You have a good width for the joint. What is the magnitude of movement?
You might look into using a sheet membrane adhered to each side, or use a backing material and a flowable caulk material with a bond breaker (polyurethane or polysulfide depending on how pristine the surfaces are). Depending on type of movement or load, you might want to provide a stainless cover plate or something to protect the joint.
The gap width is 12 cm which is equal to the expansion joint width. in fact I am thinking of adding a flexible pipe connected at both ends of the concrete ditch.
A few ideas,
Could be a fabricated sheet metal "flume", attached and sealed/caulked on the upstream side. Could use slotted connections on the downstream end to accomodate expansion/contraction. If you are worried about the seal on the downstream side a bearing plate sealed to the concrete deck beneath the end of the flume might enable a tight enough fit with the flume section that seepage would be minimal, yet still provide for sliding from expans/contract.
