Surface attribute modifier

I’m trying to modify one face of my model to increase the wall count from 2 to 4. The model is basically a 15 mm thick arc. The ends are square so there are 4 sides, a top, and bottom. I only want the 4 walls on the front face surface.

I tried using the modifier with a cube. It modifies the line count to four, but also puts a wall through the model where the back of the modifier cuts through the model. If I make the modifier deeper, off the back of the model, I get the same as a 4 wall global setting. I then tried using a torus shaped modifier with the same result. Its not modifying just the model, it is adding additional structure inside the model.

Is there any way to select a surface to modify?

Thanks