Evaluation of the Antecedent Saturation and Rainfall Conditions on the Slope Failure Mechanism Triggered by Rainfalls

Abstract

The stability analysis of rainfall-induced slope failures considers a number of factors including the characteristics of the rainfall, vegetation, geometry of the slope, unsaturated soil characteristics, infiltration capacity, and saturation degree variations. Amongst all these factors, this study aims to investigate the effects of the antecedent rainfall and saturation conditions. A numerical modeling study was conducted using finite difference code software on a representative slope geometry with two different soil types. Two scenarios were followed: The first involved the application of three different rainfall intensities for varying initial saturation levels between 40% and 60%, representing the antecedent saturation conditions. The second scenario involved modeling successive rainfalls for a typical initial saturation degree of 50%. The impact of antecedent rainfall was assessed by determining the time required for failure during the application of a main extreme rainfall after a preceding rainfall of varying durations. Consequently, a zone of susceptible time for failure was suggested for use as a criterion in hazard management, allowing for the tracking of rainfall and its duration through the proposed chart for potential failures. Once the anticipated critical rainfall intensities have been determined through a meteorological analysis, a risk assessment for a specific slope can be conducted using the proposed practical procedure. Accordingly, a control mechanism may be established to detect the potential for a natural hazard. Furthermore, the proposed procedure was applied to a case study, whose modeling insights were in harmony with the real conditions of the slope failure. Thus, this demonstrated the significance of the antecedent conditions in modeling landslides triggered by rainfalls.

1. Introduction

Natural or cut slopes are inherently found in unsaturated conditions with particularly steep slopes having very deep water table levels. For elongated slopes, the ground water table (GWT) is usually assumed to be parallel to the slope surface, and, with the rainfall, the GWT is expected to rise and cause a reduction in slope stability by conventional approaches. However, with a realistic approach, it can be said that the reduction in slope stability is due to the perched water zones near the surface of the slope [1,2,3]. The change in saturation is formed by the rainfall and controlled by the infiltration characteristics of the soil. Actually, in the beginning, a thick unsaturated zone takes place naturally, resulting in negative pore pressure (matric suction) above the GWT. Rainfall infiltration results in variation in the unsaturated zone, with the highest saturation occurring at the surface and a gradual decrease in saturation level with depth. The alterations in saturation degree and/or water content result in modifications to the matric suction, effective stress, weight, and stability. A critical review on the physical foundations of unsaturated soils such as the matric, osmotic suction, and capillary cavitation was given in the study of Baker and Frydman [4].

Bicocchi et al. [5] investigated the geotechnical and hydrological parameters for different landslides as a statistical analysis to define a typical range of values only in relation to the mapped lithologies. However, the result indicated that this approach was not feasible due to the fact that the soil characteristics were not simply dependent on the bedrock type. On the other hand, conventional approaches on slope stability suggested the evaluation of classical soil mechanics assumptions; yet, the problem with natural slopes is that slopes may lose their stability after being subjected to rainfall due to the increase in their saturation, resulting in a decrease in their suction stresses [6,7,8,9,10,11,12].

Taşkıran and Aslan Fidan [13] investigated the parameters affecting the stability of the unsaturated soil slope subjected to rainfall. Low-intensity rainfalls with longer durations were found to be as destructive as high-intensity rainfalls with shorter durations. For soils with an intermediate permeability (10⁻⁴–10⁻⁷ m/s), the infiltration and drainage equilibrium were found to be very effective on the change in pore pressure. On the other hand, Rahimi et al. [14] stated that the slope stability of low-conductivity soils was affected more significantly than high-conductivity soils when subjected to three antecedent rainfall patterns in their study. Similarly, the initial degree of saturation or antecedent water content values was found to have a significant influence on the behavior of clayey soils when compared to that of silty soil [15].

Careful attention is needed when evaluating the stability of a slope for it is possible for it to end up being a geotechnical hazard. In January 2021, a huge rainfall-triggered landslide occurred after four hours of rainfall and finally caused the death of 32 people and much social and economic damage [11]. Haque et al. [16] identified deadly landslides in 128 countries over 20 years and, in this duration, 3876 landslides were found to cause almost 164,000 deaths. The study also confirmed that the events mostly took place where a risk of extreme rainfall conditions were defined. The situation also gains importance from climate change resulting in unexpected rainfall series. Thus, considering the unsaturated soil conditions is essential for natural slopes when evaluating the slope stability and studying the landslide mechanisms subjected to rainfall.

