To date, with the increasing attention of countries to urban drainage system, more and more regions around the world have begun to build water conveyance tunnels, sewage pressure deep tunnels and so on. However, the sufficient bearing capacity and corrosion resistance of the structure, which can ensure the actual service life and safety of the tunnel, remain to be further improved. Glass Fiber Reinforced Plastics (GFRP) pipe, with light weight, high strength and corrosion resistance, has the potential to be applied to the deep tunnel structure. This paper proposed a new composite structure of deep tunnel lined with GFRP pipe, which consisted of three layers of concrete segment, cement paste and GFRP pipe. A new pipe-soil spring element model was proposed for the pipe-soil interaction with gaps. Based on the C3D8R solid model and the Combin39 spring model, the finite element numerical analysis of the internal pressure status and external pressure stability of the structure was carried out. Combined with the checking calculation of the theoretical formula, the reliability of the two finite element models was confirmed. A set of numerical analysis methods for the design and optimization of the three-layer structure was established. The results showed that from the internal GFRP pipe to the outer concrete pipe, the pressure decreased from 0.5 to 0.32 MPa, due to the internal pressure was mainly undertaken by the inner GFRP pipe. The allowable buckling pressure of GFRP pipe under the cover of 5 GPa high modulus cement paste was 2.66 MPa. The application of GFRP pipe not only improves the overall performance of the deep tunnel structure but also improves the construction quality and safety. The three-layer structure built in this work is safe and economical.

As the result of the current increasing engineering requirements and more complex geographical environment, the tunnel structure has been further investigated around the world. The optimization design of the tunnel structure is an important direction of continuous development, such as the Kanda Deep Tunnel, Tokyo “underground temple,” Kuala Lumpur Tunnel, Thames Sewage Tunnel, Yellow River Crossing Tunnel and so on [

The multi-layer composite structure has been applied more and more in engineering construction. Many existing methods of multi-layer structure analysis were based on the assumption of a through-the-thickness distribution of displacements, the derivation of strain and stress, and the application of virtual work principle. At present, more scholars use finite element method to establish the calculation model of composite laminar structure, most of which are based on the equivalent single-layer theory (ESL). From the classical laminated plate theory (CLPT) [

The methods of pipe-soil interaction usually include contact surface method, PSI element method and spring element method. The contact surface method defines the contact of the pipe-soil solid model, which used to be the static analysis due to its large computational cost and difficulty in convergence during large deformation. Through the way that one side shares nodes with pipeline and other side represents the soil surface, PSI element comprehensively considers the contact surface property of the pipe-soil and the deformation characteristics of the soil, which simplifies the analysis process, but this element only has displacement freedom degree. The spring element method reflects constitutive relation of the soil by defining stiffness coefficient of the spring, which means that the soil around the pipe is discretized into springs distributed at a certain interval, without the need to establish the soil entity. Chen et al. [

This paper proposed a three-layer deep tunnel composite structure lined with GFRP pipe, which was composed of concrete segment with high resistance to external pressure, GFRP pipe with high resistance to internal pressure and cement paste, as shown in

Based on the finite element analysis of solid element model and the checking calculation of elastic mechanics theory formula, the basic characteristics of deep tunnel composite structure under internal pressure were analyzed. Based on the finite element analysis of the pipe-soil spring element model and the checking calculation of the buckling formula of M45 manual, this paper carried out research on the external pressure stability of the GFRP pipe with the gap between the soil and the pipe. The transfer law of internal pressure and strain from inside to outside and the allowable buckling pressure with gaps in tube-soil interaction were obtained to evaluate the safety and reliability of the structure and guide its structural design. The three-layer composite structure gives full play to the high external compressive strength of outer layer and high internal compressive strength of inner layer, which is a safe and economical structure.

In the analysis of pipe-soil interaction, the contact surface method is the most accurate solution, which can clearly see the stress distribution cloud diagram of the entire pipe and soil. In this paper, the contact surface method of solid elements was used to analyze the internal pressure of the three-layer structure. According to the structure size and material parameters of the deep tunnel composite structure lined with GFRP pipe, the finite element analysis model of the three-layer structure was established by ABAQUS finite element analysis software.

