Determination of Reserve Strength Ratio for a Jacket Substructure Supporting an Offshore Wind Turbine

1. Static Pushover AnalysisStatic pushover analysis has been widely used as a tool to investigate the ultimate strength of jacket structures [1]. The value of ultimate strength derived from the pushover analysis in turn determines the Reserve Strength Ratio (RSR), which serves as an estimate of the capability of the structure to survive loads in excess of the design values [2]. Ultimate strength analyses serve as a means to identify the critical structural members of the jacket, thereby aiding the planning and scheduling of inspection and repair schemes [3]. The RSR is defined as the ratio of base shear at collapse to that at the 100-year environmental load [4]. Static pushover analyses were conducted, by first applying the time invariant dead loads - self-weight of the structure and the static wind toad at the tower top - were first incremented to a factored value of unity, followed by gradually increasing the lateral environmental (wave and current) loads, till the structure collapses. [4]. The maximum of wave loads are identified using Stokes' 5th order wave theory. The RSR was calculated using the following formula [2]:

where BScollapse is the base shear at collapse, and BS100, that at the 100-year design load. The latter is identified in USFOS with an environmental load factor of 1, while the former is the maximum base shear corresponding to structural collapse. The operating and storm wave date for a location off the western coast of India (74m water depth), has been taken from a published thesis [5]. Wave and Current Data (Reproduced from [5]):Wave data:- operating caseDirectionWave height (m)Wave period (s)

All eight directions12.211.0

Wave data:- extreme load case - 100 year stormDirectionWave height (m)Wave period (s)

N15.0913.0

N 45 W16.7713.7

W17.0713.9

S 45 W17.6814.2

S18.0014.4

S 45 E14.4812.5

E13.2611.8

N 45 E16.0013.8

Current speed data:- operating caseElevation from mudline (m)Current speed (m/s)

00.45

250.77

500.92

751.10

Current speed data:- extreme load case - 100 year stormDirectionCurrent speed (m/s) and elevation from mudline (m)

0 (m)25 (m)50 (m)75 (m)

N0.510.971.191.40

N 45 W0.310.690.861.02

W0.210.610.750.90

S 45 W0.270.660.820.99

S0.370.811.021.21

S 45 E0.310.721.081.20

E0.250.650.830.95

N 45 E0.250.650.820.98

2. ResultsThe maximum base shear on the platform, for operating and extreme load cases, considering the directionality of waves and currents are tabulated below.Base shear for operating and extreme load cases:-DirectionOperating Condition (MN)Extreme Condition (MN)

FixedPilesFixedPiles

N6.282.6711.004.81

N 45 W5.922.449.314.03

W5.281.918.163.26

S 45 W4.351.078.192.60

S4.030.429.742.76

S 45 E4.351.076.672.05

E5.281.915.722.47

N 45 E5.922.448.503.75

Pushover analyses performed with respect to the 100-year loading (wave and current), yield the ultimate strength. This can in turn be used to determine the RSR, using the equation given in section1. In the present analysis, the wind load is represented as a static point load acting on the top of the tower, representing the parked condition of the OWT. USFOS detects the collapse regime using a current stiffness parameter, which will be negative in the post-collapse range, with an accompanying sign-reversal for the load increment [6]. The values of ultimate strength along with the calculated RSRs are given in the table below. RSR:-DirectionExtreme Condition (MN)Ultimate Strength (MN)RSR

FixedPilesFixedPilesFixedPiles

N11.004.8157.1630.655.206.37

N 45 W9.314.0351.6021.325.545.29

W8.163.2652.7328.286.468.67

S 45 W8.192.6053.3023.196.518.92

S9.742.7657.0529.445.8610.67

S 45 E6.672.0553.3123.508.0011.46

E5.722.4756.9327.709.9511.21

N 45 E8.503.7551.7821.226.095.66

3. References1. Golafshani, A.A, Bagheri, V., Ebrahimian, H. and Holmas, T. (2011), Incremental wave analysis and its application to performance-based assessment of jacket platforms, Journal of Constructional Steel Research, 67, 1649 - 16572. Kurian, V. J., Voon, M.C., Wahab, M.M.A. and Liew, M.S. (2013), Reliability of Jacket Platforms in Malaysian Waters - Pushover and Regression Analysis Methods in Obtaining Reserve Strength Ratio, IEEE Symposium on Business, Engineering and Industrial Applications, Kuching, Malaysia3. Potty, N.S., and Akram, M.K.B.M., (2009), Structural Integrity Management for Fixed Offshore Platforms in Malaysia, World Academy of Science, Engineering and Technology, 58, 1079 - 10874. Solland, G., Hellan, O., Bolt, H., Fuglum, I. and Yasseri, S. (1999), Best Practice Guidelines for Use of Non-linear Analysis Methods in Documentation of Ultimate Limit States for Jacket Type Offshore Structures, DNV-SINTEF -BOMEL5. Vishnu, C. (2013), Pushover Analysis of Wellhead Platform in Mumbai High, Masters' Thesis of the Indian Institute of Technology - Madras, India6. SINTEF Group (2001). USFOS Getting Started. Structural Engineering, Marintek, SINTEF Group