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MINISTRY OF EDUCATION AND TRAINING NATIONAL UNIVERSITY OF CIVIL ENGINEERING VU DAN CHINH ASSESSMENT OF OVER-DESIGNED LOAD-BEARING CAPACITY OF FIXED STEEL OFFSHORE STRUCTURES IN EXTENDED DURATION – APPLICATION FOR VIETNAMESE CONDITIONS Major: Offshore Enginerring Code number: 9580203 SUMMARY OF DOCTORAL DISSERTATION Ha Noi - 2019 The Dissertation has completed at: National University of Civil Engineering Academic Advisor: Prof.Dr Pham Khac Hung 1st Reviewer: Assoc.Prof.Dr Pham Van Thu 2nd Reviewer: Assoc.Prof.Dr Bui Duc Chinh 3rd Reviewer: Assoc.Prof.Dr Nguyen Van Vi The Dissertation will be defensed in University Committee meeting at…………………………………………………………………………………… At ……… hh ……… dd ………… Mm ………… yy ……… The Dissertation can be found in National Library and NUCE Library ………………………………………………………………………………………… INTRODUCTION Idea of the dissertation topic There are two reasons for the dissertation: (1) The demand of life extension for existing fixed platforms in Viet Nam which are out of design life now and in the future is necessary; (2) Life extension assessment methods for the structures haven’t fully mentioned in current standards and these are the lastest trends worldwide for real project applications Research Objectives and Contents Objectives of the dissertation is to study to develope a method to assess the fixed steel platforms suffering over-designed environmental loadings to predict allowable life extension duration for the expired platforms in Vienamese sea conditions Contents of the dissertation includes chapters to provide overview of the problems, to summarize theorical basis for structural analyses, to develope a structural assessment method and to apply it to a typical structure under Vietnamese sea conditions Subjects and Scope of the dissertation The subjects are jacket platforms which are out of date in terms of design The scope are to develope an assessment method for the structures suffering over-designed environmental loadings, according to full plastics and fatigue crack propagation at cross sections of the structural elements, take account of random properties as wave loads, cross-section dimension, Young’s modulus and yield strength of steel materials Scientific Basis The dissertation builds an assessment method for the structures based on scientific basis as below: Non-linear analysis of frame structures in terms of geometric and physical aspects; Fatigue crack propagation analysis on hot spots of the structures; Random Processes Theory; Probabilistic and Structural Realiability Methods Research Method + Theorical research: to study and assess elasto-plastic structures and analyse fatigue under crack extension in random simulations + Applicable research: to study and build up procedures and typical calculation sheets, asscociated with commercial sofwares to assess fixed steel platform structures suffering over-designed environmental loads according to probabilistic simulations + Application for an actual structure to estimate and validate new approach of the dissertation New Contributions Scientific Aspect: The dissertation suggests a new approach to assess the safety of expired over-designed load-bearing jackets in Vietnamese seas in the extended duration The method is built based on realiability model of full plastic conditions and fatigue-caused crack limitation according to slow-speed propagation of cracks of the structural main members Practical Aspect: In practical meanings, it serves directly to the life extension and upgrading of the platforms, and is an important problem in Vietnam recently CHAPTER 1: OVERVIEW OF SAFETY ASSESSMENTS OF FIXED STEEL PLATFORMS AND IDEAS OF THE DISSERTATION 1.1 Overview of the development of fixed steel platforms worldwide and in Vietnam 1.1.1 Introduction about fixed steel platform structures Fixed steel offshore structures (or jackets) are framed structures supported by piles or gravity based foundations The platforms are built in offshore zones to serve oil and gas exploitation, other economical services and national security…In this dissertation the main subjects are the piled structures 1.1.2 The development and application range of fixed steel offshore structures The fixed steel offshore structures are commonly used over the world with about 6800 jacket platforms distributed over 53 countries Recently, in Viet Nam, there are more than 70 fixed steel