Analytical solution for estimating the stand-up time of the rock mass surrounding tunnel

[Display omitted] •An analytical solution to predict stand-up time of the rock mass was developed.•The solution was based on the rheological deformation model and Abel’s creep kernel.•Allowable displacement of the tunnel wall was also used in calculation.•The results of examples showed the same trend with Lauffer’s and Bieniawski’s suggested method.•Moreover, analytical method is simple and easy in calculation but is still consideration to the rock mass properties. The term “stand-up time” is used first time in Lauffer’s rock mass classification (1958) in relation to the so called “effective unsupported span” and then modified by Barton et al. (1975) and Bieniawski (1993). Until now stand-up time is a useful parameter in rock mechanics and tunnel design. It affects the selection of excavation method, excavation cycle and rock reinforcement method and time to install rock support. In other words, the stand-up time is a function not only of rock mass properties but also of excavation technique. Because classification methods are based on rock mass quality empirical evaluation through specific parameters, however, the determination of the rock mass properties to evaluate rock mass quality and also the stand-up time is very difficult in in-situ. Therefore, the development of a mathematical model is necessary and have great meaningful to estimate the stand-up time in the tunneling. The objective of the paper is to develop an analytical solution to predict stand-up time of the rock mass surrounding tunnel based on the rheological deformation model using Abel’s creep kernel and allowable displacement of the tunnel wall. The results of numerical example shown in good agreement with Bieniawski’s suggested method.