Capturing the footprints of ground motion in the spatial distribution of rainfall-induced landslides

The conditions promoting the occurrence of a landslide are governed by various climatic, morphologic, geomorphologic, geotechnical, seismic and anthropic factors and their complex interactions (Budimir et al. 2015; Reichenbach et al. 2018). These causative factors are categorized as predisposing conditions and triggering factors (e.g. IAEG 2001; Tanyaş et al. 2019a; Fan et al. 2019). Predisposing conditions (e.g. weathering, morphology) typically refer to slowly changing processes which tend to keep the slope in a marginally stable state (IAEG 2001). Landslide triggering factors (i.e. rainfall, earthquake, human activity, snowmelt, volcanic processes), on the other hand, generally refer to external stresses that cause an immediate response in terms of slope stability (Crosta et al. 2012). Therefore, triggering factors might be most crucial in terms of rapid assessment of landslide hazard because they mostly dictate the timing of landsliding.

Earthquakes and rainfall are the most frequently observed triggering factors (Petley 2012), and a body of literature focuses on landslide hazard assessment associated with both rainfall-induced landslides (RFIL) (Crozier 1999; Rossi et al. 2012; Kirschbaum and Stanley 2018) and earthquake-induced landslides (EQIL) (Godt et al. 2008; Robinson et al. 2017; Nowicki Jessee et al. 2018; Tanyaş et al. 2019a). However, the coupled effects of earthquakes and rainfall are rarely examined (e.g. Bontemps et al. 2020; Chen et al. 2020a; Sæmundsson et al. 2018; Sassa et al. 2007).

To capture the coupled effects of earthquakes and rainfall, first we need to refer to the concepts of triggering and predisposing factors. There are two possible scenarios (Fig. 1): scenario A where an earthquake triggers landslides after a rainfall event(s), and scenario B where rock masses that are already disturbed by ground shaking subsequent rainfall event triggers landslides.

In scenario A, the preconditioning effect of rainfall followed by (or during) an earthquake is dependent on rainfall intensity and duration, which may cause an increase in pore pressure and a reduction in the ratio of resisting forces to driving forces (factor of safety, FoS) (Sassa et al. 2007; Wang et al. 2007; Faris and Wang 2014; Zhang et al. 2019; Martino et al. 2020).

In scenario B, the preconditioning effect of seismic shaking followed by a rainfall event could be related to multiple earthquakes, which may have previously and permanently modified the force balance in a given hillslope (Saba et al. 2010; Fan et al. 2018). Because of the multiple earthquakes responsible for the damage given to rock masses, the accumulated effect of seismic shaking in a given area may add another level of complexity that is difficult to account for.

There are several studies showing how earthquakes increase landslide susceptibility and play a major role in RFIL events in post-seismic periods (Lin et al. 2006; Saba et al. 2010; Tang et al. 2016; Yang et al. 2017; Fan et al. 2018; Tian et al. 2020; Kincey et al. 2020). Specifically, for the 2008 Wenchuan earthquake, the post-seismic landslide evolution has been examined in several articles (e.g. Chen et al. 2020a; Tang et al. 2016; Xiong et al. 2020; Zhang and Zhang 2017). For instance, Fan et al. (2018) assess post-seismic slope failures for a subset of the area affected by landslides since 2008 and until 2015. They report an elevated landslide susceptibility after the Wenchuan earthquake, with the majority of landslides being observed as remobilized co-seismic failures. They examine the elevated susceptibility by monitoring the variation in landslide rate, which is a term referring to the number of landslides mapped over a period of time. They show that the landslide rate gradually decreases and returns to its pre-earthquake level within approximately seven years. Fan et al. (2018) also note that the recovery of the landslide rate to pre-earthquake periods may be longer in areas affected by stronger earthquakes. Chen et al. 2020a) examine another subset of the area affected by co-seismic landslides for the Wenchuan earthquake, in the period between 2008 and 2018. And, they report that hillslopes and landslide deposits largely stabilize 10 years after the earthquake. Besides, several studies suggest a possible link between these long periods where we observe an elevated landslide susceptibility and large co-seismic landslide deposits (e.g. Chen et al. 2020a; Fan et al. 2018; Xiong et al. 2020; Yunus et al. 2020) estimated to sum up to 2.8 km³ specifically for the Wenchuan case (Li et al. 2014). As regards the factors controlling the length of the period characterized by the elevated landslide susceptibility, Fan et al. (2018) refer to possible contributions of various processes such as progressive strengthening of the deposits due to grain coarsening (Hu et al. 2018) and, in particular, revegetation (Chen et al. 2020b; Yunus et al. 2020). In fact, studies examining the same concept associated with vegetation recovery argue that landslide recovery has not been fully completed yet (Xiong et al. 2020; Yunus et al. 2020), and it may take up to 25 years in total (Chen et al. 2020b).