platforms, concentrated in 50m water depth areas The deepest one is Lan Tay Platform with water depth of 125 m, the smallest one is Thai Binh Platform with water depth of 29m In current situation, to safe cost, investors of oil and gas fields in Viet Nam are trying to reduce new constructions and focus on two main solutions: + To upgrade and connect fields to increase output; + To extend platform duration of exploitation compared with design life 1.2 Current Standards applied in design and safety assessments of fixed steel platform structures There are limit states applied in current standard systems in terms of design such as API, DnV, ISO… as Ultimate Limit State (ULS), Fatigue Limit State (FLS), Service Limit State (SLS), Progressive Collapsed Limit State (PLS) and Accidental Limit State (ALS) These limit states shall be used to assess existing platforms API RP 2A re-checks the assessment procedure into levels: Design Level, Global Ultimate Strength and Risk Assessment 1.3 Related Studies 1.3.1 Some Research over the world a) Non-linear analysises for fixed steel platform structures using probabilistic theory b) Random Fatigue Crack Propagation according to Fracture Mechanical Theory c) Research on safety assessments of the structures based on strength – fatigue interactions using probabilistic methods by authors, such as Moan, T., (2002); Gerhard Ersdal, (2005) or Surrey University, (2000) 1.3.2 Safety Assessments of offshore structures based on probabilistic methods taking account of strength – fatigue interactions in Viet Nam a) Assessment methods according to Prof PHAM Khac Hung opinion; b) Doctor Dissertation of Dr PHAM Hien Hau (2010); c) Doctor Dissertation of Dr MAI Hong Quan (2014); 1.4 Research Ideas According to the analysises of standards and related research, the dissertation aims to study in order to develope a method to assess over-designed loading-bearing capacity of expired fixed steel platform structures in terms of full plastic and fatigue crack propagation conditions of main member cross sections Based on the evaluation results, extended durations of the structures will be decided with an acceptable risk probability 1.5 Main contents of the dissertation - 1st Content: Research on prediction of appearance probability of an over-designed environmental condition in Vietnamese seas in the extended duration - 2nd Content: Research on developing an assessment method for the structures in the extended duration based on strength reliability, according to full plastic and fatigue reliability conditions in terms of crack propagations on member cross sections - 3rd Content: Research on Risk Assessment and Determination of Allowable extended duration of the platform structures 1.6 Dissertation Scope - - - - - To reduce complexity of the research but ensure practicality, the dissertation suggests some limits as below: Random characteristics: Young’s Modulus, Yield Limit of steel materials and cross-section properties of main members are considered as random variables with standard distributions; Waves are considered as Stationary, Ergodic Random Processes Non-linear structural analysis method: The structures are analysed with large strain theory; the structures area analyzed with quasi-static method while wave loads are considering as quasi-static loading Global Strength Analysis: Using elasto-plastic model for structural materials; the structures are collapsed if one or more main members (Legs, Piles) are fully plastic; Not consider to plastic condition of joints Fatigue Analysis: Analyze the fatigue-caused crack propagation according to Paris’s Law; with the assumption that crack propagation is slow, in a sea state the propagation velocity of a crack is constant; shape of crack widening is semiellipses; Other factors: Corrosions, Marine Growth, collosion-caused deformation and geological conditions will consider with detailed survey data CHAPTER THEORICAL BASIS OF STRUCTURAL ANALYSIS OF FIXED STEEL PLATFORMS SUFFERING OVER-DESIGNED LOADS 2.1 Introduction Chapter will summarize analysis methods of fixed steel offshore structures suffering over-designed loads and apply in order to find collapse mechanisms of these typical platforms in Viet Nam seas This content is to develope the assessment method in chapter 2.2 Analysis on Over-designed Parameters in the extended lifetime of Fixed Steel Offshore Structural Platforms The dissertation only considers two main