Hydraulic Conductivity Function Research Articles

Soil hydraulic conductivity in the state of nonequilibrium

AbstractHydraulic nonequilibrium in soil during water infiltration and drainage is a well‐known phenomenon. During infiltration, water initially invades easily accessible pores before it slowly redistributes towards some state of energetic minimum. In analogy, during drainage, easily drainable pores are emptied more rapidly than those blocked by bottlenecks. The consequence is that the water content is lagging behind the water potential and both state variables do not follow a unique water retention curve as typically assumed when applying Richards equation. Current models that account for nonequilibrium allow for the required decoupling of water content and water potential; however, they do not consider the consequences for the hydraulic conductivity. In this contribution, we present a physically based approach to estimate hydraulic conductivity during nonequilibrium, which depends on both water content and water potential during nonequilibrium conditions. This approach of a dynamic hydraulic conductivity function is demonstrated for an infiltration process into relatively dry soil and for a stepwise drainage and rewetting with decreasing and increasing water fluxes (i.e., multistep flux experiment). The new approach reproduces well‐known phenomena such as pressure overshoot and preferential flow across infiltration fronts using a unified concept for hydraulic conductivity. This was not possible with existing models assuming some fixed unsaturated conductivity function depending on either water content or water potential.

Assessment of the Effects of the 2021 Caldor Megafire on Soil Physical Properties, Eastern Sierra Nevada, USA

The Caldor fire burned ~222,000 acres of the Eastern Sierra Nevada during summer–fall 2021. We evaluated the effects of this “megafire” on the physical properties of a sandy soil developed from glacial tills to document fire-induced soil modifications in this region. We measured soil water retention and hydraulic conductivity functions as well as the thermal properties of five core samples from control (unburned) areas and eight core samples from burned soil of the same soil unit. Soil water repellency was measured in terms of water drop penetration time (WDPT) in the field and apparent contact angle in the laboratory on control and burned soil as well as ash samples. Soil organic matter (SOM) and particle and aggregate size distributions were determined on control and burned soil samples. Additionally, scanning electron microscopy (SEM) was used to image microaggregates of control and burned soil samples. We found a significant difference in SOM content and sand and silt aggregate size distribution between control and burned samples, which we associated with the disintegration of microaggregates due to the fire. We found no significant difference between soil water retention and hydraulic conductivity functions of control and burned soil but observed greater variation in saturated hydraulic conductivity and systematic shifts in thermal conductivity functions of burned compared to control samples. WDPT and apparent contact angle values were significantly higher for burned soils, indicating the occurrence of fire-induced soil hydrophobicity (FISH). Interestingly, the average apparent contact angle of the control soil was >90°, indicating that even the unburned soil was hydrophobic. However, the ash on top of the burned soil was found to be hydrophilic, having apparent contact angles <10°. Our results indicate that SOM and microaggregates were readily affected by the Caldor fire, even for sandy soil with a weakly developed structure. The fire seemed to have moderated thermal properties, significantly and soil wettability but had only minimal effects on water retention and hydraulic conductivity functions. Our findings demonstrate the complex nature of fire-soil interactions in a natural environment and highlight the need for additional investigation into the causes and processes associated with FISH and structure alterations due to fire to improve our ability to rapidly determine potential problem areas in terms of hazards commonly associated with fire-affected soils.

Unsaturated bearing capacity of strip foundations by using the upper bound rigid block method

Shallow strip foundations are ubiquitous in the field of geotechnical engineering. However, most of the analyses regarding the strip foundations were performed without considering the unsaturated state of the soil. The present article aims to evaluate the upper bound collapse load of the strip footing by duly considering the matric suction developed above the water table. The effect of the vadose zone is considered by employing the suction-stress-based effective stress approach. The suction stress is modelled by employing van-Genuchten’s soil water characteristics curve and Gardner’s one-parameter hydraulic conductivity function. The kinematic admissibility of the problem is ensured by considering a Hill-type mechanism. A new bearing capacity factor is introduced into the formulation which takes care of the unsaturated soil properties and the climate changes. The obtained results are in good agreement with the available solutions.

