The Distribution Pattern of Calcium Carbonate Crystallization in Tunnel Drainage Pipes

Abstract

Severe blockages of tunnel drainage systems greatly affect the lining structure of the tunnels, thus jeopardizing their stability and safety. In order to study the blockages of tunnel drainage pipes, the flow rate of a calcium carbonate crystal tunnel was measured in the mountainous area of Southwest China. According to the actual flow velocity results, numerical simulation was combined with finite element software (ANSYS Fluent). This analyzed the calcium carbonate crystallization near the interface of the tunnel drainage pipe. The results are as follows: (1) for both the Y-shaped three-way pipe and the T-shaped pipe, the values of maximum water velocity are similar but occur at different locations. At the interface of the transverse drainage pipes, flow velocity is the highest; (2) at the three-way joint segment, the water that flows in the longitudinal drainage blind tube is influenced by the water coming from the annular drainage blind tube. At the interface of the transverse drainage pipe, water flows at a lower speed in the Y-shaped three-way pipe than in the T-shaped pipe—the difference is about 3.75 times; (3) the smoothness of calcium carbonate deposition is correlated with water velocity and the content of calcium carbonate. The calcium carbonate crystal will occupy a larger space at locations with a higher calcium carbonate content and a lower flow velocity; (4) the drainage capacity of tunnel drainage pipes declines most when the volume fraction of calcium carbonate reaches 80%. Compared with the situation when calcium carbonate does not exist, the drainage capacity decreases by 84.78% for T-shaped pipe and by 77.64% for Y-shaped three-way pipe when the volume fraction of calcium carbonate is 80%.

1. Introduction

As the number of tunnel construction projects has increased in recent years, tunnel diseases become the primary challenge that Chinese engineers face during tunnel construction. Karst water is rich in calcium ions (Ca²⁺), which are easily crystallized and deposited on the pipe walls of the karst tunnels. Such deposition usually causes clogging of the tunnel and jeopardizes its load-bearing capacity; therefore, the blockage of tunnel drainage systems hinders the normal construction and operation of karst tunnels [1,2,3,4]. Consequently, researchers around the world have conducted extensive studies on tunnel crystallization and investigated its influencing factors.

Zhang Xuefu et al. [5] investigated multiple tunnels in Chongqing City in China to analyze the composition and source of blockage materials in tunnel drainage pipes, finding that crystal blockage was common in tunnel drainage systems. According to X-ray diffraction (XRD) analysis, the crystalline deposits in drainage pipes are mainly made of calcite. According to previous studies, calcium carbonate has three types of crystalline polymorphism: calcite, aragonite, and vaterite, each with different properties [6,7,8,9]. Ye Fei et al. [10] developed a tunnel model to simulate crystallization in the drainage systems during lining cracking or water leakage, with results showing that crystallization was closely related to the concrete sprayed for initial support. Dietzel and Rinder et al. conducted field experiments in tunnel drainage pipes [11,12,13]; they discovered that before entering the drainage system, groundwater that passed through the initial shotcrete would form the crystals, which were the main source of crystalline deposits.

Several studies have examined the influencing factors on crystal blockages in tunnel drainage systems. Zhai Ming [14] conducted experiments and determined that the main factors that affect the blockages in drainage systems include CO₂ concentration, temperature, pressure, pH value, and the concentrations of calcium and magnesium ions that the groundwater contains. Through both field and laboratory experiments on tunnels in Southern China, Qian Zhenyu et al. [15] found that the amount of crystallization in the pipe was closely related to the water velocity and the purity of CaCO₃ crystals. Xiang Kun et al. [16] established a model of tunnel drainage pipes under alkaline conditions to study the influence of pH values on the amount of crystallization. According to the results, if other conditions were the same, crystallization would occur more often when pH values were higher in the pipes. The amount of crystallization depended on the coupled impact of pH values and water-filling conditions. After statistical analysis of crystallization in French tunnels, Chen et al. [17] discovered that crystallization was closely related to the surrounding rock’s permeability coefficient and calcium carbonate content. It was also correlated to the tunnels’ lining materials and geometric dimensions. By analyzing the microenvironment of karst tunnels, Lu Guannan et al. [18] concluded that crystal blockages would occur less frequently under factors such as low temperature, low concentration, low flow rate, acidic environment, and low CO₂ partial pressure. These factors would effectively prevent crystallization and precipitation in tunnels. Based on actual engineering projects, Pu Chunping et al. [19] looked at the deposition of calcium carbonate scale in drainage pipes and found that the initial shotcrete used in tunnels raised the pH level of the rock water around it, which sped up the crystallization of the drainage pipe. Liu Zhan et al. [20] synthesized a copolymer of sodium (IA/SMAS), an environmentally friendly water-treatment agent, and conducted indoor scale-resistance experiments; this environmentally friendly scale inhibitor has good scale resistance. Huang Shaoxiong et al. [21] studied the influence of an electric field on calcium carbonate crystallization in tunnel drainage pipes, and under certain voltage conditions, the electric field can better prevent calcium carbonate crystallization. Li Wei et al. [22] studied the crystalline growth of calcium carbonate in karst water on the concrete surface, and the results showed that the crystalline growth of calcium carbonate involved three stages.

