Numerical Analysis of Grouting of Water-Enriched Karst Highway Tunnel Based on Critical Water-Enriched Height

: The occurrence state of groundwater in a karst area has a signiﬁcant impact on the tunnel lining structure. The impact on the groundwater is more signiﬁcant during construction. This paper used numerical simulation to study the grouting reinforcement range of the Liaoshan Tunnel. This was based on the critical water rich height. Under Grade IV and Grade V surrounding rock, the critical points of grouting reinforcement were 230 m and 240 m deep, respectively. The vertical and horizontal stress and seepage ﬂow of the tunnel arch crown and invert decreased as the circumferential grouting reinforcement range increased. In the case of no grouting reinforcement, 1/4 circumferential grouting reinforcement, 1/2 circumferential grouting reinforcement, and all circumferential grouting reinforcement, the seepage ﬂow was 7 m 3 /dm, 4 m 3 /dm, 3 m 3 /dm, and 0 m 3 /dm, respectively. With Grade V surrounding rock, when the groundwater level was 260–270 m away from the tunnel arch crown, two schemes could be adopted: 1 m radial grouting reinforcement and 1/2 circumferential grouting reinforcement. The results have guiding signiﬁcance for developing a construction scheme of a karst water rich tunnel.


Introduction
During the construction of underground works, the original water bearing structure will be destroyed, leading to the connection between the excavation free face and the groundwater seepage channel, which makes the groundwater suddenly flow into the excavation area, bringing great challenges to the structural safety and ecological environment [1,2].At present, "water stoppage and drainage restriction" is often used to treat water gushing in water-enriched karst tunnels, which starts with water cutoff grouting [3].Considering the arbitrary tunnel layout and tunnel interaction, the Schwartz alternating method combined with conformal mapping was used for the first time to successfully solve the seepage field of multiple underwater tunnels [4].Using the convolution-deconvolution method, the time-variant inflow problem was transformed to a constant flow problem.The calculation formula was developed for the conceptualized hydro-geological models for the tunnel inflow problems [5,6].The rise in the groundwater level makes the obvious phenomenon of vault sinking and invert floating appear in the tunnel.When the water level passes the vault, the lining structure has a significant reduction in the safety factor and an increase in the crack width [7].A hydraulic model was developed to assess the expected velocity and head of water when the conduits cross during construction.Based on the model and real-time meteorological and hydrological measurements, a prediction model was established to predict high flow events [8,9].As the hydrostatic head decreased, the water pressure at each characteristic point decreased approximately linearly, and the water inflow rate also had a gradual downward trend.Under the action of the hydrodynamic head, the water pressure had an obvious lagging effect, which was not conducive to the stability of the supporting structures, and could be mitigated by actively regulating the drainage rate [10].The grouting effect was analyzed and evaluated based on ground penetrating radar detection and field working conditions [11].
Shi et al. [12] adopted numerical simulation to reveal the evolution law of water pressure outside the tunnel with the thickness of the grouting ring and groundwater discharge.Zhao et al. [13] studied the relationship between the grouting ring and primary support's seepage parameters and the primary support's external water head, seepage amount, and water head difference.Based on the results, Zhao proposed a method to determine the reasonable seepage parameters of the tunnel structure.Fu et al. [14] carried out a three-dimensional fluid-structure coupling simulation for different spacings of the circumferential blind ditches in water-enriched fault areas of super long tunnels.After analyzing the seepage pressure, anchor stress, and water yield, they obtained the volume and distribution of the plastic zone.Ding et al. [15] studied tunnels with high water pressure under double-layer support.Their focus was mainly on the effect of radial grouting and curtain grouting.According to the results, the range of radial grouting achieved the optimal effect at 4.0-4.5 m.Compared with the un-grouted tunnel, the curtain grouting's external water pressure was reduced by 23%.By studying the tunnels in a water-enriched area of the Loess Plateau, Wei and Zhu [16] concluded that curtain grouting can well control groundwater gushing.
