Grout for outside, large gaps

Hi folks,
On my slab porch out front, I placed some randomly positioned/broken up slate tiles in mortar and once it dries will need to fill the gaps. normally you'd use grout, but the gaps are big - some 3 inches... what can I use to fill them? has to be something that hardens that I can seal - if I just throw sand or pebbles down, rain will leak through and dissolve the mortar. do they make grout specifically for large gaps? should I use cement or something?
Thanks everyone...

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