over-designed factors in the extended lifetime as below: - Fatigue Cracks continuously develop, leading to narrow member cross sections; - The structures meet over-designed storms; Over-designed sea states are rised from smallest in the extended lifetime Corresponding to each case, load-bearing capacity will be analysed to assess risk and estimate the allowable extended lifetime 2.3 Theorical Basis for analysis of fixed steel offshore structural suffering over design loading 2.3.1 Non-linear static analysis of fixed steel platform structures Figure 2.1 Regular of Coordinates and Displacements of frame members                                             u (2.1) v  w2    xx x          x   x     To establish shape functions u(x), v(x), w(x) at tips point of the element based on the elastic defelection equations depended on load bearing conditions Nonlinear Elastic Stiffness Matrix of the element can be expressed as below:  k uu k uv k uw  K  k vu  k vv kvw    e  k k wu wv  k ww (2.2)  Whereas, matrix blocks on main diagonal are:     T l k   l  k vv  l k ww       EI y   2 uu   EA   u  u  (2.3) dx  x  x  T l T       dx N v  v    v  v   x          x  x x  EI z   x   T T v  EI  v  z  x x     v 2  w  w  x   x  dx  T T N w  w     x  x  dx   EI y      (2.4) EA l EA  w dx x  w  w   x  x  (2.5) These two are coupling matrices between axial and lateral deformation and are linear in rotation k T l uw k uv  k vu   EA   v  u    x x  T k w l u   v     EA  u   w T  dx (2.6)  x  x  x  (2.7) The last integral give coupling matrices between the two directions of deflection: l  w v   T (2.8) T k wv  k vw  w   EA   v  dx  x  x x  x   Based on the material model, plastic stiffness matrix of the structures can be expressed as below:  (2.9) K p  K e  K e G (G T K e G ) 1G T K e Whereas: giT  Plastic Surface:      0 g G  g 2   S i  f ( N Qy Q N Q P , ,  N Q y , ,   ,  Q yP z M , x , M zP xP My M   , , Qz M x M , M y , z )1 M yP  0 M   z i (2.10) (2.11) zP Herein N, Qy, Qz, Mx, My, Mz, NP, QyP, QzP, MxP, MyP, MzP related to member force components and plastic forces of the cross sections For tubular elements:  Where: M P  Y M y2  M z2 M D d    P  D   ; NP  N  cos  Y     1    N   (2.12)  P 0  d       D    , D and d are outer and iner diameter of the element;  Non-linear analysis of the structures according to Finite Element Method Loading are increase step by step For a step, static equations are solved to decided the new states of structures for the analysis in the next step K p  V F (2.13) Herein, F is loading vector, V is joint displacement vector 2.3.2 Fatigue Crack Propagation analysis at hot spots of fixed steek offshore structures The relationship between ratio of crack range and number of cycle range and stress intensity range can be written according to Paris’s law as below: da  C ( K )m (2.14) dNw Deduced: a Nw  c da (2.15)  C ( K ( a ))m a th Herein, ath is the crack depth related to K = K th, ac is the crack depth related to collapsed time (m); Nw is the cycle number of loading; C is da/dN at K = MPa.√m (m/cycle), m is slope (from to 10) depended on materials and types of welds; K ( a )  K max  Kmin is stress intensity range, depended on a Generally, stress intensity factor can be expressed by the formula: K  Y ( a , t d ).  a  (2.16)                     a Y ( a , t d )   1, 08  0,    22,1 a t   1,  1, 24.e  357 a d  3,17.e t d td   (2.17)   For complex joints with no for available formula, the stress instensity factor can be determined by numerical methods At the ith year, related to jth wave group with number of cycle N wji, the crack depth is extended: a ji  C  ji Y ( j 1i )  a m N wji (2.18)  a j 1i  k Crack depth at ith year is determined as: a  1  aji (2.19) j1 ao is the initial crack depth, related to first stage fatigue limit It is normally determined through surveys According to tests, ao of metals can be assumed from 0.25 to 1mm 2.3.3 Fatigue cracks effects modeling As NORSOK N-004, an ellipse crack with short axis of 2a, long axis of 2c can be equivalent by a dent depth Dd: D 1 A  1 ac  (2.20) d D   cos  2  c A     cos   D d   Where D is member out diameter, Ac is crack area, A is cross area Figure 2.2 Illustration of plastic stress distribution on dented member Assuming that at a crack location, the equivalent section is modeling by a dent depth Dd (Figure 2.2) Fully plastic function equation of the section presented by the formula:   k'  N  N wji  j'1  eqj ' i m m  j ' i  wj ' i (3.3)   Herein, m is slope depended on materials (seeing Chapter 2),  j ' i is stress ranges corresponding to j’th effective wave group with number of cycle Nwj’i (j’=1k’) into jth sea-state induces stress intensity range K large than threshold (Figure 3.3) at the time of crack depth aj-1i, it means: K  j ' i  [ ji ]  th Y(a j 1i , t )  a d (3.4) j 1i Figure 3.3 Illustration of Effective Stress Ranges - For a sea-state number j with significant wave height Hsj and number of cylce Nwji in ith year, probabilistic characters of a ji can be determined based on Paris’s law: + Expected value of aji at tj: ji a a j 1 i  C Nwji  m eqji  m (3.5) G ( a j 1i ,t d ) + According to Taylor expansion, variance of aji can be calculated as: Var ( a ji )  Var ( a j 1i 2 )m C N w ji   2( m 1)  m   eqji G(a j 1 i Var (   eqji )2m  ,t ) d eqji Var ( G ( a j 1i , t d  )) G ( a j 1i , t d )   2( m1) Whereas expected value and variance of G(ai-1,td) is determined:  22,1      357 a j 1i  G(a j 1 i  1, 08  0, ,td )    td Var (G(a j 1i , t d )) Details of    2 a a j 1i a j 1 i     1, t  1, 3,17.e 24.e Var ( a j 1i )   Var (t d ) d  td j 1i are presented in dissertation (3.6) td - Probabilistic character of the crack depth at the end of ith year:      a (3.7) j 1i (3.8) 12   + Expected value: (3.9) aki (3.10) Var ( )  Var ( aki ) + Variance: variables with Gausian - Assuming crack depths at a time point are random distribution Fatigue Reliability at the end of the ith year: P  P ( a  t )  0,5 (  ) i mi d (3.11) i   a Reliability Index: a t a d (3.12) i Var ( ) Var (t d ) i 3.4.2 Strength Reliability of main member sections based on fully plastic conditions 3.4.2.1 The relationship between fully plastic surface  of a main member sectioncủa and the random variables The relationship between approximate fully plastic surface  of member cross sections and random variables according to polynomial surface type: n T n o  1 H max   F y   E    i1  D i   i1 1 2n i1 1 n  n i1  i1  n 3 i1 T 2  1 H max  2 F y Di    i1  n3 ti T T   H max F y   H max E   F y E (3.13) i1 1 T n    i1  H max D i1   T  i1  n  n H max t  i1 i1 1    n i1  n   E Di  i1 1    n n 1 Et  i1  n  i1 i1 1 i1  n    t t i1 1    i  n  2 i1 1   i1  3n3 Fyt i1 D1 D i n2 1    i1  n2 D Di 2 i1 1 n n ( n 1) i1 1 n2 n( n 1)  n i 1 1 i1 1 i  n   i1 1 i1  n  n   F y Di i1 1    n   n ( n 1) D n 1 D n    i  n   n 1 t i1 1 3E  i1 1 n  D t i  i6n3 i1 1 n ( n1) n2 n ( n1)  n ( n1) t t i1     n D n ti1 2  n3 t n 1tn Whereas: T H max  HT T H max Var ( H max T ) F E  E ; Fy  ;E ; Di1  yF y Var ( Fy ) Var ( E) D max t D i1 Var ( Di ) ; ti1  Var (ti ) t (3.14) i1 Herein i1 = 1÷n, n number of main members Factors in equation (3.13) are determined by regression method with minimum mean square error condition Total error of the regression model is estimated by S S determination factor R2  R  1 e For regression model with R2 near by 1, the S S T model is suitable with true model T 13 For each H value, to perform Monte Carlo simulation for random variables and determine eq values according to (3.13) with the large enough number of trials nt:   nt    100 z e / Var( ) e   (3.15)   Herein, e is acceptable error of the trials and ze is value corresponding to P ( z  e ze/2 )  , z is random variable with Gaussian distribution 3.4.2.2 Strength Reliability of main member cross sections based on fully plastic conditions Strength Reliability of a main member section is evaluated by the Monte Carlo simulation results with number of trials nti: p (3.16) n Pi1i  P(  i1i  0)  ti nt i where nt p i th is the total trials in i year with i1i ≤ 3.4.3 Assessment of over loading bearing capacity of structures at ith extended year a) Assessment based on fatigue condition - In case of fatigue reliability satisfying requirements, the crack depth is determined by the following formula The crack will be updated to the structural model at the same location prior to analyse strength of the structure  ai  Var ( ) - (3.17) In case of fatigue reliability not satisfying requirements: + If the crack is on the brace member, it is assumed that the brace member is released to chord member The structural model will be updated to analyse strength of structure + If the crack is on the chord member, it is assumed that the chord is collapsed, it means the structure haven’t enough load bearing capacity b) Assessment based on strength condition Reliability of structures based on strength conditions when