Analytical solutions for estimation of the settlements of buried pipelines adjacent to anchored deep excavations under heavy rainfall

Intense rainfall is a leading cause of failures in deep excavations and adjacent shallowly buried pipelines, underscoring the critical need to evaluate their adverse impacts. To calculate settlements of pipelines adjacent to anchored deep excavations under rainfall, an integrated analytical solution was developed combining the two-stage method, the Multivariate Adaptive Regression Splines (MARS) algorithm and the stratified Green-Ampt (SGA) model. After validation against field data, systematic parametric analyses were conducted. Results showed that the pipeline’s maximum settlement (uz,max) exhibited a decreasing trend with increasing burial depth, bending stiffness and strata elastic modulus. uz,max exhibited a non-monotonic trend with the pipeline-to-excavation distance, first increasing and then decreasing; its peak value occurred when the pipelines were at a distance of 0.3–0.4 times the final excavation depth. Moreover, a 12-h, 19.4 mm/h rainfall event increased uz,max by 3.2–32%. These effects were more pronounced under conditions of a smaller maximum lateral deflection (δhm). To quantify these effects, a simplified formula linking uz,max and δhm was fitted through regression analysis. By incorporating the rainfall intensity formula, an indicator-calculation flowchart was summarised and illustrated with an example, thereby demonstrating how the method enhances the application of the current indicators in heavy rainfall scenarios.