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STABILITY OF SLOPES

Faculty: S.P.ParmarDepartment of Civil EngineeringFaculty of Technology, Dharmasinh Desai University,NadiadMail Add: samirddu@gmail.com

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ANGLE OF REPOSE

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THE AIMS OF SLOPE STABILITY ANALYSES ARE

To understand the development and form of natural slopes and the processes responsible for different natural features.

To assess the stability of slopes under short-term (often during construction) and long-term conditions.

To assess the possibility of landslides involving natural or existing engineered slopes.

To analyze landslides and to understand failure mechanisms and the influence of environmental factors.

To enable the redesign of failed slopes and the planning and design of preventive and remedial measures, where necessary.

To study the effect of seismic loadings on slopes and embankments.

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SLOPES OF EARTH ARE OF TWO TYPES

1. Natural slopes - slopes exist in hilly areas

2. Man made slopes - The sides of cuttings- - The slopes of embankments

constructed for roads railway lines, canals etc.

- The slopes of earth dams constructed for storing water.

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THE SLOPES WHETHER NATURAL OR ARTIFICIAL MAY BE 1. Infinite slopes - The term infinite slope is used to

designate a constant slope of infinite extent. - The long slope of the face of a mountain

2. Finite slopes - Finite slopes are limited in extent. - The slopes of embankments and earth

dams are examples of finite slopes.

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SLOPE STABILITY:

Design and construction of earth dams. Slope failure can often be catastrophic,

involving the loss of considerable property and many lives.

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CAUSES OF FAILURE OF SLOPES:

Gravitational force Force due to seepage water Erosion of the surface of slopes due to

flowing water The sudden lowering of water adjacent to a

slope Forces due to earthquakes

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CAUSES OF MASS MOVEMENTS

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What is the cause of movement?

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FORCES THAT ACT ON EARTH SLOPES

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FORCES THAT ACT ON EARTH SLOPES

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GENERAL CONSIDERATIONS AND ASSUMPTIONS IN THE ANALYSIS 1. Testing of samples to determine the

cohesion and angle of internal friction 2. The study of items which are known to

enter but which cannot be accounted for in the computations.

3. Computation

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Slope Stability

In general you have:• Driving Force – Weight of Slope• Resisting Force – Strength of soil along slip surface

Buttress at toe

W

c

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Slope Stability• In slope stability analysis we determine the Factor of Safety as a ratio of resisting forces to driving forces

Fs = Resisting / Driving

• Theoretically, any slope with a Factor of Safety less than one will fail and any slope with a factor of safety greater than one will not.

• Design focuses on the soil parameters and geometry that will provide the maximum factor of safety.

• Sometimes, the analysis of an existing slope will be what is called a parametric study – that is establishing a factor of safety and performing an analysis that back calculates the strength parameters.

• The engineer will then determine his/her confidence level as to whether or not the soil has that strength through experience, lab, and/or field data.

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THE SHEAR STRENGTH OF SOIL IS ASSUMED TO FOLLOW COULOMB'S LAW

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FACTOR OF SAFETY

1. Factor of safety with respect to shearing strength.

2. Factor of safety with respect to cohesion. This is termed the factor of safety with

respect to height.

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THE FACTOR OF SAFETY WITH RESPECT TO SHEARING STRENGTH, FS, MAY BE WRITTEN AS

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The shearing strength mobilized at each point on a failure surface may be written as

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STABILITY ANALYSIS OF INFINITE SLOPE IN SAND

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the slice is in equilibrium, the weight and reaction are equal in magnitude and opposite in direction.

They have a common line of action which passes through the centre of the base AB. The lateral forces must be equal and opposite

and their line of action must be parallel to the sloped surface.

The normal and shear stresses on plane AB are

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If full resistance is mobilized on plane AB, the shear strength, s, of the soil per Coulomb's law is

The factor of safety of infinite slopes in sand may be written as

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STABILITY ANALYSIS OF INFINITE SLOPES IN CLAY

The depth at which the shearing stress and shearing strength are equal is called the critical depth.

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EXPRESSION FOR THE STABILITY OF AN INFINITE SLOPE OF CLAY OF DEPTH H

the developed shearing stress as Under conditions of no seepage and no pore

pressure, the stress components on a plane at depth H and parallel to the surface of the slope are

Substituting these stress expressions in the equation above and simplifying, we have

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where H is the allowable height and the term c’m/ H is a dimensionless expression called the

stability number and is designated as Ns. This dimensionless number is proportional to the required cohesion and is inversely proportional to the allowable height.

