Research paper
Modelling the hydro-mechanical behaviour of high-pressure tunnel with emphasis on the interaction between lining and rock mass

https://doi.org/10.1016/j.compgeo.2021.104382Get rights and content

Abstract

High-pressure tunnels with reinforced concrete lining have been extensively utilized in project practice. This study aims at developing a complete hydro-mechanical numerical model of high-pressure tunnels with emphasis on the interaction between lining and rock mass. In the model, a fully hydro-mechanical coupled formulation for saturated porous media is first established. A virtual element approach is proposed and combined with the master–slave contact algorithm to consider the interaction between lining and rock mass under hydro-mechanical coupling. A simple elastic-damage model is proposed to model the mechanical behaviour of the reinforced concrete lining. Moreover, the evolution formulations of the cracking and permeability of the reinforced concrete lining are derived based on China’s specifications. The proposed numerical model is first verified by simulating two examples that have analytical solutions. Then, the case study of an actual high-pressure tunnel is carried out. The whole water infilling process is numerically simulated and the obtained results are compared with the measured field data. The consistence between them further verifies the present numerical model. Consequently, some primary design-related parameters are investigated numerically with the present numerical model, and the results can be considered as general guide rules for the design of high-pressure tunnels.

Introduction

Tunnels with high internal water pressure have been extensively used in hydraulic and hydropower projects. These tunnels are generally embedded in rock masses and lined with steel or reinforced concrete. In comparison to the steel lining, the concrete lining possesses the advantages of low cost and convenient construction. However, unlike high-pressure tunnels with steel lining that is impermeable, high-pressure tunnels with concrete lining pose leakage possibility, which may lead to water loss or even threaten the stability of surrounding rock masses (Bian et al., 2016, Wang et al., 2013).

In the early design of pressure tunnels with concrete lining, the so-called surface force theory was generally utilized for structural analysis, which treats the internal water pressure as a surface force applied on the internal surface of concrete lining. However, with the significant increase of the internal water pressure level accompanied by massive constructions of tunnels, the surface force theory became inapplicable and then the so-called body force theory emerged. The basic idea of the body force theory is that the cracking of reinforced concrete lining is inevitable under high internal water pressure, and as a consequence, the lining becomes permeable after cracking and the seepage flow from inside to outside occurs. Therefore, the load applied on lining is actually a seepage body force instead of the surface force (Zhang and Zhang, 1980, Pan, 1981, Ye, 1998, Ye, 2001, Krishna, 2014). At present, the body force theory is considered to be more practical for high-pressure tunnels and has been applied in many actual projects (e.g. Ye, 1998, Ye, 2001, Hou, 2009, Su and Wu, 2009).

