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Figure 10. Map of Mettman Ridge catchment showing shallow landsliding prone areas predicted from the application of Montgomery and Dietrich model delineated in terms of steady state rainfall invensity [mm/d] necessary for slope instability. Model parameters are ’ = 45°, T= 65 m?/d, and p, = 1600 kg/m Observed shallow landslides that occurred from 1987 to 1992 are also displayed.

Figure 10 Map of Mettman Ridge catchment showing shallow landsliding prone areas predicted from the application of Montgomery and Dietrich model delineated in terms of steady state rainfall invensity [mm/d] necessary for slope instability. Model parameters are ’ = 45°, T= 65 m?/d, and p, = 1600 kg/m Observed shallow landslides that occurred from 1987 to 1992 are also displayed.

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Figure 1. One-dimensional sketch for slope equilibrium. compare model performance with that descending from application of the original approach by Montgomery and Dietrich [1994]. Finally, coupling of the model for the hydrologic control on shallow landsliding with the simple scaling model for the frequency of storm precipitation [Burlando and Rosso, 1996] can help understanding the climate control on landscape evolution associated with the occurrence of shallow landslides (see Section 6).
Figure 1. One-dimensional sketch for slope equilibrium. compare model performance with that descending from application of the original approach by Montgomery and Dietrich [1994]. Finally, coupling of the model for the hydrologic control on shallow landsliding with the simple scaling model for the frequency of storm precipitation [Burlando and Rosso, 1996] can help understanding the climate control on landscape evolution associated with the occurrence of shallow landslides (see Section 6).
Figure 2. Soil mantle equilibrium for varying relative slope ratio, tan®/tand’, versus relative groundwater depth, //z, with specific gravity G, = 2.7 and void index e of (a) 0.5, (b) 1.0, (c) 1.5, and (d) 2.0.
Figure 2. Soil mantle equilibrium for varying relative slope ratio, tan®/tand’, versus relative groundwater depth, //z, with specific gravity G, = 2.7 and void index e of (a) 0.5, (b) 1.0, (c) 1.5, and (d) 2.0.
Figure 3. Model sensitivity to void ratio, e, for different degree of soil saturation above the groundwater table: (a) dry, (b and c) intermediate, and (d) saturated.
Figure 3. Model sensitivity to void ratio, e, for different degree of soil saturation above the groundwater table: (a) dry, (b and c) intermediate, and (d) saturated.
[28] Introducing the groundwater level index, w = h/z, yields
[28] Introducing the groundwater level index, w = h/z, yields
[25] By considering the simple case of the initial condi- tion of stable piezometric at depth of (0) = 0 and intro- ducing the saturation precipitation rate, only depending on geometric and hydrologic properties of the hillslope and not from rainfall,
[25] By considering the simple case of the initial condi- tion of stable piezometric at depth of (0) = 0 and intro- ducing the saturation precipitation rate, only depending on geometric and hydrologic properties of the hillslope and not from rainfall,
Figure 7. Groundwater level index versus dimensionless time for different values of dimensionless precipitation rate, p/p*, and soil dimensionless factor, 4}.
Figure 7. Groundwater level index versus dimensionless time for different values of dimensionless precipitation rate, p/p*, and soil dimensionless factor, 4}.
with sub CR indicating the critical conditions for landslide initiation. Note that the precipitation threshold pcr given by equation (23) is a function of measurable quantities describing the physical properties of the hillslope.
with sub CR indicating the critical conditions for landslide initiation. Note that the precipitation threshold pcr given by equation (23) is a function of measurable quantities describing the physical properties of the hillslope.
Figure 8. Relationship between critical rainfall rate and storm duration for different a/b under specified conditions (a = 0.02 km, ’ = 42°, e= 1, G, = 2.65, z= 1 m) and different combination of values taken by 6, S, and 7:
Figure 8. Relationship between critical rainfall rate and storm duration for different a/b under specified conditions (a = 0.02 km, ’ = 42°, e= 1, G, = 2.65, z= 1 m) and different combination of values taken by 6, S, and 7:
Figure 9. Dimensionless critical rainfall rate versus dimensionless time for different values of relative slope ratio and specified soil parameters e, S;. and G,.
Figure 9. Dimensionless critical rainfall rate versus dimensionless time for different values of relative slope ratio and specified soil parameters e, S;. and G,.
“A rainfall event of 100 mm/d causing instability is considered. Table 1. Comparison Between the Montgomery and Dietrich Model and the Present Model in Terms of Model Performance Indexes”
“A rainfall event of 100 mm/d causing instability is considered. Table 1. Comparison Between the Montgomery and Dietrich Model and the Present Model in Terms of Model Performance Indexes”
Figure 11. Map of Mettman Ridge catchment showing shallow landsliding prone areas in terms 0 steady state rainfall intensity [mm/d] necessary for slope instability as predicted from the application o: the present model. Model parameters are ’ = 45°, T= 65 m7/d, p, = 1600 kg/m? and G, = 2.60. Observec shallow landslides that occurred from 1987 to 1992 are also displayed.
