A costly method  would be ground freezing and obtaining a required quantity of sample. If that sample is then tested for its water absorption and  retention by a water column, the structure the porosity might be obtained. But temperature of water might affect the test.

A method of choice to determine soil porosity is X-ray microtomography (XMT) coupled with software to construct 3D images of the porosity network and to calculate for example pores volumes, pore surfaces and pores connectivity.

Then if you want to determine the water/gas flow through aggregates you can use some modelling flow.

I think the main question when you want to determine soil porosity with XMT is the resolution you want to go, because higher is the resolution, longer the scan will take, higher the price will be, and more difficult the data analysis will be (each run will be many GB).

These methods have already been used on soil aggregates. If you want to scan single aggregates, you will not be able to scan "huge" aggregates (e.g. 10 cm or 20 cm), or tiny (e.g. 1 mm) as the machine present a higher limitation to the maximum size you can put in the scan, and lower limitation to the smallest resolution you can go, This is also true is you want to scan a soil core. Also, to get repeatability of your data (e.g. the porosity of a certain size of aggregates), you will have to scan several single aggregates (e.g. 8 to 10).

I paste below a link to one of my article that looked at soil porosity of soil aggregates before and after soil compaction. We used XMT and flow modelling.

https://www.researchgate.net/publication/272201766_Analysing_the_impact_of_compaction_of_soil_aggregates_using_X-ray_microtomography_and_water_flow_simulations?ev=prf_pub

Article Analysing the impact of compaction of soil aggregates using ...