Narrative:

The flight was supposed to be the first officer's leg; but I decided to fly it because of the low ceilings going south into dca. Enroute the ATIS showed 600 ft. Overcast and I sent an ACARS to dispatch telling them I was high minimums and needed to add 100 and ½ ft. The return message was wait until the next update to make a decision on the approach. I told the (first officer) first officer that if the ceilings did not improve we would go to iad. We then set up and briefed the lda (localizer type directional aid) Z runway 19 into dca. We checked the ATIS again and it was showing a slight improvement to 700 ft. And I sent dispatch a message saying we were going to ZZZ if we couldn't get in to which the response was; you'll be legal to add the 100 and 1/2 ft. Going north. Confused by the 'north' part we checked the ATIS again and it showed ILS runway 1. (2 specials had come out back to back). So with that; having begun a descent on the STAR and getting into terminal phase I set up the ILS and briefed it; we were instructed to slow to 210 kts. And I informed ATC that we wouldn't be able to make one of the altitudes to which they responded that was fine; just descend and maintain 9000 ft. My first officer had a great attitude and was keeping up as best he could but the environment started to become flustered once they switched the runways again informing us that we had to go back and set up the lda Z runway 19 again.at this point it became slightly task saturated as we were setting up again and being vectored on to the approach. Once cleared at 3000 ft. I set next altitude crossed fergi at 3000 ft. And began the approach. Everything up until the final approach fix seemed normal and it did slow down a bit but I was concerned about not getting in because we queried ATC and they told us that there were some missed approaches due to ceilings. When I called for the before landing checklist the first officer ran it. I had been doing my 'point 2 prior' calls but was slightly late on the last one and descended right on the final approach fix at which point I hit the vs button and scrolled down; I think it was between 1500/1700 ft/min. I know that at my reference speed I should only have been doing 800 or so. Before any warnings I scanned and realized what I had done and immediately scrolled to reduce the rate of descent to be below 1000 by 1000. This is when my first terrain call came; I reduced more and then ATC told us we were low; we broke out of the clouds and got one more terrain. I have no reason to have not gone around other than being task saturated and thinking of it being worse in the go around. Although the first officer was great there were some missed items as there tends to be and I had to clean up some things; as is my job. I am not blaming the first officer nor the changing of runways. I take full responsibility for not executing a go around the first time. I felt after the first terrain call that my vs reduction would have been enough to stop it but it wasn't and the next call came very quickly after. The 1700 ft/min descent at FAF was poor airmanship; not going around was poor captaincy. Not descending at proper descent rate at FAF. Not going around after the first terrain warning call. Allowing myself to become pre-occupied with breaking out instead of focusing on flying the airplane.

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Original NASA ASRS Text

Title: CRJ-700 Captain reported he failed to initiate a missed approach after receiving three terrain warnings.

Narrative: The flight was supposed to be the First Officer's leg; but I decided to fly it because of the low ceilings going south into DCA. Enroute the ATIS showed 600 ft. overcast and I sent an ACARS to Dispatch telling them I was high minimums and needed to add 100 and ½ ft. The return message was wait until the next update to make a decision on the approach. I told the (FO) First Officer that if the ceilings did not improve we would go to IAD. We then set up and briefed the LDA (Localizer Type Directional Aid) Z Runway 19 into DCA. We checked the ATIS again and it was showing a slight improvement to 700 ft. and I sent Dispatch a message saying we were going to ZZZ if we couldn't get in to which the response was; you'll be legal to add the 100 and 1/2 ft. going north. Confused by the 'North' part we checked the ATIS again and it showed ILS Runway 1. (2 Specials had come out back to back). So with that; having begun a descent on the STAR and getting into terminal phase I set up the ILS and briefed it; we were instructed to slow to 210 kts. and I informed ATC that we wouldn't be able to make one of the altitudes to which they responded that was fine; just descend and maintain 9000 ft. My FO had a great attitude and was keeping up as best he could but the environment started to become flustered once they switched the runways again informing us that we had to go back and set up the LDA Z Runway 19 again.At this point it became slightly task saturated as we were setting up again and being vectored on to the approach. Once cleared at 3000 ft. I set next altitude crossed FERGI at 3000 ft. and began the approach. Everything up until the final approach fix seemed normal and it did slow down a bit but I was concerned about not getting in because we queried ATC and they told us that there were some missed approaches due to ceilings. When I called for the before landing checklist the FO ran it. I had been doing my 'point 2 prior' calls but was slightly late on the last one and descended right on the final approach fix at which point I hit the VS button and scrolled down; I think it was between 1500/1700 ft/min. I know that at my reference speed I should only have been doing 800 or so. Before any warnings I scanned and realized what I had done and immediately scrolled to reduce the rate of descent to be below 1000 by 1000. This is when my first terrain call came; I reduced more and then ATC told us we were low; we broke out of the clouds and got one more terrain. I have no reason to have not gone around other than being task saturated and thinking of it being worse in the go around. Although the FO was great there were some missed items as there tends to be and I had to clean up some things; as is my job. I am not blaming the FO nor the changing of runways. I take full responsibility for not executing a go around the first time. I felt after the first terrain call that my VS reduction would have been enough to stop it but it wasn't and the next call came very quickly after. The 1700 ft/min descent at FAF was poor airmanship; not going around was poor captaincy. Not descending at proper descent rate at FAF. Not going around after the first terrain warning call. Allowing myself to become pre-occupied with breaking out instead of focusing on flying the airplane.

Data retrieved from NASA's ASRS site and automatically converted to unabbreviated mixed upper/lowercase text. This report is for informational purposes with no guarantee of accuracy. See NASA's ASRS site for official report.