**3. Results**

#### *3.1. Effects of the Initial Saturation Condition*

Figure 9 shows the results of FOS versus time with the saturation degrees of 70% and 87% and RI = 10 mm/h. These were cases H-1-1, H-2-1, M-1-1, and M-2-1. In these cases, the rainfall intensity was lower than the hydraulic conductivity when the saturation degree was 87%, and the rainfall intensity was slightly higher than the hydraulic conductivity when the saturation degree was 70%. Most of the rainfall water infiltrated into the soil and caused the increase of pore-water pressure by the raising of the groundwater table. The FOS results indicated the effect of the saturation condition and hydraulic conduction on riverbank stability. The higher saturation condition and higher hydraulic conductivity caused higher pore pressure; then, FOS decreased more quickly and obtained a lower value (Figure 9).

**Figure 9.** The factor of safety (FOS) results at an RI = 10 mm/h and with a different saturation degree and hydraulic conductivity.

When S = 87%, the FOS had obviously different trends that depended on the rainfall intensity and soil hydraulic conductivity. However, it was an insignificant change in the case of the analysis where S = 70%. Therefore, the below results and discussion mention only the case where S = 87 %.

#### *3.2. Effects of Rainfall Intensity and Hydraulic Conductivity on Riverbank Stability*

Firstly, both the rainfall intensity and rainfall accumulation affected the FOS. With higher rainfall intensity and rainfall accumulation, the FOS decreased to a lower value (Figure 10). That result was also found in most of the previous research that mentions rainfall intensity [21–30]. Figure 10A1,A2,B1,B2,C1,C2 shows the changes of FOS not only by rainfall intensity and rainfall accumulation but also by soil hydraulic conductivity in cases with a pond and no pond on the surface. In Figure 10, the red dashed line where FOS was equal to one on the graphs meant that riverbank failure occurred. The effects of hydraulic conductivity on the FOS were as follows:

When Ks = 7.39 × 10−<sup>3</sup> cm/s, the change in FOS had the same trend in both boundary cases. In three cases of different RIs, the FOS decreased at the same rate from the beginning of the rainfall event to approximately 30 h. After 30 h of rain, the FOS varied with the different rainfall intensities. The higher the RI was, the lower the FOS was. The riverbank was stable when RI = 10 mm/h; however, riverbank failure occurred after 36 h with RI = 50 mm/h, and after 40 h with RI = 30 mm/h. The results had the same trend as those obtained by Rahimi et al [25]. There, the FOS also decreased rapidly in the beginning of the rain event, and then FOS insignificantly changed after a threshold of RI. Once the RI reachedthethresholdRI,theFOSdidnotchangeanymoreduetoanexcessofrainwaterrunoff[25].

For Ks = 7.39 × 10−<sup>4</sup> cm/s, the range of FOS in cases with a pond was from 1.36 to 0.39 (Figure 10B1), and from 1.39 to 1.03 in cases with no pond (Figure 10B2). In both cases, the FOS change was insignificant with an RI of 10 mm/h; however, the FOS decreased rapidly after 55 h and 110 h where RI = 50 mm/h and RI = 30 mm/h, respectively. In the case with a pond, the riverbank failure occurred at 60 h and 115 h with RI = 50 mm/h and RI = 30 mm/h, respectively. In the case with no pond, riverbank failure only occurred when RI = 50 mm/h.

For Ks = 7.39 × 10−<sup>5</sup> cm/s, the FOS obviously decreased in the rainfall boundary with a pond (Figure 10C1), but that changed only slightly in the case of a boundary with no pond (Figure 10C2). In the case with a pond, the FOS decreased as the rainfall intensity and accumulation increased from 1.38 to 0.2. At higher rainfall intensity, riverbank failure occurred quickly. Riverbank failure occurred after 16 h and 26 h for rainfall intensities of 50 mm/h and 30 mm/h, respectively. In the case of no

pond, the FOS decreased indistinguishably in small ranges with all rainfall intensities from 1.37 to 1.35, and the riverbank was stable after five days of rain.

**Figure 10.** The change of FOS with different rainfall intensities and hydraulic conductivity with a pond and with no pond.

These results indicated that the drainage condition (pond or no pond) greatly affected the change of FOS. In the case of no pond, the present results regarding the change of FOS with different RIs and HC were the same as the results obtained in the same condition with no pond in [21–23,27–30]. The potential of riverbank failure was higher when the riverbank had higher hydraulic conductivity. On the contrary, the potential of riverbank failure with low hydraulic conductivity was higher than that with high hydraulic conductivity when a pond was present on the surface. With a pond on the surface, the excess rainwater not only built a loading pressure but also created a wetting front; then, the FOS decreased more quickly. With HC < RI, the FOS had a lower value in soils with lower hydraulic conductivity (Ks = 3 × 10−<sup>5</sup> cm/s) than in soils with higher hydraulic conductivity (Ks = 3 × 10−<sup>4</sup> cm/s) because the excess rainwater in the first case was much more than in the latter case. In general, it is rare to have a pond on the surface of a riverbank or slope. However, when the riverbank slope has a high saturation degree and the soil suction is completely lost, any charge-loading in the surface will cause an unbalanced loading and riverbank slope failure to occur.

