Abstract
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.
Highlights
The external pressure stability of embedded penstocks with stiffener ring includes the stability of the pipe wall between the stiffener rings and the stability of the stiffener rings
Mises formula assumes that the penstocks is a short cylinder exposed pipe, and both ends of the penstocks are rigidly restrained by the stiffener ring
The results show that after adding Compared with the Calculation model 3, the critical drainage cushion, the critical external pressure is reduced, external pressure is 5.78MPa, and the critical external and the softer the drainage cushion is, the more the critical pressure corresponding to the elastic modulus 1MPa of the external pressure decreases
Summary
The external pressure stability of embedded penstocks with stiffener ring includes the stability of the pipe wall between the stiffener rings and the stability of the stiffener rings. Based on the elastic theory, assumed that the penstocks is an ideal round pipe and the material is linear elastic, simplified as a plane strain problem, derived the analytical formula of the stiffener ring stability against external pressure. The external pressure instability of embedded penstocks is related to the elastic-plastic mechanical properties of materials, the initial gap between penstocks and backfill concrete, and the initial defects of penstocks, which is a complex geometric and material nonlinear problem. The nonlinear static calculation is carried out, and the load increment is gradually applied to make the structural stiffness change until the stiffness matrix approaches singularity At this time, the load is the critical external pressure. A three-dimensional FEM of penstocks, backfill concrete, drainage cushion and surrounding rock with initial defects is established to calculate the critical external pressure. The shape of the outer surface of the penstocks and the inner surface of the outer body are consistent, the initial defects of the penstocks do not affect the gap between the penstocks and the outer body, and the calculation is easy to converge
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