Regarding the hazards caused by unexpected rainfall activities due to global warming, the research further investigating the effect of precipitation on slopes increases. A study investigating the effect of climate change on rainfall-induced landslides was published by Oguz et al. [17] as a case study in Norway. The study mainly used intensity–duration–frequency calculations and modelled landslides for present and future climate conditions. The future conditions included 10, 50, and 100 years of scenarios. The probability of a landslide initiation (Pf) was found to increase by up to 22.3%, 16.9%, and 13.5% for a given 12 h rainfall event with 10-, 50-, and 100-year return intervals, respectively, due to climate change. Kristo et al. [18] investigated the historical rainfall of Singapore from two stations for the period of 1985–2009 and analyzed the rainfalls by duration with linear regression. Regarding the past data, a projection study was carried out, and possible rainfall intensities were determined. Factor of safety values were calculated for projected future data for the years 2003, 2050, and 2100, and a significant decrease was found in the factor of safety data for the increasing years.

Bračko et al. [19] investigated the importance of geotechnical analysis in the context of climate change adaptation and slope stability. According to the study, the climate change scenarios serve as the foundation for estimating both current extreme precipitation events with a 100-year return period and future extreme precipitation events. Precipitation results in the net infiltration of water, which is dependent upon the prevailing conditions of evaporation, transpiration, and surface water runoff. In conjunction with climate change, the increase in the net infiltration of water might be the most critical parameter to consider. The results of their parametric study demonstrated a significant influence of cohesion on the factor of safety, which exhibits a nearly linear decline of 0.1 for each 1 kPa reduction in cohesion. When the soil permeability is low (<10⁻⁷ m/s), the factor of safety exhibits a downward trend during rainfall and subsequent days. Conversely, when the permeability is higher (k ≥ 10⁻⁷ m/s), the factor of safety displays a decline during rainfall and an upward trend thereafter. The study also indicated that measures to reduce the net infiltration of water would ensure long-term stability, even when considering the potential impact of climate change.

The physical and hydrological mechanisms affecting the slope stability were intensively investigated in the study of D’Ippolito et al. [20]. The study discussed the strengths and weaknesses of the methods, together with the causes that may have hindered better results for the considered cases. In evaluating the hydrological data, it was emphasized that the type of precipitation and its duration should be carefully considered, with attention paid to aligning the assessment with the successive rainfalls, actual timing, and intensity of the event as well. Previously, the I-D threshold was regarded as a reliable indicator of landslide occurrences triggered by rainfall. However, its effectiveness was limited by its inability to account for antecedent rainfall. Yet, a new I-D threshold was established [21] by statistically analyzing hourly rainfall data of landslide occurrences in South Korea for 613 shallow landslides regarding the antecedent rainfall conditions.

According to the findings of Godt et al. [22], even though the heavy rainfall conditions following a dry period were not likely to be found to cause a landslide, a relatively low-intensity rainfall following a wet period did, which pointed to the importance of the antecedent conditions. Naidu et al. [23] utilized the cluster analysis method to demonstrate the rainfall threshold triggering the landslides in Amboori, Kerala, India, which is a tropical area. In the study, 2-, 3-, and 5-day antecedent rainfall clusters were modelled, and regression analysis was performed. When the 5-day antecedent rainfall was zero, a single instance of rainfall of 80.7 mm was found to trigger a landslide. In addition, almost 20% of triggering in the whole study was found to have happened following the 5-day antecedent rainfall. The study suggested the use of the rainfall threshold criteria and did not calculate but recommended the factor of safety values as well. Moreover, Sun et al. [24] argued that the soil became overconsolidated when it experienced a higher suction value than its residual suction value which led to the soil having a higher average skeleton stress, resulting in a state of overconsolidation. The authors concluded that, similar to the stress history, the suction history is found to be incredibly effective for the behavior of the overconsolidation process. Therefore, the antecedent rainfall conditions in terms of creating a suction history become more important to the evaluation of the triggering mechanism of a landslide.

