Numerical Simulation of Karst Groundwater Systems Under Construction of Xiushan Tunnel in Pingyanggai Syncline, Chongqing, China

Abstract

Tunnel construction in karst aquifers can substantially alter groundwater flow systems. In this study, a three-dimensional groundwater flow model based on MODFLOW-CFP was developed to simulate the Pingyanggai synclinal karst system in Chongqing, China, incorporating dynamic tunnel excavation and lining processes. Under natural conditions, groundwater recharge is approximately 4.8 × 10⁴ m³/d and is primarily balanced by discharge to the Yanmenkou and Miaolongtang underground rivers. Tunnel excavation introduced a new drainage outlet, generating an inflow of about 5.6 × 10⁴ m³/d. The two underground rivers exhibited contrasting responses to excavation. Discharge from the Yanmenkou underground river decreased by approximately 6 × 10³ m³/d (about 30%), indicating strong hydraulic connectivity with the tunnel, whereas the Miaolongtang underground river showed only minor changes. The simulated responses were qualitatively consistent with field observations during key excavation stages. These results demonstrate that tunnel excavation modifies not only the overall groundwater balance but also the internal redistribution of discharge pathways within the karst system, providing a quantitative basis for evaluating tunnel-induced hydrogeological impacts in complex karst environments.

1. Introduction

Karst regions formed by soluble rocks (mainly carbonate rocks) cover approximately 12–15% of the Earth’s surface [1,2]. Karst landscapes in China span 3.44 × 10⁶ km², roughly one-third of the national land area, with the highest concentration in Southwest and South China [3]. To accelerate economic development and promote regional integration, tunnels must be built in karst terrains. Water inflow during tunneling is one of the most hazardous geological events in underground engineering, and large-scale water–mud inflow can trigger cascading risks that seriously threaten both construction and subsequent operation [4,5,6]. Accurately predicting tunnel water inflow is therefore both a critical prerequisite for construction safety and groundwater protection and a central, ongoing topic in the academic community [7,8,9].

A karst aquifer comprises a heterogeneous assemblage of media (pores, fissures, fractures, conduits, and caves) that interact and interconnect during fluid flow. Consequently, water alternates between porous and conduit domains and transitions between laminar and turbulent regimes. The pronounced heterogeneity and anisotropy produce complex flow dynamics, which complicates the study and characterization of karst hydrology [10,11,12,13,14,15]. Although precise prediction of water inflow during tunnel construction remains challenging, recent research has advanced along several main lines: empirical, analytical, experimental, numerical, and stochastic methods [16]. Common methods for predicting tunnel water inflow often perform poorly in karst regions. For example, the analytical formula method, which is the most commonly used approach for calculating tunnel water inflow, frequently fails to yield accurate results in such settings [16,17]. Numerical methods offer greater flexibility than analytical or empirical approaches and are therefore better suited for computing water inflow in complex settings, particularly where geological features such as faults and karst caves are present [18]. However, assessing groundwater in karst regions is challenging because measured dynamic flow observations, geophysical surveys, and drilling data are limited, which hinders comparative analysis of hydrogeological conditions across different karst aquifer systems [19]. Therefore, characterizing the internal properties of karst conduit flow media remains challenging. Because karst aquifer systems are complex, results from conventional groundwater models such as MODFLOW often deviate substantially from observed measurements [20]. Scholars at home and abroad have proposed numerical simulation methods and models to describe the movement laws of groundwater flow in complex karst aquifer media [21,22]. The numerical methods mainly include the equivalent porous medium (EPM) model, the dual-continuum (DC) model, and the discrete conduit-continuum (DCC) model [23,24]. The discrete conduit-continuum (DCC) model is capable of reflecting the dual-medium flow behavior of karst aquifers and the spatial distribution of discrete conduits, and can even account for turbulence within the conduits, thus rendering it a widely adopted method in the study of karst groundwater flow [25,26,27]. MODFLOW-CFP(v1.8.00), developed by the United States Geological Survey (USGS), is a representative example of the discrete conduit-continuum (DCC) model [28]. Moreover, the conceptualization of karst underground river conduits using this model has been widely adopted [29]. Given that tunnels have definite positions and geometries, it is feasible to characterize tunnels using the conduit medium. In practical applications, the use of the CFP boundary to characterize tunnels in karst areas has also yielded excellent results [30].

In addition, in reality, the excavation of tunnels is progressive rather than instantaneous. Some scholars have developed analytical solutions to evaluate the transient flow rate varying with the tunnel excavation speed in homogeneous and heterogeneous strata [31,32,33]. The analytical solutions for the groundwater inflow into tunnels in multi—layer aquifer systems are all based on the assumption of a constant groundwater level. However, in general, the decline of the groundwater level near the tunnel is affected by the excavation progress [34]. Zhu et al. [35] proposed to use the water inflow of the excavated section during the construction period to inversely optimize the parameters, and use these parameters for the unexcavated section, and then calculate the subsequent water inflow. With the progress of numerical simulation methods in terms of calculation accuracy and speed, scholars have also made great progress in the research on the dynamic excavation of tunnels using numerical simulation. Different numerical simulation software and methods can all achieve the goal of dynamic excavation, and different simulation software have their own advantages in model construction and processing methods [36,37,38].