If in Eq. (10.7) the factor of safety with respect to friction is unity, the stability number with respect to cohesion may be written as

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The stability number may be written as

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ANALYSIS OF INFINITE SLOPE WITH SEEPAGE FLOW THROUGH THE ENTIRE MASS

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if the factor of safety with respect to friction is unity, the stability number which represents the cohesion may be written as

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ANALYSIS OF INFINITE SLOPE WITH COMPLETELY SUBMERGED SLOPE

If the slope is completely submerged, and if there is no seepage as in Fig. then

where b = submerged unit weight of the soil.

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METHODS OF STABILITY ANALYSIS OF SLOPES OF

FINITE HEIGHT

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HISTORY

Petterson (1955) first applied the circle method to the analysis of a soil failure in connection with the failure of a quarry wall in Goeteberg, Sweden.

There are other methods of historic interest such as the Culmann method (1875) and the logarithmic spiral method (Rendulic (1935).

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PLANE SURFACE OF FAILURE

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Where, Hc is the critical height of the slope.

the allowable height of a slope is

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CIRCULAR SURFACES OF FAILURE

Slope failure Toe failure Base failure

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ROTATIONAL SLIDE

SLOPE FAILURE

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TOE FAILURE

BASE FAILURE

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FAILURE UNDER UNDRAINED CONDITIONS (U= 0)

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FRICTION-CIRCLE METHOD

The friction circle method of slopeanalysis is a convenient approach for both graphical and mathematical solutions.

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THE FORCES CONSIDERED IN THE ANALYSIS ARE

1.The total weight W of the mass above the trial circle acting through the centre of mass. The centre of mass may be determined by any one of the known methods.

2. The resultant boundary neutral force U. The vector U may be determined by a graphical

method from flow net construction. 3. The resultant intergranular force, P,

acting on the boundary. 4. The resultant cohesive force C.

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ACTUATING FORCES

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RESISTANT COHESIVE FORCES

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RESULTANT OF INTER-GRANULAR FORCES

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RELATIONSHIP BETWEEN K AND CENTRAL ANGLE ’

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TAYLOR'S STABILITY NUMBER

If the slope angle , height of embankment H, the effective unit weight of material , angle of internal friction ', and unit cohesion c' are known, the factor of safety may be determined.

Taylor (1937) conceived the idea of analyzing the stability of a large number of slopes through a wide range of slope angles and angles of internal friction, and then representing the results by an abstract number which he called the "stability number". This number is designated as Ns.

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TENSION CRACKS

If a dam is built of cohesive soil, tension cracks are usually present at the crest. The depth of such cracks may be computed from the equation

Where Zo = depth of crack, c' = unit cohesion, = unit weight of soil.

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TENSION CRACK IN DAMS BUILT OF COHESIVE SOILS

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STABILITY ANALYSIS BY METHOD OF SLICES FOR STEADY SEEPAG

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FELLENIUS METHODFellenius found thatthe angle intersected at 0 in below for this case is about 133.5°.

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BISHOP'S SIMPLIFIED METHOD OF SLICES

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VALUES OF M

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MORGENSTERN METHOD OF ANALYSIS FOR RAPID DRAWDOWN CONDITION

assumptions made in the analysis are 1. Simple slope of homogeneous material 2. The dam rests on an impermeable base 3. The slope is completely submerged

initially 4. The pore pressure does not dissipate

during drawdown

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Morgenstern used the pore pressure parameter B as developed by Skempton (1954) which states

The charts developed take into account the drawdown ratio which is defined as

where Rd = drawdown ratio H (bar) = height of drawdown H = height of dam

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DAM SECTION FOR DRAWDOWN CONDITIONS

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FACTOR OF SAFETY VS DRAWDOWN RATIO

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FACTOR OF SAFETY VS DRAWDOWN RATIO

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Stability conditions for an embankment slope over a clay foundation. (From Bishop and Bjerrum, 1960.)

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SLOPE FAILURE MECHANISM

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PROGRESSIVE FAILURE OF SLOPE

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SLOPE FAILURE IMAGES FROM:

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LANDSLIDE ON CUT SLOPE AFTER INTENSE RAINFALL, HAWAII KAI VALLEY

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LANDSLIDE IN TAIWAN

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SLOPE FAILURE IMAGES FROM:

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A LANDSLIDE IN SAINT-JUDE, QUE. IS SHOWN FROM THE AIR ON MAY 11, 2010.

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What to do ???

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MONITORING TECHNIQUES

Where is the location of slip surface?

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Thank You