Experimental Study on Frost Heave Characteristics of Silty Clay Beneath Operating Stations in Twin Tunnel Freezing

Abstract

Artificial ground freezing method construction is widely applied in the subway construction in Shanghai. In the project of the twin tunnel freezing method crossing the operating Line 10 station at No.18 Guoquan Road in Shanghai, the tunnel is located in the silty clay with a water content of 38.5%. The frost heave pressure of the silty clay will cause uplift and even cracking of the already operating station. Taking the Shanghai silty clay as the research object, this study investigates the influence of the cold end temperature and conductive temperature on the frost heave pressure of the soil through laboratory frost heave experiments and similar simulation experiments. The results show that under closed freezing conditions, there is a good linear relationship between the frost heave pressure of the silty clay and the cold end temperature, while under open freezing conditions, the frost heave pressure of the soil has a quadratic relationship with the temperature difference of the soil under the structure’s base plate. The research findings will provide valuable references for projects such as the freezing method for crossing operating stations and existing lines in Shanghai subway construction.

1 Introduction

The freezing method has been widely applied in the construction of Shanghai subway, and it is commonly used in projects such as auxiliary tunnels, underground pump rooms, and station entrances [1, 2]. It has shown good performance in water-rich soil layers, but has also caused safety accidents [3]. With the large-scale construction of subway lines in Shanghai, the issue of intersections and transfers between different lines has emerged, leading to the construction of multiple station crossings, surface buildings, and inter-station tunnels. This poses new challenges for the design and construction of subway systems when crossing through water-rich soil layers. Ensuring the safety of the structures above in such engineering projects becomes a key and difficult task.

In the project of the twin tunnel freezing method crossing the operating Line 10 station at No.18 Guoquan Road, Shanghai, the tunnel is designed to underpass through the soft soil layer using the freezing method. The proposed internal diameter of the up and down tunnels is 5.9 m, with assembled segment thickness of 0.35 m. To ensure smooth excavation by shield tunneling and provide a clearance diameter of 7 m, the distance between the top of the tunnel segments and the station floor is 2.209 m, and the designed distance between the freezing pipes and the station floor is 0.76 m, as seen in Fig. 1.

Fig. 1

The map of the proposed tunnel and frozen wall and station

According to the design, the station platform is located below the 0 °C line. The station is greatly affected by low temperatures, and frost heave has a significant impact on the upper operating station. Therefore, it is necessary to study the frost heave characteristics of the grayish powdery clay at the ⑤11 layer.

Currently, a large number of studies are conducted in laboratories, following the “MT/T 593.2-2011 Physical Mechanical Properties Test of Artificial Frozen Soil Part II: Soil Frost Heave Test Method” for frost heave pressure testing. The frost heave pressure in a closed frost heave test refers to the average axial thrust per unit area generated after a unidirectional freezing process under conditions without lateral deformation and with restrictions on the upper and lower surfaces (no deformation). However, the frost heave pressure in engineering occurs under conditions with lateral deformation, so there is a difference between the frost heave pressures induced under closed and non-closed conditions. The objective of this study is to investigate the frost heave pressure characteristics under closed and non-closed conditions for this specific engineering scenario.

Lou and Chen [4] analyzed the technical risks of using the freezing method for the Shanghai Sports Center Station of Shanghai Metro Line 4, which crosses Line 1 at zero distance, and demonstrated the reliability of the freezing method for constructing soft soil subway stations with zero-distance crossings. Lin et al. [5] conducted theoretical calculations on the freezing design for the Shanghai Sports Arena crossing the original Shanghai Metro Line 1 at Shanghai Sports Station in the second phase of the Shanghai Metro Mingzhu Line project and concluded that the design freezing method is reliable. Tang et al. [6] conducted experimental research on the frost heave characteristics of silty clay under freezing conditions and obtained the frost heave characteristics of silty clay under closed test conditions. Cheng [7] concluded that sandy soil has a small frost heave pressure, while saturated soft clay has a large frost heave pressure. Cai et al. [8] established a time-dependent prediction model for surface frost heave displacement caused by tunnel horizontal freezing construction based on the theory of random media. Alzoubi et al. [9] proposed a two-dimensional intermittent freezing model based on mass, momentum, and energy conservation, indicating that adopting the intermittent freezing method can reduce engineering power consumption by 40%. Cai [10] conducted experimental research on the temperature field and frost heave settlement variation in double-line tunnel formations, obtaining that adopting a sequential freezing method for double-line tunnels can to some extent reduce ground frost heave displacement.

