This paper investigates the effect of deficiencies in the tunnel crown thickness on pressure tunnels with the posttensioned concrete lining. Based on the lining parameters of the Yellow River Crossing Tunnel, the modeling approach of the posttensioned concrete lining is introduced in detail and a three-dimensional finite element model is established. The three-dimensional finite element model is validated by experimental results from the full-scale model experiment of the Yellow River Crossing Tunnel. Special attention is given to the changes in the deformation, radial displacement, and circumferential stress of the posttensioned concrete lining with gradual decreases in the tunnel crown thickness. The calculation results show that the influence scopes of deficiencies in the tunnel crown thickness are mainly concentrated in the crown and its adjacent parts. The posttensioned concrete lining can still maintain a satisfactory stress state when deficiencies in the tunnel crown thickness exist, and undesirable stress levels may be caused only when the tunnel crown thickness decreases below a certain threshold. Furthermore, cracks are most likely to occur at the external and internal surfaces of the crown and at the internal surface of the crown’s adjacent parts, which is useful for taking measurements regarding the lining tightness and stability.

Antiseepage is an important requirement for tunnels subjected to high internal water pressure. The posttensioned concrete lining (PTCL) is considered to be a suitable solution to improve the water impermeability of such tunnels. For the PTCL, the anchor cable is tensioned and anchored in the anchorage slot. After the completion of tensioning and anchoring, lining concrete can be held in a fully compressed state by introducing prestress, ensuring stability and watertightness [

Details of the PTCL.

Despite the specified requirements and supervisions in quality control during the construction of the concrete lining, construction errors may exist due to careless construction [

Many negative consequences result from deficiencies in the tunnel crown thickness. For example, Bian et al. [

The above research suggests that deficiencies in the tunnel crown thickness can cause widespread damage to the concrete lining, ranging from concrete cracking to local collapses. However, all of the above achievements have focused on reinforced concrete linings. Few studies have focused on the PTCL, for which deficiencies in the tunnel crown thickness may generate more complex problems. For the PTCL with insufficient tunnel crown thickness, a void may form and the anchor cable at the crown may hang in the void, as shown in Figure

PTCL: (a) the tunnel crown thickness is equal to the design value and (b) the tunnel crown thickness is less than the design value.

The paper represents its kind analysis for the potential influence of deficiencies in the tunnel crown thickness on pressure tunnels with the PTCL for the first time. The Yellow River Crossing Tunnel in the Middle Route of the South-to-North Water Diversion Project is adopted as a reference case. Based on the soil and lining parameters of the Yellow River Crossing Tunnel, the modeling approach of the PTCL is introduced in detail and a three-dimensional finite element model is established. To evaluate the effect of deficiencies in the tunnel crown thickness on the PTCL during the construction phase and operation phase, two working conditions are analyzed: the completed cable tensioning condition (CCTC) and water in the tunnel with the design water pressure condition (DWPC). Changes in the deformation, radial displacement, and circumferential stress of the PTCL with gradual decreases in the tunnel crown thickness are investigated. Furthermore, the locations at which cracks in the PTCL are most likely to occur are also identified.

The Yellow River Crossing Tunnel, located in Zhengzhou city, China, is a key component of the Middle Route of the South-to-North Water Diversion Project. The Yellow River Crossing Tunnel passes through soft soil and was constructed by the shield tunnelling method. The precast segments are assembled to withstand the soil pressure and the external water pressure during excavation. The internal water pressure in the centre of the tunnel is more than 0.5 MPa during the operation phase. If the internal water pressure is borne only by the segmental lining, the segmental joints will be a large opening, resulting in water seepage. Therefore, the PTCL is needed as the secondary lining to withstand the high internal water pressure. When the segmental lining has already borne the external pressure and achieved stability, the PTCL begins to be poured. The bottom of the PTCL is directly poured on the segmental lining, and the others are separated from the segmental lining by the membrane. The membrane can play a role in waterproofing and drainage [

The PTCL of the Yellow River Crossing Tunnel has an inner diameter of 7 m, an outer diameter of 7.9 m, and a thickness of 0.45 m. An anchor cable has a design tension stress of 1,395 MPa and includes 12 steel strands. Each steel strand contains 7 high-strength and low-relaxation steel wires. The centre lines of the anchorage slots are located at angles of 96°, 134°, 226°, and 264°. The distance between adjacent anchorage slots is 0.45 m along the axial direction. The cross section of the PTCL is shown in Figure

Cross section of the PTCL (unit: m).