The overview above summarizes the recent literature on post-seismic landslide recovery time, taking Wenchuan simply as a reference. Notably, differences still exist in the literature in terms of recovery times in other geographic areas and even on the exact definition of recovery time itself (Kincey et al. 2020). In fact, if on the one hand, the concept of recovery time has found a large support across the whole geoscientific community. On the other hand, scientific debates are still taking place on the required time window for the recovery to take place. Taking aside the differences in opinion among research groups, one key element has certainly been agreed upon, and this corresponds to the physics behind this process. Specifically, Ambraseys and Srbulov (1995), already a few decades ago, summarized the stages of landslide genesis in co-seismic and two post-seismic phases. Co-seismically, populations of landslides trigger across a given landscape as a function of ground motion and its duration, together with the geometry of the slope, and the undrained strength of the material mobilised during the earthquake. In the first post-seismic phase, landslides can trigger in response to rainfall if the residual undrained shear strength (disturbed by the previous ground shaking) on the slip surface is less than that required to maintain static equilibrium. The second post-seismic stage is governed by creep and consolidation processes, together with destabilising hydrostatic forces. These govern the landslide pattern of occurrence whenever the given landscape is exposed to high or extreme precipitation. These post-seismic phases clearly emerge in a recent study published by Tian et al. (2020), where the authors summarize the current literature of post-seismic landslide evolution and determine two primary drivers: the amount of co-seismic source material and the precipitation pattern. They also note that stronger and more numerous earthquake aftershocks can prolong the recovery time.

Nevertheless, the abovementioned studies mostly focus on landslide rates observed at pre-, co- and post-seismic periods but not the predisposing effect of ground shaking in a multi-variate scheme implemented to model post-seismic landslides. There is no proposed method to explicitly account for the legacy of previous earthquakes as a predisposing factor in RFIL susceptibility assessment. However, some proxies (e.g. distance to fault, distance to earthquake epicenter) are suggested to use in landslide susceptibility assessments to capture part of this effect (e.g. Gallen et al. 2015; Kritikos et al. 2015; Massey et al. 2018; Parker et al. 2015). For instance, Kirschbaum and Stanley (2018) propose a predictive model for RFIL where the landslide susceptibility map created including a variable regarding the seismicity. In particular, they use distance to fault lines among the conditioning factor. They then combine the landslide susceptibility map with the landslide triggering rainfall threshold. Furthermore, Quesada-Román et al. (2019) focus on capturing the predisposing effect of earthquakes in RFIL susceptibility assessments via numerical methods and use distance to the epicenter as a proxy. Specifically, they run a logistic regression model for landslides triggered by the 2016 Hurricane Otto, Costa Rica, 4 months after the 2016 Bijagua earthquake, which affected the same site. They show that a higher landslide density is observed close to the epicentral area where intense precipitation was also recorded. However, either distance to fault line or distance to epicenter has some limitations because these approaches do not consider the distribution of ground shaking, which can vary irrespective of distance from the fault line/epicenter.

A more comprehensive alternative to distance fault lineament/epicenter is represented by ground motion parameters (GMPs). GMPs (e.g. peak ground acceleration, PGA; Modified Mercalli Intensity, MMI) are commonly used in predictive model developed for EQIL (Nowicki et al. 2014; Nowicki Jessee et al. 2018; Tanyaş et al. 2019a).

