Determination of Supporting Time of Tunnels in the Xigeda Stratum Based on the Convergence-Confinement Method

Abstract

The mechanical properties of the surrounding rock of the Xigeda stratum are easily affected by water content. In order to obtain the support characteristics of Xigeda strata, the finite difference method was used to obtain the longitudinal deformation of the surrounding rock at a certain distance from the tunnel excavation face under different water contents. Then, the longitudinal deformation profiles of a Xigeda stratum tunnel were obtained under different water content conditions. The accuracy and applicability of the results were verified through error analysis and comparison with existing research results. Based on the convergence-confinement principle, it is proposed that the best time to apply support is when the displacement increment of the surrounding rock has a sharp increase point. The support construction time under different water content conditions was obtained with the distance from the tunnel excavation face as the control index. The results show that with the increase in water content, the longitudinal deformation profile’s growth trend is steeper near the excavation surface and it is gentler when the distance from the excavation face becomes large. At a water content of 20%, the support should be applied 2.67 m behind the excavation face; at a water content of 25%, the support should be applied 1.46 m behind the excavation face. The result has a certain guiding significance for the safety of tunnel construction in the Xigeda stratum.

1. Introduction

The Xigeda stratum is a kind of semi-diagenetic rock distributed in southwest China. Its engineering properties are poor, and it is mainly composed of graygreen clay rock, gray-black clay rock, gray-yellow clay rock, silty clay rock, and siltstone. For this kind of clay rock, the variation of water content can cause it to display obvious deformation behavior. In addition, the presence of clay rock, even a very thin layer, can considerably change the conditions of tension and implicit deformation around the underground work, leading to a significant extension of the relaxation both in the direction of the vault as well as the arch bottom. In early engineering construction, the Xigeda stratum has been widely concerning because of its frequent occurrence of landslides. Some scholars have contributed much research on the genetic mechanism, formation age, and engineering geological properties of the Xigeda stratum [1]. In recent years, with the extensive implementation of infrastructure construction in western China, it is common for highway and railway tunnels to cross the Xigeda stratum.

Through field direct shear tests, ZHOU et al. [2] obtained the shear force–shear deformation curves of Xigeda semi-diagenesis under different water contents and normal stress conditions and solved the shear strength parameters. DU et al. [3] determined the mineral composition and microstructure of the specimens by X-Ray Diffraction (XRD) and Scanning Electron Microscope (SEM), discussed the influences of water and confining pressure on the strength and deformation of the semi-diagenetic rock of the Xigeda formation using a triaxial compression test, and revealed the strength characteristics of the semi-diagenetic rocks of the Xigeda formation are different from that of the soil and the soft rock. FU et al. [4] investigated the influences of both the water content and the confining pressure on the strength indices of the Xigeda formation by performing triaxial tests and established a damage constitutive model for the deformation of the Xigeda formation. ZHANG et al. [5] sampled the Xigeda stratum, conducted indoor direct shear tests, and analyzed the influence degree and mechanism of water content on the shear strength of clay rock. LU [6] studied the mechanical engineering characteristics of Xigeda strata under different soil types, stress, and water content conditions and established the evaluation criteria for the stability of the surrounding rock of Xigeda strata. ZHOU et al. [7] explored the pressure arch form and dynamic development process of the pressure arch of the tunnel in Xigeda strata through model tests and PFC simulation. Through laboratory tests and numerical simulation methods, WANG et al. [8] studied the instability characteristics of the surrounding rock of the tunnel in the Xigeda stratum under different water contents and proposed corresponding deformation control methods. Based on the constraint loss theory of the tunnel face space effect, ZHOU et al. [9] decoupled the whole process of the interaction between the surrounding rock and support and discussed the influence of multiple dependent variables. ZHOU et al. [10] analyzed the apparent failure characteristics and catastrophe mechanism of the surrounding rock of Xigeda formation tunnels with different interbed types, using field investigation, indoor test, numerical simulation, field monitoring, and theoretical research. Through laboratory tests and numerical simulation, Xu [11] studied the deformation and support stress characteristics of large section tunnels in the Xigeda stratum, gave the deformation prediction formula, and compared the construction methods.