Wang et al. [17] studied the optimal grouting length and thickness of curtain grouting in front of the fault in the water-enriched fault tunnel.Jia et al. [18] used full-curtain grouting to prevent water from gushing in the water-enriched fault zone of Junchang Tunnel.According to the results, the optimal thickness of the grouting ring was 7 m.Liu et al. [19] studied grouting rings, grouting parameters, and grouting boreholes and optimized the construction of the Qingdao subway at a water-enriched sandy layer.Tian and Wang [20] investigated the water-enriched area of Guanjiao Tunnel.Their focus was the relationship between the grouting ring's permeability coefficient with its thickness and the node flow.According to the results, the optimal thickness of the grouting ring was 3 m and the optimal permeability coefficient was 2.1 × 10 −3 m/d.Zou et al. [21] analyzed three waterproof and drainage methods and discussed the influence of the grouting parameters on the lining water pressure and water yield when adopting the three methods.Based on his analysis, Zou et al. [21] put forward grouting parameters suitable for application.Xu et al. [22,23] used FLAC3D to analyze the displacement limits of the crown, haunch, and skewback of the highway mountain tunnel under different surrounding rock grades, buried depths, tunnel section forms, excavation methods, and support material parameters.Based on cusp catastrophe theory, their study defined the displacement limit of the deformation control points around the tunnel.The corresponding rheological flow of the penetration grouting in the jointed rock masses was analyzed by modeling the field conditions as closely as possible [24][25][26].The grouting of the tunnel radius thickness could effectively reduce the inflow of groundwater.When the annular area of the radius thickness of the tunnel was grouted with a permeability reduction rate of 1/50 (similar to 1/200), the groundwater inflow could be reduced by more than 90% [27].The stability of the middle wall of the shallow and small clearance tunnel was related to the depth, spacing, and the physical-mechanical properties of the soil [28].To study the effect of grouting rings on the settlement of existing tunnels, the variations in the soil properties and relevant parameters before and after the grouting were analyzed [29,30].Results from the hydraulic tests in probe boreholes in the access tunnel to the Äsprö Hard Rock Laboratory, Sweden were compared to the amount of performed pre-grouting of the tunnel made in order to reduce the water inflow.It was found that the probe holes identified the major hydraulic conductors well [31].Combined use of time domain characteristics, spectral content, and wavelet transform revealed the effectiveness of grouting and indicated that the impact echo is valuable for the quick and reliable assessment of grouting in such cases [32].The ground reaction force curve considering the seepage force showed a greater radial displacement than that under dry conditions at the same internal pressure level because the seepage force was applied to the tunnel section as an additional physical force [33][34][35][36].A set of functional parameters to describe the rock mass for grouting purposes has been suggested, these are: the hydraulic head h; the hydraulic apertures b of the fractures; fracture frequency P-10 [37].There was a negative correlation between the hydration heat and the uniaxial compressive strength of the cement slurry sample, and the rapid temperature rise in the cement slurry caused the strength of the solidified grouting sample to decrease [38].
There are many studies on grouting technology in karst water-rich areas and they play important roles in actual tunnel projects.However, few studies have focused on the optimal grouting schemes under different groundwater levels.Therefore, this paper obtained the critical water-rich height with FLAC3D.It also analyzed the changing law of the displacement field, stress field, and seepage field under different surrounding rock grades, groundwater levels, and grouting schemes.This paper provides a clear guidance for the design and construction of similar tunnel projects.

Project Overview
Located in Longchi Town, Emeishan City, Sichuan Province, Liaoshan Tunnel is a double-hole and two-way tunnel.The left and right holes are 3197 and 3170 m long, respectively.The designed pavement elevation ranges from 813.79 to 757.42 m.The maximum buried depth of the tunnel roof is about 280 m.The surface water system in the tunnel area mainly consists of tributaries of the Dawei River, Longchi River, and surface gullies.The unfavorable geology in the tunnel site area is mainly soluble limestone, with the development of karst funnels.The larger karst pipelines are located in Baiyangou, which are grooves on the ground, and the karst intensity is medium to weak.In Baiyangou, there is a large karst passageway with a grooved surface and a moderate to weak karst intensity.The daily water yield is 13,788 m 3 /d, and the extreme water yield is 40,411 m 3 /d.Grade V accounts for about 40%, and Grade IV accounts for 60% of the total surrounding rock types.The Grade IV and V surrounding rocks represent the strength grade of the surrounding rocks, reflecting the geological conditions of the tunnel.Generally, the strength of the Grade IV surrounding rock is lower than that of the Grade V surrounding rock, and the surrounding rock is also relatively broken.

