pseudo-static analysis in PLAXI

Dear Navid,

When doing a pseudo-static analysis a constant acceleration is applied for an infinite amount of time. This is of course not so related to real earthquakes where the acceleration continously changes direction and magnitude and for a limited amount of time. So the question is, what information related to practice would the factor of safety and failure mechanism resulting from a Safety analysis would give you knowing that it's based on a constant acceleration over infinite time?

With kind regards,

Dennis Waterman

Thanks for the reply, Dennis. 

As you may be aware, many codes and standards advise employing pseudo-static analysis rather than more complex dynamic analysis to evaluate the stability and safety of small projects as well as large projects during the early design phase or when the seismicity study is not available. This simplified method of capturing the safety factor with limit equilibrium has been widely used and is advised in several guidelines. Since PLAXIS is a finite element programme and must solve equations with both stress and strain, I was wondering if there was any convergence issue that might call into question the accuracy of the safety factor calculated using the C-phi reduction, or if the safety factor was either over or understated in comparison to conventional limit equilibrium?

Thanks for the reply, Dennis. 

As you may be aware, many codes and standards advise employing pseudo-static analysis rather than more complex dynamic analysis to evaluate the stability and safety of small projects as well as large projects during the early design phase or when the seismicity study is not available. This simplified method of capturing the safety factor with limit equilibrium has been widely used and is advised in several guidelines. Since PLAXIS is a finite element programme and must solve equations with both stress and strain, I was wondering if there was any convergence issue that might call into question the accuracy of the safety factor calculated using the C-phi reduction, or if the safety factor was either over or understated in comparison to conventional limit equilibrium?

Dear Navid,

I'm well aware of the fact that pseudo-static analysis is widely used, but being widely used and even advised does not mean it always makes sense or is even correct. For instance, for excavation and tunnel projects pseudo-static analysis doesn't make sense as results depend on the model size. This can also be seen from the examples in the article you're referring to.

For similar situations with simularly shaped failure surfaces at least in static analysis strength reduction will give very similar results as a Limit Equilibrium analysis. However, it of course highly depends on what method of slices one uses in the LE analysis (Bishop, Janbu, Morgernstern-Price, Spencer, Fredlund etc.) as all those methods can give quite a range of safety factors. Not to mention other differences between LE and FE when for instance using structural elements that depend on skin friction etc.

I'm not aware of users doing a strength reduction analysis on the results of a pseudo-static analysis, but since pseudo-static analysis is not more than in increase of effective stress I would expect that  the factor or safety from both strength reduction method and LE would be equally close for the same failure surface. So if that is your concern I would say  you're fine.

However, that does not answer your original question how reasonable it is to assume that the numerical value of the factor of safety on a soil mass with permanent constant acceleration is correct.

With kind regards,

Dennis Waterman