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Rainfall and earthquakes are the primary causes of landslides. In order to reveal the occurrence mechanisms and spatial differentiations of the rainfall-seismic coupling effect induced landslide, the landslide hazard assessment was carried out in Boshan District as an example. First, the different PGA exceedance probabilities in the next 50 years for 48 sites in Boshan District were calculated using the CPSHA method of the fifth-generation seismic ground motion parameter zonation map in China. The seismic hazard maps of Boshan District were drawn with the Kriging interpolation method. Second, the Green-Ampt infiltration model was improved by the characteristic parameters of the Philip infiltration model, and the formula for the variation of rainfall infiltration depth with rainfall duration was derived. Lastly, on the basis of the above study, the formula of landslide safety factor considering pore water pressure was derived based on the Newmark cumulative displacement model, and the slope cumulative displacement and the landslide probability under the sheer seismic effect and the rainfall-seismic coupling effect were calculated, and the landslide hazard assessment results with different PGA exceedance probabilities and different rainfall recurrence intervals were compared. The research results show that under the effect of PGA with an exceedance probability of 10% in the next 50 years, the maximum slope cumulative displacement is 2.52 cm, and the maximum probability of seismic landslide is 29.6%. The areas with maximum cumulative displacement are the east of Yuanquan Town and the south of Chishang Town. Under the coupling effect of PGA with an exceedance probability of 10% in the next 50 years and the once-in-50-year rainfall, the maximum slope cumulative displacement is 3.76 cm, and the maximum probability of the rainfall-seismic coupling effect induced landslide is 33.2%. The areas with maximum cumulative displacement are the central part of Yucheng Town, the south of Chishang Town and Boshan Town, and the east of Yuanquan Town. As a result of either the sheer seismic effect and the rainfall-seismic coupling effect, the slope cumulative displacement and landslide probabilities with lower PGA exceedance probabilities and higher rainfall recurrence intervals will increase significantly.

Accumulation landslides are prone to occur during the continuous infiltration of heavy rainfall, which seriously threatens the lives and property safety of local residents. In this paper, based on the Green-Ampt (GA) infiltration model, a new slope rainfall infiltration function is derived by combining the effect of air resistance and lateral seepage of saturated zone. Considering that when the soil layer continues to infiltrate after the saturation zone is formed, the air involvement cannot be discharged in time, which delays the infiltration process. Therefore, the influence of air resistance factor in soil pores is added. According to the infiltration characteristics of finite long slope, the lateral seepage of saturated zone is introduced, which makes up for the deficiency that GA model is only applicable to infinite long slope. Finally, based on the seepage characteristics of the previous analysis, the overall shear strength criterion is used to evaluate the stability of the slope. The results show that the safety factor decreases slowly with the increase of size and is inversely correlated with the slope angle and initial moisture content. The time of infiltration at the same depth increases with the increase of size and slope angle, and is inversely correlated with the initial moisture content, but is less affected by rainfall intensity. By comparing with the results of experimental data and other methods, the results of the proposed method are more consistent with the experimental results than other methods.

Infiltration of irrigation water is an important factor affecting the stability of loess slopes. In this study, based on the Green-Ampt infiltration model. We analysed the cumulative effect of drip irrigation on the stability of loess slope through an indoor cumulative drip-irrigation infiltration test with a single-point source, which was combined with the Geo-Studio finite-element software. Our results show that: (1) infiltration of drip irrigation in loess slopes has an obvious cumulative phenomenon. The depth of infiltration and volumetric water content of underlying soil increase with increasing cumulative number of drip irrigation; (2) the infiltration time calculated by the classical and improved Green-Ampt infiltration models is more in line with the experimental results, with errors ranging from 4 to 11%. (3) Short-term 3-day drip irrigation creates a layer of infiltration area on the slope surface. The safety coefficient of the slope body is reduced by 0.01, which has less impact on the slope. Long-term 3-year drip irrigation increased the volumetric water content of the entire slope, and decreased the safety coefficient by 0.91, which had a greater impact on the slope. Our results have important scientific significance slope-disaster warnings, and prevention in loess areas.

In recent years, increasing slope instability accidents caused by rainfall occur. In order to quantitatively analyze the influence of rainfall infiltration on slope stability more accurately, based on the traditional Green–Ampt infiltration model, the influence of the slope’s angle and the characteristics of unsaturated loess were considered and the saturated zone and unsaturated zone were calculated separately in this paper. Through the energy conservation equation, this paper transferred the influence of rainfall infiltration into generalized penetration force and changed the penetration force and composite soil nailing wall supporting force into vertical article point method using the Bishop internal force hypothesis. The slope was divided into two parts, which were calculated, respectively, and integrated by the weighted solving method, and the calculation formula of overall stability of composite soil nailing wall retaining structure was deduced under the action of rainfall. For example, the difference of 1.165 obtained in this paper’s formula is 0.122 compared with the traditional Bishop method (1.043), which not only verifies the correctness of the formula in this paper but also reflects the weakening of the stability coefficient caused by rainfall. Since the soil parameters of unsaturated soil are weakened by rainfall, there may be some errors, and the result provides reference for similar support under special natural environment.

