Study on the Characteristics of Surrounding Rock and Design of Backfill Material Parameters for Tunnels Passing through Giant Caverns and Underground Rivers

Abstract

The influence on tunnel construction of karst and underground rivers is always an important problem in tunnel engineering. In order to demonstrate the rationality of backfill parameters and the effectiveness of supports under the influence of groundwater when a tunnel passes through a large karst cave, the finite element software FLAC3D was used for numerical analysis. Converting the mean values and standard deviations of mechanical response results of the surrounding rock and the supports on multiple sections into the ECULID distance from the origin point on a two-dimensional plane as evaluation indexes, the influence of the reinforcement parameters on the mechanical response of the surrounding rock and the supports was analyzed by orthogonal experiments. Based on fuzzy decision theory, by regarding the ECULID distance between the simulated result of each group and the global optimal value of the multiple evaluation index as the comprehensive evaluation index, a backfill parameter design method was proposed. By comparing the results which used optimal and worst parameters in the FLAC3D, 10 times and 2.5 times differences in longitudinal and horizontal displacement were observed, respectively. Then, the optimal backfill parameters were applied to the actual project for verification. The field monitoring results showed that the optimal backfill parameters can effectively reduce the displacement around the tunnel. After constructing a diversion for the underground river, the water flow in the karst cave did not rise during a rainstorm. This study provides a reference for the design and construction of other projects in the future.

1. Introduction

Limestone and karst are widely distributed in Central and Western China. The distribution area of soluble rocks in China is more than 3.4 × 10⁴ km², accounting for about one third of the land area, mainly in Yunnan and Guizhou in the southwest [1]. Karst landforms are common geological obstacles in the construction of mountain tunnels and urban underground tunnels. In the complex geological environment, a tunnel needs to pass through strata containing karst caves, and various geological disasters, such as collapses, rock bursts and water and mud inrushes, make for a large number of accidents in tunnel construction [2,3], as shown in

Table 1. Social and economic losses caused by karst adverse geological disasters in recent years.

Unfavorable Geological Phenomena of Karst	Social and Economic Losses
Foundation collapse of the Lizhan railway	Economic loss reached 1 million yuan
Large water and mud inrush in Yesanguan Tunnel of Yiwan Railway	10 deaths and the economic loss was more than 13 million yuan
Water and mud inrush and surface collapse in the Hejiazhai Tunnel	Construction period delayed by half a year and the economic loss was 10 million yuan
Water inrush in the Maluqing Tunnel	11 deaths
Water and mud inrush in the Dayaoshan Tunnel	Economic loss exceeeds 10 million yuan

.

A huge risk of karst disaster is water gushing. There have been many studies on water-filled limestone caves that are in front of tunnels [4,5,6,7], including field tests, model tests and numerical simulations.

Li et al. [8], based on the actual conditions of the engineering section from Wangfuzhuang Station to Dayangzhuang Station of the Jinan Metro Line R1, derived a calculation formula of the reserved safe thickness of the tunnel face given the presence of a water-filled limestone cave using COMSOL. Li et al. [9] established a 3D water-filled karst cave and tunnel model, simulated the tunnel’s excavation under different height–span ratios and revealed the variation law of stress and displacement during tunnel excavation. Pan et al. [10], through a model experiment to study the failure process of tunnel faces at the front of water-filled limestone caves, divided the failure processes in the model into the production of group cracks, the formation of water inrush channels and the complete collapse of water-resistant plates. Meng et al. [11] independently developed a model test system for water and mud inrush in a tunnel to study the structural instability characteristics and seepage law of karst pipeline fillers with different permeability coefficients. Gao et al. [12] took Kaiyuansi Tunnel as an example, carried out physical model and numerical simulations and analyzed the water leakage, vertical displacement and water pressure results for the monitored section. Li et al. [13,14,15], based on the highly dangerous karst tunnel in Qiyue Mountain and numerically simulated five tunnel floor water inrush cases using FLUENT software, analyzed the variation characteristics of velocity and pressure and discussed and summarized the water flow characteristics after water inrush at the tunnel floor. However, research on the impacts of underground rivers on tunnels are not enough [16,17].

The existing research mostly focuses on small-size karst caves. Zhao et al. [2] carried out similar simulation experiments and a simulation analysis to study the influence of karst cave size on the stability of surrounding rock. Cheng et al. [18] used the principle of limit analysis to analyze tunnel damage due to collapses caused by the existence of karst caves and obtained the damage range of intermediate surrounding rock. Huang et al. [19], in order to predict the collapse range of a rock mass when excavating a tunnel above a karst cave, used a variational method within the framework of an upper bound theorem to obtain an analytical expression for the collapse surface. Most current research is focused on the location relationship, distance and relative size of karst caves and tunnels.

For super-large tunnels, there is still little research. Chen et al. [20] analyzed the Naqiu Tunnel as an example. The karst cave is 170 m long, which is 10 times the radius of the tunnel. Due to the karst cave not being high, the method of drilling, grouting and bridging has been selected to pass through. Cao et al. [21] took Yangqiaoba Tunnel as an example; the maximum length, width and height of the karst cave are 267, 180 and 120 m respectively. A changing line was selected for the left tunnel and backfilling for the right tunnel. Ma et al. [22] took Longlingong Tunnel as an example; the bottom axial length of the karst cave is 171 m, the width is 65 m, and the distance to the ground surface is 110 m. The roof of the karst cave collapsed to the surface. Finally, the crossing mode of backfilling the cavity was determined and the treatment mode of dynamic compaction plus grouting was adopted to improve the foundation.

