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QUESTION

For X60 steel pipe, plot the maximum water depth depth(m) versus R/t (7.5 < R/t < 20) for various f 0

(f 0 = 1, 2 and 3)



SOLUTION

The effects of initial ovality, from DnV 2000 rules gives us the following equation;

2 2( )( ) 2 ..................(1)c ecr c y ecr y c o

R p p p p p p p f

t

Where;

is the collapse pressure

is the elastic critical pressure

is the circumferential yield pressure

is ovality

If we expand the brackets in equation (1), we obtain the following;

If we collect like terms,

...............(2)

The above equation is in the form of the general cubic equation;

......................................(3)

Equations (2) and (3) are similar, so we have the following relationships;

a = - b = -

c =

In solving our cubic equation, we use Cardano’s method of solving cubics. The discriminant

of

the cubic equation is found to be negative and the is a complex number, therefore all roots of

the cubic equation are real and different.

Thus, the roots of the equation are;



Where

( √ )

The roots of our cubic equation are given by;

The circumferential yield pressure,

. y y

t p

R

The elastic critical pressure,

3

24 1

where:E=young's modulus (210Gpa)

=poisson ratio for steel(0.30)

ecr

E t p

R

The collapse pressure,

. .c p g h



TABLES OF VALUE

Parameters Unit

Steel Grade - X60

SMYS, σ MPa 414

R/t - 7.5 - 20

Ovality, f 0 - 0.01 - 0.03

Acceleration due to gravity, g m/s2

9.81

Density of sea water, ρ Kg/m3

1025





f0 R/t Py - Pecr - (Py 2

+2 P ecr P y f 0 R/t) Pecr P y 2

q p r ф P c1 P c2 P c3 WD

- - MPa MPa MPa MPa MPa m

0.02 7.5 55.16 -136.75 -5305.12 416037.28 -15230 -11538.8 238539.8 1.5389 153.66 -61.17 44.26 4402.074

0.02 8.0 51.71 - 112.68 -4538.40 301292.71 24853.44 -8770.68 158076.76 1.6495 129.76 - 57.48 40.40 4017.443

0.02 8.5 48.67 -93.94 -3923.02 222507.13 38249.87 -6864.74 109459.6 1.7464 111.23 -54.20 36.91 3670.876

0.02 9.0 45.96 -79.14 -3422.20 167196.05 40204.98 -5509.86 78709.908 1.8291 96.65 -51.26 33.75 3356.377

0.02 9.5 43.54 -67.29 -3009.59 127591.15 37517.72 -4518.89 58460.852 1.8975 85.04 -48.61 30.87 3069.548

0.02 10.0 41.37 -57.69 -2665.92 98727.60 33236.05 -3775.38 44643.639 1.9522 75.68 -46.22 28.23 2807.188

0.02 10.5 39.40 -49.84 -2376.83 77355.65 28702.23 -3204.73 34914.503 1.9944 68.06 -44.03 25.81 2566.955

0.02 11.0 37.61 -43.35 -2131.51 61302.07 24472.87 -2757.78 27871.289 2.0253 61.79 -42.04 23.60 2347.078

0.02 11.5 35.97 - 37.93 -1921.66 49085.06 20743.2 -2401.31 22646.016 2.0465 56.57 - 40.21 21.58 2146.133

0.02 12.0 34.47 - 33.39 -1740.84 39676.41 17546.05 -2112.4 18684.512 2.0596 52.18 - 38.53 19.74 1962.866

0.02 12.5 33.09 -29.54 -1583.99 32351.06 14845.72 -1874.83 15622.906 2.0659 48.45 -36.97 18.06 1796.095

0.02 13.0 31.82 -26.26 -1447.11 26590.21 12582.07 -1676.96 13216.117 2.0669 45.25 -35.53 16.54 1644.647

0.02 13.5 30.64 -23.45 -1326.98 22017.59 10690.64 -1510.26 11295.205 2.0638 42.48 -34.19 15.16 1507.351