As per Intergovernmental Panel on Climate Change (IPCC), the global average surface temperature is suggested to increase by 1.4 °C to 5.8 °C degrees within the period of 1990 to 2100. Due to this increase, the rainfall patterns are expected to be more intense and less frequent. Today, rainfall exceeding 3 days is a small possibility; however, with the global warming effect, intense rainfalls with longer durations will not be surprising. Future conditions will likely include challenging precipitation patterns, such as prolonged heavy rainfall and/or extreme rainfall events occurring after periods of heavy rainfalls. However, these are rarely incorporated into models, particularly in the case of rainstorms that occur after a preceding period of a rainfall [25]. This is a significant issue because the antecedent rainfall saturates the soil, thereby preparing it for the subsequent heavy rainfall which is the actual trigger for slope failure.

This study investigates the effect of antecedent rainfalls on the slope stability when the soil was subjected to different rainfall intensities such as 2.5 mm/h, 5 mm/h, and 10 mm/h. Moreover, the slope stability was also investigated regarding the historical extreme rainfall data given on the web site of the Turkish State Meteorological Service (TSMS) when subjected to a prior antecedent rainfall or not. The time required for failure for a particular slope subjected to an extreme rainfall record was investigated and the susceptible time zone for the given situation is suggested. An application for a real case situation was also carried out and the results were discussed in terms of the antecedent conditions in the slope failure model. These analyses are expected to form a basis for evaluating the potential slope failure mechanisms which are prone to be affected by climate change due to global warming.

2. Materials and Methods

During the study, a representative typical slope model and representative soil properties were used to investigate the impact of antecedent conditions on the slope stability. The slope stability analyses were carried out by using a numerical program, Fast Lagrangian Analysis of Continua (FLAC), which is a finite difference code software [26]. FLAC is able to run two-phase flow (tp-flow) of water and air in a 2D environment representing an unsaturated soil and computes the stability of a slope through deformation analysis. The slope geometry was also chosen as the one used in FLAC manual (see Figure 1). The model is 60 m wide and has a height of 30 m on the left side and 10 m on the right side. The relatively flat parts are both 20 m on the left and right sides. The highest slope angle is 45° with a former secondary 27° angle. The analyses were conducted by using two different soils. One of them was the soil given in the manual of FLAC (FLAC sample) and the other soil was obtained from a natural slope (this study).

The average saturated hydraulic conductivity of the soil used in this study was measured by a flexible wall permeameter with falling head procedure [27]. The soil sample was taken directly from the natural slope origin and carefully trimmed to fit in the permeameter. During the tests, the confining stress was 35 kPa, the average hydraulic gradient was 10, and no backpressure was applied. In addition, the soil was left for prehydration for the first 24 h to obtain a homogeneous diffusion environment. Tests were terminated regarding the conditions of consecutive measurements of hydraulic conductivity being less than 25% and the ratio of the inflow and outflow being constant at least for the last 3 measurements.

The suction measurements were carried out by using filter paper method [28]. A bio-incubator-type incubator (Santez SI-150K, Santez, İstanbul, Türkiye) was used, and the equilibrium time was 1 week. Following the suction measurements, the unsaturated soil parameters were determined by constructing the SWRC of the soil in SWRC-Fit [29,30]. SWRC-Fit is a general model for multimodal unsaturated soil hydraulic properties. It can fit several soil hydraulic models to laboratory- or field-measured soil water retention data. This study used the van Genuchten model and constructed the SWRC of the soil as matric suction related to the volumetric water content. The constructed SWRC is given in Figure 2. To obtain the saturated mechanical properties of the soil, conventional direct shear tests were run for soaked conditions [31]. The geotechnical and hydromechanical properties of the soils used during the modeling study are presented in

Table 1. Some geotechnical and hydromechanical properties of the soils.

Property	FLAC Sample	This Study
Dry density (kg/m3)	2000	1720
Drained cohesion (Pa)	0	10,500
Drained friction angle (degrees)	30	18
Saturated hydraulic conductivity (m/s)	10−5	6 × 10−7
Porosity	0.10	0.30
van Genuchten parameter, a	0.336	0.335
van Genuchten parameter, P0 (MPa)	0.015	0.035

as used in FLAC. Any relevant details of each test can also be found in the study of Durukan and Başarı [32].

