A Soil Resistance Model forPipelines Placed on Sandy Soils

7/22/2019 A Soil Resistance Model forPipelines Placed on Sandy Soils

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R. L. P. VerleySTATOIL,Postuttak,7004 T rondheim, Norway

T. So tbergSintef,Trondheim, Norway

A Soi l Resistance Modelfo rPipelines Placed o n Sandy Soi lsThis paper presents a p ipe-soilinteractionmodel for sand soils capableof predictingthe development of pipepenetrationinto the soil and theassociatedsoilresistancethat may be mob ilized against horizontal pipe motions. The model is based ondimensional analysisa nddevelopmento fappropriate empirical equations whicharefitted tolarge-scale laboratory datafrom severalsources. The development of penetration is described byconsidering the w ork done by the pipe on thesoil.For agiven penetration, theforce-displacementcurve isdescribed. The model has beenusedtopredict timehistoriesof penetration and horizontal pipe displacement fromlarge-scale laboratory testsw here pipesectionsweresubjectedto forcesrepresentativeof thosefrom irregular waves and currents. A goodreproduction of the time development of both penetration anddisplacement is given over the whole range ofrelevanthydrodynamic andsoilparameters.

IntroductionWhen a pipe is placed on a sandy soil and subjected tobasically oscillatory forces, for example from waves and currents, there is a complex interaction between pipe m ovements,penetration into the soil, and soil resistance. For small movements the pipe tends to penetrate into the soil, increasing thesoil resistance , whereas for large movem ents the pipe will breakout of the soil. Pipe movements are thus dependent on thepenetration, which is itself dependent on the movements.Three major investigations have addressed the problem ofpipe-soil interaction, the PIPESTAB project (Brennodden etal., 1986), the AGA project (Brennodden et al., 1989) and aproject at the Danish Hydrau lic Institute, DH I, (Palmer et al.,1988). The PIPESTA B and AGA investigations have producedsoil resistance models (Wagner et al., 1987; and Brennoddenet al., 1989, respectively). The PIPESTAB model has beenfound to be very conservative (Verley and Reed, 1989). TheAGA model exhibits nonphysical behavior when used in certainrealistic param eter ranges. N ot withstanding this, Verley et al.(1990) showed that the equations for maximum bre ak -ou tresistance for a given penetration give a good prediction ofexperimental results provided the relative density p arameter inthe equations is set to a pa rticular fixed value independent of

the actual soil relative density.The major factors governing pipe response in a realisticdesign situation where movements of some meters may bepermitted, are the penetration and, for that penetration, themaximum ( break-out ) resistance force that can be mobilized. Of lesser importance is the resistance force to furthermovements after break-ou t. Details of the shape of the force-Contributed by the OMAE Division and presented at the 11th InternationalSymposium and Exhibit on Offshore Mechanics and Arctic Engineering, Calgary, Alberta, Canada, June 7-12, 1992, of T H E AMERICAN SOCIETY O F M E CHANICAL ENGINEERS.M anuscript received by the OMA E Division, 1992; revisedmanuscript received February 4, 1994. Associate Technical Editor: D. Myrhaug.

displacement curve are of minor impo rtance. The present modelis based on primarily evaluating development of penetration,the maximum resistance force and the post-break-out resistance force through dimensional analysis and fitting of physically representative empirical equations to a large range oflaboratory data from the PIPESTA B, AGA , and DH I investigations.In the following, the dimensional analysis and model fittingis described. The model has been implemented in a pipelinesimulation program and results are presented from simulationsofvariouslaboratory data , including data from pipes subjectedto realistic irregular wave and current forcing, in order to fine-tune, test, and validate the model.Dimensional Analysis

The following simple variables describe the total horizontalsoil resistanceFhfor a unit length of pipe, of diameterDandsubmerged weight Ws,oscillating with relatively small, but notnecessarily constant, amplitude on a sand soil, of density ps,due to fluctuating horizontal and vertical forcesFxandFt(e.g.,hydrodynamic forces):g,D,W s,y,s,n,z (1)The pipe is subjected tonoscillations covering a total (scalar)distance s and is at a particular instant of time a distance yfrom some representative origin and has a penetration z intothe soil. The C oulom b friction coefficient is /x, the density ofwaterp ,and the gravitational accelerationg .A large numberof dimensionless parameters may be formed from (1).Analysisis simplified by considering separately the soil resistance for agiven penetration and the development of that penetration.

