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Research Journal of Applied Sciences, Engineering and Technology 4(19): 3544-3551, 2012
ISSN: 2040-7467
© Maxwell Scientific Organization, 2012
Submitted: January 12, 2012                Accepted: February 17, 2012             Published: October 01, 2012

      Reliability Analysis of Jacket Platforms in Malaysia-Environmental Load Factors
           1
            Nelson J. Cossa, 1Narayanan S. Potty, 1Arazi B. Idrus, 2Mohd Foad Abdul Hamid and
                                            1
                                              Zafarullah Nizamani
        1
          Department of Civil Engineering, Universiti Teknologi PETRONAS, Bandar Seri Iskandar,
                                       31750, Tronoh, Perak, Malaysia
     2
       Principal Engineer-Structural, Scientige Sdn Bhd, Kuala Lumpur, Currently on leave of absence
                 from Faculty of Mechanical Engineering, University Technology, Malaysia

    Abstract: In recent years, there has been a significant trend for adoption of the ISO-19902 standards for design
    of fixed steel offshore structures. The implementation of this standard aims to provide a harmonized
    international framework of design. Unlike, the traditional and currently used, WSD-method, the ISO-19902,
    follows the LRFD-method, that consists of both partial load and resistance factors. These partial factors are
    usually calibrated through reliability analysis. In these analyses, the performance of a structure is defined by
    the limit state function for the critical mode of failure. This paper, focuses mainly on the ultimate (strength)
    limit state which is directly related to the (highest) environmental loading. The partial environmental load
    factors contained in the ISO 19902, were calibrated for the Gulf of Mexico and UK's North Sea conditions,
    which are relatively harsh than those in Malaysia. The study presents the steps taken for the determination of
    the environmental load factor for tubular members of jacket platforms in Malaysia. The factor was determined
    such that the reliability of tubular members of jacket designed as per the LRFD-method is at the level of target
    reliability obtained by the WSD-method.

    Keywords: Environmental load factor, reliability analysis

                   INTRODUCTION                                elastic zone. The risk was catered by reducing the yield
                                                               stress of the structural elements that is tubular members in
     Offshore structures are likely to be subject to various   this case. In practice of design, the actual loads are
types of loads and deformations arising from service           calculated first and then members’ dimensions are
requirements ranging from the routine operating loads to       selected such that the stresses remain below certain limit
the extreme storm or accidental loads. Hence, the              of the yield strength. Thus, the global safety factor is an
structure has to be designed such that it can withstand        implicit nominal value of 1.67. For extreme storm
these demands throughout its expected design life. The         condition a one-third increase in allowable stress is
designers have been able to achieve this through the use       permitted, hence the safety factor becomes 1.25 (=
                                                               1.67/1.33) (API, 2005).
of the design codes. In the offshore industry, the design of
                                                                    Most of the fixed steel offshore structures designed
fixed steel offshore structures, typically known as jacket
                                                               as per WSD have not experienced failures related to the
platforms, has been based on the API RP2A-WSD                  design approach, however there are limitations associated
standard (API, 2005). The Working Stress Design (WSD)          with it, such as (FHWA, 2001):
method is based on safety factor provided only to the
resistance of the material without considering the             C   Does not properly account for variability of loads and
uncertainties related to the loads:                                resistances. Loads are considered to be without
                                                                   variation i.e., are assumed to be deterministic.
    Rn/SF$D + L+W                                   (1)        C   Does not provide a reasonable measure of strength,
                                                                   which is a more fundamental measure of resistance
where, SF is the global safety factor and it covers the            than is allowable stress.
loads (D dead load, L, live load and W environmental           C   The factor of safety is in most of the cases applied on
load) and Rn the nominal resistance (strength) related             resistance side. Its selection is subjective and does
uncertainties. The safety factor was selected, on basis that       not provide measure of reliability in terms of
stresses in the structural element shall not exceed the            probability of failure.


Corresponding Author: Nelson J. Cossa, Department of Civil Engineering, University Technology PETRONAS, Bandar Seri
                      Iskandar, 31750, Tronoh, Perak, Malaysia
                                                           3544
Res. J. Appl. Sci. Eng. Technol., 4(19): 3544-3551, 2012

     The need to overcome these definciencies, lead to              Table 1: Platforms details
changes in the design concepts. Strutural reliability               Platform                                 Installation
                                                                    name         Location      Depth (m)     year           No. of legs
analysis was applied to evaluate the risks and                      A            PM            61.00         2006           4
uncertainities associated with the safety of structure. In          B            SK            72.40         2003           4
this analysis, the safety of the structures is defined in           C            SB            42.80         2007           6
mathematical terms, in which the uncertain variability of           PM: Peninsular Malaysia; SB: Sabah; SK: Sarawak
the load and resistance are assumed to be independent and
represented by their respective probability density                 analysis adopted in this study is based on the component-
functions. The mathematical expression is based on the              reliability as defined by Bomel (2003).
purpose for which the structure is designed. The condition
beyond which the structure fails to meet its intended                            MATERIALS AND METHODS
design purpose, is called limit state, e.g. ultimate strength
limit state, fatigue limit state, etc. For a certain limit state,        The research study was carried out on the fixed
a mathematical function can be developed and                        offshore platforms fabricated during the period of 2005-
subsequently the safety perfomance can be evaluated in              2010 and installed in the Malaysian offshore operational
terms of its probability of failure or reliabity index. This        waters. This section presents and discusses the criteria for
process is termed reliabilty-based design or Load and               selection of the platforms, the determination of the load
Resistance Factor Design (LRFD). The generalised safety             and resistance statistical parameters and the methods
criterion for the LRFD takes the following format (ISO              adopted for the reliability evaluation and determination of
19902, 2007):                                                       the environmental load factor.

     Rn/(R $ (D D+(LL+(ww                                (2)        Selection of the platform: Data was collected from three
                                                                    platforms, of which one was selected for this study. The
where, (R is the partial resistance factor, that cater to the       selection was based on the availability of complete
uncertainties associated with the resistance and varies             metocean parameters and the completeness of the
with the mode of failure being evaluated e.g., axial,               platform model, such that it better represents the actual
bending, shear and so on. (D,(L and (w are the partial              structure as installed.
dead, live and environmental load factors respectively.
The partial environmental load factor, in particular, is            Operating regions: Malaysia is divided by South China
very crucial as it depends mainly on the local conditions           Sea into two namely Peninsular Malaysia and Borneo
at the location in which the structure is installed. The            Island consisting of Sabah and Sarawak states. It was
selection of the partial factors is done through calibration        thought necessary that one platform from each region
methods and determined such that optimum level of                   should be selected and Table 1 shows the details of the
safety is achieved, at an acceptable cost (Nowak et al.,            platforms. Their depth varies from 42 to 73 m. They were
1986, 2000). Depending on the function of the structure,            designed as per API RP2A-WSD 21st edition (current
different levels of safety maybe recommended. For                   edition). The number of legs in platforms in Malaysia
example for unmanned and manned fixed steel offshore                varies from three to eight but the most typical is four. In
structures, the ISO recommends an annual probability of             general, it can be assumed that listed platforms are
failure at range of about 10!3 and 10!5, respectively (ISO          representative of the vast other installed structures in the
19902, 2007). Alternatively, the partial factors can be             Malaysian waters.
evaluated so that the safety is at the same level as that of
                                                                    Table 2: Members selected for calibration
existing structures that were designed as per API RP2A-             Diameter Wall           Length                     Slenderness
WSD.                                                                (D)       thickness(T) (L)              K factor   %         D/T
     During the course of the development of the API                1650      25.0          9344            1.0        0.23      66.00
RP2A LRFD and later the ISO 19902 code for design of                1630      15.0          17500           1.0        0.43      108.70
fixed steel offshore structures, Moses et al. (1987, 1988,          660       12.7          15370           0.7        0.65      51.97
                                                                    711       15.0          11000           0.7        0.43      47.40
2000) carried extensive calibrations works, for the Gulf of         610       12.7          11800           0.7        0.54      48.03
Mexico. Similarly, Bomel (2003) conducted studies that              660       19.0          11940           0.7        0.51      34.74
covered the North Sea conditions requirements. In Asia,             406       12.7          12000           0.7        0.83      31.97
Duan et al. (2006a, 2006b) carried out the recalibration            508       12.7          12400           0.7        0.68      40.00
                                                                    610       12.7          47400           0.7        2.18      48.03
works for selected platforms located at the China's Bohai           610       25.0          7000            0.7        0.32      24.40
Sea. The objective of this research is to evaluate the              559       25.0          8450            0.7        0.42      22.36
reliability index of tubular members of selected existing           559       15            5100            0.7        0.26      37.27
jacket platforms in Malaysia, for both API RP2A-WSD                 547       19            7200            0.7        0.37      28.79
and ISO (LRFD) methods and subsequently determine a                 610       25            7900            0.7        0.36      24.40
                                                                    610       12.7          9790            0.7        0.45      48.03
suitable environmental load factor. The method of


