8 Te Oen Oean Engineering Journal, 21,, 8-44 Effets of te Sudan Penetration on te Adjaent Foundations Yongren. Wu*, Xiaobing u and Xuui Zang Oen Aess Institutie of Meanis, Cinese Aademy of Sienes, Beijing, Cina Abstrat: To study te effets of sudan enetration on te adjaent foundations of offsore latforms, exeriments and numerial simulations (using business software ABAQUS) are arried out. It is sown tat te enetration of sudan an ause te soil layer affeted in an annular zone. Te affeted zone as a maximum widt of one times te diameter of te sudan. Te defletion of te latform s foundation inreases wit te enetration of sudan. Te smaller te density of soil layer is, te bigger te dislaement of te foundation is. Howeer, te maximum dislaement at te to of te foundation anges little one te enetration det is oer a ritial alue. Te bigger te diameter and te enetration det of te sudan are, te bigger te dislaements of te foundation are. Keywords: Sudan, saturated fine sand, latform s foundation. INTODUCTION Jak-u rigs are used extensiely in offsore engineering to drill oil and gas wells or used to work-oers on a fixed jaket installation. Deending on te jaket footrint and te ositioning of te jak-u rig, te sudans may be lose to te ermanent iled foundations of te jaket. It will result in stressing of te iles due to te lateral deformations aused by te enetration of te sudan. Te bearing aaity of te soil layer may be affeted as well. Terefore, te effets of te sudan enetration on te ile or buket foundation of latform sould be onsidered [1]. Te degree of moment restraint alied at te bottom of te leg by te soil to te sudan is quite unertain due to te unknown effets of te soil-struture interation between te sudan and te sand in seabed [2, ]. Efforts ae been ut into te soil-struture interations by many researers [4, ]. Howeer, it is diffiult to obtain te exat solution of tis roblem beause of te omlexity [6-8]. Te key issue in determining te effets of sudan enetration on te iles is te soil-sudan and soil-ile interation. Te effets of sud-an enetration on te foundations of fixed latforms are studied first by exeriments. Ten, numerial simulation is arried out based on te exerimental results. Te effets of fators, su as te density of soil layer, te enetration det and te enetration eloity of sudan, are inestigated. DIMENSIONA ANAYSIS First, dimensional analysis is arried out to obtain te main fators and simlify te exerimental and numerial simulations [9, 1]. In tis roblem, te main indeendent ariables are as follows (Fig. 1): arameters of ile foundation: te det, te diameter, te density, te stiffness of anti-bending EI, Poisson s ratio and te load P ( P x, P y are te sum of te self-graity of te latform and te alied load in te x and y diretions, resetiely). Te sudan is assumed to be a rigid body and wit a diameter of and a eigt of D d. Te soil layer s arameters: te elasti modulus E s, te oisson s ratio s, te Coesion C, te internal frition angle s, te density s. Te distane between te foundation and te sudan. Te frition angle between te sudan and te soil layer s. Te enetration eloity. Te oter arameters are te graity aeleration g. Te unknowns are te defletion of te foundation. Considering g g ( EI)<< 1, te dimensionless form of te relation between te unknowns and te ariables an be exressed as follows: = f D EI d,,,,, g g Sudan D1 D2 soil layer P y P Px ile, g (1) *Address orresondene to tis autor at te Institutie of Meanis, Cinese Aademy of Sienes, Beijing, Cina; Tel: 8618244192; E-mail: xbinlu@sou.om 1874-8X/1 Fig. (1). Sket of sud-an enetration. 21 Bentam Oen