Generally, large karst caves are mainly dry. Common crossing methods include route diversion, subgrade backfilling and excavation and bridge construction. The specific method to be used should be determined according to the actual situation and cost. However, the number of projects crossing large karst caves with water are few, and there are few studies that have been made on this subject worldwide. Therefore, it is necessary to study the safety of passing through large karst caves with water.

This paper takes the Yujingshan Tunnel as an example to study the impact of rising groundwater on the project. Firstly, an actual investigation of the surrounding rock properties and groundwater conditions of the Yujingshan Tunnel was carried out; the main parameters of the backfill body include: elastic modulus, density, cohesion, internal friction angle, porosity and softening coefficient of water to surrounding rock. Orthogonal experiments were used to design a test group, and the six parameters of backfill layer settlement, tunnel vault settlement, convergence on both sides and the internal force and bending moment of the initial support were used as evaluation indicators. The finite element software FLAC3D was used for a simulation, and the values of the evaluation indicators in each experimental group were extracted to calculate the means and standard deviations. Then, the range standardization process was performed, and the means and standard deviations for the experimental group were normalized to the [0,1]. $d_{ECULID}^{ik}$ is the ECULID distance between $\left(x_{ik}^{\ast },{\sigma }_{ik}^{\ast }\right)$ and the origin of coordinates. The backfill parameter corresponding to the minimum value of $d_{ECULID}^{ik}$ is the optimal parameter. Comparisons with on-site monitoring were made to verify the correctness of the method described in this article. This study provides a reference for engineering design and construction in the future.

2. Tunnel Overview

2.1. Karst Cave Overview

As shown in Figure 1, the tunnel in the Chengdu–Guiyang Railway is located in the section between Xingwen county and Weixin county, within Yunnan Province. The design speed is 250 km per hour. There are double tracks in a single tunnel. The longitudinal slope of the line is a single upward slope of 30‰, with a total length of 6306.28 m and a maximum buried depth of 350 m.

The tunnel mainly passes through coal measure strata and soluble rock strata, of which 71 m of section passes through the coal-bearing stratum of the Permian Changxing Formation (P2C), which is a high gas section; 439 m of section crosses the coal-bearing stratum of the Longtan Formation (P2l), which is a gas outburst section, and 795 m of section crosses the limestone of the Qixia Maokou Formation (P1m + Q) of the Lower Permian system, and karst is strongly developed there.

When the guide gallery was excavated to d3k279 + 948, a huge karst cave was revealed, in the shape of a dome, about 100 m along the line direction and about 200 m perpendicular to the line. The height of the karst cave is 50~120 m. It is high on the right side of the line and low on the left side. The tunnel is located near the top of the karst cave. Most of the extent of the karst cave is stable. However, under the influence of cracks, joints, groundwater and blasting, local block falling from the surface of the cave wall has occurred. The thickness of the bottom accumulation layer is 30~90 m, and its composition is complex, including soft clay, gravelly soil and medium coarse sand. An underground river has developed at the foot of the slope on the left side of the line in the karst cave. The river is 5~15 m wide and flows from the right side of the line to the left. The flow of the underground river during the dry season was observed to be 4~15 m³/s, and the maximum flow during the rainy season is about 20.16 m³/s. According to the drilling and geophysical data, it is very likely to be unstable and damaged due to the influence of branch pipeline water at the bottom and in surrounding areas, the scouring and erosion of the underground river and unbalanced loading on the upper part of the later backfill body. See Figure 2 for details [23].

2.2. Underground River Overview

An underground river has developed at the foot of the slope on the left side of the line within the karst cave, its surface elevation about 961 m, which is about 114 m, below the tunnel rail, and a measurable section length of the underground river is about 739 m. The underground river roughly intersects with the line at 70°, developing in an S shape, and the runoff is discharged from the right side to the left side of the line. The overall runoff direction is N64°E, which is basically developed along the bedding plane of surrounding rock, with a flow of 13.55~20.16 m³/s. The upper reaches of the underground river enter the cave hall 30 m from the left side of d3k279 + 985. The entrance of the underground river is nearly rectangular, about 14 m wide and about 1.6 m high.

Downstream, the underground river flows out of the cave hall at 281 m on the left side of d3k279 + 895, which is a deep pool. From 15 October to 23 October 2016, it rained continuously in the tunnel site. On 26 October 2016 (the third day after the rainfall stopped), the water surface of the pool fell to 30 cm below the roof, with a width of about 8 m.

In order to explore the maximum water inflow of the underground river, the atmospheric precipitation infiltration method was used to predict the water inflow in the catchment area in the section the tunnel passes through. Application of the atmospheric precipitation infiltration method involved selecting areas with similar hydrogeological and meteorological characteristics in the area the tunnel passes through and using multi-year average precipitation data to estimate water inflow in the tunnel. The calculation formula is as follows:

$$Q_s=2.74\times \lambda \times h\times F$$

(1)

where $Q_s$ is the calculated water inflow (m³/d); $\lambda$ is the infiltration coefficient (L/s km²); h is the average rainfall (mm); and F is the distribution area of the aquifer (km²).

According to the investigation of the catchment area of the underground river, the total catchment area is about 85 km², so F = 85 km². The infiltration coefficient is taken to be for soluble rock: $\lambda$ = 0.71 L/s km². In order to calculate the most unfavorable situation, the historical daily maximum rainfall in Weixin County was taken, so that H = 132 mm (1 July 2008). With these parameters, Equation (1) was used to calculate the maximum water inflow of the underground river: $Q_s$ = 8 × 10⁶ m³/d = 92.6 m³/s.