This study aims to capture the role of ground motion as a predisposing factor in a landslide susceptibility assessment for RFIL in Indonesia. We map multi-temporal landslide inventories covering both co- and post-seismic phases associated with four earthquakes occurred in Indonesia: 2012 Sulawesi (M_w = 6.3), 2016 Reuleut (M_w = 6.5), 2017 Kasiguncu (M_w = 6.6) and 2018 Palu (M_w = 7.5) earthquakes. We hypothesize that the peak ground acceleration (PGA) map of the last strongest earthquake can partially explain the spatial distribution of landslides triggered by rainfall after an earthquake. To test this hypothesis in the validity domain of the areas under study, we opt to test the PGA contribution in RFIL susceptibility models built by using a binary logistic regression (BLR), which is the most common statistical model used in landslide susceptibility assessments (e.g. Reichenbach et al. 2018). Then, we run two separate tests to address the question mentioned above.

The first one involves fitting a BLR model to examine the relative contributions of both PGA map and two morphometric covariates (i.e. slope and distance to stream) in landslide susceptibility assessments carried out for co- and post- seismic multi-temporal landslide inventories. In doing so, we monitor how the contribution of PGA (i.e. regression coefficient of PGA) changes through time from co-seismic to post-seismic periods.

The second test consists of fitting a BLR model for a case where ground motion and rainfall data are contextually available. In this case, the susceptibility model features morphometric properties, the PGA of the last strongest earthquake, together with rainfall proxies (i.e. daily accumulated and 7-day antecedent precipitation) associated with RFIL. This operation ensures not only that we can estimate the PGA contribution to the estimated probability but also that we can compare it to the contribution of the rainfall proxies.

We should note that all our analyses are representative only for the areal boundaries encompassing multi-temporal inventories, which are mapped for a subset of the total area affected by co-seismic landslides. Notably, the characteristics of landslides may vary spatially, and therefore, the contribution of PGA that we assess in the susceptibility analyses is representative for the boundaries of examined areas.

We examine two seismically active sites (study areas A and B) from Indonesia (Fig. 2) and create multi-temporal landslide inventories via visual interpretation of PlanetScope (3–5 m), rapid eye (5 m) images acquired from Planet Labs (Planet Team 2017) and high-resolution Google Earth scenes.

To create the multi-temporal landslide inventories, we examine all available satellite images and choose the largest available cloud-free regions, for both sites. All the multi-temporal images we use for mapping convey the real landslide distribution over time during co- and post-seismic phases. Notably, the inventories are not created following a fixed temporal resolution. We map as many inventories as the imagery availability allowed. In each inventory, landslides that have previously occurred are eliminated, and only new failures are included. We systematically examine the satellite scenes through visual observation and map landslides as polygons. We delineate landslide source and depositional areas as a part of the same polygon.

The study cases we examine are different from most of the previously investigated situations in the geomorphological literature where the effect of major earthquakes (7.9 > M_w > 7.0) (e.g. 1999 Chi-Chi, 2005 Kashmir, 2008 Wenchuan, 2015 Gorkha earthquakes) is tested against a large sample of co-seismic landslides (Lin et al. 2006; Saba et al. 2010; Fan et al. 2018; Kincey et al. 2020). For those earthquakes mentioned above, USGS ShakeMap reports maximum PGA values ranging from 0.83 to 1.36 g (PGA_max,chi-chi = 0.83 g, PGA_max,Kashmir = 1.36 g, PGA_max,Wenchuan = 1.14 g and PGA_max,Gorkha = 0.87 g) (Worden and Wald 2016). Here, we examine two sites where ground motion originated from strong earthquakes (6.9 > M_w > 6.0) with one exception, which is the 2018 Palu earthquake. Overall, the maximum PGA values are lower than other cases examined in the literature (PGA_max,Sigli = 0.20 g, PGA_max,Reuleut = 0.60 g, PGA_max,Sulawesi = 0.32 g, PGA_{max,Kasiguncu} = 0.25 g and PGA_max,Palu = 0.85 g) (Worden and Wald 2016) (Table 1).

We structure our analyses in a three-stepped procedure summarized in Fig. 6. In step 1, we identify a suitable landscape partitions and pre-process morphometric, seismic variables and rainfall proxies to organize the dataset required to run a susceptibility model for each study area. In step 2, as part of susceptibility analyses, we examine ground shaking as a predisposing factor of landslides and investigate its relevance in each model trained by using the available inventories. As a result, we monitor how the PGA role in each model changes through time. In step 3, we focus on study area A and examine the coupled effect of PGA and rainfall proxies on the spatial distribution of a RFIL inventory. In particular, we use the first post-seismic inventory associated with the Reuleut earthquake (M_w = 6.5) because it appears as a rare event where many RFIL occur on a site although only a few landslides are triggered by the earthquake. Our rationale is that the higher post-seismic landslide rate (compared to its co-seismic counterpart) may be due to the legacy effect of the Reuleut earthquake. If this is the case, then the PGA of the Reuleut earthquake should be able to explain part of the spatial dependence in a susceptibility model built with RFIL.