The deformation of the surrounding rock of the hard rock tunnel is small and most of the deformation occurs instantaneously after blasting excavation. It is of little significance to discuss the supporting time of the tunnel in the hard rock, but the time effect of the surrounding rock deformation in the soft rock tunnel is obvious. The determination of supporting time has a practical and positive significance for soft rock tunnel engineering. Based on many experiments, the researchers represented by Sun put forward the shear strain control theory [12]. This theory holds that the maximum shear strain calculated by a certain theoretical formula is equal to the allowable shear strain of the stratum, which is the best support time, and gives the experimental formula to determine the best support time. ZHANG et al. [13] introduced the global safety factor as the critical indicator to evaluate a tunnel’s stability, established the comprehensive graphic relationship between the global safety factor and the distance to the tunnel face, and proposed a methodology to determine the appropriate timing of initial support installation. LIU et al. [14] proposed the stress release law of the surrounding rock under support based on the displacement back analysis method and determined the optimal supporting time of the initial supporting structure by comparing the stress release ratio with surrounding rock displacement. LOHAR et al. [15] studied the time-dependent deformation of a road tunnel in squeezing ground conditions and performed a series of 2D plane strain finite element analyses to reproduce the monitored time-dependent convergence. The results highlight the necessity of considering time-dependent phenomena in the selection of support systems. ZHAO et al. [16] provided an analytical approach to estimating the influence of the compressible layer on the tunnel performance including the influences of the lining installation time. HU et al. [17] proposed an analytical model for the tunnel supported with a tangentially yielding liner in viscoelastic ground and analyzed the influence of the installation time of liner. QIN et al. [18] proposed an analytical model to provide a good prediction of the time-dependent tunnel convergences in the Saint Martin La Porte access adit and studied the influence of the installation time of yielding lining. GAO et al. [19] provided a semi-analytical approach to accurately address the elastic stress and displacement around shallow lined tunnels induced by tunnel excavation and lining installation. ZAHERI et al. [20] presented a theoretical solution to predict long-term tunnel convergence and long-term induced lining pressure and further studied the problem by numerical approach using FDM. The results show that the support installation time and the radius of the altered zone have remarkable effects on the output results. IASIELLO et al. [21] conducted a non-linear finite element analysis to reproduce the convergences measured focusing on time-dependent rock behavior. ZHANG et al. [22] studied elastic-plastic solutions for frost heaving force of cold region tunnels and proposed that a proper supporting time is beneficial to the safety of construction and operation for tunnels in cold region. ZHAO et al. [23] analytically built a mechanical model of a circular tunnel with a rock bolt-lining combined system, derived mathematical formulas for the stresses and displacements around the tunnel, and investigated the influence of the installation time of the rock bolts and the lining.

In summary, the current research on the tunnel in the Xigeda stratum mainly focuses on its mechanical properties and deformation control. Few scholars have studied the influencing factors of tunnel deformation in the Xigeda stratum and the timing of support construction. In this paper, a longitudinal deformation formula considering the water content factor is proposed based on numerical simulation and numerical analytical methods. Then, the recommendations on the timing of tunnel support construction in Xigeda strata is given combining the convergence-constraint method. The results provides a reference for similar tunnel engineering construction.