suffering T year returned period at ith year Pi1 estimated by the minimum value of reliability of n1 main member cross sections 14 Pi1  Pi1i  với (i1=1÷n1) (3.18) Whereas, Pi1i are determined by the formula in section 3.4.2.2 If Pi1 are satisfied the requirements, the structures will be considered as enough bearing capacity 3.4.4 Risk Assessment for structures suffering over design wave loading Risk probability when structures meet a wave height HmaxT : Pr  (1  Pi H maxT ).P ( H  HmaxT ) Herein, Pi HmaxT are determined by formula (3.18) when (3.19) wave heighs are increased in step by step According to DnV “Risk Acceptance Criteria and Risk Based Damage StabilityPart 1”, risk criteria divided into three zones 1st zone: Acceptale Risk, where Pr ≤ 106 /1 year; Zone 2: As low as reasonably practicable, where 10 -6 ≤ Pr ≤ 10-3 /1 year; Zone 3: Not Acceptable Risk, where Pr ≥ 10-3 /1 year 3.4.5 Assessment of reducing of over loading bearing capacity of the structures and prediction of maximum extended duration The maximum extended duration are limited by minimum value of tb and tm, where: - tm are determined based on fatigue reliability, tm = i with: P (  t d )  0,5  ( a )  [P ] (3.20) i - tb are determined based on acceptable risk probability Pr related to T year returned period (T ≥ 100), tb = i’: (3.21) P H maxT   T ( Pr 1) i' 3.4.6 Procedure of assessment of over loading bering capacity and extended duration of fixed steel offshore structures 15 16 17 3.5 Softwares using in dissertation The dissertation uses commercial softwares: SACS, USFOS to analyse and uses Jrain to determine the number of stresses cycles using rain flow counting method 3.6 Conclusion of Chapter In chapter 3, the dissertation has developed a new method to assess over loading bearing capacity of fixed steel offshore structures and to predict the extended durations of the structures in Vietnamese sea conditions The method is fitted with calculation methods and softwares in the world The method can be used to assess offshore platforms for life extension in Vietnamese sea areas when cooporating with survey data The method has some limitations, such as errors control, reduction of calculating amount, calculating time These things are needed to improve in the next researchs The method is performed through the combination of the softwares listed above and calculation sheets of the author The method will be applied in chapter to assess an actual fixed steel platform in Vietnamese sea conditions CHAPTER A VIENAMESE CASE STUDY 4.1 Introduction The method was developed in chapter will be applied in chapter to analyse and assess over loading bearing capacity of a fixed steel offshore structure in Su Tu Den field, Viet Nam offshore Input data and analysis results are expressed in sections as below 4.2 Input data summaries 4.2.1 Structural Data Platform Substructure is a jacket with four legs, piles in legs The main parameters are summarized in table 4.1 Table 4.1 Structural data summaries Items Parameters Topside Living Quarter Platform 40x20x9 (m) Topside Weight 800 (T) Legs 810x20,6 (mm) Piles 720x20 (mm) Braces 609x12,7(mm) Function 18 4.2.2 Environmental data Mean Still Water Level: 45,6m; heighest: +2,0m; lowest: -2,5m Table 4.2 Maximum Wave Height Data Parameters Wave Direction NE E SE S SW 12,27 14,78 8,23 7,88 8,91 10,88 12,79 8,00 7,76 8,47 N 12,90 11,35 Max Wave Height (m) Period (s) W 11,61 10,40 NW 12,58 11,11 Table 4.3 Fatigue WaveData Hs(m) 0,0 0,5 1,0 1,5 2,0 2,5 3,0 3,5 4,0 4,5 o 45 0,0131 0,0723 0,0785 0,0516 0,0388 0,0192 0,0050 0,0009 0,0000 0,0000 o o 90 0,0041 0,0137 0,0209 0,0199 0,0144 0,0054 0,0003 0,0000 0,0000 0,0000 135 0,0007 0,0016 0,0018 0,0010 0,0003 0,0000 0,0000 0,0000 0,0000 0,0000 o o 180 0,0008 0,0022 0,0019 0,0020 0,0014 0,0007 0,0003 0,0000 0,0000 0,0000 225 0,0056 0,0322 0,0614 0,0856 0,0803 0,0661 0,0462 0,0265 0,0145 0,0069 o 270 0,0080 0,0205 0,0006 0,0001 0,0000 0,0000 0,0000 0,0000 0,0000 0,0000 o 315 0,0130 0,0347 0,0066 0,0008 0,0001 0,0000 0,0000 0,0000 0,0000 0,0000 4.3 Structural Assessment according to current standards 4.3.1 1st stage fatigue analysis results Using SACS software to analysis fatigue in 1st stage according to spectral method, the minimum fatigue life results are expressed in table 4.4 Table 4.4 Minimum Fatigue Life Results Joint 202L 101L Member Crack Location 101L-202L Crown point, on 101L-201L chord Crown point, on Life (year) Impacted Wave