Effect of the Wetting Hydraulic Property of Soil on 1-D Water Infiltration

Rainwater infiltration is primarily governed by the soil-water characteristic curve (SWCC) and hydraulic conductivity function (HCF) of soil. Both the SWCC and the HCF are hysteretic during the drying and wetting processes. In a numerical simulation, different seepage results can be obtained by incorporating different hydraulic conductivity functions of soil. In practice, the wetting HCF is commonly estimated from the wetting SWCC using the statistical method, which is named HCFswcc,w in this note. However, there is no study that has verified the results from seepage analyses using HCFswcc,w. Therefore, the objective of this study is to investigate the influence of wetting SWCC and wetting HCF on 1-D water infiltration. The results from the numerical simulations were verified with the instrumentation reading from a soil column. It was observed that the results from the model using wetting HCFPSDF, which defines the wetting HCF estimated using the concept of pore-size distribution function, gave better agreement with the instrumented data. Therefore, both wetting SWCC and wetting HCFPSDF are advised to be used as input information for the numerical simulation of rainwater infiltration.

Temperature effects on the hydraulic properties of unsaturated rooted soils

Soil temperature of vegetated landfill earthen covers varies with time during their service, due to heat released by the degradation of municipal solid waste. In this study, an experimental campaign to capture soil water-retention curve (SWRC) and hydraulic conductivity function (HCF) of unsaturated rooted soils was conducted at different temperatures (25, 45, and 60 °C). Simplified evaporation tests were conducted by subjecting soil specimens to a prolonged drying period at maintained temperature. Based on the responses of matric suction and water content, SWRC and HCF were determined by the instantaneous profile method. It was found that increasing temperature reduced water-retention capacity, due to root shrinkage, thermal expansion of liquid phase, and reduction in forces of capillarity and adsorption. Soil hydraulic conductivity was enhanced by the increase in soil temperature due to reduction of water viscosity and potential preferential flow at root channels induced by root shrinkage. Temperature effects on SWRC and HCF of rooted soils are suction-dependent. A new nonisothermal SWRC model was developed to capture the dual effects of roots and temperature. By using the same set of calibrated parameters, the model demonstrates its ability to predict SWRCs reasonably well within the range of temperature investigated.

Effect of Soil-Water Characteristic Curve on the Stability of Unsupported Vertical Trenches in Unsaturated Soils

In geotechnical engineering practice, unsupported vertical trenches are typically excavated in unsaturated soils. In this case, the variation of shear strength and hydraulic conductivity with respect to soil suction is key information to analyze the stability of an unsupported vertical trench. Most shear strength and hydraulic conductivity models use the soil-water characteristic curve (SWCC) as a main tool. Various models are available to determine SWCC, shear strength, and hydraulic conductivity for unsaturated soils. Scholars or practitioners use one the existing models in numerical analyses to estimate the stability of unsupported vertical trench considering rainfall events. However, limited studies have been undertaken to investigate the effect of SWCC and hydraulic conductivity functions on the stability of unsupported vertical trenches in unsaturated soils. In the present study, numerical stability analyses are carried out by using different SWCCs and hydraulic conductivity functions to investigate their influence on the estimated safe height and stand-up time of unsupported vertical trenches. The same shear strength model was used for entire numerical analyses.

Estimation of unsaturated hydraulic conductivity function using extrapolated saturated front widths of line source field dripper

Estimation of unsaturated hydraulic conductivity function using extrapolated saturated front widths of line source field dripper

Physically-based reduction function to model unsaturated flow associated with plant transpiration

Vegetation plays an important ‘hydrological’ role in stabilising geostructures. Soil water is extracted by the roots due to transpiration, this increases soil suction and, hence, soil shear strength. Transpiration occurs in two different regimes, energy-limited and the water-limited regimes respectively. These two regimes are reflected in the two branches of the transpiration reduction function used to model the hydraulic boundary conditions for vegetated ground. The water-limited branch accounts for the reduced transmissivity of the soil-root system when the degree of saturation and, hence, the hydraulic conductivity declines. The water-limited branch of existing reduction functions (e.g., Feddes function) is defined in purely phenomenological fashion with parameters that have no clear link with the complex interaction between soil hydraulic properties and root architecture. A paradigm shift can be achieved through physically-based reduction functions. These require analytical closed-form solutions of radial water flow at the soil-root interface that, in turn require introducing simplifying assumptions, i.e., steady-state flow and a simplified hydraulic conductivity function. This paper explores the implications of these assumptions by i) benchmarking the water-limited branch of the reduction function derived analytically against the one derived numerically for more realistic hydraulic behaviour and ii) assessing the steady-state assumption.