According to the body force theory, the hydro-mechanical behaviour exists throughout the water infilling process and the whole operation period of high-pressure tunnels, which is a crucial behaviour to understand the operation mechanisms of high-pressure tunnels. In fact, the analysis of the hydro-mechanical behaviour is a major concern in the design of tunnel engineering. Many researchers have contributed to this topic in recent years. The majority of these studies concern the hydro-mechanical behaviour during tunnel excavation and lining stages (e.g. Zhang et al., 2017, Zhang et al., 2019, Bui and Meschke, 2020, Guayacan-Carrillo et al., 2021). Meanwhile, a few studies focus on tunnels under internal water pressure. Analytical approaches were primary utilized in earlier years. Schleiss (1986) proposed a systematic analytical design method for high-pressure tunnels, taking into account the seepage force and the secondary permeability of lining and rock mass. Cao and Liu (1991) afterward conducted a similar work. With the development of computational techniques (e.g. Zhang et al., 2018a, Yuan et al., 2021a, Yuan et al., 2021b, Zhang et al., 2021, Zhao et al., 2021), numerical modelling of the hydro-mechanical behaviour of high-pressure tunnels attracts more attention recently (e.g. Cividini et al., 2012, Wang et al., 2013, Lamas et al., 2014, Bian et al., 2016, Zhang et al., 2018b). A distinct advantage of numerical modelling is that more complicated factors can be considered in comparison to analytical approaches, e.g. irregular geometry of lining, inhomogeneous rock mass and complex constitutive models for lining and rock mass. Based on the three-dimension elastoplastic finite element method (FEM), Bian et al. (2009) proposed a coupling method to simulate the hydro-mechanical process with lining cracking, and applied this method to an actual project, viz. Xiaowan Hydropower Station in China. Chen et al. (2014) proposed a fully coupled seepage–elastoplasticity–damage model for saturated porous media, which can reproduce the evolution of tensile and compressive damage, plasticity, porosity, permeability. Unfortunately, all the aforementioned numerical models did not consider the interaction between lining and rock mass. Actually, the interface between lining and rock mass is not always continuous. When the tensile stress of the interface achieves a certain value, the separation between lining and rock mass may occur, which is a common phenomenon for high-pressure tunnels (Fernandez, 1994, Bobet and Nam, 2007, Hou, 2009, Cividini et al., 2012, Zhou et al., 2015). This separation definitely has a significant influence on the mechanical behaviours of both lining and rock mass. In view of this, Zhou et al. (2015) incorporated a water-filled joint element into a coupling model based on FEM. However, indirect coupled method is adopted in their study, which may lack rigour. For example, the effect of volumetric strain on the seepage field is not considered in the governing equations. Furthermore, the lining and rock mass are not always fully contacted with each other at the very beginning. In most cases, there exists an initial gap between them due to the contractions of concrete and cement grouting material (Schleiss, 1987, Olumide and Marence, 2012). However, this initial gap between lining and rock mass cannot be considered with the water-filled joint element.

To fully capture the hydro-mechanical behaviour with the interaction between lining and rock mass of high-pressure tunnels, the following factors should all be incorporated in the model: the hydro-mechanical behaviour in saturated porous media, the interaction between lining and rock mass, and the material non-linearity of lining and rock mass. This study aims at developing a complete hydro-mechanical numerical model for high-pressure tunnels. Following the framework of Sloan and Abbo, 1999a, Sloan and Abbo, 1999b, a fully hydro-mechanical coupled formulation for saturated porous media is first established. To consider the interaction between lining and rock mass under hydro-mechanical coupling, a virtual element approach is proposed and combined with the master–slave contact algorithm. With this approach, contact restraint between lining and rock mass can be satisfied while the hydraulic head remains continuous. Furthermore, the surrounding rock mass is treated as an elastoplastic material with the Drucker–Prager model, while the reinforced concrete lining is modelled with a simple elastic-damage model to capture the main mechanical behaviour. The evolution formulations of the cracking and permeability of lining are derived according to China’s specifications (SL279, 2016, DL/T5057, 2009). The complete numerical model is implemented based on a self-developed FEM code (Zhang et al., 2017, Yuan et al., 2019). With the developed code, two benchmark problems are first solved to verify the proposed numerical model. Then, the whole water infilling process of an actual high-pressure tunnel is simulated and the numerical results are compared with the measured field data. Consequently, parametric studies are carried out to analyse the effect of some primary design parameters from the perspective of both structural safety of lining and leakage control.

Section snippets

Theoretical framework of modelling the hydro-mechanical behaviour in saturated porous media

The fully coupled hydro-mechanical behaviour in saturated porous media is governed by Biot’s consolidation equations, which consist of two parts: the equilibrium equation of solid phase and the continuity equation of fluid phase (Sloan and Abbo, 1999a).

The equilibrium equation of solid phase can be expressed as σ+b=0in which σ is the total stress tensor and b represents the body force vector. Note that the equilibrium equation is derived based on the total stress which can be related to the

Modelling the interaction between lining and rock mass

The interaction between lining and rock mass can be considered as a frictional contact problem, and thus the master–slave contact algorithm can be incorporated. In this study, the lining is treated as a slave body, while the rock mass is treated as a master body, as shown in Fig. 1. The node to segment contact scheme is utilized, i.e. slave nodes of lining elements contact with master segments of rock mass elements.

