Background  Bunds are embankments constructed across the slope and along the contour, and play a key role in controlling soil erosion on sloping farmlands. Recently, it is unclear yet of the relationship between soil bund stability and scales. The aim of this work is to provide a basis for soil bund planning and design in the purple sloping farmland consolidation and lower-yield field reconstruction projects in the Three Gorges Reservoir area and even the upper Yangtze River, by revealing the purple soil bund stability response to scales.

Methods We carried out field investigation, laboratory test, simulation and response surface analysis to reveal the stability of soil bunds under different height and slope conditions. We defined 4 levels of height (0.8, 1.0, 1.2, and 1.4 m at intervals of 0.2 m) and 4 levels of slope (50°, 60°, 70°, and 80° at intervals of 10°), a total of 16 soil bunds. The limit equilibrium analysis was adopted to calculate the stability coefficients, and the response surface analysis was adopted to build the model of purple soil bund stability responses to the bund size.

Results The minimum of stability coefficient was 3.526, which indicated that all soil bunds defined in the present study were stable. When the outside slope was constant, the soil bund stability coefficients displayed a nonlinear reduction with the height increasing; however, when the height was constant, the soil bund stability coefficients decreased generally along with the outside slope, the average reduction was greater than 10% at each increasing interval under these two changing patterns. Overall, both the height and the outside slope had significant influences on the stability of soil bunds (P < 0.01), while the interactive effect was not significant. Regression equation fitted by height, outside slope and their quadratic terms of soil bund can be used for describing the relationship between stability and scales perfectly, the adjustment determination coefficient and variation coefficient were 93% and 5.88, respectively. The potential sliding surface of soil bund was characterized by a shear resistance force greater than the moving shear force. With an increasing of the base shear mobility force and the right side normal force, the soil bund stability coefficient showed a decreasing trend, with no noticeable change trend along with the base normal force and the right side shear force change.

Conclusions The reasonable scale is 1.0~1.2 m of height and 60° of outside slope while considering purple soil bund stability features, slopping farmland conditions and ease for farmers to cultivate.