Due to the large number of finite element mesh generated, it is difficult to use full-scale model to simulate large-section underground engineering, especially considering the coupling effect. A regional model is attempted to achieve this simulation. A variable boundary condition method for hybrid regional model is proposed to realize the numerical simulation of large-section tunnel construction. Accordingly, the balance of initial ground stress under asymmetric boundary conditions achieves by applying boundary conditions step by step with secondary development of Dynaflow scripts, which is the key issue of variable boundary condition method implementation. In this paper, Gongbei tunnel based on hybrid regional model involving multi-field coupling is simulated. Meanwhile, the variable boundary condition method for regional model is verified against model initialization and the ground deformation due to tunnel excavation is predicted via the proposed hybrid regional model. Compared with the monitoring data of actual engineering, the results indicated that the hybrid regional model has a good prediction effect.

The ground surface deformation due to construction is one of the most concerning issues in shallow-buried underground excavation [

For the large-scale structure, there are two methods to deal with local regions. One is to refine the mesh of local region in the whole model, but only for the case where the whole model adopts the solid element and the shell element [

But for underground engineering, the model becomes more complicated because it involves the balance of initial ground stress [^{TM} [

This paper presents hybrid regional model to realize the numerical simulation of such large-section tunnel construction, which is the first attempt in underground engineering. Two input files are written through secondary development of Dynaflow script to implement the calculation of hybrid regional model. The proposed hybrid regional model can realize the balance of ground stress under asymmetry boundary condition. The verification of the model is made by initialization and comparing the computational results of the model with the monitoring data. The computing realization of hybrid regional model can serve as a reference for similar large-section underground engineering.

Due to the ground stress equilibration involved, the core issue of using regional model to simulate an underground engineering case is the processing of boundary conditions. The simulation process is divided into two major stages, the balance of initial ground stress and the construction. As shown in

Considering that the ground stress equilibration can only be carried out under symmetric boundary condition, in order to set up the boundary conditions under asymmetric condition, the process needs to be divided into two steps, corresponding to two input files, file A and file B.

The simulation is performed by the script of Dynaflow^{TM}, which is a finite element software. The preprocessing of hybrid regional model depends on Gmesh [

The Freeze-Sealing Pipe Roof (FSPR) method is applied to Gongbei tunnel that is a critical link of Hongkong-Zhuhai-Macau Bridge. Meanwhile, it is the first application in the world. The definition of FSPR method is that large diameter steel pipes are laid out in a circle around the cross section of tunnel in advance, and then the artificial ground freezing method is adopted to freeze soil between pipe roof to form waterproof curtain [^{2} with 18.8 m in width and 20.6 m in height, which is the largest single tunnel excavation in China. The tunnel is buried within soft sandy about 4.5 m below the ground surface at the Gongbei customer port.

Some scholars did research about the mechanical mechanism of steel pipes-frozen soil composite structure through laboratory test. A preliminary model test study of simplified composite structure with two pipes and three pipes was conducted, respectively [

There're three stages before excavation, pipe jacking, concrete filling and ground freezing. The roofing pipes are designed to be jacked section by section with a sectional length of 4 m from the construction shaft at one end of the tunnel alignment and received in the construction shaft at the other end of the tunnel alignment. To control the ground movement during pipe jacking, small tunnel boring machines (TBMs) are applied to tunnel through the ground, followed by the jacking of the pipe sections [

In consideration of mesh scale effect and computational capability, the local part of the composite structure was chosen to simulate.

According to the simplified model above,

In actual construction, tunnel excavation starts from the top of the crown where the deformation is the largest.

The constraints of each face of actual project are shown in

The incomplete constrain mentioned above is related to the displacement and restraint capability of the face itself. The constraining force on the faces are different and the situation is more complicated. In

The balance of initial ground stress under asymmetric boundary conditions is the key to the implementation of hybrid regional model. Unlike full-scale model, the boundary condition of hybrid regional model will change after ground stress equilibration. In order to realize such process, the boundary condition of different direction should be added step by step. Thus, the process is divided into two steps.

As the calculation flow described in

There are gravity, water pressure and temperature in simulation. The initial soil temperature is 28°C. The water pressure is distributed evenly and the initial water pressure of ground surface is 0.

The simulation of this model considers the stress field [

(1) Solid equation can be expressed as

where

For saturated porous media applications, it can be expressed as

(2) Heat equation can be expressed as

where

(3) Darcy flow equation can be expressed as

where

(4) Mohr-coulomb model

The yield function is of the following type:

In which:

Among

In which:

According to the governing equation above, the relationship between each one is associated through common parameters.

