Objective
To determine the deformation state of a cylindrical pipe subjected to soil pressure.
Reference
P. Panagiotopulos. Inequalities in mechanics and their applications. M.: Mir, 1989, p. 387.
Problem statement
To determine the size of the contact zone and the radial displacement at the bottom of the pipe.
Design model
A pipe subjected to soil pressure.
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Geometry
Radius r = 1,315 m
Wall thickness h = 0,04 m
Embedment depth hw = 1,18 m
Material properties
Modulus of elasticity Е = 6*105 kN/m2
Poisson's ratio ν = 0,3
Stiffness of the unilateral restraints EF/l = 107 kN/m
Boundary conditions
Unilateral restraints prevent radial displacements away from the centre.
Loads
The external pressure varies linearly with depth z, 0 < z < 2r according to the following expression Fr = 5,8(1,18+z) kN/m2.
Notes
The problem is solved in 3D formulation (model type 5).
A half-ring model is considered in the analysis. The omitted half is represented by symmetry boundary conditions.
The model is generated with FE type 10 – arbitrary 3D bar (ring elements) and FE type 262 – 2-node FE of unilateral elastic spring between nodes (radial elements).
A step-by-step solution is used to solve the nonlinear problem (number of load steps = 1, minimum number of iterations = 15000).
Nodes: 182. Elements: 361.
Output data
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Design model with restraints indicated
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Design model with load cases indicated |
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Mosaic plot of displacements along Y, m
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Size of contact zone
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Comparison of calculation results
| The unknown value | Numerical solution | LIRA-FEM | Error, % |
| φ, о | 120 | 124 | 3,33 |
| ur, m | 0,01118 | 0,01074 | 3,95 |
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