2 Project Overview

Please follow these instructions as carefully as possible so all articles within a conference have the same style to the title page. This paragraph follows a section title so it should not be indented [2, 3].

The construction method for the Shanghai Metro Line 18, which crosses the operational Line 10 at Guoquan Road Station, involves reinpressurement through freezing followed by excavation using the underground mining method to form the tunnel for Line 18.

The proposed dual-line tunnel intersects with the station vertically. The centerline elevation of the frozen excavated tunnel is −19.011 m, while the ground elevation is +3.2 m. The up and down lines of the tunnel need to sequentially pass through the main structural elements of the newly built Line 18 Guoquan Road Station, including the A-wall, the eastern main structure of Line 10 Guoquan Road Station (B-wall), the western main structure of Line 10 Guoquan Road Station (C-wall), as well as the maintenance structure of Exit 4 of Line 10 Guoquan Road Station (D-wall), see in Fig. 2.

Fig. 2

Location map of the proposed tunnel and Guoquan Road Station

The ⑤11 layer consists of grayish powdery clay with the presence of calcareous nodules, organic matter, etc. The soil is relatively uniform, very moist, in a soft-plastic state, and exhibits high compressibility. The parameters are shown in the Table 1.

Table 1 Soil parameters

3 Enclosed Frost Heaving Test

3.1 Test Procedure

• (1) Prepare a cylindrical soil sample with a diameter of 50 mm and a height of 100 mm by configuring the moisture content and filling the soil into a sample cylinder. Put the sample into the frost heaving testing machine.

• (2) Set the temperature of the top and bottom plates of the frost heaving testing machine. The temperature of the hot plate is set to 20 °C. The temperature of the cold plate is divided into 4 groups, which are set to −20 °C, −15 °C, −10 °C, and −5 °C, respectively. Repeat the tests.

3.2 Results and Analysis of Enclosed Frost Heaving Test

The frost heaving pressure curves at different cold-end temperatures are shown in the Fig. 3.

Fig. 3

Frost heave pressure curve at different cold end temperatures

As can be seen from the Fig. 3, with the decrease of the cold-end temperature, the frost heaving pressure of the ⑤11 grayish powdery clay sample gradually increases. From the change pattern of the frost heaving pressure–time curve, the frost heaving process of the ⑤11 grayish powdery clay body can be divided into four stages: the (1) freezing and shrinking stage where the volume of the soil body reduces before cooling to 4 °C; the (2) rapid growth stage of frost heaving pressure where the water begins to freeze and the frost heaving pressure starts to increase rapidly; the (3) slow growth stage of frost heaving where the ice formation is gradually sufficient and the frost heaving grows slowly; and the (4) stable stage where the ice formation reaches good stability. It can be obtained that there is a good linear relationship between the maximum frost heaving pressure of the soil and the experimental cold-end temperature, which can be expressed as F1 = 0.03|T1|.

