Numerical Simulation on the Effect of Infiltration and Evapotranspiration on the Residual Slope

Abstract

Soil suction plays an important role in governing the stability of slopes. Environmental sustainability could be jeopardized by hazards, such as slope failures (forest destruction, landscape alteration, etc.). However, the quantification of the suction effect on slope stability is a challenging task as the soil suction is usually affected by the precipitation and evapotranspiration. Numerical simulation plays an important role in the estimation of contour in soil suction due to rainfall and evapotranspiration as long-term and widespread monitoring is rarely conducted. The result of numerical simulation is highly dependent on the accuracy of the input parameters. Hence, suction monitoring plays an important role in verifying the result of numerical simulation. However, as a conventional tensiometer is limited to 100 kPa soil suction, it is hard to verify the performance of numerical simulation where suction is higher than 100 kPa. The osmotic tensiometer developed by Nanyang Technological University (NTU) can overcome this problem. It is now possible to monitor changes in soil suction higher than 100 kPa (up to 2500 kPa) for an extended period in the field. In this study, a procedure was proposed to estimate suction changes in residual soil based on rainfall and evapotranspiration data. Numerical simulation was carried out based on the soil properties and geometry of a residual soil slope from Jurong Formation Singapore. Changes in soil suction due to rainfall and evaporation were simulated and compared with the readings from the NTU osmotic tensiometers installed at 0.15 m and 0.50 m from the slope surface in the field. It was observed that numerical simulation was able to capture the variations of suctions accurately at greater depths. However, at shallow depths, erratic suction changes due to difficulties in capturing transpiration.

1. Introduction

Numerous steep slopes are stable in nature. However, the stability of these slopes is affected by climatic conditions [1]. Climatic conditions are gradually changing due to global warming. From a sustainability perspective, it is important to understand the variation in the stability of the loess soil slope in different scenarios. Brand [2], and Rahardjo, Satyanaga [1] indicated that the infiltration of rainwater was commonly recognized as the main factor leading to rainfall-induced slope failure. The works of Crosta [3], Basile, Mele [4] and Ost, Eeckhaut [5] indicated that several factors, such as climatic conditions, geological features, topography, vegetation or a combination of these factors, could result in the failure of a slope under rainfall condition

Due to extreme rainfalls, numerous slope failures have occurred all over the world [6]. Residential and commercial buildings, as well as farmland, are at risk of destruction from slope failure. Environmental sustainability could be jeopardized by hazards, such as slope failure (forest destruction, landscape alteration, etc.). Infiltration causes a reduction in soil suction, which then leads to a reduction in soil shear strength [7,8,9], an increase in ground water level [10,11] and the formation of a perched water table [12,13]. The change in soil suction is not only affected by infiltration rate but also by slope geometry, the position of the ground water table and soil properties [14].

Numerical simulation is commonly employed to simulate the changes in soil suction due to infiltration and evapotranspiration. The soil-water characteristic curve (SWCC) and permeability function are required to perform a numerical simulation of infiltration in unsaturated soil. SWCC is a curve relating to water content and suction of a soil, which can be represented by gravimetric water content (w), volumetric water content (θ) and degree of saturation (S) [15,16], while permeability function represents changes in permeability due to the changes in soil suction [17]. It is important to note that several known unsaturated soil behaviors are commonly ignored when conducting numerical analysis, such as: 1. effect of shrinkage, which causes gravimetric water content based SWCC (SWCC-w), volumetric water content based SWCC (SWCC-θ) and degree of saturation based SWCC (SWCC-S) to be different [15,18]; 2. hysteresis between drying and wetting SWCC [19,20,21]; 3. change in SWCC due to change in density [22]; and 4. permeability function, which could be different when it is estimated from SWCC-w, SWCC-θ and SWCC-S [23].

