Rainfall Infiltration Research Articles

A new kinematic wave model that describes lateral subsurface flow and percolation in hillslopes

Kinematic wave (KW) models are commonly used for flood forecasting in large river basins, but have limitations in their ability to simulate percolation effects. Here, we suggest an extended KW model wherein the vertical pressure head is under non-hydrostatic conditions. The proposed model uses the Brooks Corey and Mualem models to estimate the water retention curve and unsaturated hydraulic conductivity and adopts the pressure head gradient as a new variable to calculate runoff based on changing water content distributions over time due to percolation. The increase in the pressure head gradient with rainfall infiltration is determined from the relationship between water storage and pressure head distribution, while the decrease in pressure head gradient due to percolation is modeled as exponential decay with time. A comparison of the proposed KW model and a numerical solution of the Richards equation shows that the proposed KW model can reproduce the storage effect caused by percolation, delaying runoff and reducing peak discharge. The agreement between the proposed KW model and the Richards equation is high for soils with high water retention. Conversely, the agreement becomes lower for soil with low water retention or deep soil layer thickness, where the complexity of water content distribution requires further refinement. The proposed model can easily be incorporated into distributed models while low computational cost with keeping the important percolation effects.

“Cutting effect” of needles on the raindrop characteristics

Plant leaves (both in the canopy and on the land surface) can substantially alter raindrop characteristics, which link to rainfall evaporation, infiltration, raindrop energy, and land surface erosion. The effect varies depending on the leaf morphology. Because of the magnitude difference between needle diameter (∼1 mm) and raindrops (up to ∼8 mm), there should be a “cutting effect” of the needle on falling raindrops. However, no study has beem performed to address how this effect alters raindrop characteristics. In this study, we investigated the effect using artificial water drops, high-speed photography, and staining method in the laboratory. Masson pine (Pinus massoniana Lamb.) needles were collected from the field including fresh green needles (FGN) withered yellow needles (WYN) partially decomposed needles (PDN). The needle properties (i.e., surface repellency, cross-section morphology, and flexural stiffness) were measured to determine the factor controlling the cutting effect. Results showed that after the cutting effect, one raindrop could be cut into up to 12 small raindrops. Their velocities owned a bimodal distribution. Compared to the diameter before the cutting effect occurred, the raindrop diameter decreased by an average of 59 %, and the raindrop velocity decreased by an average of 19 %. This caused a substantial decrease in the raindrop energy (∼85 %). The cutting effect included three sub-processes: collision, splitting, and interception. Our analysis suggested that the splitting process was the main reason for the cutting effect to reduce raindrop energy. The cutting effect was affected by the needle properties and raindrop falling heights. The cutting effect was enhanced when the needle developed from FGN and WYN to PDN. The cutting effect was positively related to the falling height of raindrops. Changes in the raindrop characteristics due to the cutting effect should enhance rainfall evaporation and infiltration and thus decrease soil erosion, which needs to be evaluated in further studies.

Implications of climate change on water quality and sanitation in climate hotspot locations: A case study in Indonesia

Abstract Southeast Asia is vulnerable to climate change with over half of its population already being impacted by drought, flooding, and rise in sea levels recently. This work reviews the current water resource challenges in Indonesia, prone to the rising impacts of climate change. A baseline assessment of Indonesia's water and drinking water resources related to its original sources is presented. In response to a growing concern over chronic challenges that undermine water supply nationwide, this study analyses drinking water safety supervision. To accomplish this, a literature survey (100 studies published during the 2000–2023 period) was performed to identify regional groundwater resources sustainability and water security issues. Among the main findings of this study, only 10% of rainfall infiltrates to the groundwater, while 70% of its rivers are heavily polluted by domestic waste. During the study period, water availability decreased to 1,200 m3/year in 2020, with only 35% of the resources being economically feasible for reuse. The water supply deficit in Indonesia was estimated to be 5.5 hm3/year with roughly 67% of the population's water demand satisfied in 2021. Although this deficit might be fulfilled with private vendors, water supply/demand forecasts in 2030 suggest that the gap could not be closed by increasing water supply.

