  The identification of earth pressures acting on in-service transportation
tunnel linings is essential for their health monitoring and performance
prediction, especially for those exhibiting poor structural performance. Since
pressure gauges incur substantial costs, the inversion of pressures based on
easily observed structural responses, such as deformations, is desirable. The
inherent challenge in this inverse problem lies in the non-uniqueness of
solutions, which arises from the fact that various pressures can yield
structural responses fitting equally well with the observed data. However,
existing approaches for pressure inversion predominantly rely on a
deterministic framework, often neglecting a detailed discussion on this
non-uniqueness. In addressing this gap, this study introduces a Bayesian
approach. The proposed statistical framework enables the quantification of
uncertainty induced by non-uniqueness in inversion results. The analysis
identifies the uniform component in distributed pressures as the primary source
of non-uniqueness. The mitigation of solution non-uniqueness can be achieved by
increasing the quantity of deformation data or incorporating an observation of
internal normal force in a tunnel lining -- the latter proving to be notably
more effective. The practical application in a numerical case demonstrates the
effectiveness of this approach and the associated findings. 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.
