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

 

If there is a tension crack in the active case, the depth of the tension crack (z0) is,

 

 

 Passive Case

 

Kp n also obtain from the table

 

 

 (2). Coulomb Theory (Universal solution - wall also can be angular but no water table)

One of the earliest method developed to estimate the lateral earth pressure is by C.A. Coulomb. Soil is isotropic and homogeneous and has both internal friction and cohesion. The rupture surface is a plane surface, and the backfill surface is planar (it may slope but is nit irregularly shaped). the friction resistance is distributed uniformly along the rupture surface and the soil to soil friction angle is phi. there is wall friction, as the failure wedge moves with respect to the back face of the wall a friction force develops between soil and wall. this friction angle is usually called as delta (simple delta).

Active case

Passive case

 Example

(3). Culman's Graphical Method

An expedient method for creating a graphic solution coulomb's earth pressure theory was givenby culmann.

Active case

This is a graphical method, therefore we need to follow below procedure step by step,

1) First draw the embankment according to a scale
2) Draw phi' line from the bottom as base (friction angle in degrees)
3) Draw reference line (alpha - delta) from phi' line
4) Assuming failure planes mark certain failure wedges (Ex: 1, 2, 3 ..)
5) Then calculate weights w1, w2, w3 ... of wedges
6) Select another scale and mark w1, w2, w3 ... on the phi' line
7) From that points draw parallel to reference line
8) Draw the smooth curve connecting intercept points
9) Draw tangent to the curve parallel to the phi' line
10) The line passes through intercept is the actual failure plane. dotted w line shows the pressure acting on the wall ( lateral soil pressure - Pa)
11) We can find weight of the failure wedge and also we can complete the force polygone to find the wall reaction, using coulomb method.

Apply sin rule for this triangle and we can easily find the Pa.

Passive case

This also same as active case procedure, the only differences in,
1) We need to draw phi' line in clockwise from the base
2) From that line (as active case) we need to draw the reference line.