You can take one fast look at the design and see where the biggest problem is going to be: the lateral (spreading) forces against the ends of the bridge will require some clever anchor or ground lock of sorts, otherwise the ends will just shove apart and the middle will collapse.

Notice in the modern model, they have the ends not only anchored, but actually blocked within boundaries that prevent spreading.

Other bridges have used a similar design, but they had much more of a vertical component. Then the forces at the ground were more perpendicular to the earth plane, so gravity and mass of the stones (and friction of the stones against the earth) could better prevent separation.