Linear drainage ???? - How to clear water from concrete steps ?

[newtonslot]

Hi I'm building a new 6' retaining wall for my front garden
which will be faced eventually in stone.
I've put footings in and am allowing for water drainage through
tanking ,aggregates and weepholes and in one place a 3" pipe
straight across the footings into a small soakaway.
Problem is I have 50 year old concrete steps coming down
through the middle of the wall ,these have water seeping through from between the slabs below the lower 3 rising treads after any rain and presumably backing up behind the step area and finding a route through.
The steps between the wall faces is approx 1 m and the
treads are approx a block and a half wide so I'm minded to
grind out and install a small linear drain at the foot of each of these lower risers with a horizontal outlet pipe draining towards the new weep hole area.
Is this the right way forward in your opinion ?
I was meticulous about designing drainage from the bank
(which caused the previous ancient wall to collapse) but
had no idea that the steps were going to cause such a problem with large amounts of standing water on them after rain.
I really appreciate this site and its fascinating forum
Thanks newtons lot
???

[Tony McC]

Wouldn't cutting out part of the tread threaten the structural integrity of the steps?

Without seeing the site, it's difficult to comment, but I wonder if perhaps installing a perforated pipe to, say, every other tread, and linking it into the existing wall drainage system prior to casting a new concrete overlay to the steps might not be a more realistic option?