Abstract:

Based on complete measurement information, it has important practical value for guiding back analysis practice in geotechnical engineering to study the identifiability and optimal measured arrangement of elastic back analysis of parameters. Via planar elastic function of complex variable technique and general elastic theory, the analytic formulas of displacement and stress are derived; and based on the displacement and disturbed stress solutions for the plane elasticity problems, this paper studies the identifiability and optimal measured arrangement of back analysis of elastic parameters by use of differentiability condition of parameters and most sensitive principle of optimal measured arrangement, and uses a simple example to validate the conclusion. The study shows, based on the complete measured information to carry out elastic back-analysis, the five parameters P, Q, M, E and ? can be identified uniquely under condition that the measured arrangement is appropriate and the parameters satisfy the restrictive conditions. The identifiability of inversion parameters is influenced by the shape complexity of tunnel; and with the shape complexity of tunnel increasing, the restrictive conditions of the parameters are decreased; the requirement for the measured arrangement is also reduced. To avoid the substantial fluctuation of inversion results arisen from a small error of measurement data in engineering practice, the combination of measured points (lines) which has the largest sensitivity coefficient value of each inversion parameter should be chosen as the optimal measured arrangement based on the most sensitive principle.

Key words: underground tunnel, elastic back analysis, information completeness, identifiability, optimal arrangement