For both sites, we created SUs with median SU size of 0.46 km² (study area A) and 0.48 km² (study area B) (Fig. 7). These are the two respective spatial partitions we use to run a BLR for each inventory using six covariates (β_Dist2Stμ, β_Dist2Stσ, β_Slopeμ, β_Slopeσ, β_PGAμ, β_PGAσ).

Figure 8 shows the regression coefficients of examined covariates obtained for each of the modelled inventories. The boxplots are obtained from 1000 bootstrap replicates and represent the sampling distribution of the relative contribution of each covariate to the probability of landslide occurrence. Overall, slope steepness and PGA have positive regression coefficients for all co-seismic inventories. To examine how the regression coefficient of PGA changes through time, we also plotted the coefficient obtained for each temporal inventory as well as the corresponding AUC value (Fig. 9). Same as above, the sampling distribution of each parameter is retrieved by bootstrapping.

In study area A, for the co- and post-Reuleut susceptibility models, we used the Reuleut PGA map. The results indicate that the PGA has a positive weight on classifying a given slope unit as “landslide” instead of “non-landslide” given the choice of predictors (Fig. 9a). We observed a gradual decay in both regression coefficients (Fig. 9a) and AUC values (Fig. 9b) from the 1st to 3rd post-seismic inventories, indicating that the positive contribution of seismic shaking decreases over 2 years (from 14th December 2016 to 5th January 2019). Specifically, within 2 years, the median regression coefficient of PGA decreases from ~0.6 to ~0.2.

For the co-Reuleut landslide inventory, the regression coefficient of PGA and the AUC of the corresponding susceptibility model indicate a pattern we do not observe in the study area B (Fig. 9). In particular, both the AUC and the PGA regression coefficient of co-Reuleut inventory are lower than their counterparts calculated for the first post-Reuleut landslide inventory (Fig. 9a). Notably, the uncertainty—here calculated by bootstrapping for 1000 replicates—around the median of the PGA regression coefficients also changes through time, which is due to the difference in sample sizes (or to the fewer number of unstable SUs per temporal inventory).

As for the modelling performance, for each model, we calculated the bootstrapped AUC distribution, whose median values range from 0.64 to 0.72 overall (Fig. 9b). Specifically, the median AUC estimated for and from the co-seismic to the 2nd post-seismic landslide inventory is above 0.6. Conversely, almost the entire range of AUC calculated for the 3rd post-seismic landslide inventory is below 0.6, which is the limit of acceptable modelling performance (Hosmer and Lemeshow 2000). The goal of this work is not necessarily to obtain the best modelling performance, which could be achieved by including additional covariates, but rather to capture the relative contribution of PGA through time. In this regard, on the one hand, we did not add the rainfall signal because the examined post-seismic landslides were triggered by unknown rainfall events over a large time span. On the other hand, we did not include additional terrain properties to avoid the effect of variable interactions. By variable interaction, we refer to the fact that, in a multi-variate scheme, the effect of one variable may depend on the value of another variable. So, by assuming a much larger covariate set than the one we used, our interpretation should have also accounted for inter-dependencies among covariates, which we avoided by keeping the model as simple as possible to better asses the contribution of ground motion.

As a result, the AUC values show reasonable modelling performance for a model simply built on 6 covariates (Fig. 9). Results also show that the lowest AUC value is obtained for the 3rd post-seismic RFIL inventory where we also identified the lowest positive weight on landslide occurrences associated with PGA layer. The statistically significant drop in AUC value from 2nd (AUC = 0.70) to 3rd (AUC = 0.64) may imply that the contribution of PGA impact may have decayed over time (lower β values) and that, in general, the model is less able to explain the unstable SU distribution over space.

For study area B, we again examined three post-seismic landslide inventories per each earthquake (Fig 9 c and d). By observing the post-Sulawesi susceptibility models, which are all mapped approximately 3 years after the Sulawesi earthquake, the mean PGA regression coefficient appears to be either very low and positive or negative for all the post-seismic inventories (Fig. 9c). This shows that the positive weight of PGA is low for RFIL susceptibility model conducted 3 years after an earthquake. As for the modelling performance, we identified a gradual decrease in AUC values from co-seismic to post-seismic periods (Fig. 9d) as we observed in study area A.