When studying with FLAC for rainfall-triggered slopes, the first case is to run the seepage calculations which give the pore water distributions, and the second case is to combine the case with deformation analysis, determining the FoS. For seepage calculations, the left, right, and bottom boundaries are set as impermeable boundaries. The surface of the slope is the rainfall infiltration boundary and set as the flow boundary. The rainfall infiltration boundary depends on the relation between the rainfall intensity and the soil infiltration capacity. If the rainfall intensity is lower than the infiltration capacity, then the boundary is flow boundary allowing the water to flow through the surface. However, if the rainfall intensity exceeds the infiltration capacity, then a runoff mechanism would ensue. For this condition, in order to prevent the accumulation of water at the surface, the boundary was fixed. The unsaturated parameters for seepage calculations were van Genuchten characteristics, and, for stress and strain calculations, model had the Mohr–Coulomb criterion, which allows for normal iterative computation. During the deformation calculations, the left and right boundaries are constrained in the horizontal direction, and the bottom boundary is fixed in all directions.

FLAC runs tp-flow of water and air as wetting (w) and non-wetting (g) fluids, respectively. The capillary pressure (P_c), namely, the matric suction, is defined as the difference between the pressures of non-wetting (P_g) and wetting (P_w) fluids, as follows in Equation (1):

$$P_c=P_g-P_w$$

(1)

The capillary pressure, Pc, can be related to the effective saturation ($S_e$) where both can also be related to the residual saturation ($S_w^r$) and actual saturation ($S_w$). Equation (2) presents the relation between the capillary pressure and the saturation characteristics.

$$S_e={\left[{\left({\displaystyle \frac{P_c}{P_0}}\right)}^{{\displaystyle \frac{1}{1-a}}}+1\right]}^{-a}={\displaystyle \frac{S_w-S_w^r}{1-S_w^r}}={\displaystyle \frac{\theta -{\theta }_r}{{\theta }_s-{\theta }_r}}$$

(2)

where:

• P₀ is used in FLAC as being related to the air entry value;
• a is used in Flac as the m constant in van Genuchten parameters;
• $\theta$ is the actual volumetric water content;
• ${\theta }_r$ is the residual volumetric water content;
• ${\theta }_s$ is the saturated volumetric water content.

Then, matric suction (as capillary pressure, P_c) can be derived as follows in Equation (3).

$$P_c=P_0{\left[{S_e}^{(-{\displaystyle \frac{1}{a}})}-1\right]}^{(1-a)}$$

(3)

Equation (3) can be used to determine the matric suction values for any saturation degree in relation with the effective saturation, air entry value, and van Genuchten parameter, a. The mobility coefficient (k) in FLAC is related with saturated hydraulic conductivity (k_s), gravitational acceleration (g), and density of water (r_w), and given in Equation (4).

$$k={\displaystyle \frac{k_s}{g.{\rho }_w}}$$

(4)

For all classical equations used during the seepage calculations and deformation analysis, comprehensive explanation can be found in the manual of FLAC [26] and related core studies [10,33,34,35,36].

During the analyses, the rainfall intensities were chosen as 2.5 mm/h, 5 mm/h, and 10 mm/h, representing the light, moderate, and heavy rainfall conditions, respectively. The initial saturation degrees were selected to vary between 40% and 60%. In order to conduct an analysis, it is first necessary to arrange the initial saturation degree. This should be carried out using the proper initial pore pressure and infiltration characteristics related to the soil’s unsaturated properties. Otherwise, it is not possible to arrange the desired saturation degree unless the appropriate pairs of characteristics are input. Thus, initially, each parameter was calculated and applied to the model to enhance the desired initial saturation degree value. The mentioned saturation degrees were valid for the soil part close to the surface where the shallow slope failure is expected due to the rainfall. For the rest of the soil profile, the saturation degrees were set to increase gradually. An example for the unsaturated zone of the soil profile for 55% saturation for FLAC sample is given in Figure 3.

The effects of antecedent saturation and rainfall conditions were investigated with different approaches combined. As a start, the factor of safety (FoS) values for each soil at its initial saturation degrees between 40% and 60% were determined for comparison. Then, each rainfall conditions were applied for varying durations to ascertain whether the slope failed or not for different initial saturation degrees, solely for the soil exhibiting the smallest FoS values.

In addition, the historical extreme rainfall data were searched from the web site of Turkish State Meteorological Service [37]. Amongst the given historical data, one record was selected. The rainfall record was given as 252.8 mm for 3 h in 10–11 August 2021, in TSMS for Bartın, Ulus, Ceyüpler area, which is in west northern part of Black Sea Region of Türkiye. The selected record used in this study was 84 mm/h. The selected record was used as 84 mm/h in this study. The behavior and the time required for the failure of the slope were investigated in four main groups: the 84 mm/h rainfall (a) itself with no antecedent rainfall, (b) with an antecedent rainfall of 2.5 mm/h, (c) with an antecedent rainfall of 5 mm/h, and (d) with an antecedent rainfall of 10 mm/h, each for varying durations, all with the same initial saturation degree of 50% for all soils. The application of rainfalls for each scenario can be tracked from Figure 4.