The interaction between lining and rock mass should satisfy the following

Verification of the present numerical model

To verify the proposed numerical model, two examples are numerically simulated. The first example considers one-dimensional soil column consolidation, which has an analytical solution and thus can serve as a benchmark to verify the capacity of modelling the hydro-mechanical behaviour of saturated porous media. In the second example, an idealized case of pressure tunnel is considered. In this case, analytical solutions can be derived and thus can be used to verify the present numerical model.

Simulation of the whole water infilling process

The present numerical model is utilized to model the whole water infilling process of an actual tunnel, viz. the high-pressure tunnel of Huizhou Pumped Storage Power Station. For a high-pressure tunnel, the water infilling process after construction is crucial because it is the first time of load bearing and the potential construction defects can be detected. This process generally lasts 10 20 days due to the restriction of loading rate. Simulation of the whole water infilling process can not

Conclusions

High-pressure tunnels with reinforced concrete lining have been extensively used in hydraulic and hydropower projects. To obtain a rational design for high-pressure tunnels, it is crucial to first understand their operation mechanisms under hydro-mechanical coupling, and numerical simulation can play an important role. This study presents a complete numerical model for hydro-mechanical analysis of high-pressure tunnels with an emphasis on the interaction between lining and rock mass.

In the

CRediT authorship contribution statement

Wei Zhang: Methodology, Software, Formal analysis, Writing - review & editing. Ming Liu: Data curation, Investigation, Writing - original draft. Kang Bian: Validation. Pei-Tong Cong: Supervision. Wei-Hai Yuan: Software, Methodology.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

The research is supported by the Natural Science Foundation of China (No. 41807223), the Natural Science Foundation of Guangdong Province, China (No. 2018A030310346), and the Water Conservancy Science and Technology Innovation Project of Guangdong Province, China (No. 2020–11).

References (44)

  • BianK. et al.

    Research on seepage of high pressure hydraulic tunnel when reinforced concrete lining cracking

    Chin. J. Rock Mech. Eng.

    (2010)
  • BobetA. et al.

    Stresses around pressure tunnels with semi-permeable liners

    Rock Mech. Rock Eng.

    (2007)
  • CaoK.M. et al.

    Research on design theory of reinforced concrete lining for tunnel under high inner water pressure

    Hydropower Technol. East China

    (1991)
  • CividiniA. et al.

    Investigation on the cause of damages of a deep tunnel

    Int. J. Geomech.

    (2012)
  • DL/T5057-2009A.

    Design Specification for Hydraulic Concrete Structures

    (2009)
  • FernandezG.

    Behavior of pressure tunnels and guidelines for liner design

    J. Geotech. Eng.-ASCE

    (1994)
  • FrancoB. et al.
  • HouJ.

    Observed data analysis of water filling test of the high-pressure tunnel in Tianhuangping Pumped-Storage Power Station

    Adv. Sci. Technol. Water Resour.

    (2009)
  • KrishnaK.P.

    Norwegian design principle for high pressure tunnels and shafts: Its applicability in the himalaya

    Hydro Nepal J. Water Energy Environ.

    (2014)
  • LamasL.N. et al.

    First infilling of the venda nova II unlined high-pressure tunnel: Observed behaviour and numerical modelling

    Rock Mech. Rock Eng.

    (2014)
  • MonforteL. et al.

    Low-order stabilized finite element for the full Biot formulation in soil mechanics at finite strain

    Int. J. Numer. Anal. Methods Geomech.

    (2019)
  • OlumideB.A. et al.

    A finite element model for optimum design of plain concrete pressure tunnels under high internal pressure

    Int. J. Sci. Technol.

    (2012)
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