Keywords

1 Introduction

Significant progress has been made in the study of retrogressive and progressive slope failure in both saturated and unsaturated soils over the last few decades. In general, progressive and retrogressive slides that grow in the same or opposite direction of motion are the two recognized types of successive slope failures. Due to the obvious removal of the nether section of ground support, retrogressive slides were thought to be a series of simple columnar or circular cylindrical slides [1, 2]. Several laboratory-based flume experiments coupled with numerical models have been conducted over the last two decades to capture retrogressive failure phenomena [3, 4]. A recent study reported that an increase in slope toe saturation on river sand and residual granite could have resulted in a dominant failure mode of shallow retrogressive sliding [4]. Several papers have reported limited comparative studies of physically measured and numerical model responses, implying that more work is needed to capture the mechanisms of failure in natural slopes [5, 6]. Recent studies have developed theoretical and empirical models for complex infiltration analysis solutions [7, 8]. The empirical model developed by [7], based on the concept of wetting front advancement, has been the most widely used. Infiltration, combined with the assumption of uniform porous media, plays a significant role in slope instability, which is less likely to be true for natural soils [9, 10]. It has often been assumed that failures in many natural slopes begin at the toe as a consequence of the fact that, toe stress concentration is likely to be higher [11]. Classical research findings revealed that failure began far from the toe; however, it is invalid to assert that failure must always begin at the upper parts of a natural slope [13].

2 Background and Rationale

Since hillslope stability analyses include so many space-time variables, it may be difficult to fully address the effects of seepage and infiltration in variable saturation conditions. However, the geologic time series influence of infiltration around the toe slope was investigated in the current work with some conceptualized premises as one of the major controlling variables. When a physical-based model is combined with numerical analysis, the premises may be able to aid in understanding the mechanism that triggers retrogressive failure in natural slopes. Hence, the current study focused primarily on the true cause of slope toe failure and subsequent retrogression, which is not adequately addressed in the existing literature and research findings. The author was intrigued by the previously mentioned frequent failure initiation of the toe slope and decided to look into it further.

The coarser material in the toe portion not only filters and dissipates seepage energy but also acts as back support, enhancing stability under higher toe shear stress. According to research, cutting or eroding the slope toe support from a long natural slope can result in slope failure According to a recent review of the literature on the subject, reducing river erosion can help to slow the progression of slope-toe retrogressive landslides. However, when excessive deformation is applied, retrogression accelerates and the soil mass detaches irreversibly. As a result, it was fair to conclude that a mode of slope failure at the toe has received little attention thus far. Because of the prolonged hydrogeologic environment, the material stiffness in the toe soil may be greater than in the upslope portion, and the failure mode may be elastic.

3 Material and Methods

3.1 Instrumentation

Virtual-hydromet digital soil suction recorder: The virtual-hydromet is a microcontroller digital soil moisture-temperature recorder that embodies the cutting-edge microcontroller instrumentation design to evaluate volumetric water content and the corresponding soil suction. The assessment of moisture variation due to rainfall application was carried out using the Virtualhydromet moisture sensor product.

Pore pressure transducers:Positive and negative pore pressure measurements using piezometers and miniature tensiometers have been used in both field and laboratory-scale experiments to assess slope stability. In the current study, strain gauge type pore pressure transducers with 350 Ω resistance having a measuring capacity of 200 kPa and accuracy of 1.6mV/V (3200x10–6 strain) were used. Matric suction dissipation and the subsequent increment of pore water pressure due to rainfall infiltration were measured using tensiometers and pore pressure transducers located at different points in the flume (Table 1). The number of available sensors and the depth of the flume dictated the general location of the embedded pore pressure and suction sensors (Table 1).

Table 1. Location matrix of embedded sensors
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Strain transducers and cameras:In civil engineering, strain gauge technology has long been used to measure deformation and compare it to analytical models. In the current study, 120-Ω strain transducers were used to capture the deformation characteristics during an increase in slope angle and rainfall infiltration. Strain gauges were embedded in both vertical and horizontal configurations to capture the real-time deformation and subsequent stress accumulation. The transducers were attached to a 1 mm steel rod and vertically embedded in various locations in the soil during compaction. Since the current study was focused on toe retrogressive failure initiation, most of the strain transducers were embedded near the toe of the slope. Even though stress sensors were not employed, the deformation characteristics and the pore pressure transducer observation could be enabled to estimate the location of stress accumulation.

This inorganic compound is a purplish-black crystal that dissolves when it comes into contact with infiltrated rainwater, producing intensely pink to purple color intensity gradients. The initial moisture content dissolved some of the tracing crystals that had been left for 24 h for moisture equilibration (Fig. 1). To observe the boundary of the tracer, the photo image was processed using ImageJ software, and the gray image is shown in Fig. 2b. Thus, the purple-colored area coverage could serve as a reference point in the future. The initial linear schematics of the tracing color scheme, shown in Fig. 1a, were compared to the dilated pattern of the color during rainfall infiltration.

