## 5 Conclusions  
This study investigated to what extent different rainfall intensities and durations affect the maximum transport distance of eroded sediment using a physical simulation experiment in a flume. The physical experiment simulated rainfall-induced surface soil erosion events. The hydrological monitoring data, sediment yield volumes under rainfall events, and the eroded soil transport distance were measured or calculated. Meanwhile, a geometry-based model was developed to evaluate the maximum transport distance of rainfall-eroded soil sediment. Based on these results, our understandings and conclusions areas as follows:  
Firstly, the pore water pressure (PWP) and moisture content in different positions of the slope are influenced greatly by the rainfall intensities and durations. At the first minute, PWP increases rapidly in the toe part because of surface water runoff concentration at the foot of the slope. The moisture content at the soil layer is characterized by slow growth. The moisture content at the middle of the slope increases faster compared with the moisture content at the top. Furthermore, high intensive rainfall events result in the rapid appearance of surface water runoff.  
Secondly, total soil sediment yield increases with rainfall duration for each intensity sequence, and at the same time step sediment yield increases with rainfall intensity. Moreover, under time domains soil erosion volume linearly relates to cumulative rainfall. Soil erosion volume can be estimated using two fitted equations: (1) considering rainfall intensity and duration affecting the sediment separately, and (2) cumulative rainfall affecting the sediment. The former has a \(R\)-square of 0.79 and a RMSE of 0.00073 m\({}^{3}\) and the latter has a \(R\)-square of 0.95 and a RMSE of 0.00035 m\({}^{3}\).  
Thirdly, based on the linear relationship of soil erosion volume and cumulative rainfall obtained from the experimental results, a geometry-based model for calculating the maximum transport distance (\(L_{\mathrm{xmax}}\)) is developed using just three parameters: cumulative rainfall, slope angle, and debris  
Figure 14: Frequency of sediment angle: (**a**) histogram based on physical test (\(n=29\)); (**b**) histogram based on random field (\(n=147\)).  
angle. The cumulative rainfall and slope angle may be obtained by consulting local hydrological and geological data. The debris angle may use the resident friction angle. According to the experimental results, this flexible and straightforward soil erosion transport distance model can predict maximum transport distance with low error.  
This research was supported by the Opening Fund of State Key Laboratory of Geo-hazard Prevention and Geo-environment Protection (Chengdu University of Technology)-SKLGP2013K007. The National Natural Science Foundation of China (51304170), China Postdoctoral Science Foundation (2014M560728), and the Young Scholars Development Fund of SWPU (201231010031) are thanked for their support. All the authors are grateful for the suggestions from [PERSON], Institute of Port, Coastal and Offshore Engineering, Zhejiang University, China.  
Drafting of manuscript: [PERSON] and [PERSON]. Acquisition of data: [PERSON]. Analysis and interpretation of data: [PERSON] and [PERSON]. Model construction: [PERSON] and [PERSON]. Planning and supervision of the research: [PERSON].  
The authors declare no conflict of interest.