Prediction of hydraulic gradient for backward erosion piping in river levees considering flow regime and pipe geometry

The hydraulic gradient that causes backward erosion piping in river levees is of significant concern in geotechnical engineering. Traditionally, the mechanism of pipe progression beneath levees has primarily been studied using small-scale model experiments. Prediction methods for the critical hydraulic gradient have been developed in which the simple pipe geometry and laminar pipe flow were assumed. However, recent studies have suggested that turbulent flow is more likely in the pipes of prototype-scale levees and that both the pipe geometry and flow regime significantly influence pipe progression and the resulting gradient. The present study proposes a prediction method that accounts for the effects of the foundation’s soil properties, levee scale, flow regime, and pipe geometry. The method is validated by comparing the predicted results with those from centrifuge tests. All the analytical results are found to be consistent with the test observations, demonstrating that the proposed method can satisfactorily predict the effects of the testing parameters on the hydraulic gradient. The scale effect of levees on the critical hydraulic gradient remains a critical issue, as the direct application of small-scale test results to prototype levees often results in the overprediction of the gradient. The method is also used to evaluate the progression gradient of full-scale levees, confirming that the gradient is inversely proportional to the square root of the levee width (L^−1/2) under laminar pipe flow conditions. Under turbulent flow conditions, which are more likely in field-scale levees, the exponent may be even smaller.