Any way to give thickness to an object with opacity map?

V-Ray V-Ray Common Off-topic
1

I have a plane with an material with opacity map. I want this plane have some thickness. Like extruding but only the areas which are white on opacity map.

Is there any way to make this?

2

I’m not sure I understand correctly but maybe clipmapping could a viable alternative

3

Thanks. I alreay tried this: I play with shift and water level but shadows look fake because my object is adjacent and in front of poly of another object.