Effect of Wave Headings on the Dynamic Response of the Continuous Mating Operation of Floatover Installation

The topside floatover installation is always a great challenge and is sensitive to environmental conditions. In this study, experimental analysis on the mating operation of the floatover installation in different wave headings is presented. The continuous mating operation using the rapid transfer technique was experimentally simulated with the assistance of the jacking system and the ballast system. In the continuous transfer modeling, the topsides loads were transferred onto the jacket by several consecutive steps, including the first rapid jack-down for the 30% loads, continuous 30%–70% load transfer and the second repaid jack-down for the remaining 30% loads. Motions of the barge and the topsides as well as loads on the Deck Support Unite (DSU) and the Leg Mating Unite (LMU) in different wave headings were measured. Experimental results illustrated the complex motion behavior and load characteristics of the continuous transfer operation. Results indicate that the rapid jack-down operations will lead to impact loads and larger lateral DSU loads. The bow quartering seas are much more dangerous as it gives rise to the larger motions and loads. Comparisons with the traditional steady-state modeling indicate that the continuous transfer modeling has greater advantages over the steady-state modeling on predicting the loads.


Introduction
It is always a great challenge for the topsides installation of offshore oil and gas platforms. During the past decades, the individual module lifting method, the heavy lifting method, and the floatover method have been developed to operate the offshore topside installation (Chu et al., 1998;Gros and Lescurat, 1982;O'Neill et al., 2000;Wang et al., 2010;Tian et al., 2018). In the module lifting method, the individual functional module of the topside is lifted separately and welded together offshore. However, the offshore hook-up and commissioning work is economically inefficient and time-consuming. In the heavy lifting method, the integrated topside is lifted by the heavy lift crane vessels. Nevertheless, the limited capacity of the heaving lifting crane restricts the application. Compared with the module lift method and the heavy lift method, the floatover method is a more attractive and competitive method for the topsides installation due to the relatively few costs and the larger capacity. There are several substantial advantages in installing an integrated topside by the floatover method, particularly for the mega topside that exceeds the single lift capacity of the available heavy lift crane. In the floatover method, the entire floatover operation generally includes transportation, docking, mating, and undocking phases. After the topsides were transported to the location by a single barge or a catamaran, the mooring line, the fender, and the monitor system are prepared to assist the barge in approaching substructures during the docking phase. When the weather window is suitable for the mating operation of the floatover installation, the topsides are transferred onto the jackets, conventionally relying on the tide level and the barge ballast system. After the offloading of the topside, the barge is separated from the topside and withdrawn from the slot of the jacket.
The mating phase is very dangerous as the mating operation is subject to a variety of technical challenges. The limited weather window is a critical issue for the mating phase. It is quite common to require 24−48 hours of critical weather windows for the mating operation of the floatover installation. The environmental loads on the topsides and barge will induce the excessive motions and thus lead to the impact loads on the LMU and the fender, which would threaten the safety of the jacket and the topsides (Seij and De Groot, 2007;Wang et al., 2014). How to quickly and safely transfer the topsides onto the jackets is the main concern of the floatover installation.