Studies on crystal blockage in tunnel drainage systems, both domestic and international, adopt various models and experiments to examine the causes of crystallization and the factors that influence it. In addition, there is a lack of a theoretical framework to analyze the research problems. To form the framework, we first need to analyze the distribution of crystallization in tunnel drainage systems. Therefore, this study uses numerical models to simulate the distribution of calcium carbonate—the main component of crystallization—in tunnel drainage systems and analyzes its impact on blockages.

2. Determination of Flow Velocity in Tunnel Drainage Systems

In tunnel drainage systems, the groundwater velocity is influenced by topography, geomorphology, and atmospheric conditions (Figure 1). As the water velocity in the drainage pipe cannot be directly measured by a flowmeter, we used a graduated cylinder to measure the flow volume (i.e., flow rate) within a certain interval of time and calculated the cross-sectional area of the drainage pipe based on the water depth and diameter of the drainage pipe. Then, we applied the numbers into Formula (1) to obtain the groundwater velocity in the drainage pipe. Table 1 shows the data from the on site measurements.

$$v=\frac{Q}{A}$$

(1)

where

v represents the flow velocity;

Q denotes the flow rate which is the volume flow rate;

A represents the cross-sectional area of the flow passage.

According to Table 1, groundwater velocity may change at different locations in the tunnel due to the complex geological structure of karst terrains and seasonal variation in precipitation; however, the average flow velocity in the tunnel remains relatively constant, ranging between 0.4 m/s and 0.6 m/s.

Table 1. Statistical analysis of groundwater flow velocities in karst tunnel drainage systems.

Velocity Check Locations (Tunnel Longitudinal Drainage Pipe)	Zhongliangshan Tunnel (Chongqing)	Station-to-Station Tunnel from Danzishi to Tushan (Chongqing)	Station-to-Station Tunnel from Chongqing North Station to Yulu Station (Chongqing)	Tuzhu Tunnel (Chongqing)	Shisungou Tunnel (Guizhou)
Velocity Check Time	August 2016	June 2018	June 2018	January 2022	May 2022
Flow Velocity (m/s)	0.2	0.45	0.35	0.8	0.46
	0.31	0.37	0.27	0.51	0.38
	0.62	0.76	0.44	0.61	0.56
	0.49	0.47	0.58	0.34	0.74
	0.77	0.82	0.62	0.32	0.91
Average Flow Velocity (m/s)	0.48	0.57	0.45	0.52	0.61

Table 1. Statistical analysis of groundwater flow velocities in karst tunnel drainage systems.

Velocity Check Locations (Tunnel Longitudinal Drainage Pipe)	Zhongliangshan Tunnel (Chongqing)	Station-to-Station Tunnel from Danzishi to Tushan (Chongqing)	Station-to-Station Tunnel from Chongqing North Station to Yulu Station (Chongqing)	Tuzhu Tunnel (Chongqing)	Shisungou Tunnel (Guizhou)
Velocity Check Time	August 2016	June 2018	June 2018	January 2022	May 2022
Flow Velocity (m/s)	0.2	0.45	0.35	0.8	0.46
	0.31	0.37	0.27	0.51	0.38
	0.62	0.76	0.44	0.61	0.56
	0.49	0.47	0.58	0.34	0.74
	0.77	0.82	0.62	0.32	0.91
Average Flow Velocity (m/s)	0.48	0.57	0.45	0.52	0.61

Figure 1. Research area map.

Figure 1. Research area map.

3. Numerical Simulation Methods and Approaches

3.1. Principles of Numerical Simulation and Model Selection

3.1.1. Finite Element Software Simulation Principles

The finite volume method (FVM) was used to solve the discrete equations. The integral conservation of the dependent variable was satisfied for every control volume; therefore, the entire computational domain met the requirement for integral conservation of the dependent variable.

