Quadratic Characterization of Non-Destructive Internal Loading Responses of Buried RC Pipes Under Different Deterioration and Burial Conditions

Buried reinforced concrete (RC) pipes in water, irrigation and sewer networks are aging, and their renewal must be prioritized without excavation, yet few non-destructive methods measure the stiffness of the pipe–soil system directly. The Internal Loading Method (ILM) loads the pipe wall from inside, and its response has so far been reduced to a single linear slope. This preliminary study examines whether a forced-origin quadratic representation, y = ax2 + bx, can describe load-dependent changes in slope that this linear stiffness cannot, using one RC pipe under four deterioration states and three burial conditions (above ground, 30 cm and a simulated 60 cm; 45 loading cycles). The sign of a gave the direction of curvature of the fitted response (negative in 40 cycles), but its statistical support, evaluated separately, was found in 28 cycles (significantly negative in 27 and significantly positive in one); the magnitude of a did not follow deterioration severity. The mean initial tangent stiffness b¯ decreased by 38–51% from the original to the maximum state and was higher at 60 cm than at ground level in all four states of this specimen, by 19% at maximum deterioration and 42–53% otherwise. In this dataset, b¯ was the most consistent descriptor examined, and burial must be considered when ILM stiffness is interpreted. The results require confirmation on further specimens.