Figure 11. Map of Mettman Ridge catchment showing shallow landsliding prone areas in terms 0 steady state rainfall intensity [mm/d] necessary for slope instability as predicted from the application o: the present model. Model parameters are ’ = 45°, T= 65 m7/d, p, = 1600 kg/m? and G, = 2.60. Observec shallow landslides that occurred from 1987 to 1992 are also displayed.
Figure 12. Coupling of the relationship between critical rainfall rate and duration of precipitation with the IDF curves for the failure return period under specified hillslope (0 = 35°, a= 0.02 km’, o’ = 42°, e= 1, S,= 0.5, G, = 2.65, T=40 m?/d and z= 1 m) and climate conditions (k = 0.05, a = 0.30, ¢ = 0.80, m,; = 68 mm and n = 0.45). Different values of topographic index a/b and return period Tp are considered.
Figure 12. Coupling of the relationship between critical rainfall rate and duration of precipitation with the IDF curves for the failure return period under specified hillslope (0 = 35°, a= 0.02 km’, o’ = 42°, e= 1, S,= 0.5, G, = 2.65, T=40 m?/d and z= 1 m) and climate conditions (k = 0.05, a = 0.30, ¢ = 0.80, m,; = 68 mm and n = 0.45). Different values of topographic index a/b and return period Tp are considered.
This provides the critical frequency for initiation of hillslope instability, as represented by the value of x; that satisfies equation (23) for a given rainfall duration t. One notes that the critical duration tcp that yields the minimum return period for slope instability can be determined by the further condition Op;(t)/Ot = Opcr(t)/0t, for t = tcr. This yields
This provides the critical frequency for initiation of hillslope instability, as represented by the value of x; that satisfies equation (23) for a given rainfall duration t. One notes that the critical duration tcp that yields the minimum return period for slope instability can be determined by the further condition Op;(t)/Ot = Opcr(t)/0t, for t = tcr. This yields
Figure 13. IDF curves for Allegany rain gauge station for different values of return period Tr. Twenty-two years of the hourly rainfall data set are considered.
Figure 13. IDF curves for Allegany rain gauge station for different values of return period Tr. Twenty-two years of the hourly rainfall data set are considered.
Figure 14. Map of Mettman Ridge catchment showing shallow landsliding prone areas as predicted from the application of the present model in terms of return period of potential failure considering an initial condition of stable piezometric at the depth of bedrock, h(0) = 0. [45] One notes that soil cohesion and the effects of vegetation on the stability of the aggregate are not deeply analyzed in these exercises, so these simplifications can highly affect the results in terms of return period of rainfall triggered landslides. According to Montgomery and Dietrich [1994], the effect of roots on shear stress resistance was taken into account by increasing of 40% the value of the shear stress resistance angle. Schmidt et al. [2001] and
Figure 14. Map of Mettman Ridge catchment showing shallow landsliding prone areas as predicted from the application of the present model in terms of return period of potential failure considering an initial condition of stable piezometric at the depth of bedrock, h(0) = 0. [45] One notes that soil cohesion and the effects of vegetation on the stability of the aggregate are not deeply analyzed in these exercises, so these simplifications can highly affect the results in terms of return period of rainfall triggered landslides. According to Montgomery and Dietrich [1994], the effect of roots on shear stress resistance was taken into account by increasing of 40% the value of the shear stress resistance angle. Schmidt et al. [2001] and
Table 2. Percentage of Unstable Topographic Elements for Different Duration and Rainfall Height Considering Initial Condition of Stable Piezometric at the Depth of Bedrock, (0) = 0
Table 2. Percentage of Unstable Topographic Elements for Different Duration and Rainfall Height Considering Initial Condition of Stable Piezometric at the Depth of Bedrock, (0) = 0
Figure 15. Map of Mettman Ridge catchment showing shallow landsliding prone areas as predicted from the application of the present model in terms of return period of potential failure considering an initial condition of stable piezometric at the depth of h;, with 40) = 0.15 m. [49] Finally, the model for the hydrologic control on shallow landsliding is coupled with the simple scaling model of storm precipitation in the frequency domain. This can help understanding the climate control on landscape evolution associated with rain triggered landslides. Model application for the Mettman Ridge study area in Oregon
Figure 15. Map of Mettman Ridge catchment showing shallow landsliding prone areas as predicted from the application of the present model in terms of return period of potential failure considering an initial condition of stable piezometric at the depth of h;, with 40) = 0.15 m. [49] Finally, the model for the hydrologic control on shallow landsliding is coupled with the simple scaling model of storm precipitation in the frequency domain. This can help understanding the climate control on landscape evolution associated with rain triggered landslides. Model application for the Mettman Ridge study area in Oregon
Table 3. Percentage of Unstable Topographic Elements for Different Duration and Rainfall Height Considering Initial Condition of Stable Piezometric at the Depth of /;, With (0) = 0.15 m
Table 3. Percentage of Unstable Topographic Elements for Different Duration and Rainfall Height Considering Initial Condition of Stable Piezometric at the Depth of /;, With (0) = 0.15 m
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