Let J be the flux density of a standard dependent variable $\phi$ and the dimensions of the control volume to be dx, dy, and dz (Figure 2). Then, J_x represents the flux density entering the dydz face of the control volume, while the flux density leaving the opposite face can be defined as the following:

$$J_x+\frac{\partial J_x}{\partial x}dx$$

(2)

Through that face, the net flow rate of water exiting the entire area can be expressed as follows: $\frac{\partial J_x}{\partial x}dxdydz$. Likewise, the net flow rate of water coming out the surfaces dxdy and dxdz can be represented as $\frac{\partial J_z}{\partial z}dxdydz$ and $\frac{\partial J_y}{\partial y}dxdydz$, respectively. Hence, the net flow rate per unit volume can be expressed as the following:

$$div(J)=\frac{\partial J_x}{\partial x}+\frac{\partial J_z}{\partial z}+\frac{\partial J_y}{\partial y}$$

(3)

The idea behind the control volume formulation is to divide the computational domain into many non-overlapping control volumes. Each grid node should be surrounded by a control volume [23]. In this way, any group of control volumes will satisfy the integral conservation law, so we can obtain an accurate solution in the computational region without partitioning the grid.

3.1.2. Model Selection

From the perspective of physics, there are three common phases of matter on Earth: solid, liquid, and gas. The simultaneous flow of materials with two or more thermodynamic phases is known as multi-phase flow. The tunnel drainage systems often face a multiphase flow problem, involving a continuous flow of the mixed solution of calcium carbonate crystals (solid phase) and groundwater (liquid phase). The calcium carbonate crystals deposited in the mixture solution will eventually clog the drainpipes.

An Eulerian multiphase flow model is adopted to simulate the crystal blockage in the tunnel drainage systems. This is because water flows as usual in the drainage system after calcium carbonate crystals deposit but such deposition will also affect flowing water’s momentum. The Eulerian multiphase model allows for the modeling of multiple separate yet interacting phases. In this case, separate solutions are obtained for the calcium carbonate crystals (solid phase) and the groundwater (liquid phase).

3.2. Conditions for the Numerical Simulation

In practical tunnel construction, the spacing between transverse drainage pipes and annular drainage pipes is determined by the conditions of the surrounding rock and the amount of water that flows into the tunnel. Sometimes, transverse drainage pipes are deployed crossing over the annular drainage pipes. The connections between longitudinal drainage pipes, transverse drainage pipes, and annular drainage pipes can be divided into two categories:

(1)

When annular drainage pipes have a relatively large spacing from transverse drainage pipes and longitudinal drainage pipes, their influence on the flow in the other two types of drainage pipes can be ignored. In such a drainage system, the transverse drainage pipes and the longitudinal drainage pipes form a T-shaped connection;

(2)

When annular drainage pipes are closely spaced to transverse drainage pipes and longitudinal drainage pipes, they will affect the water flow in the other two types of drainage pipes. In this case, transverse drainage pipes, longitudinal drainage pipes, and annular drainage pipes form a Y-shaped three-way connection.

Table 2. Model dimension parameters.

Model	Transverse Drainage Pipe Size	Longitudinal Drainage Pipe Size	Annular Drainage Pipe Size
T-junction pipe section	Diameter 110 mm, Length 1.5 m	Diameter 110 mm, Length 6.0 m	/
Three-way junction pipe section	Diameter 110 mm, Length 1.5 m	Diameter 110 mm, Length 6.0 m	Diameter 50 mm, Length 0.1 m

shows the parameters for the transverse drainage pipe, the longitudinal drainage pipe, and the annular drainage pipe. The parameters for the simulating model are based on the real data of tunnel construction. In Configuration ②, the distance between the interface of the annular drainage pipe and the transverse drainage pipe is set to be 1 m.

Regardless of the source or influencing factors, crystals in tunnel drainage systems will flow along with groundwater and deposit, gradually blocking the drainage system. Therefore, the problem of crystal blockage in a tunnel can be simplified as the deposition of calcium carbonate crystals that are transported by the water flowing in the drainage system. In this study, different volume fractions of calcium carbonate (20%, 50%, and 80%) were used to study the deposition of calcium carbonate crystals at the interfaces of the drainage system. The three volume fractions and two types of drainage pipe connections can be combined into six computational analysis conditions (

Table 3. Computational conditions.