Layout of the internal surface of the PTCL (unit: m).

The numerical model is established by taking a 9.6 m length along the axial direction of the tunnel. The numerical model is restrained in the horizontal direction at the lateral boundaries and is restrained in both the vertical and horizontal directions at the bottom boundary. The upper boundary has no constraints. The lateral and bottom boundaries of the discretization are placed at positions with a sufficient distance, namely, 4 times the tunnel diameter. The upper boundary is placed directly on the ground surface with a sufficient distance, which is approximately 5 times the tunnel diameter. The soil strata, where the Yellow River Crossing Tunnel is situated, comprised medium sand. Small amounts of clay strata are present below the tunnel. The strata distribution is shown in Figure

Distribution of the soil strata.

A typical finite element mesh of the Yellow River Crossing Tunnel is shown in Figure

Finite element models.

Material properties.

Part | Material | Elasticity modulus, |
Poisson’s ratio, |
Unit weight, ^{−3}) |
---|---|---|---|---|

PTCL | C40 concrete | 3.25 × 10^{4} |
0.167 | 24.5 |

Segmental lining | C50 concrete | 3.45 × 10^{4} |
0.167 | 25 |

Membrane | Composite material | 1.5 | 0.3 | — |

Anchor cable | Steel | 1.95 × 10^{5} |
0.3 | 78.5 |

Reinforcing bar | Steel | 2.0 × 10^{5} |
0.3 | 80 |

The interfaces between the internal surfaces of the membrane and the external surfaces of the PTCL and interfaces between the soil excavation boundary and the external surfaces of the segmental lining are simulated by contact elements. The contact behaviour in the radial direction is simulated as a hard contact transmitting compressive stresses but cannot transmit radial tensile stresses [

Six simplified cross sections of the PTCL with insufficient tunnel crown thickness are introduced, as shown in Figure

Six cases considering different concrete thicknesses in the tunnel crown: (a) before tensioning of the anchor cable and (b) after tensioning of the anchor cable.

When the anchor cable tension is completed, the prestresses (_{1}) are not constant due to friction between the anchor cable and the duct. The shapes of the anchor cables at the crown are curved when _{1} considering the frictional losses should be divided into two cases. When _{1} can be expressed as

Calculation of the prestress: (a)

When _{1} can be calculated by

Prestress losses of the anchor cables are inevitable, and prestress losses after tensioning of the anchor cable considered in the numerical model mainly include _{l1} caused by anchorage deformation and anchor cable retraction, _{l2} caused by stress relaxation of the anchor cable, and _{l3} caused by concrete shrinkage and creep [_{l1}, _{l2}, and _{l3} can be calculated following the formulas recommended by the Code for Design of Concrete Structure [_{l1} can be expressed as follows:_{l2} and _{l3} can be expressed as follows:

Finally, the effective prestresses

The effective prestresses are converted into the temperature loads, and the temperature loads are applied to the anchor cable elements [

According to the construction process and the operating conditions of the Yellow River Crossing Tunnel, two main calculation stages are considered. The first stage is the CCTC, in which the PTCL is poured and the anchor cable tension is completed. The second stage is the DWPC, in which the internal water pressure is applied on the PTCL. The load combinations of each working condition are shown in Table

Load combinations of the working conditions.