In ABAQUS, the types of solid elements based on stress-displacement are the most abundant. The 8-node hexahedral linear reduction integral element-C3D8R was adopted, and the contact pair properties of frictionless and hard surface contact were adopted. The calculation results of displacement by linear reduction integral element are more accurate, and the analysis accuracy will not be greatly affected when there is distortion or large deformation of mesh. The dimensions and material parameters of the three-layer structure were shown in

Layer number | Material | Inner diameter (mm) | Thickness (mm) | Inner radius (mm) | Outer radius (mm) | Modulus (MPa) |
---|---|---|---|---|---|---|

1 | Concrete segment | 3600 | 250 | 1800 | 2050 | 34500 |

2 | Cement paste | 3400 | 250 | 1550 | 1800 | 5000 |

3 | GFRP pipe | 3000 | 50 | 1500 | 1550 | 14610 |

Layer number | Internal strain ( |
External strain ( |
Internal stress (MPa) | External stress (MPa) |
---|---|---|---|---|

1 | 70.58 | 60.52 | 2.504 | 2.501 |

2 | 95.89 | 74.60 | 0.667 | 0.525 |

3 | 103.9 | 100.2 | 1.698 | 1.626 |

In this paper, another set of simulations was performed to verify the reliability of the above simplified constraints. The three-layer structure was embedded into the surrounding elastic medium, that was, solid elements of soil with modulus 15 MPa were established outside the three-layer structure. Internal pressure of 0.5 MPa was applied inside to observe its mechanical response. Also, there was only continuum mechanics, and there was no elastic mechanics. The finite element analysis model 2 was shown in

The material parameters of the three layers were shown in

Layer number | Internal strain ( |
External strain ( |
Internal stress (MPa) | External stress (MPa) |
---|---|---|---|---|

1 | 70.76 | 58.80 | 2.511 | 1.996 |

2 | 96.21 | 72.46 | 0.669 | 0.516 |

3 | 103.0 | 98.81 | 1.686 | 1.607 |

The three-layer structure proposed in this paper was composed of concrete segment, Cement paste and GFRP pipe. Under the action of internal pressure P, the pressure, stress and strain of each layer were deduced through elastic mechanics theory. The theoretical calculation model of three-layer structure was shown in

For the convenience of analysis, the three-layer structure was divided into _{i}_{i}_{i}_{ia}_{ib}_{i}

where, _{i}_{i}_{i}_{i}

where, _{ia}_{ib}_{3a} was equal to _{1b} was equal to 0, _{3b} and _{2b} were calculated according to the following equation:

The basic characteristics of the three-layer structure under the action of internal pressure P were analyzed by numerical simulation of finite element and checking calculation of theoretical formula. According to the requirements of different materials, sizes and working conditions, we can continuously optimize the structural design through a set of numerical analysis methods established by solid element model and theoretical calculation formula. The stress–strain results of each layer obtained by finite element analysis and theoretical calculation are consistent, the external hoop strains of the concrete segments are 60.52 and 62.40

_{ia} |
_{ib} |
|||||
---|---|---|---|---|---|---|

1 | 0.32 | 0 | 71.67 | 62.40 | 2.47 | 2.15 |

2 | 0.44 | 0.32 | 95.31 | 71.67 | 0.48 | 0.36 |

3 | 0.5 | 0.44 | 99.56 | 95.31 | 1.45 | 1.39 |

Considering the influence of water seepage in the outer structure, a new spring element model of pipe-soil interaction was proposed to analyze the external pressure stability of GFRP pipe, and the allowable buckling pressure with gaps was obtained. In the three-layer structure, GFRP pipe is surrounded by cast-in-place cement paste, which is equivalent to a high modulus soil cover, and does not need to consider the impact of buried depth and

