Based　on　nonlinear　simulation　of　progressive　collapse　of　single-layer　Kiewitt　spherical　shell,　this　paper　studies　the　characteristics　of　deformation,　load-bearing,　and　damage　development　of　members,　and　presents　a　theory　called　three-phase　that　explains　the　progressive　collapse　mechanism　very　well　in　detail.　Then,　the　development　of　deformation　during　the　three　phases　is　analyzed　under　different　peak　ground　accelonations　(PGA)　and　thus　a　new　description　of　behavior　level　of　spherical　shell　is　set　up　with　a　damage　assessment　index　based　on　relative　displacement　of　gravity.　All　the　work　is　useful　for　further　study　on　the　catastrophic　mechanism　of　space　structure　under　severe　earthquake.