A similar situation is shown for the Palu earthquakes (Fig. 9 c and d), where the susceptibility model of co-seismic landslide inventory shows a positive regression coefficient that decreases with time. In this case, the post-seismic landslide inventories are mapped within a year from the Palu earthquake. Here, although we observed a decay, the regression coefficients are still positive and relative higher than the Sulawesi case.

Our observation out of three cases presented above (i.e. Reuleut, Sulawesi and Palu) are consistent with each other. Up to 3 years, the PGA in each model contributes to increase the probability of landslide occurrence. However, the Kasiguncu case reveals a slightly different pattern in terms of variation in regression coefficient of PGA. In particular, similar to other cases, the regression coefficient of PGA is positive for the co-seismic phase and decays in post-seismic period (Fig. 9c). Nevertheless, the Kasiguncu is different from other cases since the median regression coefficient of PGA associated with the second post-seismic inventory became negative within 4 months after the earthquake. This is the most rapid decay among the examined cases. Also, the regression coefficient in the third post-seismic inventory, which is mapped a year after an earthquake, is relatively higher than its former post-seismic counterparts, and this is not consistent with other observations. We will elaborate this observation from an interpretative standpoint in “Discussion.”

Aside from these observations on regression coefficient of PGA, the AUC values show a gradual decay in each case examined in study area B (Fig. 8d).

To further elaborate on the role of PGA, we also run alternative models excluding the PGA itself (hence keeping only β_Dist2Stμ, β_Dist2Stσ, β_Slopeμ, β_Slopeσ). We do so by using exactly the same sampling strategy to create 1000 bootstrap replicates. As a result, we could calculate the performance difference between the initial models we presented above and the alternative models. Figure 10 shows that the differences are always positive, which implies that the ground motion, when included, captures some spatial dependence in the landslide distribution which is otherwise unaccounted for in the new set of alternative models without PGA. As expected, relatively larger differences are associated to the models corresponding to co-seismic landslide inventories. The Reuleut case is the only exception, though this is not entirely surprising because the regression coefficients of PGA we calculated for the Reuleut inventories revealed the same variation from co-seismic to post-seismic phases.

In the next phase of the analyses, we focus on the first post-Reuleut RFIL inventory for which the estimates are shown in Fig. 9a highlights that the PGA is a positive contributing factor. More specifically, we run a BLR-based susceptibility model for this inventory, including all covariates we used in step 2 plus a time series of rainfall proxies (daily accumulated and 7-day antecedent precipitation) (Fig. 6). Each element of the time series and associated proxies has been identified in Fig. 11 a and b as an extreme event compared to the last 20 years of precipitation within the same season.

The red peaks in Fig. 11 show that a large number of extreme rainfall events could be responsible for the first post-Reuleut RFIL inventory. These rainfall events are graphically summarized in Fig. 12. The plots show the spatial distribution of normalized landslide density (i.e. number of landslides per km² rescaled from zero to one) (Fig. 12a), PGA (Fig.12b), the identified daily accumulated (Fig. 12c–i) and 7-day antecedent (Fig. 12j–n) rainfall. The figure shows some degree of similarity between the spatial distribution of RFIL (Fig. 12a) and the PGA (Fig. 12b), with a decreasing pattern from northeast to southwest. Conversely, there is no explicit agreement between the landslide distribution and any rainfall pattern.

Beyond the visual comparisons, to statistically isolate the most likely triggering events, we initially perform a LASSO variable selection. We assume that irrelevant rainfall patterns or events that are not responsible for the landslide initiation should not be selected by LASSO. We tested 100 λ values to shrink the parameter space, running a 10-fold cross-validation for each λ and storing the associated AUC values. Figure 13 a graphically summarizes this information. Two possible best λ choices are reported in the figure, corresponding to the vertical dashed lines. The dashed line to the left corresponds to the most conservative choice where a relatively large number of covariates is still allowed to keep the AUC performance stable or even to improve it. The dashed line to the right corresponds to the most penalized model with acceptable AUC performance with respect to the initial one featuring all the covariates. The corresponding sets of covariates are fourteen and six, respectively. From the second limit, the AUC rapidly decays.