These known unsaturated soil behaviors are commonly ignored due to the difficulties incorporating them in numerical analysis. Therefore, the difference between the estimated change in soil suction due to infiltration and evaporation with the actual suction in the field is expected. Field instrumentation, especially field suction measurement, plays a vital role in verifying that the difference between the numerically simulated suction change and the actual change in soil suction on the site is still within tolerance. However, most field suction measurements suffer several limitations, such as: a typical tensiometer can only measure up to 100 kPa suction; other suction measurement devices which can measure beyond 100 kPa suffer a delay in the measurement of soil suction; and a tensiometer suffers from cavitation problem and hence requires maintenance.

In order to solve the cavitation issue and get a wider measurement range, there are two basic approaches [24]. The first technique is to create a high capacity tensiometer (HCT) by breaking air bubbles or nuclear particles in water by applying high pressure to the water in the tensiometer’s chamber. This makes it possible to measure a high matric suction because air bubbles will not form while taking the measurement if water is under high tension. Other scientists have reported measuring a high matric suction of 7 MPa [24]. To provide a wide measurement range, HCTs need high-air-entry-value ceramics or nanoporous glass. Additionally, the performance of HCTs can be impacted by both the saturation of HCTs and the water chamber’s surface roughness. Additionally, it has been demonstrated that the cavitation issue would arise during the measurement. As a result, such a tensiometer might not be appropriate for long duration matric suction to monitor [24].

The second approach involves adding polymer particles to the tensiometer’s water chamber to raise the water’s osmotic pressure. An osmotic tensiometer is the common term for this kind of tensiometer. Its measurement range is same as the osmotic pressure of water inside its polymer chamber. Water with a positive osmotic pressure will not get tense inside the OT’s measurement range, preventing the cavitation issue [24,25].

The matric suction of the soil can cause a decrease in the osmotic pressure of the water in the polymer compartment of the osmotic tensiometer during the measurement; this decrease is matric suction of the soil’s value. Polymers that absorb water, such as sodium polyacrylate (NaPA), polyvinyl pyrrolidone (PVP), polyacrylamide (PAM) and polyethylene glycol (PEG), are typically employed for this purpose [24].

In order to tackle most of this problem, a polymer based tensiometer, such as the Nanyang Technological University (NTU) osmotic tensiometer [26], has been developed, as shown in Figure 1. NTU osmotic tensiometers, as opposed to HCTs, can monitor a high soil suction by employing a polymer to raise the water’s osmotic pressure inside the tensiometer. The measuring range of the NTU osmotic tensiometers is considered to be the rise in osmotic water pressure. It has been established that cross-linked super water-absorbent polymers are appropriate for the production of NTU osmotic tensiometers. NTU osmotic tensiometer preparation is less complicated than HCT preparation because there is no need to pressurize the water inside the tensiometer beforehand. However, pressure decay and temperature variation may have an impact on the precision of high soil suction detection using osmotic tensiometers, which limits widespread use of NTU osmotic tensiometers [24].

The NTU osmotic tensiometer has several benefits compared to the conventional tensiometer (i.e., water based tensiometer), such as the possibility of measuring up to 2000 kPa soil suction, resistance to cavitation and application for long duration measurements. Verification of the NTU osmotic tensiometer performance has been conducted by Hamdany, Shen [26] by installing the NTU osmotic tensiometer, a conventional tensiometer and moisture sensors at a residual slope in Singapore (referred to as CEE slope) as shown in Figure 2, and the results for the suction monitoring are shown in Figure 3.

As shown in Figure 3, suction at the site can be higher than 100 kPa which is beyond the capacity of the conventional tensiometer. Hence, it is of interest whether numerical simulation has the capability to realistically simulate changes in soil suction due to infiltration and evaporation.

While suction measurement remains uncommon in practice, weather stations are quite common, and they can be used for the measurement of infiltration and evapotranspiration. Hence, it is possible to obtain infiltration and evapotranspiration data to estimate change in soil suction.