                                                                3545
Res. J. Appl. Sci. Eng. Technol., 4(19): 3544-3551, 2012

Table 3: Statistical properties of the resistance
                          Malaysia (Idrus et al., 2011a, b)                                             ISO 19902
                          --------------------------------------------------------------------          ----------------------------------------------------------------------
Parameter                 MC                      COV                   Distribution                    MC                          COV                      Distribution
Diameter                  1.001                   0.002                 Normal                          1.000                       0.0025                   Normal
Thickness                 1.024                   0.016                 Normal                          1.000                       0.015~0.050              Normal
Yield strength            1.193                   0.035                 Lognormal                       1.1193                      0.050                    Normal
Tensile strength          1.183                   0.033                 Normal                          NA                          NA                       NA
Young’s modulus           NA                      NA                    NA                              1.000                       0.050                    Normal
Idrus et al. (2011a)

Availability of SACS models: Most of the fixed steel                                   Table 4: Gravity (dead & live) loads statistical parameters, ISO19902
offshore platforms installed in Malaysia were designed                                 Load type                               Bias                 COV
                                                                                       Dead load of structure G1               1.0                  0.06
using the Structural Analysis Computer Software (SACS).                                Dead load of fixed facilities G2        1.0                  0.06
The modeling and design of platforms is conducted by the                               Long-term live load Q1                  1.0                  0.10
engineering consultants and transferred to owner for                                   Short term live load Q2                 1.0                  0.10
archiving. The SACS models made available for the
research must be as per design, that is API RP2A-WSD                                   members. Thickness of tubular members were obtained
and as per in-place structure. This is to ensure that the                              based direct measurement of tubular members available
loads modeled should resemble to the actual loads on the                               at site and dimensional drawings i.e. data record available
structure. The loads obtained from the SACS model                                      with the company. Diameter was obtained based on
analysis consist of dead load, live load and environmental                             drawings only. Material strength uncertainty was based on
load.                                                                                  test reports available with the fabricator. Details on the
     Based on the above two points, platform A was                                     statistical analysis of resistance parameters are presented
selected for the conduct of this research, because it                                  and discussed by Idrus et al. (2011a). The Table 3 shows
contained all the data required, to ensure that the results                            the stochastic parameters obtained, which were found to
obtained were reliable.                                                                be similar to those suggested in the ISO 19902, that is due
                                                                                       to the fact that the quality standard in fabrication of steel
Selection of members: The method followed here is                                      worldwide are uniform.
based on ISO 19902, which is explained in Bomel (2003).
Members are selected from primary members based on                                     Load statistical parameters: The loads acting on a fixed
maximum force effects, which include Leg members,                                      offshore jacket platform consist of:
Vertical Diagonal members and Horizontal members at
the periphery. These members are subjected to maximum                                  Dead load: This load consists of mainly of the self-
actions from dead, live and environmental load effects.                                weight part of gravity load. ISO categorizes the dead load
Table 2 shows representative members which are selected                                into two classes (API, 2005; ISO, 2007).
for finding the target reliability index. They were selected
based on the slenderness (k*L/r) and Diameter to                                       :C        Permanent load action: G1 includes self-weight of
Thickness (D/T) ratios where r is radius of gyration. The                                        structure and associated or mounted equipment on
k values used were recommended in ISO 19902 (2007).                                              the structure.
                                                                                       C         Permanent load action: G2 represents the self-
Resistance statistical parameters: Resistance of the                                             weight of equipment and other objects that remain
jacket platforms tubular members is modeled based on the                                         constant for long periods, but which can change from
variations of the resistance parameters, as shown in the                                         one mode of operation to another or during a mode of
Eq. (3). The major sources of uncertainty can be divided                                         operation.
into three groups namely Geometry/Fabrication, Material
and Model Uncertainties:                                                                    The gravity load is treated as normal random variable
                                                                                       that is because they are not subject to excessive
      R = f(D, T, Fy, E, Xm, …et)                                      (3)             variability. The statistical parameters are taken from ISO
                                                                                       code and shown in Table 4.
where, D diameter and T, thickness make up the geometry
uncertainty. Fy , yield strength and E, Youngs modulus                                 Live load: This load comprises of the operating load and
constitute the material uncertainty and Xm is the model                                the equipment mounted on the structure for short term
uncertainty.                                                                           loading. Like the dead load is divided in two parts:
     The statistical data for resistance was based on
material test report and field measurements at one of the                              C         Variable action: Q1, which is made up of weight of
leading fabrication yards in Malaysia. Field data collected                                      consumable supplies and fluids in pipes, tanks and
include the geometry (diameter and thickness) of                                                 stores; weight of transportable vessels and containers

                                                                                3546
Res. J. Appl. Sci. Eng. Technol., 4(19): 3544-3551, 2012

Table 5: Statistical parameters of metocean data
                                                          Weibull parameters                                      Statistical parameters
                                                          --------------------------------------------------      -------------------------------------------------
Parameter                   Distribution                  Scale                          Shape                    Mean                        Std. Dev
Sig. wave height            Weibull                       4.46                           8.83                     4.22                        0.57
Peak period                 Dependent of the significant wave height
Current speed               Weibull                       0.84                           2.73                     0.75                        0.30
Wind speed                  Weibull                       19.90                          4.96                     15.51                       3.59
Idrus et al. (2011b)