After the underground river was revealed, hydrological observation points were set at the outlet and middle part of the underground river. According to the calculation formula for ditch flow in the tunnel design manual, the calculation formula for these aspects is as follows:

$$Q=\omega c{\left(Ri\right)}^{1/2}$$

(2)

where Q is the flow of underground (m³/s); V is average velocity (m/s), $V=c{\left(Ri\right)}^{1/2}$; $\omega$ is the cross-sectional area of overflow (m²); R is hydraulic radius (m); $R=\omega /X$; C is the coefficient, $C=\left(1/n\right)R^y$; X is the wet perimeter, which refers to the length of the contact surface between the fluid and the trench wall in the section (m); y is the coefficient, $y=2.5n^{1/2}-0.7R^{1/2}\left(n^{1/2}-0.1\right)-0.13$; and n is the roughness coefficient of the trench wall, which can be obtained from the relevant table.

According to the field measurement, the minimum cross-sectional area of the underground river entering the cave hall is about 29 m², rectangular in shape, 13 m wide and 2.23 m high. According to on-site observation, there are obvious and strong scouring traces on the wall of the intake, indicating that the intake must be filled with an underground river in rainy seasons. The maximum water inflow of the main pipeline intake of the underground river in the Karst hall, Q = 338 m³/s, can be obtained.

The underground water of the cave wall is not developed; there is dripping at the top of the cave. There is seasonal fissure water in some cracks, and many karst pipelines are developed at the bottom of the cave hall.

As shown in Figure 3, on the whole, the karst cave is mainly affected by the underground river. The underground river has been diverted many times in history, and there are many empty pipelines in the lower part of the karst cave. These pipelines also form a mainstream–tributary relationship with the current main underground rivers. These pipelines will have a great adverse impact on the stability of the upper cavity structure. In the rainy season, the groundwater level will rise rapidly, which will have a significant erosion effect on the karst cave. At the top of the giant karst cave, there is a partially permeable part, which is mainly affected by the upper overburden.

2.3. Solution

The section from d3k279 + 855 to d3k279 + 960 of the tunnel passes through the huge karst cave. Combined with the hydrogeological conditions and the development of the karst cave, many expert joint reviews were organized, and it was decided to adopt the overall treatment scheme of “underground river diversion + karst cave backfilling + roof reinforcement + bridge crossing” for passing the karst cave.

2.3.1. Karst Cave Backfilling

In order to provide the excavation construction platform for the tunnel arch, reduce the risk of falling blocks from the tunnel arch and eliminate the influence of the instability of the tunnel wall in the later stage, the karst cave was backfilled. Due to the maximum drop of the karst cave of 120 m, in order to ensure that the backfill body is dense, it is necessary to backfill in layers. As shown in Figure 4, the karst cave was backfilled in five levels. The karst cave was backfilled step by step through channel 4 (988 m elevation), channel 6 (1008 m elevation), channel 7 (1028 m elevation), channel 1 (1048 m elevation) and the upper steps of the tunnel (about 1082 m elevation).

Considering that the karst cave below the elevation of 1008 m is mainly located in the underground river section (close to the bottom of the karst cave), there are many through-cracks in the hall, making for water seepage. In order to ensure drainage fluently at the bottom of the karst cave and prevent the impact of excessive bottom water pressure on the superstructure, the part below the elevation of 1008 m was backfilled with block stones, the block diameter not less than 30 cm. In order to ensure fluent drainage of groundwater such as fissure water and karst pipeline water near the wall of the karst cave, block stone backfilling could also be adopted within 3 m near the wall of the karst cave, the block diameter also not less than 30 cm.

2.3.2. Bridge Crossing

In order to avoid backfilling body settlement during tunnel operation and ensure driving safety, a bridge structure is to be adopted for crossing the karst cave section. In order to prevent the shotcrete of the tunnel wall spalling and falling off, light steel scaffolding shall be set on the bridge for protection to ensure operational safety. The bridge structure crossing the karst cave shall include a 38.85 + 108 + 38.85 m short side span prestressed concrete continuous beam with a beam height of 5–8 m.

2.3.3. Roof Reinforcement

Considering the location relationship between the tunnel and the karst cave, the different stability of surrounding rock and the requirements of bridge construction, overhaul and maintenance, the tunnel crossing the karst cave section has an A-type straight side wall composite lining and a B- and C-type curved side wall composite lining. The B- and C-type sections are located in the scope of the karst cave hall, and anchor mesh shotcrete was used as a permanent protective measure. In order to ensure the operational safety and the stability of the karst cave roof, it was provided with anchor cables to strengthen the protection, as shown in Figure 5.

3. Numerical Simulation

In order to study the influence of groundwater in the karst area on tunnel construction when crossing the karst cave and selecting appropriate backfill materials, the 279 + 923 section with the lowest design elevation of tunnel was selected as the research object, and a model was established using the finite difference software FLAC3D for a simulation. Figure 6a is the grid element division diagram, and Figure 6b is the distribution diagram of surrounding rock in the karst cave. So that the tunnel width on both sides is five times that of the width of the karst cave, the calculation range of the model was set to be 50 m in the longitudinal direction, 1300 m in the transverse direction and 700 m in the vertical direction, including 270 m from the tunnel crown to the model top surface, 120 m from the tunnel bottom plate to the karst cave bottom and 400 m from the model bottom. The simulation range was relatively large, and a total of 1 million elements were generated. Only the upper surface is free; all other surfaces are constrained. Therefore, the surrounding and bottom boundaries were set to be impervious.

