mysql> update table_name set field_name=concat(field_name, 'append_string');
example:
mysql> select * from table1;
+----+--------+
| id | field1 |
+----+--------+
| 1 | aaa |
| 2 | bbb |
| 3 | ccc |
| 4 | ddd |
| 5 | eee |
+----+--------+
5 rows in set (0.00 sec)
mysql> update table1 set field1=concat(field1, '1');
Query OK, 5 rows affected (0.01 sec)
Rows matched: 5 Changed: 5 Warnings: 0
mysql> select * from table1;
+----+--------+
| id | field1 |
+----+--------+
| 1 | aaa1 |
| 2 | bbb1 |
| 3 | ccc1 |
| 4 | ddd1 |
| 5 | eee1 |
+----+--------+
5 rows in set (0.00 sec)