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# Numerical simulation

(5) The whole pipeline is homogeneous, regardless of the joints between sub-pipes.

4.3.2 Contact properties

To verify the jacking force obtained from the simulation, overcut and lubrication were included in the model by setting the contact range and changing the frictional coefficient between pipeline and surrounding ground. To simulate the overbreak, the soil-pipe contact range was specified in the model. With the presence of the overcut, the soil and pipes would not be in direct contact with each other, but pipe-slurry and slurry-soil interaction instead. In contrast, the other contact properties would be set according to the various frictional coefficients of the lubricants applied (Yen & Shou, 2015). In addition, the frictional coefficients, including cohesion and friction angle, of the contact range depends on the ground temperature as shown in Figure 4.3 (Liu et al., 2014). The contact surface behavior involves the behavior in the tangential and the normal direction. Contact pressure and stress acting on the pipe outer surface would be created from the weight of soil directly. The pipe jacking machines possess the copy cutters for the overcut excavation which helped to reduce the area of contact and the friction between the soil and pipes. The overcut can be simulated by changing the range of contact between the pipes and surrounding ground. Based on the results of previous research (Shou, Yen, & Liu, 2010; Yen & Shou, 2015), it was suggested that the 1/2 and 1/3 range of contact conditions are more distinguishable and representative. Therefore, the contact range parameters are set as full, one 2nd, and one 3rd of the pipe surface in contact with the soil as shown in Figure 4.2 a) ~ c).

4.3.3 Simulation process

In order to take the effect of ground temperature into consideration, a coupled thermal-mechanical model should be built as well and the thermal-mechanical simulation is conducted by following the thermal results. The numerical simulation process of jacking force is comprised of the following steps: 1) conducting the thermal simulation by setting 10℃

of bottom boundary and -5℃ ~ -20℃ of surface ground, respectively; 2) obtaining the initial stress in the frozen soil by only considering the gravity; 3) changing the Bulk and

Shear modulus of frozen soil based on the temperature distribution by using FISH function following the relationship between modulus and temperature, automatically;

4) clearing the initial deformation and removing the elements representing the soil to simulate the excavation; 5) defining the contact interface between concrete pipe and surrounding frozen ground according to the lubricant conditions and over cutting area;

6) activating the elements standing for concrete pipes to simulate the support lining; 7) applying a velocity of 10-8 m/s at the tail of pipe to simulate the hydraulic jacks and after reaching stable, the forces at the tail of pipe are considered as the jacking force. In order to simulate the effect of lubricant and overbreak conditions and to avoid the possible simulation difficulties due to the thin gap between the pipe and soil, this study considers the shear properties of lubricant (Khazaei et al., 2006) in the over cutting area.

4.3.4 Simulation schemes

As mentioned in Chapter 2, the deformation modulus of frozen soil increases following Eq. 3.1, which is also adopted in this chapter. Besides, to fully understand the relationship between jacking thrust with geometric parameters of jacking tunneling, geological condition of frozen soil, contact properties of pipe and surrounding ground with lubricant, and ground temperature, the parametric study is performed by using FLAC3D with the parameters listed in Table 4.1. Different jacking distance from 20m to 80m is also presented to estimate the jacking force along with jacking distance. As long-distance pipe jacking needs large jacking force, the one-time jacking distance is limited and the intermediate jacking station is necessary. Therefore, the ultimate strength of concrete pipe is considered to calculate the one-time jacking distance by which the intermediate jacking station and lubricant requirements can be determined.

In this thesis, the common-used C40 concrete pipe is selected as the jacking pipe, and the uniaxial compression ultimate strength is 40MPa (Nilson, 1997). In addition, Table 4.2 and Table 4.3 give the frictional parameters, friction angle and cohesion, between concrete pipe and frozen ground with different temperatures and lubricants, respectively.

Considering temperature increasing with cover depth, the friction angle and cohesion between concrete pipe and frozen soil decreases with cover depth. Therefore, contact

strength reduces with increasing cover depth, because the contact friction angle and cohesion reduce. Table 4.4 lists the simulation scheme, which is a univariate and multivariate analysis.

Table 4.1 Numerical parameters

Tunnel geometric parameters

Jacking length (L): 20m, 40m, 60m and 80m;

Diameter (D): 1m, 2m, 3m and 4m;

Cover depth (C): 4m, 6m, 8m and 10m.

Geological properties

Friction angle: 20 degrees, 30 degrees, 40 degrees and 50 degrees;

Cohesion: 10kPa, 30kPa, 50kPa and 70kPa.

Interaction between frozen soil and concrete pipe

Friction coefficient (f): f (-5℃), f (-10℃), f (-15℃) and f (-20℃);

Contact range: full contact, 1/2 contact, and 1/3 contact.

Concrete pipe

Concrete pipe: C40, Ec=3.25×104MPa, μc=0.2.

Table 4.2 Interface properties of lubricant

Interface properties Friction angle/degree Cohesion/kPa

lubricant 9.89 2.66

Table 4.3 Interface properties between concrete pipe and frozen soil

Interface properties Friction angle/degree Cohesion/kPa

f (T >0℃ ) 20 7.5

f (-5℃ ) 25 10

f (-10℃ ) 31 13

f (-15℃ ) 37 17

f (-20℃ ) 42 21

Table 4.4 Simulation schemes Ground

temperature/℃

Cohesion /kPa

Friction angle /degree

Cover depth/m

Diameter /m

-5 10 20 2 6

-10 10 20 2 6

-15 10 20 2 6

-20 10 20 2 6

-5 10 20 2 6

-5 30 20 2 6

-5 50 20 2 6

-5 70 20 2 6

-5 10 20 2 6

-5 10 30 2 6

-5 10 40 2 6

-5 10 50 2 6

-5 10 20 1 6

-5 10 20 2 6

-5 10 20 3 6

-5 10 20 4 6

-5 10 20 2 4

-5 10 20 2 6

-5 10 20 2 8

-5 10 20 2 10

4.3.5 Numerical models

As mentioned before, the simulation model is a coupled thermal-mechanical model, and the thermal model is the same with that in Chapter 3. In order to avoid the boundary effect, the model size is set as 20m in width and 30m in height. Figure 4.4 and Figure 4.5 show the numerical model with taking the 2m of diameter, 6m of cover depth and 40m of jacking distance as an example, and interface between concrete pipe and frozen soil. The symmetrical nature of the model test allows using only half of the actual pipe-soil system, which can satisfy the accuracy requirements and at the same time, save a lot of computing time. The boundary conditions are as follows: the bottom face is confined by hinges, and the surrounding vertical faces are fixed by rollers and the surface ground is the free boundary as shown in Figure 4.6.

30m

20m L

Pipe

Soil

Velocity

Figure 4.4 Numerical model. (D=2m, C=6m, L=40m)

L

Interface

Figure 4.5 Interface between concrete pipe and frozen soil.

Figure 4.6 Boundary conditions.

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