In this paper, numerical simulation will be conducted and compared with the instrumentation data provided in Hamdany, Shen [26]. In the numerical simulation, evaporation and infiltration will be the input parameters, while change in soil suction will be compared with instrumentation data. The objective of this paper is to verify change in soil suction higher than 100 kPa recorded by the osmotic tensiometer through numerical modelling.

2. Literature Review

One of the most important parts of the hydrological cycle is evaporation in the natural environment. The rate of evaporation is either directly measurable or it can be anticipated using weather information. The mechanism of evaporative flow has been the subject of extensive investigation throughout the past few decades. Acceptance of the energy budget idea in the prior works also implied the relationship between evaporation, solar radiation and other heat flow components. Water supply at the evaporation surface, evaporation energy and aerodynamic function are three important elements that determine surface evaporation [27]. Water accessibility is a result of soil water content and water permeability [27]. The possible evaporation has been predicted using a wide variety of climatological methodologies. Common climatic variables, such as relative humidity, temperature, and net radiation, are all that are needed to test such notions. There are limitations to applying these theories to an unsaturated soil surface because they were developed using a saturated soil surface or a free water surface. Yet, they can still be used as a benchmark for many geotechnical applications, including estimating the rate of soil surface evaporation.

The first theory for the calculation of potential evaporation was developed by Penman [28]. An equation that could be utilized to calculate the potential evaporation (PE) was developed. Evaporation from a vast water body could show relative humidity that is equivalent to uniformity. Penman’s equation relies upon a few elements, such as: slope of saturation vapor pressure; net radiation; and psychrometric constant wind speed [29]. When applied in dry areas, Penman’s formula frequently overestimates actual evapotranspiration [30]. Therefore, the Penman-Monteith theory [31] offers advancement in the determination of the soil surface evaporation. The authors suggested incorporating water diffusion across the water-air interface within soil pores. The Penman-Monteith method is a complex method that is closest to a physical model that considers the mass, momentum and energy transfer with built-in external and internal conductance and resistance. The method also could be modified to estimate evaporation from the saltwater surface by considering the relative humidity of the evaporating surface. Advancement in evaporation methods and measurements will always improve the performance of evaporation estimation models.

Soil surface relative humidity may not be as consistent as previously thought, but it has been demonstrated to be a good predictor of actual evaporation (AE) from the soil surface. According to the research conducted by Sattler and Fredlund [32], AE accounts for almost 70% of the PE in the Canadian province of Saskatchewan. Determining the soil’s relative humidity is challenging, but it is possible to do so using knowledge of the soil’s surface temperature and suction. To evaluate AE from exposed soil bodies, researchers have devised two methods so far. The principal approach relies on surface soil temperature and suction [33,34]. The second method relies on the actual vapor pressure and the surface resistance [35].

Abdullah, Mohd Arif Zainol [36] estimated potential evaporation in Singapore using the Thornthwaite equation [37] based on air temperature, while Qu, Jia [38] used a combination of the Penman equation and the Thornthwaite moisture index for the Singapore climate in their numerical study on the impact of evaporation and infiltration of rainwater on the pore-water pressure changes in a slope of residual soil. These studies showed that the cross-sections of pore-water pressure from seepage analyses by considering rainfall evaporation and infiltration give a sensibly decent concurrence with those acquired from field estimations. That is why an accurate forecast of evaporation is crucial in anticipating pore-water pressure profiles for stability investigation of slope [39].

