Uncertainty is an essentially challenging for safe construction and long-term stability of geotechnical engineering. The inverse analysis is commonly utilized to determine the physico-mechanical parameters. However, conventional inverse analysis cannot deal with uncertainty in geotechnical and geological systems. In this study, a framework was developed to evaluate and quantify uncertainty in inverse analysis based on the reduced-order model (ROM) and probabilistic programming. The ROM was utilized to capture the mechanical and deformation properties of surrounding rock mass in geomechanical problems. Probabilistic programming was employed to evaluate uncertainty during construction in geotechnical engineering. A circular tunnel was then used to illustrate the proposed framework using analytical and numerical solution. The results show that the geomechanical parameters and associated uncertainty can be properly obtained and the proposed framework can capture the mechanical behaviors under uncertainty. Then, a slope case was employed to demonstrate the performance of the developed framework. The results prove that the proposed framework provides a scientific, feasible, and effective tool to characterize the properties and physical mechanism of geomaterials under uncertainty in geotechnical engineering problems.

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Keywords: Geological engineering, Geotechnical engineering, Inverse analysis, Uncertainty quantification, Probabilistic programming