Background Terrace is an important soil and water conservation and agricultural measure in the Loess Plateau of China. Due to the implementers of terrace are mostly farmers, the section of terrace is arbitrary, and the quality of terrace might be poor, the landslide disaster of terrace occurs frequently in this area. Therefore, it is of a great theoretical and practical significance to study how to optimally design the section of terrace under the premise of ensuring slope stability in the Loess Plateau.

Methods On the basis of field investigation and indoor geotechnical test, the section and soil mechanical parameters of loess terraces were obtained, and the finite element simulation model of stability analysis of loess terraces under rainfall conditions was established by using the general finite element software ABAQUS. The model was used to calculate the safety factor (F_s) of level terrace, alternate terrace, and original slope (control) under different rainfall conditions (rainfall infiltration intensity (20-40 mm/h), rainfall duration (24-168 h), and multi-factorial covariance analysis was carried out to obtain the main factors affecting the stability of loess terrace. The orthogonal test design was used to calculate the range for the slope of ridge, slope of ground, field width of three level terrace design parameters, and combined with the grey correlation method to conduct a secondary correction of the range, in order to get the sensitivity of the design parameters and optimize the design scheme.

Results 1) The main factors affecting the stability of loess terrace was: duration of rainfall > slope of ground > rainfall infiltration intensity > type of terrace. The stability of level terrace and alternate terrace were significantly higher than that of the original slope, but the stability difference between level terrace and alternate terrace was not significant. 2) The sensitivity of the three design parameters to safety factor (F_s) was as follows: slope of ground (0.081) > field width (0.007) > slope of ridge (0.001). The sensitivity of slope of ground to safety factor was 12 times than that of the field width and 81 times than that of the slope of ridge, and the sensitivity of the field width to safety factor was 7 times more than that of the slope of ridge. 3) Under the level of design parameters, the optimal design scheme of terrace was as follows: slope of ground=18°, slope of ridge=65°, and field width=9 m.

Conclusions Rainfall is an important factor affecting the stability of loess terrace. When level terrace are designed under rainfall conditions, the smaller the slope of ground is, the better the stability is, but the best combination can be determined only after the range analysis of the field width and slope of ridge. When the slope of ground cannot be changed, special attention should be paid to the design of the field width in order to make the loess terrace more stable.