The entire continuous floatover installation is susceptible to the complex interaction of the multi-body as well as the nonlinear dynamic impact and is extremely sensitive to the weather condition. In the past decades, the field measurement, physical model tests, and numerical simulations have been developed to analyze the floatover installation. Tahar et al. (2006) investigated the dynamic response of the floatover installation in swell conditions by using the numerical simulations in which the dynamic load transfer process was simplified as several steady-state steps. They analyzed the tension of the lash lines between the semi-submersible barge and the jacket. Koo et al. (2010aKoo et al. ( , 2010b simulated the catamaran floatover installation of the spar through the physical model tests and measured the motions and loads in the transportation phase and the dynamic mating phase (i.e. 20%−50% load transfer). To compare with the experimental results, the quasi-static numerical simulations (i.e. 20% and 30% load transfer) were conducted in both time and frequency domain with the proprietary software MLTSIM and FREDOM, which were developed by Paulling (1995). Chen et al. (2014Chen et al. ( , 2019 and Hu et al. (2017) used the state-space model to numerically simulate the complex nonlinear impact loads during the 0% load transfer stage and the 100% load transfer stage in which the stabbing cone has zero clearance. The impact map, bifurcation diagram, Poincare maps, and phase portraits were employed to investigate the motions and the impact behavior of the barge-deck system. Jung et al. (2009) andChoi et al. (2014) applied the time-domain steady-state simulation to investigate the LMU loads under different loading conditions and the ballasting operation. Sun et al. (2012) and Xu et al. (2014) conducted numerical modeling to investigate the interaction effects of the multi-body in the floatover installation. As to the field measurement, Luo et al. (2015) monitored the motions of the barges and the sea environments with the field measurement techniques in the floatover installation in Bohai Bay, China. Tian et al. (2018) presented the design of the monitor system for jacket platform floatover installations. The innovative floatover installation methods were proposed recently. For example, Geba et al. (2017) proposed the floaters floatover method with relatively small waterplane area and large mass, which could reduce the heave, roll and pitch natural frequency and thus avoid the resonance. Wang et al. (2018) introduced an innovative low-deck floatover installation method with the strand jack lifting scheme and addressed the advantages and the limitations of the method. To improve the efficiency and the control accuracy of the floatover installation, the method by using the dynamic positioning transport vessel was developed (Bai et al., 2014;Wang et al., 2017, Yi et al., 2018. Although extensive research has been conducted, stud-ies related to the mating phase of the floatover installation are still inadequate. Less literature is currently available for the continuous dynamic load transfer process, especially for the rapid transfer technique. The limited weather windows and the time-consuming operation make the floatover installation extremely difficult in the open sea. To circumvent this issue, Technip proposed a jacking assisted floatover installation concept that enabled the topside to be installed much more quickly and safely to avoid high dynamic impact loads during the mating phase (Cholley and Cahay, 2007;Tribout et al., 2007). Yu et al. (2018) introduced the rapid load transfer technology with the hydraulic jacking system as well as the ballast system and applied for the innovative T-shaped barge which was designed to reduce the jacket slot requirement and accommodate the tall deck support frame. Kagita et al. (2019) numerically simulated the mating phase of the floatover installation to capture the transient impact effect during the jacking down operation using the software MOSES. The rapid load transfer technique based on the joint use of the jacking system and the ballast system could shorten both the initial mating phase and the final separation within one minute and thus enable the floatover installation to be suitable to the harsh sea conditions.
In this study, the floatover installation with the rapid load transfer technique in heading, bow quartering, stern quartering, and following seas was experimentally investigated with the goal of demonstrating the dynamic response of the floatover installation and determining the technical feasibility in different wave directions. With the rapid load transfer technique by the joint use of the jacking system and the ballast system, the continuous dynamic load transfer process was simulated in the physical model test. The motions of the T-shaped barge and the topsides in various wave conditions were analyzed as well as the loads on DSUs and LMUs. Moreover, comparisons between the continuous transfer modeling and the traditional steady-state modeling were carried out to demonstrate the advantage of the continuous transfer modeling. The paper is organized as follows. Section 2 introduces the set-up of the physical model tests and the rapid load transfer procedure. In Section 3, the dynamic responses of the floatover installation in heading, bow quartering, stern quartering and following seas are illustrated and the sensitivity to the wave conditions is analyzed. Section 4 presents the conclusions.

Model description
The tests were carried out in the wave basin at the State Key Laboratory of Hydraulic Engineering Simulation and Safety, Tianjin University, China. The experiment is briefly introduced in this section and more details can be referred to our previous paper (Bai et al., 2020a). The wave basin is 45 m long, 50 m wide and 1.8 m deep. The model scale was 1:40. The water depth of the experiment was set to 1.5 m, corresponding to 60 m in prototype. Fig. 1 is the photo of the floatover installation model under the action of the stern quartering seas. Fig. 2 shows the T-shaped barge and the jacket. Fig. 3 illustrates the layout of the experimental model. The principal parameters of the T-shaped barge model and the topsides model are listed in Table 1.
