Keywords

1 Introduction

The development of China’s infrastructure construction within the karst landscape of southwest China poses significant challenges. The complex geological conditions and higher instances of groundwater in karst areas result in immeasurable negative impacts on tunnel construction. These challenges seriously threaten construction safety and impede the progress of project1. Numerous tunnels fail to recognize the karst geological conditions and groundwater distribution characteristics, resulting in severe water and mud surges. Frequent disasters in water-rich karst tunnels require extensive and thorough research into key scientific issues, namely predicting tunnel water ingress and preventing and managing major water and mud surges. Such research can efficiently inform engineering practice and guarantee the safety of construction projects.

Although predicting water surges during tunnel construction is challenging, scholars at home and abroad have recently made significant progress in forecasting such phenomena in water-rich karst tunnels. Wang et al. devised an equation for computing the water surge at the tunnel face when exposed to fault fragmentation using the potential function’s superposition method [2]. Zhang Qingsong used a model test system to investigate the changes in physical quantities such as seepage pressure, stress-strain displacement and surge material in the tunnel perimeter rock after fault exposure in the fault fragmentation zone [3, 4]. Fu Hailin et al. have established a simplified model of tunnel seepage near faults by equating faults with a certain dipping angle in the tunnel cross-section to a vertical dipping angle. They have deduced a formula for calculating the water influx in the tunnel [5]. However, traditional research oversimplifies the geological model, often neglecting the complex geological conditions and hydraulic properties of karst aquifers. In areas of strong karst development, the water-bearing medium exhibits highly non-homogeneous characteristics, resulting in extremely uneven spatial distribution of karst groundwater. The hydrogeological conceptual models and associated mathematical models can often provide an insufficient representation of the characteristics of karst groundwater movement [6]. As a result, current predictions of water inflow in karst tunnels continue to deviate significantly from observations. Therefore, it is crucial to identify water surge conditions systematically in karst tunnels to predict water surge effectively. To achieve this, a more efficient method of water surge prediction in the tunnels needs to be found, and a karst groundwater model should be established within the study area of the tunnels. This will enable a precise description of their structural features and water flow behavior [7, 8].

Currently, numerical simulation has become a widely used tool for predicting tunnel water infiltration in various complex geological environments. Chiu and Chia [9] employed a modular three-dimensional finite difference groundwater flow model (MODFLOW) in order to reproduce the groundwater seepage field whilst simultaneously utilising a drainage package with the aim of predicting the activity of the tunnel. Using the numerical simulation method, Fang Yong [10] conducted a simulation of surge water behaviour in tunnels located in complex tectonic areas.

This study focuses on the issue of water-rich karst present in the Yangmuling tunnel at Maoping Harbor Relief Railway in the Three Gorges Hub. Firstly, the monitoring results of the pore water pressure are analysed, and subsequently, a numerical model is created using the finite element method. The study examines the issue of sudden water influx in the Yangmuling tunnel due to karst formation in the absence of relief holes. The research incorporates numerical calculations to determine the extent of water influx in the karst area of the tunnel without relief holes, providing a robust foundation for simulating the surge water in the karst region. The study conducts a numerical calculation of water ingress in Yangmuling Tunnel in the absence of a water discharge hole. The findings offer valuable reference and guidance for estimating water inflow in karst tunnels and preventing water surge disasters.

2 Project Overview

The Yangmuling Tunnel spans 3648.3 m and is situated in Yiling District, Yichang City, Hubei Province, between Mouyang Village and Taojiaxi. Figure 1 shows the regional geographic location of the tunnel site area. The tunnel inlet’s designed shoulder elevation is at 305.026 m, while the tunnel outlet’s is at 292.743 m. The maximum depth of the tunnel reaches 428.934 m. The strata in the tunnel location are mainly composed of Shipai Formation (∈1t), Shuijingtuo Formation (∈s), and Tianzhushan Formation (∈sh) of the Lower Cambrian alongside Dolomite from the Upper Aurignacian Lampshade Formation (Z2dn). Dolomitic greywacke from the Upper Aurignacian Steep Mountain Tuo Formation (Z2d), conglomerate from the Lower Aurignacian Nantuo Formation (Z1n), and sandstone from the Lower Aurignacian Liantuo Formation (Z1l) can be found in the tunnel area.