2. Materials and Methods

2.1. Principle of Convergence-Confinement Method

The convergence-confinement method is a theoretical method developed with the maturity of the new Austrian tunneling method. It can explain the interaction process of surrounding rock and support during tunnel excavation and determine the appropriate time for the support installation. Its theoretical basis includes a Ground Response Curve (GRC), Support Reaction Curve (SRC), and Longitudinal Deformation Profile (LDP), as shown in Figure 1. In Figure 1, P_i is the supporting force of the tunnel wall, P₀ is the force generated by the tunnel wall at the moment of tunnel excavation, u_r is the displacement generated at the tunnel wall, and u_max is the maximum displacement generated at the tunnel wall. The Ground Response Curve (GRC) describes the relationship between the displacement of the tunnel wall and the supporting force after excavation. With the continuous increase of the displacement of the tunnel wall, the surrounding rock stress releases accordingly. When the tunnel wall reaches the maximum displacement, the surrounding rock stress wholly releases in theory, and the supporting force of the tunnel wall is 0. The Support Reaction Curve (SRC) reflects that the support stress increases with the displacement of the tunnel wall after the construction of the support structure. When the SRC intersects with the GRC, it indicates that the surrounding rock and the support have reached the force equilibrium state.

The Longitudinal Deformation Profile (LDP) represents the radial displacement along the tunnel’s axis for sections located ahead of and behind the face. It reflects the spatial effect of tunnel excavating. Figure 1 indicates that the surrounding rock has already undergone deformation some distance ahead of the advancing face. When the face moves well away from the monitoring face, the radial displacement reaches the maximum, which means the spatial effect has disappeared. Based on this, a large number of studies have been conducted to investigate the support parameter design [24,25,26,27,28].

Based on the current research results, the GRC needs to be obtained by numerical simulation with the stress release method. According to reference [29], Hoek and Brown studied the typical supporting structures such as arch, shotcrete, and radial bolt and obtained the specific SRC formula. The LDP can be obtained by a three-dimensional excavation simulation. Because the Xigeda stratum is a particular stratum, there are few studies on its LDP, and there is no curve for reference. Therefore, the numerical method was used to study the LDP of the Xigeda stratum in the next section.

2.2. Numerical Simulation

2.2.1. Project Overview

This paper relies on a tunnel on the Emi-Miyi section of the newly built Chengdu-Kunming Railway, located in Dechang County, Liangshan Prefecture, Sichuan Province. It is one of the high-risk and complex control projects on the Emi line. The total length of the tunnel is 14,280 m, including 5375 m of grade II surrounding rock, 5440 m of grade III surrounding rock, 2070 m of grade IV surrounding rock, 1395 m of grade V surrounding rock, and the maximum buried depth is 1032 m. The stratum lithology in the tunnel area is relatively single, overlying the quaternary holocene slope residual layer of silty clay, Quaternary Middle and Upper Pleistocene (Q₂₊₃) silty clay, and pebble soil. The underlying bedrock is mainly tertiary upper Xigeda formation mudstone intercalated sandstone and Pre-Sinian granite.

The Xigeda Formation mudstone intercalated sandstone is distributed in the inlet and outlet sections of the tunnel. The distribution length of the inlet section is 314.3 m, and of the outlet section is 208.5 m. The physical and mechanical properties of Xigeda formation mudstone intercalated sandstone are poor, especially in moist conditions. Mudding occurs after encountering water, so the rock strength is further weakened and is prone to large deformation during tunnel construction. According to the construction site test, the water content of the Xigeda formation in its natural state is usually 17~24.6%, the saturation is 85~100%, the compressive strength is 1.07~1.73 MPa, the compressive strength in the drying state is 13.2~13.4 MPa, and the compressive strength in the saturated state is 0.79~0.89 MPa.

The DK494 + 725~DK494 + 775 section of the tunnel was selected as the research scope. The primary rock stratum passing through the tunnel is Xigeda formation mudstone intercalated sandstone, and the three-step temporary inverted arch method is adopted. Figure 2 shows the exposure of the tunnel face. The average buried depth of this section is about 45 m, the net span of the tunnel is 12.47 m, and the net height is 11.30 m.