Force/Displacement for Given Penetration. Consider thesituation after a number of cycles of constant amplitude a(ors/n) which have led to a penetration z. The vertical contactJournal of Offshore Mechanics and Arctic Engineering AUGUST 1994, Vol. 11 6/ 14 5

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force is given by (W s - F/) = Fc. The resistance may beexpected to be related to the weight of soil to be moved, i.e.,p s p, v, and g can be combined to y's. Consider the resistanceFh to be made up of a friction contribution, Fj = JX FC ,and anadditional resistanceFn due to the penetration. From Eq. (1),the penetration-depend ent resistance may then be expressed as

F r J z y\ y'sD2' af\ 1 l. D (2)The parameter a expresses the effect of overburden, i.e., theexcess soil in front of the p ipe due to the cycling with amp litudea. When considering the maximum resistance force Fr2, y/Dmay be omitted. The effect of overburden (i .e .,a) should alsobe of minor importance, as the maximum resistance forceoccurs for fairly large displacements of the pipe when theoverburden is a smaller proportion of the soil involved in theinteraction. The maximum resistance is thus

Frl fiy's^Y'D (3)(The subscript rl for the maximum resistance Fr2 anticipatesthe shape of the force displacement model, see Fig. 6.)Note that the classic passive resistance, Fr = ky'sz2, is alsodescribed by Eq. (3). The constant k is related to the ratiobetween shear and nor mal forces,Fc/Fr. Therefore, one mightexpect the param eter Kin Eq . (3) to be of subsidiary im portanc ecompared to z/D.

Penetration Development. Considering the developmentof penetration during thencycles of amplitu deaprior to breakout and again form ing 7^ and Fc, the following relationshipmay be formed from Eq. (1):7s n,K,^,n) (4)D J\D' ' D'

Penetra tion into the soil is caused by pipe movem ents p ushingsoil to each side, and is related to the work done by the pipeon the soil. It is supposed that frictional forces do not movesoil and Fh may be replaced byFr and the work done is thusthe integral ofFr(s)ds. Groups y'sFP'/Fha nds/D may then becombined to form = E/y^D3, whereE is the work done bythe horizontal force Fr on the soil . The groupss/D an d n may

Fig. 1 Simplified system fo rsoil being removedby an object

be combined as a. Furthermore, the development of penetration from cycle to cycle (the maximum penetration, say) is ofinterest rather than the development of penetration within acycle, and y/D may be omitted. E quation (4) may then besimplified toD =/(>>) (5)

Insight into the possible form of Eq. (5) may be obtained byanalyzing the simplified situation sketched in Fig. 1. This represents removal of soil by an object (pipeline) forming a depression of half-width aand side slope , the soil rem ove d form inga mound of height h and side slopes . By considering thework done against friction and gravity to move the soil, it mayeasily be shown that the penetration is related to the workdone as

D -k \ za

- = - ? \ zaD ji

(6a)

(6b)where k contains circular functions of . Equations (6), although not directly applicable to a real situation, illustratedirectly two of the three groups in Eq. (5). The third group,K, plays a role in the factor k. Kis analagous to the rou ghnessin passive earth pressure theory, which determines the angle(shape) of the failure surface in the soil and will here affect4> , and indeed the shape of the depression formed. L abora torywork shows that depressions formed show little or no flatbottom (for sand) and a slope of varying angle (varying both

N o m e n c l a t u r e

a = amplitude of pipe displacementC u = soil gradation n o.D = pipe diameterG ? 5 O = me dian soil particle sizeDr = relative density of soilE = work done by force Fr on soilFc = vertical soil contact force (= Ws - F{)Ff = frictional hor izon tal soil resistanceFh = total hor izon tal soil resistance =Ff + Fr)Fi = lift force on pipeF, = horizontal soil resistance due to penetration

f f 1 2 3 = hor izon tal soil resistance at points 1, 2, and 3 ofmodel (Fig. 6)Fx = external horizontal force on pipeg = gravitational constantks = soil stiffnessk = constants defined in textn = no. of oscillations5 = total distance traveled by pipeW s = submerged weight of pipey = distance of pipe from origin of model

^1,2,3 = distance from origin to points 1, 2, and 3 ofmodel (Fig. 6)z = penetration of pipe into soilZi = initial penetration of pipe due to weight Wsz2 = reference penetration for break-o ut (maximumpre-break-out penetration)z\ = maxim um value of z2 found in simulation up toinstant of time of interestZ2 = equivalent penetration at point 3 of the model(Fig. 6)a = a/D or y/D7/ = subm erged unit weight of soil

K = KEP/FCKa = y'sD2/F c#v where Fc,m is average value over cycleK; = 7.,'E^/Ftf, where Fci is value at instant of maximum horizontal soil resistance F f 2K0 = ysD2/Wsfj. = Co ulo mb friction coefficientp s = mass density of soilp w = mass density of water = E/y'sD14> - side slope of depres sion formed by oscillating pipe

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(a) \\I-

\ A \ _ /

rr \ yIA- A Vy

/ \

J: \(b)

- \

TIME (s)

AAAAAAA :

J V;TIME (s)

(c)

" ^

(d)

y (cm)Fig.2 Example of data from PIPESTAB and AGA tests used to developsoil resistance model

laterally andasthe pipedigsdown).Onemight therefore expecta relationship rather nearer to (6a) than (6b),i.e., a power of of about 1/3, with a dependence on Kand some dependenceon the a mplitude of oscillationsa.This information has beenutilized in the development of the model equations.Data Used in Developing and Testing the ModelData from three sources, PIPESTAB , AGA, and D HI, havebeen used, firstly to develop model equations fitting (3) and(5) to data from simple tests, and secondly to fine-tune, test,and validate the model using data fromtests where pipesectionswere subjected to realistic forcing. The data is summarizedbriefly in the forthcoming and, for some of the data, in moredetail by Verley and Reed (1989) and Verley et al. (1990).

