Study on calculation method of stability for embedded penstocks with stiffener ring under external pressure

A three-dimensional FEM(finite element model)is established, including penstocks with initial defect (ovality), backfill concrete, drainage cushion and surrounding rock. The nonlinear static calculation of the model is carried out. The stability of penstocks with backfill concrete, drainage cushion and surrounding rock under external pressure is studied. The sensibility of the embedded penstocks to initial defect, initial gap and elastic modulus of drainage cushion is analyzed. The results of finite element method, Jacobsen method and strength formula in SL281 are compared and analyzed. The results indicate that the FEM of penstocks, backfill concrete and surrounding rock with initial defects is easy to converge by nonlinear calculation; the ovality and gap have little influence on the critical external pressure of the embedded penstocks with stiffener ring, while the drainage cushion has a certain influence on the critical external pressure; the critical external pressure calculated by SL281 is low and safe; compared with Jacobsen method, the critical external pressure of the finite element method is increased by about 14%; for the embedded penstocks with drainage cushion, the finite element method can be used to calculate the influence of the drainage cushion on the critical external pressure, and the appropriate reduction factor can be obtained, and then the Jacobsen result can be modified by the reduction factor.