Frequent road collapses caused by water leakages from pipelines pose a severe threat to urban safety and the wellbeing of city residents. Limited research has been conducted on the relationship between pipeline leakage and soil settlement, thus resulting in a lack of mathematical models that accurately describe the soil settlement process resulting from water erosion. In this study, we developed an equation for pipeline leakage, conducted physical model experiments on road collapses induced by drainage pipeline leakage, investigated the functional relationship between drainage pipeline leakage and soil settlement, and validated this relationship through physical experiments with pipelines of various sizes. The results indicated that drainage pipeline leakage triggered internal erosion and damaged the soil layers in four stages: soil particle detachment, seepage channel formation, void development, and road collapse. When the pipeline size was increased by a factor of 1.14, the total duration of road collapse induced by pipeline leakage increased by 20.78%, and the total leakage water volume increased by 33.5%. The Pearson correlation coefficient between the theoretical and actual settlement exceeded 0.9, thus demonstrating the reasonableness and effectiveness of the proposed settlement calculation method. The findings of this study serve as a basis for monitoring soil settlement and issuing early road collapse warnings.

The leakage of drainage pipes is the primary cause of underground cavity formation, and the cavity diameter-to-depth ratio significantly affects the overall stability of roads. However, studies on the quantitative calculation for road comprehensive bearing capacity considering the cavity diameter-to-depth ratio have not been extensively explored. This study employed physical model tests to examine the influence of the cavity diameter-to-depth ratio on road collapse and soil erosion characteristics. Based on limit analysis theorems, a mechanical model between the road comprehensive bearing capacity and the cavity diameter-to-depth ratio (FB-L model) was established, and damage parameters of the pavement and soil layers were introduced to modify the FB-L model. The effectiveness of the FB-L model was validated by the data derived from eight physical model tests, with an average deviation of 14.0%. The results indicate a nonlinear increase in both the maximum diameter and fracture thickness of the collapse pit as the cavity diameter-to-depth ratio increased. The pavement and soil layers adjusted the diameter and fracture thickness of the collapse pit to maintain their load-bearing capacity when the cavity diameter-to-depth ratio changed. The fluid erosion range increased continuously with increasing depth of buried soil and was influenced predominantly by gravity and seepage duration. Conversely, the cavity diameter decreased as the buried depth increased, which is associated with the rheological repose angle of the soil. Furthermore, the damage parameters of the pavement and soil layers decrease as the distance from the collapse pit diminishes, with the pavement exhibiting more severe damage than the soil layer. This study provides a theoretical basis for preventing road collapses.