change theL and d of the mortar bolt and the resin bolt, study the Smax·M and Smax·M produced by the surrounding rock based on the numerical method, and give the optimal support recommendations. The support parameters can be seen in Tables 4 and 5.Table 3
Bolt support parameters.
Anchor typesLength (m)Ring distance (m)Longitudinal distance (m)Diameter (mm)Mortar bolt4.51.01.0φ22Resin anchor4.51.01.0φ22Table 4
Encrypted bolt support parameters.
Anchor typesLength (m)Ring distance (m)Longitudinal distance (m)Diameter (mm)Mortar bolt4.50.70.7φ22Resin anchor4.50.70.7φ22Mortar bolt4.50.40.4φ22Resin anchor4.50.40.4φ22Table 5
Parameters of lengthened bolt support.
Anchor typesLength (m)Ring distance (m)Longitudinal distance (m)Diameter (mm)Mortar bolt7.51.01.0φ22Resin anchor7.51.01.0φ22Mortar bolt6.01.01.0φ22Resin anchor6.01.01.0φ22


## 3.2.3. Model Establishment

Using FLAC3D finite element software, a two-dimensional numerical model of the Duimenzhai Tunnel is established. After considering the excavation of an underground tunnel, only the rock mass within the excavation range of 5 times the size of the tunnel has a disturbing effect, and the tunnel height of this project is 11.58 m, and the width is 10.60 m. Therefore, the height × width of the proposed model is 60 m × 60 m, and the model size and grid division are shown in Figures5 and 6.Figure 5
Model size diagram.Figure 6
Mesh division.


## 3.2.4. Analysis of Surrounding Rock Stress and Displacement

Figure7 shows that when the mortar bolt is used to support the tunnel, Smax·M = 0.487 cm and σmax·M = 681.92 kN/m2; when the resin bolt is used to support the tunnel, Smax·M = 0.398 cm and σmax·M = 228.55 kN/m2.Figure 7
Original parameter mortar bolt and resin bolt support: (a)Smax of dangerous point; (b) σmax of dangerous point.
(a)(b)The results show that compared with the tunnel supported by mortar bolts,Smax·M is reduced by 22.36% and σmax·M is reduced by 66.48% for resin bolts. The supporting effect of resin bolts is significant.Figure8 shows that when the mortar bolts are used to support the tunnel, Smax·M = 0.320 m and σmax·M = 220.55 kN/m2; when the resin bolts are used to support the tunnel, Smax·M = 0.177 m and σmax·M = 183.65 kN/m2.Figure 8
The distance between mortar bolt and resin bolt support is reduced to 0.7 m: (a)Smax of dangerous point; (b) σmax of dangerous point.
(a)(b)The results show that compared with mortar bolts support,Smax·M is reduced by 32.46% and σmax·M is reduced by 47.08%, and its supporting effect is significant.Figure9 shows that when the mortar bolts are used to support the tunnel, Smax·M. = 0.114 m and σmax·M = 243.38 kN/m2; when the resin bolts are used to support the tunnel, Smax·M = 0.077 m and σmax·M = 128.80 kN/m2.Figure 9
The distance between mortar bolt and resin bolt support is reduced to 0.4 m: (a)Smax of dangerous point; (b) σmax of dangerous point.
(a)(b)The results show that compared with mortar bolt support, resin bolts have a reduction ofSmax·M by 44.68% and a reduction of σmax·M by 16.73%. The supporting effect is significant.Figure10 shows that when the mortar bolts are used to support the tunnel, Smax·M = 0.078 m and σmax·M = 165.38 kN/m2; when the resin bolt is used to support the tunnel, Smax·M = 0.036 m and σmax·M = 87.99 kN/m2.The results show that compared with mortar bolts support, Smax·M is reduced by 53.85% and σmax·M is reduced by 46.80%, and its supporting effect is significant.Figure 10
The length of mortar bolt and resin bolt support is 6.0 m: (a)Smax of dangerous point; (b) σmax of dangerous point.
(a)(b)Figure11 shows that when the mortar bolts are used to support the tunnel, Smax·M = 0.056 m and σmax·M = 148.55 kN/m2; when the resin bolts are used to support the tunnel, Smax·M = 0.032 m and σmax·M = 95.65 kN/m2.Figure 11
The length of mortar bolt support and bolt support is 7.5 m: (a)Smax of dangerous point; (b) σmax of dangerous point.
(a)(b)The results show that compared with the tunnel supported by mortar bolts, theSmax·M is reduced by 42.85% and the σmax·M is reduced by 35.61%, and the supporting effect is significantly improved.From the comparative analysis of Figures5–9, when mortar bolts are used for support, Smax·M and σmax·M are approximately 1.6 times and 3 times than that of resin bolts support; Figures 6 and 7 are compared with Figure 5, the surrounding rock deformation decreases with the reduction of the bolt spacing, and when it is reduced to 0.4 m～0.7 m, the resin bolt support has a significant effect on controlling the surrounding rock deformation; Figures 8 and 9 are compared with Figure 5; when the length of the bolt is 4.5 m～6 m, the effect of using resin bolt support to control surrounding rock deformation is significant, but with the increase in the length of the bolt, the mortar bolts or the resin anchor effect of rod support in controlling the deformation of surrounding rock is small.


## 4. Conclusion

The gray theory is used to derive new tunnel deformation and monitoring time series, combined with the differential method, matrix transformation method, least square method, and other methods, to summarize the large deformation prediction model of the soft rock tunnel and finally support design inSmax·R, numerical analysis of its supporting effect is carried out, and the relevant conclusions are as follows:(1)
After predicting the large deformation of the supporting project, it is found that the gray theory prediction model is more accurate, the best prediction time is one week, and the maximum error is not more than 3%.(2)
According toSmax·R, the mortar bolts and resin bolts support are designed, and the Smax·M and σmax·M generated by the surrounding rock under different parameters of the bolts support are analyzed by numerical software. Compared with mortar bolts, resin bolts have a more significant effect on controlling surrounding rock deformation, and Smax·M and σmax·M can be reduced by about 50%.(3)
The study finds that when the length of the bolts is 4.5 m～6 m and the local density range is 0.4 m～0.7 m, resin bolts support should be selected; for the rest, the effect of mortar bolts support and resin bolts support of difference is smaller.(4)
The shortcoming of the gray model is that it can only make short-term forecasts. If the forecasting time increases, the error will be within the allowable range of the project, but it will increase over time.



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*Source: 6630546-2020-12-22.xml*