Model Building
The section of the tunnel model can be delineated as a five-center circle (Figure 1).The maximum excavation span of the tunnel was 12.27 m.The excavation height was 10.73 m.The center line of the tunnel excavation direction is the Y-axis, the X-axis is perpendicular to the Y-axis, and the Z-axis is vertical.The Y-axis excavation depth was 2 m, which is one cyclical footage.The numerical simulation model of the tunnel (Figure 2) had a range of 135 m × 2 m × 350 m and was divided into 24,597 nodes and 17,196 units.The numerical simulation was performed on the buried depth section.The section needs further grouting under different grades of surrounding rock.A 1 m thick grouting ring was adopted to form a circular cover around the crown.The three grouting methods included 1/4 ring grouting, 1/2 ring grouting, and full grouting (Figure 3).They all followed the axisymmetric distribution on the crown.

Boundary Conditions
(1) Displacement boundary conditions of the model: Except for the top surface of the model, which has a free boundary, the normal displacement of the other five surfaces should be constrained.(2) Seepage boundary conditions of the model: Before the tunnel is excavated, it is assumed that the internal rock and soil that bear the water is rich in water and is saturated.The static pore water pressure and the buried depth follow a proportional linear relationship.Model Z = max is a permeable boundary with zero pressure of pore water.Other surfaces are impermeable boundaries.As more surrounding rock is excavated, seepage will occur on the free face, which serves as a permeable boundary with zero pore water pressure.

Material Parameters
The Mohr-Coulomb elastic-plastic model was used to simulate the surrounding rock.As the tunnel is deeply buried, the self-weight stress must be accounted for in the initial crustal stress field of the rock and soil.The pore water pressure is hydrostatic.The primary support and secondary lining were simulated by solid elements and the tunnel excavation was simulated by an empty model.The parameters of the material and support structure for the numerical calculation are shown in Table 1.

Convergence Criterion Level Grid Sensitivity
Generally speaking, the default convergence standard (or relative convergence standard) of FLAC3D can be used for most problems, that is, when the ratio R of the maximum unbalanced force to the typical internal force of the system is less than the fixed value 10-5, the calculation is terminated.The maximum unbalanced force of the system refers to the maximum value of the difference between the external force and the internal force of all nodes when the external force is transferred and distributed to each node of the system through grid nodes in each calculation cycle (or calculation time step).The so-called typical internal force refers to the average value of all grid point forces of the calculation model.Since R is dimensionless, it is applicable to different unit systems.Sometimes, the maximum unbalanced force of the system is less than a certain critical value (command: SET mech force <value>) as a convergence standard, also known as the absolute convergence standard.Because this critical value needs to be defined by the user, and there is no relatively uniform value range, taking a smaller value will undoubtedly be very harsh for complex models with a large number of elements, so it has greater limitations.
In this paper, the FLAC3D default convergence criterion, namely, the relative convergence criterion, was used for calculation.
In this paper, the principle of sparse outside and dense inside was adopted in the grid division, that is, from the surrounding rock around the tunnel to the tunnel lining, the grid size gradually becomes smaller, which is about 0.5 times that of the decreasing change, to better analyze the specific location of the displacement and stress changes of the tunnel support structure.

Simulated Working Conditions
Based on the engineering facts of the project, the surrounding rocks of 60 m to 280 m below the crown are at IV and V grades.Therefore, bench excavation was adopted and the critical water-enriched height (the critical point of grouting) at the 280 m buried depth was determined for analysis.Based on these conditions, we further tested the effects of 1/4 ring grouting, 1/2 ring grouting, and full-ring grouting, respectively.