     used for delivering supplies; weight of personnel and                      Table 6: ISO target reliability
                                                                                                            API RP2AWSD                     ISO (( = 1.35)
     their personal effects and weight of scaffolding and                                                   -----------------------         -----------------------
     temporary access systems.                                                  Load effect                 Pf             $                Pf              $
C    Variable action: Q2, represent the short duration                          Compression and bending     2.40E-4        3.49             5.8E-5          3.84
     action, such as, lifting of drill string, lifting by                       Tension and bending (brace) 1.39E-4        3.64             5.8E-5          3.85
                                                                                All                         2.6E-4         3.50             5.9E-5          3.85
     cranes, machine operations, vessel mooring and                             Bomel (2003)
     helicopters.
                                                                                     In design practice, the designers are interested in the
     The live load is assumed to be normally distributed                        characteristic values of load, defined at the maximum load
and its statistical parameters are presented in Table 4. The                    effect generated by the peak significant wave height and
bias represents the mean value of the ratio of the                              associated peak wave period, of a 50 or 100 year return
measured to nominal value. COV is the coefficient of                            period 3 h storm and the 10 min storm wind (Tarp-
variance of the ratio.                                                          Johansen, 2005). The wave, current and wind are location
                                                                                based. The metocean (wave, current and wind) data used
Environmental         parameters        statistics:   The                       in this research was collected from several points within
environmental load action makes up most of the load                             the areas of interest in the Malaysian offshore operations
effect on the structure. It results from the action of the                      and parameters were statistically analyzed and presented
wave, current and wind. The prediction of the                                   by Idrus et al. (2011b). The metocean data were assumed
environmental load action on the offshore jacket requires                       to be of Weibull distribution and their properties are
a proper understanding of the irregular and uncertain                           shown in Table 5.
behaviour of the hydrodynamic effect of the wave, current
and wind on the structure. Various theories have been                           Environmental load modeling: Given the large number
developed to assist the designers predict the wave and                          of members and complexity of the offshore jacket
current characteristics, namely the wave height, wave                           platform, structural analysis programs i.e., SACS is used
period, wave velocity and acceleration. These theories are                      to evaluate the force on each member of the structure at
based on studying the water particle kinematics associated                      certain environmental load parameters. The output loads
with the oceanic conditions and assuming at acceptable                          on the members dependent on the wave, current and wind
level that the waves are regular. Among all, the most                           input parameters and the size and location of the member
common theories are the Linear (Airy) and Stokes wave                           on the structure. To execute the reliability analysis, loads
theories. The Airy wave theory is preferred because it is                       acting in the members must be represented with their
                                                                                statistical properties, which are mean, coefficient of
simple and provides the basis for other theories
                                                                                variance and distribution type. Since, the variability of the
(Chakrabarti, 1987). In cases were regular wave theories
                                                                                load depends on the variability of the primary input
cannot be applied, i.e. highly irregular sea states, the
                                                                                (wave, current and wind), the response surface method
energy spectra are sought to describe the wave                                  was applied to find an expression that relates the input
characteristics. The most common spectrum is the Pierson                        variables and the load on each member. According to
and Moskowitz (P-M) wave spectrum (Chakrabarti,                                 Tarp-Johansen (2005) in drag-dominated structures, the
1987).                                                                          hydrodynamic response model is quadratic, given that the
     The environmental load effect on the structure is                          wave height is raised to the second power. Therefore, the
evaluated using the Morison’s Equation. This equation                           expression takes the following form:
allows the designer to calculate the force per unit length
acting on the submerged member. This force is due to the                        W = a+bH2Max+cHMax+dVc2+eVc+fVw2+gVw                                       (4)
wave interaction of the wave kinematics at the certain
elevation, from the seabed. The main input parameters in                        where, the coefficients a, b, c, d, e, f and g depend on the
the equation are velocity to evaluate the drag force and                        structural element location and these values could be
the acceleration to evaluate the inertia force. Detailed                        different for each element. Equation (4) indicates that the
explanations on the application of the Morison’s equation                       load variability can be directly evaluated from the
are given in Chakrabarti (1987).                                                variability of the basic input parameters.

                                                                          3547
Res. J. Appl. Sci. Eng. Technol., 4(19): 3544-3551, 2012

Table 7: Leg members reliability index values
                                        Failure
Group      d       l          w          mode     Pf            $
L3B        0.19    0.01       0.80      T+B       4.00x10-4     3.35
L3F        0.11    0.06       0.82      C+B       1.99x10-4     3.54
L4E        0.20    0.07       0.73      T+B       1.99x10-4     3.54
LG2        0.18    0.01       0.81      T+B       4.28x10-4     3.33
LG3        0.20    0.05       0.75      T+B       9.36x10-5     3.74
LG4        0.12    0.07       0.82      C+B       2.62x10-4     3.47
LG7        0.21    0.09       0.70      C         1.30x10-3     3.02
Average                                           3.98x10-4     3.44

Table 8: Vertical brace members reliability index values
                                         Failure
Group      d         l       w           mode       Pf          $
VA3        0.22      0.09    0.69        T+B        2.46x10!4   3.49
VA6        0.17      0.09    0.74        C+B        3.80x10!3   2.67
VB2        0.02      0.00    0.98        C+B        9.96x10!4   3.09
VB4        0.13      0.01    0.85        C+B        1.72x10!2   2.12      Fig. 1: Reliability index definition
VB8        0.08      0.06    0.85        C+B        1.04x10!2   2.31
VD4        0.19      0.09    0.72        T+B        9.90x10!3   2.33
VE2        0.17      0.07    0.76        C+B        1.73x10!3   4.14      failures less than 10!5. Based on the previous study, such
VF2        0.20      0.08    0.72        T+B        7.80x10!6   4.32      as Moses, it was found that the offshore probability of
VF9        0.28      0.14    0.58        T+B        1.30x10!5   4.21      failure, is within the 10-5 limit and therefore it is practical
Average                                             4.23x10!3   3.26
                                                                          to apply the MCS method (Moses et al., 2000)
Table 9: Horizontal brace members reliability index values                     The MCS method uses the predefined probability
                                       Failure                            distributions to generate random samples of the basic
Group     d          l       w         mode        Pf           $         variables, which are then used to evaluate the limit state
HA8       0.45       0.09    0.46      C+B         1.90x10!3    2.90
HA9       0.05       0.06    0.89      T+B         4.92x10!4    3.29      equation. This process is repeated for a certain N times,
HB1       0.25       0.10    0.65      T+B         4.65x10!5    3.91      for instance 5,000,000. The probability of failure is
HG1       0.18       0.05    0.77      T+B         8.25x10!4    3.15      evaluated by finding the ratio of number of failed samples
HL3       0.26       0.17    0.57      T+B         2.24x10!4    3.51
HL5       0.12       0.10    0.78      C           5.29x10!4    3.27
                                                                          to the total number of simulations. If the limit state
HL6       0.14       0.02    0.84      C           2.30x10!3    2.83      function is defined as:
HM4       0.18       0.04    0.78      T+B         3.46x10!4    3.39
Average                                            8.51x10!4    3.26           G(R, Q) = R-Q                                       (5)
Load proportion: The original SACS models were                                 The failure occurs when g(R,Q)<0. Thus, probability
designed as per API RP2A-WSD, in which the                                of failure Pf can be expressed as:
characteristic values of loads (gravity and environmental)
were combined. However, in this study, these loads
                                                                               Pf = P{g(R,Q)<0}                                    ( 6)
needed to be separated and their effect on the structure
evaluated individually. The contribution of each of the
                                                                              Probability of failure is also represented by reliability
loads is shown in Table 7 to 9, in form of ratios. These
ratios are based on the characteristic environmental loads                index, $ using the function g(R,Q) as follow:
i.e., 100 year values for wind, wave and current. The
environmental load accounts for the most of the loading                        $ = L-1(Pf)                                         (7)
on the members, than the both the gravity loads
combined. These results concur with the earlier studies by                where, L is the standard normal distribution function. The
Moses et al. (1987, 1988, 2000) and Bomel (2003).                         geometrical representation of $ and Pf are shown in
                                                                          Fig. 1.
Reliability analysis: The reliability analysis in offshore
structures is used to determine the probability of failure or             Limit state equations: Basic reliability analysis evaluates
the reliability index of the structure. Different methods                 the structural failure by determining if the limit state
can be applied for the computation. The most used                         function, also known as performance function is
methods of reliability analyses are Monte Carlo                           exceeded. The performance function indicates the margin
Simulation (MCS) and FORM/SORM. The choice of                             of safety between resistance and the load of structures
these methods is based on the computational ability, data                 (Galambos, 1981; Choi et al., 2007).
availability and the level of accuracy desired. For                            In this research, the limits state equations are based
instance, the MCS is simple and easy to be applied,                       on the formulations provided on the API RP2A-WSD and
compared to others methods, however it requires long                      ISO19902 codes of design. The evaluation of the
computational time and is less accurate for probability of                following equation was performed in MATLAB.