PIPESTAB and AGA Data. The rig used in the PIPESTAB and AGA tests has been described by Brennodden etal .(1986), Wagner et al. (1987), and Brennodden et al. (1989).The rig applies horizontal and vertical forces or displacementsto a pipe section of 0.5 m or 1.0 m diame ter. The PIP ESTA Bdata used in the analysis is taken from Wagner et al. (1987)and the AGA data from Brennodden et al. (1988) and Lienget al. (1988).The data used in the development of the model consists ofdata from tests in which pipe sections were initially placed on

the surface of the soil and were then subjected to variousnumbers (0-30) of small, constant amplitude (0.1-1.0D),displacement oscillations. These oscillations caused the pipe section to dig into the soil. The pipe section was then pulled alarge distance causing it to bre ak ou t from its penetratedposition and m ove into virgin soil. The initial, small am plitudecycles are used to determine the increase in penetration withwork done by the pipe on the soil. The final bre ak -ou t cycleis used to define the maximum soil resistance for a given penetration and also the shape of the force-displacement trace andthe residual resistance after break-out. Tests were conductedon various sands and for various values of simulated pipelinesubmerged weight. The soil geotechnical parameters for thePIPESTAB and AGA tests, and also for the DHI tests, aresummarized in Table 1of Verley et al. (1989).Data from the PIPESTAB and AGA tests includes timehistories of work done by the pipe against the soil as

(7)(t)= F rds, F r=Fh-ix.F c, ^ = 0.6i.e., a friction coefficient of 0.6 was used in the original rawdata reduction.Figure 2 shows some data from a specimen AGA test consisting of4 cyclesof am plitude0.5Dfollowed byalarge brea kou t oscillation. Figures2 a) and (b )show displacement andpenetration versus time. Figure 2(c) shows the hysteresis curve,Fhversusy,for the last cycle of0.523amplitude and the breakout cycle. Figure 2(d) shows the development of penetrationversus displacement and Fig.2 e) versus energy, the envelopeof which is used to develop the penetration equations. Fcisevaluated at the time when maximum resistance occurs in thebre ak -ou t cycle, and also as an average value during thefinal pre-break-out cycle.The data used to fine-tune, test and validate the model consists of penetration and displacement time histories for testsin whicha pipesectionwassubjected totimevarying h orizontaland vertical forces representative of those from combined irregular waves and curre nts. The manner in which the test datawas obtained, the tests conducted and the corrections andanalysis applied are fully described by Verley and Reed (1989)and are summarized in Tables 1 to 3 therein.

DHI Data. The DHI equipment and tests have been described by Palmer et al. (1988). In the tests, a pipe section of0.295 m diameter, placed on the surface of a soil bed or in apre-formed depression of up to 0.5 diameter, was subjectedto sinusoidal forces, nominally equal in the horizontal andvertical directions. The am plitude of the applied forces startedat a low value and was increased in increments of 1-2.5 percentevery 20 cycles, and continued un til the pipe had moved one-half diameter from its initial position, typically after 500-1000cycles. Tests were conducted with smooth and rou gh pipe surfaces, for medium and coarse sand, and for various values ofsimulated pipeline submerged weight. In some tests, break-outhad not occurred when the tests were stopped (see Verley etal.,1990, Table 2 and Fig. 3).The final cycle of tests in which break-out was achieved ornearly achieved has been used in the development of the breakout force equations (together with the PIPESTAB and AGAdata). The DHI data is also used indirectly to fine-tune theequations for penetration through the comparison of simulation time series of penetration with those measured in thetests. Table 1 summarizes the DH I tests used in the tunin g/testing of the model.The data utilized from a test consists oftimeseries envelopesof the horizontal and vertical forces applied to the pipe andtime series of the displacement and penetration. The forcesare used as input to simulations, the results of which are compared with the measured displacements and penetrations.

Journal of Offshore Mechanics and Arctic Engineering AU G U ST 1994 , Vo l . 1 16 / 14 7

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Table 1 Summary of DHI tests used in testing and fine-tuning themodel. The approximate number of cycles in the test,n, and the approximate upper limit of thehorizontal andvertical forcesat the end ofeach test, Fmax, areindic ated.

Table 2 Summary of test data used to develop maximum break-outforce equations

No

01030405Of071014i'518

Dia.(m)0.30.30.30.30.30.30.30.30.30.3

z/D

0.000.330.080.200.08O . O O0.000.000.000.00

z/D(max)0.270.230.160.250.310.300.13'0.160.130.18

w.(kN/m)1.00.50.50.51.01.50.51.50.51.5

n(approx)76013007707609001000650680940650

Fapprox)(kWrn)0.650.450.40.40.81.00.30.80.350.8

2,0001,8001,6001,4001,2001.000 0,8000.6000,4000,2000.000

"J?+

B PIPESTAB/AGA te gt s, D-. PIPESTAB/AGA te s ts , D=+ PIPESTAB/AGA te s ts , D=o P IP ES TAB/AGA t e s t s , D-

D HI t e s t s , D = 0 .3 ra, v.

a s s ~

o

I 1 1

. 0

.5

.0

.0

m l oos e s andm , l oo se sandra, 0 .5 m, l ooses i m p l e b r e a km , dense sand

dense sand

H

-dhi9

~ia a

1 H

"f;=?