Direction 27,01 225 o 53,75 225 o chord 4.3.2 Strength checking based on WSD The results of the most dangerous members for ULS (100 returned period) are listed in table 4.5 19 Table 4.5 Strength Checking Results for ULS Member Location UC Direction 0,912 Hmax (m) 14,78 102L-202L Last bay of Row A 004P-104L Pile element of Row B 0,973 14,78 East East 4.3.3 Ultimate Global Strength Assessment Results Table 4.6 Ultimate Global Strength Assessment Results Design Wave Direction Collapsed Wave Height (m) RSR Height (m) East 14,78 2,0 20,9 Collapsed Modal [RSR] The chord member of last bay Row B is unstable and fully plastic 1,6 4.4 Structural Assessment based on the method of dissertation 4.4.1 Prediction of crack propagation According to results in table 4.4, joint number 202L has minimum fatigue life of 27 years, so it will be selected to analyse crack propagation in second stage in each year to make basis for prediction of structural life extension 4.4.2 2nd stage fatigue analysis results Crack propagation of member 102L-202L at the crown point of joint 202L is analyzed corresponding to each short term sea-state in each year Probabilistic characters results of the stress range in every year are summarized in table 4.7 The analysis results of fatigue crack sizes in every year are summarized in table 4.8 Table 4.7 Probabilistic characters results of the stress range in every year Year µ Hs 1 2 3 4 (MPa) (MPa) (MPa) (MPa) (MPa2) 95,88 90,89 0,00165 0,00218 0,00268 89,88 79,24 89,88 79,24 84,73 75,39 84,73 75,39 84,73 69,5 90,89 0,0013 93,06 83,54 93,06 83,54 87,9 83,54 87,9 78,04 85,62 75,22 95,88 (m) 4,5 3,5 4,5 3,5 4,5 3,5 4,5 3,5 4,5 3,5 (MPa) (m) 0,001 92,12 75,16 92,12 75,16 92,12 69,23 90,89 79,24 90,89 79,24 84,06 70,88 92,428 81,39 92,428 81,39 88,91 78,333 88,91 76,958 86,633 71,208 5,293 4,623 5,293 4,623 8,179 11,666 8,179 3,017 10,343 5,758  Var() 20 Year Hs (m) 0,00362 0,00520 0,00837 (m) 4,5 3,5 4,5 3,5 2,5 4,5 3,5 2,5 Var() 1 2 3 4 µ (MPa) (MPa) (MPa) (MPa) (MPa) (MPa2) 84,9 68,56 80,27 64,78 54,3 78,42 61,96 54,3 78,31 68,54 76,3 66,77 51,97 70,16 61,65 51,97 86,94 66,06 82,41 63,31 80,76 68,9 78,56 64,61 75,62 60,98 74,31 60,44 82,728 68,015 79,385 64,868 53,135 74,628 61,258 53,135 11,463 1,294 5,033 1,530 1,357 8,857 0,348 1,357  Table 4.8 Fatigue crack analysis Year a i (m) 0,001 0,0013 0,00165 0,00218 0,00268 0,00362 0,00520 0,00837 Hs (m) 4,5 3,5 4,5 3,5 4,5 3,5 4,5 3,5 4,5 3,5 4,5 3,5 4,5 3,5 2,5 4,5 3,5 2,5 µ  Var() (MPa) (MPa ) 92,428 81,39 92,428 81,39 88,91 78,333 88,91 76,958 86,633 71,208 82,728 68,015 79,385 64,868 53,135 74,628 61,258 53,135 5,293 4,623 5,293 4,623 8,179 11,666 8,179 3,017 10,343 5,758 11,463 1,294 5,033 1,530 1,357 8,857 0,348 1,357 Average of N in year 49,35 15,52 49,35 15,52 67,86 38,79 67,86 46,55 81,43 131,90 113,51 217,24 146,82 341,38 39,60 222,09 535,35 39,60 µ a (m) 0,00121 Var(a) (m) 2,2e-05 0,00155 2,61e-05 0,00198 4,96e-05 0,00247 5,34e-05 0,00328 9,89e-05 0,00468 0,000146 0,00759 0,000223 0,01371 0,000467 The reliability index in 8th year are calculated: a   td a  3,53 Var ( a ) Var (t d ) So in the 8th year of extension, the fatigue reliability is approximate 0,9993 4.4.3 Assessment Results of Over loading bearing capacity of the structure in extended duration According to the analysis results as above, the reliability of structural strength and risk probability are assessed at the most dangerous member section (joint 202L of member 102L-202L) in 7th and 8th years The results are presented as below: 1st case: At the 7th year, the fatigue crack is equivalent with a dent depth Dd = 0,94cm eq at the considered section is written as: 21  eq 2  0, 580  0.086 H max  0, 040 F y  0, 0700t  0, 025t  0, 033 H max  0, 0100F y 2  0, 070t  0, 035t  0, 081H max F y  0, 021H max E  0, 021H max D1  0, 021H max D2  0, 021 H max D1  0, 021 H max D4  0, 034 H max t1  0, 003 H max t  0, 011 H max t3  0, 021 H max t4  0,130 F y t  0, 020 F y t  0, 060 F y t  0, 01Et  0, 01D2 t  0, 01t1 t3  0, 05t t3 Sum of Square errors of the equivalent function is 0,004 The residual sum of squares is 2,992 Determination factor R2 = 1- 0,0004/2,992 = 0,999 Due to R is aprroximate so the equivalent fuction can be accepted To increase Hmax from 18m to 20,5m For each wave height, the reliability of the structure and the risk probability are estimated The results are summarized in table 4.9 Table 4.9 Structural assessment and risk probability resutls–7 