Groundwater rise was simulated by using the seepage module that exists in the FLAC3d software. When the groundwater flow rises, the seepage calculation mode is turned on, and a stable pore pressure field is obtained through single seepage calculation, and then the fluid modulus K_f is set to 0 to achieve the mechanical equilibrium calculation [24,25].

During the supplementary survey of karst caves and underground rivers, 11 holes were drilled in the karst cave hall, with a total length of 575.6 m. A total of nine groups of rock samples and two groups of underground river water samples were obtained on site for the experiment. In addition, TEM, geological radar, seismic imaging, the active source surface wave method and the natural source surface wave method were also used to carry out geophysical exploration on the basement of the karst hall and the excavated tunnel. The properties of surrounding rocks inside the karst cave hall were determined by integrating various test methods, as shown in

Table 2. The parameters of the surrounding rock.

Type of Surrounding Rock	Elasticity Modulus E/MPa	Poisson’s Ratio µ	Density p/kg m−3	Cohesion c/kPa	Internal Friction Angle φ/°	Porosity n/%	Permeability Coefficient k/(m2/Pa s)
Limestone	10,000	0.22	2650	2000	65	0.05	1 × e−11
Backfilling Crushed stone	500	0.25	2200	30	40	0.30	1 × e−1
Backfilling Crushed slag	1000	0.25	2400	500	45	0.20	1 × e−6
Original crushed stone	100	0.30	2200	5	38	0.30	5 × e−2
Original crushed clay	10	0.35	1860	100	7	0.20	1.2 × e−6

.

In order to study the impact of the rise of groundwater on the tunnel’s construction, this paper uses orthogonal experiments to study the different effects of the mechanical properties, the degree of compaction and the softening coefficient of water on surrounding rock of backfill materials on the tunnel project. In this paper, six main factors are selected for analysis: the elastic modulus, density, cohesion, internal friction angle, porosity and reduction coefficient. The standard orthogonal table L₂₅ (5⁶) is used to design the experimental team, and each parameter takes five levels, as shown in

Table 3. Levels of sensitivity factors.

Factor Name	Elastic Modulus E/MPa	Density p/kg m−3	Cohesion c/kPa	Internal Friction Angle φ/°	Porosity n/%	Reduction Coefficient k
Level 1	600	2160	300	35	0.16	5%
Level 2	800	2280	400	40	0.18	10%
Level 3	1000	2400	500	45	0.20	15%
Level 4	1200	2520	600	50	0.22	20%
Level 5	1400	2640	700	55	0.24	25%

. The variation amplitude of the elastic modulus and cohesion is 20%, the variation amplitude of the internal friction angle and porosity is 10% and the variation amplitude of the density and reduction coefficient is 5%.

Counting the numerical calculation results of nine sections which are at intervals of 5 m from Y = 5 m to 45 m, a total of six average parameters were taken as an evaluation index, including the displacement of 0~20 m under the bottom plate, the crown settlement, the convergence of both sides and the internal force and bending moment of initial lining. In order to make the orthogonal experimental results comprehensively reflect the influence of groundwater on tunnel construction, according to fuzzy mathematics, after taking the absolute value of experimental results in each group, the average value $\overline{x_i}$ and standard deviation $\sigma$ in the group can be calculated according to Formulas (3) and (4). In practical engineering, it is always required that the average level of each evaluation index is small to ensure the safety of tunnel excavation. The degree of dispersion is low, so there is no local deterioration. Therefore, the smaller the average value and standard deviation in the group, the more favorable the situation is for tunnel excavation. The whole test group is range standardized according to Formula (5), and the average value and standard deviation of the test group are normalized to the interval of [0–1]. According to Formula (6), $d_{ECULID}^{ik}$, which is the distance between $\left(x_{ik}^{\ast },{\sigma }_{ik}^{\ast }\right)$ and origin, can be calculated as follows:

$${\overline{x}}_{ik}=\frac{1}{n}{\displaystyle \sum _{j=1}^m\left|x_{ijk}\right|}$$

(3)

$${\sigma }_{ik}=\sqrt{\frac{1}{n}{\displaystyle \sum _{j=1}^m{\left(\left|x_{ijk}\right|-{\overline{x}}_{ik}\right)}^2}}$$

(4)

$$\{\begin{array}{l}{x}_{ik}^{\ast }=\frac{{\overline{x}}_{ik}-{\overline{x}}_{\min }}{{\overline{x}}_{\max }-{\overline{x}}_{\min }}\\ {\sigma }_{ik}^{\ast }=\frac{{\sigma }_{ik}-{\sigma }_{\min }}{{\sigma }_{\max }-{\sigma }_{\min }}\end{array}$$

(5)

$$d_{ECULID}^{ik}=\sqrt{\frac{{\left(x_{ik}^{*}\right)}^2+{\left({\sigma }_{ik}^{*}\right)}^2}{2}}$$

(6)

where i is the experimental group, $1\le i\le 25$; j is the serial number of the tunnel section, $1\le j\le 9$; k is the sequence number of six surrounding rock stability evaluation indexes: tunnel crown settlement, backfill body displacement under the bottom plate, convergence around the tunnel and internal force and bending moment of initial lining, $1\le k\le 6$; ${\overline{x}}_{ijk}$ represents the value of k evaluation index of j tunnel section in i test group; ${\overline{x}}_{\max }$, ${\sigma }_{\max }$, ${\overline{x}}_{\min }$ and ${\sigma }_{\min }$ is the average value of the k evaluation index and the maximum and minimum value of standard deviations in 25 experimental groups, respectively; and $x_{ik}^{\ast }$ and ${\sigma }_{ik}^{\ast }$ are the range standard value of the average value and the standard deviation of k evaluation index in group test i, respectively.