                                                                       3548
Res. J. Appl. Sci. Eng. Technol., 4(19): 3544-3551, 2012

C   Axial tension and bending:
                                                                                            4.00      ISO 19902
                                                                                                      APIRP2A-WSD
              S       Sb, yi 2  Sb, zi 2 
                                                                                            3.75
     Gi  1   ti                                     (8)




                                                                       Reliability index
                                                                                            3.50
               Rti
              
                              Rbi          
                                           
                                                                                            3.25

C   Axial compression and bending:                                                          3.00

                                                                                            2.75
              S       Sb, yi 2  Sb, zi 2   
     Gi  1   ci                                     (9)
                                                                                            2.50
                                                                                                1.0    1.2        1.4        1.6       1.8   2.0
               Rci
                            Rbi             
                                                                                                            Environmental load factor

                                                                   Fig. 2: Environmental load factor for axial tension and bending
C   Axial pure compression:
                                                                                            3.50      ISO 19902
    Gi = Rci!Sci                                         (10)                                         APIRP2A-WSD

                                                                                            3.25



                                                                        Reliability index
Target reliability index: The determination of the
environmental load factor requires that an acceptable level
                                                                                            3.00
of safety or target reliability be established. In this
research, the target reliability index is based on the
reliability of the structures as it was installed. For each                                 2.75
failure mode (axial, bending,...), the target reliability is
evaluated for the structure designed as per API RP2A-                                       2.50
WSD. The values established for the calibration of ISO                                          1.0    1.2        1.4        1.6       1.8    2.0
                                                                                                             Environmental load factor
19902 for the North Sea are shown in Table 6 (Bomel,
2003).                                                             Fig. 3: Environmental load factor for axial compression and
                                                                           bending
            RESULTS AND DISCUSSION
                                                                   Environmental load factor: The environmental load
Reliability index: The API RP2A-WSD reliability index              factors are evaluated for each critical failure mode, by
evaluated for different type of members respectively, leg,         plotting the curves of the target reliability index, as
vertical brace and horizontal bracing members, is shown            calculated for API RP2A-WSD standard and the
                                                                   reliability indices evaluated for different environmental
in Table 7, 8 and 9, respectively. For each member, the
                                                                   load factors as per ISO 19902 standards. The
load proportions are as per SACS output of the applied             environmental load factor is selected at the point of
stresses. The reliability index was obtained under the             intersection of the two curves. That is the point where the
critical failure condition. In the tables, it can be observed      ISO 19902 (to be adopted) gives the same safety index as
that the load proportions for environmental load is in most        the API RP2A-WSD standard in practice.
of the cases higher that 70% of the total load on the
member. This indicates that the structures are exposed to          C               Axial tension and bending: The target reliability
high environmental loads.                                                          index as calculated for API RP2A-WSD, for
     As this study is based on the actual stress results of                        members under the combined effect of axial and
obtained from the SACS model, of the selected                                      bending load, was used to obtain the corresponding
representative members, no weightage or member                                     environmental load factors, which was found to be
occurrence factors were used, thus all member are                                  1.60 as shown in the in Fig. 2.
considered to be of equal importance. The average
                                                                   C               Axial compression and bending: In this case, an
reliability index for leg members is found to be 3.44,                             API RP2A-WSD target reliability index of 3.04 was
which is relatively higher than 3.26 for vertical and                              achieved for members under combined axial
horizontal brace members.                                                          compression and bending and the equivalent
     These results are comparable to those obtained in the                         environmental load factor is 1.44 as shown in Fig. 3.
Bomel (2003) report, as shown in Table 6 and they are
within the acceptable level of the probability of failure for      C               Axial compression: For members under the effect of
a manned fixed offshore steel structure.                                           pure compression effect the API RP2A-WSD target


                                                                3549
Res. J. Appl. Sci. Eng. Technol., 4(19): 3544-3551, 2012

                        3.75
                                                                                                   NOMENCLATURE
                                  ISO 19902
                                  APIRP2A-WSD
                        3.50                                                      FORM    :   First Order Reliability Method
    Reliability index




                                                                                  SORM    :   Second Order Reliability Method
                        3.25                                                      W       :   Load on the member
                                                                                  Hmax    :   Maximum wave height
                        3.00
                                                                                  Vc      :   Current Speed
                        2.75                                                      Vw      :   Wind Speed
                                                                                  Gi      :   Limit state function
                        2.50                                                      Rbi     :   Bending design resistance as per ISO 19902
                            1.0    1.2        1.4        1.6       1.8   2.0
                                         Environmental load factor                Rci     :   Compression design resistance as per ISO
                                                                                              19902
Fig. 4: Environmental load factor for axial pure compression                      Rti     :   Tension design resistance as per ISO 19902
                                                                                  Sb,ji   :   Y-axis bending load effect as API RP2A
            reliability index computed was 3.03 similar to the                                WSD/ ISO 19902
            member under combined compression and bending                         Sb,fi   :   Z-axis bending load effect as API RP2A
            effect. The environmental load factor was 1.4, as                                 WSD/ ISO 19902
            illustrated in Fig. 4.                                                Sci     :   Compression load effect as API RP2A WSD/
                                                                                              ISO 19902
     The values of environmental load factor of 1.44, 1.45                        Sti     :   Tension load effect as API RP2A WSD/ ISO
and 1.60 for this particular platform are extremely high,                                     19902
compared to the environmental load factor of 1.35
suggested in the ISO 19902 for extreme conditions.                                               ACKNOWLEDGMENT
Noting, that the ISO 19902 values were calibrated based
on the storm conditions that are harsher than Malaysian                                The authors thank Universiti Teknologi PETRONAS
waters, the results were unexpected. This difference and                          for supporting this project.
contradiction could be a result of the possible errors in
modeling the uncertainty of the environmental design                                                 REFERENCES
load. Noting that environmental load modeling was
conducted based on the metocean data obtained from the                            API., 2005. Recommended Practice for Planning, Design
design reports, instead of the hindcast or recorded data. In                          and Constructing Fixed Offshore Structures-Working
addition, the structure was not redesigned when                                       Stress Design. 21st Edn., API Publishing Services,
evaluating the reliability index for ISO19902. Thus,                                  Washington.
considering that structural dimension are as per API                              Bomel, L., 2003. Component-based Calibration of the
RP2A-WSD and that they are generally overdesigned, the                                North West European Annex Environmental Load
corresponding environmental load factor for ISO19902 is                               Factors for the ISO Fixed Steel Offshore Structures
likely to be high.                                                                    Code 19902. Health and Safety Executive.
                                                                                  Chakrabarti, S.K., 1987. Hydrodynamics of Offshore
                         CONCLUSION AND FUTURE WORK                                   Structrures. WIT Press, ISBN: 9780905451664.
                                                                                  Choi, S.K., R. Grandhi and R.A. Canfield, 2007.
     Structural reliability analysis of jacket platform has                           Reliability-based Structural Design. Springer.
been undertaken. Reliability indices of existing structures,                      Duan, Z.D., D.C. Zhou and J.P. Ou, 2006a. Calibration of
designed as per API RP2A-WSD were evaluated and                                       LRFD Format for Steel Jacket Platforms in China
found to be 3.26 for brace members and 3.44 for leg                                   Offshore Area(1)-Statistical Parameters of Loads and
members. These results agree with the values that are                                 Resistances. China Ocean Engineering, pp: 1-14.
rationally accepted for the manned offshore structure.                            Duan, Z.D., D.C. Zhou and J.P. Ou, 2006b. Calibration of
     The environmental load factors obtained were on the                              LRFD Format for Steel Jacket Platforms in China
range of 1.44-1.60, which are higher than the expected                                Offshore Area(2)-Load, Resistance and Load
1.30-1.35, as mentioned in the literature for 100 year                                Combination Factors. China Ocean Engineering, pp:
loading situations and platforms structural life of 30 years.                         199-212.
This research provides basis for future calibration works                         FHWA, 2001. Load and Resistance Factor Design
of fixed steel offshore platforms in Malaysia. It is                                  (LRFD) for Highway Bridge Substructure. National
recommended that future studies increase the calibration                              Highway Institute, U.S. Department of
points and proper evaluation of the statistical parameters                            Transportation. Federal Highway Administration,
of environmental loading.                                                             Washington.