Here, we stress something peculiar out of the two covariate sets. The most conservative model selects 14 covariates out of which 8 (magenta rhombi) are rainfall proxies. These are associated with a negative regression coefficient (Fig. 13b). This is an unrealistic effect. The rainfall is the primary cause of the instability process; therefore, it is expected to be positive. Hence, a negative regression coefficient, even if statistically significant, should suggest that the specific rainfall covariate does not have any realistic or interpretable meaning. Therefore, our expert choice would be to remove the eight rainfall proxies with an unexplainable role. Interestingly, the second λ, which is more aggressive in constraining the parameter space, selects six covariates (blue rhombi) by removing the eight rainfall proxies. As a result, we consider the second λ to be the most reasonable out of the two. And, on the basis of the six selected covariates, we have run an additional set of analyses featuring 1000 bootstrapped replicates whose distributions of regression coefficients are plotted in Fig. 13c.

Results show that PGA_μ has the largest contribution to the model (Fig. 13c) and that the most likely rainfall trigger corresponded to the 4th January 2017 event, which appears to be the third contributor out of the six, after slope_σ.

In this study, we primarily used the regression coefficients of ground shaking (i.e. PGA) to explore the relevance of the earthquake legacy effect on RFIL susceptibility assessments. We extent this consideration with a time-variant approach and examine how the ground shaking effect changes through time.

In this study, we focus on a rarely investigated concept in landslide susceptibility assessments that looks at the coupled effect of earthquakes and rainfall in triggering landslides (Sassa et al. 2007). We approach the concept by initially considering seismic shaking as a predisposing factor over two time series of landslide inventories, both triggered by earthquakes and rainfall. Subsequently, we focus on a specific case aiming to capture the legacy effect of ground motion on RFIL susceptibility and compare it to the precipitation effect. The analyses have all been carried out in a BLR framework to study the distribution of covariate effects. These have been estimated via 1000 bootstrap simulations. We also run an additional LASSO-penalized framework to select the best set of explanatory variables for RFIL.

Our findings suggest that the signal of ground shaking evolves through time in post-seismic periods. Specifically, we show that the PGA map of the last strongest earthquake can be used as a predisposing factor for RFIL occurring after the earthquake (i.e. up to 3 years) within the two study areas. This seismic proxy captures part of the spatial dependence in post-seismic RFILs, and it does so with a decreasing capacity through time. In fact, on the basis of the four cases we examined, the signal completely disappears. In other words, the mean or median regression coefficient in each case starts from a largely positive value and decreases down to near-zero values after approximately 3 years from the initial earthquake. Furthermore, we observe that the coupled effect of earthquakes and rainfall, if co-existing in a susceptibility model, improves the accuracy of the susceptibility estimates for subsequent RFIL, induced by extreme precipitation discharges. Regarding the latter, we statistically notice that the effect of extreme precipitation and the ground motion legacy is particularly relevant if it occurs shortly after the earthquake for we assume that the mobilization of weakened slopes is promoted in this stage of the landscape evolution. Actually, for the specific case we examined, we statistically observed that the ground motion legacy explains the RFIL distribution more than the actual rainfall trigger (the PGA mean and/or median regression coefficient is positive and larger than the rainfall proxy). This consideration is also statistically significant as the vast majority of the PGA coefficient distribution is larger and outside the 95% confidence interval of the rainfall coefficient distribution.

It should be noted that both the cases we examined are located in Indonesia, which are in a tropical environment. Therefore, our conclusions still need to be verified in other contexts. Future work could demonstrate similar ground motion and rainfall combined effects, which could represent a further advancement in regional/global near-real time statistically and physically based susceptibility modelling, or early warning systems. In fact, currently, none of these fundamental applications for planning and preparedness contextually feature the potential triggering effect of seismic shaking and precipitation. Therefore, current models lack the ability to explain the residual spatial dependence that the weakening effect of the ground motion may exert onto a given landscape, thus preparing it to potentially fail with a larger landslide rate than the expected. However, to achieve such tasks, the geotechnical characteristics of hillslope materials will need to be continuously monitored. Such monitoring context will make it possible to assess the actual effects of ground motion and its legacy effects on slope stability as the slope materials are exposed to rainfall discharges through time.