To investigate the failure mechanism and causes, the slope was analyzed using the two-dimensional finite element program, PLAXIS, Version 8.2. The cross section BB’ shown in Fig. 10 was used to analyze the slope stability. The size of numerical model was 395 m in length and 176 m in height. The bottom boundary was fixed in both horizontal and vertical directions, and the side boundaries were fixed horizontally but free to move vertically. Fig. 11 presents the numerical model of the slope with the fully-grouted anchors, anchor cables and grid beams. The 15-node triangular element was used in the numerical model, which includes 860 elements and 7113 nodes, with very fine meshes. The initial stress field of the slope was obtained using the gravity loading procedure. Hydrostatic water condition was considered in the analyses.
The soil and rock were modeled with the linear elastic-perfectly plastic Mohr-Coulomb model. The nod-to-nod anchor element and the geogrid element were used to simulate free section and bond section of the anchor cable, respectively, as recommended in PLAXIS manual. The elastoplastic model was employed for both the anchor element and geogrid element. Since the anchor cables were prestressed to 520 kN, the mean horizontal spacing of anchor cables was 2.5 m, thus a 208 kN/m prestress load was applied to the anchor cables. The fully-grouted anchors were modelled with the geogrid element using the linear elastic model. The grid beams were simulated with plate element using the linear-elastic model. The physical and mechanical parameters of the anchors, anchor cables and grid beams in the numerical model are summarized in Table 3.
Stability analysis in PLAXIS code is performed using the strength reduction method, where shear strength parameters φ and c are reduced by the same ratio until equilibrium state is reached (Brinkgreve et al., 2004):
where FS is the factor of safety; cr and φ r are the reduced cohesion and friction angle, respectively; ΣMsf is the total multiplier, which is increased in a step-by-step procedure until failure occurs.
5.1 Analyses of the first slope failure
To investigate the cause of the first landslide, the stability of the cut-slope was analyzed considering two scenarios: under natural conditions (initial groundwater level), and under extreme rainfall conditions (water level close to the ground surface). Due to the uncertainty of groundwater level during the first slope failure, the effect of the heavy rainfall on slope stability was modeled by applying the different water levels. It should be noted that the assumed extreme rainfall condition was implemented by increasing groundwater level until the slope reached the limit state. The reinforced structures were set to be in a non-activation state (grey state in the numerical model) to simulate the slope without reinforcement. The parameters listed in Table 1 were used in this analysis.
As shown in Fig. 12a, under natural water table condition, the slope after excavation has a FS value of 1.22, and the potential slip surface lies in the limited zone of upper part of the slope. However, under extreme rainfall condition (see Fig. 12b), the critical slip surface enlarges and propagates upwards because of the rising of ground water, and the FS value of the slope reduced to 1.01, which is at limit state. This means that the cut-slope was certainly stable under natural condition, but it failed under heavy rainfall. In Fig. 12b, the predicted failure surface develops along the contact of top layer and second layer and lies in between the investigated ones. It can be inferred that the failure might have been induced by the rapid increase of pore water pressure within the slop after long-lasting rainfall, even though the numerical model only predicted one slip surface. It is worth noting that, the lower part of the slope surface was covered with shotcrete but the drain holes were not installed in this part, which have blocked the drainage of the slope and resulted in the high pore water pressures in the local part of the slope. This situation may mainly cause the occurrence of deep slip surface observed in the field. However, the pore pressure distribution in the field is not simulated accurately in the numerical modeling (Liu et al., 2012). Therefore, the assumed water table in the model may be unrealistic and is only for simplicity. Also, the recharge of water from the gully (R3), could make the water regime in the slope more complicated than the one assumed in the numerical model.
For comparison, the stability analysis of the slope before excavation was also conducted using the FEM. The results show that the FS values of the slope are 1.29 under natural conditions and 1.06 under extreme rainfall conditions. As compared to the analytical results after excavation (i.e., 1.22 under natural conditions and 1.01 under extreme conditions), the difference of the FS between them is relatively small. This is due to the fact that potential slip surface only develops within the top soil layer and the shear outlet is mainly along the contact between the first layer and the second layer, which are very similar to that shown in Fig. 12. The excavation was performed to mainly cut the second to fourth rock layers, which has minimal effect on the resistance to the upper sliding mass. It should be mentioned that the FS value of the slope without excavation is 1.06 under extreme conditions, which does not indicate that the natural slope under this condition is absolutely stable. The instability of the slope is likely to occur or the slope is at limit state, even under the calculated FS larger than 1.0. However, before excavation the slope in the field is very stable all the time. In this case, the calculated FS may be less than the actual FS of the slope without any construction activities.
The cutting at the toe of the slope may have resulted in the expansion of cracks and fissures in the strongly weathered argillaceous shales. This may have further increased the seepage of water into the cracks and weakened the soil in the shale layer. As indicated by Lee et al. (1996), many forms of geologic damage such as erosion and slope failure could occur in the mudstone formation when wetted under rainfall. After investigating the slope failures in southwestern Taiwan, Lee et al. (2007) found that failure rate in mudstone slopes is the highest among all rock types. Since there were no data available, this factor is not considered in this analysis, but will be considered in the second slope failure.