Determination of Critical Water-Enriched Height
This paper integrated the findings of Xu et al. [22,23] with the reality of this tunnel construction project.It determined the correlation between the average relative displacement at various positions.The situations under IV or V surrounding rock and the buried depth were investigated (Figure 4).The relative displacement of arch crown settlement is represented by the ratio of arch crown settlement value to the tunnel's net height.The relative displacement of arch waist convergence is denoted by the ratio between the sum of absolute values of horizontal convergence of the two points at the arch waist and the distance between the two points.The relative displacement of the arch foot convergence is indicated by the ratio between the sum of absolute values of horizontal convergence of the two points at the arch foot and the distance between the two points.In the Liaoshan Tunnel, the distance between the crown and the skewback is 10.73 m; the haunch's horizontal distance is 12.27 m; and the skewback's horizontal distance is 10.78 m.Based on the average percentage of relative displacement (Figure 4), we can derive the relationship between the displacement limits of crown settlement, haunch convergence, skewback convergence, and the buried depth under Grades IV and V surrounding rock.The relationship between the simulated and displacement limits and the buried depth under IV and V surrounding rock is plotted in Figure 5. Linear relationships are shown in the simulated and displacement limits and the buried depths (Figure 5).For the IV surrounding rock, at the buried depth of 230 m, the simulated displacement of crown settlement was greater than its displacement limit.At the buried depth of less than 230 m, the simulated displacement was smaller than the displacement limit.Thus, for IV surrounding rock, the critical water-enriched height was 230 m, which can be determined as the critical point of grouting.As for the V surrounding rock, the critical water-enriched height was 240 m, which is also a critical point of grouting.
According to the analysis above, for the IV surrounding rock, the grouting ranges were 230 m, 240 m, 250 m, 260 m, 270 m, and 280 m.For the V surrounding rock, the grouting range should be 240 m, 250 m, 260 m, 270 m, and 280 m.

