Amstutz’s Method And Its Application On Buckling Analysis For Plain Tunnel Linings

Buckling is one of main failure mode of plain tunnel linings under external pressure.At present,the Amstutz’s method(AM)for calculation critical external pressure are recommened by a few design specifications of penstocks around the world.However,the buckling mechanism and governing differential equation of AM are not systemically illuminated.More influence factors and their coupling relationship have been the problems to unify the applications method of AM.In this paper,AM and its application on buckling analysis for plain tunnel linings is systemically investigated.The main contents are follows:(1)Based on the single lobe buckling mechanism and its basic assumption,governing differential equations of AM are systemically deduced for calculating critical external pressure,and the simplified solution is provided.Drawn the relational graphs to quickly determine the critical external pressure of plain tunnellinings.Programed the corresponding calculation procedures of AM.Meanwhile,pointed out some problems still existedin AM derivation.(2)The main influence factors to critical external pressure and their coupling relationship are discovered,and some application suggestions are given on simplified AM for stability analysis.Studies show that the radius-thickness ratio,the gap between the steel pipe and reinforced concrete envelope and.the yield strength of material are the main influence fators of plain tunnel linings without flaw.It is necessary to consider the strength design and stability analysis when the radius-thickness ratio is less than 30.Adopting the exact AM toensure good accuracy results When the diameter thickness ratio is greater than 30 and less than 60.When the radius-thickness ratio is more than 60,the simplified AM is well applied to the pipe and compared with the exact AM results,the error of the simplified AM is less than 5%.While the radius-thickness ratio is more than 100,the critical external pressure decreasese with the increase of steel strength,(3)Three iterative calculation methods of simplified AM in codes of China,America and Japan are compared.Gave rational adviceson the selection ofiteration formulas,the calculation ofthe gap and the value of the safety factor.The mistakes existed in AM derivation,ASCE provision and EM provision were listed.Studies show that the simplified iterative calculation method in each specification has a range of use and the results of the critical external pressure calculation in the range of the main engineering parameters are similar.Gap value has greater influence on critical external pressure Pcr and should be combined with the actual monitoring and analysis The safety factor of the external pressure is 1.5 to adapt technical progress status and international competitiveness requirements.