10 , 0 0 0 . 0 , 050 0,100 0,150 0 , 200 0 ,250 0 ,300 0 ,350

Fig . 3 Ratio between total resistance force F,,zpredicted throughEqs.(8)andthat measured in the tests

M aximum B r e ak-Out For c eData f rom the AGA, PIPESTAB, and DHI tests have beenincorporated in a spreadsheet program and used to developand test various empirical relationships basedon Eq. (3).Forzintheparameter z/DinEq. (3),themaximum pene tra t ionin the cycle immediately prior to the break-out cycle, z2> isemployed. ForFcintheparameter K,both theconta ct forceat theinstant ofmaxim um break -out force (i .e ., K,-)andtheaverage contact force in thebreak-o ut cycle (K) have beenemployed; however, thefirst ofthese has been found togivethe best correlation.Data utilizedindeveloping themodel coversD 0 .3-1 .0m,D r 0 .05-1 .0 , zi/D 0 .01-0 .35, < c, 1-25, anda 0 .1-1 .0 . Theindividual tests includedinthe analysis are summarizedinTable2, and the following givesagoodfit totheda ta :c / \'-25

sD1 = (5 .0-0 .15/c;) D

ysD T = 2.0

K ; < 2 0

K ; > 2 0

(8f l)

(8*)Figure 3shows theratio between themaxim um total soilresistance force, Fh2 (=Fr2 + F f) predic ted through Eqs. (8)and measured inthe tests. The three points marked dh i6,d h i 7, and dhi9 arefrom D HI data where full break ou t wasnotachieved, the measured forces were lower thanfor full break-out, and thepoints onFig . 3artificially high .The standard deviation of thepredicted to measured totalresistance force (neglectingtheforegoing D HI data points)isabout 12percent. Nodependence on theparameter a wasfound.The cut-off valueofK,=20inEqs . (8)israther uncertaindu etothescarcityof data with such high K, values. Thecut-

Ho . I 0IA1PTT~P2.7P2.9P2.SA2.10A2.12A2.16P2.10P2.6A2.13P2.18A2.8P2.19A2.1P2.15P2.16A2.2A2.17A2.20A 2 . l lP2.12P2.13A2.5A2.6P2.8P 2 . l lA2.18A2.14A2.19A2.7P2.14

(ml1,001.001.001.001.001.001.001.001.001.001.001.000.500.500.500.500.501.001.001.000.500.500.500.501.001.001.001.001.000.500,50A2.4 | 0.50

amp

U lO.bU.l0.10.1O.b0.50.30,10.10.1O.bO.bO.b0.5O.b0,50.50.30.10.10.10.10.1b.i0.56.50.30.10.10.10.10.1

B2.182 . 4B2.3S2.51.001.001.001.00

O.bi- 1O.b0.1P l l OPL8PL5PU6PL9

l.ocr1.001.001.001.00PD5P 0 8PD4PD7

1.001.001.001.00DHI4OHI5OHI9OHI10OHI11OHI17DHI6

OHI14OHI16OHI7OHI10

0.300.300.300.300.300.300.300.300.300.300.30

Simula tests.IcPI.4P1.5PI.6PI.11P1.25A1.3A1.7ALIOAl .SPI.12PI.13A1.6A1.9A1.2

1.001.001.001.001.001.001.001.001.001.001.001.001.000.50

ose

simpta tests, densiB l . lS1.2 1.001.00

n

105441030104410441041010301044154441010101044430430

"oo0u0uuou0uti

JL

p _ .(aval(kN/mHOTT0.340.400.370.500.500.500 . 6T0.620.52

0.901.000.250.250.260.250.240.951.001.000.280.270.240.252.002.201.401.502.000.480.520.490.950.951.951.95

0.490.490.490.490.490.500.981.501.501.481.50

0.3S0.801.001.101.101.200.951.501.402.002.102.002.000.5017082.00

Kappas(aval

~ T 2 . 425.021.323.017.017.017.013.113.716.39.43.58.58.58.23.58.93.98.58.57.67.98.98.54.33.96.15.71.34.44,14.3

10.510.55.15.1

1.31.81.31.81.81.70.90.60.60.60.6

24.310.63.57.77.17.1a.95.76.14.34,04.34.34.3

10.05.0

Tc(atFhmaxi(kM/ml1 . 1S"0.500.630.561.151.441.110.900.720.73t.ao1.740.370.420.900.370.491.661.441.150.570.380.540.332.402.602.501.752.140.700.640.601.301.702.402.870.721.151.391.261.461.300.591.841.650.080.090.100.200.080.160.220.640.640,550.67

0.3S0.801.001.101.101.200.951.501.402.002.102.002.000.501.002.00

"Kappas( a t -f^hmpa)T T17.013.515.27.45.97.79.411.811.64.74.95.75.12.45.74.35.15.97,43.75.63.96.43.53.33.44.94.03.03.33.56.55.0"1.53.0

