3.1 Hydraulic equilibrium time
When a tensiometer is placed in the soil sample, a small amount of water is exchanged between the soil sample and the high air entry (HAE) ceramic tip of the tensiometer. The recorded suction data using tensiometer with the elapsed time using initially-wet and initially-dry tensiometer in the loose and compacted states at different initial water content conditions of RBS were presented in Fig. 3a-3d. The suction values increased with time with the initially-wet tensiometer and decreased with the initially-dry sensor before reaching the equilibrium. The required hydraulic equilibrium time and the corresponding measured suction for different initial water contents of RBS using an initially-wet and initially-dry sensor conditions are shown in Table 2. The hydraulic equilibrium time for the tensiometer varied from a few hours to several days depending upon the magnitude of suction and initial condition of the sensor (i.e., wet or dry). Further, a higher hydraulic equilibrium time was observed for the sample having a higher initial suction value. A similar finding was also reported by (Oliveira and Marinho, 2008).
Moreover, it is noteworthy to point out from Fig. 3 that the suction equilibrium time was found to be in the range of 0.2 to 4 days with initially-dry sensors and 0.6 to 14.58 days with initially-wet sensors at all different moisture conditions under loose conditions. Similarly, it was observed to be in the range of 0.05 to 0.4 days with initially-dry sensors and 0.4 to 1 day with initially-wet sensors at all different moisture conditions under compacted conditions (refer to Table 2). the suction equilibrium time was found to be smaller with initially-dry sensors as compared to initially-wet sensors at all different moisture conditions under both loose and compacted conditions. This can be attributed to the higher hydraulic conductivity of RBS than the HAE ceramic tip, which allows an easy flow of water from the saturated soil to the HAE tip when the sensor is dry. Moreover, the compacted soil sample took less time to achieve hydraulic equilibrium than the sample in loose conditions with both initially-wet and dry sensors (Table 2). This may be due to the lesser tortuous pathways and availability of continuous flow channels in an adequately compacted soil compared to loose soil. In the case of loose soil, the tortuosity is more due to the presence of more air in the soil, and hence more time is required to reach the equilibrium.
Fig. 4 shows the initial water content and equilibrium suction value obtained using both initially-wet and dry sensors in loose and compacted conditions. The measured suction under equilibrium conditions was found to be slightly higher for initially-dry sensors than that of initially-wet sensors. A slight difference between the measured suction value with initially-wet and dry sensors can be described based on water exchange between the soil and the HAE ceramic tip leading to the hydraulic equilibrium. When an initially-wet tensiometer was used for suction measurement of a soil sample, a small amount of water was withdrawn through the saturated HAE ceramic tip to the soil sample to achieve hydraulic equilibrium. In this case, the saturated HAE ceramic tip of the tensiometer undergoes a marginally drying process, whereas the soil sample undergoes a slightly wetting process. In contrast, when an initially-dry tensiometer was used for measuring the soil suction, a marginal amount of water flows from the soil sample to the HAE ceramic tip of the tensiometer to attain the hydraulic equilibrium. In this case, the HAE ceramic tip of the tensiometer undergoes a slight wetting process, whereas the soil undergoes a slightly drying process. Therefore, the final equilibrium suction value was observed to be less for the initially-wet tensiometer as compared to the initially-dry sensor due to the hysteretic effect. The hysteretic effect of the HAE ceramic tip of the tensiometer on the SWCC can be seen in Fig. 4. In both loose and compacted conditions, the drying SWCC (i.e., the soil is drying by initially-dry sensors) remains above the wetting SWCC (i.e., the soil is wetting by initially-wet sensors), which is consistent with the hysteretic trend of the other soils, but the effect is marginal. Therefore, for an accurate estimation of the SWCC of soils utilizing the tensiometer, sufficient equilibration time needs to be provided based on whether the sensor is initially-dry or wet.
3.2 Instantaneous and equilibrium SWCC
The temporal variation of volumetric water content (VWC) and suction during the wetting and drying processes for establishing instantaneous-SWCC data under the ponding condition were shown in Fig. 5a-5b. During the wetting process, the VWC of the soil, as recorded by the 5TM moisture sensor, increased rapidly, but a change in suction was negligible until t = 0.125 hours. Moreover, the soil column nearly took 0.25 hours for complete saturation, but the tensiometer reading showed a constant suction value (y = 0 kPa) after half an hour. This was mainly due to the requirement of a large equilibrium time for the tensiometer in comparison to the moisture sensor. In contrast, the disparity between the suction and moisture sensors was not observed in the drying process, wherein a decrease in moisture content and increase in suction occurred nearly simultaneously (Fig. 5b). This was attributed to the slower drying rate of evaporation, where the suction sensor got sufficient time to achieve equilibrium with the soil. The drying process was run for nearly 200 hours, and during that time interval, the soil suction reached 40 kPa.
The temporal variation of VWC and suction, measured during the stepwise wetting and drying process in the equilibrium-SWCC method estimation for RBS, was presented in Fig. 6a-6b. During each stage, sufficient time was allowed for the moisture sensor and suction sensor to achieve hydraulic equilibrium with the soil. Therefore, a steady decrease in suction was observed for the studied soils, unlike in the previous case due to wetting (Fig. 5a). The RBS took 32 days to undergo complete saturation by the proposed method (Fig. 6a), while the soil drying process took 20 days, and during that time interval, soil suction reached nearly 40 kPa, as shown in Fig. 6b. The time required to achieve equilibrium VWC and suction at each stage varied for all the tests, as shown in Fig. 6a-6b. At each wetting-drying step, the equilibrium values of suction and VWC were recorded to obtain the equilibrium point on the SWCC. Further, these equilibrium data points were used to establish the equilibrium-SWCC, as shown in Fig. 7.
