Comparative Study On Single Wave Failure Theories Of Pressure Tubes In Hydropower Station

The main failure type of buried pressure tubes(buried tubes for short)in hydropower station is buckling under external pressure.At present,it is considered that buckling of buried tubes encased in concrete under external pressure is a constrained stability failure problem.However,strength failure or pure stability failure may still occur.In view of this,this article analyzed the failure theories of calculating the critical external pressure of buried tubes,i.e.the strength failure theory,the constrained stability failure theory and the pure stability failure theory.Their representative methods,i.e.the boiler formula,the Jacobsen method and the Boot method were formulated too.The relevance among three formulas was illuminated by using the main mechanical factors of the critical external pressure of buried tubes.The application scopes of three formulas were qutified by the design parameters of buried tubes,i.e.the radius-thickness ratio(r/t),the gap rate(e/r)and the yield strength(?s).For the convenience of application,the quick query graphs of the application scopes of three formulas were given and the result query graphs of the critical external pressure by three formulas were summarized.The main conclusions are as follows:(1)The boiler formula is based on the strength failure mode and strength failure criterion.The Jacobsen method is based on stability failure mode and strength failure criterion.The Boot method is based on stability failure mode and stability failure criterion.The failure criterion of the Jacobsen method and boiler formula is that the maximum stress of elements reaches the yield strength,so it is a strength failure criterion.The Boot method bases on the stationary value condition of the maximum strain energy in the buckling area.The Jacobsen method and Boot method have similar failure mode,and it is considered that there is only one buckling area with buckling waves on the cross section of tube.This failure mode is a typical stability failure mode.The failure mode of the boiler formula does not consider the buckling area and waves.(2)The radius-thickness ratio(r/t)is a key factor influencing the failure type of buried tubes under external pressure.When the radius-thickness ratio(r/t)decreases,the amplitude of buckling waves decreases.At the same time,the element with the maximum stress is closer to the concrete and the constraint on the tube wall is strengthened.The failure type of buried tubes thus trasitions from the constrained stability failure to the strength failure.When the radius-thickness ratio(r/t)increases,the amplitude of buckling waves increases.At the same time,the element with the maximum stress is far away from the concrete and the constraint on the tube wall is weakened.The failure type of buried tubes thus trasitions from the constrained stability failure to the pure stability failure.(3)With the influence of the gap rate(?/r)and the yield strength(?s),the strength failure of buried tubes will happen when the radius-thickness ratio(r/t)is approximately below 30 and the boiler formula is recommended.When the radius-thickness ratio(r/t)is between 30 and 120,the constrained stability failure will happen and the Jacobsen method is recommended.When the radius-thickness ratio(r/t)is approximately above 120,the pure stability failure of buried tubes will occur and the Boot method is recommended.In order to provide a more detailed formula for calculating the critical external pressure and convenient application,quick query diagrams are given.