The smaller the $d_{ECULID}$ of the experimental group, the higher the degree of optimization. Using this method can not only avoid redundant calculations when predecessors analyze multiple tunnel sections or multiple factors but also avoid the one-sidedness of single section and single factor analysis.

Table 4. Standard orthogonal experimental results (indicated by d_ECULID).

Serial Number	Factor Level Combination	Backfill Floor Displacement	Crown Settlement	Left Convergence	Right Convergence	Initial Lining Shaft	Initial Lining Bending Moment
1	$E_1{\rho }_1{c}_1{\phi }_1{n}_1{k}_1$	0.700	0.367	0.526	0.222	0.134	0.321
2	$E_1{\rho }_2{c}_2{\phi }_2{n}_2{k}_2$	0.674	0.491	0.652	0.559	0.451	0.413
3	$E_1{\rho }_3{c}_3{\phi }_3{n}_3{k}_3$	0.642	0.724	0.791	0.855	0.736	0.535
4	$E_1{\rho }_4{c}_4{\phi }_4{n}_4{k}_4$	0.641	0.902	0.646	0.846	0.934	0.730
5	$E_1{\rho }_5{c}_5{\phi }_5{n}_5{k}_5$	0.701	1	0.809	1	1	1
6	$E_2{\rho }_1{c}_2{\phi }_3{n}_4{k}_5$	0.275	0.543	0.782	0.650	0.319	0.744
7	$E_2{\rho }_2{c}_3{\phi }_4{n}_5{k}_1$	0.224	0.454	0.365	0.418	0.649	0.342
8	$E_2{\rho }_3{c}_4{\phi }_5{n}_1{k}_2$	0.284	0.448	0.404	0.464	0.848	0.424
9	$E_2{\rho }_4{c}_5{\phi }_1{n}_2{k}_3$	0.414	0.491	0.628	0.609	0.769	0.478
10	$E_2{\rho }_5{c}_1{\phi }_2{n}_3{k}_4$	1	0.521	0.698	0.265	0.081	0.596
11	$E_3{\rho }_1{c}_3{\phi }_5{n}_2{k}_4$	0.051	0.426	0.381	0.510	0.679	0.291
12	$E_3{\rho }_2{c}_4{\phi }_1{n}_3{k}_5$	0.094	0.926	0.544	0.609	0.367	0.388
13	$E_3{\rho }_3{c}_5{\phi }_2{n}_4{k}_1$	0.121	0.254	0.326	0.366	0.661	0.207
14	$E_3{\rho }_4{c}_1{\phi }_3{n}_5{k}_2$	0.576	0.102	0.415	0.036	0.075	0.298
15	$E_3{\rho }_5{c}_2{\phi }_4{n}_1{k}_3$	0.433	0.252	0.645	0.465	0.437	0.550
16	$E_4{\rho }_1{c}_4{\phi }_2{n}_5{k}_3$	0.049	0.245	0.316	0.289	0.455	0.107
17	$E_4{\rho }_2{c}_5{\phi }_3{n}_1{k}_4$	0.033	0.320	0.360	0.384	0.712	0.237
18	$E_4{\rho }_3{c}_1{\phi }_4{n}_2{k}_5$	0.492	0.436	0.744	0.472	0.123	0.807
19	$E_4{\rho }_4{c}_2{\phi }_5{n}_3{k}_1$	0.182	0.089	0.269	0.265	0.609	0.078
20	$E_4{\rho }_5{c}_3{\phi }_1{n}_4{k}_3$	0.314	0.194	0.237	0.221	0.199	0.222
21	$E_5{\rho }_1{c}_5{\phi }_4{n}_3{k}_2$	0	0.125	0.215	0.176	0.492	0.116
22	$E_5{\rho }_2{c}_1{\phi }_5{n}_4{k}_3$	0.174	0.111	0.248	0.123	0.211	0.151
23	$E_5{\rho }_3{c}_2{\phi }_1{n}_5{k}_4$	0.206	0.225	0.337	0.112	0	0.179
24	$E_5{\rho }_4{c}_3{\phi }_2{n}_1{k}_5$	0.219	0.213	0.424	0.256	0.312	0.281
25	$E_5{\rho }_5{c}_4{\phi }_3{n}_2{k}_1$	0.144	0	0.213	0.228	0.627	0

illustrates the results of $d_{ECULID}^{}$ evaluation indexes corresponding to the different parameters of each test group. The test group of factors $E_2{\rho }_4{c}_5{\phi }_1{n}_2{k}_3$ represents the elastic modulus, density, cohesion, internal friction angle, porosity and water reduction coefficient for the backfill body, and their values are 800 MPa, 2520 kg/m³, 700 kPa, 35°, 0.18 and 15%, respectively. Based on the negative index characteristics of each evaluation index, the influence of six backfill parameters on different evaluation indexes within the given factor level range is obtained, and the optimal group for different evaluation indexes is obtained, as shown in

Table 5. Direct analysis results of L₂₅ (5⁶) standard orthogonal experiment.