Infiltration-runoff-slope instability mechanism of macropore slope under heavy rainfall is unclear. This paper studied its instability mechanism with an improved Green-Ampt (GA) model considering the dual-porosity (i.e., matrix and macropore) and ponding condition, and proposed the infiltration equations, infiltration-runoff coupled model, and safety factor calculation method. Results show that the infiltration processes of macropore slope can be divided into three stages, and the proposed model is rational by a comparative analysis. The wetting front depth of the traditional unsaturated slope is 17.2% larger than that of the macropore slope in the early rainfall stage and 27% smaller than that of the macropore slope in the late rainfall stage. Then, macropores benefit the slope stability in the early rainfall but not in the latter. Macropore flow does not occur initially but becomes pronounced with increasing rainfall duration. The equal depth of the wetting front in the two domains is regarded as the onset criteria of macropore flow. Parameter analysis shows that macropore flow is delayed by increasing proportion of macropore domain ( ω f ), whereas promoted by increasing ratio of saturated permeability coefficients between the two domains ( μ ). The increasing trend of ponding depth is sharp at first and then grows slowly. Finally, when rainfall duration is less than 3 h, ω f and μ have no significant effect on the safety factor, whereas it decreases with increasing ω f and increases with increasing μ under longer duration (≥ 3 h). With the increase of ω f , the slope maximum instability time advances by 10.5 h, and with the increase of μ , the slope maximum instability time delays by 3.1 h.

This paper presents an estimation study based on calculus of variations for parameters in a real hydrological system, namely Tondi-Kiboro catchment, in Niger. The considered dynamical representation for this system is first given, from the well-known Saint-Venant equations under some simplifying assumptions. A cost function is then defined based on the gap between measured and predicted water discharges at the real sensor position, and the calculus of variations along with the first order optimality condition are used to find the gradients of Lagrangian objective functional with respect to the parameters to be estimated. Depending on the infiltration model used in the system model, two applications of this adjoint-based approach are finally presented: the first one only estimates the friction coefficient, with the assumption that infiltration is described by the physical so-called Green-Ampt model, while the second one additionally estimates the parameters of an alternative infiltration representation called Horton model. Some simulation-based validation and robustness discussion concludes the paper.

One sustainable method of stormwater management is surface infiltration with retention. Proper design of stormwater infiltration facilities ensures a reduction in flood risk within urban catchments. However, this is not possible without considering the key design parameters of such facilities. The aim of this paper is to determine the influence of the parameters characterizing the catchment area on the size of the stormwater infiltration facilities. The research used SWMM 5.1 and Statistica software. It was carried out on the example of model catchments and a real urban catchment. The analysis showed that it is of key importance in the design of stormwater infiltration facilities to accurately determine the total catchment area, the type of soil within it, and the proportion of impervious surfaces. The relevance of the other parameters that characterize the catchment area is clearly lesser. However, they cannot be completely ignored, and their values should be determined as accurately as possible. These research results can guide stakeholders in the decision-making process during investment planning and implementation.

In this work, a distributed two-dimensional (2D) shallow water (SW) flow model is combined with a fractional-order version of the Green-Ampt (FOGA) infiltration law to improve rainfall/runoff simulation in real catchments. The surface water model is based on a robust finite volume method on triangular grids that can handle flow over dry bed and multiple wet/dry fronts. When supplied with adequate infiltration laws, this model can provide useful information in surface hydrology. The classical Green-Ampt law is generalized by using a Caputo fractional derivative of order less than or equal to 1 in Darcy's law. The novelty of this combination is that, on the one hand, the distributed SW simulation provides a detailed surface water distribution and, on the other hand, the FOGA model offers the possibility to model infiltration rates not monotonically decreasing. In order to obtain the best results, a non-uniform order of the fractional derivative depending on the cumulative infiltration and the existence of available surface water is proposed for realistic cases. This allows significant improvement of previous published numerical results in the literature for several storm events in catchments where the infiltration process occurs.

In the prediction of overland flow, infiltration is an essential component, which should be modeled accurately to achieve optimum runoff rates. Many mathematical models that simulate the details of runoff and erosion process in hillslopes, where the rill-interrill configuration significantly affects overland flow, employ Horton’s model for infiltration due to its simplicity. However, Horton’s model does not handle adequately antecedent moisture condition (AMC) of soil. In this study, the Green-Ampt infiltration model is incorporated into a physically based overland flow model, which was originally coupled with Horton’s equation in an effort to improve the overland flow model’s prediction ability. In so doing, the model used the Horton and Green-Ampt model as an infiltration component separately and simulated flow to directly compare which infiltration equation performs better with the overland flow model. Calibration using laboratory data produced good results for both Horton with NSE = 0.88 and r ² = 0.92 and Green-Ampt with NSE = 0.90 and r ² = 0.95 while in validation, the Horton-coupled model produced lower NSE = 0.64 and r ² = 0.84 than the Green-Ampt which produced NSE = 0.85 and r ² = 0.85. The results suggest that the Green-Ampt equation can improve the performance of the overland flow model with its ability to account more accurately the AMC and flow processes in the soil.

Soil erosion is an open topic, not only because soil fertility is lost, but also because nutrients are spilled into water bodies, thereby causing pollution. Research carried out in this field has amply described this process, but the interaction between these factors is complex and experimental research is needed to understand the production of loads of nutrients for different land uses. This paper describes a long-term monitoring case study using high-resolution rainfall data and runoff samples, carried out in the Lake Vico basin (Central Italy) to determine the phosphorus (P) export during erosive rainfall events. State of the art GIS-based basin characterization and advanced rainfall-runoff models are employed in order to describe the relationship between nutrient export and rainfall or runoff time distribution. Results show that the phosphorus export is strongly related to such time distributions, and less to the cumulative amount of rainfall or runoff.