Pore network modeling approach for simulating soil water retention curve under different stress conditions

The field of unsaturated soil mechanics has recently seen the introduction of pore network models, which attempt to replicate the void structure of porous materials. They are robust physically-based simulation tools and have been used to simulate constitutive relationships like soil water retention curves (SWRC) and unsaturated hydraulic conductivity functions. This work aims to present a pore networkmodeling approach for predicting hysteretic SWRC at various stress states using only grain size distribution and porosity data of the granular soils. The soil sample subjected to given stress conditions is simulated using the Discrete Element Method to obtain a stable packing of spherical particles representing the soil structure. From this packing, an algorithm based on the medial axis is availed to extract a network of pores and throats that describes the geometry and topology of the void structure of the granular soils. Various pore-scale mechanisms like the piston-like advance, corner flow, pore body filling, and snap-off are then used to model fluid displacements at the pore scale to simulate SWRC along the drying and wetting paths. The modeled SWRC under various stress conditions is compared with the measured curves obtained for granular soils from the literature, and the predictions are in good agreement with the experimental results.

Seasonal and Soil Use Dependent Variability of Physical and Hydraulic Properties: An Assessment under Minimum Tillage and No-Tillage in a Long-Term Experiment in Southern Italy

Defining the optimal sampling time across the growing season is crucial to standardize sampling protocols for soil physical status monitoring and to achieve comparable results under different experimental conditions and on different sites. In this study, the seasonal variability of soil physical and hydraulic properties under two conservative soil management strategies, minimum tillage and no-tillage, was evaluated in a long-term field experiment. On two sampling dates, autumn 2021 and summer 2022, soil bulk density (BD) and volumetric soil water content at the time of the experiments (θi) were measured in each experimental unit and Beerkan infiltration experiments were performed. The soil water retention curve and the hydraulic conductivity function were then estimated using the Beerkan estimation of soil transfer parameters (BEST) methodology. In this way, the saturated hydraulic conductivity (Ks) and a set of capacitive indicators—plant available water capacity (PAWC), soil macroporosity (PMAC), air capacity (AC) and relative field capacity (RFC)—were obtained. Results underlined the role of soil moisture conditions as a main factor affecting variability in soil physical properties. Different soil moisture under autumn and summer samplings significantly affected BD (1.0093 and 1.1905 g cm−3, respectively, in autumn and summer) and Ks (0.0431 and 0.0492 mm s−1). Relationships observed between BEST-derived variables, such as PMAC (or AC) and RFC, and measured variables, such as BD, showed consistent results, with increases in PMAC to BD decreases. However, a comparison of capacity-based indicators obtained by BEST with those obtained from measured soil water retention curves, in a previous year but under comparable soil conditions, highlighted some discrepancies. This finding drives the focus towards the need to use more robust datasets deriving from experimental measurements or from coupling information obtained from measured and estimated data. Finally, this study provided further evidence that, in the long-term field experiment investigated, the two soil management systems allowed keeping the values of key soil physical quality indicators, such as bulk density and saturated hydraulic conductivity, within the optimal or near- optimal reference ranges.

Impact of the loess’ hydraulic characteristics on its degree of saturation for the purpose of radon index measurements (Northeast Bulgaria case study)

Radon gas has high mobility and is driven by advection and diffusion with the soil gas throughout connected and water-unsaturated pores and/or cracks in permeable rocks and soils. Therefore, there is a need for quantitative assessment of the saturation state, even on a daily-base in order to estimate the radon potential correctly. The more so as, the permeability is one of the key factors in the radon risk assessment. For the purpose of such investigation, a vertical profile model was elaborated for a study site in Northeast Bulgaria. On the base of pedotransfer function analyses, the hydraulic parameters describing the retention function and the hydraulic conductivity function were determined for each case study. The results show that even in a month with high amount of rainfall precipitation (13% of the total amount per year), the loess profile at certain depths remains unsaturated, regardless the difference in the hydraulic characteristics.