Fig. 1.
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(a) Linear orientation of trace element; (b) Boundaries of tracer (Gray image analysis)

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4 Measurements and Observations

Rainfall characteristics: As can be seen from Table 1, the rainfall scheme began with a smooth transition from antecedent to main rainfall, with an intensity ranging from 4.4 mm/hr to 14.2 mm/hr applied on the slope of 25°. Figure 2a shows the impact of antecedent rainfall on the surface and Fig. 2b, c on side soils (tracer) during the first 48 h of periodic rainfall applications. To achieve a consistent distribution of rainfall, the spray nozzle locations (vertical and lateral distance) and subsequent raindrops on the soil surface were examined in a controlled environment. The initial tracer extent in Fig. 2was monitored after 24 h to account for moisture equilibration time; however, an additional 48 h were required to observe the effect of antecedent rainfall (Fig. 2b, c). When compared to the initial color extent depicted in Fig. 2, there was an increase in both pinkish area coverage and color signal strength at distances of 55 cm and 70 cm in the X-direction (Fig. 2b, c).

Slope failure: It was observed in both densities that the finer particles eroded from the uppermost part of the slope settled around the base-toe intersection and contributed to the stability of the slope temporarily. Given the significance of erosion, it is reasonable to conclude that the top surface fine particles were steadily eroded, resulting in the surface being fully degraded. The increase in slope angle caused a significant decrease in infiltration on the upper portion of the slope. During test label FMT4, the rainfall intensity increased to 43.3 mm/hr and the slope angle reached 40°. For in-situ testing conditions, the toe slope failure continued, accompanied by gradual retrogressive failure. The modified density testing, on the other hand, did not fail at label FMT4 but rather revealed a complete change in surface morphology.

Fig. 2.
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(a and b) Surface and side view; (c) Enlarged side view at X about 55 cm – 70 cm

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Fig. 3.
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Retrogressive failure for a modified density state

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As shown in Fig. 3a, b, soil suction measurements were grouped based on their characteristics, namely early and late dissipation of soil suction. It was observed that the matric suction of the soil for suction sensors namely SS3, SS4, and SS6 became nil at about 45 h, 35 h, and 80 h, respectively (Fig. 3a). However, SS4 showed extended near-zero reading oscillation after 80 h with a maximum magnitude of 7 kPa. It was also discovered that sensors positioned at shallower depths, namely SS2 and SS6, recorded suction changes in response to infiltration (Fig. 3a, b). Damping of the suction shown in Fig. 3 was observed due to intermittent application of rainfall. The first two-day rainfall application, illustrated in Table 1, significantly reduced the soil suction as shown in Fig. 3.

Tracing chemical: This inorganic compound (KMnO4) had a purplish-black crystal when it was placed as a single-line orientation in the flume during soil compaction. It can be seen from Fig. 1a that the initial dissolved color was purple when in contact with field moisture content during compaction. A subsequent increment of the purple area coverage images during infiltration was taken by a continuous camera record and compared with the initial image (Reference area coverage). Finally, ImageJ software was used to process and analyze sequential side photo images to determine area coverage by the diluted tracer. Gray image analysis was used to calculate the area and perimeters of the individual tracer images, shown in yellow cross-dots and red boundaries, and these are used to calculate, the area perimeter ratio. The area perimeter ratio represents the merging of the neighborhood tracer area during further infiltration, resulting in a single larger tracer area. Based on the observations, the area perimeter ratio for the second day was greater than the first day, indicating that infiltration has increased at the lower 2/3 section (Fig. 4a, b). Some intermediate image analysis results were not shown as the first and last results captured the effect of infiltration.

5 Numerical Modeling

In the current study, slope stability analyses were performed under both in-situ and modified density states of saturated steady seepage conditions using GeoStudio 2021 V3 software's SEEP/W and SLOPE/W. The analyses also considered the groundwater table condition in a similar region to the soil sampling region. The slope geometry and rainfall characteristics shown in Fig. 4a were nearly identical to the laboratory physical flume experiments. The modified and enlarged portion of the slope toe has different observation sections, as shown in Fig. 4b. At the lower one-third slope portion, section profile j is parallel to the slope surface with elevation-distance coordinates of 4.56 to 2.61 and 8.57 to 11.78, respectively (Fig. 4b). Until it reaches the modified bottom section, the stress profile in Fig. 5a is nearly constant.

Fig.4.
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(a) Model geometry, rainfall, and flow gradients; (b) Modified slope toe section

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Because the profile section was parallel to the slope face, the stress profile remained unchanged. However, an abrupt change in stress was observed beginning around a modified section and continuing to the end of the profiling line. This revealed that higher stresses were accumulated at the toe section, not only as a result of increased compactive effort but also as a result of slope angle and the resulting increase in driving gravity stress. Higher slope inclination may exacerbate this phenomenon in response to rainfall infiltration. Similarly, until they reached the modified section, the corresponding strains remained constant. Following that, the strain changes were increased and accumulated at a specific location and near zero strain value. Figure 4a depicts how the stress fields increase in depth. However, up to 1.2 m depth, constant strains were observed, followed by abrupt changes in strain increment at a distance of 11.9 m. (Fig. 4b). This layer above could be regarded as the zone of maximum shear mobilization.

