Failure of Infinite slopes - Part 01

Considerable evidence is available that slope failure in homogeneous soils usually occur on curved failure surface. In many circumstances ( for  example zoned dames and foundations on weak strata), stability analysis using plane failure of sliding is more appropriate and yields excellent results.

 Failure of infinite slopes, we can analyze using several techniques,

(1). Using planer failure surface (transnational slides)
     - Culman method

(2). Using curved failure surface (rotational slides)
     - Circular failure surface
         1. Circular arc method
         2. Stability number method
         3. Method of slice  (widely use, base the many softwares) 
         4. Morgestern and Bishop method
         5. Cousins charts
    - Non - Circular failure surfaces

Slope Stability

If the ground surface is not horizontal, a component of gravity will tend to move the soil downwards.

How slope failure will occur : If the driving force can overcome the resistance offered by the surrounding material along a rapture surface, slope failure will occur.

Slope stability analysis involves comparison of the developed shear stress along the most likely rapture surface and the shear strength of the soil.

Slope Failure - Land slides

Slope failures

Slope failure describes a wide variety of processes that result in the downward and outward movement of slope - forming materials including rock, soil, artificial fill or a combination of these processes. the various types of landslides can be differentiated by the kinds of material involved and the mode of movement.

Types of slope failures / movements

1) Slides
2) Falls
3) Topples
4) Flows
5) Lateral spreads

(1). Slides 

There are two major types,

- Rotational slides

The surface of rupture is curved concavely upward and the slide movement is roughly rotational about an axis that is parallel to the ground surface and transverse across the slide.

Lateral Earth Pressure - Part 03

Sloping back fills - Cohesive

For this there are 3 methods,

 (1). Extended Ranking Theory 

If the soil have both cohesion and friction Rankine method was extended by Mazindrani and Ganjali.

Active Case
 

Ka n we can observe from the table using alpha and phi ' and c'/gamma z, z is the height of the fill

 

Lateral Earth Pressure - Part 02

Cohesion less Back fills

For Cohesion less back fills,
(1) Active state,
(2) Passive state,

Without water table - as usual method (please go through part 01)
With water table - Need to draw horizontal pressure distribution and water pressure diagrams. sum of those two diagrams equal to the final diagram. (using final diagram we can find final force and the line of action)

If there is a surcharge, on top of the ground it is also need to draw diagram for that and add up all diagrams to get the final.

If there is a surcharge, due to that this diagram need to add,

 

Lateral Earth Pressure - Part 01

If the wall AB is static, if it does not move either to the right or to the left of its initial position. The soil mass will be in a state of elastic equilibrium, that is the horizontal strain is zero. ( at rest condition - there is no lateral deformation.

The ratio of the effective horizontal stress to the vertical stress is called the coefficient of earth pressure at rest - K0

Stress Distribution of Soil (Layered Soil Medium)- Part 04

Stress distribution through layered soil mediums

Burmister developed the chart given below to estimate the vertical stress distribution through a two layer medium. the chart is developed to estimate the vertical stress below the center lines of a circular loaded area and the thickness of a layer 1 is assumed ti be equal to the radius of the circular loaded area.

Stress Distribution Trough Soil - Part 03

Stress Isobars

Isobars of the vertical stress under footing are developed based on the Boussinesq Equation. Pressure isobars, developed to estimate the vertical stress under a squire and a strip footing, is given below.

Stress Distribution Through Soil - Part 02

Newmarks charts 

The Boussinesq equation for the vertical stress given in previous equation. to develop Newmarks charts we need to re-arrange that equation. 


where,
qv = point stress (delta sigma)
q0 = vertical stress increment in foundation level

As the stress ratio qv/q0 varies from 0.1 to 0.9, the ration r/z varies as given in following table.

Stress Distribution Trough soil - Part 01

When a footing is loaded, a certain stress will be applied on the soil immediately below the footing. the applied stress in the soil will decrease away from the footing location as the stress is distributed over a large area.

Consider a small soil element as shown below and the stress applied on the element under 'Plain strain condition' (plane strain condition : strain is applied in one plane - Y direction no strain)