5.2 Analyses of the second slope failure
Firstly, stability of the reinforced slope under extreme rainfall conditions was analyzed using the parameters listed in Table 1, which were used in the original remediation design. The result from Fig. 13 shows that the potential slip surface of the reinforced slope mainly develops within the third rock layer (i.e., moderately weathered argillaceous shale layer). The slope is stable, with the FS value of 1.11. This suggests that provided the strength of slope materials was not decreased owing to the rainfall and excavation, the reinforced slope could be stable even under extreme rainfall conditions.
However, the laboratory tests after the second slope failure revealed that the strength parameters of the weathered shale layer reduced dramatically. As discussed earlier, the mechanical strength of the mudstone interlayers would reduce when wetted, especially after being wetted and disturbed by the construction of anchor cables. This factor might not be properly recognized in the original remediation design of the slope after the first failure. To consider this factor, the reinforced slope was reanalyzed by using the shear strength parameters listed in Table 2 and keeping other parameters identical to that listed in Table 1.
In the analysis, different heights of groundwater table were considered to obtain the relationship between the safety factor of the slope and the groundwater level. The results in Fig. 14 show that the slope stability decreases with rising of groundwater level. Under natural water table condition, considering the reduction of soil strength, the FS of the reinforced slope is about 1.12. But the slope would have failed when water table increases by 7 m. This value is very close to the mean increment of water level revealed from the site investigation as described in Section 4.3. As shown in Fig. 15, the critical slip surface of the slope with an elevated water level passes through the ends of anchor cables, indicating a global failure. The computed slip surface is very close to the deep failure surface revealed from the site investigation as described earlier. This indicates that the second slope failure was partly due to the heavy rainfall, and partly due to improper design of the anchor cables.
Again the assumption of the water table used in this analysis is an ideal shape. As reported by Sun et al. (2013b), localized slump could change the water flow in a slope and cause a second landslide. The first landslide may have changed the water flow path in the second layer. During the site investigation after the landslides, this issue was not considered, and therefore this factor can not be confirmed. Investigation on this issue is strongly recommended before adopting any further remediation measures.
In the first design, grid beams and shotcrete were installed on the slope surface to improve the slope stability and protect the exposed slope surface from erosion. However, this reinforcement system had very limited effect on the global stability of the slope. During rainy season, the rain water from the gully on the top corner of slope could easily infiltrate into the upper part of the slope and then flow into the lower part of the slope through the strongly weathered, highly permeable rocks revealed after the second slope failure. The application of shotcrete on the highly fissured rock surface could have blocked the natural drainage of ground water out of the slope, without installing horizontal drain holes immediately. This could have caused the rapid rise of water table and high pore pressure in the local part of the slope. In addition, two weak mudstone interlayers were revealed by excavation, but were not considered in the design. The shear strength of slope materials was reduced due to the transient high water pressure and softening of mudstone interlayers, thus triggering the first slope failure.
After the first failure, the remedial works were performed without proper understanding of the soil properties. The reduction of soil strength, especially strongly weathered argillaceous shale layer, and the two weak interlayers might not be appropriately recognized. The adoption of the soil shear strengths overestimated the stability of the reinforced slope. In fact, the natural drainage of ground water was blocked, possibly due to the first landslide and the application of shotcrete on the slope surface. Moreover, the drain holes were insufficient to completely dissipate the raised ground water during heavy rainfall. These could have caused the rapid rise of groundwater level within the slope, increased the weight of the sliding mass, and reduced the shear strength of materials along the potential sliding surface (Song and Cui, 2016). Therefore, the stability of the reinforced slope decreased significantly. In addition, the anchor cables were installed in the weak rock layer, and did not provide enough resisting forces to the slope under rainfall. These factors could have caused the second failure only few days after the remediation. The global failure of the slope, i.e. the deeper slip surface, resulted in the great loss of reinforcement effect of the anchor cables. The instability of the lower sliding mass could trigger the movement of upper section of the slope (Song and Cui, 2016), i.e., another two shallow sliding bodies shown in Fig. 10. Since once loosened, unlike the fully grouted anchors, the anchor cables can not provide any resistance for overall stability of the slope.
Overall, heavy rainfall was a major factor that induced the initial landslide and the subsequent slope failure. In addition to rainfall, several other influence factors triggered the slope instability. The adverse geological conditions such as weak interlayers and improper subdrainage system had harmful impact on the stability of the slope. The heavy rainfall infiltration through the strongly weathered, highly permeable rocks resulted in the increase of transient water pressure and decrease of shear strength of materials. Insufficient geological and hydrogeological investigation contributed to the instability of engineered slope and misled remedial works. Therefore, the design of engineered slope should be conducted not only based on the prescriptive standard but also considering the particular geological and hydrological conditions.