It is not possible to describe or even summarize foundation design principles in a single post. So first of all, we refer the readers to other posts we made in Geotechnical engineering and foundations. Below we did not distinguish shallow or deep foundations.
We will only list some major points to consider below:
Settlement, such as elastic settlement for all soils and primary and secondary consolidation settlement for clays
Potential for deep seated failure, when a weak layer can be present beneath a stronger layer
Frost heave cycle
The soil parameters are reliable to the degree of the reliability of tests to determine them. The engineer must use his or her judgment heavily when choosing parameters such as angle of internal friction or the K value for lateral earth pressure
Interpretation of subsurface data such as boring logs
The effectiveness of compaction and ground improvement methods (as well as choosing the proper ground improvement method in the first place)
Consideration of water table and seepage effects
Flexible vs. Rigid footing design for shallow foundations or mats
Effect of any eccentric loading / moment from the column / pile cap above. Same for lateral loading. Loads as a result of seismic events.
Consideration of uplift in certain situations that are prone to overturning or subject to uplift force of water
Effect of soil-structure interaction
Expansion potential for clay soils
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