th year No Hmax (m) 18 18,5 19,4 20 20,5 T 600 800 1400 1900 2500 P(H≥Hmax) 0,00167 0,00125 0,00071 0,00053 0,0004 P(< 0) 1,0000 1,0000 0,9920 0,8210 0,0001 Pr 0,00000 0,00000 0,00001 0,00010 0,00040 As the results in section 4.4.2, the operating duration of the structure can be extended to 7th year with fatigue reliability approximately 1,0000 At the end of th year, wave height of 20,5 m will induce maximum risk probability, approximately 0,04% According to section 3.4.4, due to Pr ≤ 10-3 so the risk level can be acceptable 2nd case: At the 8th year, as the same as 1st case , the fatigue crack is equivalent a dent depth of 2,57cm eq of the considered section is expressed as: 2  eq 0, 480  0.176 H max  0,095Fy  0,040t  0,015t  0,004 H max  0,035F y  0,005E 2 0,040t  0,025t  0,078H max F y  0,005H max E  0,005H max D1  0,005H max D2  0,005H max D3 0,005H max D4  0,014 H max t1  0,005H max t2  0,033H max t3  0,005H max t  0,020 F y t  0,020F y t3 0,010 F y t  0,010 Et  0,020 Et3  0,010 D1 t  0,020 D1 t  0,010 D t  0,020 D t  0,010D3 t2 0,020 D3 t  0,020 D t  0,020 D t  0,010t1 t2  0,020t1 t3  0,010t2 t3  0,030t t  0,020t3 t Factor R2 = 1- 0,007/2,162 = 0,996 Due to R is aprroximate so the equivalent fuction can be accepted To increase Hmax from18m to 20,3m For each wave height, the reliability of the structure and risk probability are estimated The results are summarized in table 10 Table 4.10 Structural assessment and risk probability resutls–8 th year No Hmax (m) 18 18,8 19,4 20 20,3 T 600 950 1400 1900 2174 P(H>Hmax) 0,00167 0,00105 0,00071 0,00053 0,00046 P(< 0) P 1,0000 0,9920 0,8200 0,4920 0,0001 0,00000 0,00001 0,00019 0,00027 0,00046 r 22 As the results in table 4.22, the operating duration of the structure can be extended to 7th year with fatigue reliability approximately 0,9993 At the end of th year, wave height of 20,3m will induce maximum risk probability, approximately 0,046% According to section 3.4.4, due to Pr ≤ 10-3 so the risk level can be acceptable Comments for the analysis results: + As the analysis results, the total difference of the regression model is from 0,1% to 0,4% + Corresponding to Monte Carlo trials number large than one hundred thousand, the error is approximate 0,1% 4.4.4 Conclusion According to assessment method suggested in the dissertation, after appearing the first crack due to fatigue at 27 th year (fatigue life follow by standards), the operating duration can be extended on about th year with safety and an acceptable risk probability As the suggested method, in the 8th year after design life, the structure can resist a wave height large than the design value, 14,78m, and smaller than 20,9m which is collapsed wave height, corresponding to different risk levels in different years It means that the method allow structures resisting loading large than design value according to standard regulations with a certain safety factor CONCLUSIONS OF THE DISSERTATION Research Results and New Contributions of the Dissertation The dissertation has developed a method for assessment of over load-bearing capacity of fixed steel offshore platforms and prediction extended duration for the expired structures in Vietnamese conditions The method includes main contents as below: - To establish formula in order to predict occurence probability of every incident over-designed wave height based on field-trip data These formula can be used for risk analysis of the structures in the extended duration; - To analyse fatigue crack propagation in terms of random simulations in order to estimate the maximum extended duration of the structures and modelize loadbearing cross-section decrease accumulated every year in order to evaluate over load-bearing capacity; - To establish formula and procedures in the assessment of the structural loadbearing capacity impacted by over-designed wave heights according to random simulations; 23 - To establish formula in risk assessments of the structures related to overdesigned wave scenarios in Vietnamese sea conditions The results will be used to predict allowable extended duration of the structures Applicable Capability of Dissertation According to research results of the dissertation and through the case study in chapter 4, there are some comments as below: + If the existing jackets designed by current standards can resist over-designed loads in terms of inelastic-stage working; + In spite of strength reduction damaged by