Some Approaches to the Prediction of Permeability Parameters in a Finite Element Program for Early Warning

Recently, landslides often occurred in natural soil slopes in the tropical region, which correlate with the rainy season. Rainfall infiltration leads to groundwater level fluctuations. The increased positive pore-water pressures due to rainfall influence have affected the properties and behavior of the unsaturated soil slope. In this research, the Finite Element Method of SEEP/W and SLOPE/W analyzes the factor safety of the slope affected by pore water pressure change due to rainfall. The Soil Water Characteristic Curve (SWCC) and Hydraulic Conductivity function were obtained from sieve analysis and Atterberg's limit. In addition, unsaturated soil properties from the UNSODA code are estimated based on grain-size distribution using the SWRC program. The study area is in Khanom District, southern Thailand. The results show that the soil slope at the site became unstable on November 18, 2021, with F.S. = 1.0, which agrees well with the date of the disaster. In conclusion, the slope stability analysis without the parameters from the unsaturated soil hydraulic database (UNSODA) leads to the F.S. value being higher than the actual value, and the alarm estimation would be inaccurate. Doi: 10.28991/CEJ-2022-08-12-014 Full Text: PDF

Investigating the Spatial Structure of Soil Hydraulic Properties in a Long-Term Field Experiment Using the BEST Methodology

Understanding the spatial structure of soil properties at field scale and introducing this information into appropriate data analysis methods can help in detecting the effects of different soil management practices and in supporting precision agriculture applications. The objectives of this study were: (i) assessing the spatial structure of soil physical and hydraulic properties in a long-term field experiment; (ii) defining a set of spatial indicators for gaining an integrated view of the studied system. In seventy-two georeferenced locations, soil bulk density (BD), initial volumetric soil water content (θi) and cumulative infiltration curve as function of the time (I(t)) were measured. The soil water retention curve (θ(h)) and the hydraulic conductivity function (K(h)) were then estimated using the Beerkan Estimation of Soil Transfer parameters (BEST) methodology. The volumetric soil water contents at soil matrix (h = −10 cm), field capacity (h = −100 cm) and wilting point (h = −15,300 cm) were considered. In addition, a set of capacitive indicators—plant available water capacity (PAWCe), soil macroporosity (PMACe), air capacity (ACe) and relative field capacity (RFCe)—were computed. The data were first analyzed for overall spatial dependence and then processed through variography for structural analysis and subsequent spatial interpolation. Cross-correlation analysis allowed for assessing the spatial relationships between selected physical and hydraulic properties. On average, optimal soil physical quality conditions were recorded; only PMACe values were indicative of non-optimal conditions, whereas mean values of all the other indicators (BD, Ks, PAWCe, ACe, RFCe) fell within optimal ranges. The exponential model was found to be the best function to describe the spatial variability of all the considered variables, except ACe. A good spatial dependence was found for most of the investigated variables and only BD, ACe and Ks showed a moderate autocorrelation. Ks was confirmed to be characterized by a relatively high spatial variability, and thus, to require a more intensive spatial sampling. An inverse spatial cross-correlation was observed between BD and Ks up to a distance of 10 m; significant cross-correlations were also recorded between Ks and PMACe and ACe. This result seems to suggest the possibility to use these soil physical quality indicators as covariates in predictive multivariate approaches.

Inverse Estimation of Soil Hydraulic Parameters in a Landslide Deposit Based on a DE-MC Approach

Extreme rainfall is a common triggering factor of landslide disasters, for infiltration and pore water pressure propagation can reduce suction stress and shear strength at the slip surface. The subsurface hydrological model is an essential component in the early-warning system of rainfall-triggered landslides, whereas soil moisture and pore water pressure simulated by the Darcy–Richards equation could be significantly affected by uncertainties in soil hydraulic parameters. This study conducted an inverse analysis of in situ measured soil moisture in an earthquake-induced landslide deposit, and the soil hydraulic parameters were optimized with the Differential Evolution Markov chain Monte Carlo method (DE-MC). The DE-MC approach was initially validated with a synthetic numerical experiment to demonstrate its effectiveness in finding the true soil hydraulic parameters. Besides, the soil water characteristic curve (SWCC) and hydraulic conductivity function (HCF) described with optimized soil hydraulic parameter sets had similar shapes despite the fact that soil hydraulic parameters may be different. Such equifinality phenomenon in inversely estimated soil hydraulic parameters, however, did not affect the performance of simulated soil moisture dynamics in the synthetic numerical experiment. The application of DE-MC to a real case study of a landslide deposit also indicated satisfying model performance in terms of accurate match between the in situ measured soil moisture content and ensemble of simulations. In conclusion, based on the satisfying performance of simulated soil moisture and the posterior probability density function (PDF) of parameter sets, the DE-MC approach can significantly reduce uncertainties in specified prior soil hydraulic parameters. This study suggested the integration of the DE-MC approach with the Darcy–Richards equation for an accurate quantification of unsaturated soil hydrology, which can be an essential modeling strategy to support the early-warning of rainfall-triggered landslides.