4 Open Freeze–Thaw Experiment

4.1 Similarity Criteria

During the experiment, the physical model must satisfy a series of similarity criteria such as temperature, humidity, stress, displacement, etc. In the construction process of the upper structure under the frozen tunnel, the following criteria are primarily considered:

• (1) The temperature field similarity criterion for the absorption of heat from the soil by low-temperature saline water, leading to the freezing of moisture in the soil, is expressed as Eq. (1):

  $$F\left( {F_{0} ,K_{0} ,R,\theta } \right) = 0$$

  (1)

  Here, F₀ represents the Fourier criterion, K₀ denotes the Kosovic criterion, R represents the geometric criterion, and θ refers to the temperature criterion. The experimental soil is taken from the actual construction site, hence the temperature and water content parameters in the model are equivalent to those of the in-situ soil. Thus, the similarity ratio for parameters such as soil temperature, internal friction angle, Poisson’s ratio, porosity, etc., during the experiment is 1.

  The humidity field criterion for the soil in Eq. (2):

  $${\Theta } = \frac{w}{{w_{0} }}$$

  (2)

  Here, w_d represents the humidity of the soil after freezing, and w₀ is the initial soil humidity. According to the humidity criterion, the heat conduction process and the water migration process are mathematically similar, both of which abide by the Fourier criterion. Therefore, under the conditions of geometric similarity, as long as the temperature field is similar, the humidity field can achieve “self-simulation” and be similar.

• (2) The non-dimensional stress-displacement field equation for deformation caused by freezing and excavation of the overlying soil can be expressed as Eq. (3):

  $$F\left( {\frac{{E_{d} }}{\sigma },\frac{{\mu_{d} }}{{D_{s} }},\frac{H}{{S_{d} }},\frac{{E_{d} }}{rH}} \right) = 0$$

  (3)

  Here, H is the depth of the tunnel, D is the tunnel diameter, S_d is the thickness of the frozen wall, μ_d represents displacement, σ denotes stress, r is the bulk density, and E_d is the modulus of deformation.

• (3) Stiffness criterion: Deformation occurs in the upper structure due to frost heave or thaw settlement. According to linear elastic mechanics, the deflection of a structure under external forces is inversely proportional to its stiffness, i.e., as in Eq. (4)

  $$u_{{\text{s}}} \infty {1}/K$$

  (4)

  Here, u_s represents the displacement caused by frost heave pressure, K = EI is the stiffness of the structure’s base plate, and I is the moment of inertia.

  Based on the aforementioned criteria, the similarity ratios for temperature, stress, time, length, density, and displacement can be expressed as Eq. (5):

  $$\begin{gathered} C_{{\text{T}}} = C_{{\text{S}}} = 1 \hfill \\ C_{{\text{t}}} = n^{2} \hfill \\ C_{{\text{L}}} = C_{{\uprho }} = C_{{\text{d}}} = n \hfill \\ \end{gathered}$$

  (5)

  Here, n represents the geometric scale ratio, C_T, C_S, C_t, C_L, C_ρ, and C_d are the similarity ratios for temperature, stress, time, length, density, and displacement, respectively.

4.2 Similar Simulation Experiment Design

According to the actual engineering size and reserved reasonable boundary conditions, the length direction of the boundary condition is set to 75 m and the width and depth are set to 36 m. The geometric reduction ratio is n = 1/25 and the net size of the simulated test is 3 × 1.5 × 1.5 m. The actual diameter of the tunnel is 7 m, which is converted to a diameter of 280 mm. The tunnel mainly lies in the grayish powdery clay layer of layer ⑤11. The model soil is taken from the site, and the thickness of the model soil layer is based on the actual thickness and calculated by the geometric similarity ratio. The compactness of the soil is controlled by using the press plate, and after filling each layer, an environmental-consistent sample is taken with a ring cutter to measure its moisture content.

To ensure the reasonable placement of freezing pipes in the model experiment, the principle of equal total heat dissipation must be used to select the position and number of freezing pipes. In the model experiment, the actual arranged freezing pipes need to be simplified. The total heat dissipation capacity of the freezing pipes is Q = ndhk, where n is the number of freezing pipes, d is the outer diameter of the freezing pipes, H is the freezing depth, and k is the heat dissipation coefficient of the freezing pipes. Using calcium chloride solution as the refrigerant, the specific gravity is 1.265, and the flow rate reduction ratio is 1/25. The flow rate reduction ratio and the cooling capacity reduction ratio are both 1/15625.

