Biaxial response of buried pipelines to arbitrary excavation-induced ground-movement fields: A pipe–soil interaction solution with Bayesian updating from sparse field settlement monitoring

Ground movements induced by deep excavation impose simultaneous vertical and horizontal deformation on adjacent pipelines. Excavation pipeline solutions commonly prescribe a specific movement function, and field monitoring generally provides sparse settlement data. This study develops a biaxial pipe soil interaction (PSI) solution that accepts arbitrary discretised vertical and horizontal free field profiles and assimilates field settlement through Bayesian updating. Two orthogonal Euler Bernoulli beam Winkler equations are transformed into sparse finite difference equations for displacement, rotation, bending moment and shear. A bivariate spline model represents spatial variability. Settlement monitoring results condition the vertical response, and the horizontal response is propagated through cross directional dependence. A PSI benchmark produced correlations of 0.993, 0.994 and 0.987 for displacement, rotation and moment, with peak errors of 2.92%, 2.88% and 1.34%, respectively. In model consistent experiments, a five-sensor centre edge layout achieved a resultant moment normalised root mean square error (NRMSE) of 0.0557, empirical coverage of 0.954 for nominal 95% intervals and variance reduction of 0.717. Application to the Pukou Wanhui Station pipeline reconstructed a peak vertical displacement of 28.578 mm from an eleven-point settlement profile; leave one out prediction yielded a root mean square error (RMSE) of 1.614 mm and a mean absolute error (MAE) of 1.505 mm. The full array reduced vertical displacement and vertical moment variances by 94.11% and 72.37%. Horizontal observability increased with cross directional dependence, and a targeted horizontal monitoring result supplied more information than an additional vertical sensor. The framework couples arbitrary ground movement shapes, mechanically admissible biaxial response, field data updating and response-oriented monitoring design.