Initial conditions at each grid-cell are assumed to be in steady-state. Given the
observed discharge at the catchment outlet, the discharge from every grid-cell is
assigned in proportion to each of the grid-cells upstream to it, and the assigned
discharge in each grid-cell is converted to the value of the water depth according to
the stage-discharge relationship (Eq. 11.1).
11.2.3 Slope Stability Model
Based on the concept of the infinite slope model, the slope stability model is
developed by using a factor of safety (FS) with considering a failure surface.
There are five important points which has been concluded in the slope stability
model, such as (i) failure is the result of translation sliding, (ii) the failure plane and
water table are parallel to the ground surface, (iii) failure occurs as a single layer,
(iv) the failure plane is of infinite length, and (v) the impacts of adjacent factors are
not taken into account (Apip et al. 2010). In the hill slopes, the safety factor is
generally calculated as the ratio of the available resisting force (shear strength) to
the driving force (shear stress). Instability occurs due to the shear strength of a soil
layer becomes smaller than the shear stress acting on the soil. In this study, the
Mohr-Coulomb failure criterion has been used for the governing equation of the
safety factor (Apip et al. 2010).
In Fig. 11.4, it presents the detail structure of the forces acting on a point along a
slope with potential for failure. The resisting force of a soil layer is the shear
strength (s) as a combination of forces, including the normal stress (σ), pore
pressure within the soil material (p), cohesion factors (c), and the effective angle
of internal friction (β). The difference between normal stress and pore pressure is
the effective normal stress. Shear strength based on the Mohr-Coulomb law is
presented as follows:
s ¼ c þ σ À p
ð
Þtan β
ð11:2Þ
Normal stress is the vertical component of gravity that resists down-slope
movement as follows:
σ ¼ δ s g h cos θ;
ð11:3Þ
where δ s is the wet soil density (kg/m
3 ), g is the gravitational acceleration (¼
9.81 m/s
2 ), h is the vertical soil depth perpendicular to the slope (ψ), and θ is the
slope angle (deg). Soil moisture increases the unit weight of soil material and
therefore increases both the resisting and driving forces. Soil moisture creates
pore pressure, which reduces the effective normal stress and shear strength. Pore
pressure in the slope differs among sites and also has large temporal variation. It is
difficult to estimate these values and to include them in this model of a large
catchment. Therefore, we simplified the condition of pore pressure in the slope by
228
P. Luo et al.
observed discharge at the catchment outlet, the discharge from every grid-cell is
assigned in proportion to each of the grid-cells upstream to it, and the assigned
discharge in each grid-cell is converted to the value of the water depth according to
the stage-discharge relationship (Eq. 11.1).
11.2.3 Slope Stability Model
Based on the concept of the infinite slope model, the slope stability model is
developed by using a factor of safety (FS) with considering a failure surface.
There are five important points which has been concluded in the slope stability
model, such as (i) failure is the result of translation sliding, (ii) the failure plane and
water table are parallel to the ground surface, (iii) failure occurs as a single layer,
(iv) the failure plane is of infinite length, and (v) the impacts of adjacent factors are
not taken into account (Apip et al. 2010). In the hill slopes, the safety factor is
generally calculated as the ratio of the available resisting force (shear strength) to
the driving force (shear stress). Instability occurs due to the shear strength of a soil
layer becomes smaller than the shear stress acting on the soil. In this study, the
Mohr-Coulomb failure criterion has been used for the governing equation of the
safety factor (Apip et al. 2010).
In Fig. 11.4, it presents the detail structure of the forces acting on a point along a
slope with potential for failure. The resisting force of a soil layer is the shear
strength (s) as a combination of forces, including the normal stress (σ), pore
pressure within the soil material (p), cohesion factors (c), and the effective angle
of internal friction (β). The difference between normal stress and pore pressure is
the effective normal stress. Shear strength based on the Mohr-Coulomb law is
presented as follows:
s ¼ c þ σ À p
ð
Þtan β
ð11:2Þ
Normal stress is the vertical component of gravity that resists down-slope
movement as follows:
σ ¼ δ s g h cos θ;
ð11:3Þ
where δ s is the wet soil density (kg/m
3 ), g is the gravitational acceleration (¼
9.81 m/s
2 ), h is the vertical soil depth perpendicular to the slope (ψ), and θ is the
slope angle (deg). Soil moisture increases the unit weight of soil material and
therefore increases both the resisting and driving forces. Soil moisture creates
pore pressure, which reduces the effective normal stress and shear strength. Pore
pressure in the slope differs among sites and also has large temporal variation. It is
difficult to estimate these values and to include them in this model of a large
catchment. Therefore, we simplified the condition of pore pressure in the slope by
228
P. Luo et al.