SLEM (Shallow Landslide Express Model): A Simplified Geo-Hydrological Model for Powerlines Geo-Hazard Assessment
Abstract
:1. Introduction
2. Materials and Methods
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- Cr and Cs: the cohesion of plant roots and soil [kPa] on vegetated terrain slopes;
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- ρw and ρs: the density of water and sediment under saturated conditions [kg/m3];
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- g, ht, and B: the acceleration of gravity (9.81 m/s2), depth of the ground [m], and contour length [m];
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- β and φ: slope and ground friction angle [°];
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- W: additional weight of plant biomass [kPa] on vegetated terrain slopes.
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- T: the transmissivity of the shallow soil [m2/s], obtained as a product of soil thickness ht for the saturated hydraulic permeability Ksat [m/s];
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- a(d): the Dynamic Contributing Area (DCA) [m2] of the upstream subsurface runoff, which can evolve (increase or decrease) depending on the rainfall duration d up to the maximum contributing area amax;
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- rcrit(d) is the critical intensity of precipitation [mm/h] of duration d that solves Equation (1).
2.1. Hydrological Model
2.2. Slope Stability Model
2.3. Coupling Hydrological Model with Slope Stability Model
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- The rainfall duration dependency within rcrit(d) is assured only by the term a(d) (the DCA);
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- The critical rainfall rcrit able to trigger the failure is steady precipitation, neglecting possible intermittencies;
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- The transmissivity T is obtained as the product of Ksat and ht under the hypothesis of a free surface (not confined) aquifer formed within shallow soils.
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- The first one concerns the intensity of the critical rain rcrit, which is considered constant for a defined duration d. This hypothesis is unlikely when compared with the rainfall data collected by meteorological stations (rain is strongly intermittent [2,15]), but it is generally accepted for statistical analysis on extremes, such as the evaluation of the corresponding return time through the use of Intensity Duration Frequency curve (IDF) [80,81]. Using local valid IDF curves, the relation between critical precipitation intensity rcrit and the return time (TR) is uniquely determined. However, a shallow landslide is not a repetitive phenomenon that follows the cyclicity of precipitation, especially when investigated at the very local scale of the single slope portion [2,9,34,61,62,82]. Looking at the watershed basin scale, this assumption could be more accepted, admitting that adjacent areas may experience similar behaviour under the same triggering factors [52].
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- The second one concerns the determination of the contributing area a(d) as a function of time (namely rainfall duration d). As a precautionary measure, the contributing area could be considered as a constant that corresponds to the maximum upstream area amax at each point of the basin [50]. The contributing area can be evaluated in a fairly simple way using a GIS (Geographic Information System) software through the determination of flow accumulation [77,83]. However, this parameter may evolve with time because of the downstream propagation of subsurface water flow in the soil ground and across the basin so that it is a dynamic quantity and not a stationary one [84]. The authors [50,70,71] have assumed the stationary hypothesis with a = amax, not providing a unique analytical approach for expressing it as a function of d. To overcome this limitation, our study investigated this problem by proposing a closed formulation of the dynamic contributing area a(d) (DCA), recalling some similarities with surface hydrology, as presented in the next paragraph.
2.4. Determination of the Dynamic Contributing Area (DCA) for Subsurface Flow
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- The subsurface or hydrogeological basin is coincident with the hydrographic one (generally accepted if we consider surface layers lay on an impermeable crystalline substrate) [87];
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- The average saturated permeability Ksat of the surface terrain is variable across broad ranges, but for the loam soil type, which is one of the prevalent across the Italian landscape [88], a representative value may be around 10−5–10−6 m/s. Because the surface runoff velocity Vsup has an order of magnitude around 1 m/s, it is reasonable to increase the corrivation time of the subsurface flow Tc_sub as a function of the ratio of the two flow velocities (Equation (18)).
2.5. Initial Soil Moisture Influence on DCA
2.6. Case Study Description
2.7. Python Scripts and Model Parameters Derivation
- 1_SOIL_Elaboration.py:
- 2_DCA_Elaboration.py:
- The HydroSHED DEM [92] was considered in this study. This DEM has a nominal spatial resolution of 90 m at the equator (~70 m at 45° latitude), and it has been conditioned (void-filled) and made hydrologically continuous to be easily implemented within hydrological and hydraulic models. Other high-resolution DEMs are advisable to improve computation performances, but accurate preprocessing is recommended;
- 3_SLEM_Model.py:
- 4_TR_Evaluation.py:
3. Results
3.1. Determination of the Return Time of the rcrit
3.2. Threshold Curves Comparison for a Quantitative Validation of the Model
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- The index value is 0 (blue) when the critical rainfall for slope instability rcrit is equal to or above the correspondent rainfall threshold intensity;
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- The index value is 1 (red) when the calculated critical rainfall rcrit is settled below the threshold curve.
