If you can find the July-August issue of "American Scientist", the magazine of Sigma Xi, the scientific research society, on page 280 is an article titled "William Barclay Parsons, The man behind the subway brought engineering to New York high society". This covers his design using trenches covered with concrete with utilities above instead of tunneling and also some of his other work such as helping with the design of the Panama and Cape Cod canals and building a thousand mile railroad in rural China. I think the journal may be online.
I see that you have to be a member or pay a subscription so an excerpt is below. You can probably find public domain information by searching on the name (the son, not the father)
"....What underlay the island of Manhattan remained largely unexplored before the age of skyscrapers, which naturally required deep and firm foundations and thus deep and firm knowledge of the bedrock on which they would rest. In preparation for designing a subway system, Parsons had to map the ground through which it would pass. In the course of assessing the geology of New York, he walked and plumbed much of the projected subway route and discovered that the island's bedrock—known as Manhattan schist—was not located uniformly deep underground. In lower Manhattan and in what is now known as Midtown (and not by accident the two areas where the city's tallest buildings would become clustered), the rock was relatively close to the surface, but elsewhere on the island it was very deep. The undulating configuration and irregular composition of the bedrock would have presented technical difficulties to conventional tunneling, which led Parsons to opt for alternative methods of constructing the subway tunnels.
Parsons's recommendation of relatively shallow tunnels constructed by means of cut-and-cover technology stemmed from his direct exploration of the geology of Manhattan Island. This differed greatly from that of London, which was underlain with relatively soft clay through which deep tunnels could easily be driven. But the deep-tunnel system demanded elevators to get people between the streets and underground stations, a necessary adjunct that was costly to build and time-consuming to use. Anyone who has entered or exited the London tube at the Russell Square station, for example, knows how frustrating it can be to wait for the large but limited lifts and how exhausting it can be to have to use the stairs when the elevators are out of order. Placing New York's subway close beneath the street surface would enable riders to move quickly in and out of most of its stations by means of relatively short flights of stairs. ..."