At the basic level, Staad/Pro has facility for moving loads. Some examples are given along with the software. Have a look at it. It generates multiple load cases, based on load path. Will that be fine for your work ? If you need more detailed non-linear analysis with soil material model, you may try other software, like, PLAXIS. You may need to check the user manual. SAP2000 will have limited non-linear modelsfor soil and moving loads. You may start experimenting the same.
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