Fig. 1.
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Geographical location of the tunnel site area

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Based on the excavation situation on site, the surrounding rock in the tunnel construction section predominantly comprises medium to weakly weathered sandstone. The rock body also features soft and weak interlayers, leading to poor rock stability. Additionally, the rock body exhibits a fragmented structure, with joints and fissures more developed, resulting in poor rock stability and high water content. Due to the non-soluble rock stratum in this section, the surrounding rock does not contribute to tunnel water surge. However, the rock body contains ample bedrock fissure water, resulting in water surges in the form of rain or strand surge, with a minor amount of water surge. Given that the tunnel excavation is about to penetrate the soluble rock layer, the rock mass displays a high degree of fragmentation and there is a plentiful groundwater system. Water disasters in this area often exhibit a high incidence and suddenness, and feature abundant water and sediment. Hence, it is imperative to anticipate the volume of water inflow in the tunnel of the karst water-rich area and present appropriate measures for prevention and management to ensure tunnel construction safety. Figure 2 illustrates the water leakage at the site of the Yangmuling Tunnel.

Fig. 2.
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Water leakage in Yangmuling Tunnel site

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3 Pore Water Pressure Monitoring in Tunnels

3.1 Instrument Introduction and Installation

For this water pressure test on the Yangmuling Tunnel, the JYKYJ-370 vibrating string-type permeameter is utilized to measure fluid pressure. Figure 3 shows a photograph of the vibrating string seepage manometer and a schematic diagram of the installation of the seepage manometer in the tunnel wall.

Fig. 3.
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Photo of sinusoidal osmometer and schematic diagram of installation osmometer

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3.2 Osmotic Pressure Analysis

The water pressure on the surrounding rock of the tunnel section is measured by the seepage manometer, and the monitoring results of the Yangmuling Tunnel exit DK22+354 point 1 and DK22+370 point 2 are shown in Fig. 4.

At measurement point 1 of the Yangmuling Tunnel (Fig. 4a), data shows that as of July 31st, there is a maximum water pressure of 6.84 kPa on the tunnel’s surface at the Yangmuling Tunnel point. This pressure corresponds to a groundwater depth of 0.68 m, and the pore water pressure remains stable at 6. Technical term abbreviations are explained when first used. At pressures ranging from 0 to 6.84 kPa, the pore pressure on the tunnel surface is low, and the water level only reaches 0.6 to 0.68 m. Although there is a consistent water influx in the section, the overall amount is not significant. The main water source comes from the bedrock fissures, which has a relatively minor impact on the tunnel’s construction. The construction of the tunnel is minimally affected. Data from Point 2 of the Yangmuling Tunnel (Fig. 4b), as of 31st July, indicates that the maximum water pressure at the tunnel surface is 2.55 kPa, corresponding to a groundwater depth of 0.26 m. The pore water pressure is stable at 2.0–2.55 kPa, and the tunnel surface pore pressure is relatively low, with a head of only 0.2–0.26 m.

Fig. 4.
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Pore water pressure variation curve of surrounding rock at measuring points 1 and 2 of Yangmuling Tunnel

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4 Numerical Calculation Model for Tunnel Seepage and Surge

4.1 Modelling

To investigate sudden water flow in a tunnel that has a karst pipe in front of the tunnel face, we utilized the Abaqus finite element software to develop a 150 m × 70 m × 70 m three-dimensional geological model based on the actual geological conditions of the Yangmuling Tunnel. Refer to Fig. 5 for the model’s visual representation. The tunnel has a depth of 428.9 m and features a bottom section designed as a side wall, while the top section is shaped like a horseshoe. The tunnel is 6.5 m wide and 8.6 m high, with the side wall measuring 3.25 m in height. In this model, a karst pipeline with a diameter of 6 m is present in front of the tunnel face. The rock layer contains groundwater, with the water level 40 m above the tunnel base. The aim is to simulate the pore pressure distribution of the tunnel, and the seepage and surge of the tunnel water, over a 100-h period after excavation. The peripheral rock and tunnel surfaces serve as free drainage boundaries after tunnel excavation. The tunnel’s left, right, front, and rear boundaries are set to hydrostatic pressure according to the actual groundwater level. The bottom boundary is a no-flow boundary.

Fig. 5.
figure 5

3D geological model and tunnel profile

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4.2 Governing Equation

Effective Stress Principle.

The overall stress upon any plane located inside a saturated geotechnical body can be split into two distinct entities: the effective stress and the pore water pressure [11]. Pore water pressure is defined as such.

$$ \overline{\sigma } = \sigma + (\chi uw + (1 - \chi )ua)I $$
(1)

where σ is the total stress, \(\overline{\sigma }\) is the effective stress, χ is related to the surface tension between the saturated geotechnical body and the liquid-gas, χ = 1.0 for fully saturated geotechnical body and χ = 0.0 for dry geotechnical body.

