Simmakers Ltd. company

Computer Simulation of Artificial Ground Freezing during the Building of Underground Tunnel

In Germany, during the construction of a new intersection between the regional carrier, Deutsche Bahn, and a city underground railway line, a new railway section with a total length of 1.3 kilometers was required. A specific feature of this section is that its path crosses a large complex of buildings protected by law and it was therefore decided to construct a tunnel at this section. However, this task was seriously complicated by high groundwater flow rates in one segment of this section. As a result of the high filtration rate during tunnel drilling in this segment, there is a distinct probability that the earth under the foundations will be subject to settling. This situation may compromise any structures built on top of this underlying area, which is of course, unacceptable.

 

As a solution to this nonstandard problem, an artificial ice shield over the drilling area was proposed. This measure allows the strengthening of the ground and securing the foundations while performing construction of the tunnel. The tunnel consists of two paths, each of which requiring separate drilling operation. The image below shows a vertical section of the ground in the tunnel drilling area.

 

Tunnel section where ground is artificially frozen

 

The blue color shows the area to be frozen.
Verwitterungshorizont – weathered rock in sediments layer.
Keupergestein – rock bed.
GW – top ground surface.

 

In order to justify the application of the proposed design solutions, it was necessary to perform computer simulation of artificial ground freezing in the tunnel construction area using specialized software.

 

When building a computer model, the following geometrical dimensions of the computational domain were set:

• Length – 62 meters.

• Width – 20.2 meters.

• Height – 18.4 meters.

 

The magnitudes of the computational domain were chosen on the basis of the geometric dimensions of the tunnel and cooling devices and the geological and lithological structure of the ground. The influence of the boundaries on the thermal processes inside computational domain was also factored in.

 

Ground layers in the area under consideration have a complex structure. A geotechnical survey was carried out and the following table with borehole heights was obtained.

 

Name of well

 

Mouth elevation [m]

Sediments and weathered rock layer capacity [m]

Rock bed layer, capacity [m]

Borehole 1

18.4

7.3

11.2

Borehole 2

18.4

5.7

12.8

Borehole 3

18.4

4.3

14.1

Borehole 4

16.7

9.3

7.4

Borehole 5

16.7

9.3

7.4

Borehole 6

16.7

9.3

7.4

Borehole 7

17.8

10

7.8

Borehole 8

17.8

10

7.8

Borehole 9

17.8

10

7.8

 

The plan of wells is shown in the following image:

 

Scheme of boreholes at the tunnel drilling site

 

Geostatistical tools were used to create a three-dimensional reconstruction of the ground within the computational domain, as shown in the image below. This also shows the area of tunnel paths and freezing pipes to be laid.

 

3D ground reconstruction via simulation software for tunnel construction

 

23 freezing pipes with a total length of more than 1,200 meters were proposed for ground freezing and the creation of an ice shield. The diameter of each pipe is 3.5 inches. The cooling performance of the freezing aggregate is 465 kW, which allows the temperature of -40 oC. A 30% calcium solution was selected as the freezing agent.

 

Collocation of the freezing pipes is presented in the section diagram below.

 

Collocation of thermosyphons for soil freezing at the tunnel construction site

 

The drilling of pipe-holes is executed at a slight angle. A summary table of the initial and final depths of the freezing pipes to be laid is presented below.

 

Freezing pipe number

 

Altitude at the beginning of the freezing area, meters  

Altitude at the end of the freezing area, meters  

Cooling Tube 1

7.09

8.80

Cooling Tube 2

8.06

9.77

Cooling Tube 3

8.95

10.66

Cooling Tube 4

9.73

11.44

Cooling Tube 5

10.29

12.00

Cooling Tube 6

10.67

12.38

Cooling Tube 7

10.8

12.51

Cooling Tube 8

10.64

12.35

Cooling Tube 9

10.18

11.90

Cooling Tube 10

9.45

11.16

Cooling Tube 11

8.71

10.42

Cooling Tube 12

7.70

9.41

Cooling Tube 13

6.72

8.43

Cooling Tube 14

9.47

11.18

Cooling Tube 15

10.18

11.90

Cooling Tube 16

10.62

12.33

Cooling Tube 17

10.78

12.50

Cooling Tube 18

10.66

12.37

Cooling Tube 19

10.26

11.97

Cooling Tube 20

9.68

11.39

Cooling Tube 21

8.90

10.60

Cooling Tube 22

8.00

9.70

Cooling Tube 23

7.02

8.73

 

Water filtration velocity in sand layer comprises 1.25 meters per day; the groundwater temperature is +12.9oC.

 

Ground characteristics are shown in the table below.

Ground layer

 

Ρdry, [kg/m33]

 

kf, [m/s]

 

λ2, [W/m*K]

 

λ1, [W/m*K]

 

C2, [MJ/m3*К]

 

C1, [MJ/m3*К]

 

α, [%]

 

β, [-]

 

Sediments and weathered rock

1700

10-4

2.20

3.40

2.78

2.03

1.5

-0.7

Rock bed

2000

10-14

2.00

2.16

2.40

1.95

 

Ρdry – ground density; kf – filtration coefficient; λ2,1 – heat conductivity in the thawed and frozen ground; C2,1 — heat capacity of thawed and frozen ground; α, β – coefficients that describe the content of unfrozen moisture.

 

The First-type boundary condition is set on the surface of the computational domain as a dependence of temperature change over time, shown in the diagram below.

 

The First-type boundary condition for ground freezing simulation

 

The Second-type boundary condition in the form of heat flow equal to zero is set on the side boundary of the computational domain. The First-type boundary condition representing a constant temperature of +12.9 oC is set on the lower boundary.

 

As a result of computational domain discretization, we obtain a computational mesh consisting of 2,037,312 nodes.

 

Meshed site for ground freezing simulation during tunnel construction

The simulated period was 120 days (from February to June); the time spent to carry out the computation was 35 minutes

 

 

Simulation results of ground freezing in tunnel

Cross section of the middle of the computational domain on the 30th day of operation of the cooling devices

 

The simulation results of the performance of the cooling devices showed that on the 120th day, the ice shield over both paths was fully formed. Moreover, the first path was almost completely frozen by this time. This can be clearly seen in the image representing the computation results below.

 

Temperature simulation results of artificial ground freezing in tunnel using thermosyphons

Simulation results on the 120th day of operation of the cooling devices

 

Temperature distribution in the tunnel in the form of isolines after 120 days freezing by thermosyphons

Isolines of the YZ plane section on the 120th day of computation

 

 

FROST 3D UNIVERSAL

Software package for simulation of artificial ground freezing applied in the construction of:

 

  • Tunnels
  • Mines
  • Foundation pits
  • Dams and embankments
  • Underground storages and tanks

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The performance of the development was very satisfying and clearly demonstrated in weekly reports regarding the progress of the software development.

D.G. Dolgikh
Deputy CEO
Fundamentstroyarkos RPA Ltd, Russia

 

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