Soil material is simulated by Mohr-Coulomb yield criteria. Roofing pipes and concrete materials are set up on the basis of elastic theory. Due to the diversity of soil layers based on Chinese standard of JTG D63–2007, it is considered as homogeneous soil here for the convenience of analysis [

Classifications | Density(kg/m^{3}) |
Poisson ratio | Elastic modulus(Pa) |
---|---|---|---|

Soil | 1950 | 0.29 | 2.0e+7 |

Roofing pipe | 7850 | 0.3 | 2.06e+11 |

Concrete | 2400 | 0.2 | 3.0e+10 |

Classifications | Parameters | Value |
---|---|---|

Mechanical parameters | Fluid mass density(kg/m^{3}) |
1.0e+3 |

Fluid bulk modulus(Pa) | 2.0e+9 | |

Porosity | 0.2 | |

Cohesion(Pa) | 100 | |

Internal friction angle | 27 | |

Calculate mobilized friction angle(Pa) | 6.2e+6 | |

Hydraulic parameters | Fluid compressibility(Pa^{−1}) |
4.5e-10 |

Grains compressibility(Pa^{−1}) |
1.0e-7 | |

Mobility(m/s) | 1.0e-10 | |

Thermal parameters | Specific heat capacity of soil matrix(J/(kg |
1450 |

Specific heat capacity of fluid(J/(kg |
4200 | |

Specific heat capacity of roofing pipe(J/(kg |
450 | |

Thermal expansion of soil(^{−1}) |
12.e-6 | |

Thermal expansion of pipe(^{−1}) |
18.e-6 | |

Thermal conductivity(w/(m k)) | 1.8 |

According to the test of laboratory, we know that the temperature have effect on the material parameters. The relationship of material parameters and temperature of frozen soil lists below, shown in

Temperature( |
−5 | −10 | −15 |
---|---|---|---|

Elastic modulus(Pa) | 4.7e+7 | 8.3e+7 | 12.2e+7 |

Note: where the parameter determination of frozen soil is carried out in a low temperature condition.

The fitting formula of elastic modulus is as follows, which represents the effect of temperature field on stress field.

To make the step time of construction simulation as real as possible, time dependence should be taken into account. There are 227 steps of the numerical simulation, which contains the process of initialization, pipe jacking, soil digging, backfilling pipe with concrete, freezing, tunnel excavation. The time for each construction step is simulated and the arrangement of each step shows in

The thermo-hydro-mechanical coupling model is divided into 9 zones, including 23 groups. It is illustrated by the following

Phases | Stagger | Pressure | Stress | Temperature | Duration | Steps | Time |
---|---|---|---|---|---|---|---|

Initialization | step0 | 0 | |||||

stagger1, 2, 3 | pressure0 | stress0 | temperature0 | 0.235 d | |||

Pipe inserted | step1 | t1 | |||||

stagger4, 5 | consolidation1 | temperature1 | 0.235 d | ||||

Soil digging | step2 | t2 | |||||

stagger6, 7 | consolidation2 | temperature2 | 0.235 d | ||||

Fill concrete | step3 | t3 | |||||

stagger8, 9 | consolidation3 | temperature3 | 0.235 d | ||||

Freezing process | step4 | t4 | |||||

stagger10, 11 | consolidation4 | temperature4 | 51.759 d | ||||

Excavation | step224 | t5 | |||||

stagger12, 13 | consolidation5 | temperature5 | 0.7 d | ||||

End | 53.4 d | step227 | t6 |

Note: where d = day, dt = 0.235 day, t1 = “dt” = 0.235 day, t2 = “2*dt” = 0.471 day, t3 = “3*dt” = 0.706 day, t4 = “4*dt”= 0.941 day, t5 = “224*dt”= 52.7 days, t6 = “227*dt”= 53.4 days, consolidation means the coupled of water pressure and stress.