Effets of te Sudan Penetration Te Oen Oean Engineering Journal, 21, Volume 9 Water surfae VDT ile Fore transduer Sudan ile Sand troug a ale. A 2 m tik oarse sand layer is laid at te bottom of te box to allow te water to rise uniformly and reent te iing. Wen te water leel is 1m oer te sand layer surfae, aly auum in te sand for 8 ours to inrease te saturation degree. Te saturation degree is about 98% in tests, wi is tested by measurement of te ore ressure. Te saturation degree is te ratio of te ore ressure diided by tat in full saturation ondition. Two VDTs are used to measure te enetration det of te sudan and te defletion of te ile, resetiely. Wen te enetration det is oer a gien alue, te load is stoed. Te design of exeriments is sown in Table 1. (Te osition of te ile is te ratio of te distane between te enter of sand layer and te side of sudan to te diameter of sudan). Coarse sand Sudan eliability of Exeriments To alidate te reliability of exeriments, reeated exeriments are arried out first. Fig. () sows te deeloment of te defletion on te ile s to wit te enetration of sudan. It is sown tat te results in 6 exeriments are all agreement well. -. Fig. (2). ayout of te model. EXPEIMENTA POCEDUES AND ESUTS Te ayout and Proedures of Exeriments Exeriments are arried out in an organi glasses box wit a size of mmm. Te sudan is enetrated from te enter of te box (Fig. 2). Te soil layer is onstituted of fine sand wit a seial graity 2.69, aerage grains diameter (D).14m and ermeability oeffiient 11-4 m/s. After te dry sand samle as been reared, te sand layer is saturated by filling water from te bottom of te tank Penetration det of sudan / adius of sudan.. 1. 1. 2. 2.. Test No. 1; left ile Test No. 2; left ile Test No. ; left ile Test No. 4; left ile Test No. ; left ile Test No. 6; left ile Test No. 1; rigt ile Test No. 2; rigt ile Test No. ; rigt ile Test No. 4; rigt ile Test No. ; rigt ile -.4 -.2..2.4.6.8 1. 1.2 1.4 1.6 1.8 2. Deformation of ile's to / adius of sudan Fig. (). Deformation at ile s to in six reeated exeriments. Table 1. Exerimental Conditions No. Dry Density of Sand (g/m - ) Diameter of Sudan (m) Penetration Veloity (mm/min) Position of te eft Pile Position of igt Pile 1~ 1.6 7 2 1 1 6 1.6 7 2 1 1. 7 1. 7 2 1 1. 8 1.7 7 2 1 1. 9 1.6 12. 2 1 1. 1 1.6 12. 4 1 1. 11 1.6 12. 6 1 1. 12 1.6 12. 8 1 1.
4 Te Oen Oean Engineering Journal, 21, Volume Wu et al. -. -1 Penetration det / adius of ile.. =.19;r=1 1. 1. r=.22;=1 =rrs/r; =/ sudan2. 2.. -.1..1.2..4. Fig. (4). Effet of soil density on te defletions on te ile s to. Effets of Fators on te Dislaement on te To of te Foundation Effets of te Soil s Density and te Pile s Position Te effets of te soil s density and te ile s osition on te orizontal defletions on te ile to are inestigated by anging te arameters (= s / ) and i ( = / ). Fig. (4) and Fig. () sow te relation of dimensionless arameter / (te defletion on te to of ile is diided by te diameter of sudan) and D d / (te enetration det is diided by te diameter of sudan). It is sown tat te smaller / is, te bigger / is. Te defletion on te ile to inreases wit te inrease of te enetration det and wit te derease of te soil s density and te distane between te sudan and te ile foundation. Wen te distane between te sudan s side and te ile foundation is oer one times of te sudan s radius, te dislaement of ile s to may be negleted. Penetration det / adius of ile -. r=.19;=1. r=.2;. Deformation of ile's to / adius of. =1.r=.22;=rrr1. s/ ; ile=1. =/ 1. 