The　statistical　uncertainty　characteristics　of　random　parameters　in　geotechnical　engineering　makes　the　reliability　design　have　certain　risks.　The　robust　geotechnical　design　(RGD)　method　can　minimize　the　effects　of　variation　in　the　geotechnical　parameters　on　the　system　response,　by　explicitly　considering　robustness　in　the　design　process　along　with　safety　and　economic　requirements.　Aiming　at　the　influence　of　the　statistical　uncertainty　characteristics　of　random　parameters　on　the　independent　foundation　design　under　the　column,　the　foundation　geometry　is　regarded　as　controllable　design　parameters　to　conducting　design　analysis.　Analysis　considers　the　influence　of　the　statistical　uncertainty　of　the　mechanical　parameters　of　rock　and　soil,　concrete　and　steel　material　and　based　on　reliability　theory　and　robust　design　method　of　geotechnical　engineering.　In　this　paper,　the　robustness　design　of　the　structural　system　under　multiple　failure　modes　is　carried　out,　and　the　relationship　between　structural　geometric　parameters　and　structural　system　reliability　under　multiple　failure　modes　is　analyzed　by　viewing　four　failure　modes:　independent　foundation　bearing　capacity,　foundation　deformation,　infrastructure　punching　shear　failure　and　foundation　bending　failure　as　series　system.　Finally,　the　optimal　solution　of　the　design　of　independent　foundation　under　column　is　determined　combining　with　robustness　and　economic　efficiency.　©　2019,　Science　Press.　All　right　reserved.