In dealing with projections of the rate of evaporation from ground surfaces, geo-environmental and geotechnical engineers started adopting soil suction more generally. Analysis of the thin soil region (soil thickness of 0.5–1 mm) showed that actual evaporation is equal to potential evaporation up to the point when the soil suction surpasses the indicator at roughly 3000 kPa of the total suction [35]. The soil suction when the AE from the ground surface begins to diminish from the PE has been sought [40]. This relates to the air-entry indicator and suction of residual soil that SWCC identifies as crucial boundaries of an unsaturated soil. Calculating transpiration from leaf stomata and a tree canopy gave rise to the concept of “surface resistance” to the diffusion of vapor water [31]. The determination of surface resistance has been the subject of a growing body of research as scientists strive to better understand and depict evaporation resistance. The resistance of the surface to the passage of vapor in drying soil close to the ground surface can be estimated using a technique developed by van de Griend and Owe [41]. At 15% soil volumetric water content within 0–1 cm depth, it was understood that the surface resistance of fine sandy loam began to increase during the drying process. The Penman equation, used to estimate the amount of water lost to evaporation from a given soil surface given its water content and temperature, is a regularly exponential form of the relationship between soil cover moisture and surface resistance (PE).

The Thornthwaite-type water-balance model [35] uses the actual monthly average climatic data to estimate the monthly actual evapotranspiration. If water input is larger than potential evapotranspiration, actual evapotranspiration takes place at the potential rate. On the other hand, if water input is less than the potential evapotranspiration, then actual evapotranspiration is the sum of water input and an increment removed from soil storage [42]. The FAO-56 Penman-Monteith Equation simplifies the evapotranspiration equation by utilizing some assumed constant parameters for clipped grass as a reference crop [43].

Table 1. Summary of Potential Evaporation.

Equation	Author	Description
$PE=\frac{1}{\lambda }\left[\frac{\mathsf{\Gamma }A+{\rho }_a{c}_{p}D/r_a}{\mathsf{\Gamma }+\eta \left(1+r_s/r_a\right)}\right]$	Monteith [44]	PE = potential evaporation; $\mathsf{\Gamma }$ = slope of saturation vapor pressure; λ = latent heat coefficient (J/kg); $\eta$ = psychrometric constant (mmHg/°C); A = Qn − G (MJ/m2day); Qn = net radiation; G = soil heat flux density; ${\rho }_a$ = air vol heat capacity (MJ/m3°C); D = portion in one day which is covered by sun; rs, ra = ratio between vapor transfer and canopy and aerodynamic resistance (day/m); cp = the deficit in vapor pressure (kPa);
$PE=\frac{\mathsf{\Gamma }{Q}_n+\eta E_a}{\mathsf{\Gamma }+\eta }$	Penman [28]	PE = potential evaporation; $\mathsf{\Gamma }$ = slope of saturation vapor pressure; Qn = net radiation (m/s); $\eta$ = psychrometric constant (mmHg/°C); Ea = (0.35 × 1 + 0.15 Ww)($p_{vsat}^{air}-p_v^a)$ (m/s); Ww = wind speed (km/h) $p_v^a$ = vapor pressure above surface unaffected by evaporation; pv = vapor pressure at the surface; $p_{vsat}$ = saturated vapor pressure; $p_{vsat}^{air}$ = vapor pressure at soil surface under saturated condition
$AE=\frac{\mathsf{\Gamma }{Q}_n+\eta E_a}{\mathsf{\Gamma }+\eta A}$	Modified Penman [45]	AE = actual evaporation; Ea = 0.35(1 + 0.15 Ww) $p_v^a$ (B$-A)$ (m/s); RHair = relative humidity of air; B = 1/RHair; RH = relative humidity; A = 1/RH;

summarizes some equations that are commonly used to calculate potential evaporation and actual evaporation.

3. Material and Method

3.1. Surface Geometry

In order to conduct 3D slope stability analysis, it is required to obtain the surface geometry of the slope and also the elevation of the ground water table, which varies spatially. A digital elevation model (DEM) of the CEE slope is obtained from light detection and ranging (LIDAR) on 1 m × 1 m resolution. Ground water table data are obtained from borehole information that spread across the CEE slope. Spatial interpolation is carried in order to estimate the ground water table elevation at the CEE slope. Figure 4 shows the DEM model and the ground water table (GWT) elevation constructed using ArcGIS. Both DEM and GWT elevations are converted into contour lines and then imported to terrain geometry maker (MIDAS GTS NX add in) in order to construct surface geometry and ground water surface, which are shown in Figure 5.

