As I understand it (and it's a long time since I studied it) ASR requires alkali, reactive silica in the aggregate (at a pessimum concentration) and water to progress. Assuming you cannot eliminate the silica, you should try to reduce the other two:

 - use a low-alkali cement

 - use pozzolanic cement replacement materials, esp. silica fume or possibly low-alkali fly ash or slag, to reduce the alkalinity of the system with time

 - prevent water from being able to migrate within the concrete by using a low water-cement ratio and carefully monitored curing to reduce capillary porosity

 - ensure proper compaction to prevent gross porosity and water ingress. If using a super-plasticiser, check with the supplier what the alkali concentration is.

- ensure that water management maintenance arrangements for the structure (drainage, guttering etc) are properly designed and adhered to.

ASR (and most other degenerative conditions in concrete) only tends to affect poor quality concrete, or concrete structures where water runoff management is poor.

additional to Dr Prunell: Coarse aggregate grading can be preffered coarser to decrease the expansion levels in long term as seen the results of study given below. The method can also be decreased paste volume necessary with decrease of total surface area according to similar consistency and get economy.  However the fresh mix can be tend to harsh mix, so it must be checked

http://www.sciencedirect.com/science/article/pii/S0008884616300680

0.075-5 mm size portion of aggregates that more tends to ASR may be decreased and 0-0.075 mm can be increased . Because reactive aggregates generally works as pozolanic materials below 0.075 mm in long term. So there is no need extra cementitious materials such as silica fume etc.

Isolate the entire structure to avoid contact with water, or even with moisture in the air. Use of epoxy resin may be an alternative allied with a metallic envelope.