Abstract: In order to analyze the stability and limit displacement of the Tertiary water-rich sand mudstone tunnel, the abrupt discriminant equation of tunnel vault subsidence is derived by applying the abrupt point abrupt model of abrupt theory.By changing the stress release coefficient of surrounding rock, the abrupt points of plastic strain, velocity and acceleration of the corresponding joints of surrounding rock are found out, and then the ultimate displacement value of the tunnel is judged.The results show that when the stress release rate of surrounding rock is 75%,the sudden acceleration of plastic strain appears, and the arch roof subsidence is 17.06cm.In the second part of excavation, when the stress release rate of surrounding rock is 75%,the acceleration of plastic strain appears a sudden point, and the arch roof subsidence is 19.77 cm.In the third part of excavation, when the stress release rate of surrounding rock is 65%,the acceleration of plastic strain appears a sudden point, and the arch roof subsidence is 24.77 cm.In the fourth part of excavation, when the stress release rate of surrounding rock is 60%,the acceleration of plastic strain appears a sudden point, and the arch roof subsidence is 25.52 cm.In the fifth part of excavation, when the stress release rate of surrounding rock is 50%,the acceleration of plastic strain appears a sudden point, and the arch roof subsidence is 25.87cm.When the stress release rate of the surrounding rock is 45%,the acceleration of plastic strain appears a sudden point and the vault subsidence is 25.93 cm.