Retaining wall design in California

[koodi]

The California Building Code (the UBC97 code with the state's additional guidelines) states, retaining walls over 12 ft must be designed for earthquakes--a quake with a 500 yr recurrence interval.

The peak acceleration for the quake is 0.65 gravities. Using this acceleration in the Monobe Okabe equation results in RW's with a stability F.S. >8 under normal service conditions.

IS THERE AN ALTERNATIVE EQATION THAT IS MORE CONSERVATIVE THAN THE MONOBE EQ? SHOULD THE PEAK ACCELERATION BE USED IN THE EQUATION? IS THERE ANY GUIDANCE FOR WHAT "EARTHQUAKE DESIGN FOR RETAINING WALLS" ENTAILS?

P.S. The CBC offers virtually no guidance. The walls will result in NO collateral damage if they fail. The height of the wall varies and it will have a maximum height of 25 ft. The soil is typical sandy gravel. Ground water is not an issue.

 

[jdmm]

Usually the static factor of safety of 2 or greater will satisfy your earthquake condition (ref. SEED et al)although 0.65 is a very large acceleration. Mononobe Okabe should be applied upsidedown. That is, the earthquake component should be applied with the component 2/3 above the base (triangular distribution with the apex down) This tends to reduce the overturning factor of safety.

The earthquake acceleration can be reduced if the wall is allowed to move. A paper by Richards and Elms presents a method of reducing the acceleration for use in Mononobe Okabe by allowing horizontal movement of the wall. Allowing horizontal translation of about an inch can reduce the acceleration by about half. If you would like I could get the precise reference.

 

[koodi]

Yes jdmm,
Please tell me the reference.

I think my design problem is determining: What is the "design" horizontal acceleration that should be plugged into the M.O. equation?

If I plug in an acceleration of 0.65 gravities into the M.O. equation, it produces a soil wedge that is forced against the wall at >1 gravity!

IN SUM, AN EARTHQUAKE IS A NUMBER OF IMPULSES. The M.O. equation reduces a number of dynamic impulses into a statics problem. By definition an impulse is a short duration, & an earthquake is a number of impulses. Thus, there must be a "design" acceleration that is plugged into the M.O. equation--that averages peak accelerations.
All is good.

 

[jdmm]

koodi

true,

Newmark used this approach to determine the displacement of slopes and walls. On each impulse the shear strength or resistance is exceeded for a short period of time and then the impulse is reversed. The result is a step-wise displacement. If you have to resist all of the horizontal motion then you have to design for the full horizontal acceleration. If you can accept some displacement without collapse then the design accceleration can be reduced.

Richards and Elms say that the design horizontal acceleration can be reduced to:

Horizontal design acceration=((0.2*Vh^2*ah^3)/d)^(1/4)

where Vh is the design horizontal velocity
ah is the horizontal acceleration of the earthquake
d is the limiting displacement (what you will allow)

to check your equation, for an acceleration of 0.65g and a horizontal velocity of 0.65 inches/second and a limiting displacement of 1 inch the design acceleration is reduced to 0.39g

I will find the reference at work and post it tommorrow if possible

 

[koodi]

jdmm,

How did you arrive at the "design horizontal velocity," Vh, in the equation above.

It would help me out if you could post the reference. I don't want to submit my design calc's without backup.

The USACE, FEMA, and UBC are deliberately vague.
Go figure,
Koodi