Implementation of a new time-dependent shotcrete constitutive model for 3D tunnel modeling

Shotcrete behaviors, including modulus and compressive strength, are highly time-dependent. Moreover, freshly applied shotcrete is subjected to loading immediately after application, making its realistic representation both essential and challenging in numerical modeling. The objective of this study was to improve the numerical prediction of shotcrete creep by developing a constitutive model that accounts for the time-dependent evolution of modulus.The constitutive equation was formulated by incorporating a time-dependent modulus, and the new shotcrete constitutive law was implemented in the finite-difference code FLAC3D using C++. Accordingly, a new shotcrete creep constitutive law was developed, capable of simulating shotcrete creep while capturing the time-dependent evolution of modulus, a feature not included in FLAC3D’s built-in creep constitutive models.The mathematical plausibility of the material law was verified over a 14-day creep period, with good agreement between the analytical and numerical solutions. A key aspect of the model is its ability to simulate different shotcrete layers with varying installation ages by considering the shear modulus as time-dependent. This understanding enables a more accurate representation in the computational design of shotcrete-supported tunnels. The applicability of the new time-dependent material law was also validated through three-dimensional tunnel modeling over 30 days of creep, confirming that the developed shotcrete model can reliably reproduce shotcrete creep behavior. Accurately modeling shotcrete's time-dependent properties in numerical simulations can enhance the safety and efficiency of shotcrete-supported tunnels.