As of imagery dated 08 Jan 2020, the following observations were made:
Two impact craters were identified within the base perimeter. One was located on a small portion of the southern taxiway and the other was located in the southeast portion of the base near hardened air shelters/bunkers. It is assessed that air operations were not affected as damage to the taxiway was minimal and neither of the runways were struck.
Eight aircraft hangars were destroyed, with an additional two sustaining major damage and two sustaining what appeared to be minor damage. Smoke from a possible destroyed vehicle was observed in the vicinity of hangars located in the eastern portion of the base. While no damage to aircraft was observed, it is possible that aircraft were located within hangars at the time of the strike and sustained damage, as indicated in open source reporting [Ref. 1].
Approximately 50% of a probable barracks was destroyed. It is likely that this is the same building that is referred to in a video and article published by CNN [Ref. 2] based on the visible damage as well as observations of the surrounding area.
Open source reporting indicates that 10 missiles struck al-Asad [Ref. 3]. This number is consistent with the amount of damage observed on imagery but does not to appear to have affected the operational status of the base.
Ref. 1: https://www.washingtonpost.com/national-security/2020/01/11/irans-attack-us-forces-exposes-pentagons-challenge-with-stopping-ballistic-missiles/
Ref. 2: https://edition.cnn.com/2020/01/11/middleeast/iran-strike-al-asad-air-base-exclusive-intl/index.html
Ref. 3: https://www.dailymail.co.uk/news/article-7863629/U-S-troops-took-cover-bunkers-Iranian-missile-attacks.html