Dear Ms. Erickson,
Thank you for posting your request on History Hub!
We searched the National Archives Catalog and located the series Project Operation and Maintenance Basic Files, 1916-1993 and the series Project Operation and Maintenance Basic Files, 1916-1999 in the Records of the Office of the Chief of Engineers (Record Group 77) that includes records related to the Fort Randall Reservoir and that might contain photographs related to it. These records have not been digitized. Please contact the National Archives at Kansas City (RM-KC) at firstname.lastname@example.org for access to and information about these and similar records.
You may also wish to contact the National Archives at College Park - Still Pictures (RDSS) at email@example.com to see if they can offer you any additional assistance.
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We hope this information is helpful, and best of luck with your family research!
According to this Wiki post Fort Randall Dam was not authorized to be built until 1944 so I am a little confused by your dates.
Here is a photo/postcard that was sold on Ebay, it shows workers at the dam site, it is dated 1948.