"11.87.4""5.1~~57T-5.8

l.i14.44.6'5.29.28.27.43.79.24.63.41.21.21.31.1

24.310.63.57.77.7-7.18.95.76.14.34,04,34.34.3XT'4.3

stnaalasteye.(ml*on. 0350.0600.0500.1210.180a.i i i0.O7O0.0670.0830.1230.1510.0540.0750.1100.0550.0900.1350.1200.1120.0510.0550.1210.0550.1770.1500.1840.1440.1600.1170.0840.076

- r a -( m axkN / mX o T0.651.000.853.005.303.001.401.351.663.354.006.850.922.500.851.224.004.253.700.850.702.050.685.104.806.254.765.792.661.401.25

0.0500.0900.0670.1241.753.252.866.00

0.036a.on6.0550 . 0640.0886.011.071.982.122.16

0.0110.0710.0190.019

1.161.791.571.586.0506.6?10.0710.0440.068IS. 050"0.0940.0380.0530.0940.053

6.466.520.440.400.500.400.800.860.841.056.82

0.15520.0480.0560.0380.0340.0440.0440.0640.0540.1020.0820.0906.0550.023

0.461.251.601.301.201.401.352.101.803.503.103.202.300.513.0140.014 0.901.70

off value hasbeen setconsidering theresults of simulationsof irregular wave tests,inwhich 12 tests achieved value sofK,>30.Although Eqs. (8) giveagood fitto the data, the sensitivityto K is not strong and other equations can be found that wouldfit thedat a equ ally well,e.g.Z7 / \ ' -2 5Fn l l c n.JZ2\ (9)r f - ( 4 . 5 - 0 . 1 lie,)ysIT \D)

(with some limitto,-notinvestigated furthe r).14 8 / V o l . 116 , AU G U ST 1 99 4 T r a n s a c t i o n s of th e A S M E

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T a b le3 S u m m a r yoft e s t d a t a u s ed tod ev e l o p p en e t r a t i o n v e r s u s ene rgy equ a t i o n sNo.

P2.3P2.7P2.9A2.10A2.12A2.16P2.4P2.10P2.18A2.8P2.19A2.1P2.15P2.16A2.2A2.17A2.20A2.11P2.12P2.13A2.18A2.14P2.8P2.11A2.1SA2.19A2.7

B2.2 jB2.1B2.4B2.3B2.5

D A ;amp

(m) I (m)1,001,001,001,001,001,001,001,001,001,000,500,500.500.50

0,50,10,10,50,50,30,10,10,50,50,50.50,50,5

0,50 I 0,5

n

1044103010444.44410410

1,00 I 0,3 I 101,00 1 0,11,00 j 0,10.50 I0,10,50 I0,1

301044

1,00 I 0,3 101,00 | 0,1 101,00 0.5 | 41,00 1 0,5 1 41,00 1 0,5 41,00 I 0,1 I 100,50 0,1 I 10

I1,00 I 0.5 i 301,00 l 0,5 4 '1,00 1 0,1 ; 30 :1,00 i 0,5 4 f1,00 i 0,1 30 I

Ws{nom)(kN/m)

0,250,250,250,500,500,500,500,501,001,000,250,250.250,250,251,001,001,000,250,251,501,502,002.002.002,000,50

1,001.001,00 2,00 i2,00

Zi/D

0,0150,0080,0150,0300,0400,0200,0150,0150,0350,0500,0300,0400,0500,0160,0400,0300,0300,0450,0200.0400,0800,0400,0600,0200,0600.0500,080

0,0100,0060,0100.0100,015

Fc(ave)

(kN/m0.380,340,400,500,500,500,700,650,901,000.250,250,260,250.240.951,001,000,280,271,401,502.002,201,902,000,48

0,800,950,951,951,95

Kappas(ave)

22,425,021,317,017,017,012,113,19.48,58,58,58,28,58,98,98,58,57,67,96,15,74,33,94,54,34,4

12,510.510,55,15,1

_ ^ _ , , 0 ^ 5 0 , . 0 . 2 5 , . ,S 1.0-10/.5 0.5-10/.5

* - 1.0-7/.3 O - 1.0-7/.1* 1.0-10/.5 a 1.0-10/.1

_ ^ _*__ - a - * - -

10-15/.5 -1Q-10/.310-5/.510-5/.5 '

-a - -

.*-- 1 .0 - 1 5/ . 3 o 1 . 0 - 1 5 / . 1- 1.0-10/.1 o 0.5-KV.1

1.0-5/.1 - - - - 0.5-5/.11.0-5/.1

a.ooo 0.200 0.400 0,600 0.& 1.000 1.200

Fig .4 D ev e l o p m en t ofp en e t r a t i o n w i t h en e rgyfor all t e s t s i n d i c a t edby d iameter , K anda m p l i t u d eofm o t i o n s (D-n.Ja)

Penetration DevelopmentTable3summarizes the individual tests included in the analysis.Based on Eq . (5), the information inEqs.(6) and througha process oftrialand e rror and curve fitting using a spreadsheetprogram,the following equation hasbeen found todescribethe developmentof penetration:

