Backward erosion piping, which is one of the leading causes of levee and dam failures, is more likely to occur when a flow is concentrated on a defect with an overlying low-permeability layer and a shallow erosion channel forming and progressing towards a seepage source. Two analytical models are presented to allow assessment of the seepage regime on the initiation stage of BEP. The variations between the two models are analysed, indicating that the effects of soil loosening have a major role in the assessment of BEP mechanisms. This paper also describes the reliability of using Xiao’s model in 3D analysis, which includes results and parametric analysis. Although the head in front of the tip of the erosion channel can be predicted by this accepted calculation model, which is essential for laboratory work on this topic, the model also has range and boundary limitations that need to be addressed for general prediction when BEP progresses with channel development.

The location of a hydraulic jump is a key parameter for analysing the slab stability of the stilling basin in a sluice. A simple method to locate the toe of a hydraulic jump in sloping channels is presented. The essential idea of this method applies the interacting relationship between the sequent depth and jump length to locate a point, satisfying them both simultaneously. The implementation details and the involved sequent depth and jump length equations of this method are discussed, and verification of the method is also presented. The predicted results match well with the published test data, even for a steep sloping channel up to 45°. The method’s application in the failure analysis of a sluice sloping connecting slab is also presented briefly. It is important for the analysis to account for the static hydraulic jump effect. The proposed method can yield a key parameter for such an analysis.

A fully penetrating cut-off wall is a vertical seepage barrier that fully penetrates an aquifer and is embedded in an underlying aquitard to a certain depth. Groundwater seepage with this type of wall occurs through three paths: leakage through the body of the wall in the aquifer, leakage through the body of the wall embedded in the aquitard, and seepage under the wall. Seepage through the first path can be simply treated as one-dimensional flow. However, due to the mutual influence of seepage through the latter two paths, the seepage problem is complicated and still needs to be studied. An analytical method is proposed to solve this problem in this study. Mathematic expressions for flow rate and head value are obtained by superposition of drawdowns of two exact models, namely, the model with only leakage through the wall body and the model with only seepage under the wall, respectively. Exact solutions are quoted or derived for the exact models, but they involve Legendre’s elliptic integrals of the first and third kinds. To facilitate an engineering application, approximate models of the exact models are introduced and their solutions are applied to the analytical formulas. The accuracy and applicability of the proposed method are verified compared with the numerical method. The proposed method provides a simple but effective method for quickly estimating the quantity of seepage in the aquitard (including leakage through the wall body and seepage under the wall) when simultaneously considering the effects of wall permeability and thickness.