fatigue accumulation after exploitation, the jackets can still operate longer than design-based life; The methods and formula developed in the dissertation apply for the assessment of fixed steel offshore structures in terms of life extension in Vietnamese conditions The method has implications for practice, supporting investors and the authorities to allow the structures to operate continiously after the end of design life This method can apply for safety assessments of upgrading offshore platforms; To apply this methodology in actual projects, it is necessary to provide reliable insitu-surveyed data, such as: Real-measured environmental data of fields; Periodic crack data; Corosion data, structural deformation caused by impact; Actual Marine growth data; Pile scour data…; To utilize their capacity and exploiting period as a demanding of almost oil and gas fields in Viet Nam recently, structural evaluation should perform associated with this method at the same time with their design Developments of the dissertation in the future - Study on determination of non-linear random vibrations of structures in order to assess over-designed load- bearing capacity of fixed steel offshore structures in deep water conditions; - Study on crack propagation analysis based on non-linear fracture mechanical theories and associated with experiments for existing offshore structures in Vietnamese seas; - Study on utilization of working capacity for existing offshore structures based on reliability analysis in terms of global systems; - Study on assessment of fixed steel offshore platforms taking account of random effections of survey data; - Study on assessment of effects of over designed waves on fatigue cracks propagation at hotspots of fixed steel offshore structures; - Study on assessment of over designed load-bearing capacity on fixed steel offshore structures in terms of plastic conditions of tubular joints; - Study on reduction of calculating errors in actual projects; 24 - Study on software establishment to automatical analyse and assess fixed offshore structures for life extension; - Study on methods of risk assessment and mitigation for fixed steel offshore structures when suffering environmental conditions due to climate changes 25 Publications Vu Dan Chinh, Dinh Quang Cuong (2014), “An estimation of static stress effects on fatigue life of fixed steel offshore structures in Vietnamese sea conditions”, Journal of Science and Technology in Civil Engineering No 21 (Vietnamese) Pp - 10 Dinh Quang Cuong, Vu Dan Chinh et al (2015), “Study on assessing the vibration of DKI fixed steel structures piled in coral ground based on progressive collapse limit state”, Journal of Science and Technology in Civil Engineering No 26 (Vietnamese) Pp 74 – 79 Vu Dan Chinh, Pham Khac Hung (2016), “Ultimate Strength Assessment of Fixed Steel Offshore Structures on Account of Fatigue Crack Effects in Viet Nam Sea Conditions”, EASEC 14 Conference of Structural Engineering and Construction ISBN 798-604-82-1684-9 Page No 759 – 767 Vu Dan Chinh (2016), “Assessment of Fixed Steel Offshore Structures When Suffering Over-Design Environmental Loading in Vietnamese Sea Conditions””, Proceeding of Scientific Conference of 35th anniversary of Vietsov Petro (Vietnamese) Pp 273 – 280 Vu Dan Chinh (2018), “A method for reliability assessment of fixed steel offshore structures under over-design loading”, Journal of Science and Technology in Civil Engineering Vol 12, No (Vietnamese) Pp 30 – 39 Vu Dan Chinh (2019), “Safety Assessment of Fixed Steel Offshore Structures When Suffering Over-Design Environmental Loading in Vietnamese Sea Conditions”, Proceedings of the 1st Vietnam Symposium on Advances in Offshore Engineering, ©Springer Nature Singapore Pte Ltd 2019, M F Randolph et al (Eds.): VSOE 2018, LNCE 18, pp 537-543, 2019 ... Vienamese sea areas a) Bach Ho Field b) Su Tu Trang Field c) Thang Long – Dong Do Field d) Thien Ung Field Figure 3.1 Relationship between maximum wave heights and the returned periods – Vienamese... Vienamese sea conditions 3.3.1 Relationship between over design wave heights and the probability of occurences in Vietnameses conditions According to survey data, maximum wave height in Vietnamese... structures in Vietnamese sea conditions The method is fitted with calculation methods and softwares in the world The method can be used to assess offshore platforms for life extension in Vietnamese sea