                                                                               3550
Res. J. Appl. Sci. Eng. Technol., 4(19): 3544-3551, 2012

Galambos, T.V., 1981. Load and resistance factor design.    Moses, F. and R.D. Larrabee, 1988. Calibration of the
    National Engineering Conference, AISC.                      draft RP2A-LRFD for fixed platforms. 20th Offshore
Idrus, A.B., N.S. Potty, M.F. Hamid, N.J. Cossa and             Technology Conference OTC, Houston, pp: 171-180.
    Z. Nizamani, 2011a. Resistance Parameters Statistics    Nowak, A.S. and M.M. Szerszen, 2000. Structural
    for Jacket Platforms in Offshore Malaysia.                  reliability as applied to highway bridges. Prog.
    International Offshore and Polar Engineering
                                                                Struct. Eng. Material, 2: 218-224.
    Conference Maui, ISOPE, Hawai, pp: 226-232.
Idrus, A.B., N.S. Potty, M.F. Hamid, Z. Nizamani and        Nowak, A.S. and R. Taylor, 1986. Reliability based
    N.J. Cossa, 2011b. Selection of Environmental               design criteria for timber bridges in Ontario. Can. J.
    Parameters for Offshore Jacket Platform Design in           Civil Eng., 13(1): 1-7.
    Malaysia. International Conference on Steel and         Tarp-Johansen, N.J., 2005. Partial Safety factors and
    Aluminum Structures Research Publishers, Kuching,           characteristics values for combined extreme wind and
    pp: 383-387.                                                wave load effects. J. Solar Energy Eng.,
ISO 19902, 2007. Petroleum and Natural Gas Industries-          127: 242-252.
    Fixed Steel Offshore Structures. 1st Edn., ISO,
    Geneva.
Moses, F., 1987. Application of Reliability to
    Formulation of Fixed Offshore Design Codes.
    Marine Structural Reliability Symposium, pp: 15-30.
Moses, F. and S. Bernard, 2000. Calibration Issues in
    Development of ISO Standards for Fixed Steel
    Offshore Structures. International Symposium and
    Exhibition of Offshore Mechanics and Artic
    Engineering. The American Society of Mechanical
    Engineers, Lisbon, 122: 52-56.




                                                       3551

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Reliability Analysis of Jacket Platforms in Malaysia-Environmental Load Factors

