Keep in mind that being need blind is an admissions process and meeting 100% demonstrated need (which Dartmouth commits to do for all admitted students) is a financial aid process.
As an international student, your ability to pay was a factor in the admissions process.
Based on the financial aid office evaluating your family’s income and assets, they felt that your family could afford to pay approx $30k even though they only want to or are committed to only paying 10k.
As txstella stated, your financial aid package is calculated based on what Dartmouth feels your family can afford to pay, not what they are willing to pay or self imposed limits on the max that they feel that they are going to pay.
If you feel that there is something that Dartmouth overlooked (not my parents only want to pay this, we live in an expensive area, etc.) when calculating your financial need (unreimbursed medical expenses, job loss, etc) then contact financial aid and request a financial review. Be ready to provide documentation to substantiate your case.