There are many elements that can be used to simulate springs in ANSYS finite element analysis software, and they have their unique applications in many aspects, such as link180, combin39, and combin40. The link180 element is defined by two nodes, cross-sectional area, mass per unit length, and material properties. It can simulate the soil around the pipe, but it cannot simulate the special case of existing gap between the pipe and soil. The combin39 spring element is a unidirectional element with nonlinear function, defined by two nodes and a generalized force-deformation curve, as shown in

where, _{1} is the elastic modulus of the spring element (Pa), ^{2}), _{1} is the length of the spring element (m), _{s}

In the spring element model of pipe-soil interaction, GFRP pipe was established by shell63 element, and the combin39 element was established through the nodes on the surface to simulate the cement paste, as shown in

The external pressure stability of GFRP pipe under the soil condition of low modulus without gap and high modulus with gap was analyzed respectively. The first-order stability coefficient was extracted to obtain its critical external pressure, as shown in

Pipe-soil spring element model | |||
---|---|---|---|

Soil modulus (MPa) | 3 | 5 | 5000 |

Gap (mm) | 0 | 0 | 0.2 |

Buckling allowable pressure (MPa) | 0.367 | 0.558 | 2.66 |

The American Water Works Association (AWWA) Manual M45, Fiberglass Pipe Design, contains detailed information on the design, specification, procurement and installation of fiberglass pipe and fittings. The M45 manual is usually used for reference and planning of new fiberglass piping design projects. For buckling analysis of buried pipes, the appropriate external load should be equal to or less than the allowable buckling pressure. Due to the restraining effect of soil around the pipe, the external radial pressure that causes the buckling of buried pipe will increase a lot. The allowable buckling pressure in the M45 manual is determined by the following formula [

where, _{a}_{n}^{2}/m), and _{s}_{v}_{h}

The M45 buckling formula does not consider the gap between pipe and soil, and is often used to calculate the allowable buckling pressure of buried pipe under low soil modulus, such as 3 and 5 MPa. In this paper, the allowable buckling pressure of GFRP pipe under low soil modulus was calculated by the M45 buckling formula in order to verify the reliability of the pipe-soil spring element model. Due to the effect of the concrete segment and cement paste, the influence of _{v}_{h}

Theoretical formula for M45 | Pipe-soil spring element model | |||
---|---|---|---|---|

_{s} |
3 | 5 | 3 | 5 |

_{a} |
0.376 | 0.529 | 0.345 | 0.551 |

Based on the numerical analysis of finite element and the verification of theoretical formulas, the following research conclusions were obtained in this paper.

A new deep tunnel composite structure lined with GFRP pipe was presented. Based on solid element model, pipe-soil spring element model and theoretical formulas, a set of numerical analysis methods for evaluating the safety and reliability of the structure and guiding its structural design and optimization were proposed.

In internal pressure analysis, the internal pressure was mainly borne by the innermost GFRP pipe. The errors for the external hoop strains of the concrete segments and the GFRP pipe were respectively 3.01% and 5.13%. The stress–strain of each layer obtained by finite element analysis and theoretical calculation was basically consistent, which confirmed the reliability of the C3D8R solid element model in this paper.

A pipe-soil spring element model was proposed to analyze the external pressure stability of GFRP pipe under the soil condition of 5 GPa high modulus with 0.2 mm gap, and allowable buckling pressure of GFRP pipe was 2.66 MPa, which met the external pressure requirement of deep tunnel.

Under the soil condition of 3 and 5 MPa low modulus, the allowable buckling pressures obtained by the M45 were 0.376 and 0.529 MPa, the allowable buckling pressures obtained from the pipe-soil spring element model were 0.367 and 0.558 MPa, with errors of 2.39% and 5.48%, respectively, which confirmed the reliability of the pipe-soil spring element model.

The outer lining of the three-layer structure was concrete segments with high resistance to external pressure, and the inner lining was GFRP pipe with high resistance to internal pressure. The three-layer structure gave full play to the characteristics of the material. The application of GFRP improved the overall performance of tunnel structure. Compared with the traditional cast-in-place prestressed reinforced concrete, it simplified the construction process and greatly improved the quality and safety of construction, which was a safe and economical structure.