According to Fourier’s criterion, the time ratio is n² = 1/625. That is, 1 min in the model experiment is equivalent to 625 min in reality. The freezing time is set to 45 days, so the experimental time is 104 min. According to the Kosovich criterion, the temperature similarity ratio is 1, which means that the temperature of any point in the model is the same as that of the corresponding point in the prototype. The stress field ratio is 1:1, and the similarity ratio of the specific weight of the soil is 1/25. That is, the specific weight of the model soil should be 25 times that of the site soil. Since the model material is the same as the prototype, a loading method is used to satisfy the similarity ratio of the specific weight of the soil. Based on the weight of the overlying station, the applied pressure is calculated to be 80t. Two 50t jack are set up for the reaction pressure under the overlying station, and each jack applies a pressure of 40t to satisfy the similarity ratio of the specific weight of the soil, as seen in Fig. 4.

Fig. 4

Experimental principles and field

4.3 Monitoring System

A total of 85 DS18B20 digital temperature sensors are used for temperature monitoring, which are installed on the station floor, tunnel excavation axis horizontal plane, and vertical plane. For the frost heaving pressure of the lower frozen soil mass on the station floor, four LY-350 miniature soil pressure boxes with a size of Ф17 × 8 mm are installed on the bottom surface of the station floor model and directly above the tunnel. The static strain acquisition instrument DH3815N from Donghua Testing is used to collect data in full bridge mode. 6 linear displacement sensors are used to collect data on the frost heaving displacement of the station floor, see in Fig. 5. The probes are supported on the station floor to collect data on frost heaving displacement at different locations.

Fig. 5

Location of micro-earth pressure gauges

4.4 Results and Analysis of Open Frost Heaving Tests

The frost heaving pressure rise curve and temperature difference curve are extracted and synthesized in table form using error bars, as shown in Fig. 6.

Fig. 6

Temperature difference curve of soil at the bottom of station

Figure 6 shows that there is a certain linear relationship between temperature difference and time. The formula can be derived as follows: T = 0.5481t + 0.2729 (t > 5d), where t is the active freezing time.

Figure 7 shows that there is a quadratic equation relationship between frost heaving pressure and time. The formula can be derived as follows: F = 0.0219t² + 1.6854t − 3.6537 (t > 5d), where t is the active freezing time.

Fig. 7

Frost heave pressure curve at the bottom of the structure

In the different projects, the active freezing time is different, which leads to different freeze effects (temperature differences) on the upper soil mass. Therefore, a more reasonable temperature difference is used as a variable to express frost heaving pressure, as seen in Fig. 8. After combining these two factors and solving them, we obtain F2 = 0.0729t2 + 3.30351t − 4.4873, where T2 is the freezing temperature difference of the structural floor with active freezing time > 5d.

Fig. 8

Compared of measured frost heave pressure and calculated value

5 Conclusion

In closed system tests, there is a good linear relationship between the maximum frost heaving pressure of soil and the experimental cold end temperature, and the calculated formula is F₁ = 0.03|T₁|. In open system tests, as the twin freezing tunnel underpass station, the maximum frost heaving pressure on the bottom plate of the station no longer follows the above formula, which is related to the temperature difference between the lower soil mass and the bottom plate in a certain regularity. The frost heaving pressure gradually increases with the increase of the bottom plate temperature difference. The formula is F₂ = 0.0729t² + 3.30351t − 4.4873, which T₂ is the freezing temperature difference of the structural floor with active freezing time > 5d.

This formula has some reference value for evaluating the frost heaving pressure in underpass frozen tunnel engineering and can calculate the temperature of the constructed floor by expanding speed of the freezing wall indirectly. By evaluating the frost heaving pressure size through the floor temperature, we can estimate the potential damage caused by freezing to the structure.