Dynamic Analysis - sub steps definition and element size

Question

Hello, 
 I'm assembling a 3D dynamic analysis that incorporates part of the bedrock due to the irregular profile of this stratum. Because of the size of the model, I have small elements for the soil layer and bigger elements for the bedrock (of the order of 40 m). The bedrock has a Vs value that is about 4 to 5 larger than the Vs of the soil deposits on top. 
 My doubts are related to the size of the mesh for the bedrock. 
 1. Does the recommendation of the effective element size equal to the critical wavelength divided by ten shall be considered for the bedrock? 
 2. Can I proceed with an element size for the bedrock as long as the distance traveled by the fastest shear wave during one time step is less than the element's size? The distance is calculated as a function of the Vs of the material, the time step, and the number of substeps. For example: 
 a. I have a Vs=650 m/s, Plaxis time step = 0.005, substeps=4; then 
 b. The distance traveled during a time-step is 650 * 0.005/4 = 0.81 m. 
 c. Element size should be larger than 0.81 m. 
 Thanks for the assistance on this request.

Dennis Waterman · Answer

Dear Daniel, 
 It depends a little bit on the kind of dynamics analysis you're doing. In principle the two recommendations are meant to assure sufficient accuracy: 1) Since waves are discretized in the stress point of an element, we want sufficient discretization points to model a wave. We wouldn't want to discretize a sine wave in only 4 points for instance, because that would give us a saw (triangle) wave. Or even worse, have elements so big that a wave can completely disappear in between 2 stress points/ 2) This is more a time step recommentation: we don't want time steps to be so large that in a single time step the wave will skip one or more elements entirely. 
 So generally we use 1) to determine the element size and then 2) to determine the step size, whereas you in your example actually use 2) to determine the element size. But to come back to my first remark....if the source of the dynamic load is something at ground level, for instance pile driving or traffic load, then we don't care too much about the accuracy close to the boundaries as the signal will be already weaker there anyway and is going to be dissipated. However, if you're doing a seismic analysis where the earthquake signal is applied at the bottom, we do want the smaller elements there to not immediately make the earthquake signal inaccurate when it enters the soil. In general the idea of only refining the mesh close to the project area doesn't work that well for seismic analysis. For a seismic analysis a more regular mesh with approximately the same element size everywhere is better in terms of accuracy. 
 With kind regards, 
 Dennis Waterman