The objective of this study is to quantitatively assess the hydrogeological impacts of tunnel construction on karst groundwater aquifers. Using the Pingyanggai Syncline karst aquifer as the study area, a three-dimensional, high-resolution discrete conduit–continuum model was developed with the MODFLOW-CFP package. Both the tunnel and the underground river were represented within the CFP framework. The model was calibrated using hydrogeological parameters and groundwater level observation data. Considering the detailed schedule of tunnel excavation and lining, the construction period was simulated, and the hydrogeological impacts induced by tunnel construction within the karst zone were analyzed and discussed.

2. General Situation of Study Area

2.1. Hydrogeological Conditions

The study area is located in the hinterland of the Wuling Mountains, in the southwestern part of Xiushan County, Chongqing. The core tectonic structure is the Pingyanggai Syncline. Geographically, it extends from 108°53′ to 108°59′ E and from 28°29′ to 28°35′ N, covering an area of approximately 70 km². The mean annual temperature is 15.7 °C, and the mean annual precipitation is 1379.2 mm. The regional topography is mainly controlled by the Pingyanggai Syncline structure and is characterized by medium- to low-altitude mountains and hilly landforms. The terrain is higher in the west and lower in the east, gentle in the north and steep in the south, with elevations ranging from 300 m to 1000 m. Along the synclinal axis, due to mild tectonic compression, the terrain is broad and flat, forming ridge platforms that provide a gentle base level for karst development. On both flanks, influenced by tectonic uplift, the slopes are steep, and deeply incised valleys are well developed. Superficial karst features such as solution grooves are commonly observed along these valleys.

The stratigraphic lithology in the study area is regularly distributed under the control of the Pingyanggai Syncline structure. The exposed strata are dominated by carbonate rocks favorable for karst development, while shales and sandstones appear from the margins of the syncline toward the outer boundary of the study area. The regional surface water system consists mainly of the Rongxi River and the PingJiang River on both sides of the syncline. Within the synclinal area, surface water systems are sparse, but numerous karst springs and underground rivers are well developed, with discharge rates ranging from 5 L/s to 200 L/s. Influenced by rainfall intensity, these groundwater features exhibit rapid fluctuations in flow. As shown in Figure 1a, the study area is surrounded by hydrogeological boundaries, forming a relatively independent hydrogeological unit. The main recharge source at the study site is atmospheric precipitation. The main boundaries of the study site can be divided into the following sections according to their locations:

(1)

Lateral boundaries: The lateral boundaries of the numerical model are defined by the natural boundaries within the study area. The northwestern and southeastern sides are the structural boundaries of the Pingyanggai syncline, while the northeastern and southwestern boundaries are the watersheds along the axial direction of the syncline system.

(2)

Bottom boundary: Since the lowest altitude of the deeply incised rivers around the syncline is 250 m, an altitude of 200 m is used as the bottom boundary of the hydrogeological model. Below this depth, karst development is poor and has little influence on the model, so it is regarded as an impermeable boundary.

(3)

Top boundary: The land surface interpolated at a horizontal resolution of 30 m × 30 m is used as the top boundary. The top unit of the hydrogeological system is recharged by atmospheric precipitation.

The syncline core of the study area consists of carbonate karst fissure water-bearing rock formation strata, and the two wings are composed of non-soluble rock strata, mainly including a total of 8 stratigraphic units, namely T₁d, P₂c, P₂w, P₁m, P₁q, S₂h, S₂x, and S₁b. Among them, the rocks of the Permian and Triassic are mainly limestone and dolomite, while all the rocks of the Silurian are shale or sandstone. It is worth noting that the bottom of the syncline core stratum T₁d is a layer of shale about 25–35 m thick, which has good water-resisting properties. These aquicludes enable the syncline to form a unique “boat”-shaped water storage structure, as shown in Figure 1b. This also determines that the runoff area of groundwater in the Pingyanggai area is mainly the soluble rock strata of the karst trough valley. Meanwhile, such a special structure controls the development of the underground river.

According to the hydrogeological survey, two major karst conduits have been identified within the study area: the Miaolongtang Underground River and the Yanmenkou Underground River as shown in Figure 1b. The delineation of these subterranean rivers is primarily based on the distribution of karst depressions and skylights, as well as the regional groundwater flow patterns.

The Miaolongtang Underground River is developed under the influence of the lower aquiclude of the T₁d formation, extending northward along the axis of the syncline toward a low-lying area. The elevation of its outlet is approximately 580 m, and its discharge is about 0 L/s. The tunnel passes beneath the Miaolongtang Underground River at a point approximately 4.2 km upstream from the outlet, with a vertical separation of about 250 m as shown in Figure 2a.