3. Results and Discussion

There are two fundamental works in this study: the first one involves the main rainfalls of three different rainfall intensities applied to present varying saturation degrees, while the second one is the analysis of a historical rainfall record after different antecedent rainfalls for varying durations. Thus, several analyses were run, such as 10 analyses for the initial case conditions, 84 analyses for the first scenario, and 37 analyses for the second scenario.

3.1. Initial Conditions

Table 2. Factor of safety values of the soils for each initial saturation degree.

Initial FoS for	Initial Saturation Degrees
	S = 40%	S = 45%	S = 50%	S = 55%	S = 60%
FLAC sample	1.428	1.345	1.291	1.236	1.182
This study	1.502	1.420	1.338	1.283	1.228

presents the FoS values of soils when their saturation degrees varied between 40% and 60%, representing the initial conditions before the rainfalls. The parameter P₀ (see Table 1) used in FLAC addresses the air entry value (AEV), and AEV is known to represent the critical suction state of soils where the air can enter into the soil and desaturation starts. The AEV is known as one of the most important indicators of the suction capacity. Kenanoğlu et al. [38] studied the rainfall intensity and duration threshold in terms of unsaturated parameters by using hypothetical soils. Among the parameters in their study, the AEV was found to be the most critical. Thus, when the P₀ values of the soils were compared where the other variables were neglected, a higher AEV resulted in a higher FoS value.

3.2. Effect of Antecedent Saturation

The analysis of the rainfalls of 2.5 mm/h, 5 mm/h, and 10 mm/h for varying initial saturation degrees were evaluated. The resulting FoS values with respect to the time for the FLAC sample are presented in Figure 5. Since the FoS values for the soil given in this study were found to be higher, the detailed evaluation on the effect of the antecedent saturation degree was only made for the results of the FLAC sample for practical purposes. It is also a reminder that the main purpose of this study is not the soil properties or the comparison of them, but how to use them when evaluating the natural unsaturated slopes and how to follow the procedure given in this study regardless of the soil type. This is because there can be huge variations in the soil properties of slopes and each condition should be evaluated eventually.

To achieve a realistic evaluation depending on the anticipated critical rainfall times, the calculated threshold amounts of times were also evaluated. Thus, the calculated threshold amounts of heavy rainfall at standard times given on the TSMS web site [37] are utilized. These durations are indicative of the typical length of precipitation under standard conditions. According to the given thresholds of TSMS, the expected time for rainfalls of 2.5 mm/h, 5 mm/h, and 10 mm/h are found to be 24 h, 9.1 h, and 2.5 h, respectively. And the critical times given for each instance of rainfall are marked with a vertical dashed line in Figure 5a–c. It can be clearly seen that no failure was expected within the critical time durations even when the thresholds would be doubled.

A decrease in FoS was determined when the initial saturation degree increased due to the decrease in matric suction and its positive effect on the soil strength. Moreover, a similar decrease in FoS with increasing durations was determined as well. When the rainfall of 2.5 mm/h was applied to each model with varying initial saturation degrees, the time for failure was dramatically changed (Figure 5a). The time for failure in rainfall conditions was found to be approximately twice as long for samples with an initial saturation degree of 40% as for those with a saturation degree of 60%. If the initial saturation degree was held constant, in the 60% instance, the time for failure against 2.5 mm/h, 5 mm/h, and 10 mm/h are found to be 50, 24, and 10 h, respectively. The possibility of a 2.5 mm/h rainfall for 50 h is higher than 5 mm/h for 24 h and 10 mm/h for 10 h in real conditions. The data indicate that slope failure due to rainfall is more likely to occur when there is a constant light rainfall and a long duration of rainfall in this condition. Similar results were given in the study of Taşkıran and Aslan Fidan [13]. The graphics in Figure 5 demonstrate that the rainfall intensity and duration are not independent variables. Furthermore, when the slope stability was considered, the initial saturation degrees are essential to begin with, which are likely to change significantly according to weather conditions. Furthermore, when examining a slope stability issue, it becomes evident that evaluating the stability based on a single saturation condition is not a sufficient approach. The impact of saturation levels on the failure mechanism demonstrates the crucial importance of in situ volumetric water content measurements for slope stability assessments.