Conditions	Drainage System Models	Volume Fractions of Calcium Carbonate
1	T-junction pipe section	20%
2	T-junction pipe section	50%
3	T-junction pipe section	80%
4	Three-way junction pipe section	20%
5	Three-way junction pipe section	50%
6	Three-way junction pipe section	80%

).

3.3. Model Establishment

Two analytical models (Figure 3 and Figure 4) were built with meshes (Figure 5). After having verified the mesh quality and proportions, we set the gravity, which had a magnitude of 9.8 m/s² along the negative z-axis. The fluid was simulated using the Eulerian multiphase flow model, which included water and calcium carbonate as components. To simulate actual crystallization, the size of calcium carbonate particles was set to range from 5 μm to 30 μm. Based on our field investigation, the average groundwater velocity in karst tunnel drainage systems was determined to be between 0.4 m/s and 0.6 m/s; therefore, the initial flow velocity for the simulation was set at 0.5 m/s. After confirming boundary conditions, we started the numerical simulation calculations (

Table 4. Model boundary conditions.

Models	Inlet	Longitudinal Drainage Outlet	Horizontal/Annular Drainage Outlet	Pipe Wall
T-junction pipe section	Velocity-inlet	Pressure outlet (gauge pressure 0)	Free flow (p = 0)	Stationary wall
Three-way junction pipe section	Velocity-inlet	Pressure outlet (gauge pressure 0)	Free flow (p = 0)	Stationary wall

).

4. Numerical Analysis of Flow Velocity Distribution

4.1. Flow Velocity Distribution in Different Drainage Systems

According to Figure 6a, the overall flow velocity in the tunnel drainage system is uniform within the T-shaped pipe section (without considering the presence of the annular drainage pipe). There is a sudden drop in water velocity at the interface between the longitudinal pipe and the transverse pipe. This is because when the longitudinal water flow passes through the transverse drainage pipe, some water is diverted to the transverse pipe. After passing this interface, the water velocity becomes more stable. Before passing the interface with the transverse pipe, the maximum water velocity in the longitudinal pipe is 0.62 m/s. In contrast, at the interface, when the water enters the transverse pipe, the maximum water velocity drops to 0.41 m/s. After a sudden drop in velocity at the interface, water in the longitudinal pipe gradually gains momentum and becomes faster due to a steeper slope. The flow velocity in the transverse drainage pipe is lower than in the longitudinal drainage pipe when considering the entire velocity distribution. According to Figure 6b, the presence of the annular drainage pipe—which forms a Y-shaped three-way pipe section with the other two types of pipes—causes more variation in flow velocity distribution in the tunnel drainage system. To be specific, sections at both ends have higher water velocities and the middle sections have lower water velocities. Affected by the water inflow from the annular drainage pipe, water running in the longitudinal drainage pipe slows down when passing the interface. The decline is more significant (3.75 times lower) than the sudden velocity decline in the T-shaped pipe section. The minimum flow velocity is 0.02 m/s, which occurs at the interface of the transverse drainage pipe and the annular drainage pipe; this is because the flow from the annular drainage pipe is from a different direction, which disrupts water movement in the longitudinal drainage pipe. However, the flow velocity in the longitudinal drainage pipe increases to 0.65 m/s after the water passes the interface with the annular drainage pipe; this is because water from the annular drainage pipe supplements the longitudinal flow. The flow velocity in the transverse drainage pipe shows a similar distribution pattern as the one observed in the T-shaped pipe section. Nevertheless, the overall flow velocity in the transverse drainage pipe of the Y-shaped three-way section is higher than that in the T-shaped section; this is because the water coming from the annular drainage pipe disrupts the flow in the longitudinal pipe and diverts more water into the transverse drainage pipe.

The velocity distribution in the tunnel drainage system is disrupted at the interface of the pipes (Figure 6). To analyze the distribution pattern in different drainage systems, we plotted velocity distribution curves along the longitudinal axis of the pipes (Figure 7). At both the T-shaped pipe section and the Y-shaped three-way pipe section, the maximum velocity of the transverse drainage pipe was observed at the interface. At the same place, minimum velocity was also observed. At the T-shaped pipe section, the water flow in the longitudinal drainage pipe suddenly slowed down at the interface, with minimal variation elsewhere. As for the three-way pipe section, the water flow in the longitudinal pipe suddenly slowed down at the interface—just the same as the T-shaped section—but there were also significant velocity changes at the interface of the annular drainage pipe. The flow velocity dropped to an extremely low 0.02 m/s before flowing through the interface with the annular drainage pipe. After passing the annular pipe, the water velocity increased abruptly, reaching a maximum value of 0.65 m/s near the interface.