#### *3.3. Effects of Rainfall Intensity and Hydraulic Conductivity on the Water Infiltration Mechanism*

The mechanics of rainfall infiltration for different cases of RI and HC are indicated here by the changes of pore-water pressure and the wetting line. Pore-water pressure increased with the raising of the groundwater table, and the wetting front was linearly propagated from the surface and separated the saturated area and the initial unsaturated area by rainwater infiltration.

In the case with a pond on the slope surface, the rainfall infiltration occurred in both processes: (1) the pore-water pressure or the groundwater table rose, and (2) the wetting front propagated. The changes in the groundwater table or the wetting front depended on the rainfall intensity and the soil hydraulic conductivity.

The rainfall infiltration caused the raising of the groundwater table when the hydraulic conductivity was higher than the rainfall intensity. Figure 11 shows the groundwater table versus raining time for the case H-1-1, which had an RI/HC = 0.09. The rainwater infiltrated and moved quickly into the soil and could raise the groundwater table. The transient seepage area above the groundwater may not even have obtained full saturation, as shown in [17]. The cases of H-1-1, H-2-2, H-2-3, and M-1-1 with the ratios of RI/HC = 0.38; 0.28, 0.46, and 0.93, respectively, had the same mechanics. In these cases, an increase of pore-water pressure was the main reason causing the decrease of the FOS and riverbank failure. These results had the same trend as shown in [8,29] when the soil hydraulic conductivity was higher than the rainfall intensity.

**Figure 11.** The raising of the groundwater table when the RI/HC is less than one.

The second process, in which the rainfall infiltration caused the wetting front to descend, occurred when the hydraulic conductivity was lower than the rainfall intensity or the ratio of RI/HC was higher than one (i.e., the cases of M-2-2, M-2-3, L-2-1, L-2-2, and L-2-3). With a high ratio of RI/HC or low hydraulic conductivity, as in cases L-2-1, L-2-2, and L-2-3, the rainwater infiltrated very slowly into the riverbank soil and did not cause a change in groundwater. Because of the slow transient seepage and the high rainfall intensity, an amount of excess water created a pond on the surface. When a pond was present, the wetting line appeared and descended deeper into the riverbank soil as rainfall accumulation increased. Figure 12 shows the wetting front descending in the case of low hydraulic conductivity, i.e., Ks = 7.39 × 10−<sup>5</sup> cm/s, with the pond above the riverbank surface when the rainfall flux exceeded the soil infiltration capacity. The increased wetting depth caused the fully saturated

zone to expand to nearly the riverbank surface. The rainfall intensity greatly affected the depth of the wetting front and the height of the pond. In these cases, the rainfall intensity and changes in the saturation condition caused by the wetting front were the main factors affecting the FOS and the riverbank stability.

**Figure 12.** The wetting front descending when the RI is much higher than HC.

When the rainfall intensity was slightly higher than hydraulic conductivity (as in cases M-2-2 and M-2-3), the riverbank became saturated from both the groundwater table and the wetting front, as shown in Figure 13. Similar to the case of high hydraulic conductivity, the groundwater table rose by transient seepage through the unsaturated area. However, the groundwater rose at a slow rate. The wetting front appeared when excess rainwater was present on the surface. With only the rising of the groundwater table, the FOS decreased slowly, but the FOS changed more quickly when the wetting front descended. In this case, both the groundwater table and wetting front influenced the FOS and the riverbank stability.

**Figure 13.** The rising of the groundwater table when the RI is lightly higher than HC.

In cases where the riverbank had good drainage conditions and no pond on the surface, the excess rainwater ran off the slope. When RI < HC (cases H-1-1, H-2-1, H-2-1, H-2-3, and M-2-1), the change of groundwater was the same as in the cases with a pond on the surface.

In cases with low hydraulic conductivity, (cases M-2-2, M-2-3, L-2-1, L-2-2, and L-2-3), the rainwater seepage occurred very slowly. The excess water ran off the slope, and the wetting front also spread slowly. In a short time, the groundwater table and the wetting front did not significantly increase. Then, the FOS slightly decreased (Figure 10C2). The decreasing of the FOS was due to the transient seepage change of the unsaturated soil properties as well as losing soil suction. This result also matched that in [2,5,19,22] when the rainfall intensity was smaller or equal to the soil hydraulic conductivity.

#### *3.4. Effects of Rainfall Infiltration and River Water Level Fluctuation*

The effects of multiple rainfall events and RWL in the rainy season are shown in Figure 14. The change in FOS was nearly the same as the change in RWL, which meant that the FOS increased with the increase in RWL, and the FOS decreased with the decrease in RWL. These results agreed with those of previous studies [39–42], which studied the effect of RWL on FOS. When the riverbank had a soil hydraulic conductivity lower than 10−<sup>4</sup> cm/s, the FOS always depended on the change in RWL because of confining pressure [42]. The effect of rainfall on the riverbank was insignificant compared with the effects of changes in RWL. The results from the long-term analysis during the rainy season showed that low-intensity rainfall (less than 140 mm/day, average 5.8 mm/h) caused the FOS to decline at a low rate. Riverbank failure occurred only when the riverbank had a high slope and had cracks in the riverbank surface. In fact, there was a high slope angle and some cracks along the riverbank in the study area. In general, a riverbank with a high slope angle and some cracks has a high potential of failure during the rainy season. Moreover, the change in RWL was the factor with the greatest influence on the FOS of the riverbank. The riverbank was more damaged when multiple factors occurred together.

**Figure 14.** The FOS change with fluctuations of RWL and rainfall in the long-term.