The outlet of the Yanmenkou Underground River is located on a cliff, at an elevation of approximately 466 m, with a discharge of around 220 L/s. The tunnel passes beneath this underground river at a point roughly 4.5 km upstream from its outlet, with a vertical distance of about 100 m between the tunnel and the river as shown in Figure 2b.

2.2. Water Inflow Situation of Xiushan Tunnel

The G65 Chongqing-Changsha Expressway is a major traffic artery connecting Chongqing and Central-Southern China. The Xiushan Tunnel is a key and challenging control project of the Chongqing-Changsha Expressway. During the construction process, large-scale water inflow disasters occurred in multiple locations of the karst sections on both wings of the syncline in the tunnel, which also led to a decrease in surface water flow and had an adverse impact on the environment.

Xiushan Tunnel is designed as a separated tunnel, extending from the southeast to the northwest. The total length of the right tunnel is 3355 m, and that of the left tunnel is 3345 m. The elevation of the tunnel entrance road surface is 411.20 m, the elevation at the middle of the tunnel is 440 m, and the elevation of the exit is 421 m. Construction of the tunnel started in July 2006 and was completed and opened to traffic in 2010.

During the construction of the tunnel, water inflow and gushing occurred in six sections. The specific locations can be seen in the section of Figure 1b, and the specific water inflow volumes and times can be found in Figure 1b. Multiple large-scale water gushing events have occurred at the G5 water gushing point. The specific water gushing situations are as follows: On 3 January 2008, when the excavation reached near G5, the first geological disaster of mud and water inflow occurred, with an initial water inflow of nearly 100,000 m³/d. Around 24:00 on the night of 9 November 2008, a second geological disaster of mud and water inflow occurred at the same location, with an initial water inflow of about 350,000–400,000 m³/d. Around 14:00 on 25 November 2008, a third geological disaster of mud and water inflow occurred at the same location mentioned above, with an initial water inflow of about 100,000 m³/d. Among them, the main cause of the water inflow in the second large-scale water gushing event at the G5 water gushing point was heavy rainfall. Under the action of external forces (mainly high water head pressure), the rock mass was fractured, deformed and damaged, and gradually connected. After forming a unified passage, the karst water stored in the syncline structure gushed into the tunnel through this passage.

3. Numerical Simulation Conceptualization

3.1. Conduit Flow Simulation

In this study, the discrete pipe-continuous medium (DCC) model MODFLOW-CFP was used to model. Tunnels and underground rivers are considered as pipelines, which are generalized by CFP boundaries. MODFLOW-CFP is modified based on the USGS MODFLOW-2005 program, in which the CFP subroutine is added to simulate pipe flow in karst aquifers separately.

When MODFLOW-CFP is used to simulate the karst water-bearing system, the karst water-bearing system is generally divided into two parts: the fissure system and the pipeline system. The fissure system includes the rock matrix and some micro-cracks in the water-bearing system, while the pipeline system refers to the large fissures and corrosion pipes in the water-bearing system. Under normal circumstances, the groundwater flow rate in the fracture system is slow and obeys Darcy’s law. It can be generalized to an equivalent porous medium and simulated using the traditional three-dimensional groundwater flow equation [39]:

$${\displaystyle \frac{\partial }{\partial x}}\left(K_{xx}{\displaystyle \frac{\partial h}{\partial x}}\right)+{\displaystyle \frac{\partial }{\partial y}}\left(K_{yy}{\displaystyle \frac{\partial h}{\partial y}}\right)+{\displaystyle \frac{\partial }{\partial z}}\left(K_{zz}{\displaystyle \frac{\partial h}{\partial z}}\right)\pm W=S_s\left({\displaystyle \frac{\partial h}{\partial t}}\right)$$

(1)

Among them: $K_{xx}$, $K_{yy}$, $K_{zz}$ are the permeability coefficients along the X, Y, and Z directions in the main direction of penetration (L T⁻¹); h is the groundwater head (L); W is the source-sink term (T⁻¹); S_s is the water storage coefficient (L⁻¹); t is the time (T).

The conduit system is generalized into multiple segments of circular conduits. Depending on the specific water level in each conduit, the conduit may be in a confined or unconfined state. For confined conduits where groundwater flow is laminar, the conduit flow is calculated using the Hagen–Poiseuille equation [40]:

$$Q_{ip}=-A{\displaystyle \frac{g{d}^2\partial h}{32\nu \partial x}}=-A{\displaystyle \frac{\rho g{d}^2\Delta h}{32\mu \tau \Delta l}}$$

(2)

When groundwater flow in the conduits is turbulent, the conduit flow is calculated using the Darcy-Weisbach equation:

$$Q_{ip}=-2A\sqrt{{\displaystyle \frac{2\left|\Delta h\right|gd}{\Delta l\tau }}}\log \left({\displaystyle \frac{k_c}{3.71d}}+{\displaystyle \frac{2.51v}{\sqrt{\frac{2\left|\Delta h\right|g{d}^3}{\Delta l\tau }}}}\right){\displaystyle \frac{\Delta h}{\left|\Delta h\right|}}$$

(3)

where d is the conduit diameter (L); A is the cross-sectional area of the conduit (L²), $A=\pi d^2/4$; $\rho$ is the groundwater density (M/L³); $g$ is the gravitational acceleration (L/T²); $\nu$ is the kinematic viscosity coefficient (L T²), $\nu =\mu /\rho$; $\partial h$/$\partial x$ is the hydraulic gradient of the conduit, $\partial h$/$\partial x$ = $\Delta h$/$\tau \Delta l$, $\tau$ is the tortuosity of the conduit, dimensionless, l is the actual length of the conduit (m).