3.2. Material Properties

Soil samples were obtained from the crest of the slope for SWCC and soil properties test [46]. The basic soil properties of the soil are shown in

Table 2. Soil properties.

Properties	NTU
Unified Soil Classification System (USCS)	CL
Specific gravity, Gs	2.73
Gravel (%)	8
Sand (%)	57
Fines (%)	35
Total density (Mg/m3)	2.08
Void ratio, e	0.61
Liquid Limit, LL (%)	40
Plastic Limit, PL (%)	23
Plasticity Index, PI (%)	17
Saturated permeability, ks (m/s)	10−6

. SWCC was obtained by using a centrifuge [47] and WP4 [48]. SWCC experimental data were then best fitted using the Fredlund and Xing [49] SWCC equation as follows:

$$\theta ={\theta }_s\frac{C\left(s\right)}{{\left\{\ln {\left[\exp \left(1\right)+\left(\frac{s}{a_f}\right)\right]}^{n_f}\right\}}^{m_f}}$$

(1a)

$$C\left(s\right)=1-\frac{\ln \left(1+\frac{s}{{\mathsf{\Psi }}_r}\right)}{\ln \left(1+\frac{{10}^6}{{\mathsf{\Psi }}_r}\right)}$$

(1b)

where θ is volumetric water content, θ_s is saturated volumetric water content, a_f, n_f, m_f and Ψ_r are curve fitting parameters, s is soil suction and C(s) is a parameter which forces the SWCC function to reach 0 at 1,000,000 kPa. The SWCC of the soil is shown in Figure 6 along with the Fredlund and Xing [49] curve fitting parameters.

Aside from SWCC, it is required to determine the relative coefficient of permeability (k_r) for the determination of unsaturated permeability function k(s) which is defined as:

$$k(s)=k_s{k}_r(s)$$

(2)

where k_s is the saturated coefficient of permeability. The relative coefficient of permeability is obtained by using the Fredlund, Xing [17] statistical method which is given as:

$$k_r\left(s\right)=\frac{{\displaystyle \underset{\ln s}{\overset{\ln s_u}{\int }}\frac{\theta \left(e^y\right)-\theta \left(s\right)}{e^y}\theta \prime \left(e^y\right)dy}}{{\displaystyle \underset{\ln s_L}{\overset{\ln s_u}{\int }}\frac{\theta \left(e^y\right)-\theta \left(s_L\right)}{e^y}\theta \prime \left(e^y\right)dy}}$$

(3)

where s_L is the suction at the lower limit of integration, s_U is the suction at the upper limit of integration and e is Euler’s number. Based on SWCC (Figure 6) and Equation (3), the relative coefficient of the permeability of the soil is determined and shown in Figure 7. As the soil of interest is at the top surface, simplification is made with the soil layer where the soil is assumed to be homogeneous.

3.3. Finite Element Model

Finite element simulation was carried out using MIDAS GTS NX with a 3D model, as shown in Figure 8. The 3D model of surface geometry and ground water surface was constructed using terrain geometry maker which is an add-in for MIDAS GTS NX software. Surface geometry and GWT were imported from contour lines that were originally from ArcGIS DEM and GWT elevation. Figure 9 shows the flux calculation recap based on weather station data and the Penman model. The flux was then applied to the 3D model of the CEE slope to the blue mesh (Figure 8) that indicates the area subjected to infiltration. The flux was applied to simulate rainfall and evaporation that occurred throughout the total duration of the numerical simulation processes. The seepage simulation was conducted for more than 60 days, from 26 January 2020 to 4 April 2020. Rainfall data were obtained from the weather station installed on site, while evaporation was calculated using the modified Penman method. Results from the numerical simulation were compared with NTU osmotic tensiometer readings located at 0.15 m and 0.5 m depths.

