# 209672999 Slope Stability

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SLOPE STABILITY CONTENTS:

1.0 Introduction

1.1 Types of slips

1.2 Procedure for estimating stability

2.0 Total stress analysis 2.1.0 Rotational analysis

2.1.1 Effects of tension crack

2.1.2 Partly submerged slopes

2.1.3 Rapid draw-down

2.2 Estimation of stability (Taylor)

2.2.1 Undrained cohesive soil 2.2.2 Frictional resistance

2.2.3 Layered soil

2.2.4 Location of the critical circle

3.0 Effective stress analysis

3.1 Soil strength considerations 3.2 Effective strength parameters

3.3 Total stress conditions

3.4 Method of slices

3.4.1 Swedish method

3.4.2 Bishops method 3.5 Summary of methods of slices

4.0 Choice of factor of safety

5.0 Cuttings in over-consolidated clays

REFERENCES

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Slope Stability v1.00 October 2010

STABILITY OF SLOPES 1.0 INTRODUCTION

The degradation of natural or artificial slopes (in deep cut excavations or high embankments) is the result of mass movements which occur chiefly owing to the

action of gravitational forces, sometimes supplemented by earthquake forces.

The downward movement of rock or soil masses occurs when the equilibrium is disturbed along a certain plane (within the slope) and the shear stresses along it exceed the available shearing resistance; this can occur as the result of either an

increase in the shear stresses or a reduction or deterioration of the shear strength. A distribution of landslides (nearly 7000) in the UK is shown in Fig.1A.

The manner in which a slope fails is chiefly controlled by the following factors;

geological

hydrological topographical

climatic conditions extent of weathering of rocks / soils

This results in a great variety of types of mass movements see Fig.1 below.

1.1 Types of slips

Figure 1 Basic types of mass movement

Falls are usually associated with short-term failure of steep slopes (in artificial excavations or river banks) usually in rock with vertical joints, Fig.1(a). As the lateral support is removed, bulging occurs at the slope foot and tension cracks

open behind its crest, usually along the pre-existing fissures. This leads to progressive increase of stresses in the root of the separating mass and to the

eventual collapse; the process is frequently accelerated by water entering the tension cracks.

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Slope Stability v1.00 October 2010

Figure 1A Landslide distribution in the UK

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Slope Stability v1.00 October 2010

Rotational slides occur characteristically in slopes of fairly uniform clay. The failure surface is curved and usually deep seated. The slipping mass slumps,

sinking at the rear and heaving at the toe, Fig.1(b). Approximately circular rotational slips are associated with cut slopes of uniform clays whereas non-

circular rotational slips with natural slopes of over-consolidated clays in which weathering has produced a softened upper layer.

Translational slides generally result from the presence of a heterogeneity, in the form of a weak soil layer, located at shallow depth beneath the slope. The

failure surface is approximately planar and parallel to the ground surface, Fig.1(c). If the plane of weakness is at a moderate depth beneath the slope, a compound slide of partly rotational and partly translational character may occur.

Flows are mass movements in which there are no well-defined failure planes,

Fig.1(d). Skempton and Hutchinson (1969) differentiate between earth flows and mud flows; the latter are glacier-like in form whereas the former are considered to be transitional in character between the slides and mud flows.

From the slope stability point of view the most dangerous conditions are

encountered in areas where in the past the soils have been deformed and folded by tectonic activities or ice advances or where previous mass movements have

taken place. In these circumstances pre-existing slip planes (slickensides) are usually present along which the shear strength is only a fraction of the strength of the intact soil.

The typical features of landslide areas are the following:

a) The presence of depressions and bulges on natural slopes. b) The presence of deformed trees with trunks bent in random

directions. c) The existence of springs on slopes and outcrops of water-bearing

strata. d) The existence of slickensides and deformed layers of clays (these

can be best observed in trial pits or by breaking down undisturbed

tube samples).

Above information may be found in Z Wiln and K Starzewski 1972, Vol 2 Chapter 3, section 3.1 pp73-74 [Book out of print].