Working conditions | Gravity | Soil pressure | External water pressure | Effective prestress | Internal water pressure |
---|---|---|---|---|---|

CCTC | √ | √ | √ | √ | — |

DWPC | √ | √ | √ | √ | √ |

The external water pressure in the horizontal line of the tunnel centre is 0.323 MPa. The internal water pressure in the tunnel centre is 0.517 MPa. Separate calculations of water pressure and earth pressure can be used when the tunnel is covered by sandy soil [

The numerical model is validated by experimental data from the full-scale model experiment of the Yellow River Crossing Tunnel [

The average circumferential stresses of the observation points under the CCTC and DWPC are summarized in Table

Average circumferential stresses of the observation sections (unit: MPa).

Section I | Section II | Section III | ||||
---|---|---|---|---|---|---|

CCTC | DWPC | CCTC | DWPC | CCTC | DWPC | |

Experimental results | −7.74 | −4.19 | −7.36 | −2.98 | −7.14 | −4.21 |

Numerical results | −7.00 | −3.31 | −7.12 | −2.88 | −6.62 | −3.27 |

A series of finite element analyses have been performed to examine the effect of deficiencies in the tunnel crown thickness on the PTCL. Section II is selected as the typical section, and the numerical results of section II are shown in Figures

Deformations of the PTCL under the CCTC: (a)

Deformations of the PTCL under the DWPC: (a)

Radial displacement of the PTCL: (a) CCTC and (b) DWPC.

Circumferential stresses of the PTCL’s internal surface: (a)

Circumferential stresses of the PTCL’s external surface: (a)

Locations where the tension stresses have already exceeded the tensile strength of the PTCL under the DWPC: (a)

The calculated deformations of the PTCL under the CCTC and DWPC are shown in Figures

According to Figure

In contrast, a different trend occurs when

The calculated radial displacement of the PTCL under the CCTC and DWPC in six cases is shown in Figure

The maximum radial displacement of the PTCL is located at the crown (

When

The circumferential stresses of the internal surface and external surface of the PTCL are shown in Figures

According to Figures

In contrast, when

The results in Figures

According to Figures

In contrast, when

The above findings imply that the PTCL will be subjected to tensile stresses under the DWPC if the deficiencies in the tunnel crown thickness exceed a certain threshold. Figure

This paper investigates the effect of deficiencies in the tunnel crown thickness on the PTCL. The Yellow River Crossing Tunnel is adopted as a reference case, and numerical analyses are performed using a three-dimensional finite element model. The three-dimensional finite element model is validated by experimental data from the full-scale model experiment of the Yellow River Crossing Tunnel. The possible damage and corresponding locations are discussed. The following conclusions are drawn from the results with the conditions and assumptions given in this study:

The influence scopes of deficiencies in the tunnel crown thickness are mainly concentrated in the tunnel crown and its adjacent parts. There are only small changes in the deformation, radial displacement, and circumferential stress in the other parts of the PTCL considering variations in the tunnel crown thickness.

The PTCL can still maintain a satisfactory stress state with the existence of deficiencies in the tunnel crown thickness. Undesirable stress levels may occur only when the tunnel crown thickness decreases below a certain threshold.

Compressive stress concentration of the tunnel crown’s internal surface is notable, and the internal surface of the tunnel crown concrete may be crushed under the CCTC. Because the cracks form during the tensioning process, such crushing may be readily detected.

Cracks at the external surface of the crown and internal surface of the crown’s adjacent parts may be expected under the DWPC. Because the cracks form during the filling of the tunnel with water, they may not be readily detected until serious damage to the lining has been produced, generally in the form of severe cracking, leaking, or even failure.

The authors declare that there are no conflicts of interest regarding the publication of this paper.

This work is supported by the Hubei Province Natural Science Foundation of China (no. 2017CFB667), the State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering Foundation (no. 2015494711), and the National Natural Science Foundation of China (no. 51079107). Additionally, the provision of the original data by the Changjiang Institute of Survey, Planning, Design and Research is gratefully acknowledged.