Done some searching to figure out why this drive could not be added back in the array. The result was *dmsetup*.

For an unknown reason, the device mapper (dmsetup) created a map of my drive:

[root@my_server ~]# dmsetup table
[...]
nvidia_eedbfecj: 0 3907029166 linear 8:48 0
[...]

First, the name "nvidia_eedbfecj" sounded very weird for a low level device map.

Then, check out the device major and minor which mathed my drive:

[root@my_server ~]# ll /dev/sdd
brw-rw---- 1 root disk 8, 48 20 juil. 22:25 /dev/sdd

Bingo. the device mapper locked the drive and prevent adding it back to RAID array.

So the solution is quite easy: remove the map of the drive with the command:

dmsetup remove nvidia_eedbfecj

And put the drive back in the RAID array:

[root@my_server ~]# mdadm /dev/md1 --manage --add /dev/sdd
mdadm: re-added /dev/sdd
[root@my_server ~]# cat /proc/mdstat 
Personalities : [raid10] 
md1 : active raid10 sdd[0] sdc[2]
      1953383424 blocks super 1.2 2 near-copies [2/1] [_U]
      [>....................]  recovery =  1.7% (33554496/1953383424) finish=7.6min speed=4194312K/sec
      bitmap: 9/15 pages [36KB], 65536KB chunk

unused devices: <none>