0.02 14.0 29.55 -21.02 -1221.00 18356.86 9111.279 -1368.35 9741.2289 2.0574 40.06 -32.95 13.91 1383.04

0.02 14.5 28.53 -18.92 -1127.06 15402.76 7791.23 -1246.44 8468.8185 2.0488 37.93 -31.78 12.78 1270.57

0.02 15.0 27.58 -17.09 -1043.42 13001.16 6685.734 -1140.83 7415.6096 2.0384 36.04 -30.70 11.75 1168.846

0.02 15.5 26.69 - 15.49 -968.65 11035.20 5757.485 -1048.65 6535.3025 2.0269 34.34 - 29.68 10.83 1076.829

0.02 16.0 25.85 -14.09 -901.53 9415.40 4975.7 -967.663 5793.0121 2.0147 32.81 -28.72 9.99 993.5548

0.02 16.5 25.07 -12.84 -841.08 8072.70 4315.116 -896.063 5162.0937 2.0020 31.43 -27.82 9.23 918.1354

0.02 17.0 24.33 -11.74 -786.45 6953.35 3755.047 -832.411 4621.9417 1.9891 30.17 -26.97 8.54 849.7624

0.02 17.5 23.64 - 10.76 -736.91 6015.18 3278.56 -775.536 4156.4358 1.9762 29.02 - 26.17 7.92 787.7053

0.02 18.0 22.98 -9.89 -691.86 5224.88 2871.784 -724.481 3752.8311 1.9634 27.96 - 25.42 7.35 731.3072

0.02 18.5 22.36 -9.11 -650.78 4555.96 2523.334 -678.456 3400.9522 1.9509 26.98 - 24.70 6.84 679.9804

0.02 19.0 21.77 -8.41 -613.22 3987.22 2223.846 -636.801 3092.6011 1.9386 26.07 - 24.02 6.37 633.2003

0.02 19.5 21.21 -7.78 -578.79 3501.59 1965.596 -598.966 2821.1178 1.9266 25.22 - 23.38 5.94 590.4998

0.02 20.0 20.68 -7.21 -547.15 3085.24 1742.194 -564.485 2581.0493 1.9151 24.44 - 22.77 5.55 551.4633

Cardano method



f0 R/t Py - Pecr - (Py 2

+2 P ecr P y f 0 R/t) Pecr P y 2

q p r ф P c1 P c2 P c3 WD

- - MPa MPa MPa MPa MPa m

0.03 7.5 55.16 -136.75 -6436.54 416037.28 -66804.8 -12670.3 274470.73 1.4488 160.70 -64.24 40.30 4007.84

0.03 8.0 51.71 -112.68 -5470.66 301292.71 -10162.4 -9702.94 183938.79 1.5432 136.58 -60.42 36.51 3631.2

0.03 8.5 48.67 -93.94 -4700.25 222507.13 13911.51 -7641.97 128565.98 1.6249 117.81 -57.00 33.14 3295.323

0.03 9.0 45.96 -79.14 -4076.96 167196.05 22932.69 -6164.62 93148.904 1.6942 102.96 -53.93 30.11 2994.268

0.03 9.5 43.54 - 67.29 -3566.32 127591.15 25030.57 -5075.61 69590.51 1.7516 91.07 - 51.16 27.39 2723.487

0.03 10.0 41.37 - 57.69 -3143.23 98727.60 24056.85 -4252.7 53372.238 1.7981 81.41 - 48.65 24.93 2479.418

0.03 10.5 39.40 -49.84 -2789.16 77355.65 21852.57 -3617.06 41865.031 1.8348 73.47 -46.35 22.72 2259.186

0.03 11.0 37.61 - 43.35 -2490.13 61302.07 19291.45 -3116.39 33480.87 1.8630 66.87 - 44.25 20.72 2060.391

0.03 11.5 35.97 -37.93 -2235.51 49085.06 16774.78 -2715.16 27227.713 1.8839 61.33 -42.31 18.91 1880.955