2.2.2. Numerical Model, Boundary Conditions, and Material Properties

Based on the basic situation of the selected research scope of the tunnel, the numerical calculation model was established using FLAC3D 5.0 finite difference software. According to the Saint-Venant principle, to reduce the boundary effect of the model, the distance between the model’s boundary and the excavation boundary should be 3 to 5 times the tunnel span. Therefore, in this study, the distance between the left and right boundaries of the model and the tunnel side boundary is 4 times the tunnel span. The distance between the lower boundary and the bottom surface of the tunnel is 4 times the tunnel span. The upper boundary is taken to the surface, and the front and rear boundaries are 3.5 times the tunnel span. The left and right sides of the model’s boundary are subjected to horizontal constraints, the bottom is subjected to vertical constraints, and the top is the free surface. Figure 3 shows the numerical calculation model. The LDP curve is the deformation curve of the tunnel in the open hole state, so the numerical simulation does not set the support and only follows the excavation sequence of the construction method, the footage of tunnel excavation is 1m. The rock mass adopts the Mohr–Coulomb yield criterion, the vertical stress is simulated by the self-weight stress field, and the lateral stress coefficient is set to 0.5.

The water content greatly affects the mechanical properties of the surrounding rock of the Xigeda stratum. Based on the engineering site survey data and the current research results [30], the physical and mechanical parameters of the surrounding rock of the Xigeda stratum under different water content conditions are determined, as shown in

Table 1. Physical and mechanical parameters of surrounding rock under different water contents.

Water Content/%	Density/g·cm−3	Elastic Modulus/MPa	Poisson Ratio	Cohesion/kPa	Friction Angle/°
0	1.95	193.89	0.4	343.4	44.5
5	1.95	189.54	0.4	322.8	40.7
10	1.95	184.80	0.4	302.1	36.8
15	1.95	180.06	0.4	281.4	33.0
20	1.95	175.35	0.4	260.7	29.1
25	1.95	121.65	0.4	196.3	24.8

.

Considering the complexity of the engineering site and the limitations of numerical simulation, the numerical simulation is simplified as follows:

(1)

The surrounding rock in the model is a continuous and homogeneous ideal body, and the surrounding rock adopts the Mohr–Coulomb model constitutive relation.

(2)

The initial in situ rock and soil mass stress only considers the gravity stress and does not consider the effect of tectonic stress and groundwater seepage.

(3)

Assuming the surface of the study area is horizontal.

3. Results

Geological conditions have a great influence on the mechanical behavior of the tunnel [31]. Through calculation, the longitudinal displacement results after tunnel excavation under different water content conditions are obtained. The results show the deformation trend of tunnel surrounding rock under different water content conditions is consistent. Figure 4 shows the longitudinal deformation contour of surrounding rock with different conditions of water content. The figures indicate that the longitudinal deformation of surrounding rock mainly manifests as vault settlement and arch bottom uplift.

Taking vault settlement as the main research object, the longitudinal deformation ur of surrounding rock at a certain distance from the tunnel excavation face under different water content conditions is obtained, as shown in Figure 5. The figure shows that, with the increase in water content, the longitudinal deformation of the surrounding rock becomes larger and larger. Especially under 25% water content, the deformation is obviously larger than other water content. Compared with 20% water content, the maximum deformation in the condition of 25% water content increases by 70.2%. This is consistent with the existing research results [30].