Z2-ZD = * ( * * , 1 - l / 2 v 0 . 3 1i a ) (10)wherez,isthe initial penetration when the pipe sectionisplacedon the soil and the average contact force is usedinK.A valueofk =0.28 has been found from the data. However, throughsimulationsof tests with realistic loading, the valueofkhasbeen adjusted tok=0.23 and theinstantaneous valueof K(i.e., K,)isused. Dueto thedifficulty indefining amplitude,a is replaced byy/Dwhereyisthe instantaneou s distanceofthe pipe from the origin (definedinthe m odel, see later).Thesensitivitytoamplitudeofmotion, which varied between0.1and 1.0diameter,isvery lowand avalueof a- 1inEq. (10),combined withasmall adjustment tok,gives an equally goodfittothe data.Figure 4 shows the developmentofpenetration with energyfor all tests and Fig. 5 show resultsforall tests with amplitudea =0.1 and allvaluesofK . From Fig.5 andother similarfigures, itisseen that thereis,fora given am plitude of motion, {a maximum penetration that can be achieved, and that thisisgiven approximatelybyZl-Z(D 2, k~l.2 (11)However, through simulations, the value ofkhasbeen adjustedto 1.0and the instantaneous valueofK (i.e., K,)isused.Residual Force After Break-Out

If the pipe section continuestomoveinthe same directionafter break-out, thereis a residual horizontal resistance(inaddition to friction) due to a m ound ofsoilbeing pushed aheadof the pipe. This residual force, Fri, will haveaneffect on

0 , 0 0 0 0 , 2 0 0 0 , 4 0 0 0,6 0,800 1,0005

Fig .5 D ev e lo p m en tofp en e t r a t i o n w i t h en e rgyfora=0.1a n d a l l v a lu eso f K T e s t s i n d i c a t e d byd i a m e te r , K a n d a m p l i t u d eofm o t i o n s D-KJa).

howfara pipe section will move after break -out while externalforcesarestill actinginthe same direction.The post-break-out force Fr3hasbeen found to berelatedtothemaximum penetration in thepre-break-out cycle (i.e.,Zi/D) in asimilar manne rtothe maximum forceFr2,thoughwith more scatter. Although one might notexpectthepenetration priortobreak-outto affect the resistance after asufficiently large displacement has occurred, the laboratory testsshow that even for the largest displacement (4D ), the resistanceforce F r3isstill governed by the pre-break-out penetration z2.Through Eq. (8),Frim aybeexpressedas anequivalent penetration after break-out,z3,which maybeapproximatedby

- =0 .82-3 .2(V-O),Zizl.Zl 0.5

(z 2/>)0.1

(12f l )

(12b)The force-displacement model modifiesthenominal penetration zias the pipe moves from the position associated w ithzi,to that associated with z3(see later). Therefore,ziin Eqs. (12)is in the final model replaced byZi ,the maximum penetrationz2 realizedin thesimulationup tothe instantoftime considered.

J o u r n a lofO f f s h o r e M e c h a n i c s a n d A r c t i c E n g in e e ri n g AUGUST 1994, Vol. 116/149Downloaded 15 Jan 2013 to 223.27.129.246. Redistribution subject to ASME license or copyright; see http://www.asme.org/terms/Terms_Use.cf


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Fig. 6 Force displacemen t model

FOR

0 1 1)

new origos;y c i DISPLACEMENT. 1

Fig. 7 Force displacement model 1 cycle with amplitude > y 2

Force-Displacement ModelFigure 6 shows the shape chosen for the force-displacementcurve of the penetration-dependent force Fr defined throughthe force levelsFri, F r2 , and Fri and corresponding displacementsyu y2,and j ^ Fr2andFr3 and the equivalent penetrationsZiandZ3are determined as in the foregoing. The displacementsyu y% > andj>3have initial values which may all be modified bypipe movements. The model is symmetric about the origin;i.e.,acertain pen etration and resistance force due to m ovementin one direction will apply, after the pipe reverses direction,in the other direction (with the obvious sign change). Note,however, that the origin of the model, 0, may move.For movements within 0 and yu the resistance is linearlyelastic and no work is done. The pipe penetration does notchange nor does the origin move. The di st an ce s is determinedfrom the elastic stiffness of the soil and the force level F r l ,which is related to the force levelFr2(see later).Betweeny\ andy2, the displacement corresponding to themaximum resistance, the work done by displacement causesincreasing penetration, given by Eqs. (10) and (11). This increasing penetration causes the force levelFr2 (and thereforeF rl and Fr3) to increase. The origin does not move.For displacementy > y2,the origin is translated a distance(y y%)and the pene tration decreases until y = y3, afterwhich it remains constant.During simulation of a pipe section subjected to irregularwave forcing, the model may go through many force-displacement cycles of different amplitude. As an exam ple, Fig. 7indicates a cycle of amplitude greater than y2, causing boththe force levelFr2(and therefore Fri andFri) to decrease andthe origin to move.The laboratory tests indicate that maximum (break-out)forces occur for displacements, y2, of about one-half to onediameter. Through simulations, the value ofy2 has been adjusted to 0.5 diameter.The value of j>3, i.e., where the resistance force becomesstable after brea k-out, was estimated from the tests and foundto depend on the pre-break-out penetration and is fitted approximately by

8 . 0 '7 . 0 -6 . 0 -

H 5 - -a 4 . 0o(0 3 . 0 ->1

2 . 0 .