Providing solutions for data scarcity in urban flood modeling through sensitivity analysis and DEM modifications

Abstract Developing countries face significant challenges in accessing sufficient and reliable hydro-meteorological data, hindering the implementation of effective disaster management strategies. This research proposes solutions for limitations on performing flood simulations through parameter sensitivity analysis and digital elevation model (DEM) modifications. The methodology provides alternatives to account for insufficient rainfall, roughness coefficient, infiltration data in simulating large-scale rainfall-runoff, and high-resolution DEMs incorporating road and building networks for urban flood modeling. By applying the method to an extreme flood event in the Marikina Basin, Philippines, a combination of ground-based and remotely retrieved rainfall data, roughness (n = 0.3861–0.5005), and infiltration parameters (Δθ = 0.326–0.505 and ψ = 0.4547–1.565) set at the maximum range were found to replicate the increase in the upstream water level. Simulations were able to accurately capture the flood propagation along the natural and artificial barriers in the urban area compared to untreated digital terrain and surface model (DTM and DSM) data, with root-mean-square error range improvements from 0–7.13 (DTM) and 0.29–4.20 (DSM) to 0–0.63 (modified DEM). The proposed methodology significantly improved the accuracy of the simulations, which is crucial for proposing adequate flood action plans, despite the lack of high-resolution data available for under-developed nations.

Conditional random field-based stochastic analysis of unsaturated slope stability combining Hoffman method and Bayesian updating

This paper proposes a new framework for discretizing the conditional random fields that combines the Hoffman method and Bayesian updating, where multiple types of geotechnical data can be utilized, such as the field monitoring data and the site investigation geological borehole data. The feasibility of the proposed method is demonstrated using a rainfall-induced slope example in spatially varying soils. Results showed that the proposed framework of incorporating Bayesian updating to Hoffman method can effectively reduce the uncertainty in site characterization and guarantee precise risk assessment of unsaturated slope stability. Otherwise, the slope failure probability and landslide sliding volume would be overestimated when only the Hoffman method is adopted for site characterization. Subsequently, the developed method is further used to estimate the probabilistic stability of Baishuihe landslide in the presence of rainfall infiltration and reservoir water level fluctuation. It is hoped that this study can provide a reference for risk assessment of the unsaturated slope stability in reservoir areas.

Phreatic surface calculation and stability analysis of three-dimensional slopes under rainfall infiltration

Phreatic surface calculation and stability analysis of three-dimensional slopes under rainfall infiltration

Influence of rainfall pattern and infiltration capacity on the spatial and temporal inundation characteristics of urban waterlogging.

The rapid development of the city leads to the continuous updating of the land use allocation ratio, particularly during the flood season, which will exacerbate the significant changes in the spatial and temporal patterns of urban flooding, increasing the difficulty of urban flood forecasting and early warning. In this study, the spatial and temporal evolution of flooding in a high-density urban area was analyzed based on the Mike Flood model, and the influence mechanisms of different rainfall peak locations and infiltration rate scenarios on the spatial and temporal characteristics of urban waterlogging were explored. The results revealed that under the same return period, the larger the rainfall peak coefficient, the larger the peak value of inundation volume and inundation area. When the rainfall peak coefficient is small, the higher the return period is, and the larger the peak lag time of the inundation volume is, in which P = 50a, r = 0.2, the peak lag time of the inundation volume reached 32min and 45min for the inundation depths H > 0.03 m and H > 0.15 m, respectively. There are also significant differences in the peak lag time of waterlogging inundation volume for different inundation depths. The greater the inundation depth, the longer the peak lag time of the inundation volume, and the higher the return period, the more significant the effect of lag time prolongation. It is worth noting that the increase in infiltration rate may lead to an advance in the peak time of inundation volume and inundation area, and the peak time of the inundation area is overall more obvious than that of inundation volume. The effect of infiltration rate on the peak time of inundation volume for larger inundation depths was relatively large; the peak times of inundation volume and inundation area were advanced by 4-6 min and 4-8 min for H > 0.03 m and H > 0.15 m, respectively, after the increase in infiltration rate, and the higher the rainfall return period, the longer the advance time. The spatial and temporal characteristics of waterlogging under different peak rainfall locations and infiltration capacities obtained in this study can help provide a new perspective for temporal forecasting and warning of urban waterlogging.

