What are the main problems of designing a metro in an existing city?

Encroachment is the main problem alongwith traffic movement during construction phase.

Asuming that its underground ,

You will have to avoid piles of buildings there by changing you initially proposed route .

Avoiding existing bulk  water services.

Depending with the technology you are using you might have to continously pump outwater.

Using precast structural member would be highly recommended to aviod ground movement and collapsing of tunnel.

All kind of challenges including Environmental to solve the Transportation issues. 

I have no idea, except what commonsense tells me (Or what I have seen. Chicago El, London underground,  New York Metro or Delhi Metro). Congested streets force you to build underground ducts. No flyovers in the old town. Etc & etc.

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