In summary, a slip can occur due to

(A) An increase in shear stress (e.g. adding a surcharge) OR

(B) A deterioration of soil strength over a number

of years (20 100 years) OR

(C) A combination of the above These notes cover the analysis of rotational circular slips.

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Slope Stability v1.00 October 2010

1.2 Procedure for estimating stability

There are 3 steps in process of estimating stability:

1. Estimate disturbing forces The components are;

gravity acting on body of soil

super-imposed loads (if any) seepage force due to water flow (if any) earthquake forces (not dealt with in these notes)

2. Shearing resistance of soil

- Determine the number, thickness and average strength parameters of each soil layer.

- Soil strength equation for;

total stress, f = cu + n tan u

effective stress, f = c + ( n - u) tan

where;

f = shearing resistance at failure.

- Include a factor of safety, F, to limit the maximum mobilised shearing resistance on a failure plane;

= f

F REF: DW Taylor, 1948 Fundamentals of soil Mechanics; section 16.6 pp 414-

417 describes in detail how different F values for Fc and F may be combined

3. Select appropriate analysis

There are 2 approaches;

(a) Limit state equilibrium:

- Determines the overall stability of the sliding mass.

- Method is to analyse various potential failure surfaces to determine which has the lowest F.

- This method of analysis is generally not sensitive to the chosen shape of failure surface.

- A circular arc is chosen because it is the simplest to analyse and

is usually sufficiently accurate. [These notes consider limit state analysis in detail]

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Slope Stability v1.00 October 2010

NOTE: The computed critical failure arc may not coincide with the actual failure surface, however, their factor of safety (F) values will be similar.

(b) Stress analysis: [Not covered in these notes]

- Uses the principles of elasticity to evaluate stress and strain

throughout a slope.

- Finite element analysis is a powerful analytical tool, but its potential accuracy is limited by the highly variable and non-

linear characteristics of most soils.

2.0 TOTAL STRESS ANALYSIS

(Stability of cohesive soils)

- Undrained conditions apply (i.e. during or at end of construction).

- Soil strength parameters are cu and u (N.B. if Sr=1 then u =0o).

- The excess pore water pressure due to loading has not had time to dissipate to any extent.

2.1.0 Rotational Analysis

A series of trial slip surfaces with various centres of rotation, O and radii, R (see Fig.2) are analysed to determine the most critical combination of O and R values, i.e. to find which potential failure circle has the lowest F value.

Figure 2 Rotational analysis

Where; G = centre of gravity

Length of arc, A-B = R x rad

= R x o / 180

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Slope Stability v1.00 October 2010

Taking moments about O;

W d = cu R rad R = cu R2 rad

[NB analysis for a 1m wide strip of arc AB]

F = Restraining moment

= cu R

2 rad

Disturbing moment W d

2.1.1 Effect of Tension Crack A tension crack, see CD in Fig.3, always develops behind the crest of a slope as

failure start to occur in cohesive soil. Therefore, regular inspections of the ground behind the crest is advisable when a cutting is being excavated.

Figure 3 Rotational analysis with tension crack

Cohesive soil can support a vertical face, C-D in Fig.3, to a maximum height, zc;

zc = 2cu

It is likely that the tension crack will fill water - this causes an extra thrust

adding to the disturbing moment (lever arm, yc);

= 0.5 w zc2

yc

NOTE: The tension crack reduces the weight of the arc to Wt and its lever arm

to dt and the sector angle to c radians;

F = cu R

2 c ( / 180)

Wtdt + 0.5 w zc2 yc

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Slope Stability v1.00 October 2010

2.1.2 Partly submerged slopes

Figure 4 Partly submerged slope In the above diagram;

W = total weight of soil and water in area B

W = submerged weight of soil particles in area A

The pressure of water provides and additional restoring moment (i.e. resisting movement about O). This moment exactly balances the moment (about O) of a

mass of water filling the space below the external water level and above the rupture surface.

Therefore, use submerged unit weight, sub to allow for external water level;

sub = ( sat - w)

where

w = 9.81 kN/m2

F = cu R

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