Contents preface (VII) introduction 1—37

526
15.4.6.1. Standard Method of Slices

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This method (also known as the Swedish method of stability analysis) is the simplest method of stability analysis of embankment dams. It assumes that the forces acting on the sides of a slice do not affect the maximum shear strength which can develop on the bottom of the slice. This method of stability analysis was originally developed only for circular slip surfaces. However, it can be extended to non-circular slip surface also. The procedure for this method is as follows (4):

(i) The trial sliding mass (i.e., the soil mass contained within the assumed failure sur-face) (Fig. 15.28) is divided into a number (usually 5 to 12) of slices which are usu-ally, but not necessarily, of equal width. The width is so chosen that the chord and arc subtended at the bottom of the slice are not much different in length and that the failure surface subtended by each slice passes through material of one type of soil.

1	2
	3	Gravel shell
	4
		2
		5
	1
			6
Gravel shell
Clay core	7

Assumed failure surface

Fig. 15.28 Swedish method of stability analysis
(ii) For every slice of the trial sliding mass, the following forces are determined assum-ing the dam section to be of one unit length:
(a) The total weight (W) of the slice which is equal to the area of the slice multiplied by suitable gross unit weight of the soil mass.
(b) The force (U) due to pore pressure acting on the slice bottom is equal to the average unit pore pressure u, multiplied by the length of the bottom of the slice i.e., U = ub/cos α where, b is the width of the slice and α is the angle between the vertical and normal drawn at the centre of the bottom of the slice under consid-eration.
(c) The shear strength (C) due to cohesion for the slice under consideration is c′ b/ cos α where, c′ is the unit cohesion.
(d) The normal and tangential components of the total weight W are N ( = W cos α) and T ( = W sin α).

(e) The total shear force, i.e., shear strength S which develops on the bottom of the slice at failure equals C + (N – U) tan φ′. Here, φ′ = angle of internal friction in terms of the effective stress.

In addition, there are intergranular forces (E) and forces due to pore pressure (U) acting on both sides of any given slice. While the magnitude and direction of

EMBANKMENT DAMS

527

forces due to pore pressures can be estimated, the intergranular forces are not known. To make computational procedure simple, these forces (E_L and U_L) act-ing on one side of a given slice are assumed to be equal (in magnitude) and oppo-site (in direction) to the forces acting on the other side of the slice (i.e., E_R and U_R). It should, however, be noted that Σ (E_L – E_R) and Σ (U_L – U_R) for the entire sliding mass are not zero.

(iii) The results of these computations are tabulated and the sums of the forces S and T are determined.
(iv) The factor of safety is computed from the relation

F =	ΣS	=	Σ [C + (N − U) tan φ′ ]	(15.33)
ΣT	ΣT

By this method of analysis, one obtains a conservative value of the factor of safety. This is due to complete neglect of the intergranular forces and pore pressures acting on the sides of slices in the computations.
Alternatively the factor of safety for the chosen slip surface is computed using Taylor’s ‘‘Modified Swedish Method’’. This method assumes that: (i) the directions of the intergranular forces acting on the sides of the slices are parallel to the average exterior slope of the embankment, and (ii) an equal proportion of the shear strength available is developed on the bottom of all the slices (4). The computational steps for Taylor’s method applied to failure surface of any arbitrary shape (Fig. 15.28) are as follows (4):
(i) The trial sliding mass is divided into a suitable number of slice so that their chord length and arc length (subtended at the bottom of the slice) do not differ much and the entire bottom of a slice is within one type of soil material.
(ii) For each slice [Fig. 15.29 (a)] following forces are computed: (a) The total weight W,

(b) The forces due to pore pressure acting on the bottom and sides of the slices, i.e., U_L, U_R, and U_B, and

(c) The cohesion force C acting on the bottom of the slice.
(iii) For each slice, the known forces W, U_L, U_R and U_B are resolved into a resultant R [Fig. 15.29 (b)].
(iv) The direction of the intergranular forces acting between the slices is assumed paral-lel to the average exterior slope of the embankment.
(v) Assume a suitable value of factor of safety, say F_D, on the basis of stability analysis carried out by some approximate method, or otherwise, and determine
C
^CD ⁼ _FD

(vi) Draw composite force polygon [Fig. 15.29 (c)] for the whole trial sliding mass includ-ing all the forces acting on the individual slices.

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2

1

3

^E2–3

^E3–4

UL

W3

UR

^UB

C

A

C

D

=

FD

_D
(a) Forces acting on slice 3

R = Resultant

W

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			2
	3
A4	E
	3	–
			4			C
	4
				D3
	E
	4	–
			5
						C
A5						D4
			5
						R	=
						5		W
	2					5
			E			1
			5	–
					6

6

Trial 1
Trial 2
	7
Trial 3

_UB ^UL ^{– U}R

2. 
   Resolution of known forces on a slice
   

(c) Composite force polygon

Fig. 15.29 Modified Swedish method of stability analysis
If the force polygon does not close, choose another value of F_D and compute C_D and redraw the composite force polygon. This is continued until one obtains the safety factor which closes the force polygon. This method can be similarly applied to two-wedge as well as three-wedge systems (Fig. 15.30). The modified Swedish method should be used for final stability analysis in all major embankment dams.