Calculation Results and Analysis of Displacement Field
Haunch convergence and skewback convergence are both horizontal displacements and are controlled within the displacement limit.Therefore, the analysis of the displacement field only considered the vertical displacement.Figure 6 shows the cloud diagrams of vertical displacement at a 60 m buried depth.According to Figure 6, under the same surrounding rock, a larger circumferential range of the grouting reinforcement ring will lead to smaller arch crown settlement displacement.As the grouting reinforcement range increases, the arch crown settlement of Grade IV surrounding rock gradually decreases from 28.9 mm to 28 mm, with a decrease of about 3%.The arch crown settlement of Grade V surrounding rock decreased gradually from 35.8 mm to 33.2 mm, with a decrease of about 7%.The arch crown settlement of Grade V surrounding rock decreased by about twice as much as that of Grade IV surrounding rock.When the grouting reinforcement method was the same, the surrounding rock grade became greater, with worse surrounding rock lithology, and greater arch crown settlement displacement.In the case of 1/4 circumferential grouting, the arch crown settlement of Grade V surrounding rock was 24% higher than that of the Grade IV surrounding rock.It was 22% higher in the case of 1/2 circumferential grouting, and 18% higher in the case of all circumferential grouting.Therefore, the range of grouting reinforcement can well control the deformation of the surrounding rock around the tunnel.In addition, the displacement nephogram showed that the influence range of the vault settlement of Grade IV surrounding rock was about three times that of the tunnel's net height, while that of the Grade V surrounding rock was about five times.
As the buried depth increased, the maximum displacement of crown settlement under different grouting ring ranges increased (Figure 7).Under the same buried depth, the maximum displacement of the crown settlement can be ordered from high to low as follows: ring 1/4 ring grouting, 1/2 ring grouting, and full-ring grouting.This demonstrates that for a given grouting ring thickness, a larger grouting ring will result in a smaller maximum displacement of crown settlement, hence producing a more effective grouting result.Under the IV surrounding rock, when the groundwater level was at a 230-280 m distance from the crown, the maximum displacements of the crown settlement of all the three types of grouting ring were within the displacement limit; under the V surrounding rock, when the groundwater level was 270-280 m away from the crown, the maximum displacement of crown settlement under 1/4 ring grouting exceeded the limit.
Under the IV surrounding rock, we used the percentage of the maximum displacement of crown settlement after grouting to that of no grouting to reflect the effect of the grouting technique (Figure 8).As the grouting ring increased, this percentage decreased.The changes in the maximum displacement before and after grouting were basically less than 3%.The reduced percentage was controlled between 7% and 12%.Under the IV surrounding rock, the reduced percentage of the maximum displacement of crown settlement (compared with displacement limit of crown settlement) was more than 5% (Figure 9).As long as the maximum displacement of crown settlement does not exceed the critical displacement, the 1/4 ring grouting should be utilized.Under Grade V surrounding rock, the maximum value of arch crown settlement became a percentage smaller than the arch crown without grouting reinforcement.After eliminating the circumferential 1/4 grouting reinforcement method under the Grade V surrounding rock, the change range became 7~15%.There was little difference in the amplitude.Compared with the limit value of arch crown settlement, when the distance between the groundwater level and the tunnel arch crown was 270 m, the displacement reduction in the arch crown reinforced by circumferential 1/4 grouting was only 0.32%, which is not safe enough.When the underground water level was 280 m away from the tunnel arch crown, the displacement of the lower arch crown reinforced by 1/4 circumferential grouting exceeded the limit displacement value.Moreover, the reduction in the 1/2 circumferential grouting reinforcement was only 0.78%, not safe enough.The reduction in all of the circumferential grouting reinforcement rings was 3.88%, which meets the safety requirements.The grouting schemes based on the calculation and analysis of the displacement field are provided in Table 2.The pore water pressure and groundwater seepage under four working conditions (i.e., no grouting reinforcement, circular 1/4 grouting reinforcement, circular 1/2 grouting reinforcement, and circular full grouting reinforcement).The Grade IV surrounding rock was selected for analysis and the water rich height was 230 m.The grouting reinforcement only changed the pore water pressure and seepage volume of the groundwater in a certain range around the tunnel.If the tunnel construction has a large impact to the range of 3-5 times the tunnel span, the impact will be very small after the range is increased.Therefore, it is necessary to comprehensively study the local groundwater seepage around the tunnel and the initial support displacement of the tunnel.We used the gp.flow command in the FISH programming language and the specified displacement command stream to calculate the total water yield per length of the tunnel.We added all of the imbalanced flow of the nodes around the primary support.Under no grouting, 1/4 ring grouting, 1/2 ring grouting, and full-ring grouting, the seepage discharges were 7, 4, 3, and 0 m 3 /dm, respectively.The reduced percentages of water yield were 37.18, 61.51, and 98.97%, respectively.Grouting can reduce the water yield in the tunnel free faces.The water yield decreases as the grouting ring expands.This is because the permeability coefficient of grouting is very small, which serves as a barrier against the groundwater.With this barrier effect, the water yield into the tunnel becomes smaller per unit time.When the grouting's circular distribution extends, the barrier effect can be more obvious.

Calculation Results and Analysis of Stress Field
The cloud diagrams describe the total stress of primary support and the total vertical stress of the surrounding rock at a water-enriched height of 230 m for each of four different grouting techniques.σ xx denotes the total horizontal stress, and σ zz represents the total vertical stress (Figure 10).
According to Figure 10, for the initial support stress, as the reinforcement range increased, the maximum tensile stress in the horizontal direction gradually decreased from 1.94 MPa to 1.49 MPa.The drop was about 23%.The location of the decrease was mainly near the left-and right-side walls of the tunnel, which are shown in red in the figure.The maximum vertical compressive stress gradually decreased from 0.84 MPa to 0.72 MPa.The reduction was about 14%.It also occurred near the left-and right-side walls of the tunnel, which are shown in blue.The maximum tensile stress was mainly outside the initial support.It was on the side close to the surrounding rock.The maximum compressive stress was mainly inside the initial support, on the side facing the free face.The horizontal stress increased with the hoop range of the grouting reinforcement ring at the arch crown, the vertical stress and horizontal stress of the arch crown and inverted arch were smaller.The corresponding stress concentration area was also smaller because the grouting reinforcement improved the strength of rock and soil mass, and the grouting reinforcement ring could bear more vertical stress, which makes the stress borne by the initial support smaller.