The rapid load transfer technique employed the ballast system and the jacking system to transfer the topsides loads continuously. Three ballast tanks were installed at the stern, mid-ship and bow of the T-shaped barge, respectively. The properties of the jacking system and the ballast system are listed in Table 2. The load transfer process involves the contact forces on the jacket legs and the stabling pins of the topsides, which are generally absorbed by the shock absorbers DSU and LMU. The capacity and the stiffness of DSUs and LMUs are listed in Table 2. In the model test, eight LMUs and four DSUs were installed at the jacking legs and at the bottom of the topsides, respectively. To measure the contact forces on LMUs and DSUs including the lateral force and the horizontal force, the three-axis load cells were installed as shown in Fig. 2.
The fenders were designed to absorb the collision loads between the barge and the jacket legs, including the transverse fenders and the longitudinal fenders. The stiffness of the transverse fender was 750 t/m and the stiffness of the longitudinal fender was 100 t/m. The mechanical characteristics of the mooring lines are also listed in Table 2. The loads on the mooring system were measured with a set of axial load cells located at the fairlead positions. The layout of the mooring line system is shown in Fig. 3a.
To measure the motions of the barge and the topsides, the optical motions capture system was applied and installed above the topsides, as illustrated in Fig. 4. Two coordinate systems were defined: the coordinate system O 1x 1 y 1 z 1 and the coordinate system O 2 -x 2 y 2 z 2 respectively, as shown in Fig. 4. The 6 DOF motions of the barge and the    To investigate motions and loads systematically, four wave directions were considered, namely heading seas, following seas, bow quartering seas, and stern quartering seas. The definition of the wave direction is shown in Fig. 3a. Table 3 shows all the irregular wave tests considered in the experiments, where H s is the significant wave height, T p is the peak wave period. Seven repeated simulations for each sea state were carried out and a total of 28 tests were conducted. Prior to the tests, the specified waves were calibrated in the wave basin to ensure that the input to the floatover installation test was of sufficient accuracy. During the wave calibration, the resulting spectral density distribution, the significant wave height, and the peak period were matched to the corresponding target values. The currents with the velocity of 0.6 m/s and the winds with the speed of 10 m/s in full scale were simulated for all cases in the tests.

Experimental procedure
The continuous dynamic load transfer process of the floatover installation was simulated based on the joint use of the jacking system and the ballast system. The continuous load transfer installation was modeled within about totally 11 minutes in the model tests, which is illustrated in Fig. 5. Different operational stages, including twice jack-down operational stages and the continuous ballasting operational stage, were carried out as follows: (1) First jack-down operational stage, i.e. 0−30% load transfer stage. After the pre-mating operation, jacking the topsides down quickly by the retraction of the jack was carried out in approximately ten seconds until about 30% of topsides loads were transferred. To gain deeper insight into the stochastics of the dynamic response during the jackdown operations, the timing of the jack-down operation was randomly selected for each realization.
(2) Continuous ballasting operational stage, i.e. 30%−70% load transfer stage. With the assistance of the water pumps and the jacking system, the topsides loads were gradually transferred onto the jacket legs. In the traditional method, only the ballast system together with the tide level was used to increase the draft of the barge and offload the topsides loads. Nevertheless, the relatively quick change of the barge draft may threaten the stability of the topsides and increase the impact load on the LMU. To surmount the barriers, the jacking system was designed to lift the topsides up very slightly during the 30%−70% load transfer stage. By joint use of the jacking system and the ballast system, the topsides loads were gradually and safely trans-  ferred onto the jacket in this stage. The duration of this stage was approximately 200 seconds, corresponding to 20 minutes in full scale. Honestly, in engineering practice, the duration of such load transferring process can be adjusted based on the capacity of the ballast system and the hydraulic jacking system.
