According to the features of displacement-time curves on tunnel, the possibility to use displacement acceleration form curve model as a stability criterion of rockmass is analyzed. By means of GM(1,1) model of Grey system, the stable displacements and the ultimate convergence displacements of rockmass are predicted. The formula of predicting unstable time with tangent angle is established.


It is well known that there are many Grey systems in reality, which are complex systems formed by both known and unknown factors or indefinite factors. To define all of factors, and erect corresponding mathematical model for these systems is almost impossible. We can avoid these difficulties completely, according to a group of tested data in a happened time-series, begin from time-series analysis method and establish mathematical model, which is applied to forecast future action of systems directly. That is the character of Grey system[1]. The change of displacement convergence in tunnel rockmass is a Grey system in fact. This system composed of known factors (such as the geometrical figure, dimension, mechanical performance) and many unknown factors (such as mechanical state of rockmass-support system, rockmass mechanical performance). By means of the Grey system, we can predict the future development tendency according to measurement data, and pre-control the rockmass to avoid fatal accident and significant property loss. We select the displacement convergence of tunnel rockmass as the basic physical parameter for predicting, because the measurement is more convenient, and original data more reliable. Utilizing the Gray theory model GM(1,1), the stable displacement and ultimate displacement can be predicted. Therefore the result of stability analysis is given to spot engineering timely, on the other hand, some predicted data such as initial stress, and elastic modulus can be used for stability analysis.

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