There is a flow exchange between each conduit node and its corresponding fracture grid, and the exchange flux ($Q_{ex}$) has a first-order linear relationship with the head difference between the two nodes [28]:

$$Q_{ex}={\alpha }_{j,i,k}\left(h_n-h_{j,i,k}\right)$$

(4)

where: ${\alpha }_{j,i,k}$ is the conduit wall conductance (L²T^−l) at MODFLOW grid cell j, i, k; $h_{j,i,k}$ is the groundwater head (L) at MODFLOW grid cell j, i, k; $h_n$ is the groundwater head (L) at the corresponding conduit node.

During the simulation, the conduit wall conductance ${\alpha }_{j,i,k}$ can either be auser-defined constant or a variable, which is calculated from the permeability coefficient of the fracture grid where the conduit is located and the specific internal parameters of the conduit according to the following equation [28]:

$${\alpha }_{j,i,k}={\displaystyle \sum _{ip=1}^{np}\frac{{\left(K_w\right)}_{j,i,k}\pi d_{ip}\frac{1}{2}\left(\Delta lip\tau ip\right)}{r_{ip}}}$$

(5)

where: np is the number of conduits connected to conduit node j, i, k, ${\left(K_w\right)}_{j,i,k}$ is the hydraulic conductivity of the wall (L T⁻¹); $d_{ip}$ is the diameter (L) of the ip-th conduit; $\Delta l_{ip}$ is the straight-line distance (L) between the two conduit nodes connected by the ip-th conduit; ${\tau }_{ip}$ is the tortuosity of the ip-th conduit; $r_{ip}$ is the radius (L) of the ip-th conduit.

In the conduit network, water exchange between conduits and the matrix occurs at the nodes. For each conduit node, the equation is established based on the principle of mass conservation [28]:

$${\displaystyle \sum _{i=1}^{np}{Q}_{ip}}-Q_{ex}+Q_R\pm Q_s=0$$

(6)

where: $Q_{ip}$ is the difference between the inflow and outflow rates (L³ T⁻¹) of water at the conduit node; $Q_{ex}$ is the exchange flux (L³ T⁻¹) between the conduit node and the fracture grid node; $Q_R$ is the rainfall recharge rate (L³ T⁻¹) at the conduit node; $Q_s$ is the change rate of water storage (L³ T⁻¹) in the conduits adjacent to the conduit node; $Q_s$ is derived from the difference in water volume within the conduit between time t₀ and t₁:

$$Q_S={\displaystyle \frac{V_{t1}-V_{t0}}{t_1-t_0}}$$

(7)

where: V_t is the water volume (L³) in the conduit, t is the time (T).

3.2. Dynamic Tunnel Excavation

In this study, the CFP (Conduit Flow Process) pipeline model is employed to simulate and analyze water inflow during and after tunnel excavation. Since tunnel excavation is a dynamic, progressive process carried out section by section, the continuous advancement of the tunnel face causes the stress field, hydraulic field, and boundary conditions of the surrounding rock mass to evolve accordingly. Based on this characteristic of dynamic evolution, a CFP-based dynamic modeling approach for tunnel excavation is proposed in this study. Specifically, when the tunnel advances to a particular computational unit, the continuous medium mesh of that unit is converted into a CFP boundary unit to simulate the formation of a water-conducting boundary following excavation at that location as shown in Figure 3.

Because the actual tunnel cross-section is horseshoe-shaped rather than circular, an equivalent representation of its hydraulic characteristics is required within the MODFLOW-CFP framework, where conduits are idealized as circular sections. In this study, the tunnel diameter was defined based on the concept of an equivalent hydraulic diameter, which preserves the hydraulic radius and flow conveyance capacity of the actual tunnel cross section under both pressurized and free-surface flow conditions [41].

In addition, to more accurately represent the actual engineering conditions, the model incorporates the blocking and regulatory effects of the tunnel lining structure on groundwater flow. In this study, it is specified that when the tunnel advances to the next excavation section, the conduit wall conductance—which characterizes the degree of hydraulic connectivity between the CFP conduits and the surrounding medium—in the previously excavated and lined tunnel section is reduced to 0.01 times its original value. This adjustment effectively simulates the mitigating effect of the tunnel lining on water inflow after its installation.

