Alter column opreation failed due to disk space in SQL Server

When i apply alter column on table, it full log file and disk too, and failed alter operation. Why this happened even table size is less than free disk? Can please suggest a way to complete this operation without making free space in disk.

Scenario :

1. Alter column size from numeric(9,10) to numeric(18,6)

Statistics :

1. Table size - 40 GB


2. Table rows - 40 million


3. Disk free space where this table located - 50 GB


4. Database Recovery model : Full and configured mirroring


5. SQL Server version - 2012 ENT