## Pseudo static acceleration and model size

## Pseudo static acceleration and model size

(OP)

When using numerical modeling software such as Plaxis 2D to model slope stability or a tall retaining wall with seismic loads, a quick method is to use the pseudo static acceleration (as opposed to several time histories and full dynamic analysis).

However, the stability and/or back of wall force results are dependent on the model size (horizontal X axis dimension).

If the model is very large dimensionally, the lateral inertia forces tend to accumulate artificially high at the wall face. I couldn't find any guidance from Plaxis on the Knowledge Base.

Is there a rational way of sizing the X and Y dimensions of the model so the inertia loads are in proportion to what a limit equilibrium model would show? Or is there a way to apply the acceleration to a portion of the soil clusters but not other clusters?

Yes, I realize I can simply run a Slide analysis, but limit equilibrium provides no real displacement or soil state information.

However, the stability and/or back of wall force results are dependent on the model size (horizontal X axis dimension).

If the model is very large dimensionally, the lateral inertia forces tend to accumulate artificially high at the wall face. I couldn't find any guidance from Plaxis on the Knowledge Base.

Is there a rational way of sizing the X and Y dimensions of the model so the inertia loads are in proportion to what a limit equilibrium model would show? Or is there a way to apply the acceleration to a portion of the soil clusters but not other clusters?

Yes, I realize I can simply run a Slide analysis, but limit equilibrium provides no real displacement or soil state information.

## RE: Pseudo static acceleration and model size

I don't think there is a guidance, but do you think that force on wall incrase as you incrase X? Linearly? It seems impossible, if you want I can work on a parametric analysis for an embedded wall. Would not take too much time. Increasing X and checking the moment and shear on the wall.

## RE: Pseudo static acceleration and model size

Yes, increasing the horizontal dimension X behind the wall increases the lateral force on a wall when using a pseudo-static acceleration. That is, applying a horizontal acceleration at the base boundary.

Not linearly, as you will see from a parametric study. There is a certain range of sensitivity. The insensitive range (very long) is not the correct range.

My experience and preference is Plaxis 2D, but I am certainly interested in the results of any nonlinear FEA program.

Not the case for time history.

Think about a pan full of not-so-rigid Jello, 1 inch thick. Then think about a pan that is 1/3 full of Jello, also 1 inch thick.

Now take both pans, and rotate them 90 degrees about the horizontal axis, so the Jello is now vertical, being sheared by gravity. More Jello in the pan = more force parallel with gravity. So it is with soil.[If you mother made very stiff Jello, this visual does not work so well. My mom made semi-fluid Jello that would drip in this experiment.]

I am not inferring this is reality. It is certainly not, of course. Pseudo-static is a crude approximate for structural analysis, and very crude for soil-structure interaction, but we use it because it is quick and relatively easy and somewhat intuitive. Just trying to bound this error inherent in the uniform, perfectly coherent acceleration simplification.

## RE: Pseudo static acceleration and model size

As you say, pseudo-static analysis is really easy. I use it mostly on excavations and slopes. However, if this is the case, we have really a problem.

I get your jello example. However, I would expect dissipation of lateral force through soil into the boundaries. I will perform a simple parametric analysis to see for myself, in 2-3 days.