Comparing Different Coupling and Modeling Strategies in Hydromechanical Models for Slope Stability Assessment

The dynamic interaction between subsurface flow and soil mechanics is often simplified in the stability assessment of variably saturated landslide-prone hillslopes. The aim of this study is to analyze the impact of conventional simplifications in coupling and modeling strategies on stability assessment of such hillslopes in response to precipitation using the local factor of safety (LFS) concept. More specifically, it investigates (1) the impact of neglecting poroelasticity, (2) transitioning from full coupling between hydrological and mechanical models to sequential coupling, and (3) reducing the two-phase flow system to a one-phase flow system (Richards’ equation). Two rainfall scenarios, with the same total amount of rainfall but two different relatively high (4 mm h−1) and low (1 mm h−1) intensities are considered. The simulation results of the simplified approaches are compared to a comprehensive, fully coupled poroelastic hydromechanical model with a two-phase flow system. It was found that the most significant difference from the comprehensive model occurs in areas experiencing the most transient changes due to rainfall infiltration in all three simplified models. Among these simplifications, the transformation of the two-phase flow system to a one-phase flow system showed the most pronounced impact on the simulated local factor of safety (LFS), with a maximum increase of +21.5% observed at the end of the high-intensity rainfall event. Conversely, using a rigid soil without poroelasticity or employing a sequential coupling approach with no iteration between hydromechanical parameters has a relatively minor effect on the simulated LFS, resulting in maximum increases of +2.0% and +1.9%, respectively. In summary, all three simplified models yield LFS results that are reasonably consistent with the comprehensive poroelastic fully coupled model with two-phase flow, but simulations are more computationally efficient when utilizing a rigid porous media and one-phase flow based on Richards’ equation.

Model Test Study of Rainfall Factors on Failure Process of Xiashu Loess Slope with Gravel Layer

Rainfall is an important factor affecting the stability of Xiashu loess slope, so it is particularly important to understand the infiltration law and induction process of rainfall in Xiashu loess slope. In this paper, a Xiashu loess slope model with a slope ratio of 1 : 1.2 is constructed in the model box. The rainfall infiltration law, vertical stress characteristics, pore-water pressure characteristics, and deformation failure mode of the slope under two different rainfall types and four different rainfall degrees are analyzed. The instability and failure mechanism of Xiashu loess slope with gravel layer under different rainfall conditions is studied. The test results show that the influence of rainfall intensity factors on the gravel soil slope is mainly reflected in the degree of erosion of the slope. With the increase in rainfall frequency and intensity, the rainfall infiltration rate gradually increased, reached the highest value after standing, and then decreased with the increase of rainfall intensity. Rainfall has a great influence on the pore-water pressure in the gravel soil slope, and the pore-water pressure at the monitoring point of the slope toe changes the most. The vertical stress curve will change abruptly in the later stage of intermittent rainfall and during continuous rainfall.

The Groundwater Resources in the Mazovian Lowland in Central Poland during the Dry Decade of 2011–2020

This article addresses the issue of droughts in recent years in Poland and their impact on the state of groundwater resources. This paper presents the challenges arising from the increasing demand for the use of groundwater for irrigation in agriculture, supplementing water shortages, and potential threats to the water supply of rural waterworks. The main part of this paper focuses on a small catchment area in the Mazovian Lowland, which is one of the driest regions in the country. This article includes definitions, characteristics, and causes of hydrologic and hydrogeologic droughts during the period 2011–2020. In the discussed area, there is generally one groundwater level of the Quaternary age, primarily recharged by rainfall infiltration, which is utilized by all dug wells and a number of drilled wells. The source material consisted of daily measurements of groundwater levels with a free surface from three piezometers located in different land use areas (forest, agricultural, and sparse development). Additionally, daily flows of the Zagożdżonka River at the Płachty Stare gauge station were examined, where the drying of the riverbed in the upper reaches has been observed in recent years. This study investigated the dynamics of hydrogeologic droughts in renewable groundwater resources and the rate of their decline in relation to hydrologic droughts of surface waters.

Study of seepage patterns and calculation of infiltration coefficients of loose stacked layers on slopes under rainfall action

Rainfall is one of the most important factors inducing landslide occurrence, and previous researchers have carefully studied the stages of rainfall infiltration as well as the factors that affect infiltration (e.g., rainfall intensity, rainfall duration, initial water content and dry density). However, previous studies using homogeneous soils were overly idealised and ignored the effects of water content and dry density on infiltration, which vary with depth. In this paper, based on indoor rainfall infiltration tests under the above initial conditions and influencing factors, the following patterns were found: (1) dry density and water content of natural soils tend to increase along the direction of gravity under long-term gravity and repeated rainfall evapotranspiration; (2) stepped dry density increases infiltration resistance, which increases the total response time; stepped initial water content decreases infiltration water volume, which decreases the total response time; stepped dry density and water content have the shortest total response time;(3) The increase in dry density delayed the sudden change point in the permeability coefficient, and the initial moisture content had little effect on the sudden change point.