Evaluating Indicator	Primary and Secondary Factors	Optimal Combination
Backfill floor displacement	$E>c>\rho >\phi >k>n$	$E_5{\rho }_1{c}_4{\phi }_5{n}_4{k}_1$
Crown settlement	$E>k>c>n>\rho >\phi$	$E_5{\rho }_1{c}_1{\phi }_3{n}_1{k}_1$
Left convergence	$E>k>c>\phi >\rho >n$	$E_5{\rho }_2{c}_4{\phi }_5{n}_5{k}_1$
Right convergence	$E>k>c>\phi >n>\rho$	$E_5{\rho }_1{c}_1{\phi }_2{n}_1{k}_1$
Initial lining shaft	$c>\phi >E>\rho >k>n$	$E_5{\rho }_1{c}_1{\phi }_1{n}_5{k}_5$
Initial lining bending moment	$E>k>\phi >\rho >c>n$	$E_5{\rho }_2{c}_4{\phi }_1{n}_3{k}_1$

. When the crown settlement is taken as the index, the elastic modulus of backfill soil has the greatest influence, followed by the reduction coefficient of water on backfill, cohesion, porosity and density. The internal friction angle has the least influence. When the elastic modulus, density, cohesion, internal friction angle, porosity and water reduction coefficient are 1400 MPa, 2160 kg/m³, 300 kPa, 45°, 0.16 and 5% respectively, the optimization of the tunnel crown settlement is the best.

In order to comprehensively consider the influence of various mechanical parameters of backfill soil on tunnel construction under the influence of groundwater and optimize the scheme design for the backfill soil, the weighted relative deviation distance minimum method [26] was adopted to form a comprehensive evaluation scheme for backfill reinforcement with the whole tunnel as the evaluation scheme, which is based on the principle of fuzzy mathematics and multi-objective comprehensive decision making. The schemes are compared and selected and combined with orthogonal experimental analysis.

According to the principle of fuzzy mathematics, the six evaluation indexes are assigned according to importance degrees. Therefore, the importance degrees of backfill bottom displacement, crown settlement, left-side convergence, right-side convergence, initial lining axial force and initial lining bending moment were determined as 20%, 20%, 15%, 15%, 15% and 15% respectively. Therefore, the fuzzy set of evaluation index weight can be obtained as X = (0.20,0.20,0.15,0.15,0.15,0.15). We employed Equation (7):

$$\{\begin{array}{l}{g}_i^{\ast }=g_i\left({\nu }_i,{\nu }_0\right)=\frac{1}{x}{\left[{\displaystyle \sum _{k=1}^m{\left(x_k{\delta }_{k\left(i\right)}\right)}^2}\right]}^{0.5}\\ x=\frac{1}{m}{\displaystyle \sum _{k=1}^m{x}_k}\end{array}$$

(7)

where m is the number of evaluation indexes; x is the average value of index weight; $x_k$ is the weight value corresponding to k evaluation index; $g_i^{*}$ represents the distance between the i test group and the optimal effect within the given factor level range. The smaller the $g_i^{*}$ value, the higher the optimization level of the test group.

When the proposed weight fuzzy set is X, the range situation of $g_i$ is shown as in Figure 7. The main influencing factor obtained by the comprehensive evaluation method is the elastic modulus of the backfill body and the selected optimal scheme is $E_5{\rho }_1{c}_3{\phi }_1{n}_1{k}_1$. If the decision makers adopt different evaluation index weight preferences, the results will be different, but the optimization design of backfill reinforcement parameters can still be carried out according to the method proposed in this paper.

The strength parameter group of the reinforcement optimized using this method is defined as group 26, and the weighted deviation distances of 26 conditions are calculated at the same time. The results are shown in

Table 6. Calculation results of weighted relative deviation distance.

Item Number	${\mathit{g}}_{\mathit{i}}$	Item Number	${\mathit{g}}_{\mathit{i}}$	Item Number	${\mathit{g}}_{\mathit{i}}$	Item Number	${\mathit{g}}_{\mathit{i}}$	Item Number	${\mathit{g}}_{\mathit{i}}$	Item Number	${\mathit{g}}_{\mathit{i}}$
1	0.0325	2	0.0401	3	0.0514	4	0.0555	5	0.0645	6	0.0411
7	0.0291	8	0.0340	9	0.0392	10	0.0465	11	0.0289	12	0.0405
13	0.0236	14	0.0244	15	0.0335	16	0.0183	17	0.0259	18	0.0397
19	0.0192	20	0.0168	21	0.0152	22	0.0119	23	0.0149	24	0.0203
25	0.0178	26	0.0057

.

It can be determined that when considering the comprehensive evaluation index, the d_ECULID distance between this method and the optimal evaluation index group is the smallest, which is 0.0057, indicating that the backfill material scheme designed by this method can effectively reduce the settlement around the tunnel and control the mechanical response of the surrounding rock and lining at a low level, and the mechanical response of each section is evenly distributed. The design goal of backfill reinforcement is achieved.

4. Effect of Comparion

In order to show the impact of different backfill materials on tunnel construction, the largest group $E_1{\rho }_5{c}_5{\phi }_5{n}_5{k}_5$ and the smallest group $E_5{\rho }_1{c}_4{\phi }_5{n}_4{k}_1$ of $g_i$ in Table 6 are selected for comparison. The two groups are compared to ensure the feasibility of the methods used in this study.

4.1. Backfilling Body Displacement

Figure 8 illustrates the settlement of two different backfill materials under the action of self-weight. The settlement trends of the two different backfill materials are almost the same but the difference in settlement amplitude is large. The main displacement of backfill is concentrated in the upper part of the karst cave. However, due to the principle of coordination deformation between continuous grids in the numerical simulation software, the top part of the backfill which is in contact with limestone is not the largest, and the displacement of this part is from 0 to the maximum, which is slightly different from the actual situation.

When using the optimal backfill material parameters, the maximum settlement of the backfill body is 70 cm, and the settlement of most of the area is below 35 cm. When using the worst backfill material parameters, the maximum settlement of the backfill body reaches 1.18 m and the average settlement is about 55 cm, which is 1.7 times and 1.6 times that of the best material, respectively. At the same time, it can be clearly found that when the worst backfill material is used, the settlement gradient is large, which is not conducive to the compaction of the backfill body and will cause certain damage to the tunnel construction. Therefore, it is necessary to roll the backfill in layers to ensure the compactness of each layer of soil, which can effectively reduce the settlement of the backfill under the influence of self-weight and construction.