3.3. Powerline Hazard Estimation
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- TR > 100 yrs, very rare;
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- 50 < TR < 100 yrs, rare;
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- 25 < TR < 50 yrs, fairly rare (range of the span life of powerlines);
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- 10 < TR < 25 yrs, frequent;
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- TR < 10 yrs, very frequent.
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- For short but intense rainfall, the pylons are mainly classified into two groups, the stable pylons (where the failure is “rare”, around 270, 65% of the total) and the unstable pylons (where the failure is “very frequent”, around 130, 30% of the total). These clusters are also confirmed by Figure 16, where rcrit and TR were plotted against the topographical slope, which is a predisposing factor of slope instability. As can be appreciated, failure can happen at whatever slope inclination, but there is a consistent number of pylons that do not experience any instability.
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- For long-lasting precipitation (d > 24 h), the overall pylons at risk are reduced to 20–25% of the total, increasing the ones in safer conditions from 270 (d = 48 h) to 310 (d = 120 h). The pylons located in always unstable areas reduce to ~70–60 (around 15% of the total). The TR is more uniformly distributed for classes with TR < 100 yrs, showing a consistent reduction of the “very frequent” event (located across the ridges), while an increasing number of pylons within the “middle” TR classes is observed. Figure 16 also highlights how the rcrit is not able to distinguish safe and unsafe pylons, while with the TR data, stable pylons are clearly detected with respect to unstable ones.
4. Discussion
- ▪
- SLEM permits a faster simulation of the shallow landslide failure by simply merging an infinite slope stability model and a kinematic routing of subsurface flow. The parameters required are reduced to the minimum because it needs only information about topographical slopes, soil textures, and saturated permeabilities of shallow soils, which can be gathered from national and worldwide available databases. The parameterization of cohesion and friction angle coefficients is trickier, but it is possible to relate them to soil coverage and texture for retrieving a spatial distribution;
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- SLEM made explicit the relation between critical rainfall rate and slope stability through an approximate but physically consistent description of the hydrogeological water cycle. In fact, with respect to the classical simple slope stability model where each cell of DEM is considered independent of the other [12,42,44], the subsurface flow hydrological effect is quantified as a process that directly affects the stability of the terrain;
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- A sensitivity analysis was conducted to try to consider the perturbation of the initial soil moisture on the hydrological model included in SLEM. Taking inspiration from the works of [48,86], the soil moisture influence has been included within the DCA term. The former has been calculated as a function of Ksat_ini through the term Tc_sub, which could be expressed as a function Sr_ini. These dependencies were detected during the sensitivity analysis conducted in varying initial soil moisture conditions (as reported in Table 1), giving reasonable results that are in accordance with the literature studies [42,43,55];
- ▪
- The definition of the critical rainfall rate that triggers instability for a defined duration across a basin establishes the link between the cause and the effect and mimics the geo-hydrological interaction at the slope scale. In fact, for each point of the watershed (i.e., cell of the domain), the expected frequency of that critical rainfall could be estimated (i.e., return time). From TR, it is possible to measure the magnitude of the rainfall phenomena and consequently infer the magnitude of the geo-hydrological event and the probability of powerline failure;
- ▪
- The SLEM model represents an evolution of a well-established geo-hydrological routine that has been implemented in plenty of studies focusing on shallow landslide stability and susceptibility [46,48,49,50]. Its validation has been assessed in different case study areas of the world, considering one or a few reference rainfall events where a detailed slope failure census was available [48,70,71]. In our case, sufficiently precise data on past rainfall-induced slope failure events were not available, so the validation has been carried out following a statistical approach, adopting the locally available rainfall thresholds as a reference. To do that, the performance indexes inherited by ROC methodology were considered to assess the validation of SLEM, which has shown a slope failure detecting behaviour comparable to the rainfall thresholds indications. Implicitly, this procedure allows for sound model validity with respect to an ensemble of rainfall events previously considered for reconstructing the reference thresholds. In this way, the parameter calibration necessary to validate the model is not constrained to fit a single event but can be guided to match the typical statistical behaviour of the rainfall-induced landslides that happened in the past over the investigated area. This strategy allows to avoid parameter overfitting to a single-event analysis [43,55,72], increasing the robustness of the slope failure prediction. This procedure depends on how the threshold curve has been retrieved, but considering more than one threshold, possible discrepancies in reference curves could be detected easily, speeding up the model parameters calibration phase.