The unsaturated zone of the soil profile for 55% saturation was given in Figure 3 above. The saturation variations for the same soil conditions after the application of 2.5, 5, and 10 mm/h rainfalls at the limit of the failure conditions are also given in Figure 6, for comparison purposes. The saturation variations of each model at their limits of failure differ from each other. The maximum saturation degrees were found to be 85%, 95%, and 100% for the 2.5, 5, and 10 mm/h rainfalls, respectively. The saturation degree of 85%, which is for the 2.5 mm/h rainfall, was observed in a wider depth when compared to other saturation variations of 5 and 10 mm/h. However, the saturation degrees for the 5 and 10 mm/h rainfalls reached higher values (95% and 100%, respectively) but with narrow depths even for shorter durations when compared to the 2.5 mm/h rainfall saturation variations. When the slope reaches the saturation conditions as determined in Figure 6, then a slope failure is likely to be expected. Similar to the aforementioned situations, with the help of in situ measurements, a mutually controlled mechanism can be established between the failure status and saturation conditions for future studies.

3.3. Effect of Antecedent Rainfall for an Instance of Extreme Rainfall of 84 mm/h

The second scenario is an application of a historical extreme rainfall event. The extreme rainfall (84 mm/h) was applied to a model with an initial saturation degree of 50% for varying application conditions such as directly with no antecedent rainfall and with antecedent rainfalls of 2.5, 5, and 10 mm/h for varying durations. The primary objective is to assess the impact of antecedent rainfall, including its duration, in relation to the actual rainfall event that triggers the slope instability and to seek the time required for failure. Several analyses with different durations with three antecedent rainfall intensities were run for the extreme rainfall condition. The results are presented as the time (minutes) required for failure for each condition in Figure 7 for all cases. The times required for failure when there is no antecedent rainfall were found to be 52 and 80 min for the soils in the FLAC sample and this study, respectively. It is important to remember that the actual time for the recorded rainfall was 3 h at the actual location. For all soils, the slope failure would be achieved with the selected extreme rainfall.

When the successive rainfalls were considered, the antecedent rainfall directly affected the time for failure. The light intensity rainfall, 2.5 mm/h, may practically have a duration as long as a day, and, after 24 h, a storm may happen. When this condition was considered, the time required for failure for the 84 mm/h rainfall intensity was found to be 23 min for the FLAC sample and 26 min for this study’s sample. In another point of view, the storm may happen after the 5 or 10 mm/h rainfalls eventually. In this instance, after an hour of the 5 mm/h and 10 mm/h rainfalls, the time required for failure for the 84 mm/h rainfall was found to be 48 and 44 min, respectively, for the FLAC sample. The time required for the soil of this study was found to be 59 and 53 min for the same condition. If there were a possibility of an extreme rainfall condition exceeding these durations according to the meteorological expectations, a warning may be called, or precautions can be carried out before the rainfall takes place.

For each different duration of antecedent rainfalls, a zone appears in Figure 8a for each soil, and these zones were marked as dashed areas for the susceptible time for failure in Figure 8b. In Figure 8, three antecedent rainfalls were used, and the limitations of the zone were pointed out with lines where the upper limit belonged to the 2.5 mm/h rainfall and the lower limit to the 10 mm/h rainfall. For the other rainfall intensities between 2.5 and 10 mm/h, interpolations can easily be made.

It is critical to remember that the initial saturation was 50% for the second scenario in this model. Such evaluations can be carried out for other possible initial saturation degrees. In real conditions, the saturation variations can be determined by in situ observations, and calculations can be carried out according to the in situ measurements. In this instance, the natural water content was measured around 7% of the soil sample of this study which corresponded to a saturation degree of 40%. Consequently, the failure time for 40% saturation degrees for the soil in this study was found to be 108 min, when there was no antecedent rainfall for the 84 mm/h rainfall.

This type of graphical presentation may also be multiplied for other possible triggering rainfall conditions with site-specific investigations. The actual anticipated rainfall conditions can easily be compared to the chart and the detection of a possible failure can easily be guessed. Thus, a basis for an early warning system can be carried out for slopes along with their own unsaturated soil parameters with the help of on-time and in situ observations and data collection. The preliminary results of this study are believed to give hope towards the development of a control mechanism with which to detect the potential of a natural hazard such as landslides as a simple and effective process. To facilitate the tracking of the proposed procedure, a schematic representation of the workflow is provided in Figure 9.