4. Analysis and Results

Comparisons between the 3D finite element analyses where infiltration and evaporation are considered and NTU osmotic tensiometer readings at 0.15 m and 0.50 m depths are shown in Figure 10a,b, respectively, while Figure 11 presents a cross-section which shows the simulation result after 45 days and 50 days, with suction values at 0.5 m depth. Figure 10a,b show that the suctions computed from the numerical simulation are lower than the suctions measured by the NTU osmotic tensiometer, despite showing a similar trend, especially during the period from 22 February 2020 to 23 March 2020 where precipitation was very low. One of the possible reasons was the presence of vegetative roots that caused transpiration which affected suction readings significantly and produced erratic responses, especially at shallow depths (Figure 10a) when precipitation was very low. This phenomenon is not properly captured in the numerical simulation.

However, both numerical simulation and the NTU osmotic tensiometer show that it is possible for soil suction to be higher than 100 kPa, especially at shallow depths where climatic effect and transpiration significantly affect soil suction. This illustrates the limitation of the conventional tensiometer in capturing soil suction higher than 100 kPa. Figure 10b shows that the numerical simulation and NTU osmotic tensiometer are in closer agreement at depth 0.5 m compared to those at depth 0.15 m. For example, in the after 45-day numerical simulation (8 March 2020), the suction value is obtained as 55 kPa, while the suction value based on the NTU osmotic tensiometer reading is about 80 kPa. One of the possible reasons was the effect of transpiration diminishing at greater depths, resulting in less erratic responses from the NTU osmotic tensiometer.

Another possible cause of the difference is that drying SWCC was used in the numerical simulation while the soil at the site had been subjected to a cycle of drying and wetting. However, as shown in Figure 10, the estimated soil suction from the numerical simulation is lower than the actual soil suction measured by the NTU osmotic tensiometer. Therefore, the estimated soil suction gives a conservative result of analysis, from a stability point of view.

Figure 11 shows the cross section of the slope with pore water pressure contour based on numerical simulation. The suction value at 0.5 depth is 55 kPa and 24 kPa after 45 and 50 days of numerical simulation. These suction values were obtained from the point located near the location of the NTU osmotic tensiometer placement. The decrease of suction value is corresponded to the rainfall event happens on the 45th day (indicated by the increase of flux around 8 March 2020, as shown in Figure 8). It is also interesting to note that the suction at the surface is quite varied, where the suction at the slope region is higher than the suction at the flat area where the tensiometer is located. Suction at the slope area is higher than 100 kPa (up to 350 kPa) which verifies the possibility of having suction higher than 100 kPa through numerical simulation.

5. Conclusions

In this study, numerical simulations have been carried out and the results were compared with NTU osmotic tensiometer readings. The following results can be concluded:

• The study shows that numerical simulations give a comparable result with NTU osmotic tensiometer readings. For example, after 45-day numerical simulation (8 March 2020), the suction value is obtained as 55 kPa, while the suction value based on NTU osmotic tensiometer reading is about 80 kPa.
• Based on numerical simulations and the osmotic tensiometer, suctions at shallow depths can be higher than 100 kPa (up to 2500 kPa), indicating the limitation of the conventional tensiometer for suction monitoring at shallow depths.
• However, at a shallow depth, transpiration is very dominant and erratic changes in soil suction due to transpiration cannot be captured in the numerical simulation.
• For greater depths, the effect of transpiration becomes less dominant and suction readings from the NTU osmotic tensiometer coincide with the results from the numerical simulation.
• As suction estimated from numerical analysis using drying SWCC appears to underestimate actual suction measured by the NTU osmotic tensiometer, the estimated suction will yield a conservative result of slope stability analysis.
• The numerical analysis shows that the pore water pressure distribution varies along the cross section of the slopes. The slope region has higher suction (up to 350 kPa) compared to the suction at a flat area where the tensiometer is located. This result verifies the possibility of having suction higher than 100 kPa through numerical simulation.