Jurijs Kovzels This is a fantastic idea! There are a number of directions or add-on benefits we can retrofit this project with. Keeping the SpongeMat City idea intact, if we remove the insulation layer on the bottom portion of the structure you can lead water to be permeate to the bottom to be collected. Collected rainwater can be stored to be utilized and/or filtered for toilet flushes, sinks, showers, etc. In this regard, we have created insulation, a water collection system, and a structural element to a building.
Naman Mandhan Rubber has been used as an aggregate for concrete previously and if used as a non-fine aggregate - this can allow for water to permeate through at a quicker rate than some other concretes. In regards to 1:1 replacement for soil/vegetation, I'm not an expert on soil qualities, but I would assume this would have to depend on the quality of the soil in the region that you intend to build upon and what may be the best approach. Worst case scenario might be a setting where you have an impermeable and unstable soil base to build off of. This would be a two fold problem - Permeability of a soil works in favor of this design seeing as it allows excess water that does not dry up to be absorbed. A solution may be to create channels from the building leading the water to an appropriate release area. Instability in the soil has many ways to be dealt with, so again the solution to this would depend on the type of soil in the area.
As a non-fine concrete aggregate, a "rubber mat" style application can be utilized in road infrastructure and applied on runways, sidewalks, streets, drive-ways and more! I'm picturing a design similar to Permeable Concrete, which allows water to permeate through the solution at an incredibly quick rate given the right soil conditions. In areas/environments where heavy rain may be a relatively common condition, incorporating this into certain strategic locations of its infrastructure may make roads and walkways safer for drivers and pedestrians, while also reducing flood damage risk to areas that may be at risk.
I'd love to hear any thoughts on some of these suggestions or ways to improve these approaches!