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Re: Pole Embedment Formula

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Thanks for the reply.  It was very responsive,
exactly what I was looking for.  The key elements
I was missing were the shape of soil pressure near
the top and the location of the c.g.'s of the two
opposing soil pressures, and you have provided

Assuming the model is correct and unvarying for
all values of 1) soil stiffness, and 2) the ratio
h/d, the information you have given is all one
would need.  I agree with you that it seems
unlikely that the points do not change, but that
it woould not necessarily have a large affect on
the outcome.

Now it all makes sense to me for piers in soil,
and is consistent with information I have received
in the past with respect to precast piles in soft
soil.  I was always stumped before when I used to
do pier-and grade beams as to what the shape of
the soil pressure distribution was.

As you said, with this information one can
determine the value as well as location of the
maximum moment.  The "point of fixity" in this
model is really just a fiction, a point below the
surface where if one were to assume a cantilever
with a fixed base, the resulting max (reaction)
moment would match the moment obtained in your
model.  That was how several soils engineers I
worked with in the past used to explain it to me. 
They would say that the "point of fixity" was 2'
into the rock, so then the max moment would be P(h
+ 2).  Now that I have a model to work with, the
"point of fixity" has no function or relevance. 
This point obviously occurs somewhere above the
0.68d depth, but would vary depending on the value
of h/d.  I think it would be the depth
corresponding to where the extension of the
straight portion of the moment diagram reaches the
max moment determined at 0.68d.

It is interesting that this model apparently has
the same constants (resultant locations as a
percent of d) for all values of h/d, including (I
assume), h/d=0.  This particular condition occurs
in many pier-and-grade beam-supported buildings,
such as when the bottom of the grade beam is in
the rock already and the pier-to-grade beam
connection is assumed pinned.  Then h=0.

With this model one can also determine the max
soil pressure given P, h, d, and an effective
width of the pier.  Now I am beginning to see why
the formula to determine the required depth is so
convoluted.  If I ever find myself with nothing
better to do :-) I'll see if I can derive the code
formula from the model you presented.... (yeah
right ;-)

Thanks again....

Mark Swingle, SE
Oakland, CA


Charles Greenlaw wrote:
> At 03:38 PM 9/24/99 -0700, Mark Swingle, SE, wrote:
> >Charles, can you elaborate on your [9/16/99] reply?
> >
> >1.  If the pole formlae don't apply in rock, then how would one
> >    determine the depth of embedment required to resist the
> >    lateral force P?
> Answer:   Darned if I know. I would have to figure some way other than those
> two formulas. I could ask this list, but that sorta already happened, to no
> avail. Whoops, Joseph Grill's reply just came in with a method.
> >2.  Then, how would one determine the point of fixity in rock?
> >    How did you come up with fixity at d/6 below the surface?
> >    I was "taught" by several engineers that fixity is at d/3,
> >    although no justification was given.  Sometimes soils
> >    engineers would allow fixity at 2' below the top of rock,
> >    but not all are willing to give an answer.
> Answer: I never said where the point of fixity is. I don't even know what
> "point of fixity" means in these usages. That's why I suggested going back
> to the soil engr for an explanation. That's who used the term.
> Any engineer who can't or won't explain what they are recommending is an
> engineer who worries me. This even includes soil engineers. I still believe
> in "well-established principles of mechanics" that designs are supposed to
> admit of a rational analysis in accordance with.
> Suppose you had a "pole" to be of reinforced concrete cast in place, and
> instead of it being cast in earth, or in rock, you cast it into a great mass
> of monolithic poured concrete, that would have a cylindrical hole formed for
> the purpose. (Or maybe you cast the surrounding concrete around a precast
> pole.) The questions still are: How deep should the embedment be? How far
> down is the point of fixity, whatever that is?  Fancy asking a soil engineer
> the question now. The only difference is the "bedrock" now is man-made to a
> specification, instead of the specification being discovered later by
> testing old rock that's been found there.
> In the max moment quantity and depth determinations I have made, I merely
> used the shape of soil reaction against the pole that the original
> researchers published for the unconstrained condition. I was taught this by
> Walt Buehler, and later came across the research. They agreed.
>         In this shape the upper horizontal soil reaction curve, opposing the
> applied load P, is parabolic with no load at both ground surface and at 0.68
> d; max pressure in that stretch (and its centroid) is at 0.34d. At 0.68 d,
> the pole is rotated but not displaced laterally, hence no reaction pressure
> there. Below 0.68 d, soil reaction on the pole acts in the other direction;
> max value of it is at the bottom and the centroid is at 0.90d. In the
> published model, these proportions are constant. They evidently presume the
> pole is stiff enough that it is rigid compared to the soil. (I am aware that
> the subject of total rigidity is touchy right now --sorry.) At no location
> is the pole unrotated, and at no point between ends is the pole moment
> zero.(ie, no point of contraflexure.) How a so-called "point of fixity"
> relates to this has me stumped.
>         Knowing P, h, d, and the centroid locations for the resisting pair
> of soil reactions, statics gives you the magnitude of the two horizontal
> soil resultants. From the upper one the plf soil load distribution may be
> figured from the ordinates of a parabola. At the depth below effective grade
> where opposing soil reaction totals up to the magnitude of P, pole shear is
> zero and that's where max moment occurs. Find moment it by statics. All done.
>         In spite of the original research's reported findings, I'm not
> satisfied that the height of soil reactions in terms of d are actually quite
> so unvarying, for all ratios of h to d, but forseeable variations would not
> change the outcome much compared to the effect of all the usual
> uncertainties of load and material properties.
> Hope that's responsive,
> Charles O. Greenlaw  SE   Sacramento CA