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- SLEM could be interpreted as an evolution of the rainfall threshold curves because it practically could detect through rcrit stability and instability situations at the level of a single DEM cell. This is a remarkable point because, using SLEM, the slope stability could be evaluated taking into account the local terrain susceptibility factors that, in rainfall threshold curves, are “hidden” within curves parameters athrs and nthrs;
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- In the end, the closed formulation proposed in Equations (22) and (23) permits the implementation of SLEM rather easily in Python language. The availability of PCRaster and PYSHED libraries has been considered to make hydrological elaborations faster. The flexibility of the code allows for the inclusion of further features, such as soil data elaboration and DCA calculation, by simply importing the required input data from external databases. Therefore, the SLEM equations scripting was rather fast and the sensitivity analysis for model calibration and validation was carried out quite rapidly.
4.1. Model Limitations
4.2. Model Application to Assess Powerline Hazard
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Soil Moisture Type | Code | Sr_ini Value |
---|---|---|
VERY_DRY | 0 | 0.0–0.2 |
DRY | 1 | 0.2–0.4 |
MILD | 2 | 0.4–0.6 |
WET | 3 | 0.6–0.8 |
VERY_WET | 4 | 0.8–1.0 |
ID | CLC Categories | Cr [kPa] | W [kPa] |
---|---|---|---|
1 | City | 0 | 0 |
2 | Agriculture | 2 | 0 |
3 | Deciduous | 10 | 1 |
4 | Evergreen | 20 | 2 |
5 | Grassland | 3 | 0 |
6 | Bare soil | 0 | 0 |
7 | Water body | 0 | 0 |
8 | Scarce vegetation | 2 | 0 |
a1 | n | Duration Range | |||
---|---|---|---|---|---|
24.56 | 0.3212 | 0.2804 | −0.0898 | 0.8108 | 1–24 h |
24.64 | 0.3305 | 0.2552 | −0.0533 | 0.8310 | 1–5 days |
Author | athrs | nthrs |
---|---|---|
Ceriani | 20.1 | −0.55 |
Segoni | 22.46 | −0.64 |
Ciccarese_1 | 21.25 | −0.403 |
Ciccarese_2 | 35.68 | −0.403 |
Statistics on rcrit | 1 h | 6 h | 24 h | 48 h | 72 h | 120 h |
---|---|---|---|---|---|---|
Mean [mm/h] | 533.66 | 89.49 | 22.80 | 11.69 | 7.98 | 5.02 |
Median [mm/h] | 516.49 | 86.12 | 21.53 | 10.77 | 7.18 | 4.31 |
Variance [mm/h]2 | 288,845.36 | 7962.67 | 479.65 | 114.24 | 48.46 | 16.00 |
Mean Square Error [mm/h] | 537.44 | 89.23 | 21.90 | 10.69 | 6.96 | 4.00 |
Statistics on TR | 1 h | 6 h | 24 h | 48 h | 72 h | 120 h |
---|---|---|---|---|---|---|
Mean [yrs] | 67.43 | 67.24 | 66.88 | 68.02 | 72.04 | 81.29 |
Median [yrs] | 100.00 | 100.00 | 100.00 | 100.00 | 100.00 | 100.00 |
Variance [yrs2] | 2199.27 | 2200.61 | 2180.22 | 2003.10 | 1735.91 | 1305.46 |
Mean Square Error [yrs] | 46.90 | 46.91 | 46.69 | 44.76 | 41.66 | 36.13 |
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Abbate, A.; Mancusi, L. SLEM (Shallow Landslide Express Model): A Simplified Geo-Hydrological Model for Powerlines Geo-Hazard Assessment. Water 2024, 16, 1507. https://doi.org/10.3390/w16111507
Abbate A, Mancusi L. SLEM (Shallow Landslide Express Model): A Simplified Geo-Hydrological Model for Powerlines Geo-Hazard Assessment. Water. 2024; 16(11):1507. https://doi.org/10.3390/w16111507
Chicago/Turabian StyleAbbate, Andrea, and Leonardo Mancusi. 2024. "SLEM (Shallow Landslide Express Model): A Simplified Geo-Hydrological Model for Powerlines Geo-Hazard Assessment" Water 16, no. 11: 1507. https://doi.org/10.3390/w16111507