A comparative study of critical failure surface in unsaturated soil slopes

Landslides are rapid downslope movements triggered by factors such as rainfall, earthquakes, or human activity, where factors like relative permeability, air flow, and variations in hydraulic conductivity affect the mechanisms behind rainfall infiltration and landslide occurrence. This study investigates these phenomena using the finite difference method (FDM) and finite element method (FEM) in FLAC and PLAXIS software. These methods account for the coexistence of water and air, including the Two-phase flow option, in evaluating unsaturated slope stability and identifying critical failure surfaces. The efficiency of these approaches is gauged by varying soil parameters and exploring the impact of different values of suction and hydraulic conductivity, as well as soil-water characteristics, on the safety factor. It was observed that there are disparities between both software packages at high suction values, which impact the safety factor. FLAC is noted for its conservative approach and superiority in representing unfavourable conditions.

Numerical simulation of the interaction between mine water drainage and recharge: A case study of Wutongzhuang coal mine in Heibei Province, China

Water inflow poses a critical safety concern in coal mining. The pressing challenge in current mine water inflow research is the need to enhance the prediction of dynamic changes in mine water inflow across different mining stages. In this study, the hydrogeological conditions and aquifer structural characteristics of the Wutongzhuang Coal Mine in Hebei Province, China were analyzed, and the results were combined with pumping test and drilling data. A numerical model of groundwater flow in the study area was established using Visual MODFLOW and the model was calibrated and verified by comparing its results with the measured values to ensure that it realistically reflected the state of groundwater movement in the study area. The results of numerical simulation indicated that: (1) The water level of the Ordovician aquifer varies significantly by season. A large exposed area of Ordovician limestone in the western mountainous region receives a large amount of rainfall infiltration recharge in the summer rainy period that raises the water level of the Ordovician aquifer in the study area. (2) The groundwater system in the study area is in an equilibrium state, with the water inflow approximately equal to the outflow. (3) The recharge of mine drainage water has a slight positive effect on the Ordovician water level and the floor water inflow, with the impact on the water level of the aquifer decreasing as the distance from the recharge well and the import of Ordovician limestone water increase. In cases in which there is mine water recharge, the water level of the Ordovician aquifer is approximately 0.33 to 1.37 m higher than in cases without recharge, resulting in an increase in water inflow of approximately 10.6 m3/d. (4) In cases in which there is recharge of all drainage water, the maximum water inflow into the fifth mining area is 3,491.3 m3/d, which is 12.5 m3/d higher than in the case without recharge. These results provide important technical references for the formulation of mining schemes and water prevention measures in mining areas.

Interactions of macropores with tides, evaporation and rainfall and their effects on pore-water salinity in salt marshes

Salt marshes, a type of coastal wetlands, are influenced by various hydrogeological processes. These processes affect water and salt transport and play a critical role in determining the ecosystem services of salt marshes. Responses of pore-water flow and soil moisture to individual factors (e.g., macropores, evaporation and semidiurnal tides) have been well examined. However, how macropores interact with spring-neap tides, evaporation and rainfall and affect pore-water salinity in salt marshes remains unclear. This study investigated this question by analyzing water exchange across the marsh surface and the distribution of pore-water salinity in marsh sediment, based on a three-dimensional marsh-creek model. The results reveal high spatial heterogeneity of pore-water salinity in the presence of macropores. Due to the lateral recharge of macropore water, a negative salinity gradient is formed from macropore walls toward adjacent sediment. Additionally, macropores’ impact on water exchange and salt transport varies with distance from creeks. This results in two mechanisms by which macropores affect pore-water salinity, flushing and recharging. In well-drained near-creek areas, macropores reduce salt accumulation (flushing) compared with salt marshes without macropores. Whereas in the poorly-drained marsh interior, the recharge from macropores inhibits rainfall infiltration. This, together with enhanced evaporation, increases pore-water salinity (recharging) in the shallow soil layer. Moreover, the macropores’ impacts on pore-water salinity vary remarkably with macropore density. This study improves the understanding of pore-water salinity distribution in coastal wetlands and has potential implications for related biogeochemical processes.