0.03 12.0 34.47 -33.39 -2017.07 39676.41 14471.95 -2388.62 22466.727 1.8987 56.63 -40.53 17.29 1719.033

0.03 12.5 33.09 - 29.54 -1828.38 32351.06 12439.45 -2119.22 18775.09 1.9085 52.60 - 38.88 15.82 1572.949

0.03 13.0 31.82 -26.26 -1664.37 26590.21 10680.36 -1894.22 15865.91 1.9141 49.12 -37.35 14.49 1441.17

0.03 13.5 30.64 -23.45 -1520.98 22017.59 9174.284 -1704.26 13540.085 1.9164 46.09 -35.93 13.30 1322.284

0.03 14.0 29.55 - 21.02 -1394.95 18356.86 7892.186 -1542.3 11656.582 1.9161 43.42 - 34.61 12.22 1214.996

0.03 14.5 28.53 -18.92 -1283.63 15402.76 6803.594 -1403 10113.616 1.9138 41.05 -33.37 11.24 1118.121

0.03 15.0 27.58 -17.09 -1184.85 13001.16 5879.879 -1282.25 8836.4682 1.9100 38.95 -32.21 10.36 1030.581

0.03 15.5 26.69 - 15.49 -1096.82 11035.20 5095.551 -1176.83 7769.4289 1.9049 37.06 - 31.13 9.57 9 51.4013

0.03 16.0 25.85 -14.09 -1018.07 9415.40 4428.577 -1084.2 6870.3651 1.8989 35.35 -30.11 8.85 879.7025

0.03 16.5 25.07 -12.84 -947.34 8072.70 3860.232 -1002.32 6106.9939 1.8924 33.80 -29.15 8.19 814.6965

0.03 17.0 24.33 - 11.74 -883.60 6953.35 3374.76 -929.565 5454.2815 1.8853 32.39 - 28.25 7.60 755.6784

0.03 17.5 23.64 -10.76 -825.97 6015.18 2958.983 -864.598 4892.6001 1.8780 31.10 -27.40 7.06 702.0196

0.03 18.0 22.98 -9.89 -773.71 5224.88 2601.905 -806.326 4406.4035 1.8705 29.92 - 26.59 6.57 653.1607

0.03 18.5 22.36 -9.11 -726.17 4555.96 2294.366 -753.842 3983.2618 1.8629 28.82 - 25.83 6.12 608.6044

0.03 19.0 21.77 -8.41 -682.81 3987.22 2028.734 -706.391 3613.1509 1.8554 27.81 - 25.11 5.71 567.9088

0.03 19.5 21.21 -7.78 -643.16 3501.59 1798.641 -663.339 3287.9209 1.8478 26.87 - 24.42 5.34 530.6815

0.03 20.0 20.68 -7.21 -606.81 3085.24 1598.769 -624.149 3000.8963 1.8404 25.99 - 23.77 4.99 496.5741

Cardano method



CONCLUSION

From the results obtained, we observe that the collapse pressure is directly proportional to the

water depth, that is, for an increasing water depth, there is a corresponding increase in the collapse

pressure . Secondly, we notice that the pipeline radius to thickness ratio (R/t) has an inverse

relationship with the water depth. Also, for a given (R/t) ratio, as the ovality of the pipe increases,

the pressure the pipe can resist before collapse decreases. This implies that as the radius to

thickness ratio(R/t) increases, the external pressure the pipeline will be able to resist decreases. We

can therefore conclude from our results that, a pipeline with high radius to thickness ratio (R/t),

should be used at low water depths to prevent the pipeline from collapse.

0

1000

2000

3000

4000

5000

5.0 10.0 15.0 20.0

W a t e r D e p t h ( m )

Pipeline Radius to Thickness Ratio, R/t

Comparison of Collapse Prediction for varying Ovality using DnV rule

1% Ovality

2% Ovality

3% Ovality



REFERENCES

S Huang, Marine Pipelines, Department of Naval Architecture and Marine Engineering,

University of Strathclyde, 2012.



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