Time-Dependent Behavior in Tunnel Engineering

Time-dependent behaviour in tunnel engineering arises from the gradual deformation and strength evolution of the ground and lining materials after excavation. In rock masses and soils, rheological phenomena such as creep, stress relaxation and long-term strength reduction drive ongoing convergence of the tunnel profile and progressive loading on support systems. This behaviour is influenced by geological factors (mineralogy, jointing and anisotropy), hydrogeological conditions (pore pressure changes and seepage), construction methods (sequential excavation and lining installation) and environmental variables (temperature and chemical interactions). Accurately predicting time-dependent deformation is critical for the design of support systems, maintenance scheduling and risk management in deep or high-stress tunnels, hydraulic diversions and metro systems. Analytical, numerical and empirical-probabilistic approaches have been developed to capture the interplay between material rheology and structural response. Advances in constitutive modelling, laboratory characterisation and field monitoring have enhanced our ability to anticipate long-term performance, extending service lives and reducing maintenance costs. The global expansion of underground infrastructure underlines the need for robust assessment of time-dependent effects to ensure safety and sustainability.

Research from Nature Portfolio

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Research from all publishers

Recent studies have applied probabilistic and numerical methods to capture the effects of rock rheology and groundwater on tunnel performance. A 2024 investigation adopted a visco-elastoplastic constitutive model to represent both intact and blast-damaged rock around pressurised tunnels. By coupling Monte Carlo simulation with response surface methodology and three-dimensional numerical analyses, researchers quantified the statistical distributions of tunnel convergence and lining pressure under varying geological strength and water pressure conditions, revealing that elevated pore pressure amplifies both displacement variability and design uncertainty.

Research on cross-fault diversion tunnels has addressed the combined influence of faulted geology and creep on segment lining deformation during construction and operation. In a 2022 study, time-displacement monitoring data informed selection of an appropriate creep model via regression-comparison, while intelligent inversion techniques provided in situ rock parameters. Three-dimensional numerical simulations showed that faults alter deformation patterns asymmetrically and that lining subsidence rates vary according to the relative position of the fault, informing targeted support strategies in complex geological settings.

Modelling of anisotropic, time-dependent rock behaviour has seen advances through the implementation of a transversely isotropic Burgers constitutive model in finite-element software. Validation against analytical and isotropic solutions confirmed the model’s reliability. Parametric analyses explored the effects of material anisotropy, initial stress orientation and constitutive selection on tunnelling response, demonstrating that neglecting anisotropic viscosity can lead to underestimation of both convergences and support loads in layered rock masses.

Time-Dependent Behavior in Tunnel Engineering publication trend

The graph below shows the total number of articles in time-dependent behavior in tunnel engineering across all publications each year (not limited to Nature Index journals).

Technical terms

Rheology: Study of deformation and flow characteristics of geomaterials under stress over time.

Creep: Time-dependent, permanent deformation of rock or soil under sustained load.

Constitutive model: Mathematical description of material stress–strain behaviour, including time-dependent effects.

Response surface methodology: Statistical technique to approximate relationships between input variables and engineering responses.

Burgers model: Viscoelastic representation combining Maxwell and Kelvin elements to simulate primary and secondary creep.

References

1. Reliability analysis of deep pressurized tunnels excavated in the rock mass with rheological behavior. Transportation Geotechnics (2024).
2. Investigation on the Deformation of Segment Linings in Cross-Fault Tunnel Considering the Creep Behavior of Surrounding Rock during Construction-Operation Period. Buildings (2022).
3. Modelling underground excavations in rock masses with anisotropic time-dependent behaviour. Geomechanics and Geophysics for Geo-Energy and Geo-Resources (2022).