"But updating those data is also a problem."
That is a very good point. You never put more than one piece of information in one field of a database.
If you want to store more than one phonenumber, make a new 'phonenumbers' table.
Not only is it difficult to update a 'serialized' field, you cannot really use it inside query at all.
For ex: if you want to select all users who have phonenumber=555, you will have to do something like "WHERE phonenumbers LIKE '%555%'" and that can be very slow.