Fig. 5.
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Observation section f: (a) Stress profile; (b) Strain profile

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In Fig. 5b, the in-situ/uniform compaction profile was compared to the modified section profile. Constant changes in strain were observed, as shown in Fig. 5b, in contrast to a modified section, which had an abrupt change in strain for an equal section length. Even though the soil was modeled with a 10% density increase, the unique property escalation of c’ indicates that the region was more consolidated than the entire slope. Similarly, a sudden increase in shearing resistance was observed at approximately 10.5 m along the slip surface (Fig. 6). A 10% increase in density at the slope toe results in a 10.69 unit increase in shear resistance, according to Fig. 6b. This demonstrated that a minor change near the slope's toe could potentially improve slope stability and thus be used as a mitigation measure.

Fig. 6.
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(a) Variation in shear on in-situ and modified compaction; (b) Calculated shear area

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6 Results and Discussions

As shown in Fig. 5a, the matric suction for SS3, which was placed in the lower third of the slope with PWT_C2, steadily dissipated suction and reached zero within 45 h. The corresponding pore pressure at PWT_C2 steadily increased due to superficial infiltration. Image processing and area-perimeter ratio analysis results verified that the infiltration and subsequent wetting front reached PWT_C2 (Table 2). Given this sensor (PWT_C3) was so close to the slope's toe, the suction should have dissipated as soon as feasible. In contrast, the pore pressure sensor PWT_C3, which was positioned alongside SS4, had continuously raised. In general, suction and pore pressure sensors have been expected to produce inverse results. However, a rise in PWT_C3 was found while soil suction climbed, which might be attributed to the combined influence of moist soil weight and pore air pressure. Despite this, image analysis revealed that the wetting front advancement had not reached PWT_C3 and had even shown modest infiltration during failure (Figs.4). As a result, the premise for the observation of increased pore pressure at PWT_C3 was accepted. Suction measurements for SS1, SS2, and SS7 were retained until the slope collapsed, and values for SS7 were retained even after the slope failed (Fig. 3b). Since the suction sensor SS1 was placed around the slope toe, the soil suction should have dissipated sooner, but it had a magnitude of around 15 kPa (Fig. 3b). The phenomenon reveals how a smaller proportion of finer soil can significantly impede infiltration. It can be deduced that slope toe modification using a finer proportion and proper drainage can improve soil suction and thus maintain slope stability. Otherwise, improper drain installation or trench excavation at the slope toe could remove the resisting soil mass and potentially trigger slope failure.

Numerical modeling (SEEP/W and SLOPE/W) sectional observation results revealed that stress fields crossing the modified slope toe are increasing and subjected to overstress (Fig. 6a). The subsequent changes in strain were increasing and also concentrating towards the assumed exit slip surface (Fig. 6a). When stresses exceed the maximum shear stresses, the under drained shear strength getting lower and hence progress of failure most likely initiated at the slope toe and ends following a potential slip surface. This revealed that modifying the slope toe in conjunction with appropriate drainage can improve slope stability and thus be used as a mitigation measure. Studies show that slope failures can be triggered by slope toe excavation for any use of engineering activity and are also believed as a hazardous procedure. The premises dictated in the introduction above, in natural slopes, the initial stress field at slope toe had been subjected to an additional change in stress due to geological slope formation. A subsequent time-induced hydrogeological and morphological phenomenon had also been superimposed on the original stresses. This significant phenomenon could be due to the fact that the overstressed slope toe had been already enhanced in stress-bearing through hydrogeologic changes.

7 Conclusions

The results of both physical experiments and numerical modeling show that the slope toe section contributes significantly to slope stability and can be more than theoretically confirmed. The abrupt change in slope toe stress due to an increase in slope angle and pore water pressure has resulted in a drastic change in strain which led to sudden failure. Since the stresses and the corresponding strains were accumulated at the slope toe, excessive deformation was the final stage of slope toe triggering. Thus, the retrogression accelerated along the slip surface, and the soil mass detached irrevocably and irreversibly. It may not be concluded that landslides often occur abruptly, however, natural slopes, particularly overstressed slope toes most often fail suddenly. Therefore, hillsides and toes associated with intensive public activities should be investigated in the manner that the slope toe material has a potential sudden risk or not. The premises and the subsequent results of this study applied not only to the slope toe but can also be extended upslope since the toe stress resistance capacity ascends. It can be concluded from a coupled physical and numerical modeling that a smaller enhancement of slope toe material, i.e., installation of the displacement pile, slope toe reinforcement, anchor, and jet grouting might be cost-effective and feasible. In addition, the slope toe modification using a finer proportion and proper drainage can improve soil suction and thus maintain slope stability.