4.2. The Analysis of Calcium Carbonate Deposition in the Transverse Drainage Pipes

In both the T-shaped pipe section and Y-shaped three-way pipe section, calcium carbonate is deposited at the bottom of the transverse drainage pipes. Figure 8 shows its volume fraction, which is nearly 1. This indicates that some places of the transverse drainage pipes are completely occupied by calcium carbonate, leading to blockage. According to Figure 8a–f, as the calcium carbonate solution’s volume fraction increases, calcium carbonate crystals gradually occupy the space of the transverse drainage pipes. This phenomenon occurs for both the T-shaped pipe section and the Y-shaped three-way pipe section. Therefore, higher calcium carbonate content will increase the probability of blockage in the drainage system. In the transverse drainage pipes of both the T-shaped pipe section and the three-way pipe section, calcium carbonate spreads in a similar pattern. However, calcium carbonate crystals take up less space in the transverse drainage pipes of the three-way pipe section than those of the T-shaped pipe section. This is because the annular drainage pipe in the three-way pipe section increases the flow velocity in the transverse drainage pipes, causing the calcium carbonate layer to wear away faster. The quality of the calcium carbonate sediment also declines.

According to Figure 6 and Figure 8, when the flow velocity slightly changes, the calcium carbonate scale will evenly cover the bottom of the pipe, forming a smooth layer of deposits. At the inlet of the transverse drainage pipe, the volume fraction of calcium carbonate is around 1 but the space it occupies is smaller. As the flow passes through the inlet, the occupied space gradually increases. Therefore, the probability of crystal blockage at the inlet of the transverse drainage pipe is lower than in other parts of the pipe. According to Figure 6, the change in flow direction disturbs velocity distribution at the transverse drainage pipe’s inlet, where the maximum flow velocity occurs. Such disturbance hinders the deposition of calcium carbonate.

4.3. Analysis of Calcium Carbonate Deposition in the Longitudinal Drainage Pipes

According to Figure 8 and Figure 9, the distribution of calcium carbonate in the longitudinal drainage pipes is consistent with that in the transverse drainage pipes. The calcium carbonate tends to accumulate at the bottom of the drainage pipes, forming an even layer of deposits. When calcium carbonate accumulates in the solution, it occupies more space, leading to a higher likelihood of pipe blockage. When there is 80% calcium carbonate in the solution, the longitudinal drainage pipes are almost completely occupied by calcium carbonate crystals, with over 80% of the cross-sectional area clogged. In the longitudinal drainage pipes of the T-shaped pipe sections, especially at its interface with the transverse drainage pipe where the volume fraction of calcium carbonate is 1, the flow velocity decreases. This is because the transverse drainage pipe drains away some of the water and more calcium carbonate deposits occupy the spaces. The flow velocity also plummets in the three-way section pipes between the interface of the transverse drainage pipe and the annular drainage pipe, which facilitates calcium carbonate deposition. Consequently, calcium carbonate accumulates and occupies more space. At the interface of the annular drainage pipes, however, the flow velocity suddenly increases and disrupts the velocity distribution; this is caused by the water flowing from different directions. Compared to other locations, the volume fraction of calcium carbonate at the interface of the annular drainage pipes decreases sharply and only a small space is occupied; however, as the water passes through the interface, the flow velocity decreases, and calcium carbonate occupies more space again.

According to Figure 6 and Figure 7, the flow velocity in longitudinal drainage pipes tends to decrease at its interface with the transverse drainage pipe or with the annular drainage pipe. After the water passes the interface between the longitudinal pipe and the transverse drainage pipe and flows to the downstream section, it will slow down. At places with a low flow velocity, calcium carbonate tends to deposit faster and occupy more space. These places are more likely to be clogged by crystals. In contrast, at places with a high water flow velocity, disrupted flow velocity distribution, or high local water flow velocity (e.g., at the interface of the annular drainage pipe), calcium carbonate crystals seldom occupy the entire space, and the probability of crystal blockages is lower.

4.4. Analysis of Displacement Change in Drainage System under Different Volume Fraction of Calcium Carbonate

The displacement of the tunnel drainage system (per unit time flow) is the flow rate in the tunnel drainage pipe per unit of time. To analyze the CaCO₃ crystal blockages’ impact on the drainage capacity of a tunnel drainage system, we established a control group with a CaCO₃ volume fraction of 0. Figure 10 shows the variation in drainage capacity at the outlets of the longitudinal drainage pipes and the transverse drainage pipes when calcium carbonate’s volume fractions are 0%, 20%, 50%, and 80%, respectively.