An Explicit Equation for the Maximum Water Application Depth in Center Pivot Irrigation

A simple explicit formula was derived to determine the maximum irrigation depth (Dmax) that can be applied per irrigation without any runoff under a center pivot and/or linear move irrigation system. The analysis is built on the assumption that Dmax is achieved when the water application rate is tangential to the Green-Ampt infiltration rate function. The surface storage was not considered here but tillage effects can be inherently incorporated if parameters of the Green-Ampt equation are properly measured. A power form formula was proposed to simulate the infiltration rate, while the application rate pattern had a parabolic shape. The proposed equation for Dmax is a function of soil saturated hydraulic conductivity, sorptivity, and the peak application rate. Numerical examples covering different combinations of soil properties and peak application rates indicated the high accuracy of the proposed formula with maximum and average absolute errors of 1 and 0.4 mm from the numerical stepwise solution, respectively. The quick calculation of Dmax here allows us to easily estimate a minimum lateral speed that will not trigger runoff under center pivots.

Properties governing flow of solution and air through crushed ore for heap leaching: Part II unsaturated dual-phase flow

Heap leaching of low-grade ores is often restricted by the hydrology of the bed, which limits the rate of dissolution of the target mineral. Although much research has been published on the flow of solution and air through sand, little has been published on the hydrology of coarser rocks. Physical and hydraulic testing of rocks and agglomerates is often incorporated as a part of heap leach design, however, much still relies on experiential rules. Over the past decade, the lead author has performed physical and hydraulic testing of a large number of ore samples considered for heap leaching. In reviewing the data, it was found that the hydraulic conductivity function (HCF), relating the hydraulic conductivity to the degree of saturation, can be modelled with traditional capillary models such as Brooks-Corey (BC) and van Genuchten-Mualem (VGM), but only at lower moisture contents. Furthermore, it was found that the HCF can be modelled as a discontinuous J-curve, with the hydraulic conductivity equal to the saturated hydraulic conductivity (Ks) above the air-entry point, rather than a continuous J-curve with a fitted Ks value, as recommended by other authors. Previous authors have also suggested that the discontinuity represents a transition between capillary- and gravity-controlled flow. However, the author(s) propose that the discontinuity is caused rather by the presence of “dead voids”, which fill up at higher moisture contents without generating additional flow channels. The point of discontinuity was found to correspond to the air-entry value obtained independently from the air conductivity curves. The experiential rule of a maximum void saturation of 65% for heap aeration appears to correspond on average with the experimental data.

Spherical Interpretation of Infiltration from Trickle Irrigation

The hypothesis of this paper is that infiltration into drip irrigated soils can be described by simple spherical considerations as well as two dimensional (2D) numerical modeling. The major goal was to test a very simple model based on geometry of a sphere formulas, and compare it with elaborated numerical solutions and field experiments. Detailed analysis of soil–water infiltration under trickle regimes is shown to be pre-requisite in the search for the optimal design of system layout. Optimality and simplicity are sought by modeling a sphere for subsurface trickle/drip (SDI) and hemisphere (DI) pattern of moisture distributions during infiltration. Numerical simulations by MATLAB software were used to describe the distribution of soil water. The data produced by this simulation were successfully compared with analytical models and numerical results of Panoche clay loam. To simulate the four discharge rates (0.5, 1, 2, 3 Lh) under DI and SDI we used the input of Panoche soil properties, i.e., hydraulic conductivity function (Kθ) and soil water retention curve (ψθ). The resulting regression equation of numerical analysis (N) vs. spherical interpretation (S) was N = 0.97 × S − 19.1; r2 = 0.98. This result exposes the novelty of the approach by showing that infiltration from a drip/trickle source can be described by simple spherical radial symmetry in addition to analytical or numerical simulations. An example of a design parameter for 3000 cm3h suggested more emitters per meter laterals for SDI than for DI (100 vs. 77 unites, respectively) due to the shorter distance between SDI emitters that are required in order to maintain wetting continuity. At a discharge of around 500 cm3h of three different soils’ SDI, positive pressure was detected near the orifice and it caused discharge reduction. This is a self-compensating property of SDI that regulates individual emitters according to the soil hydraulic properties. In conclusion SDI is associated with larger capital investment compared to DI, but it can be compensated by improving the water use efficiency due to increased productivity while reducing losses of water through evaporation, but this option should be investigated as part of specific research.

