What is the procedure for probabilistic seismic hazard analysis to study the behavior of shallow foundation?
Probabilistic seismic hazard analysis (PSHA) and Behaviour of shallow foundations are two different topics. You may need to apply the results from PSHA for reliability based design of shallow foundations. For any specific site, PSHA gives you the the probable earthquake scenarios at various earthquake sources around you and their distribution with time. With this data, you can check if your shallow foundation built at that site can withstand the predicted seismic effects within its design life or not.
You probably mean probabilistic seismic hazard analysis of shallow foundations. You have to use an existing empirical or developed analytical model of your choice with known parameters and variable types to determine the safety indices and their corresponding probabilities of failure using any suitable software. You may consider First Order Reliability Method, MATLAB, etc.
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