2. 2.. -.1..1.2..4. Fig. (). Soil density s deformation at ile s to ( / = 1. ). Penetration det / adius of ile 1 2 4 6 7-2 -1 1 2 4 6 7 8 Fig. (6). Sud-an radius s deformation at ile s to ( / = 1. ). Effets of Sudan s adius Te effets of sudan s radius are inestigated by anging te dimensionless arameter / (Fig. 6). It is / ae small effets on te sown tat te anges of maximum dislaement. Te dislaements on te to of ile are mainly formed at te first stage wit te inrease of /. Wen te sudan s enetration det is oer some ritial alue, te defletion of te ile dereases. Te bigger te dimensionless arameter te dimensionless arameter / is, te smaller / is. Tat means, te defletion of te ile dereases wit te inrease of te distane between te sudan and te foundation. d Deformation of ile's to / adius of iler=2.; =1r=41.7; =1r=2.; =1.r=41.7; =1.r=/; =/ Effets of te Penetration Veloity of te Sudan Te effets of te enetration eloity of te sudan is inestigated by anging te dimensionless arameter g. Figs. (7 and 8) sow te relation between / and D / under different dimensionless enetration eloity g and different distanes between te sudan and te ile /. It is sown tat te effets of g are obious on te roess of ile foundation s dislaements but not on te maximum. Wen te enetration eloity is big, te dislaement deelos fast. Oterwise, te maximum dislaement ours only wen te sudan is enetrated into some det. Te sloe of te settlement zone aused by te enetration of sudan ranges from 28 to 1 (Table ). Te sket of te settlement zone is sown in Fig. (9). Te diameter of te settlement zone is about two times te diameter of sudan. Altoug it inreases obiously under te sudan, te density of te soil anges little in te oter zones. Te den-
Effets of te Sudan Penetration Te Oen Oean Engineering Journal, 21, Volume 41 Table 2. Soil Densities After Exeriments Penetration Veloity of Sudan (m/min) Sloe Angle of Settlement Zone Density of Soil Under Sudan (g/m - ) Density of Soil Surrounding te Settlement Zone (g/m - ) Density of Soil at te Uer Part Surrounding te Suan (g/m - ) Density of Soil at te ower Part Surrounding te Suan (g/m - ).2 29.4 1.74 1.61 1.62 1.66.4 28.4 1.77 1.6 1.8 1.67.6 28.6 1.68 1.8 1.6 1.67.8.9 1.6 1.6 1.8 1.67 Table. Parameters of Soil ayer Modul us E 1 Pa Poisson s atio Coesion C Pa Internal Frition Angle Floating Density g/m - Zone.2 2.692 Zone.2 2.692 Zone.2.692 Zone below te sudan 6.2.692 sity of te soil under te sudan inreases wit te derease of enetration eloity (Table 2). -1 Penetration det / adius of ile -1 =4.2*1 1 2 4 6 7-1 1 2 4 6 7 Defomration at ile's to / adius of ile- ; =1 =8.4*1 - ; =1 =12.6*1 - ; =1 =16.8*1 - ; =1 =/ (g) 1/2 ; = / Fig. (7). Deformation at te ile s to s. enetration eloities ( / = 1. ). NUMEICA SIMUATION Business software ABAQUS are used ere to simulate te effets of te sudan enetration on te ile foundation of fixed latforms. Firstly, te numerial results are omared wit te entrifugal exerimental results to ertify te onstitutie relation and te numerial net model used in omuting. Seondly, effets of te sudan s enetration on te ile s stresses, deformation and te deformation of te Penetration det / adius of ile =1. =1. 1 =4.2*1 - ; - ;=8.4*1 Deformation at ile's to / adius of 2 =12.6*1 ile =16.8*1 - ; 4 =/ (g) 1/2 ; = / 6 7-1 1 2 4 6 7 Fig. (8). Deformation at ile s to s. enetration eloities ( / =1. ). eft ile Settlement zone Sudan igt ile Fig. (9). Soil surfae osition after exerimenting.