Non‐Darcian flow toward an injection well fully penetrating a leaky confined aquifer with clogging‐induced permeability reduction

AbstractManaged aquifer recharge (MAR) using aquifer injection wells is generally developed with the validity of Darcy's law and assumption of a constant hydraulic conductivity, hence ignoring the non‐Darcian nature of groundwater flow and the spatiotemporal permeability reduction owing to well and aquifer clogging. In this study, an Izbash's law‐based analytical model is proposed for constant‐rate recharge (CRR) and constant‐head recharge (CHR) with special consideration of well and aquifer clogging using a time‐dependent hydraulic conductivity (K) function. By means of linearization approximations, variable substitutions and Hankel and Weber transforms, approximate analytical solutions for the model are derived. The early‐time and late‐time solutions and the steady‐state solutions are also derived using the developed approximate solutions. A comparison with numerical solutions indicates that the approximate solutions are highly accurate except during the short period of initial recharge stage. Then, a semi‐log graphic approach based on the developed solutions is tendered for estimating parameters associated with the clogging effect and non‐Darcian aquifer property. The proposed model offers a straightforward way for the quantitative assessment of the non‐Darcian flow dynamics in confined aquifers experiencing clogging and can be adopted for the estimation and prediction of clogging‐related permeability reduction in MAR using aquifer injection wells.

Determining Soil Available Water Capacity and Reasonable Irrigation Volume in Dryland Pasture

Among the methods used to describe soil-available water in terms of yield, field water capacity and permanent wilting coefficient were considered as the upper and lower boundaries, respectively, for normal plant growth. This study investigated the soil properties and groundwater resources of the Hailiutu pasture in Inner Mongolia, China. Soil water characteristics and hydraulic conductivity function curves of the pasture soil were measured based on filter paper method. Experimental results showed that air-entry and residual value were determined to be 34.6% and 13.1%, corresponding to the field water capacity and permanent wilting coefficient, respectively, and the available water capacity was 218.0 mm. The downward velocity of the soil wetting front in the silt is 3.0 mm/h. Site investigation revealed that the pasture was a natural capillary barrier, and its critical suction could optimize the upper boundary of irrigation. Considering the limited underground water resources, shallow water level, and the transpiration of Caragana Korshinskii in the pasture, an available drip irrigation method was designed. The spacing between drip irrigation pipes is 60 cm, the spacing between drip holes is 60 cm, the drip irrigation volume per hole is 475.2~838.8 mL/d, the drip irrigation time is 110~200 min at each night. Each hectare pasture exhausts 13.5~22.5 m3 water each day. Field tests showed that the proposed method is feasible and can be used for irrigation in dryland pastures.

Parametric Analysis of Rainfall-Induced Loess Soil Slope Due to the Rainwater Infiltration

Hydraulic properties (such as soil–water characteristic curves (SWCC) and hydraulic conductivity function (HCF)) play an important role in evaluating the stability of unsaturated soil slopes. Loess soils are widely distributed in Gansu Province in China, and most of them are in unsaturated conditions due to the deep groundwater table (G.W.T). In this study, twenty-eight sets of data published in the literature were analyzed to develop the upper and lower bounds of the SWCC for loess soil in Gansu. The variation of HCF for the loess soil was estimated from the upper and lower bounds curve developed in this study. Subsequently, numerical analyses incorporating scenarios considering different SWCCs, HCFs, and rainfall conditions were conducted for investigating the effects of those factors on the rainfall-induced slope stability. The results of analyses indicate that the infiltration plays an important role in the rainfall-induced slope stability. Higher permeable soil leads to a larger infiltration amount, which, in turn, results in a lower safety factor. In addition, the effect of the hydraulic property on the rainfall-induced slope stability decreases with the increase in slope angle.