Conclusions
In this paper, the grouting reinforcement schemes of Liaoshan Tunnel under different surrounding rock grades and different groundwater levels were compared and analyzed through finite element software, and the following conclusions were obtained: (1) At the same tunnel burial depth, the arch crown settlement displacement decreased with the increase in the circumferential grouting range, which decredses by 5-15%.In the case of Grade V surrounding rock, the groundwater level was 260-270 m higher than the tunnel arch crown.Two schemes can be adopted, namely, 1 m radial grouting reinforcement thickness and 1/2 circumferential grouting reinforcement.When the underground water level was 270-280 m higher than the tunnel arch crown, two schemes could also be adopted, namely, 1 m radial grouting reinforcement thickness and circumferential grouting reinforcement.(2) The seepage flow without grouting reinforcement, 1/4 circumferential grouting reinforcement, 1/2 circumferential grouting reinforcement, and all circumferential grouting reinforcement was 7 m 3 /dm, 4 m 3 /dm, 3 m 3 /dm, and 0 m 3 /dm, respectively; with the increase in the reinforcement range of circumferential grouting, the water inflow of the tunnel decreased gradually.(3) With the enlargement of the circumferential range of the grouting reinforcement ring at the arch crown, the horizontal and vertical stresses of the tunnel initial support gradually decreased, with a smaller range of 10%, and the stress concentration area became smaller and smaller.

Figure 2 .
Figure 2. Numerical simulation model of the tunnel built by FLAC3D and grid division.

Figure 4 .
Figure 4. Relationship between the average relative displacement at different positions and the buried depth under different surrounding rock grades.(a) Grade IV surrounding rock; (b) Grade V surrounding rock.

Figure 5 .
Figure 5. Relationship between the simulated and displacement limits and the buried depth under different surrounding rock grades.(a) Grade IV surrounding rock; (b) Grade V surrounding rock.

Figure 6 .
Figure 6.Cloud diagram of the vertical displacement at a 60 m buried depth.(a) Cloud diagram of the vertical displacement under Grade IV surrounding rock and 1/4 ring grouting; (b) Cloud diagram of the vertical displacement under Grade V surrounding rock and 1/4 ring grouting; (c) Cloud diagram of vthe ertical displacement under Grade IV surrounding rock and 1/2 ring grouting; (d) Cloud diagram of the vertical displacement under Grade V surrounding rock and 1/2 ring grouting; (e) Cloud diagram of the vertical displacement under Grade IV surrounding rock and full-ring grouting; (f) Cloud diagram of the vertical displacement under Grade V surrounding rock and full-ring grouting.

Figure 7 .
Figure 7. Maximum displacement of crown settlement under different grouting ring ranges and the surrounding rock grades.(a) Grade IV surrounding rock; (b) Grade V surrounding rock.

Figure 8 .
Figure 8. Decreased percentage of the maximum displacement of crown settlement under different surrounding rock grades (compared with no grouting).(a) Grade IV surrounding rock; (b) Grade V surrounding rock.

Figure 9 .
Figure 9. Decreased percentage of maximum displacement of crown settlement under different surrounding rock grades (compared with displacement limit of crown settlement).(a) Grade IV surrounding rock; (b) Grade V surrounding rock.

Figure 10 .
Figure 10.Cloud diagrams of the total stress of the primary support and total vertical stress of the surrounding rock under four different grouting ring ranges.(a) Cloud diagram of σ xx under no grouting; (b) Cloud diagram of σ zz under no grouting; (c) Cloud diagram of σ xx under 1/4 ring grouting; (d) Cloud diagram of σ zz under 1/4 ring grouting; (e) Cloud diagram of σ xx under 1/2 ring grouting; (f) Cloud diagram of σ zz under 1/2 ring grouting; (g) Cloud diagram of σ xx under full-ring grouting; (h) Cloud diagram of σ zz under full-ring grouting.

Table 1 .
Material parameters for the numerical simulation.

Table 2 .
Grouting schemes under different buried depths, surrounding rock grades, and grouting ring ranges.