1 . 0 2 . 0 3 . 0 4 . 0 5 . 0 6 . 0 7 . 0 8 . 0y / D - p r e d i c t e d

Fig.8 PIPESTAB/AGA realistic loading testsmaximu m displacementachieved, actual versus predicted

. 3 2 -

. 2 8

. 2 4

. 2 0

. 16

. 12

/ /

/ /

./. /

V // /

.08 .12 .16 .20 .24 .28 .32z/D-predicted

Fig. 9 PIPESTAB/AG A realistic loading tests () and DHI increasingamplitude tests (x)maximum penetration achieved, actual versus predicted

D D \D$ = ^ 0.8,D D

Z2D~ 0.15 > o . 1 5

(13a)

(136)However, through simulations, the values 0.3 and 0.8 in Eq.(13) were modified to 0.1 and 0.6, respectively. Furtherm ore,z2 is replaced by z2.Comparison of the idealized force-displacement model withhysteresis loops from the labora tory tests indicated a value ofF rl between 0.2Fr2 and 0.5Fr2. Through simulations, a valueof 0.3Fr2was chosen.When a pipeline is placed on a plane flat sand surface, someinitial, usually small, penetration occurs. Simulations indicate,as expected, that pipeline response is insensitive to this initialpenetration. However, the laboratory data is approximatelyfitted by

^ = 0 . 0 3 7 * 0 -2 /3 (14)This is equivalent to the pipe displacing about (1/22) of itsweight of sand.Pipeline Response Simulations

The soil-resistance model described in the preceding sectionshas been implemented in a pipeline simulation prog ram w hichwas then used to predict displacement and penetration timehistories from the PIPESTAB, AGA, and DHI tests. The150 / Vo l . 116 , AU G U ST 1 99 4 T r a n s a c t i o n s o f t h e A S M E



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ACTUAL PREDICTED

200 500 400 SOO EDO 700 BOO 900 1000 1 IOO

time s)

"2"

5 a0 HHrd

s1csi

A C T U A L

r ~ HrJ H

M , Mr"fiJ 'r _ / i ^ rf"

r -

PREDICTED

0 '0 0 2DO 500 400 SOO 600 70 0 9 0 0 t O O O I tOO O IOO ZOO SOO 0 0 SOO

t i m e (s) t i m e ( s )Fig.10 Actu al and predicted time seriesof displacement and penetration forPIPESTAB test no.8

A C T U A L P R ED I C TED

IOO SOO 6D0 700 800 900 IO0O tOO

PCIIDOid

d

to o 2O0 SOO

t i m e (s) t i m e (s)

ACTUAL PREDICTED

5O -IOO SOO 600 00 800 900 IOOO IOO

t i m e (s)

-pidM+J0)c0>

IO O 200 soo *o o eoo 600 roo eoo 900 1000

t i m e (s)Fig.11 Ac tual and predicted time seriesof displacement and penetration forPIPESTAB tes t no.13

Journal of Offshore Mechanics and Arctic Engineering AUGUST 1994, Vol. 116 /151Downloaded 15 Jan 2013 to 223.27.129.246. Redistribution subject to ASME license or copyright; see http://www.asme.org/terms/Terms_Use.cf


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ACTUAL PREDICTED

B ?

ftw-HT3.-V

time (s)

PREDICTEDIrl5- f

5-3 , r

iH yT p i - Ip - \1 '

|Q0 200 500 400 500 GOO 700 900 IOOO 1100

0'0BH O.07

O 100 20O SOO 40O 50O GOO 700t i m e ( s ) t i m e ( s )

Fig . 12 Ac t u a l a n d p red i c t ed t im e s e ri e s o f d i s p l a c em en t a n d p en e t r a t i o n f o r P IPEST A B t e s t n o . 19

Fig. 13n o .0 4

< i U -19 -.S -

12 -1 0 -

uu06 04 -0 2 -0 0 -

0 1 0 0 2 0 0 3 0 0

J~~^ 1H 1

4 0 0

_L ^ r

5 0 0

_f2. /

6 0 0N o. o f c y c l e s

M ea s u red ( ) a n d p red i c t ed ( ) p en e t r a t i o n f o r D H I t e s t

laboratory tests, analysis, and simulations of the PIPESTABand AGA tests are fully described by Verley and Reed (1989).The simulation of DHI tests was straightforward, the forcesapplied in the horizontal and vertical directions in the testsbeing obtained from the envelope curves and used directly asinput to the simulation program.The large range of soil parameters covered in these tests(sand relative density 0.05 to 1.0) and the considerable differences in forcing between the PIPESTAB/AGA tests (irregular wavelike forces) and DHI tests (sinusoidal withmonotonically increasing amplitude) provide an effective fine-tuning and validation of the model. Altogether, some 1000simulations were conducted varying and fine-tuning the model