  • 1. Research Journal of Applied Sciences, Engineering and Technology 4(19): 3544-3551, 2012 ISSN: 2040-7467 © Maxwell Scientific Organization, 2012 Submitted: January 12, 2012 Accepted: February 17, 2012 Published: October 01, 2012 Reliability Analysis of Jacket Platforms in Malaysia-Environmental Load Factors 1 Nelson J. Cossa, 1Narayanan S. Potty, 1Arazi B. Idrus, 2Mohd Foad Abdul Hamid and 1 Zafarullah Nizamani 1 Department of Civil Engineering, Universiti Teknologi PETRONAS, Bandar Seri Iskandar, 31750, Tronoh, Perak, Malaysia 2 Principal Engineer-Structural, Scientige Sdn Bhd, Kuala Lumpur, Currently on leave of absence from Faculty of Mechanical Engineering, University Technology, Malaysia Abstract: In recent years, there has been a significant trend for adoption of the ISO-19902 standards for design of fixed steel offshore structures. The implementation of this standard aims to provide a harmonized international framework of design. Unlike, the traditional and currently used, WSD-method, the ISO-19902, follows the LRFD-method, that consists of both partial load and resistance factors. These partial factors are usually calibrated through reliability analysis. In these analyses, the performance of a structure is defined by the limit state function for the critical mode of failure. This paper, focuses mainly on the ultimate (strength) limit state which is directly related to the (highest) environmental loading. The partial environmental load factors contained in the ISO 19902, were calibrated for the Gulf of Mexico and UK's North Sea conditions, which are relatively harsh than those in Malaysia. The study presents the steps taken for the determination of the environmental load factor for tubular members of jacket platforms in Malaysia. The factor was determined such that the reliability of tubular members of jacket designed as per the LRFD-method is at the level of target reliability obtained by the WSD-method. Keywords: Environmental load factor, reliability analysis INTRODUCTION elastic zone. The risk was catered by reducing the yield stress of the structural elements that is tubular members in Offshore structures are likely to be subject to various this case. In practice of design, the actual loads are types of loads and deformations arising from service calculated first and then members’ dimensions are requirements ranging from the routine operating loads to selected such that the stresses remain below certain limit the extreme storm or accidental loads. Hence, the of the yield strength. Thus, the global safety factor is an structure has to be designed such that it can withstand implicit nominal value of 1.67. For extreme storm these demands throughout its expected design life. The condition a one-third increase in allowable stress is designers have been able to achieve this through the use permitted, hence the safety factor becomes 1.25 (= 1.67/1.33) (API, 2005). of the design codes. In the offshore industry, the design of Most of the fixed steel offshore structures designed fixed steel offshore structures, typically known as jacket as per WSD have not experienced failures related to the platforms, has been based on the API RP2A-WSD design approach, however there are limitations associated standard (API, 2005). The Working Stress Design (WSD) with it, such as (FHWA, 2001): method is based on safety factor provided only to the resistance of the material without considering the C Does not properly account for variability of loads and uncertainties related to the loads: resistances. Loads are considered to be without variation i.e., are assumed to be deterministic. Rn/SF$D + L+W (1) C Does not provide a reasonable measure of strength, which is a more fundamental measure of resistance where, SF is the global safety factor and it covers the than is allowable stress. loads (D dead load, L, live load and W environmental C The factor of safety is in most of the cases applied on load) and Rn the nominal resistance (strength) related resistance side. Its selection is subjective and does uncertainties. The safety factor was selected, on basis that not provide measure of reliability in terms of stresses in the structural element shall not exceed the probability of failure. Corresponding Author: Nelson J. Cossa, Department of Civil Engineering, University Technology PETRONAS, Bandar Seri Iskandar, 31750, Tronoh, Perak, Malaysia 3544
  • 2. Res. J. Appl. Sci. Eng. Technol., 4(19): 3544-3551, 2012 The need to overcome these definciencies, lead to Table 1: Platforms details changes in the design concepts. Strutural reliability Platform Installation name Location Depth (m) year No. of legs analysis was applied to evaluate the risks and A PM 61.00 2006 4 uncertainities associated with the safety of structure. In B SK 72.40 2003 4 this analysis, the safety of the structures is defined in C SB 42.80 2007 6 mathematical terms, in which the uncertain variability of PM: Peninsular Malaysia; SB: Sabah; SK: Sarawak the load and resistance are assumed to be independent and represented by their respective probability density analysis adopted in this study is based on the component- functions. The mathematical expression is based on the reliability as defined by Bomel (2003). purpose for which the structure is designed. The condition beyond which the structure fails to meet its intended MATERIALS AND METHODS design purpose, is called limit state, e.g. ultimate strength limit state, fatigue limit state, etc. For a certain limit state, The research study was carried out on the fixed a mathematical function can be developed and offshore platforms fabricated during the period of 2005- subsequently the safety perfomance can be evaluated in 2010 and installed in the Malaysian offshore operational terms of its probability of failure or reliabity index. This waters. This section presents and discusses the criteria for process is termed reliabilty-based design or Load and selection of the platforms, the determination of the load Resistance Factor Design (LRFD). The generalised safety and resistance statistical parameters and the methods criterion for the LRFD takes the following format (ISO adopted for the reliability evaluation and determination of 19902, 2007): the environmental load factor. Rn/(R $ (D D+(LL+(ww (2) Selection of the platform: Data was collected from three platforms, of which one was selected for this study. The where, (R is the partial resistance factor, that cater to the selection was based on the availability of complete uncertainties associated with the resistance and varies metocean parameters and the completeness of the with the mode of failure being evaluated e.g., axial, platform model, such that it better represents the actual bending, shear and so on. (D,(L and (w are the partial structure as installed. dead, live and environmental load factors respectively. The partial environmental load factor, in particular, is Operating regions: Malaysia is divided by South China very crucial as it depends mainly on the local conditions Sea into two namely Peninsular Malaysia and Borneo at the location in which the structure is installed. The Island consisting of Sabah and Sarawak states. It was selection of the partial factors is done through calibration thought necessary that one platform from each region methods and determined such that optimum level of should be selected and Table 1 shows the details of the safety is achieved, at an acceptable cost (Nowak et al., platforms. Their depth varies from 42 to 73 m. They were 1986, 2000). Depending on the function of the structure, designed as per API RP2A-WSD 21st edition (current different levels of safety maybe recommended. For edition). The number of legs in platforms in Malaysia example for unmanned and manned fixed steel offshore varies from three to eight but the most typical is four. In structures, the ISO recommends an annual probability of general, it can be assumed that listed platforms are failure at range of about 10!3 and 10!5, respectively (ISO representative of the vast other installed structures in the 19902, 2007). Alternatively, the partial factors can be Malaysian waters. evaluated so that the safety is at the same level as that of Table 2: Members selected for calibration existing structures that were designed as per API RP2A- Diameter Wall Length Slenderness WSD. (D) thickness(T) (L) K factor % D/T During the course of the development of the API 1650 25.0 9344 1.0 0.23 66.00 RP2A LRFD and later the ISO 19902 code for design of 1630 15.0 17500 1.0 0.43 108.70 fixed steel offshore structures, Moses et al. (1987, 1988, 660 12.7 15370 0.7 0.65 51.97 711 15.0 11000 0.7 0.43 47.40 2000) carried extensive calibrations works, for the Gulf of 610 12.7 11800 0.7 0.54 48.03 Mexico. Similarly, Bomel (2003) conducted studies that 660 19.0 11940 0.7 0.51 34.74 covered the North Sea conditions requirements. In Asia, 406 12.7 12000 0.7 0.83 31.97 Duan et al. (2006a, 2006b) carried out the recalibration 508 12.7 12400 0.7 0.68 40.00 610 12.7 47400 0.7 2.18 48.03 works for selected platforms located at the China's Bohai 610 25.0 7000 0.7 0.32 24.40 Sea. The objective of this research is to evaluate the 559 25.0 8450 0.7 0.42 22.36 reliability index of tubular members of selected existing 559 15 5100 0.7 0.26 37.27 jacket platforms in Malaysia, for both API RP2A-WSD 547 19 7200 0.7 0.37 28.79 and ISO (LRFD) methods and subsequently determine a 610 25 7900 0.7 0.36 24.40 610 12.7 9790 0.7 0.45 48.03 suitable environmental load factor. The method of 3545
