Pipeline Stress Analysis Through Stress Function Fittings

This work presents a hybrid experimental technique for stress analysis in pipes due to soil-pipe interaction. It was used a variation of Digital Speckle Pattern Interferometry (DSPI) combined with a small indentation setup for acquiring radial displacement points. Data collected are fitted under the Airy stress functions method for the determination of displacements and strain components. The radial displacement data is fitted in to extract Airy stress function coefficients in a short combination selected specifically for the analysis of stress fields in pipes. This technique is of great utility as an auxiliary approach to the actual field data compilation.

Keywords
hybrid technique; Airy Stress Function; instrumented indentation; stress fields in pipes

Authorship

M.A.M. Cavaco ^**Corresponding author

Laboratório de Metrologia e Automatização - LABMETRO - Universidade Federal de Santa Catarina - UFSC, Florianópolis, SC, Brasil. E-mail: cavaco@labmetro.ufsc.br, mov@labmetro.ufsc.br, albertazzi@labmetro.ufsc.brUniversidade Federal de Santa CatarinaBrazilFlorianópolis, SC, BrazilLaboratório de Metrologia e Automatização - LABMETRO - Universidade Federal de Santa Catarina - UFSC, Florianópolis, SC, Brasil. E-mail: cavaco@labmetro.ufsc.br, mov@labmetro.ufsc.br, albertazzi@labmetro.ufsc.br

M. R.Viotti

G.A. Albertazzi Jr

*Corresponding author

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Figures

Figures (8)

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Figure 1
(a) Radial interferometer positioned in a 200mm diameter pipe, Fontana, (2015Fontana, Filipe, (2015).Measurements of Bending Moment of Pipes Using Instrumented Indentation Combined with Radial Interferometer, Master Dissertation, UFSC. ). (b) pipeline section modeled as a combination of loadings (p - pressure due to soil; M - bending moment, F - axial loading, T - torsional loading).

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Figure 2
Stresses modelled from the stress function

Φ_{2}

(a) and

Φ_{3}

(b).

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Figure 3
Stress/Strain element related to displacement in a point.

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Figure 4
Test bench: (a) photograph showing detailed views and (b) obtained bending stress distribution.

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Figure 5
Radial displacement output from experimental data. (a) Raw unwrapped (phase) displacement data, (b)Raw pre-processed displacement. (c) calculated displacement from Airy's fitted coefficients (post-processed).

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Figure 6
(a) Typical bending stress distribution in a pipeline cross section under combined loads. (b) Simulated bending applied to a 200mm diameter pipe. (c) Typical phase maps acquired in cross-section S4 after indentation Fontana et al, (2016Fontana, F., M.R.Viotti, A.Albertazzi Jr., (2016).Bending Stress Determination in a Pipe Test Bench Using DSPI Combined with Instrumented Indentation. Experimental Me-chanics, Society for Experimental Mechanics .).

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Figure 7
(a) Actual DSPI indentation displacement data (m) for 3x4 mm² area. (b) Airy displacement result for 50% Sy (200MPa).

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Figure 8
(a) shows the principal directions and principal stresses for P1 position. (b) shows the difference phase maps measured at point P1 in the cross-section S4.

Figure 1 (a) Radial interferometer positioned in a 200mm diameter pipe, Fontana, (2015Fontana, Filipe, (2015).Measurements of Bending Moment of Pipes Using Instrumented Indentation Combined with Radial Interferometer, Master Dissertation, UFSC. ). (b) pipeline section modeled as a combination of loadings (p - pressure due to soil; M - bending moment, F - axial loading, T - torsional loading).

Figure 2 Stresses modelled from the stress function $Φ_{2}$ (a) and $Φ_{3}$ (b).

Figure 3 Stress/Strain element related to displacement in a point.

Figure 4 Test bench: (a) photograph showing detailed views and (b) obtained bending stress distribution.

Figure 5 Radial displacement output from experimental data. (a) Raw unwrapped (phase) displacement data, (b)Raw pre-processed displacement. (c) calculated displacement from Airy's fitted coefficients (post-processed).

Figure 6 (a) Typical bending stress distribution in a pipeline cross section under combined loads. (b) Simulated bending applied to a 200mm diameter pipe. (c) Typical phase maps acquired in cross-section S4 after indentation Fontana et al, (2016Fontana, F., M.R.Viotti, A.Albertazzi Jr., (2016).Bending Stress Determination in a Pipe Test Bench Using DSPI Combined with Instrumented Indentation. Experimental Me-chanics, Society for Experimental Mechanics .).

Figure 7 (a) Actual DSPI indentation displacement data (m) for 3x4 mm² area. (b) Airy displacement result for 50% Sy (200MPa).

Figure 8 (a) shows the principal directions and principal stresses for P1 position. (b) shows the difference phase maps measured at point P1 in the cross-section S4.

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[1] *Corresponding author