Base Pressure on Retaining Walls 3

[jojolli]

I am designing a retaining wall which will rest on rock. The resultant eccentricity is required to be within the middle half of the footing. The calculated resultant is outside the middle third, but inside the middle half. This causes the bearing pressure q(min) to be negative in the equation

q=W/(B*L)[1-6e/L]

My understanding is this equation is only valid for e<L/6.

What is the proper bearing equation to use when the resultant falls outside the middle third, but inside the middle half?

 

[CarlB]

I don't know the formula, but since you have the resultant location, which acts 1/3 the distance from the toe to the point of zero pressure, you should be able to solve for q max fairly easily.

 

[austim]

hi jojolli,

The calulation is really very simple.

Assume a triangular distribution of bearing pressure (which is the basis of the middle-third rule); now draw a cross-section through your wall, with the resultant load on it, and draw a triangular pressure diagram under it, starting some way from the rear of the base slab.

The base of the triangular pressure diagram will be three times the distance from the front of the base slab to the resultant =3*(L/2-e). (since the resultant has to act at the CG of the triangular diagram). Thus the total area subject to positive pressure = B*3*(L/2-e).

The peak pressure is twice the average,
giving you pmax=2*W/[3B*(L/2-e)].

It is really quicker to calulate it than to explain it

 

[DMWWEngr]

jojolli,

The equation you posted IS valid for e>L/6. However, when e>L/6 there will be a negative value, as you got, at the heel of the wall. This just indicates that there is tension at the heel (NOT GOOD for soil). It is suggested that the wall is redesigned!!

HTH!!

 

[ishvaaag]

You have optimizing sheets in Mathcad Collaboratory able to help you on refining your design.

 

[Terzaghi]

When the eccentricity is outside the middle 1/3, the following equation should be used:

qmax = (4/3)*(V/(B-2e))

where v is the total vertical force and B is the width of your footing.


The length of the area in compression is:

(3/2)(B-2e)

Reference is Army Corps of Engineers manual for Retaining and Flood Walls (1110-2-2502). Look at page 3-12, Figure 3-5.

You can download a free copy of a portion of the manual or the whole thing in pdf format at:

http://www.usace.army.mil/inet/usace-docs/eng-manuals/em1110-2-2502/toc.htm

The soil is not in &quot;tension&quot; if you are out of the middle 1/3. Obviously the wall is just begining to tip off of the base. It could still be stable, but just won't be in full contact with the ground. Table 4.1 on page 4-5 of the reference given above list various factors of safety requirements for different scenarios including when the base is not in full contact with the soil. If you are outside the middle 1/3, you will have a greater soil pressure at the toe, which could cause problems.

Good luck, I hope this helps.

 

[DMWWEngr]

I apoligize. A more appropriate wording would be &quot;tensile stress exists at the heel&quot;. This would be more accurate than &quot;there is tension at the heel&quot;.

Again, I apoligize.

 

[austim]

Terzaghi,

Just a minor correction to your posting.

V in your formula is the load per unit length, not &quot;the total load&quot;.

Subject to that amendment, our two formulae are identical.