  • 3. Res. J. Appl. Sci. Eng. Technol., 4(19): 3544-3551, 2012 Table 3: Statistical properties of the resistance Malaysia (Idrus et al., 2011a, b) ISO 19902 -------------------------------------------------------------------- ---------------------------------------------------------------------- Parameter MC COV Distribution MC COV Distribution Diameter 1.001 0.002 Normal 1.000 0.0025 Normal Thickness 1.024 0.016 Normal 1.000 0.015~0.050 Normal Yield strength 1.193 0.035 Lognormal 1.1193 0.050 Normal Tensile strength 1.183 0.033 Normal NA NA NA Young’s modulus NA NA NA 1.000 0.050 Normal Idrus et al. (2011a) Availability of SACS models: Most of the fixed steel Table 4: Gravity (dead & live) loads statistical parameters, ISO19902 offshore platforms installed in Malaysia were designed Load type Bias COV Dead load of structure G1 1.0 0.06 using the Structural Analysis Computer Software (SACS). Dead load of fixed facilities G2 1.0 0.06 The modeling and design of platforms is conducted by the Long-term live load Q1 1.0 0.10 engineering consultants and transferred to owner for Short term live load Q2 1.0 0.10 archiving. The SACS models made available for the research must be as per design, that is API RP2A-WSD members. Thickness of tubular members were obtained and as per in-place structure. This is to ensure that the based direct measurement of tubular members available loads modeled should resemble to the actual loads on the at site and dimensional drawings i.e. data record available structure. The loads obtained from the SACS model with the company. Diameter was obtained based on analysis consist of dead load, live load and environmental drawings only. Material strength uncertainty was based on load. test reports available with the fabricator. Details on the Based on the above two points, platform A was statistical analysis of resistance parameters are presented selected for the conduct of this research, because it and discussed by Idrus et al. (2011a). The Table 3 shows contained all the data required, to ensure that the results the stochastic parameters obtained, which were found to obtained were reliable. be similar to those suggested in the ISO 19902, that is due to the fact that the quality standard in fabrication of steel Selection of members: The method followed here is worldwide are uniform. based on ISO 19902, which is explained in Bomel (2003). Members are selected from primary members based on Load statistical parameters: The loads acting on a fixed maximum force effects, which include Leg members, offshore jacket platform consist of: Vertical Diagonal members and Horizontal members at the periphery. These members are subjected to maximum Dead load: This load consists of mainly of the self- actions from dead, live and environmental load effects. weight part of gravity load. ISO categorizes the dead load Table 2 shows representative members which are selected into two classes (API, 2005; ISO, 2007). for finding the target reliability index. They were selected based on the slenderness (k*L/r) and Diameter to :C Permanent load action: G1 includes self-weight of Thickness (D/T) ratios where r is radius of gyration. The structure and associated or mounted equipment on k values used were recommended in ISO 19902 (2007). the structure. C Permanent load action: G2 represents the self- Resistance statistical parameters: Resistance of the weight of equipment and other objects that remain jacket platforms tubular members is modeled based on the constant for long periods, but which can change from variations of the resistance parameters, as shown in the one mode of operation to another or during a mode of Eq. (3). The major sources of uncertainty can be divided operation. into three groups namely Geometry/Fabrication, Material and Model Uncertainties: The gravity load is treated as normal random variable that is because they are not subject to excessive R = f(D, T, Fy, E, Xm, …et) (3) variability. The statistical parameters are taken from ISO code and shown in Table 4. where, D diameter and T, thickness make up the geometry uncertainty. Fy , yield strength and E, Youngs modulus Live load: This load comprises of the operating load and constitute the material uncertainty and Xm is the model the equipment mounted on the structure for short term uncertainty. loading. Like the dead load is divided in two parts: The statistical data for resistance was based on material test report and field measurements at one of the C Variable action: Q1, which is made up of weight of leading fabrication yards in Malaysia. Field data collected consumable supplies and fluids in pipes, tanks and include the geometry (diameter and thickness) of stores; weight of transportable vessels and containers 3546
  • 4. Res. J. Appl. Sci. Eng. Technol., 4(19): 3544-3551, 2012 Table 5: Statistical parameters of metocean data Weibull parameters Statistical parameters -------------------------------------------------- ------------------------------------------------- Parameter Distribution Scale Shape Mean Std. Dev Sig. wave height Weibull 4.46 8.83 4.22 0.57 Peak period Dependent of the significant wave height Current speed Weibull 0.84 2.73 0.75 0.30 Wind speed Weibull 19.90 4.96 15.51 3.59 Idrus et al. (2011b) used for delivering supplies; weight of personnel and Table 6: ISO target reliability API RP2AWSD ISO (( = 1.35) their personal effects and weight of scaffolding and ----------------------- ----------------------- temporary access systems. Load effect Pf $ Pf $ C Variable action: Q2, represent the short duration Compression and bending 2.40E-4 3.49 5.8E-5 3.84 action, such as, lifting of drill string, lifting by Tension and bending (brace) 1.39E-4 3.64 5.8E-5 3.85 All 2.6E-4 3.50 5.9E-5 3.85 cranes, machine operations, vessel mooring and Bomel (2003) helicopters. In design practice, the designers are interested in the The live load is assumed to be normally distributed characteristic values of load, defined at the maximum load and its statistical parameters are presented in Table 4. The effect generated by the peak significant wave height and bias represents the mean value of the ratio of the associated peak wave period, of a 50 or 100 year return measured to nominal value. COV is the coefficient of period 3 h storm and the 10 min storm wind (Tarp- variance of the ratio. Johansen, 2005). The wave, current and wind are location based. The metocean (wave, current and wind) data used Environmental parameters statistics: The in this research was collected from several points within environmental load action makes up most of the load the areas of interest in the Malaysian offshore operations effect on the structure. It results from the action of the and parameters were statistically analyzed and presented wave, current and wind. The prediction of the by Idrus et al. (2011b). The metocean data were assumed environmental load action on the offshore jacket requires to be of Weibull distribution and their properties are a proper understanding of the irregular and uncertain shown in Table 5. behaviour of the hydrodynamic effect of the wave, current and wind on the structure. Various theories have been Environmental load modeling: Given the large number developed to assist the designers predict the wave and of members and complexity of the offshore jacket current characteristics, namely the wave height, wave platform, structural analysis programs i.e., SACS is used period, wave velocity and acceleration. These theories are to evaluate the force on each member of the structure at based on studying the water particle kinematics associated certain environmental load parameters. The output loads with the oceanic conditions and assuming at acceptable on the members dependent on the wave, current and wind level that the waves are regular. Among all, the most input parameters and the size and location of the member common theories are the Linear (Airy) and Stokes wave on the structure. To execute the reliability analysis, loads theories. The Airy wave theory is preferred because it is acting in the members must be represented with their statistical properties, which are mean, coefficient of simple and provides the basis for other theories variance and distribution type. Since, the variability of the (Chakrabarti, 1987). In cases were regular wave theories load depends on the variability of the primary input cannot be applied, i.e. highly irregular sea states, the (wave, current and wind), the response surface method energy spectra are sought to describe the wave was applied to find an expression that relates the input characteristics. The most common spectrum is the Pierson variables and the load on each member. According to and Moskowitz (P-M) wave spectrum (Chakrabarti, Tarp-Johansen (2005) in drag-dominated structures, the 1987). hydrodynamic response model is quadratic, given that the The environmental load effect on the structure is wave height is raised to the second power. Therefore, the evaluated using the Morison’s Equation. This equation expression takes the following form: allows the designer to calculate the force per unit length acting on the submerged member. This force is due to the W = a+bH2Max+cHMax+dVc2+eVc+fVw2+gVw (4) wave interaction of the wave kinematics at the certain elevation, from the seabed. The main input parameters in where, the coefficients a, b, c, d, e, f and g depend on the the equation are velocity to evaluate the drag force and structural element location and these values could be the acceleration to evaluate the inertia force. Detailed different for each element. Equation (4) indicates that the explanations on the application of the Morison’s equation load variability can be directly evaluated from the are given in Chakrabarti (1987). variability of the basic input parameters. 3547
  • 5. Res. J. Appl. Sci. Eng. Technol., 4(19): 3544-3551, 2012 Table 7: Leg members reliability index values Failure Group d l w mode Pf $ L3B 0.19 0.01 0.80 T+B 4.00x10-4 3.35 L3F 0.11 0.06 0.82 C+B 1.99x10-4 3.54 L4E 0.20 0.07 0.73 T+B 1.99x10-4 3.54 LG2 0.18 0.01 0.81 T+B 4.28x10-4 3.33 LG3 0.20 0.05 0.75 T+B 9.36x10-5 3.74 LG4 0.12 0.07 0.82 C+B 2.62x10-4 3.47 LG7 0.21 0.09 0.70 C 1.30x10-3 3.02 Average 3.98x10-4 3.44 Table 8: Vertical brace members reliability index values Failure Group d l w mode Pf $ VA3 0.22 0.09 0.69 T+B 2.46x10!4 3.49 VA6 0.17 0.09 0.74 C+B 3.80x10!3 2.67 VB2 0.02 0.00 0.98 C+B 9.96x10!4 3.09 VB4 0.13 0.01 0.85 C+B 1.72x10!2 2.12 Fig. 1: Reliability index definition VB8 0.08 0.06 0.85 C+B 1.04x10!2 2.31 VD4 0.19 0.09 0.72 T+B 9.90x10!3 2.33 VE2 0.17 0.07 0.76 C+B 1.73x10!3 4.14 failures less than 10!5. Based on the previous study, such VF2 0.20 0.08 0.72 T+B 7.80x10!6 4.32 as Moses, it was found that the offshore probability of VF9 0.28 0.14 0.58 T+B 1.30x10!5 4.21 failure, is within the 10-5 limit and therefore it is practical Average 4.23x10!3 3.26 to apply the MCS method (Moses et al., 2000) Table 9: Horizontal brace members reliability index values The MCS method uses the predefined probability Failure distributions to generate random samples of the basic Group d l w mode Pf $ variables, which are then used to evaluate the limit state HA8 0.45 0.09 0.46 C+B 1.90x10!3 2.90 HA9 0.05 0.06 0.89 T+B 4.92x10!4 3.29 equation. This process is repeated for a certain N times, HB1 0.25 0.10 0.65 T+B 4.65x10!5 3.91 for instance 5,000,000. The probability of failure is HG1 0.18 0.05 0.77 T+B 8.25x10!4 3.15 evaluated by finding the ratio of number of failed samples HL3 0.26 0.17 0.57 T+B 2.24x10!4 3.51 HL5 0.12 0.10 0.78 C 5.29x10!4 3.27 to the total number of simulations. If the limit state HL6 0.14 0.02 0.84 C 2.30x10!3 2.83 function is defined as: HM4 0.18 0.04 0.78 T+B 3.46x10!4 3.39 Average 8.51x10!4 3.26 G(R, Q) = R-Q (5) Load proportion: The original SACS models were The failure occurs when g(R,Q)<0. Thus, probability designed as per API RP2A-WSD, in which the of failure Pf can be expressed as: characteristic values of loads (gravity and environmental) were combined. However, in this study, these loads Pf = P{g(R,Q)<0} ( 6) needed to be separated and their effect on the structure evaluated individually. The contribution of each of the Probability of failure is also represented by reliability loads is shown in Table 7 