4. Case Study

The preliminary findings of this study strongly recommend a comprehensive project including pilot site investigations, and laboratory and in situ measurements as a future study. Yet, a representative case study of a slope failure triggered by rainfall is modelled based on independent and unbiased data and laboratory findings. A slope failure was announced on 11 September 1999 in Hwangryeong Mountain, Busan, South Korea which caused the loss of one life, three injuries, and approximately 9.9 million US dollars of restoration expenditure [10]. Following the devastation caused by the landslide, a project was carried out including the in situ measurements of rainfall and pore pressures, and Kang et al. [10] published a modeling study investigating the slope failure in Hwangryeong Mountain with site-specific characteristics. Their study included soil properties such as the as average values of Hwangryeong Mountain soils, given in

Table 3. Some geotechnical and hydromechanical properties of the soil subjected to rainfall in the study of Kang et al. [10].

Property	Case Study
Dry density (kg/m3)	1250
Drained cohesion (Pa)	100
Drained friction angle (degrees)	33
Saturated hydraulic conductivity (m/s)	1.97 × 10−6
Porosity	0.46
van Genuchten parameter, a	0.520
van Genuchten parameter, P0 (MPa)	0.003

, and used a simplified soil profile (Figure 10) to represent the geometry of the failed slope [10]. The soil characteristics and the soil profile were adopted and the proposed procedure in this study was conducted to be presented as a case study. The rainfall conditions were obtained by researching both the related study and recorded historical data as well.

Kang et al. [10] reported a total rainfall of 200 mm for 3 days (9–11 September 1999) and the highest hourly rainfall during this period as 39 mm/h. For any specific date, it is possible to access the records of an airport located close to Hwangryeong Mountain where the slope failure was found via an Internet web page, namely, Weatherspark. The Weatherspark web page uses METAR and Integrated Surface Database (ISD) reports. The METAR code is regulated by the World Meteorological Organization in consort with International Civil Aviation. ISD reports are maintained and published by the National Oceanic and Atmospheric Administration’s (NOAA) National Center for Environmental Information. The web site uses ISD data to complement and backfill for their METAR archive. The Weatherspark web page allows users to access a multitude of station records, predominantly airport records, for a specified date and location. Taken from Weatherspark, the rainfall records from Gimhae International Airport for September 1999 are presented in Figure 11 [39]. The precipitation that caused the collapse is marked with a dashed line on the figure.

Precipitation characteristics may vary with distance or altitude. In this instance, the rainfall record was on September 10 and no other rainfall was recorded a day before and after (9 and 11 September) in Figure 11; however, Kang reported a total of 200 mm of rainfall in 3 days. Thus, for a robust precipitation process, a comparative analysis of Kang et al. [10]’s and the station data [39] has been established. The station data in Figure 11 indicates that a thunderstorm with rain lasted a minimum of 2.5 h with an antecedent heavy rainfall which also had an antecedent light rainfall. As a point of view, when a slope is subjected to a thunderstorm, the effect of a thunderstorm triggering the initial movement considering the mechanical solicitation of the sound waves and/or wind-induced vibrations are also discussed [40]; yet, this is generally neglected in landslide studies, and this study, as well, only focuses on the saturation and rainfall antecedent conditions.

In the modeling process, the initial saturation degree and pore pressures were established to reflect the conditions resulting from the light rainfall at the onset of the day during a period of precipitation. To achieve this, a pore water pressure of approximately −10 kPa was targeted. This value was predicted as an expected piece of data in the field after light rainfalls during the rainy period in the study of Kang et al. [10]. For the application of the following rainfalls, regarding the station records and the data in Kang’s study, to apply a rainfall intensity of 5 mm/h for 5 h followed by 3 h of 39 mm/h rainfall (a total of 142 mm) was considered as a representative case study. A total of 26 analyses were conducted with varying durations of three antecedent rainfall intensities (2.5, 5, and 10 mm/h) for a specific rainfall event of 39 mm/h. The time required for failure in relation to the antecedent rainfall durations is presented in Figure 12.

