What areas do you require ? of the Finished Grade Surface or the Original Ground Surface or the lift surfaces every 1m (like a sliced area of the embankment at 1m intervals.
You could contour the surface that you want to calculate the areas from and then explode the contours and make the exploded contours into Linestrings and set them to have property Sharp and Texture boundary - Add the contours to the surface model and then if you then apply a Texture of different type to each area between each contour pair you can then use the Find Surface Area command or the Surface Information Report to determine the surface area of each textured area separately - if you want the finished area of each lift then you will have to create a surface for each lift in order to determine the surface area of each lift.
I would have to get the models from you and a detailed description of exactly what surface areas you need to be able to give you a work process for this - I am sure it is possible
ie are you starting with a corridor or a surface. What areas do you really need - we can build them into the corridor and generate the surfaces or we can define areas in the embankment sides to compute areas depending on what area it is you are chasing.