To allow zero dates (0000-00-00 00:00:00), you need to remove that restriction.
To remove particular SQL mode (in this case NO_ZERO_DATE), find the current SQL mode:
SELECT @@GLOBAL.sql_mode;
copy the result and remove from it what you don't need (NO_ZERO_DATE)
e.g.:
ONLY_FULL_GROUP_BY,STRICT_TRANS_TABLES,NO_ZERO_IN_DATE,NO_ZERO_DATE,ERROR_FOR_DIVISION_BY_ZERO,NO_AUTO_CREATE_USER,NO_ENGINE_SUBSTITUTION
to
ONLY_FULL_GROUP_BY,STRICT_TRANS_TABLES,NO_ZERO_IN_DATE,ERROR_FOR_DIVISION_BY_ZERO,NO_AUTO_CREATE_USER,NO_ENGINE_SUBSTITUTION
create and open this file:
sudo vim /etc/mysql/conf.d/disable_strict_mode.cnf
and write and past into it your new SQL mode:
[mysqld]
sql-mode=ONLY_FULL_GROUP_BY,STRICT_TRANS_TABLES,NO_ZERO_IN_DATE,ERROR_FOR_DIVISION_BY_ZERO,NO_AUTO_CREATE_USER,NO_ENGINE_SUBSTITUTION
restart MySQL:
sudo service mysql restart