The time required for failure for the 39 mm/h rainfall with no antecedent rainfall was found to be 3 h and 35 min. Regarding the actual rainfall duration, no failure would be expected when the rainfall was evaluated and analyzed individually. Yet, analogous to the real condition, when the 39 mm/h rainfall was applied after rainfall of 5 mm/h for 5 h, the time required for failure can be read as 145 min, which was indicated by the letter “b” in the chart. When compared to the actual rainfall duration, it is seen that the slope was found to fail as it was in real conditions. In practice, when evaluating the observed meteorological data for this case study, an alarm can be raised when the duration of the 39 mm/h rainfall exceeds 2 h. Nevertheless, it is recommended that potential extreme precipitation be modelled in advance, so that possible collapses could be identified and related precautions could be taken in accordance with the findings before the failure occurs.

For different antecedent rainfalls, the time required for failure can be found from the chart as well. In instance, 110 min and 165 min for 10 mm/h and 2.5 mm/h, as indicated by the letters “a” and “c”, can be read from the chart, respectively. Regarding the fact that the extreme rainfall was 3 h, it is reasonable to conclude that, when the antecedent rainfall was 2.5 mm/h instead of 5 mm/h for 5 h, then the failure would still be in consideration. The proposed procedure and the chart easily allow the tracking of many scenarios that occurred under different meteorological conditions for one expected main instance of extreme rainfall.

The analysis of a slope triggered by rainfall is typically conducted using the cumulative rainfall over a specified duration. The cumulative rainfall for the eight-hour period was 142 mm in this study. The corresponding average hourly precipitation of 142 mm in 8 h is 17.75 mm. When the analysis was conducted using a rainfall of 17.75 mm/h, the slope was found to remain stable throughout its actual duration, showing that using the average or cumulative rainfall criteria is not adequate for this rainfall condition. Furthermore, the time required for failure for the average rainfall value was found to be more than 5 days. Even more, the time required for failure for an average rainfall of 200 mm in 3 days would be higher than that of 17.75 mm/h.

The rainfall-induced slope failures were discussed in the study of D’Ippolito et al. [20] and, in terms of the hydrological methods, it was mentioned that the critical events were expressed as hourly intensity, annual rainfall, a cumulative amount for a period, and rainfall thresholds. They also indicate that the different hydrological conditions can be applied according to the state of the problem. Many researchers investigated the rainfall-induced slope failure problems regarding the rainfall duration versus cumulated rainfall event. If the real condition was consistent rainfall of a long duration, then the criteria are very well-appreciated, and the models give relatable results with real conditions [41,42]. However, the findings of this study showed that the slope stability analyses regarding only the critical rainfall with its duration and the cumulative rainfall with its duration are not adequate when there are antecedent rainfall conditions. In the event of a rainfall episode, the model should incorporate the relevant meteorological data. Similar to the findings of this study, the study of D’Ippolito et al. emphasizes the importance of the antecedent conditions and strongly recommends the use of duration with antecedent rainfall conditions [20].

The impact of landslides extends beyond the immediate damage to the soil and natural environment. They can also have significant consequences for human communities, affecting infrastructure such as roads and tunnels, and resulting in considerable economic costs. Bračko et al. [19] investigated the impacts of possible climate change on soil stability and concluded that analyzing the slopes with respect to the proper climate change factors would be a fairly simple and cost-effective measure compared to the cost of landslide remediation.

5. Conclusions

This study aimed to investigate the effects of antecedent saturation variations and rainfall conditions in terms of slope stability. The results revealed that the initial saturation degrees are directly related to the failure. With increasing saturation degrees, the FoS values were found to be decreasing. The effect of saturation degrees on the failure mechanism revealed that in situ measurements for a slope are incredibly critical when assessing the slope stability. In addition, considering the successive rainfalls, an evaluation was made, and the failure conditions were also determined. The critical time needed for the failure of a slope was determined for extreme cases according to the meteorological records. A zone of susceptible time for failure was suggested for use as an early warning tool with the help of in situ saturation measurements and meteorological forecasts. Consequently, a case study was also evaluated and the importance of the antecedent conditions in short durations were discussed. During the rainy periods when successive rainfalls take place, with controlled rainfall intensities and durations, suggestions of the hazards can be made, and precautions can be taken if needed. A case study was presented, and evaluations were made using the proposed chart under different rainfall conditions. The results were found to be in accordance with the real conditions of the case study. The proposed procedure and the chart in this study easily allows the tracking of many scenarios that occurred under different meteorological conditions for one main instance of extreme rainfall. Thus, with the proposed process, there may be a chance to guess the failure time before the hazard happens for different successive rainfall conditions.