Regions | Solid | Moi | Heat |
---|---|---|---|

zone1(upper soil) | S1(GROUP1) | D1(GROUP2) | H1(GROUP3) |

zone2(lower soil) | S2(GROUP4) | D2(GROUP5) | H2(GROUP6) |

zone3(digging soil) | S3(GROUP7) | D3(GROUP8) | H3(GROUP9) |

zone4(digging soil) | S4(GROUP10) | D4(GROUP11) | H4(GROUP12) |

zone5(left soil) | S5(GROUP13) | D5(GROUP14) | H5(GROUP15) |

zone6(right soil) | S6(GROUP16) | D6(GROUP17) | H6(GROUP18) |

zone7(left pipe) | S7(GROUP19) | H7(GROUP20) | |

zone8(right pipe) | S8(GROUP21) | H8(GROUP22) | |

zone9(concrete) | S9(GROUP23) |

Note: where “left soil” means the soil at the original position of left pipe. Similarly, the “right soil” means the soil at the original position of right pipe. “Lower soil” means the excavation part. “Digging soil” means soil inside the pipes.

Partition sketch of each phase is shown in

In order to assess the applicability of the proposed hybrid regional model, the construction simulation of Gongbei tunnel is performed. The first step is to verify the initialization of the model.

The duration of initialization is 0.22 day, which means enough time for distribute initial water pressure, temperature and ground stress. The initial vertical stress is assumed to be lithostatic. The experiments in laboratory were conducted to get the basic physical-mechanical parameters, which was directly relevant to simulated precision. The initialization is the key step to ensure the accuracy of model. The model of initialization contains zone1(S1,D1,H1), zone2(S2,D2,H2), zone3(S3,D3,H3), zone4(S4,D4,H4), zone5(S5,D5,H5), zone6(S6,D6,H6). Initial temperature is 28°C, shown in

In order to facilitate the analysis, typical feature points are set to describe the results. There are four feature points in the model, which are shown in

The artificial ground freezing technique is the key to the project. So temperature changes should be paid more attention. The initial temperature is 28°C, shown in

Feature point P1 of ground surface is far away from cold source, and the cold amount is difficult to diffuse to ground surface in 50 days, so the temperature is always 28°C, shown in

Groundwater is one of the most important factors to influence the safety of tunnel construction. The distribution of water pressure ran uniformly in this project. The construction steps had only a little effect on it, and could be redistributed in short time. The value of ground surface point P1 is always 0 in

The deformation as an intuitive index varies with each step. To visualize the deformation of each construction step, vector diagram is used to display, shown in

The feature point P1 of ground surface decreases with the freezing process and rapidly decreases when excavation, shown in

The maximum vertical displacement of each step was shown in

The deformation of ground surface was also an important index to reflect the safety of the project. Considering the symmetry of the model, the settlement curve presents the form of normal distribution. The maximum displacement of ground surface appeared at the point P1 with the value of −2.98 mm. In order to further verify the accuracy of the proposed hybrid regional model, the results calculated by the present method are compared with the monitoring data of actual project. As shown in

In this paper, a variable boundary condition method for hybrid regional model considering the thermal-hydro-mechanical coupling was used to simulate large-scale tunnel construction induced by excavation, and the model was validated against the initialization and deformation of Gongbei tunnel. Finally, it was compared with the monitoring data of ground surface deformation, and the following conclusions were drawn:

The balance of initial ground stress under asymmetric boundary conditions was successfully implemented and verified through secondary development of DTNAFLOW script, which divided the application of boundary conditions into two phases.

The accuracy of the proposed hybrid regional model was verified by comparing with the ground surface deformation of monitoring data, and the result indicated that regional model has good prediction effect.

Based on regional model, the surface settlement curve of Gongbei tunnel presents the form of normal distribution. The maximum displacement of ground surface appeared above the top of concrete-filled steel pipe (point P1) with the value of −2.98 mm.

According to the water pressure and deformation of Gongbei tunnel, the maximum vertical displacement occurred at the bottom of the right pipe after excavation. The value will reach to 4.26 mm without any support. Therefore, the phase of excavation had higher risk and should be paid more attention to. The time control for each construction step should be arranged properly, especially in the freezing and excavation steps. Besides, it might be more effective to set the temporary support at the bottom of the right pipe.

However, there are still have some shortcomings. For instance, the boundary conditions between hybrid regional model and actual engineering are not exactly the same and need further study. It should be noted that the application of the proposed hybrid regional model to Gongbei tunnel related cases will be a reference for similar large-scale underground engineering construction.

The authors wish to special thank Prof. Jean H. Prevost for the careful guidance as my supervisor during the studying period at Princeton University as VSRC scholar. Also thanks to the high-performance computing cluster of Computer Science Department at Princeton University and the editor Dr. Aubrey Dou for her careful format review.