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Re: [Fwd: passive pressure for retaining wall]

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Dave Anderson wrote:

> Have any one consider soil pressur under
> retaining wall footing
> to calculate the passive pressure resistance for
> reataining walls
> as shown in example of  REINFORCED MASONRY
> page # 278 or forth edition page # 255
> where he take the avrage soil pressre devided by
> soil weight
> and consider that hieght for passive resistance
> pressure.

His approach does seem to have some logic to it.
Essentially he is saying that the pressure from
the footing above is providing a confinement
pressure for the soil, which will make it behave
as though it is at a greater depth.  In mulling
this over though, I would think that a few
limitations should be looked at.  My first try is

(I will assume that we are ignoring passive
pressure against the face of the toe, the way that
Amrhein does).

Look at the larger picture by cutting out a free
body diagram for shear resistance as follows:

    1.  Start at the bottom of the toe of the
footing and draw a line straight down a distance
equal to your 'virtual' depth calculated by the
Amrhein method.

    2.  Draw a line from this point to bottom of
the key (the corner towards the toe).

    3.  Erase all the soil outside this trapezoid
you have defined.

Assume for the moment that the line you drew in
step 2 is equal to the angle of internal friction
of the soil.  Therefore, your only sliding
resistance comes from one place, the passive
resistance against the plane you have drawn down
from the front of the toe, and this passive
pressure resistance is equal to the Amrhein
Passive Resistance.

We can now try to come up with a couple of rules
about using the Amrhein Passive Resistance.

1.  If your actual angle of internal friction for
the soil is worse than the line that you have just
drawnin step 2, decrease your 'Amrhein Virtual
Depth' till you are comfortably on the
conservative side of this angle.

2.  Don't include more frictional resistance at
the same time as the Amrhein Passive Resistance
than you can justify based on the diagram you just
drew.  I.E.  perhaps use 30% of the typical
friction resistance if you've got lots of angle to

It would also seem reasonable to ignore or
decrease the Amrhein Passive Resistance (or make
some other adjustment) if the horizontal distance
from the front face of your key to the face of
your toe is greater than the horizontal distance
from the face of the toe to the centroid of the
pressure distribution under the footing.  Here's
why this seems (at first glance) like a good
idea.  If you have a key that is way far back, two
things could happen:

1.  The confinement pressure right next to the key
will be very low or zero and that sounds like a
non-starter to me.

2.  The key will push on the local soil which will
push upwards on the heel of your footing,
increasing your overturning problems.

Side Note:  I have seen a couple of soils reports
lately that tell you that when you use passive
resitance and friction at the same time to resist
forces, you should decrease the resistance force
for one of these two factors by 50%.  I think this
is going to be the wave of the future so keep your
eyes peeled.

All this to say, I think it can fly, but be very

Stan Johnson
BS, EIT, APR?   :)