3.3. 3D Geological Model of Syncline Aquifer

To better characterize the karst aquifer and syncline morphology, we constructed an implicit 3D geological model using Leapfrog Geo [42]. In order to make the 3D geological model more accurate, 110 virtual boreholes were set up, which were evenly distributed in the core of the syncline of the Pingyanggai, as shown in Figure 4a. Through these boreholes, the blank 3D geological model is interpolated, and the results are obtained 3D geological model of the study area shown in Figure 4b. Then, we transform the 3D geological model into a Grid that Modflow can recognize, discretize the grid into 40 m × 40 m, and divide it into 20 layers vertically, a total of 1,684,890 cells as shown in Figure 4c. In addition, tunnels and underground river pipes are represented as discrete pipes that exchange water with bedrock grids.

4. Model Calibration and Groundwater Initial Flow Field

4.1. Model Calibration

The simulation is divided into two main stages according to the construction progress: the pre-tunnel construction stage and the tunnel construction stage (which lasts about 4 years). In the first stage, the model was calibrated using groundwater level data collected from observation wells in the study area. In the second stage, transient simulation is performed based on the construction progress to study the impact of tunnel construction on the groundwater system.

According to the hydrogeological boundary conditions, the Miaolong Stream is taken as the River boundary, and the water head value is obtained by linear interpolation according to the river position and water level observation. The surface watershed on the north and south of the simulation area is the area with the highest model elevation, with the elevation range of 700–900 m on the south side and 600–800 m on the north side, which is regarded as the No-flow boundary. Owing to the limited computing power of the numerical model, the soluble rock units (P, T₁d)—as the primary research objects within the study area—were designated as active cells to participate in the calculation. The Silurian (S) strata, which have a minor impact on the model, were also defined as inactive cells, and the remaining external units were treated as inactive cells as well, being excluded from the calculation.

In this study, monthly mean precipitation was used as the recharge input for the model. This temporal resolution was selected to be consistent with the definition of the nine stress periods in the transient flow simulation, which represent different stages of tunnel excavation and lining during construction. The precipitation intensity (P_i) of each region is obtained from hydrological data. The infiltration coefficient C_i = R_i/P_i was set as the parameter to be calibrated, where Ri[LT⁻¹] is the effective recharge intensity.

Karst pipes allow rapid drainage of groundwater. The direction and elevation of the underground river system were determined by hydrogeological surveys and tunnel excavation revelations. Important model parameters for pipe flow include pipe length, diameter, roughness, and Reynolds number. The relative roughness of a conduit is defined as the ratio of the average height of the microtopography on the conduit wall to the diameter of the conduit. The diameter of the underground river conduit was determined based on tracer test results calculated using Qtracer2 [43], and field investigations further indicated that the outlet diameter of the underground conduit is also approximately 3 m. According to the pipeline outlet section, the average height of the karst pipeline microtopography is approximately 0.8 m, and the average relative roughness is 0.25. For comparison, Jeannin reported a relative roughness value of 0.25 based on measurements conducted in different karst regions [44]. The relative roughness of the tunnel should be much smaller than that of the karst pipe. The average height of the tunnel wall microtopography is estimated to be 0.04 m, while the tunnel diameter is 8 m. Therefore, this study takes 0.005 as the relative roughness of the tunnel. This paper takes 2000 and 4000 as the lower critical Reynolds number and the upper critical Reynolds number respectively [28]. Conduit wall conductance (K_exchange) is a key parameter in the CFP model. Its value was quantified using Equation (5) and further constrained by ranges reported in previous studies under different hydrogeological conditions [30,41,45,46,47]. The parameters of karst pipes and tunnels are listed in

Table 1. Parameters of karst conduits and tunnels.

Name	Length (km)	Diameter (m)	Roughness Height	K_Exchange (m2/d)
Miaolongtang Karst conduits	7253	3	0.25	2
Yanmenkou Karst conduits	8613	3	0.25	1.5
Tunnels	3358	8	0.005	10

.

The groundwater level data of four observation wells collected in the study area in 2006 and the flow rate of the underground river were used to calibrate the model, as shown in Figure 5. Since the location of the drilled holes is too concentrated, the calibration of the model is carried out manually, using the trial-and-error method. Since groundwater level observations were acquired at different locations and were measured in a single session (not continuously), we used a steady-state model for calibration. The calibrated parameters include the permeability coefficient and effective infiltration coefficient. According to the available geological information, all strata are divided into 3 groups, each with a unique permeability coefficient, such as Figure 5a, and the study area is divided into three recharge zones according to the surface topography and lithology Figure 5b, each supply belt has a unique effective infiltration coefficient.

Refer to

Table 2. Hydraulic conductivity of hydraulic parameter zone.

Zone	Main Lithology	Strata	Hydraulic Conductivity K (m/d)
HC1	Limestone	T1d2	0.612
HC2	Limestone and Dolomite Shale	P2c, P2w, P1m, P1qP1l	0.483
HC3	Mud shale	T1d1	0.005

for permeability coefficient after calibration of each parameter band. The permeability coefficient after calibration is in the same order of magnitude as that of the borehole test. The effective infiltration coefficients of R1, R2 and R3 are 65.0%, 77.2% and 43.1% respectively. The effective infiltration coefficient of R3 is relatively small, which is mainly due to the large average topographic slope in this area. R1 and R2 have higher effective infiltration coefficients because they are mostly located in trough valleys and depression sinkholes are developed.

