[1]School of Civil Engineering, Central South University, Changsha 410075, China;
[1]School of Civil Engineering, Central South University, Changsha 410075, China;
[1]School of Civil Engineering, Central South University, Changsha 410075, China;
[1]School of Civil Engineering, Central South University, Changsha 410075, China;
karst; tunnel; water; inrush; safe; thickness; of; rock; plug; upper; bound; theorem; nonlinear; failure; criterion; non-assoc; flow; rule;