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Geo Struct Sparks LLC

When Mononobe-Okabe Equation Doesn't Work


Well yes, you can "break" this program

Posted by geostructsparks on 16 September, 2015 at 19:00

After selling this program for five years, suddenly two separate clients came up with scenarios that "broke" WASP within the same month. By break, I don't mean destroy the software, but rather they managed to create scenarios with infinite results on level ground, for separate projects, one in Japan, and one in Panama.


The examples were both where the designers were in high seismic areas, were on level ground, wanted to simulate "non-moving (at-rest) Ko" conditions, and they were not using particularly strong soil materials. The example from the client below is for a 4.05m high vertical wall with soils with 30 degree friction angle. Following guidelines in the US FHWA manual on earthquake design, they figured that to get "Ko-earthquake" conditions, rather than designing for 0.5 times the PGA, they would design for 1.25 times the PGA - which resulted in 0.66 g x 1.25 = 0.75g.


Results are shown below. Basically they "broke" my promise that WASP would never come up with a infinite active pressure. This is because as the PGA was increased, their calculation actually brings the "infinite slope" scenario to flat ground (Mononobe-Okabe would also result in an imaginary result). In other words, the linear failure surface associated with M-O and the WASP code which provide the maximum active pressure dropped to, and slightly below, and 0 degree angle. At first it appears the graph is not working, but on closer examination Kae is in the range of 400,000, and this occurs only at a failure inclination of 1 degree from horizontal.



Valid options are:


  • Increase the soil strength, 30 degree friction angle would be representative of a only medium dense sand - which if saturated and 0.75g PGA, would liquefy, you've got bigger problems - or if an intermediate sand/silt/clay add cohesion. Increasing the friction angle to 37 degrees for this geometry started getting semi-realistic results.
  • The concept that to get a wall to move less in the earthquake scenario, simplify design for a higher ground acceleration, has its limits.
  • In M-O and WASP the failure occurs when the ground is accelerating away from the wall, and the wall simply cannot accelerate fast enough to keep up. In this case, the designer was developing loads for a buried underground vault, where the soil on the other side of the vault almost certainly will give the vault a push so that it does not "fall behind" the soil that is accelerating away from it at 0.75 g.
  • Be aware how big a "failure envelope" you are making - it basically extends to the horizon.
  • Despite our engineering tools, it may not be realistic to say that a structure "will not move" (the premise of Ko soil pressures) at 0.75g, You could try going to higher quality tools such as finite element programs, however I would be willing to get even these methods would have a hard time modeling 0.75 g without movement(much less being able to validate your results against a case study).

An alternate solution shown here is to increase the cohesion to 10 kPa (208 psf) with the friction angle of 30 degrees - might be appropriate for a silty sand. While for a simple problem such as the client was designing, you probably don't have enough testing, consider this implies that the soil is capable of standing in a vertical cut 1.7 m (5 feet high), which is roughly the maximum vertical cut for trenching allowed by US OSHA. If you have already seen construction on your site, you may have observed trench excavations for utilities this deep constructed vertical...


The next blog post shows how I can model the seismic active pressure using a slope stability program for the example above.

Discussion Published in ASCE JGGE

Posted by geostructsparks on 7 September, 2012 at 5:50

My discussion on Atik and Sitar's paper was published in the ASCE JGGE August 2012 issue (Jonathan Pease, Discussion of  Al Atik, L.  and N. Sitar, 2010, Seismic Earth Pressures on Cantilever Retaining Structures, ASCE Journal of Geotechnical and Geoenvironmental Engineering).  Much of the discussion and questions I included in the discussion are included under the Nay Sayers section. 

Unfortunately, there is no response / closure by the authors in this issue that would answer my questions on their paper.  I will post a copy of the discussion in the next day or two on the site.  The only problem with a discussion on a very dense (generally good) paper is that its like reading a footnote discussion where you need the entire paper to understand what the issues are.

Errata on Paper

Posted by geostructsparks on 24 July, 2010 at 9:26

There is an error in the version of the paper to be published online and in the paper proceedings version for the Toronto Conference.  Equation 10, which computes the mass or weight of the soil wedge, has four additive terms.  Each term should include gamma, or the unit weight; it is missing from one of the terms.  This is corrected in the version available for download from the "Parameter Guide" page as of the date of this entry.  This hopefully should be obvious to anyone using the paper since the units have to be consistent.