4.2. Tunnel Longitudinal Displacement during Tunnel Construction

As shown in Figure 9, the longitudinal displacement of two backfill materials during tunnel construction is quite different after completing backfilling and removing the settlement under the action of their own weight. Due to the tunnel being located near the roof of the karst cave, the mechanical properties of the surrounding rock on both sides of the tunnel vary greatly from the limestone to the backfill body. Therefore, the longitudinal displacement distribution around the tunnel is different. The maximum crown settlement of the backfill body with the optimal parameters is 6 mm, and the maximum uplift of the tunnel bottom is only 2 mm. For the backfill with the worst parameters, the maximum crown settlement and the maximum uplift of the floor are 15 cm and 2 cm, respectively, which are 2.5 times and 10 times more than those under the optimal parameters. Therefore, it can be clearly discovered that the optimal parameters obtained by using the reinforcement parameter design method proposed in this study can effectively reduce the longitudinal displacement of the tunnel, which all meet the national specifications.

4.3. Tunnel Horizontal Displacement during Tunnel Construction

Figure 10 illustrates the tunnel lateral convergence of both sides during tunnel excavation. When using the optimal parameters, the maximum displacements on the left and right sides of the backfill are only 1.8 cm and 2 cm. For the backfill with the worst parameters, the maximum displacements on the left and right sides reach 4.5 cm and 5 cm, which are 2.5 times the values obtained when using the optimal parameters. Compared with the longitudinal displacement, the difference between the two parameters in the transverse displacement is smaller.

Firstly, this is because the distance of backfilling on both tunnel sides is small, and the limestone on both sides ensures the effective horizontal deformation of the backfilling body. Secondly, the time for finishing backfill is too short and horizontal stress is small. At the same time, the displacement of the left side of the tunnel is greater than that of the right side because the right side of the tunnel is closer to the limestone and the deformation is smaller.

In general, the application of the optimal parameters obtained above can effectively reduce the displacement around the tunnel, reduce the surrounding rock stress and provide a safety guarantee for tunnel construction.

5. Field Monitoring

In order to ensure the safety of the tunnel construction process and explore the impact of the underground river on the tunnel, the flow of the underground river, the layered settlement of backfill and the settlement of the tunnel vault were monitored, respectively.

5.1. The Flow of the Underground River Monitoring

In order to achieve a clear understanding of the underground river flow, 130 m to the left of d3k279 + 938 and 70 m to the left of d3k279 + 970 were taken as observation sections in the underground river in the karst cave to observe and measure the flow in the tunnel. The statistics and the amount of rain on that day are plotted in Figure 11.

The two black lines in Figure 11 represent the flow of the underground river in the karst cave and the outlet flow, respectively. It can be seen that the outlet flow is significantly greater than the flow of the underground river in the karst cave, indicating that there are multiple tributaries in Yujing Mountain, and because the limestone belongs to soluble rock, it forms many connecting drainage routes, resulting in the collection of the whole water at the outlet. The change in rainfall and the change in underground river flow in the karst cave are relatively slight, but they have little correlation with the flow at the outlet of the underground river. Therefore, the water system is complex, and so we should pay attention to the monitoring of groundwater to prevent the water level of the underground river rising quickly.

There is a deep pool at the outlet of the karst cave. According to the flow monitoring data for the outlet, the maximum water volume of the outlet is Q = 68.75 m³/s, which is far less than the calculated maximum water inflow and underground river water inflow. Therefore, in the rainy season, the water level in the karst cave must rise. Based on the static water sediment on the surface of the accumulation at the bottom of the cave and the drilling, it is judged that the water level of the underground river in the cave once rose to the elevation of 990 m (an increase of about 30 m). Due to the great uncertainty of the drainage property of the underground river channel, it is very likely that the underground river pipeline will collapse and block the river channel during the tunnel operation, which will further aggravate the rise of the underground river in the karst cave.

In order to avoid the backfill blocking the underground river channel and adversely affecting the operation, the underground river in the karst cave section was diverted before the karst cave treatment, as shown in Figure 12.

The underground river channel mainly uses drainage and blocking to prevent the rise of underground river water level in the rainy season from having a great impact on the safety of the tunnel in the giant karst cave. After the construction of the discharge tunnel, the underground river shall be blocked upstream and downstream. At the same time, the underground river flow in the karst cave section shall be led downstream of the underground river through the NO. 4 and 5 discharge tunnels.

In addition, a new channel is to be constructed at the intersection between the underground river and the tunnel, which will be able to maintain the rapid flow of the underground river. At the foot of the slope of the karst cave, the new channel follows the flow direction of the underground river and is about 30–50 m away from the tunnel wall on the right side, and a circuitous discharge tunnel is set to divert the underground river section so as to direct the upstream water of the underground river downstream through the discharge tunnel. The discharge tunnel is about 450 m long, 7.2 m wide and 6.0 m high.

5.2. Layered Backfill Monitoring

In order to ensure the safety of the tunnel after backfilling, the settlement of layered backfill soil is monitored at d3k279 + 915, as shown in Figure 13. This paper focuses on monitoring the settlement of backfill near the underground river, so the monitoring range is 20~40 m below the tunnel floor, and a monitoring point is set every 2 m.