Fig. 7 shows the measured wetting and drying SWCC for the studied soil obtained by combining the tensiometer and moisture sensors for the instantaneous and equilibrium data. A significant difference in the instantaneous and equilibrium wetting SWCC data was observed. The instantaneous-SWCC data indicated that the suction remained constant for a wide VWC variation during the wetting process, which shows the erroneous SWCC measurement. Thus, instantaneous wetting-SWCC data should not be considered for in-situ stability analysis during rainfall. On the other hand, the equilibrium-SWCC data showed a steady decrease in suction with an increase in VWC as sufficient time was allowed for the tensiometer to reach equilibrium with the soil at any given water content. Moreover, the equilibrium and instantaneous SWCC showed a smaller disparity during the drying process, as the soil sample took considerable time for the natural drying process, which enabled the suction sensors to reach near-equilibrium conditions. Similar trends were also reported in the previous literature for instantaneous drying SWCC, where natural drying of soil occurs by evaporation. The equilibrium-SWCC data represented a typical SWCC trend observed for most of the clays in the literature by different methods (Agus and Schanz, 2005, Tripathy et al. 2014, Tripathy et al. 2016, Gapak and Tadikonda, 2018). Therefore, the application of tensiometer for the field applications should be limited as the required equilibration time for suction estimation would be longer than the water content changes in the in-situ soil due to environmental changes, especially during the rainfall events and submerged river bank conditions. Thus the proposed equilibrium SWCC method along with the moisture sensor readings could provide the temporal suction variations for in-situ stability analysis as the moisture sensor's response time is significantly small.
3.3 Hysteretic effect
The SWCC data from the hanging column method were obtained at very small suction values and nearly coincided with the proposed equilibrium approach. The wetting-drying SWCC data obtained from the proposed equilibrium approach and hanging column method were presented together to represent the hysteretic behavior of the RBS, as shown in Fig. 8. The initial wetting and main wetting data were represented by different filled markers with different colors. Similarly, the unfilled markers represent main drying and primary drying. The variation between the water contents at any given suction value was significantly high, but variation decreased in subsequent wetting–drying cycles. Hysteresis in the SWCC indicates that for any specific matric suction value, the VWC in the soil is not unique. For both the wetting and drying cycle, the drying SWCC retains more water content than the wetting SWCC for the same magnitude of suction, which is consistent with the previous literature (Lu and Likos, 2004, Fredlund et al. 2012, Gapak and Bharat, 2018). This is attributed to the different contact angles between wetting and drying at the soil particle-pore water interface, non-homogenous pore size distribution, and entrapped air (Lu and Likos, 2004). The hysteretic effect was predominant in the medium suction range, while the wetting and drying curves coincide at the saturation region and near residual water content region. This trend was in good agreement with the earlier work (Pham et al. 2003).
Several advanced models are available to predict the SWCC behavior of soil, considering the compaction rate and microstructure of soil (Kodikara et al. 2020, Ranaivomanana et al. 2022). Since pure sand is used the current study, therefore, the microstructural perspective of the soil has not been considered. It is established that the van-Genuchten equation (vG, 1980) fitted the SWCC data in a satisfactory way for sandy soil. Thus, in this study, the experimental equilibrium SWCC data were best fitted using the van-Genuchten equation (vG, 1980) with retention curve (RETC) software. The model parameters were obtained using the RETC program with m parameter constrained by n parameter as m =1-(1/n), and the fitting parameters were presented in Table 3. The SWCC data fitted in a satisfactory way with an empirical Van Genuchten equation, which demonstrates the accuracy of the measurement method.
3.4 Hydraulic characteristics
The hydraulic conductivity functions (HCFs) from the SWCCs using van-Genucten-Mualem (vGM, 1980). The van-Genuchten-Mualem (vGM, 1980) model is most widely used for sand, silt, silty loam, and clayey soil to predict the hydraulic conductivity function using SWCC data. However, the model shows a large deviation in the predicted hydraulic conductivity for clayey soil (Van Genuchten, 1980). Since pure sand is used in this study, therefore, this model can simulate the hydraulic conductivity very well. The hydraulic conductivity function in terms of normalized volumetric water content is given by
In this study, the HCFs is determined using the RETC program with m parameter constrained by n parameter as m =1-(1/n), as shown in Fig. 9. A significant difference in the HCF predicted from the transient-SWCC was observed between the wetting and drying paths, as shown in Fig. 9 (a). Further, a wide variation in the predicted hydraulic conductivity was found for the constant suction during the wetting process, while during drying, the hydraulic conductivity decreased with an increase in the suction. On the other hand, the hydraulic conductivity predicted from equilibrium-SWCC data showed a steady decrease in the conductivity with an increase in the suction during the wetting and drying paths. Similar trends were also reported by various researchers (Singh and Kuriyan, 2003, Zhai and Rahardjo, 2015, Sobti and Singh, 2017). As the water content reduces in the soil with increased suction, the air enters into the largest pore of the soil matrix. The connected paths available for water flow shrink to become smaller and more tortuous with the increase in suction, which causes a reduction in the hydraulic conductivity. Thus, it is concluded from the experimental laboratory results that for studied soil, the instantaneous SWCC varied significantly when compared to the equilibrium SWCC during the wetting process. As the rainfall-induced slope failures require accurate knowledge of the soil hydraulic characteristics during the rainfall infiltration (wetting phenomenon), the applicability of the instantaneous SWCC to the development of early warning facilities remains questionable.