By normalizing the obtained data, the LDP curves under different water content can be obtained, as shown in Figure 6. The figures show that the curves tend to be gentle as the distance from the excavation surface becomes farther and farther. And the curves rise sharply on the excavation surface (i.e., x = 0), indicating that the spatial effect caused by tunnel excavation has influence range, and the influence on the excavation surface is very intense. In the vicinity of the excavation face (i.e., x = 0), with the increase of water content, the growth trend of the LDP curve is steeper, indicating that the release process of surrounding rock stress and displacement is faster. However, with the increase of x, when x > 0.3R, the greater the water content of the surrounding rock, the gentler the growth trend of the corresponding curve. The above rules are consistent with the information given in Figure 5. Near the excavation surface, the weakening affection of water content on the surrounding rock’s properties is obvious, and the surrounding rock’s deformation is severe. For the LDP curve, u_r under different water content occupies the leading influence position, reflected in the larger the water content of the surrounding rock, the steeper the LDP curve; with the increase of x, when x = 5 m (i.e., x = 0.3R), the influence of spatial effect caused by excavation reduces, the trend of surrounding rock deformation is gentle. For the LDP curve, u_max under different water content occupies the leading influence position, reflected in the larger the water content of the surrounding rock, the gentler the LDP curve. In addition, compared with the unexcavated part (i.e., x < 0), the excavated part (i.e., x > 0) is more affected.

In summary, for the Xigeda formation, the water content is an essential factor affecting the LDP, which will have a non-negligible impact on the convergence-confinement method.

4. Discussion

4.1. Current Tunnel Longitudinal Deformation Calculation Theory

For the calculation of longitudinal deformation caused by tunnel excavation, many scholars have given a series of research results.

Lee normalized the tunnel monitoring data and obtained the empirical formula for calculating the longitudinal deformation of the tunnel [32]:

$$\frac{u_r}{u_{\max }}=\frac{1}{2}[1-\tanh (\frac{1}{3}-\frac{x}{2R})]$$

(1)

where u_r is the longitudinal deformation at the distance x from the excavation face; u_max is the longitudinal deformation far enough from the excavation face; x is the axial distance from the excavation face; R is the excavation radius of the tunnel.

Based on the elastic deformation theory of surrounding rock after excavation, Panet obtained the deformation law of tunnel without support as follows [33]:

$$\frac{u_r}{u_{\max }}=0.25+0.75[1-{(\frac{0.75}{0.75+x/R})}^2] ,x\ge 0$$

(2)

Hoek performed the best fitting based on the measured value of tunnel wall convergence, and the empirical formula for calculating the longitudinal deformation of the tunnel is obtained as follows [34]:

$$\frac{u_r}{u_{\max }}={[1+\exp (\frac{-x/R}{1.10})]}^{-1.7}$$

(3)

According to the two-dimensional finite element theory, Vlachopoulos and Diederichs obtained the calculation formula for longitudinal deformation of ideal elastic-plastic surrounding rock as follows [35]:

$$\frac{u_r}{u_{\max }}=\left\{\begin{array}{ll}1-(1-u_0^{*})\exp (-\frac{3x/R}{2R^{*}})& ,x\ge 0\\ u_0^{*}\exp (x/R)& ,x<0\end{array}\right.$$

(4)

$$u_0^{*}=\frac{u_0}{u_{\max }}=\frac{1}{3}\exp (-0.15R^{*})$$

(5)

where R* = R_p/R, Rp is the maximum plastic zone radius caused by tunnel excavation, which the following formula can calculate the following:

$$\left.\begin{array}{l}{R}_p=R\exp [\frac{{({\sigma }_{r2}{m}_b/{\sigma }_{ci}+s)}^{1-\alpha }-{(p_i{m}_b/{\sigma }_{ci}+s)}^{1-\alpha }}{m_b(1-\alpha )}]\\ {\sigma }_{ci}{({\sigma }_{r2}{m}_b/{\sigma }_{ci}+s)}^{\alpha }+2{\sigma }_{r2}-2{\sigma }_0=0\end{array}\right\}$$

(6)

where σ_r2 is the radial stress at the junction of the elastoplastic zone; p_i is the supporting force; σ₀ is the initial hydrostatic pressure of surrounding rock; m_b, s, α are Hoek–Brown criterion parameters.

