Finite element method for one-dimensional rill erosion simulation on a curved slope

Rill erosion models are important to hillslope soil erosion prediction and to land use planning.The development of rill erosion models and their use has become increasingly of great concern.The purpose of this research was to develop mathematic models with computer simulation procedures to simulate and predict rill erosion.The finite element method is known as an efficient tool in many other applications than in rill soil erosion.In this study,the hydrodynamic and sediment continuity model equations for a rill erosion system were solved by the Galerkin finite element method and Visual Cþþprocedures.The simulated results are compared with the data for spatially and temporally measured processes for rill erosion under different conditions.The results indicate that the one-dimensional linear finite element method produced excellent predictions of rill erosion processes.Therefore,this study supplies a tool for further development of a dynamic soil erosion prediction model.

Quantifying spatial distribution of interrill and rill erosion in a loess at different slopes using structure from motion(SfM)photogrammetry

The spatial distribution of interrill and rill erosion is essential for unravelling soil erosion principles and the application of soil and water conservation practices.To quantify interrill and rill erosion and their spatial development,four 30-min rainfalls at 90 mm h^(-1)intensity were consecutively simulated on runoff plots packed with a loess at six slopes of 10°,15°,20°,25°,30°and 35°.The soil surface was measured using the structure from motion(SfM)photogrammetry upon each simulation run,and the runoff and sediment samples were collected and measured at every 10 min.Rills did not develop until the third simulation run.During the initial two runs,the lower third section was more severely eroded than the upper and middle thirds along the slope direction,yet the interrill erosion was statistically uniform from left to right.Rills tended to emerge by both sidewalls and in the lower portion in the third run.The corresponding rill erosion increased with slope from 10°to 20°and then decreased for the slopes steeper,which was consistent with the slope trend of the sediment yield directly measured.The rills expanded substantially primarily via head retreat and to a lesser extent via sideward erosion after receiving another 30-min rainfall.Rill erosion contributed 69.3%of the total erosion loss,and shifted the critical slope corresponding to the maximum loss from 20°to 25°.These findings demonstrate the significance of rill erosion not only in total soil loss but also in its relation to slope,as well as the effectiveness of SfM photogrammetry in quantifying interrill and rill erosion.

Rill flow velocity affected by the subsurface water flow depth of purple soil in Southwest China

Subsurface water flow above the weakly permeable soil layer commonly occurs on purple soil slopes.However,it remains difficult to quantify the effect of subsurface water flow on the surface flow velocity.Laboratory experiments were performed to measure the rill flow velocity on purple soil slopes containing a subsurface water flow layer with the electrolyte tracer method considering 3 subsurface water flow depths(SWFDs:5,10,and 15 cm),3 flow rates(FRs:2,4,and 8 L min^(-1)),and 4 slope gradients(SGs:5°,10°,15°,and 20°).As a result,the pulse boundary model fit the electrolyte transport processes very well under the different SWFDs.The measured rill flow velocities were 0.202 to 0.610 m s^(-1) under the various SWFDs.Stepwise regression results indicated a positive dependence of the flow velocity on the FR and SG but a negative dependence on the SWFD.The SWFD had notable effects on the rill flow velocity.Decreasing the SWFD from 15 to 5 cm increased the flow velocity.Moreover,the flow velocities under the 10-and 15-cm SWFDs were 89%and 86%,respectively,of that under the 5-cm SWFD.The flow velocity under the 5-,10-and 15-cm SWFDs was decreased to 89%,80%,and 77%,respectively,of that on saturated soil slopes.The results will enhance the understanding of rill flow hydrological processes under SWFD impact.

几种土壤的细沟侵蚀过程及其影响因素

通过间隔为11h的二次人工模拟降雨和冲蚀槽试验研究了10种土壤的侵蚀过程,发现在第2次降雨中大多数土壤出现了细沟侵蚀形式。采样微形态观察发现,在第1次降雨中形成结皮的土壤在第2次降雨中出现了细沟侵蚀;产流产沙观测发现所有出现细沟侵蚀的土壤在第1次降雨中径流含沙量逐渐减少,而第2次降雨中有一个先剧增后减少的过程。土壤理化分析及多元逐步回归分析结果表明,土壤颗粒组成、有机质含量、铁铝含量等因素对细沟侵蚀的影响表现不明显,而与土壤团聚体有关结构指标、细沟侵蚀、产流产沙速率及总量呈显著相关关系。分析表明,团聚体分散度、崩解速率与渗透系数之比两个指标能较好地预测细沟侵蚀发生的可能性,同时也能很好地预测侵蚀产沙量。

Plot investigation on rill flow resistance due to path tortuosity

The path tortuosity t is an indicator of rill morphology accounting for the deviation of the thalweg from a straight alignment.The effect of t on flow resistance has been little investigated for rills.This paper reports the results of a plot investigation aimed to establish the suitable accuracy of the rill thalweg measurement to determine the tortuosity parameter and to test the reliability of a theoretical flow resistance law.Four rills were incised in clay soil(CS)and clay-loam soil(LS)and shaped by a clear flow discharge.The three-dimensional Digital Terrain Models were created by the Structure from Motion technique.For rills on LS,an approximate thalweg was tracked by photo-interpretation,and a specific calculation routine was applied to identify the cross sections with a constant spacing d.The actual rill thalweg was obtained as the line joining the lowest points of these cross-sections.Among the different tested d values,d=0.075 m was chosen to determine t.For both CS and LS,the Darcy-Weisbach friction factorffeatured a non-monotonic relation with t,which was explained as the result of three additive components due to bed roughness,sediment transport,and localized energy losses due to curves.The effect of the former two components onff contrasts that of the third,resulting in a linearly decreasing f-t relationship and constant flow velocity for the three lowest tortuosity values,and an increased friction factor and reduced flow velocity for the highest tortuosity value.The flow resistance law was positively tested,and the predicted friction factor was dependent on t.

Determination of rill erodibility and critical shear stress of saturated purple soil slopes

The hydrological conditions near the soil surface influence the soil erosion process,as determined by the soil erodibility and critical shear stress.The soil erodibility and critical shear stress of saturated purple soil slopes were computed and compared with those of unsaturated purple soil slopes.The detachment capacities computed through the numerical method(NM),modified numerical method(MNM)and analytical method(AM),from rill erosion experiments on saturated purple soil slopes at different flow rates(2,4,and 8 L min-1)and slope gradients(5,10,15,and 20°),were used to comparatively compute the soil erodibility and critical shear stress.The computed soil erodibilities and critical shear stresses were also compared with those of unsaturated purple soil slopes.At the different slope gradients ranging from 5°to 20°,there were no significant differences in the soil erodibilities of the saturated purple soil and also in those of the unsaturated purple soil.The critical shear stresses slightly varied with the slope gradients.The saturated purple soil was relatively significantly more susceptible to erosion.The NM overestimated the soil erodibility of both saturated and unsaturated soils by 31%and underestimated the critical shear stress.The MNM yielded the same soil erodibility and critical shear stress values as the AM.The results of this study supply parameters for modeling rill erosion of saturated purple soil slope.