Comparison study between traditional and finite element methods for slopes under heavy rainfall

Peer review under responsibility of Housing and Building National Research Center.

Figures & data

Fig. 1 State of slope under rainfall.

Fig. 2 Stress conditions in infinite slope with seepage parallel to the slope. (a) Diagram of slope. (b) Force polygon. (Cedergren [9]).

Fig. 3 Stress conditions in infinite slope with vertical seepage. (a) Cross section. (b) Force polygon. (Cedergren [9]).

Fig. 4 Division of potential sliding mass into slices.

Fig. 5 Forces acting on a typical slice.

Fig. 6 Janbu’s correction factor for the simplified method.

Fig. 7 Illustration of Fellenius method.

Fig. 8 The Mohr–Coulomb failure criterion.

Table 1 Parameters of the Mohr–Coulomb model.

Symbol	Description	Units
E	Elasticity modulus	[kN/m^2]
υ	Poisson’s ratio	[–]
${\phi }^{⧹}$	Effective friction angle	[0] Degree
${\text{C}}^{⧹}$	Effective cohesion	[kN/m^2]
ψ	Dilatancy angle	[Degrees]
Einc	Incremental increase in elasticity modulus with depth	[kN/m^2/m]

Fig. 9 Dimensions and boundary conditions of finite element model.

Fig. 10 Profile of slope in case study.

Table 2 Parameters used in the case study.

	Unsaturated	Saturated
Volumetric water content θ (%)	28	42
Bulk density γ (Kn/m^3)	19	20.4
Effective cohesion c (kPa)	10	5
Effective angle of friction ϕ′ (^0)	29	27
Matrix suction Sa (kPa)	−39.375	0
Permeability coefficient k (m/min)	/	6 × 10^−4

Fig. 11 Shading of the total displacement increments for un-saturated case using finite element program Plaxis.

Fig. 12 Shading of the total displacement increments for saturated case using finite element program Plaxis.

Fig. 13 Evaluation of safety factor for un-saturated case using finite element program Plaxis.

Fig. 14 Evaluation of safety factor for saturated case using finite element program Plaxis.

Table 3 Summary of results for factor of safety.

Method	Factor of safety
	Unsaturated	Saturated
Finite element method	2.547	1.953
Simplified Bishop method	1.094	0.722
Simplified Janbu method	1.093	0.728
Fellenius method	1.065	0.723