What are some reasons why the budget deficit and non budgeted spending have been adding more than $500 billion to the national debt in recent years?

There are numerous reasons, things like war, immigration, increased poverty, or things like unpredictable natural disasters. When a hurricane strikes and destroys entire cities and housing it has to be fixed quickly and that is spending that was not planned since you can't expect things like that. Wars often cost much more than what was planned because bad things happen and they need to be fixed. Immigration can lead to an increase in social welfare spending since not all immigrants find a job quickly and establish themselves in the society.