42 Te Oen Oean Engineering Journal, 21, Volume Wu et al. soil layer surrounding te ile foundation are inestigated. It is sown tat te soil layer is affeted obiously inner te zone wi is one times te sudan s diameter away from te side of te sudan. Numerial Model To alidate te numerial model, te numerial results are omared wit te entrifugal exerimental results. Te arameters adoted in numerial omuting are all obtained from literatures [6,7]. Te sale of soil layer is lengt widt eigt =m m 26m. Te soil layer is diided into tree arts: te zone I wi te sudan is enetrated into, te damaged zone II and elasti zone III (Fig. 1). Zone I is a ylinder wit a radius of m. Zone II is an annular stri wit a widt of 1m. Te oter is zone III. Te ile foundation is loated at te osition one times of te sudan s radius away from te sudan s side. Pile ision of numerial simulation, te network is densified near te foundation and sudan. Te bottom is fixed, e.g. u x =, u y =, u z =. Te surfae is free. Te normal fixed onditions are adoted in oter boundaries. Te initial eart stresses are alied before te enetration of sudan. Te Constitutie elation Te model of Mor-Coulomb is used in Zone I and II. Te linear elasti model is used in zone III. Te arameters of onstitutie relation are sown in Table. Comarison of te Numerial and Exerimental esults Te omarison of te numerial and entrifugal exerimental results is sown in Fig. (12). It is sown tat te numerial and exerimental results are agreement well wit ea oter, exet at te zone near te bottom. Te reason of error is tat te onergene of numerial simulation is diffiult wen te enetration det is oer some alue beause te kaoline soil is ery soft. Te adoted onstitutie relation auses error at te ondition of big deformation. Deformation(mm) 1 1 2 2 I 1 III II Det(m) 1 2 2 Fig. (1). Sket of numerial model. a) Defletion of ile wen te enetration det is 14m Det(m) - 6 9 12 1 18 21 24 6 9 12 1 18 21 24 27 Sudan enetration det: m 6m 9m 12m Maximum b) Defletion of ile at different enetration det in exerimental results Fig. (11). Sket of te Network. Network and Boundary Conditions and Initial Conditions Te network is sown in Fig. (11). Te ile foundation is tied wit te soil layer. Tat means, te foundation and te soil layer ae te same dislaement. To guarantee te reision of numerial simulation, te network is densified Fig. (12). Comarison of te lateral deformation of iles. Numerial esults Fig. (1) sows te stresses distribution of te soil layer and te ile foundation. Beause it as a big elasti modulus and is tied wit soil layer in simulation model, te ile foundation bears most of te load. Tus a narrow zone wit small stress surrounding te ile ours. Te sudan enetration auses te soil below moes laterally. Te stresses distribu-
Effets of te Sudan Penetration Te Oen Oean Engineering Journal, 21, Volume 4 tion is sown in Fig. (14). It is sown tat te moement of soil indues te ile foundation bend laterally. Tere exists stress onentration at te end of te ile foundation. Te distribution of te orizontal dislaements of soil layer at te fae of y is sown in Fig. (1). It is sown tat te distribution of dislaements at te left and rigt sides of te sudan are not symmetrial. Fig. (16) sows te ertial dislaements at te surfae of soil layer. It is sown tat te ile foundation limits te lateral moement of te soil at te rigt side in some extent. Te dislaements of te soil at te left side of te sudan are big and te isoline of orizontal dislaements distributes uniform. Fig. 17(a-d) sown te settlement at different det. Fig. (17a) sows te ertial dislaements of te soil layer at 6m det. It is sown tat te ertial dislaements are smaller tan tat at te surfae. Fig. (17d) sows te ertial dislaements of soil layer at 24m det. Te maximum dislaement at tis det is only.8m Z (m) 2.14 2 -.16.22 1 -.2 -.82.68 1 -.72 -.72.68 -.72-2 -1 1 2 Fig. (1). Horizontal dislaement of te soil layer at y=. S, Mises (Ae. Crit.: 7%) +1.829e+7 +1.2e+ +1.12e+ +1.1e+ +9.44e+4 +8.7e+4 +7.71e+4 +6.8e+4 +.98e+4 +4.112e+4 +.126e+4 +2.19e+4 +1.1e+4 +1.664e+ 2 1 -.7 -.2 -.1 -.8 -.6 -.8-1 -.2 -.7 ODB: 2 1 612. odb Ste: Ste: 2 Inrene 26: Priman Var Mises ADAQUS STANDAD Version 6.- Ste: Time 1. Fig. (1). Stress distribution at y=. r i May 4 21:: 11 GNT+8: 2-2.8-2 -1 1 2 Fig. (16). Vertial dislaement at te surfae of te soil layer. S, Mises (Ae. Crit.: 7%) +1.829e+7 +1.677e+7 +1.2e+7 +1.7e+7 +1.22e+7 +1.68e+7 +9.16e+6 +7.642e+6 +6.121e+6 +4.6e+6 +.79+e+6 +1.8+e+6 +.671+e+6 ODB: Job-612.odb ABAQUS/STANDAD Version 6.-1 Fr: 2 1 Ste: Ste-2 Inrement 26: Ste Time = 1. Primary Var: S, Mises Deformed Var: U Deformation Sale Fator : +1.e+ Fig. (14). Stress distribution of te ile. CONCUSIONS A series of exeriments and numerial simulations are arried out to inestigate te effets of sudan s enetration on te adjaent ile foundations. It is sown tat te effets of enetration det, soil s density, distane between te sudan and te ile foundation are obious. Te diameter of te settlement zone is about two times te diameter of te sudan. Te sloe of te settlement zone aused by te enetration of sudan ranges from 28 to 1 wi is lose to te internal frition angle of fine sand used in exeriments. Te density of soils under te sudan inreases obiously. Te dislaement of te ile foundation dereases wit te inrease of te distane between te sudan and te ile foundation and wit te derease of diameter of te sudan. Te effets of te ratio of sudan s diameter to ile s diameter and te enetration eloity are little on te maximum dislaement of te ile but are obious on te roess.
