Via International Commission on Large Dams (ICOLD) norms, high risk dams (dams which can cause deaths if breached) are designed for either the probable maximum flood or the 10,000 year return period flood. The dams in Derna had ungated spillways, meaning they are not regulated, and require minimal maintenance. The upstream dam’s spillway appears undamaged (post-flood photos of the downstream dam I could not find). Abutments also appear intact. This indicates the likely cause of failure was overtopping followed by scour. This happens when the spillway is too small (the inflow rate too large) for the spillway to pass the inflow downstream without the water level rising higher and overflowing the dam itself.
Likely, the incoming flowrate was too large for the spillway to pass without the water level overtopping the earthen dam. Once an earthen dam is overtopped, it scours away quickly, as seen here. The cohesiveness of clay makes it less erodible than non-cohesive earth, which is why the clay core is not eroded downward as low as the earthfill material is.
Investigation is necessary to determine whether the spillway was designed too small for the historical 10,000 year flood, or if the historical 10,000 year flood is no longer accurate due to climate change, or if this was a freak event with return period greater than 10,000 years. In any case, it does not appear likely that neglect of maintenance played a large role in this disaster. More likely culprits are either mistaken design (undersized spillways) or climate change (causing extreme flows in the current climate to be larger than flows of the same return period were when the dams were designed decades ago).