When you use the phrase ‘Up a Blind Alley’ you mean that someone is following a course of action that is certain to lead to an undesirable outcome.
Example of use: “I keep telling Gina to stop chasing after Joe. She’s just going up a blind alley!”
The origin of the expression ‘up a blind alley’ comes from the mid-19th century, hundreds of years after alleyways that essentially lead to nowhere were first configured. The phrase is first seen in print in the late 1800s, with this example from the October 1874 newspaper Burlington Hawk-Eye serving as an illustration: “If, on account of these things, the overthrow of Republicanism must come, as come it will, we had better reach our destination as quickly as possible, making the issue sharp enough to be understood by all the world, and not be piddling along from year to year in a miserable blind alley of partisan passion and falsehood, getting weaker and weaker, and poorer and poorer, and madder and madder, under incessant proscription and vilification.”