At the initial stage after backfilling, the backfill body of each layer is gradually consolidated under the action of self-weight and upper construction load, displacement fluctuating frequently within the range of 5~−10 mm (positive value indicates soil uplift).

After 15 January 2019, the backfilling and compaction stage were completed, and the project entered the tunnel construction process. The first step was the tunnel step excavation. There was obvious settlement to backfill of each layer of d3k279 + 915, of which the settlement at 20 m is the largest, reaching 53 mm, and the settlement of each layer surrounding rock was concentrated in 40~50 mm. During this period, the settlement of each layer basically decreased with the increase of depth, which corresponded to the actual situation.

After the completion of tunnel excavation, grouting reinforcement was carried out for the backfill areas at the bottom and both sides, so the settlement of surrounding rock of each layer tended to decrease. Among them, the displacement of deep surrounding rock decreased significantly, and the maximum reduction degree was 10 mm. Therefore, it can be considered that grouting to the bottom of the tunnel can effectively improve the surrounding rock’s mechanical condition.

5.3. Crown Settlement Monitoring

In order to explore the state of the surrounding rock at the top of the tunnel in different construction stages, three sections d3k279 + 875~896 were selected for analysis, as shown in Figure 14a. The final crown settlement of 12 sections in d3k279 + 896~955 in the open excavation period and concealed excavation period was counted, as shown in Figure 14b.

By analyzing the data in the diagram, we can determine that:

(1)

The crown settlement increases gradually with the progress of construction, and the growth trend of each curve is basically consistent. During the open excavation period, the crown settlement gradually increases with the construction process of the step method, and it can be clearly seen in Figure 14a that it has an obvious growth gradient. In the period of concealed excavation, due to the influence of grouting and other reinforcement measures, the crown settlement is fluctuating and continues to rise as part of the whole trend.

(2)

The crown settlement of the d3k279 + 885 section is the largest of the three sections in both open excavation and concealed excavation, and the maximum settlement in the two periods reaches 28.5 mm and 37.3 mm, respectively. In addition, the crown settlement can reach a stable state through reinforcement measures, such as continuous grouting behind the lining.

(3)

Crown settlement is considered to be the main displacement in the tunnel. The final settlement of each section at the end of the open excavation period and concealed excavation period is shown in Figure 14b. The settlement range of the whole monitoring section is 0.3~13.6 mm and 4.4~15.2 mm, respectively. The crown settlement difference between sections is relatively large. Therefore, it is necessary to pay attention to the change in load caused by the change in surrounding rock stability and to strengthen the monitoring of the surrounding rock in different areas and carry out timely supplement grouting for reinforcement.

6. Discussion

Taking the tunnel of Chengdu Guiyang railway crossing the huge karst cave section as project example, this study took the underground river in the karst cave as the research object, used the finite element software FLAC3D and the measured data to explore the adverse impact of underground river level increases on tunnel construction and selected the best parameters for backfill material for practical engineering. The main findings of this study are as follows:

(1)

In this study, the commonly used parameters, including density, elastic modulus, cohesion, internal friction angle, porosity and parameter reduction coefficient in backfill, were selected as the main variables. The six data of layered settlement, tunnel crown settlement, convergence on both sides and internal force and bending moment of initial lining obtained by the finite element software FLAC3D were used as evaluation indexes. The average value and standard deviation of the mechanical response results for the surrounding rock and lining structure in multiple sections were transformed into the ECULID distance from the origin on the two-dimensional plane as the evaluation index. The parameter influence analysis was carried out based on the orthogonal test. It was found that the bulk elastic modulus of backfill and the reduction coefficient of water on materials have the greatest influence on structural mechanics.

(2)

According to the field measured data of 10 different sections, the layered settlement of the backfill body presented three different stages of slow increase, rapid increase and slow increase in the backfilling period, open excavation period and concealed excavation period. The growth range of each section was different but the trend was basically the same.

(3)

According to the measured data of tunnel crown settlement in different sections, in the open excavation period, the crown settlement increased in step with the advance of the construction steps, and the tunnel crown settlement fluctuated continuously in the concealed excavation period. However, due to the different nature of the surrounding rock, the support method and grouting amount, the settlement of each section at the end of the open excavation period and the concealed excavation period varied greatly, but they were all within a controllable range, and the impact of groundwater on tunnel construction was basically eliminated.

In general, the tunnel crossing the giant cavity was well controlled.

7. Conclusions

(1)

Based on the multi-objective comprehensive decision-making theory, the global optimal value of multiple evaluation indexes was used as the optimal backfilling effect, and the multi-dimensional ECULID distance between the test group and the global optimal solution was used as the comprehensive evaluation index. A determination method for reinforcement parameters was proposed. When the weight of the evaluation index was determined, the design group of backfilling reinforcement parameters with the optimal overall mechanical response could be obtained. In this study, the optimal scheme was $E_5{\rho }_1{c}_3{\phi }_1{n}_1{k}_1$.

(2)

The optimal parameter scheme obtained by the backfill parameter design method was applied to practical engineering. The monitoring results showed that the displacement of the tunnel mainly occureed in the backfill stage, and after optimizing the backfill parameters, the displacement of the tunnel could be effectively reduced and the stability of the surrounding rock could be improved. At the same time, after the diversion of the underground river, the water flow in the karst cave hall was significantly reduced, and there was no situation of poor drainage.

(3)

The research presented in this paper can provide a research basis and engineering reference for tunnel engineering passing through karst caves. In the next stage, we will introduce the tomographic analysis method in the process of selecting parameters, which provides a firmer basis for the selection of engineering evaluation indicators. In addition, a small tunnel model was established to simulate the changing process of groundwater erosion and damage to the tunnel backfill.