I'm not an expert at LS-Dyna, but I can share some information about Ansys Static Structrual that is relevant. I'm responding here rather than your new post since this post has the images.
In a nonlinear (large deflection ON) static structural analysis, you can turn on the Inverse Option. That takes an input mesh shape that assumes a load (gravity load in your case) is present at Time=0 and solves for the shape of the mesh that would exist when the gravity load is removed at Time=1. To perform inverse solving, simply set theInverse Optionproperty toYesin theAdvancedcategory of the Analysis Settings.
Another way to have the shape of the soil surface remain unchanged when a gravity load is applied is to use the INISTATE command. This command applies a stress to every element in the model at Time=0. If you apply the correct values of stress and a gravity load, then the mesh will be in equilibrium and the mesh won't move at the end of the first step at Time=1.
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