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Time-dependent analytical solution for loess tunnels considering water content softening effect
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DOI：10.1007/s11440-026-03200-5.png)
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Abstract
En 中文
Water-induced softening and time-dependent rheology are the primary drivers of large deformation hazards in loess tunnels. To quantitatively analyze these effects, this study proposes a fractional creep model incorporating water-content softening effects and a corresponding visco-elastoplastic analytical solution. First, triaxial creep tests were conducted to reveal the degradation laws of rheological parameters. Results indicate that water content is the governing state variable; as it increases from 8 to 23%, the elastic modulus, viscosity coefficient, and strength decrease by 44–61%. Based on these findings, a fractional derivative constitutive model incorporating water-dependent damage variables was constructed. Second, utilizing the Laplace transform and rheological series–parallel rules, an analytical solution for the excavation process—covering “rheological deterioration under initial support” and “secondary lining installation”—was derived. Parametric and engineering indicator analyses demonstrate that increased water content significantly expands the disturbance zone, creep displacement, and lining stress, while the self-stabilization capacity of the surrounding rock declines remarkably. The study elucidates the stability mechanism of loess tunnels, indicating that an optimal safe time window for secondary lining installation can be quantitatively evaluated. Water content serves as a primary controlling factor for self-stabilization, and weak initial support in water-rich conditions can lead to displacement exceeding limits within a short period. Supported by field monitoring data from the Xujiachuan Tunnel, this solution provides a theoretical reference for emphasizing proactive groundwater management alongside conventional structural support in loess tunnel engineering.
Keywords:
Deep-buried loess tunnel
Fractional rheology
Secondary lining timing
Self-stabilization
Visco-elastoplastic analytical solution
Water-induced softening
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