(3) Second jack-down operational stage, i.e. 70%−100% load transfer stage. The second rapid jack-down operation was carried out within approximately ten seconds, corresponding to about one minute in prototype. The extended jacks were quickly retracted to transfer the remaining 30% topsides loads. In the model tests, the twice rapid jack-down operations were designed at the specific constant speed. After retrieving the jacks and separating the topsides from the barges, the floatover installation was accomplished.
For the sake of comparison, the traditional separated load transfer modeling of the floatover installation were carried out, in which four intermediate stages were simulated as shown in Fig. 5. Four stages include 0%, 30%, 70%, and 100% load transfer stages.
Each stage was simulated within about 10 minutes in the tests. The pump rate and the velocity of the jacks were controlled by the control and monitoring system.

Motions of the barge and the topsides
Figs. 6−9 show the motions of the topsides and the barge in different wave directions. From the figures, it can be seen that the barge and the topsides exhibit very complex heave behavior during the entire load transfer process. For the topsides, during the first jack-down operation the topsides suffered a rapid drop in the heave direction within several seconds due to the extraction of the jacks. After the first jack-down operation, the topsides were lowered down very slightly within a limited range, even for the second jack-down operation. It can also be seen that after the first jack-down operation the amplitude of the topsides heave motion was reduced largely due to the restriction of the LMU.
The barge heave motion varied significantly during the entire load transfer process. At the first jack-down operation, the barge floated upward due to the decrease of the topsides loads. Then the barge continuously lowered at a relatively large velocity during the 30%−70% load transfer stage as the water was injected into the ballast tanks and the draft of the barge increased. During the second jack-down operation, the barge floated upward again until the topsides loads were completely transferred onto the jackets. After the separation, the T-shaped barge moved with a large heave amplitude in the waves.
The heave motion amplitudes are different in different wave directions although the topsides and the barge exhibit similar heave motions trends in different wave directions. To analyze the heave motion in 30%−70% transfer stages for each case, the statistic results of the barge heave motions for 30%−70% transfer stages are shown in Fig. 10. By comparing the results of the standard deviation in the following and heading seas, it is found that the following seas result in larger heave motions than the heading seas, which would be attributed that the width of the stern was larger than the bow width. It is also found that the stern quartering seas and the bow quartering seas lead to the relatively large deviations of heave motions although the 1.2 m wave height of the stern quartering and bow quartering seas were relatively smaller than the heading and following seas of 1.5 m. The different heave motions may be caused by the asymmetry configuration of the T-shaped barge and the complex multi-body interaction. In short, it can be concluded that the bow quartering seas would lead to the largest variations in heave motion during the 30%−70% stage.
From the results of the pitch motion in Figs. 6−9, the topsides and the barge moved in pitch direction in a similar way in different wave headings. Although the topsides pitch was slightly larger than the barge pitch, which was caused by the elasticity of LMUs and DSUs, the barge was largely synchronized with the topsides in pitch direction before the second jack-down operation. Owing to the special configuration of the T-shaped barge, the barge was trimmed by the bow before the first jack-down operation and trimmed by the stern after the second jack-down operation. In the 30%−70% load transfer stage, the mean values of the barge and topsides pitch angles were about 0°. To compare the barge pitch motions in different wave directions, the standard deviations of the pith motions in different load transfer stages were analyzed as shown in Fig. 11. It is found that  BAI Xiao-dong et al. China Ocean Eng., 2021, Vol. 35, No. 1, P. 72-83 77 the bow quartering seas resulted in the largest pitch motions among other wave directions for 30%, 30%−70%, and 70% stages. For the 30% load transfer stage, the standard deviation of 0.215° in bow quartering seas was even 50% larger than the standard deviation of 0.14° in heading seas although the 1.2 m wave height of the bow quartering seas was much smaller than the 1.5 m wave height of the heading waves. Additionally, when compared with the pitch deviation in heading seas, the following seas were more dangerous than the heading seas because the following seas induced much larger pitch motion than the heading seas. From the time-series of the roll and yaw motions in Figs. 6−9, it can be seen that the barge and the topsides were largely synchronized in yaw and roll motions before the first jack-down operation. Roll and yaw motions of the topsides sharply decreased to about 0° after the first jackdown operation. Row and yaw motions of the barge decreased largely after the first jack-down operation and in-creased after the second jack-down operation. To quantify the motions in different wave directions, the standard deviations of the yaw and roll motions were statistically analyzed, as plotted in Fig. 12. From the figures, it can be seen that as expected the heading and following seas generally    lead to fewer yaw and roll motions. The bow quartering seas resulted in the largest roll and yaw motions in both 0% and 100% load transfer stage. The yaw and roll motions in the 0% load transfer stage were slightly larger than those in the 100% load transfer stage. The roll and yaw motions of the barge will give rise to the larger impact loads on LMUs and DSUs.