According to Figure 10, when the volume fractions of calcium carbonate in the water were 20%, 50%, and 80%, the total drainage volume in the T-shaped pipe section was 390 mL/s, 220 mL/s, and 70 mL/s, respectively. When compared with the control group, the drainage volume decreased by 14.29%, 52.17%, and 84.78%, respectively. Similarly, the drainage capacity of the Y-shaped three-way pipe section also decreased as the CaCO₃ volume fraction increased, with the total drainage volume being 700 mL/s, 530 mL/s, and 190 mL/s, respectively. When compared to the control group, the drainage volumes dropped by 17.65%, 37.65%, and 77.64%, respectively. The declining drainage volume of the tunnel drainage system indicates that pipe blockage becomes severe and may damage the function of the tunnel. When the CaCO₃ volume fraction increases, the drainage volume of the longitudinal drainage pipe remains higher than that in the transverse drainage pipe, both in the T-shaped pipe section and in the Y-shaped three-way pipe section. However, in the three-way-shaped pipe section, water from the annular drainage pipe supplements the overall flow, so the drainage volume in the longitudinal drainage pipe and the flow velocity in the transverse drainage pipe all increase, as shown in Figure 7. As water flow removes some calcium carbonate deposits on the pipe wall, the pipe gains higher drainage capacity. Therefore, installing more annular drainage pipes in tunnels with high water content will facilitate the removal of calcium carbonate deposits and ensure efficient drainage.

5. Conclusions and Recommendations

This study has established a tunnel drainage system model using finite element software to reflect calcium carbonate deposition in tunnels. It has analyzed two types of pipe categories: T-shaped pipe sections and Y-shaped three-way pipe sections. It has analyzed the flow velocity variation in the drainage pipes, the distribution of calcium carbonate deposits, and changes in drainage volumes. The main findings are as follows:

(1)

In terms of the T-shaped pipe sections (without considering annular drainage pipes), water in the longitudinal drainage pipe had a maximum flow velocity of 0.62 m/s before the water passed through the interface with the transverse drainage pipe. As for the Y-shaped three-way pipe sections (considering annular drainage pipes), the maximum flow velocity of 0.65 m/s occurred at the interface with the annular drainage pipe. Influenced by the water flowing from the annular drainage pipe, there was a significant decrease in flow velocity at the interface of the transverse drainage pipe, which was 3.75 times lower than that in the T-shaped pipe section. In both cases, the maximum flow velocity in the transverse drainage pipe occurred at its inlet;

(2)

At the inlet of the transverse drainage pipe, the calcium carbonate occupied a small space compared to other parts of the pipe. Calcium carbonate deposition and blockage existed but only at a mild level. However, severe calcium carbonate deposition was observed at other locations in the transverse drainage pipe;

(3)

The deposition of calcium carbonate was closely related to the flow velocity in the tunnel drainage system. When the flow velocity in the drainage system remained constant, calcium carbonate deposits were evenly distributed. At certain locations of the drainage system, where flow velocities were low, calcium carbonate deposits occupied more space. In contrast, calcium carbonate deposits occupied less space at locations with high water flow velocities and more disrupted flow distributions. When the water in the longitudinal drainage pipe contained 80% of CaCO₃, severe calcium carbonate deposition would occur. The blockage accounted for over 80% of the cross-sectional area;

(4)

Higher calcium carbonate content in the water caused more calcium carbonate deposition and blockage in the tunnel drainage system. As a result, the drainage volume would drop. Drainage volume decreased most when the volume fraction of calcium carbonate was 0.8. Compared to the control group, the drainage volume dropped by 84.78% in the T-shaped pipe sections and by 77.64% in the Y-shaped three-way pipe sections;

(5)

The blockage of the tunnel drainage system has an important impact on the tunnel structure. According to the model simulation, higher concentrations of calcium carbonate ions in the tunnel drainage system would cause the tunnel drainage system to be quickly clogged. To ensure smooth flow and prevent the blockage of a tunnel drainage system, it is necessary to develop technologies from physical, chemical, and biological perspectives. This study provides invaluable insights to avoid the blockage of tunnels by the calcium carbonate crystals through reducing the carbonate, bicarbonate, and calcium ions in the groundwater.