Strength Analysis on Brace Structure for Semi-Submersible in Consideration of Wave Slamming

Slamming on bracings of column stabilized units shall be considered as a possible limiting criterion under transit condition based on the requirements in DNV-OS-C103. However, the wave slamming loads under survival condition were ignored for the strength analysis of the brace structures in many semi-submersible projects. In this paper, a method of strength analysis of brace structure is proposed based on the reconstruction and extrapolation of numerical model. The full-scale mooring system, the wind, wave and current loads can be considered simultaneously. Firstly, the model tests of the semi-submersible platform in wind tunnel and wave tanker have been carried out. Secondly, the numerical models of the platform are reconstructed and extrapolated based on the results of model tests. Then, a nonlinear numerical analysis has been conducted to study the wave slamming load on brace in semi-submersible platform through the reconstructed and extrapolated numerical model. For the randomness of wave load, ten subcases under each condition have been carried out. The value of the 90% Gumble distribution values of the ten subcases are used. Finally, the strength on brace structure has been analyzed considering the wave slamming. The wave slamming loads have been compared between the survival condition and transit condition with the method. The results indicate that wave slamming under survival condition is more critical than that under transit condition. Meanwhile, the wave slamming is significant to the structural strength of the brace. It should be overall considered in the strength analysis of the brace structure.


Introduction
With the exploration of deep water oil and gas resources, offshore floating structures such as semi-submersible platform, TLP and Spar have been quickly developed. The extreme response analysis play an important roles in design of brace structure for semi-submersible and slamming analysis on the brace structure. Under critical conditions, the wave slamming of the platform can lead to the destruction of the platform structure and even the casualties. If the results of structural strength analysis meet the rules requirements, partial slamming can be acceptable. That can reduce the design difficulty and the manufacturing cost. Therefore, it is more reasonable to consider the partial wave slamming to be acceptable Kazemi and Incecik (2007). In particular, the slim structures such as the brace are prone to be damaged under wave slamming. It is very important to predict the wave slamming for the design of platform.
In recent years, a large number of theoretical and experimental studies have been carried out on the wave slamming for semi-submersible platforms in engineering. Wang et al. (2017) studied the effect of hydrodynamic loads from ocean waves on the strength of the horizontal brace structures in semi-submersible platforms and the load assessment on the horizontal braces of a platform under harsh wave loads. Srikanth et al. (2016) performed the inelastic nonlinear pushover analysis on a 3-D model of a jacket-type offshore platform under the North Sea conditions. Zhang et al. (2017) introduced the PFD-SMA bracing system applied in the vibration control of JZ20-2MUQ offshore platform in the Bohai bay, which is subjected to the action of ice and seismic excitation by numerical method. Kazemi and Incecik (2007) introduced a simplified numerical method with sufficient accuracy suitable for preliminary design stages of a floating offshore platform to predict the air gap response using hybrid method and to evaluate the vertical wave impact force using the Wagner-based method. Rudman and Cleary (2013) used Smoothed Particle hydrodynamics (SPH) to simulate the fully non-linear dynamics of a large breaking wave on a semi-submersible tension leg platform. Properly applied, SPH has a wide application in predicting non-linear wave-structure interactions. Sekhar and Nallayarasu (2011) studied the slam and slap coefficients for I sections and channel sections. The results indicated that the slam and slap coefficients for I sections are smaller than those of the channel sections and the values of coefficients are few times higher than those of the circular sections. Liang et al. (2010) applied VOF method to capture the free surface and used DeepC software to predict air gap response of the moored semi-submersible platform. Shan et al. (2011) revealed wave run-up characteristics along square columns and demonstrated the relationship between air gap distributions and wave parameters by the model test of a large-volume drilling semi-submersible platform. Simos (2008) performed small-scale model tests of air gap response on a floating semi-submersible, and found that standard first-order numerical analysis seriously underestimated run-up effects in the region near the columns except for low wave steepness. Sweetman et al. (2001) used commercial program WAMIT in which second-order nonlinearities were included to predict air gap response of a semi-submersible. The model can calculate the correct location of the highest wave elevations and has clearly improved the results compared with linear potential theory. Huo et al. (2015Huo et al. ( , 2016 studied the sensitivity analysis of air gap motion and wave slamming with respect to wind load and mooring system for semi-submersible platform design. The slamming on the bracing of column stabilized units is not taken into account for the strength analysis under survival condition based on the DNV Class Rules (Det Norske Veritalas, 2015). Furthermore, the wave slamming loads under survival condition were ignored for the strength analysis of the brace structures in many semi-submersible platform practical engineering projects (Nie and Huo, 2013). The wave slamming on braces under survival condition is more critical than the slamming under transit condition for some semi-submersible platforms. This paper studied the strength analysis of the brace structure for semi-submersible under the wave slamming under survival and transit condition. The wind tunnel test of a semi-submersible platform was carried out to accurately describe the wind and current loads for an example of one typical semi-submersible platform. Meanwhile, the damping of the numerical model of platform was adjusted based on the results of the tank test. The simulations of the wave slamming of the platform brace under the survival and transit condition had been carried out accurately based on the tuning numerical model. Through this method, the wind, wave, current loads and full-size mooring system can be considered simultaneously through the non-linear software ANSYS-AWQA. Strength analysis was carried out to consider the results of the global structure strength analysis and wave slamming load, simultaneously.

