Nelson is head of mining engineering at the Colorado School of Mines (CSM). She also was a professor of civil and environmental engineering and former provost at the New Jersey Institute of Technology (NJIT). From 1994 to 2005, Nelson was at the National Science Foundation (NSF) as director of many interdisciplinary programs, and senior advisor. Prior to that, she was a professor in civil engineering at The University of Texas at Austin. She received her B.S. degree in geology from the University of Rochester and M.S. degrees in geology (Indiana University) and structural engineering (University of Oklahoma). In 1983, she received her Ph.D. in geotechnical engineering from Cornell University.

Nelson has published more than 150 technical and scientific publications in refereed journals and conference proceedings. She is a Distinguished Member of the American Society of Civil Engineers (ASCE), former president of the Geo-Institute of ASCE, a lifetime member and first president and Fellow of the American Rock Mechanics Association, and Fellow of American Association for the Advancement of Science (AAAS).

Her many honors and awards include election to The Moles, induction into Tau Beta Pi as an Eminent Engineer, the Kenneth Andrew Roe Award from the American Association of Engineering Societies (AAES), and the ASCE Henry L. Michel Award.