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It would be worthwhile knowing how permanent the construction is to be - for a season or permanently. Similarly to what scale and kind of infrastructure - is it a programme for 100s of schools or for a diplaced population camp? An idea of water table would help as well.
Initial thoughts would be that you would have to dig the latrine in the same way as a well in unconsolidated sediments with concrete rings or some other lining being lowered down as you dig.
I don't know how deep the water table is but if it is very high, you might need to consider an above ground construction with a concrete tank as the pit with the superstructure sitting on top of it accessed up steps.
Obviously the cost of either of these options is higher than for a regular latrine.
Best regards
Martin