Loads on LMUs and DSUs
Figs. 13−16 show the loads on each LMU and DSU in different wave directions. The results show that the vertical forces f z,DSU on DSUs varied slightly at the 0% load transfer stage and dramatically decreased during the 30%−70% load transfer stage. For the rapid transfer technique, it is of great interest to examine the impact loads during the twice jackdown operations. For all cases, it is found that the twice jack-down operations seem not to introduce large vertical impact loads on DSU although the DSU vertical loads reduced sharply during the jack-down operations. For example, the largest vertical DSU load during the second jackdown operation in heading seas was about 3 500 t, which was generally smaller than the DSU loads at the 0% load transfer phase.
On contrast, the twice jack-down operations induced larger lateral DSU loads f xy,DSU , especially for the second jackdown operation. For instance, for the following wave as shown in Fig. 17, the lateral DSU loads reached about 550 t and 780 t for the first and second jack-down operations, respectively. Based on the DNV guideline (DNV·GL Noble Denton, 2015), the jacking system shall be suitable to provide lateral restraint equivalent to 10% of the structure weight acting horizontally. For the modeled topsides of 16 000 t, as suggested each of the four jacks should provide lateral restraint equivalent to 400 t. However, the experi-   BAI Xiao-dong et al. China Ocean Eng., 2021, Vol. 35, No. 1, P. 72-83 79 mental results demonstrate that the maximum lateral loads exceed the limitations. For example, the lateral DSU loads for the 30%−70% load transfer stage in stern quartering seas were even three times more than the suggested value. It can be concluded that the DNV suggestion for the jacks' design was underestimated and insecure for the jacking system. It is of interest to find that the collisions after the second jack-down operation occurred. For example, several peak loads on the vertical and lateral force of DSUs and LMUs were displayed in heading waves. One explanation is the limited clearance between the topsides and the jacks. Another may be the vibration of the jacket due to the impact between the fenders and the jacket.
For the sake of comparison of the DSU loads in different wave directions, the maximum DSU loads for each case are listed in Table 4. The statistical results were based on the seven repeated tests. To simulate the randomness of the random wave and the jack-down timing, the repeated tests were carried out with different random seeds and different timing of the twice jack-down operations. From the table, it can be seen that the quartering seas induced larger impact vertical and lateral loads on DSUs even though the wave height was smaller than that of the heading and following seas. The reason may be that the bow quartering seas and the stern quartering seas may induce larger barge motions, which is analyzed before. It can be concluded that the stern quartering seas and the bow quartering seas are the most dangerous wave directions for the rapid load transfer process. Based on the experimental results, the lateral load capacity of each jack should be more than 20% of the structure weight to ensure the safety of the rapid load transfer operation.
Another concern in the design of the jacking system is the variation of the loads on the jacks during the load transfer process. The large change on the jacks loads within a limited time requires the special design of the jacking system. The variation of the DSU loads during the 30%−70% load transfer stage was statistically analyzed by reducing the moving average value, as shown in Fig. 17. From the results, it can be seen that the bow quartering seas lead to the largest variation of the vertical loads and the lateral loads. The variation of the lateral loads is slightly smaller than the vertical loads. The lateral DSU load variation in the bow quartering seas is even two times larger than those in following seas, which should be paid much attention when designing the jacking system.