2 0 0 5 0 0 6 0 0 7 0 0

Fig . 14n o .0 8 M ea s u red I

300 400N o . o f c y c l e s

- ) a n d p red i c t ed ( ) p en e t r a t i o n t o r D H I t e s t

parameters to give a best possible fit over the whole range oftests. A representative selection of results and general comments are noted in the following.The final set of parameters (i.e., Eqs. (8) and (10) to (13)with the adjustments indicated in the text) gives a good fit toall tests from all three sources. This set of parameters necessarily represents a com promise, and some tests are fitted betterwith other param eter values; however, these are generally closeto the chosen values. Certain of the param eters can be adjustedto other values and still give as good an overall fit to the tests,e.g., the use of Eq. (9), rather than (8), to describe the breakout force. Furthermore, there is an interrelationship betweenparameters and the (small) adjustment of one parameter maybe compensated by (small) adjustments to one or more otherparameters. Thus, the final set of parameters is by no meansunique, but represents a good overall fit to the data.15 2/V o l . 116 , AUGUS T 1994 Transactions of the ASME



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Ratios between laboratory-m easured (denoted A CTU AL ) and predicted maximum horizontal displacement andmaximum pe netration achieved in each test are shown in Figs.8 and 9, respectively. Representative amplitudes of displacement due to individual (large) waves are also well predicted(not shown).Figure 10 shows the time series for displacement and penetration, both from the tests and from the simulations, forPIPESTAB test no. 8, with a relatively heavy pipe. The predicted response is very similar to that measured, whereas forthe original PIPESTAB soil model, the response was greatlyoverpredicted (Verley and Reed, 1989, Figs. 7 and 12).Figure 11 shows measured and predicted time series forPIPESTAB test no. 13, with a relatively light pipe. The responseisslightly underpredicted; however, the buildup of penetration and, in particular, the breaking down of penetrationat about 550 s from the start are predicted qualitatively well.Figure 12 shows measured and predicted time series forPIPESTA B test no. 19, a case with a large current c ompon ent.The response is predicted very well. Using the P IPEST AB soilmodel, the response was grossly overpredicted (Verley andReed, 1989, Figs. 9 and 15).The DHI data, consisting of a very large number of cyclesof monotonically increasing amplitude, is particularly usefulto check the development of penetration before break-out.Figures 13 and 14 show the development of penetration withnumber of cycles in the tests and in the simulations for DHItest nos. 4 and 8. The penetration development in the testsoccurs mainly in distinct jumps, corresponding to successivecollapse of the soil, whereas in the simulations, the penetrationdevelopment is smoother. Nevertheless, the prediction of thepenetration development must be considered rather good.

ConclusionsThe soil resistance model developed is based on a largeamount of data at full scale and covering sandy soils fromvery loose to very dense. The model has been incorporated ina pipeline dynamic simulation prog ram and tested against laboratory data for a pipeline section subjected to realistic (irregular wave and current) loading, as well as data from pipesections subjected to a large number of sinusoidal forces ofmonotonic increasing amplitude.The model has been found to give a good reproduction ofthe data on which it is based and also to reproduce the resultsfrom the realistic loading and sinusoidal forcing tests.References

Brennodden, H., Sveggen, O., Wagner, D. A., andMurff, J. D., 1986, Full-Scale Pipe-Soil Interaction Tests, Proceedings, 18th Offshore Technology C onference, OTC 5338.Brennod den, H., 1988, Pipe-S oil Interaction Tests on Sand and Soft Cla y,SINTEF Report STF69 F887018, prepared for the American Gas Association.Brenno dden, H., L ieng, J. T., Sotberg, T., and Verley, R. L. P., 1989, AnEnergy Based P ipe /Soi l Inte rac t ion Model , Proceedings, 21st Offshore Technology C onference, OTC 6057.L ieng, J. T., Sotberg, T., and Brennod den, H., Ene rgy Based Pipe SoilInteraction Mode ls, SINT EF Report STF69 F887024 prepared for the AmericanGas Association.Palmer, A. C , Steenfelt, J. S., Steensen-Bach, J. O., and Jacob sen, V.,Proceedings, 20th Offshore T echnology C onference, O TC 5853.Verley, R. L. P., and Reed, K., 1989, Resp onse of Pipelines on VariousSoils for Rea lis tic Hydrodynam ic L oadi ng, Proceedings, 8th Offshore Mechanics and Polar Engineering C onference, Vol. V, pp. 149-156.Verley, R. L. P., Sotberg, T., and Brennodd en, H., 1990, Break -Out SoilResistance for a Pipeline Partially Buried in Sand, Proceedings, 9th OffshoreMechanics and Arctic Engineering C onference, Vol. V, pp. 121-126.Wagner , D. A. ,Murff, J. D. , Brenn odde n, H. , and Sveggen, O., 1987, Pip e-Soi l Inte rac t ion Model , Proceedings, 19th Offshore Technology C onference,OTC 5504.

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A Soil Resistance Model forPipelines Placed on Sandy Soils

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