it is difficult to keep the water in the chute. High velocity, supercritical flow tends to form waves and hydraulic jumps and requires substantial freeboard. splash over will run under the chute and erode the base material. if the slope is steep than headcutting will soon occur. the chute should be enlarged to contain the water and the edges should be protected with rock or concrete. filter material should be used under the rock. un-compacted, dumped soil is not recommended. base material under the chute should be good granular structural fill, properly compacted. if that is too difficult to construct, then CLSM might be a better choice. replacing the concrete chute with gabions or a pipe down drain might be a good alternative.
edit:
after reviewing the photo, it is clear that the lack of an inlet structure to the chute is probably the root cause. and furthermore, the chute looks far too small to handle anything other than a trickle of water.