Mononobe Equation
Mononobe Equation
(OP)
Anyone knows how to deal the case with the negative magnitude inside the square root of Mononobe-Okabe Equation. Can I assume zero when it becomes negative? Thanks!
INTELLIGENT WORK FORUMS
FOR ENGINEERING PROFESSIONALS Come Join Us!Are you an
Engineering professional? Join Eng-Tips Forums!
*Eng-Tips's functionality depends on members receiving e-mail. By joining you are opting in to receive e-mail. Posting GuidelinesJobs |
|
RE: Mononobe Equation
M-O is just Coulomb active theory extended to have a pseudostatic horizontal load in addition to the gravity load. There is an angle (called theta) in the paper I have) that increases with increasing PHA. Inside the square root, there is a term sin(phi-beta-theta) that goes to zero, causing the term inside the square root to have a zero in the denominator, and kaboom, the equation blows up. I believe that causes the base angle of the slide mass, called alpha, to approach zero, which makes the mass of the slide approach infinity. With level backfill, that happens when kh=tan(phi), e.g., 0.577 if phi=30.
I have refs for a couple of papers that purport to improve on that. Can't vouch for them, however. I won't type the whole list out unless you really want them and have access to "Geotechnique" and "Soils and Foundations" and "Geotechnical and Geological Engineering."
RE: Mononobe Equation
RE: Mononobe Equation
The inclination of the critical base plane (alpha) starts at 45+phi/2 at zero acceleration, then flattens out as PHA increases. In the equation for (alpha-beta), cot(alpha-beta) becomes infinite as (phi-beta-theta) approaches zero, which means alpha=beta and the base plane of the critical surface becomes parallel with the surface of the slope, making the slide mass infinite. I'm pretty sure going past there hoses up the geometry (slide going over the top of the wall as well as the load on the wall) so it violates the assumptions of the M-O equation.
Regards,
DRG