Seepage Equation.

The permeability of a geotechnical body ought to be determined within a coupled fluid permeability/stress analysis. The permeability law is Forchheimer’s permeability law [12], which defines the permeability coefficient \(\overline{k}\) as:

$$ \overline{k} = \frac{ks}{{(1 + \beta \sqrt {vwvw} )}}k $$
(2)

where: k is the permeability coefficient of saturated geotechnical soil; β is a coefficient reflecting the effect of velocity on the permeability coefficient. When β = 0.0, Forchheimer’s law of osmosis simplifies to Darcy’s law. vw is the velocity of fluid. ks is the coefficient related to the degree of saturation, and ks = 1.0 when the degree of saturation Sr = 1.0.

The flow rate of pore fluid is related to pore pressure [13], i.e.:

$$ vn = ks(uw - u_{w}^{\infty } ) $$
(3)

where: vn is the flow velocity in the direction normal to the boundary, ks is the seepage coefficient, uw is the pore water pressure at the boundary, and \(u_{w}^{\infty }\) is the reference pore pressure.

Calculation Parameter Selection Determination.

According to the geological investigation report of Yangmuling Tunnel, the rock mechanical parameters of the peripheral rock, and the permeability parameters, are as selected and shown in Table 1 below. Due to the development of peripheral rock fissures in the specified section of the model and the high degree of rock fragmentation, the material parameters of the peripheral rock area of class V are chosen for calculation in this study.

Table 1. Rock mechanics parameters of tunnel surrounding rock
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5 Results

5.1 Overall Analysis of the Seepage Field

Overall Analysis of the Water Pressure Field.

When the tunnel is excavated into the karst region, Fig. 6 and Fig. 7 show water pressure cloud maps of various profiles (XYZ = 0, YZX = 0).

Fig. 6.
figure 6

Water pressure cloud map of section XYZ = 0 when the tunnel was excavated to the karst pipeline

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Fig. 7.
figure 7

Water pressure cloud image of YZX = 0 section when tunnel excavation to karst pipeline.

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The water pressure map of the tunnel profile after excavation is shown in Fig. 6. Figure 6(a–d) shows the water pressure map under different distance conditions from the tunnel face to the karst pipe. Before excavation, the maximum pore water pressure is 312.45 kPa, and after excavation, a low water pressure zone is formed in the vicinity of the tunnel, and the outward water pressure gradually increases, and the water pressure distribution is symmetrically distributed. With the discharge of pore water, the pore water pressure of the rock around the hole will eventually be reduced to 0 kPa, which corresponds to the monitoring results of the pore water pressure in the tunnel. At this time, the zone of low water pressure in the karst area expands sharply and shows an irregular shape, the shape of which is related to the distribution of karst caves and karst pipes.

Figure 7 illustrates the water pressure map of the YZX = 0 profile following the tunnel excavation. If the tunnel is not excavated to the karst pipe, a low water pressure zone forms near the cave following excavation, where the water pressure distribution is symmetrically distributed along the Z-axis. When excavating the tunnel to expose the karst pipe, the low water pressure area surrounding both the tunnel and the vault expands. This creates an inverted triangle water pressure distribution on either side of the tunnel, and there is no alteration in the water pressure at the base of the tunnel. These findings suggest that the primary discharge location for karst water is the vault and the two gangs, and there is less water surging at the bottom.

Overall Analysis of the Seepage Field.

The cloud diagram of seepage flow in the unit nodes in the tunnel when the tunnel face is 10 m away from the karst pipe and when the tunnel is excavated to the karst pipe is shown in Fig. 8.

Fig. 8.
figure 8

RVF after tunnel excavation (a: excavate to 10 m from karst pipe; b: excavation to karst pipe)

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From Fig. 8, at a distance of 10 m from the karst pipe, the maximum nodal seepage recorded in the tunnel is a mere 9.95 × 10−2 m3/h. The overall tunnel seepage remains relatively low, with the maximum seepage occurring at the bottom foot of both sides of the tunnel. When the tunnel is excavated up to the karst pipe, there is no drainage hole to constrain the tunnel drainage. Thus, groundwater will gush into the tunnel from the karst pipe. This results in an exponential rise in the water inflow within the tunnel. At this point, the maximum nodal seepage present in the tunnel’s surrounding rock amounts to 39.3 m3/h.

5.2 Water Pressure and Fluid Velocity Analysis

In order to visually represent the changes of the water pressure and velocity fields of the surrounding rock, four probe lines were selected in the range of 50 m in front of the tunnel face to be analysed and studied. The number and location of the selected probe lines are shown in Table 2.