Experimental study of natural convection and cooling capacity of closed crushed-rock layers affected by summer rainfall in cold regions

Climate-induced rises in air temperature and humidity on the Qinghai-Tibet Plateau modify the hydrothermal conditions of closed crushed-rock embankments (CRE). This alternation arises from the infiltration of summer rainfall, which is closely correlated with the cooling performance of the crushed-rock layers (CRL). Nevertheless, the cooling performance of the closed CRL during the summer rainfall season remains unexplored. In these present, physical models were employed to examine the convective properties and hydrothermal response processes. The results reveal that summer rainfall greatly diminishes the natural convection intensity within the closed CRL. Conversely, cycle-average temperatures showed an upward trend under these conditions. Moreover, based on fluctuations in the thawing/freezing index, the cooling capacity of the CRL weakens post-summer rainfall, with a maximum decline of 27.3% compared with the initial cycle. Additionally, the humidity in the subsoil layer experiences a stepwise growth followed by a gradual decrease owing to concentrated rainwater percolation. After enduring four rainfall events, the volumetric water content in the subsoil layer presents an upward trajectory. Overall, infiltrated water introduces additional heat, modifying the hydrothermal and convective properties of closed CRE, consequently impairing the cooling efficacy of the CRL.

Blue-green roofs as nature-based solutions for urban areas: hydrological performance and climatic index analyses.

The water-regulating capacity of nature-based solutions (NBSs) plays a crucial role in providing a full range of ecosystem services and enhancing the resilience of urban systems. This work focuses on the hydrological performance of a particular NBS, the so-called blue-green roof (BGR). The BGR is designed to collect infiltrated rainfall in a water storage layer beneath the soil to support vegetation maintenance, enhance evapotranspiration and cooling, and minimize runoff and drainage system load. The study aims to evaluate the hydrological performance of the BGR at global and event scale and, for the first time, to model climatic factors (easy to measure using common sensors) that affect its stormwater retention capacity. The data collected over 2years and 2months at a 5-min resolution from a pilot study in Central Italy were analysed. Additionally, a new climatic index called AWWP-x (Antecedent Wet Weather Period index) was introduced and calculated. Results show that the BGR has an overall relevant retention rate (67.1%), although the value depends on the rainfall of the observed period. Approximately 50% of the rainfall events did not produce any runoff, and during the dry season, all events were totally absorbed by the BGR. Four climatic variables were identified as significant factors for predicting BGR retention performance (R2 = 0.50). The results suggest that AWWP-130 (number of days to reach 130mm cumulative precipitation) could be a possible proxy for the BGR stormwater retention rate. In general, this study demonstrates the potential for evaluating, planning, and designing NBSs by considering the annual and interannual climatic variability of the investigated specific location.

Analysis of the impact of green infrastructure on surface runoff from urban areas

Current construction methods and the marked increase in urbanisation are contributing to a high proportion of impermeable surfaces in built areas. Such surfaces reduce the infiltration of rainfall into the ground, which in turn leads to high amounts of surface runoff, which can have negative consequences in terms of flood safety. The introduction of green and hybrid infrastructure seeks to improve the characteristics of urban areas in terms of increasing the infiltration of rainwater and reducing stormwater runoff. In this study, we considered the larger industrial area of Rudnik in Ljubljana. Based on data on rainfall characteristics and soil properties, we calculated the surface runoff for the current situation and the situation when the improvements were introduced, where we took into account green roofs, tree planting and porous ground surfaces. Having analyzed the data, measurements, and calculations, we found that green infrastructure contributed positively to the reduction of surface runoff in urban areas, with differences of up to 20% at the annual level and up to 10% at the storm event level compared to the situation without improvements. In terms of surface runoff, the use of porous ground surfaces was identified as the best solution, with relatively small differences between the selected measures. From a financial point of view, tree planting was identified as the best solution, as trees can provide similar surface runoff reduction as green roofs and porous surfaces, with lower construction and maintenance costs.

How do the distribution patterns of exposed roots affect the rainfall-runoff processes of sloped land under simulated multi-rainfall conditions in karst region?