Semi-submersible platform properties
This paper presents a typical dual pontoons of four columns semi-submersible platform. The platform is a deep water semi-submersible DP drilling rig and suitable for operations worldwide. The effect of brace wave slamming is studied on the strength analysis of the brace structure. The geometry properties and hydrostatical data are listed in Table 1.

Test model
In order to simulate the loads of the platform more accurately, the water tanker and wind tunnel model tests of the platform had been carried out. The draught of survival condition and condition were 15.5 m and 9.75 m, respectively.
The model test of the water tanker were carried out in FORCE's 240 m×12 m×5.4 m (length×width×depth) towing tank equipped with a double flap hydraulically driven wave generator at one end and an absorbing beach at the other. Model scale was 1:38.9. The model was held by a simple four-line symmetrical horizontal soft mooring system as shown in Fig. 1. Mooring lines were attached in 0.77 m above the baseline. Simultaneously, each mooring line consisted of 2 mm Dynema line with springs inserted near the tank wall. The system was designed so that the natural period of the mooring and model will not interfere with the periods of the wave spectrum.
The wind was simulated by the NPD wind spectrum based on the wind tunnel test results. The height of the wind speed reference was 10 m above the sea surface. The test model and wind tunnel were shown in Fig. 1.
The hydrodynamic characteristics and motion parameters of the platform were obtained through the tank test, which provided the basis for the correction of the numerical Center of gravity (m) Center of buoyancy (m)

Numerical simulation model
The numerical model was established with ANSYS software. The model was discredited using a maximum element size of 1.9 m below the free surface. In order to reduce the number of panels, the deck box had a maximum allowed element size of 4 m. The platform brace wave slamming load was simulated in ANSYS-AWQA.
In order to simulate the hydrodynamic performance of the platform more accurately, the pontoon, brace structure and column were established to calculate the influence of the Morison load, and then the viscous damping of the structure was corrected. Fig. 5 shows the tubular and disk elements.
The structure of the drainage volume inside the Panel    model is considered, so its cross section size has been reduced by 100 times when creating the Morison unit. While the calculated load factor has been magnified 100 times, so that the load of its towing force will not be affected by the constant displacement of the platform. Though AQWA NAUT can calculate the hydrostatic and Froude-Krylov forces at each time step based on the actual submerged geometry, the calculation of the radiation terms is based on the initial frequency domain. The calculated wave radiation is based on the initial position of the platform with the pontoons being deeply submerged. The pontoons and braces are partly emerging through the free surface both in the model test and time domain simulations in the survival sea state. Wave radiation is strongly depending on the submergence of the pontoons as well as emergence/immergence through the free surface. Wave radiation energy is obviously underpredicted in the diffraction-radiation data base based on SWL.
Under the survival and transit condition, this paper will modify the numerical model of the platform by increasing the radiation damping.

Mooring system
The 8-point symmetrical mooring system was simulated to locate the semi-submersible platform under survival condition, as shown in Fig. 6. According to the actual needs of the platform, the cable of 90 mm diameter was selected. The unit weight in water was 32 kg/m. The breaking strength was 675 t and the length of the cable is 2726 m in 500 m water depth.

Environmental simulation
The Jonswap spectrum was used to simulate random wave conditions. The sea state (H s = 17.3 m, T z = 16.5 s) was selected for the survival condition of the brace wave slamming analysis. The sea state (H s = 5.0 m, T z = 6.0 s) was used for the transit condition of the brace wave slamming analysis.
On current load, the surface velocity of 1.2 m/s was chosen. The wind load was simulated by the NPD spectrum. The average wind speed of an hour was 37 m/s for the ana-lysis. The wind and current load coefficients were calculated according to the wind tunnel test results.
Wind load coefficient was obtained by the wind tunnel test. The wind load was calculated according to these wind load coefficients. The calculation formula of wind load was presented in Eq. (1).
where, F j is the wind load of the j-th degree of freedom; C j ( ) is the wind load coefficient in the direction of wind direction; v is the wind velocity; and v s is the platform velocity.
According to the regulation of DNV-RP-C205 (Det Norske Veritalas, 2010), the impact load on the platform plane was calculated according to the following formula: ρ where, P s is the wave slamming load on the structure; is the density of water; v is the relative velocity between the water particle and structure surface.

Interest points on brace
The interested points of brace wave slamming were selected based on the characteristics of the brace structure. The locations of the interested points on brace were shown in Fig. 7.

Natural period of the numerical model
The natural periods of the platform for the model test and simulation in still water under survival condition are presented in Table 2. Only small differences are observed between the numerical model and test model. Nonlinear evaluation of the hydrodynamics in severe motion amp-   litudes shows a large influence on the natural period of the pitch. Under large wave condition, the pontoon bow parts and the braces occasionally emerge, which can increase the pitch restoring force and reduce the pitch natural period. The pitch response peak period is obviously lower than the still water natural period.