Zhao et al. derived a theoretical formula based on Panet’s result about the relationship between the displacement of the tunnel surrounding rock and the distance from the excavation face to the monitoring section as follows [36]:

$$\frac{u_r}{u_{\max }}=\left\{\begin{array}{ll}(1-{\lambda }_0)(1-e^{-\frac{x}{X}})+{\lambda }_0& ,x\ge 0\\ {\lambda }_0{e}^{\frac{x}{X_1}}& ,x<0\end{array}\right.$$

(7)

$$X_1=\frac{{\lambda }_0}{1-{\lambda }_0}X$$

(8)

where λ₀ = u₀/u_max, u₀ is the longitudinal deformation of the tunnel at the excavation face; X is a constant.

4.2. Longitudinal Deformation Calculation of Xigeda Stratum

To quantify the influence of water content on the longitudinal deformation law of the tunnel in Xigeda stratum, the Levenberg–Marquardt method and universal global optimization method were used to perform nonlinear fast three-dimensional fitting on the numerical simulation results. Considering the ‘S-type’ characteristics of the LDP, the coordinate of the excavation face (i.e., x = 0) is used as the demarcation points to fit the formulas ahead of and behind the excavation face to improve the fitting accuracy. The fitting formula is as follows:

$$\frac{u_r}{u_{\max }}=\left\{\begin{array}{cc}\frac{p_1+p_2(x/R)+p_3{(x/R)}^2+p_4{(x/R)}^3+p_5\omega }{1+p_6(x/R)+p_7\omega +p_8{\omega }^2} & ,x\ge 0\\ \frac{p_1+p_2(x/R)+p_3\omega }{1+p_4(x/R)+p_5{(x/R)}^2+p_6\omega }& ,x<0\end{array}\right.$$

(9)

where ω is the water content and the unit is %.

Figure 7 shows the three-dimensional response surface of the fitting formula. The fitting parameters and error analysis results are shown in

Table 2. Formula fitting coefficient.

Relative Position to the Face	Formula Fitting Coefficient
$x\ge 0$	$p_1$	$p_2$	$p_3$	$p_4$	$p_5$	$p_6$	$p_7$	$p_8$
	0.08609	1.62747	−0.18503	0.02761	0.00275	1.07785	−0.00088	0.00047
$x<0$	$p_1$	$p_2$	$p_3$	$p_4$	$p_5$	$p_6$
	0.12549	0.03078	−0.00022	−2.21181	−0.27063	−0.01026

and

Table 3. Fitting formula error analysis results

Relative Position to the Face	Error Analysis Parameters
$x\ge 0$	RMSE	SSE	R	DC
	0.020753	0.067620	0.995729	0.991476
$x<0$	RMSE	SSE	R	DC
	0.004374	0.002869	0.990577	0.981242

, respectively. From the error analysis results, the maximum value of RMSE is 0.020753, the maximum value of SSE is 0.067620, the minimum value of R is 0.990577, and the minimum value of DC is 0.981242, each analysis index shows that the fitting results are effective.

The three-dimensional response surface intuitively reflects the changing trend of u_r/u_max under the coupling influence of water content ω and distance x from the excavation face. At the same x level, with the increase of ω, when x = 0, u_r/u_max tends to increase; when x = 0.3R, the above trend decreases, consistent with the previous analysis. At the same ω level, the three-dimensional response surface shows the same law as the LDP curves.

4.3. Comparison of Longitudinal Deformation Profiles

The fitting formula is compared with some current longitudinal deformation calculation formulas to verify the accuracy. According to the field test of the project, the water content in the natural state of the Xigeda formation is usually 17~24.6%, and the saturation is 85~100%. Two typical working conditions of 20% and 25% water content are selected, and Figure 8 shows the LDP curve comparison diagram.

From Figure 9, after normalizing the numerical simulation results, the fitting accuracy of Panet formula, Lee formula, and Hoek formula is poor, indicating that the current relevant research results do not apply to particular strata such as Xigeda strata. The fitting formula obtained in this paper agrees with the numerical simulation results and is more applicable to the Xigeda strata.