The time-series of the lateral forces f xy, LMU and the vertical forces f z,LMU on LMUs in different wave directions were plotted in Figs. 13−16. It can be seen that both the vertical and lateral LMU forces increased with the increase of the loads transferred. The twice jack-down operations generally induced the lateral LMU forces and vertical LMU forces, especially for the second jack-down operation. The second jack-down operation gave rise to a shape peak on the lateral LMU loads for all cases. It was found that the lateral LMU loads during the second jack-down operation were the largest during the whole load transfer process. The maximum loads on LMUs were listed in Table 4. It can be seen from the results that the largest lateral LMU loads occurred in the stern quartering and the bow quartering seas. Results indicate that much attention should be paid to the lateral LMU loads in the stern quartering seas and the bow quartering seas.   3.3 Comparison of DSU loads with the steady-state modeling For the traditional steady-state modeling method, which was widely used for simulating the floatover installation and was employed in our previous study (Bai et al., 2020b), the dynamic load transfer process is simplified as several steady-state steps without the consideration of the continuous load transfer operation. In order to compare the continuous load transfer modeling with the steady-state modeling, the steady-state experimental simulations in stern quartering seas were also carried out. The DSU loads, which are associated with the design of the jacking system, were compared for the two methods. Fig. 18 and Fig. 19 show the DSU load histories at 30% stage and 70% stage in separated steady-state modeling, respectively.
The maximum loads during the 30%−70% transfer stage for the continuous load transfer modeling were evaluated and compared with the results of 30% and 70% transfer stage in the steady-state modeling, as shown in Fig. 20. It was found that the maximum vertical and lateral DSU loads in continuous transfer modeling were slightly larger than those in steady-state modeling. The largest difference of the vertical and lateral DSU loads between the two methods were 15.2% and 14.8%, respectively. Another concern for the design of the jacking system isthe loads variation during the load transfer operation. Fig. 21 shows the standard deviation of the DSU loads by using two methods. It can be seen that the continuous load transfer operation will lead to larger variations of the vertical DSU loads. The standard deviation of vertical DSU loads for 30%−70% continuous transfer operation was 29.5% larger than the 30% stage and 30.8% larger than the 70% stage in separated steady-state modeling, respectively. The difference of the lateral DSU loads standard deviation between two methods was limited. From the comparison, it can be concluded that the steadystate modeling would underestimate the maximum and variation of DSU loads, particularly for the vertical DSU loads. The steady-state modeling results would not be conservative for the design of the floatover installation.

Conclusions
The experimental model of the floatover installation using the rapid load transfer technique was developed in this paper. The complicated continuous load transfer process was simulated in different wave directions and compared with the traditional steady-state modeling results. Based on the experimental results, the following conclusions are drawn as follows.
(1) The bow quartering seas and stern quartering seas  with smaller wave heights gave rise to relatively larger motions than the heading and following seas. The bow quartering seas also resulted in the largest barge motions in heave, roll, and yaw directions. The bow quartering seas resulted in the larger DSU and LMU loads and the largest variations.
(2) The twice quick jack-down operations would lead to the larger impact lateral DSU loads, which would be dangerous for the mating operation.
(3) The DNV suggests that the jacks provided the lateral constraint equivalent to 10% structural weight seems not to be suitable for the rapid load transfer technique. Statistical results show that the lateral load capacity of each jack should be more than 20% of the structure weight.
(4) Compared with the traditional steady-state modeling, the continuous transfer modeling could capture the complex variation of the loads and provide much more reasonable results of the dynamic floatover operation. The experimental results show that the steady-state modeling will greatly underestimate the maximum and standard deviation of DSU loads, particularly for the vertical DSU loads.
It should be noted that the floatover installation involves several technical issues such as the fender force and the mooring force, which are not included in this paper. Further research is needed to be carried out to investigate the fender and mooring forces and explore the workability of the floatover installation in extreme wave conditions, especially for the beaming waves. In addition, it is in urgent need to develop the available numerical method for modeling the continuous dynamic load transfer process and to investigate the motions and the impact loads.