Compare the observed water level with the simulated water level, as shown in Figure 6a. The simulated groundwater levels deviate from the observed data by less than 10 m in most cases. The observed groundwater level ranges from 600 m to 700 m. Considering that the elevation interpolation error is large due to the highly heterogeneous karst aquifer and complex surface topography, the root mean square error (RMSE) is considered acceptable when the error is less than 2% of the observed data [27,30]. This standard means that the RMSE should be less than 15 m. Therefore, in our calibration, an RMSE of 5.4 m is acceptable. In addition, the steady-state simulation results for the two underground rivers were compared with the observed data, showing relatively small errors. As illustrated in Figure 6b, the model successfully reproduces the discharge behavior of the two underground rivers in the natural seepage field prior to tunnel excavation.

4.2. Numerical Simulation of Initial Groundwater Flow

The model of the tunnel before excavation was used to simulate the distribution of the initial groundwater head in the study area, such as Figure 7a shows that there are two main underground river systems in the simulation area, namely the Yanmenkou underground river and the Miaolongtang underground river, which are distributed in a southeast direction and are consistent with the direction of the regional tectonic line. Under natural conditions, groundwater runoff from the watershed in the southwest direction to the northeast, the hydraulic gradient is relatively gentle as a whole, and the gradient steepening phenomenon occurs locally due to the development of karst pipelines, and the isowater level line converges to the underground river in a “V” shape, indicating the trend of centralized discharge of groundwater into the pipeline. The Yanmenkou underground river has a stronger catchment capacity than the Miaolongtang underground river, as illustrated in Figure 7b,c, because it drains a larger contributing area and its conduit sits at a lower elevation. The water accumulation effect of the two underground rivers is more obvious at the entrance section, and the convergence effect of the outlet section is weakened, which is caused by the increase in the water level in the pipeline at the outlet section. The difference between the simulated initial groundwater level and the observed initial groundwater level is small, and both are at 180–200 m above the tunnel elevation, as shown in Figure 7d.

5. Numerical Simulation of Groundwater Flow During Tunnel Construction

5.1. Transient Simulation Settings

Considering the construction progress of Xiushan Tunnel, excavation and lining are carried out from both ends, that is, the entrance and exit of the tunnel. However, since only the soluble rock part is used as the active unit, the actual mileage of the tunnel in the model is only 1539 m. The excavation and lining progress of this 1539 m are divided into 9 small sections. The sections excavated in the previous period will be lined later according to the excavation situation. We divide the tunnel construction progress into There were 4 periods: August 2007–November 2007 (the southeast part of the tunnel was excavated first), November 2007–December 2008 (the tunnel was excavated in the northwest, but the tunnel was stopped after encountering water inflow in the southeast). excavation), December 2008–March 2009 (the tunnel was excavated in the southeast, but the excavation was stopped after encountering water inflow in the northwest), March 2009–January 2010 (the tunnel excavation was completed, only lining was carried out). The corresponding excavation and lining situations in the 4 periods are shown in Figure 8.

Driven by the average monthly rainfall and considering the tunnel construction progress, a groundwater unsteady flow simulation was conducted using the natural seepage field as the initial hydraulic head. Tunnel water inflow is mainly controlled by construction progress and precipitation. As shown in Figure 9, the tunnel water inflow predicted by the MODFLOW-CFP model is in good agreement with the actual measured water inflow.

As the tunnel excavation progressed, the water inflow increased significantly during the second excavation stage (after November 2007), reaching a peak value of approximately 100,000 m³/d, and then gradually declined to approximately 20,000 m³/d due to the completion of the lining and the depletion of groundwater reserves. The rapid increase in water inflow is mainly due to the underground river at Yanmenkou and the water storage structure in the karst syncline exposed by the tunnel. A heavy rainfall-induced water inflow event occurred on 9 November 2008 (maximum about 350,000 m³/d, as shown in

Table A1. The water gushing situation in the tunnel.

Tunnel Water Inflow Point	Inflow Rate (m3/d)	Time
G1	13,400–13,200	December 2007
	3400	January 2008
G2	140	June 2008
G3	585	September 2008
G4	5 × 104	18 April 2009
	4 × 104	17 October 2009
G5	1 × 105	3 January 2008
	3.5 × 105	9 November 2008
	8 × 104	25 November 2008
G6	1.2 × 104	September 2007

) involving surrounding rock destruction and watershed catchment process, which is beyond the scope of this model, so it is not discussed.

In the third stage, the tunnel completed the lining of the water inflow point below the Yanmenkou Underground River. During the excavation on the northwest side, a relatively large water inflow was also encountered below the Miaolongtang Underground River, which caused the excavation to stagnate, but its scale was much smaller than the water inflow below the Yanmenkou Underground River. After the tunnel was completed, lining work began in the fourth stage, that is, in March 2009, and the water inflow gradually decreased.

