Hey Jeff244....welcome, sir.
Whoa...you're spookin' me with the muddy bulge description. You should be getting a number of questions and suggestions here shortly, but let me kick it off.
Were you present when the dam was constructed? Was a core trench cut the length of the dam? What kind of material was replaced into the core and the dam that it supports? (ie; clay content, any rocks or gravel or sand..and if yes, how much) How was the core and dam material laid in? (ie; layered in 6" - 9" layers and compacted by the dozer, a rubber tired scraper, a sheepsfoot, etc). Is the area adjacent to any pipes that run thru the dam? Do you have a way to draw down the water?
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Based on your intitial input, I would not run anything across the dam until I was assured of structural integrity. Yes, all dams leak to some extent, but the description you offer is not normal.