Platform movement response
To investigate the periods of the platform motion in the heave and pitch, the responses in the frequency and time domain are presented in Fig. 8 and Fig. 9. The model test of the heave motion has more peak response around the wave peak period, while the simulation has more response around the heave natural period. The pitch response in the simulations has slightly more energy around both spectral peaks than that in the model test. In terms of the periods and energy content, the agreements for the heave and pitch motion are found to be good.
The comparison of the mooring force between the model test and simulation is illustrated in Fig. 10. It can be seen that the mooring force is well presented in the numerical simulation for the model test.

Wave slamming
The relative speeds between the brace and water particles have been simulated based on the tuned numerical model in the time domain by the ANSYS-AQWA software. The viscous damping of the pontoon and brace structures was considered in the simulation.
Each load case has been carried out with ten sub-case wave realizations including 3 hours duration in each simulation. The maximum value of wave slamming on the brace was assumed to be well approximated by a Gumbel distribu-tion. The 90% of the Gumble distribution value for ten subcase wave conditions were used as the final maximum wave slamming load.
Under the survival condition, the relative speeds between the brace and water particles were presented in Table 3. The Gumbel distributions of the maximum for the ten sub-cases    are shown in Fig. 12 and Fig. 13. The maximum relative speed of the survival condition was 5.583 m/s, and the wave slamming load was 82269 N/m 2 . Under the transit condition, the relative speeds between the brace and water particles were presented in Table 4. The Gumbel distributions of the maximum for the ten sub-case were shown from Fig. 14 to Fig. 15. The maximum relative speed of the transit condition was 3.808 m/s.

Load coefficients
The wave slamming on the brace structure under the survival condition was more critical than that under transit condition. The relative velocity between the brace and water particle was larger under the survival condition. Therefore, the yield strength and buckling strength for the brace structure were calculated under survival condition.
According to the DNV-OS-C103 Structural Design of Column Stabilized Units_LRFD Method (Det Norske Veritalas, 2012), the coefficients of the loads under survival condition for Ultimate Limit States ULS were presented in Table 5.

Finite element model of the whole platform
The overall structure model of the platform is shown in Fig. 11. Relative velocities between the interested points and water particle under Case01 survival condition.  HUO Fa-li et al. China Ocean Eng., 2018, Vol. 32, No. 5, P. 536-545 541 Fig. 16. The main structures and thicknesses are shown in Figs. 17-20.

Yielding strength analysis of the brace structures without the wave slamming loads
The loads of the brace under static load and the dynamic load were considered except the wave slamming loads. According to the analysis reports of engineering project, the Von Mises stresses of the whole structure were presented in

Yielding strength analysis of brace structures including the wave slamming loads
The yielding strength of brace including the wave slamming had been calculated based on the global analysis results through the sub-model of the brace structure in SES-AM software. The load methods of wave slamming in the sum-model are shown in Fig. 23 and Fig. 24.
According to the results of the analysis, the maximum Von Mises Stress was 347.2 MPa under the survival condition including the wave slamming load in the direction of 0°. According to the stress distribution, it can be seen that the stress of the brace structure changed larger obviously in most area by considering the wave slamming load. The maximum Von. Stress increased from 300 MPa to 347.2 MPa, increased by 15.7%. In other words, the wave slamming load creates a critical stress on the brace, which should be considered under survival condition. 1.0 1.0 1.2 1) Note: 1) The coefficient is increased to 1.3 at some areas conservatively.

Conclusions
In this paper, a method of strength analysis of brace structure for semi-submersible platform is proposed based on the reconstruction and extrapolation of the numerical model. The full-scale mooring system, the wind, wave and current loads are considered simultaneously. Meanwhile, the method overall considers the wave slamming of brace, stat-ic load under static condition, dynamic load because of the pontoon and column in wave load.
The wave slamming on brace under survival condition was not required to be considered for the strength analysis of the brace structure in DNV rules. However, the environmental state under survival condition was more critical than that under transit condition. Through this method, the brace    HUO Fa-li et al. China Ocean Eng., 2018, Vol. 32, No. 5, P. 536-545 543 slamming load under the survival condition is more critical compared with the slamming load under transit condition for some semi-submersible platforms. For this example platform, the maximum relative speed of the survival condition was 5.583 m/s, and the wave slamming load was 82269 N/m 2 . However, the maximum relative speed of the transit condition was only 3.808 m/s.
According to the analysis results about an example of a typical semi-submersible platform, it can be seen that the wave slamming under survival condition is more critical than the slamming under transit condition. Meanwhile, the effect of wave slamming load on the brace is obvious. The maximum Von. stress on the brace increased about 15.7%. Therefore, the wave slamming load of slim structures such

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HUO Fa-li et al. China Ocean Eng., 2018, Vol. 32, No. 5, P. 536-545 as braces should be considered thoughtful in the structural strength analysis. The study in this paper provided valuable reference for the design of offshore platform.