The simulated groundwater inflow obtained from the transient flow model shows good agreement with the observed inflow, with a Nash–Sutcliffe efficiency (NSE) of 0.98 and a coefficient of determination (R²) of 0.99. It should be noted that, in the modeling process, tunnel excavation and lining were updated segment by segment as excavation progressed, resulting in a stepwise variation in the simulated inflow. In addition, within each sub-period, the inflow exhibits a correlation with precipitation. However, overall, the influence of precipitation on groundwater inflow is weaker than that of tunnel excavation progress on inflow variation.

5.2. Impact of Tunnel Construction on Groundwater Levels

Tunnel excavation created a concentrated drainage pathway, forming a cone of depression that caused a pronounced groundwater-level decline. Taking the excavation schedule into account, we simulated water-level change at five sequential moments, shown in Figure 10a–e; the corresponding excavation and lining stages are illustrated in Table A1. The maximum drawdown above the tunnel reaches 70 m, a consequence of long-term dewatering driven by the advancing face.

Figure 10a represents the first excavation stage, when the area of drawdown is still limited. In the second stage as shown in Figure 10b, excavation halts on the south-eastern side because of a major inflow from the Yanmenkou underground river, while the north-western side continues to advance. The south-eastern sector therefore experiences a sharp water-level drop, whereas the north-western drawdown zone expands only gradually and remains moderate.

During the third and fourth stages as shown in Figure 10c–e, excavation in the north-west is stopped by heavy inflows, and the south-eastern side is driven to breakthrough while simultaneous lining proceeds. Because the Yanmenkou conduit is now hydraulically connected to the tunnel, it continues to drain into the opening, so drawdown in the south-east keeps deepening. Thanks to the overlying aquitard T₁d¹, the T₁d aquifer remains unaffected.

The tunnel’s impact is most pronounced along the Yanmenkou underground river as shown in Figure 10g,i: the cone of depression propagates roughly 3 km along the conduit and even perturbs surface-water levels. In contrast, the Miaolongtang underground river experiences limited disturbance; drawdown greater than 5 m is neither observed in the conduit nor in its immediate vicinity. Nevertheless, prolonged drainage could eventually influence the Miaolongtang system as well.

5.3. Impact on Flow in Karst Conduits

Karst conduits are critical features controlling groundwater flow within karst aquifers. In this study, the Yanmenkou and Miaolongtang underground rivers constitute the main karst conduits within the hydrogeological unit. The discharge variations at Yanmenkou and Miaolongtang are shown in Figure 11. The Yanmenkou underground river discharge is influenced by both precipitation and tunnel excavation, whereas the Miaolongtang underground river discharge is influenced primarily by precipitation and is only weakly affected by tunnel excavation. Specifically, Yanmenkou exhibits large discharge fluctuations: prior to tunnel excavation the discharge was approximately 20,000 m³/d; as excavation progressed the discharge gradually declined, and once the tunnel had been excavated beneath the conduit the discharge fell precipitously to about 13,000 m³/d. After tunnel lining, the discharge recovered slightly, but because a hydraulic connection with the tunnel had been established, part of the conduit flow continued to be diverted into the tunnel. By contrast, Miaolongtang showed no substantial change in discharge, which is attributable to the effective aquitard properties of T₁d¹ and to the approximately 250 m vertical separation between the tunnel and the Miaolongtang conduit. These modeled responses show qualitative consistency with field records. Specifically, a significant water inflow into the tunnel was reported in January 2008, after which the discharge of the Yanmenkou underground river decreased markedly, whereas no obvious change was observed in the discharge of the Miaolongtang underground river. Similarly, during tunnel excavation beneath the Miaolongtang conduit in April 2009, a large tunnel inflow occurred, but the Miaolongtang discharge remained essentially stable. Field observations suggest that this inflow was primarily associated with fracturing within the synclinal-axis rock mass, indicating that the event did not directly affect the overlying Miaolongtang aquifer.

5.4. Groundwater Flow Budgets

To quantitatively assess the impacts of tunnel excavation on the groundwater system, Figure 12 illustrates the redistribution of the groundwater budget in the Pingyanggai synclinal karst system induced by tunnel excavation. Under natural conditions, groundwater recharge (4.7 × 10⁴ m³/d) is mainly balanced by discharge to the Miaolongtang and Yanmenkou underground rivers and surface river drainage. After tunnel excavation, a new drainage outlet is introduced, resulting in tunnel inflows of about 5.6 × 10⁴ m³/d and a noticeable reduction in groundwater storage (5.3 × 10⁴ m³/d).

