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This paper proposes a back analysis method of measured displacements for predicting deformational behavior of discontinuous rock mass. The method is formulated by the adaptive filtering combined with the Backward Discontinuous Deformation Analysis (DDA). The Backward DDA is used to derive the observation equation, and the governing equation of displacements is adopted as the state equation in this method. The final deformational behavior of rock mass is predicted from measured displacements and the present deformational behavior is also estimated.
Although a number of methods for analyzing discontinuous rock mass have been developed, predicting its mechanical behavior is still a difficult task. This is because of the difficulties in determining mechanical properties of rock mass as well as an initial state of stress at the design stage. Hence, field measurements are performed to verify the predicted behavior and to update the design. The purpose of this paper is to provide a numerical method for evaluating the field measurement results of discontinuous rock mass. The proposed method is not only used for estimating the present deformational behavior of rock mass, but is also used for predicting the final behavior from measured displacements. The method is formulated by the adopted filtering combined with the Backward DDA (Shi and Goodman 1985, Shi 1993). The system equation of the filtering is composed of the observation equation and the state equation. The Backward DDA is used to derive the observation equation, and the governing equation for displacements is adopted as the state equation. Geometric conditions of discontinuous rock mass, i.e. location and direction of discontinuities, are required as input data, but mechanical constants of rock mass and stress conditions are not required to solve the problem.
The purpose of the method is to estimate the present deformation and to predict the final deformation of discontinuous rock mass from measured displacements. The following assumptions are adopted in the method.
1. the rock mass is composed of a number of blocks surrounded by discontinuities, 2. continuous displacement and small strain occur within each block, and displacements is composed of rigid-body parallel translation and rotation, and strains of rock block, 3. rock mass deformation shows steady-state time dependent behavior. The first two assumptions are the same as those in the Backward DDA and the last considers time dependent displacement behavior of rock mass, which will be defined in Section 3.2.
This method is formulated by using the filtering method. The system equation of filtering is composed of both the observation equation and the state equation. The Backward DDA is used to derive the observation equation. The governing equation of displacements of rock block is adopted as the state equation. In this section, the fundamental equation of the Backward DDA is described and the observation equation will be derived from it. The state equation will then be deduced and finally the solution procedure of the system equation is introduced.