44 Te Oen Oean Engineering Journal, 21, Volume Wu et al. 2 2 -.16 1-1 -. -. -.67 -. -.16 -.8 -.2 -.41 1-1.21..18.11.26.66..16-2 -.16-2 -1 1 2 (a) 6m -2-2 -1 1 2 () 19m 2 2 1-1 -2.97.1.1.9.18.16.68 -.19 1-1.4..62..2.72.82.14.4-2 -1 1 2 (b) 1m Fig. (17). Vertial dislaement distribution at different dets. -2-2 -1 1 2 (d) 24m ACKNOWEDGEMENTS Tis rogram is suorted by te fund of Cinese Oean Oil Co. and Cinese Aademy of Sienes KJCX2-SW- -1 (421) and National Natural Siene Fund (No. 1772182). EFEENCES [1] X.M. Tan, J.Y. Guo, and C. u, Effet of sudan enetration on neigboring existing ile, In: Pro. 16 t Int. Offsore and Polar Engrg. Conf., San Franiso, California: USA, June 26,. 16-2. [2] M.J. Cassidy, Non-linear analysis of jak-u strutures subjeted to random waes, P. D Tesis, Uniersity of Oxford, 1999. [] C.N. Sringett,.W.P. Stonor and W. Xu, esults of a jak-u measurement rogramme in te Nort Sea and teir omarison wit te struture analysis, Marine Strut., ol. 9,. -7, 1996. [4] M. Boulon, Basi features of soil struture interfae beaior, Comut. Geote., ol. 7,. 11-11, 1989. [] Y.E. Mostafa, and M.H.E. Naggar, esonse of fixed offsore latforms to wae and urrent loading inluding soil-struture interation, Soil Dyn. Eartquake Eng., ol. 24,. 7-68, 24. [6] H. Y. Ding, J. H. iu, and C. Zang, Analysis of effets of te drawing of sudan on te ylinder foundation by FEM, Cina Offsore Oil Gas, ol. 16,. -6, 24. [7].J. Siiliano, J.M. Hamilton, J.D. Murff, and. Pillis, Effet of jaku sud ans on iles, In: Pro. 22 nd Ann. Offsore Tenol. Conf. OTC6467, Houston, Texas,. 81-9, 199. [8] Y. Xie, C. F. eung, and Y. K. Cow, Effets of sudan enetration on adjaent ile, In: Pro. Int. Conf. Pys. Model. Geote., Hong Kong, August 26, ol. 1,. 71-76, 26. [9]. I. Sedo, Similarity and Dimensional Metods in Meanis (Trans.), ondon: Infosear, 199. [1] Q.M. Tan, Dimensional Analysis, Press. Cin. Uni. Si. Tenol., Hefei: Cina, 2. eeied: July 18, 29 eised: August 2, 29 Aeted: August 2, 29 Wu et al.; iensee Bentam Oen. Tis is an oen aess artile liensed under te terms of te Creatie Commons Attribution Non-Commerial iense (tt://reatieommons.org/lienses/by-n/./) wi ermits unrestrited, non-ommerial use, distribution and rerodution in any medium, roided te work is roerly ited.