Exposed root system is used as a reference of quantifying the erosion rate on slopes, but its influence mechanism of exposed root on rainfall-runoff processes during rainfall is still unclear. This study aimed to investigate the effects of exposed root distribution patterns on the rainfall-runoff processes of sloped land. Specifically, we achieved it by conducting eight multi-rainfall events under rainfall intensity of 75- and 50-mm h−1 and fixed slope gradient of 25° on the flume (1.0 m long, 0.5 m wide and 0.3 m deep) packed with yellow soils with different exposed root distribution patterns (vertical slope arrangement, parallel slope arrangement, transverse slope arrangement) on sloped land. The results revealed that during the 1st rainfall, the initial runoff time of surface, subsurface and underground runoff was shorter on parallel and vertical slope arrangement compared to transverse slope arrangement. During subsequent rainfall, surface and subsurface runoff was reduced by 5–15 times in comparison to the 1st rainfall. Furthermore, the amount of surface runoff increased in the order of parallel slope arrangement > vertical slope arrangement > transverse slope arrangement from the 1st to 4th rainfalls, while the amounts of subsurface and underground runoff decreased. On average, the amounts of surface, subsurface and underground runoff for parallel slope arrangement accounted for 61.77 %, 29.33 % and 8.90 % of the total runoff amount, respectively, whereas for vertical slope arrangement, it accounted for 57.27 %, 26.81 % and 15.92 %, and for transverse slope arrangement, it accounted for 55.78 %, 29.71 % and 14.52 % of the total runoff amount. Our findings suggested that the distribution patterns of exposed root had a significant impact on rainfall-runoff processes. Specifically, a vertical slope arrangement was conducive to rainfall infiltration, a parallel slope arrangement resulted in more surface runoff, and a transverse slope arrangement could reduce water loss, although its effect decreased with increasing rainfall frequency. In this way, the presence of exposed roots in topsoil created a rough surface that could affect the onset of flow during the initial stages of rainfall and modify the flow direction and distribution once it commenced. The results of this study would be critical in enhancing our understanding of the relationship between plant roots and hydrological processes in karst region.

Analytical modelling of desiccation crack depth estimation for granitic soils

Desiccation cracking has been aggravated by the frequent extreme weather events and climate change in recent years. The presence of these cracks compromises the integrity of soil structures and significantly contributes to rainfall infiltration, slope stability, as well as soil deformation. According to tensile failure theory and Hookean elastic equation, an analytical model was established to predict crack depth under continuous desiccating conditions. The essential input parameters for the modelling are the modulus ratio and tensile strength, which can be determined through uniaxial tensile and shear tests. The maximum crack depth is estimated based on the suction change profile of the soil under investigation. Herein, the suction change profiles were developed from volumetric water content monitoring at various depths and utilizing the soil water characteristic curve (SWCC) of the investigated soil. Validation of the proposed method was conducted through laboratory simulations, specifically in the context of crack formation in granitic soils under continuous drying conditions. The predicted crack depth, in a range of 0.22 ∼ 0.30 m, closely aligned with the observed values. Collectively, for a specific soil with given elastic parameters and strength, crack depth can be estimated through suction change. This approach, compared with existing crack modeling methods, offers a simple and efficient way for crack depth estimation, holding promise for practical applications.

Combined influence of rotated transverse anisotropy in mechanical parameters and hydraulic conductivity of soils on reliability evaluation of an unsaturated slope under rainfalls

Natural slopes often exhibit tilted stratification with rotated transverse anisotropy in multiple soil properties, including the mechanical (e.g., friction angle φ and cohesion c) and hydraulic properties (e.g., saturated hydraulic conductivity ks). This phenomenon indicates that to achieve an accurate assessment of slope reliability under rainfall infiltration, the anisotropic spatial variation of the shear strength parameters and ks should be incorporated in a combined manner. Thus, this paper discusses the combined influence of rotated transverse anisotropy in the shear strength parameters and ks on the reliability and failure mechanism of an unsaturated slope under rainfalls. It is found that for a slope with tilted stratification, the failure mechanism and reliability estimator are dominantly influenced by the rotated transverse anisotropy in the shear strength parameters, while the influence induced by that in ks is slight. In particular, only incorporating the rotated transverse anisotropy in ks may lead to an incorrect reliability estimator of a slope with tilted stratification. Herein, the reliability index β would be estimated to be dramatically higher, and β of a slope with horizontal bedding would be higher than that of an anti-dip slope, which is inconsistent with the engineering experiences. Nonetheless, the rotated transverse anisotropy in ks should not be ignored in slope reliability assessment, because ignoring the rotated transverse anisotropy in ks would lead to overestimation of the reliability index β, which is adverse to the safety design of a slope.