The temporal evolution of the water budget components further reveals contrasting responses of the two underground river systems. The discharge of the Yanmenkou underground river shows a pronounced decline following tunnel excavation, with a reduction of approximately 6.0 × 10³ m³/d, indicating strong hydraulic connectivity with the tunnel. In contrast, the Miaolongtang underground river exhibits only minor changes in discharge (3.3–3.4 × 10³ m³/d), suggesting a weaker hydraulic response. These results demonstrate that tunnel excavation alters not only the total groundwater balance but also the internal redistribution of discharge pathways.

5.5. Limitation

Several assumptions and limitations of this numerical study warrant attention. First, continuous monitoring of hydrogeological information should be further enhanced; a paucity of groundwater observation and monitoring data—an issue common to many field studies of karst aquifers—necessitated calibration of hydrogeological parameters using steady-flow models that included groundwater level observations. This approach may introduce errors in estimated parameters and increase uncertainty in predicted groundwater fluxes. In the CFP module, conduits are treated as cylinders for calculation, whereas tunnel cross-sections are often horseshoe-shaped. In the current conduit flow model, the tunnel diameter can only be assigned by using an equivalent hydraulic radius, which may lead to certain errors. In addition to the conduit diameter, other important parameters, such as the conduit wall conductance (K_exchange), also have an impact on the model, and their effects are worth further discussion. Moreover, additional data collection and modeling are required to assess how spring discharge responds to tunnel construction. Second, given the protracted construction schedule of the tunnel (construction span > 2 years), the transient-flow model approximated the simulation period by subdividing it into shorter segments; this approximation may also introduce errors. In the present simulations, groundwater is allowed to enter the tunnel represented by the discretized conduit network abstraction of MODFLOW-CFP, whereas actual inflows along the tunnel lining often occur as spatially heterogeneous, “point-like” jets along the tunnel axis. Limited computational resources and a lack of detailed data on high-permeability fracture zones precluded representation of specific discharge points at scales below those of the rock mesh. Finally, scenarios in which extreme rainfall events induce very high pore pressures, cause host-rock fracturing, and produce large-scale catastrophic inflows cannot be simulated here. Modeling extreme rainfall would require augmenting the modelled recharge with tank models or SWAT-based watershed analysis, and host-rock fracturing cannot be represented within the finite-difference framework employed [48].

6. Conclusions

The Xiushan Tunnel crosses beneath the Pingyanggai syncline and intersects two karst aquifers within the T₁d² and P formations, where the Miaolongtang and Yanmenkou underground rivers are distributed. During tunnel construction, multiple groundwater inflow events occurred, with a maximum inflow rate reaching 1 × 10⁵ m³/d. The complex regional hydrogeological conditions pose significant challenges for numerical simulation. In this study, a discrete–continuum coupled modeling approach was adopted, in which both the tunnel and karst conduits were conceptualized as MODFLOW-CFP boundary conditions to conduct numerical simulations. The main conclusions are as follows.

(1) Based on comprehensive geological data, 110 virtual boreholes were constructed to build a three-dimensional geological structural model comprising 1,684,890 grid cells, allowing for a refined representation of the synclinal structure. Two groundwater flow models were further established: a steady-state model under natural conditions without the tunnel, and a transient model under tunnel construction conditions.

(2) In the steady-state model without the tunnel, hydraulic conductivity and rainfall infiltration coefficients were calibrated using observed borehole water level data. The root mean square error (RMSE) of the model reached 5.4 m, indicating a good fit. The model successfully reproduced the groundwater flow pattern converging toward the underground rivers.

(3) In the transient model under tunnel construction conditions, the two-year construction process was divided into nine stress periods. By dynamically updating the MODFLOW-CFP boundary conditions, the excavation and lining processes of the tunnel were continuously simulated, achieving accurate reproduction of the groundwater inflow process. the Nash–Sutcliffe efficiency (NSE) of 0.98 and the coefficient of determination (R²) of 0.99. The model successfully reproduced the scenario in which the tunnel encountered an underground river, causing the inflow rate to increase sharply from 1.2 × 10⁴ m³/d to 9.3 × 10⁴ m³/d. The results indicate that excavation and lining processes constitute essential boundary conditions in numerical simulations of tunnel water inflow.

(4) The model depicts continuous groundwater drainage during construction, leading to a regional groundwater level decline with a maximum drawdown exceeding 40 m and an affected area of 2.3 km². This result is consistent with the observed drying range of springs induced by tunnel drainage. The simulation indicates that the discharge of the Yanmenkou underground river decreased by 30%, whereas the flow of the Miaolongtang underground river did not show a significant reduction, owing to the effective hydraulic barrier provided by the low-permeability T₁d¹ formation. Water budget analysis shows that the total tunnel drainage reached 5.1 × 10⁷ m³, accounting for 36% of the total groundwater discharge. Compared with natural conditions, tunnel drainage replaced underground rivers as the dominant groundwater discharge pathway.

This study employed MODFLOW-CFP to simulate groundwater flow in karst aquifers under the influence of tunnel drainage and quantitatively revealed the spatiotemporal characteristics of disturbances to the synclinal groundwater system induced by tunnel construction. The results provide a scientific basis for the prevention and control of tunnel water inflow in similar geological settings.