4.4. Prediction and Application of Supporting Time

An essential application of the convergence-confinement method is to determine the timing of tunnel support. To determine the supporting time of tunnel in Xigeda strata, a combination of fitting formula given above and convergence-confinement method was used. And a convergence-confinement calculation model suitable for Xigeda strata was established. Firstly, based on the theory of virtual support force [37], the longitudinal deformation of Xigeda stratum tunnel under different excavation load release rates is obtained using FLAC3D numerical simulation software. Then, the displacement rate of rock around the tunnel was used as the criterion for judging the timing of support construction. This method holds that, in the initial stage of excavation load release, the deformation of surrounding rock increases with the release of excavation load, and the two are approximately linear. With the rise in excavation release rate, the deformation of surrounding rock will increase sharply at a particular stage, which can be regarded as the best construction time of primary support [29].

The timing of support construction is calculated with 20% and 25% water content as typical working conditions. Figure 9 and Figure 10 show the longitudinal deformation law of the tunnel under the two working conditions. The figures indicate that under 20% water content, the deformation increment increases when the load releasing rate reaches 60%, and the displacement release rate corresponding to the supporting time is 0.496. Then, ω = 20 and u_r/u_{max =} 0.496 are substituted into Formula (9) to obtain x/R = 0.431, x = 2.67 m, that is, the support should be applied at 2.67 m behind the excavation. Similarly, under 25% water content, the support should be applied at 1.46 m behind the excavation face.

Based on the above research results, taking the DK494 + 725~DK494 + 775 section as the test section, the lining is constructed at different supporting times, and the tunnel’s deformation and the stress of the primary support of the vault are monitored. The monitoring instruments are shown in

Table 4. Tunnel deformation and stress monitoring instrument.

No.	Monitoring Program	Monitoring Equipment
1	Crown subsidence	Total station
2	Horizontal convergence	Total station
3	Inverted arch uplift	Precise level, indium steel ruler
4	Initial support stress of vault	Vibrating wire rebar strain meter

, and the layout of displacement measuring points is shown in Figure 11. According to the field test and monitoring results, the water content of Xigeda stratum in the test section is about 25%. As the above calculation results mentioned, the best support time is 1.5m behind the working face. The monitoring results are shown in

Table 5. Monitoring data.

Supporting Time	Crown Subsidence/mm	Horizontal Convergence/mm	Inverted Arch Uplift/mm	Initial Support Stress of Vault/kN
Immediately after excavation	22.9	22.6	48.2	171.6
1.5 m behind the excavation face	16.1	15.6	30.8	120.1

. The results indicate that the support based on this paper’s research results can reduce the tunnel’s deformation and the stress of the primary support structure, which is conducive to the stability and safety of the structure.

5. Conclusions

(1)

The properties of surrounding rock in the Xigeda stratum are greatly affected by water content. Near the excavation face, with the increase of water content, the growth trend of the LDP curve is steeper, indicating that the release process of surrounding rock stress and displacement is faster. When the distance from the excavation face becomes large, the greater the water content of the surrounding rock, the gentler the growth trend of the corresponding LDP curve.

(2)

The formula for calculating the longitudinal deformation of Xigeda stratum tunnel is obtained by fitting the numerical simulation results. The formula considers the water content and distance from the excavation face the main factors. Compared with the current calculation formulas, the fitting formula obtained in this paper is more suitable for the engineering environment of Xigeda stratum.

(3)

A convergence-confinement calculation model suitable for Xigeda stratum is proposed by combining the fitting formula with the convergence-confinement method. Based on the calculation background of the project, taking the distance from the tunnel face as the control index, the supporting time under typical working conditions is given. At a water content of 20%, the support should be applied at 2.67 m behind the excavation face. At a water content of 25%, the support should be applied at 1.46 m behind the excavation face. The construction practice shows that the supporting time proposed in this paper can reduce the stress of the primary support structure to a certain extent, which is conducive to the stability and safety of the structure.