How to identify earth pressures on in-service tunnel linings: Insights from Bayesian inversion to address non-uniqueness

Identifying earth pressures on in-service transportation tunnel linings is essential for their health monitoring and performance prediction, particularly in structures that exhibit poor performance. Due to the high costs associated with pressure gauges, pressure inversion based on easily observed structural responses, such as deformations, is preferred. A significant challenge lies in the non-uniqueness of inversion results, where various pressures can yield similar structural responses. Existing approaches often overlook detailed discussions on this critical issue. In addressing this gap, this study introduces a Bayesian approach. The proposed statistical framework effectively quantifies the uncertainty induced by non-uniqueness. Further analysis identifies the uniform component in distributed pressures as the primary source of non-uniqueness. Insights into mitigation strategies are provided, including increasing the quantity of deformation data or incorporating an observation of internal normal force within the tunnel lining -- the latter proving to be notably more effective. A practical application in a numerical case study demonstrates the effectiveness of this approach. In addition, our investigation recommends maintaining deformation measurement accuracy within the range of -1, 1 mm to ensure satisfactory outcomes. Finally, deficiencies and potential future extensions of this approach are discussed.