to 9, in form of ratios. These ratios are based on the characteristic environmental loads index, $ using the function g(R,Q) as follow: i.e., 100 year values for wind, wave and current. The environmental load accounts for the most of the loading $ = L-1(Pf) (7) on the members, than the both the gravity loads combined. These results concur with the earlier studies by where, L is the standard normal distribution function. The Moses et al. (1987, 1988, 2000) and Bomel (2003). geometrical representation of $ and Pf are shown in Fig. 1. Reliability analysis: The reliability analysis in offshore structures is used to determine the probability of failure or Limit state equations: Basic reliability analysis evaluates the reliability index of the structure. Different methods the structural failure by determining if the limit state can be applied for the computation. The most used function, also known as performance function is methods of reliability analyses are Monte Carlo exceeded. The performance function indicates the margin Simulation (MCS) and FORM/SORM. The choice of of safety between resistance and the load of structures these methods is based on the computational ability, data (Galambos, 1981; Choi et al., 2007). availability and the level of accuracy desired. For In this research, the limits state equations are based instance, the MCS is simple and easy to be applied, on the formulations provided on the API RP2A-WSD and compared to others methods, however it requires long ISO19902 codes of design. The evaluation of the computational time and is less accurate for probability of following equation was performed in MATLAB. 3548
  • 6. Res. J. Appl. Sci. Eng. Technol., 4(19): 3544-3551, 2012 C Axial tension and bending: 4.00 ISO 19902 APIRP2A-WSD S Sb, yi 2  Sb, zi 2  3.75 Gi  1   ti   (8) Reliability index 3.50  Rti  Rbi   3.25 C Axial compression and bending: 3.00 2.75 S Sb, yi 2  Sb, zi 2  Gi  1   ci   (9) 2.50 1.0 1.2 1.4 1.6 1.8 2.0  Rci  Rbi   Environmental load factor Fig. 2: Environmental load factor for axial tension and bending C Axial pure compression: 3.50 ISO 19902 Gi = Rci!Sci (10) APIRP2A-WSD 3.25 Reliability index Target reliability index: The determination of the environmental load factor requires that an acceptable level 3.00 of safety or target reliability be established. In this research, the target reliability index is based on the reliability of the structures as it was installed. For each 2.75 failure mode (axial, bending,...), the target reliability is evaluated for the structure designed as per API RP2A- 2.50 WSD. The values established for the calibration of ISO 1.0 1.2 1.4 1.6 1.8 2.0 Environmental load factor 19902 for the North Sea are shown in Table 6 (Bomel, 2003). Fig. 3: Environmental load factor for axial compression and bending RESULTS AND DISCUSSION Environmental load factor: The environmental load Reliability index: The API RP2A-WSD reliability index factors are evaluated for each critical failure mode, by evaluated for different type of members respectively, leg, plotting the curves of the target reliability index, as vertical brace and horizontal bracing members, is shown calculated for API RP2A-WSD standard and the reliability indices evaluated for different environmental in Table 7, 8 and 9, respectively. For each member, the load factors as per ISO 19902 standards. The load proportions are as per SACS output of the applied environmental load factor is selected at the point of stresses. The reliability index was obtained under the intersection of the two curves. That is the point where the critical failure condition. In the tables, it can be observed ISO 19902 (to be adopted) gives the same safety index as that the load proportions for environmental load is in most the API RP2A-WSD standard in practice. of the cases higher that 70% of the total load on the member. This indicates that the structures are exposed to C Axial tension and bending: The target reliability high environmental loads. index as calculated for API RP2A-WSD, for As this study is based on the actual stress results of members under the combined effect of axial and obtained from the SACS model, of the selected bending load, was used to obtain the corresponding representative members, no weightage or member environmental load factors, which was found to be occurrence factors were used, thus all member are 1.60 as shown in the in Fig. 2. considered to be of equal importance. The average C Axial compression and bending: In this case, an reliability index for leg members is found to be 3.44, API RP2A-WSD target reliability index of 3.04 was which is relatively higher than 3.26 for vertical and achieved for members under combined axial horizontal brace members. compression and bending and the equivalent These results are comparable to those obtained in the environmental load factor is 1.44 as shown in Fig. 3. Bomel (2003) report, as shown in Table 6 and they are within the acceptable level of the probability of failure for C Axial compression: For members under the effect of a manned fixed offshore steel structure. pure compression effect the API RP2A-WSD target 3549
  • 7. Res. J. Appl. Sci. Eng. Technol., 4(19): 3544-3551, 2012 3.75 NOMENCLATURE ISO 19902 APIRP2A-WSD 3.50 FORM : First Order Reliability Method Reliability index SORM : Second Order Reliability Method 3.25 W : Load on the member Hmax : Maximum wave height 3.00 Vc : Current Speed 2.75 Vw : Wind Speed Gi : Limit state function 2.50 Rbi : Bending design resistance as per ISO 19902 1.0 1.2 1.4 1.6 1.8 2.0 Environmental load factor Rci : Compression design resistance as per ISO 19902 Fig. 4: Environmental load factor for axial pure compression Rti : Tension design resistance as per ISO 19902 Sb,ji : Y-axis bending load effect as API RP2A reliability index computed was 3.03 similar to the WSD/ ISO 19902 member under combined compression and bending Sb,fi : Z-axis bending load effect as API RP2A effect. The environmental load factor was 1.4, as WSD/ ISO 19902 illustrated in Fig. 4. Sci : Compression load effect as API RP2A WSD/ ISO 19902 The values of environmental load factor of 1.44, 1.45 Sti : Tension load effect as API RP2A WSD/ ISO and 1.60 for this particular platform are extremely high, 19902 compared to the environmental load factor of 1.35 suggested in the ISO 19902 for extreme conditions. ACKNOWLEDGMENT Noting, that the ISO 19902 values were calibrated based on the storm conditions that are harsher than Malaysian The authors thank Universiti Teknologi PETRONAS waters, the results were unexpected. This difference and for supporting this project. contradiction could be a result of the possible errors in modeling the uncertainty of the environmental design REFERENCES load. Noting that environmental load modeling was conducted based on the metocean data obtained from the API., 2005. Recommended Practice for Planning, Design design reports, instead of the hindcast or recorded data. In and Constructing Fixed Offshore Structures-Working addition, the structure was not redesigned when Stress Design. 21st Edn., API Publishing Services, evaluating the reliability index for ISO19902. Thus, Washington. considering that structural dimension are as per API Bomel, L., 2003. Component-based Calibration of the RP2A-WSD and that they are generally overdesigned, the North West European Annex Environmental Load corresponding environmental load factor for ISO19902 is Factors for the ISO Fixed Steel Offshore Structures likely to be high. Code 19902. Health and Safety Executive. Chakrabarti, S.K., 1987. Hydrodynamics of Offshore CONCLUSION AND FUTURE WORK Structrures. WIT Press, ISBN: 9780905451664. Choi, S.K., R. Grandhi and R.A. Canfield, 2007. Structural reliability analysis of jacket platform has Reliability-based Structural Design. Springer. been undertaken. Reliability indices of existing structures, Duan, Z.D., D.C. Zhou and J.P. Ou, 2006a. Calibration of designed as per API RP2A-WSD were evaluated and LRFD Format for Steel Jacket Platforms in China found to be 3.26 for brace members and 3.44 for leg Offshore Area(1)-Statistical Parameters of Loads and members. These results agree with the values that are Resistances. China Ocean Engineering, pp: 1-14. rationally accepted for the manned offshore structure. Duan, Z.D., D.C. Zhou and J.P. Ou, 2006b. Calibration of The environmental load factors obtained were on the LRFD Format for Steel Jacket Platforms in China range of 1.44-1.60, which are higher than the expected Offshore Area(2)-Load, Resistance and Load 1.30-1.35, as mentioned in the literature for 100 year Combination Factors. China Ocean Engineering, pp: loading situations and platforms structural life of 30 years. 199-212. This research provides basis for future calibration works FHWA, 2001. Load and Resistance Factor Design of fixed steel offshore platforms in Malaysia. It is (LRFD) for Highway Bridge Substructure. National recommended that future studies increase the calibration Highway Institute, U.S. Department of points and proper evaluation of the statistical parameters Transportation. Federal Highway Administration, of environmental loading. Washington. 3550
  • 8. Res. J. Appl. Sci. Eng. Technol., 4(19): 3544-3551, 2012 Galambos, T.V., 1981. Load and resistance factor design. Moses, F. and R.D. Larrabee, 1988. Calibration of the National Engineering Conference, AISC. draft RP2A-LRFD for fixed platforms. 20th Offshore Idrus, A.B., N.S. Potty, M.F. Hamid, N.J. Cossa and Technology Conference OTC, Houston, pp: 171-180. Z. Nizamani, 2011a. Resistance Parameters Statistics Nowak, A.S. and M.M. Szerszen, 2000. Structural for Jacket Platforms in Offshore Malaysia. reliability as applied to highway bridges. Prog. International Offshore and Polar Engineering Struct. Eng. Material, 2: 218-224. Conference Maui, ISOPE, Hawai, pp: 226-232. Idrus, A.B., N.S. Potty, M.F. Hamid, Z. Nizamani and Nowak, A.S. and R. Taylor, 1986. Reliability based N.J. Cossa, 2011b. Selection of Environmental design criteria for timber bridges in Ontario. Can. J. Parameters for Offshore Jacket Platform Design in Civil Eng., 13(1): 1-7. Malaysia. International Conference on Steel and Tarp-Johansen, N.J., 2005. Partial Safety factors and Aluminum Structures Research Publishers, Kuching, characteristics values for combined extreme wind and pp: 383-387. wave load effects. J. Solar Energy Eng., ISO 19902, 2007. Petroleum and Natural Gas Industries- 127: 242-252. Fixed Steel Offshore Structures. 1st Edn., ISO, Geneva. Moses, F., 1987. Application of Reliability to Formulation of Fixed Offshore Design Codes. Marine Structural Reliability Symposium, pp: 15-30. Moses, F. and S. Bernard, 2000. Calibration Issues in Development of ISO Standards for Fixed Steel Offshore Structures. International Symposium and Exhibition of Offshore Mechanics and Artic Engineering. The American Society of Mechanical Engineers, Lisbon, 122: 52-56. 3551