Table 2. Select the number and position of detection lines
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For the four probe lines mentioned above, their corresponding profiles of infiltration water pressure and fluid velocity are displayed in Fig. 9.

Fig. 9.
figure 9

Pore water pressure and velocity curves 50 m in front of the tunnel face

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Based on the data presented in Fig. 9(a), it can be inferred that the water pressure is zero at the tunnel face for both the middle line and top line of the cavern. Additionally, the water pressure fluctuates slightly within a span of 3 m in front of the tunnel face before increasing abruptly. The growth rate then decreases at a distance of 20 m, ultimately stabilising at 348.54 kPa and 321.16 kPa. The water pressure at the tunnel face is 0 kPa for both the bottom line of the tunnel and the top line of the arch. Subsequently, the water pressure gradually rises, slowly increasing until it reaches the maximum values of 381.05 kPa and 295.37 kPa. The water pressure starts at 0 kPa, gradually increases, then slowly rises again, finally tending towards the aforementioned maximum values. Once passing through the karst pipe, water pressure rises sharply and then gradually continues to increase. The water pressure in the tunnel section close to the tunnel face is evidently lower compared to the exterior, and it increases as it moves farther away from the tunnel face.

From Fig. 9(b), it can be inferred that the excavation of the tunnel uncovered the karst pipe, resulting in the maximum fluid velocity of 14.5 m/s and 13.3 m/s at the bottom line and top line of the cavern, respectively, at the tunnel face. Subsequently, the fluid velocity experiences a rapid decrease within four meters in front of the tunnel face, eventually stabilising at 1.7 × 10−4 m/s. The maximum fluid velocity at the midline of the cavern opening is 10 m/s at the tunnel face. The velocity rapidly decreases within 5 m in front of the opening and then changes gradually. The karst pipe does not extend to the top of the tunnel, resulting in minimal variation of fluid velocity at the top. The maximum fluid velocity at the tunnel face is 6.7 × 10–3 m/s. Beyond a range of 5 m in front of the tunnel face, the flow velocity remains consistent among the lines. The highest fluid velocity is observed near the tunnel face according to the tunnel excavation which uncovered the karst pipe, causing a surge in velocity in the karst region immediately ahead of the tunnel face. Then, the velocity quickly drops off and eventually levels out in the surrounding rock segment.

5.3 Surge Analysis

Based on the model calculation, the sum of seepage volume can be acquired from the nodes of the tunnel face and the 2 m perimeter of the hole behind the tunnel face. If the tunnel traverses through the crushed rock body, the estimated tunnel water influx is 35.12 m3/h. On the other hand, if the tunnel face passes through the karst pipeline, the highest influx of water in the tunnel is at 638.5 m3/h.

6 Conclusion

Taking the Yangmuling water-rich karst tunnel boring project as a case study, we constructed a numerical model via the finite element method, which was then combined with the monitoring data on pore water pressure within the tunnel. The findings demonstrate that:

  1. (1)

    The maximum water pressure on the surface of Yangmuling Tunnel is 6.84 kPa, which corresponds to a groundwater depth of 0.68 m. Additionally, the pore water pressure remains stable between 6.0 and 6.84 kPa, and the pore pressure on the surface of the tunnel is minimal.

  2. (2)

    Prior to tunnel excavation, the highest recorded pore water pressure surrounding the tunnel was 312.45 kPa. Post-excavation, a zone of low water pressure develops around the tunnel, and water pressure gradually rises. As pore water is discharged, the rock surrounding the tunnel experiences a reduction in pore water pressure, eventually decreasing to 0 kPa, in accordance with the monitored pore water pressure results within the tunnel. When the excavation of the tunnel reveals the karst pipe, the outpouring of karst groundwater leads to a dramatic expansion in the low water pressure zone within the karst region.

  3. (3)

    As the tunnel is excavated to the karst pipe, the tunnel water inflow increases rapidly, resulting in a maximum nodal seepage of 39.3 m3/h and a maximum water inflow of 638.5 m3/h.

  4. (4)

    Once it passes through the karst pipe, the water pressure in front of the face increases rapidly, followed by a slow increase. The peak velocity of the fluid appears near the tunnel face. As a result of the tunnel excavation, the karst pipe that causes a high flow velocity in the karst area ahead of the tunnel face is revealed. Nonetheless, it then swiftly decreases towards the front of the tunnel face, and then the velocity of the flow starts to change gradually in the surrounding rock section. Afterward, the flow rate in the encircling rock section tends to stabilise.