Structural Stress Monitoring and FEM Analysis of the Cutting Operation of the Main Bracket of A Semi-Submersible Platform

For a semi-submersible platform in repair, the eight old main brackets which connect columns with pontoons need to be replaced by new ones. In order to ensure the safety of the cutting operation of the old main bracket and calculate the initial stress condition of new main bracket, the structural stress monitoring of eight key spots is carried out, and then the calibrated finite element model is established according to the field monitoring results. Before cutting the main bracket and all associated structures, eight rectangular rosettes were installed, and a tailored cutting scheme was proposed to release the initial stress, in which the main bracket and associated column and pontoon plates were partly cut. During the cutting procedure, the strains of the monitoring spots were measured, and then the structural stress of the monitored spots were obtained. The stress variation characteristics at different spots during the initial cutting operation were shown and the initial stress condition of the monitored spots was figured out. The loading and support conditions of the semi-submersible platform were calibrated based on the measured initial stress condition, which made the finite element model more credible. The stress condition with the main bracket and associated structures being entirely cut out is analyzed by the Finite Element Method (FEM), which demonstrates the cutting operation to be safe and feasible. In addition, the calibrated finite element model can be used to calculate the initial stress condition of the new main bracket, which will be very helpful for the long-term stress monitoring on the main bracket.


Introduction
The structural safety of offshore structures is of significant importance in the stages of design, repair and maintenance, and is of great concern for the designers, builders and operators (Liu, 2015). As a main type of local structure in ships and offshore platforms, the main bracket generally welded and connected with other structures plays an important role in the transition of the structural stress. For a semisubmersible platform, the main bracket is usually applied to connect the column with pontoon. Consequently, the main bracket is usually of large structural stress, and is particularly prone to local yielding, buckling, and fatigue failure. Failure of the important local components may lead to the lack of global strength, resulting in the loss of life and property in safety accidents (Ma et al., 2008). Therefore, a large number of researches have been conducted for strength analysis and life prediction of typical structural nodes, especially for brackets, on ships and offshore platforms (Tame-hiro et al., 1982;Fricke et al., 2004;Fujikubo, 2005;Fricke and Kahl, 2007;Xie and Xie, 2009;Stoschka et al., 2010).
During the detailed design phase of an offshore structure, the designer checks the structural strength of each node in accordance with the rules of the classification society, to ensure the safety requirements of the structure during the service period in the operating sea. However, due to the randomness of the environmental conditions at sea, the failure of some nodes commonly occurs (Cai et al., 2013;Liu et al., 2016). The failed structure must be replaced by new one, and the general procedure usually includes cutting steel plates, removing failed structures, pre-assembling new structures, and welding. The opening formed by removing the failed structure will cause the change of the structural stress distribution, making the vicinity of the opening tend to be dangerous (Zhou et al., 2011;Wu et al., 2017). It can be seen that the removal of failed structure has a great influence on the stress condition nearby, and the structure that needs to be replaced in the docking repair is often located in the critical position of the platform. Therefore, it is necessary to study the stress redistribution on the local structure with the failed structure being cut out, further to determine whether the cutting operation is safe.
The Finite Element Method (FEM) is usually applied to evaluate the stress condition and strength of structure. Owing to the complex structure of ship and offshore platforms, the local model with the fine and dense grids are only applied in the concerned local structure, while the global model with the general grids are used to simulate the whole structure. In the FEM, the local deformation of the local structure model is usually numerically calculated by the global deformation of the whole structure under the external load, so the boundary condition of the local model is defined by the connection node between the global model and the local structure model. However, for an old ship or offshore platform in repair in the dry dock, it is difficult to accurately simulate the actual load and boundary conditions at most circumstances (Ueda et al., 1994;Seo and Jang, 1999;Li et al., 2005;Li and Ren, 2006;Deng et al., 2007;Zhu et al., 2007;Shi et al., 2017). So, it is critical to validate the numerical FEM model by field measurement before the evaluation of the structural stress condition of cutting out the failed structures.
In this paper, the cutting operation of the main bracket connecting the column and pontoon is studied for a semisubmersible platform in the dry dock. Before cutting the main bracket and all associated structures, the strain monitoring method is proposed to record the time series of strains at eight different spots, and a tailored cutting scheme is adopted to release the initial stress, in which the main bracket and associated column and pontoon plates are only partly cut off. The Von Mises stress is obtained for each monitoring spot based on the measured strains. The stress variation characteristics at different spots during the stress release procedure are shown and the initial stress condition of the monitored spots is figured out. The FEM model is established and calibrated by the field monitoring results. The stress condition with the main bracket and associated structures entirely being cut out is analyzed by this calibrated FEM model, which demonstrates the cutting operation to be safe and feasible.

Description of problem and methodology
Several fatal flaws have been found in the old main brackets connecting columns with pontoons in a semi-submersible platform during a root-and-branch inspection, which is usually performed for every five years in the lifetime of the platform. To strengthen the overall structural strength, the failed main brackets and associated structures need to be removed and replaced by the new ones. The associated structures include part of the outer plate of column, the longitudinal bulkhead plate of column, part of the outer plate of the pontoon, and the longitudinal bulkhead plate of pontoon, as shown in Fig. 1. The oxyacetylene flame is adopted to cut the old steel structure of the platform in the shipyard. In order to remove the failed main bracket and associated structures, the cutting operation is planned to perform along the edges of outer plates and the longitudinal bulkhead plates of the column and pontoon.
Although the failed structure is relatively small in relation to the column and pontoon connection areas, the main bracket inherently sustains high stress, and the structure also includes longitudinal bulkhead plate of the column and pontoon, therefore, structural stresses of the reserved structures should be evaluated to avoid large structural deformation or damage from excessive stresses at some dangerous locations, such as the edge of the cutting line. The finite element analysis (FEA) seems to be an easy way to evaluate the structural stress before and after the cutting operation, but the accuracy is limited by too many unknown constraint conditions and load distributions of the platform repairing in the dry dock. However, field stress monitoring is a helpful method to modify and validate the numerical model.
In order to obtain the initial stress condition of the main bracket and associated structures, a tailored cutting scheme is firstly proposed and applied to release the initial structure stress for filed measurement, which is different from the cutting operation to remove all old structures, and meanwhile field monitoring of stress is conducted for different spots on and around the main bracket during the releasingstress cutting operation. According to the measured stress variations, the initial stress condition can be obtained for the measured spots. And then the loading and support conditions of the semi-submersible platform in the FEM model can be calibrated by comparison with the measuring results, which make the FEM model more credible. The stress condition after cutting out all old structures can be calculated by the calibrated FEM model to validate the feasibility of the bracket removal plan. The research procedure is shown in Fig. 2. Moreover, the initial stress distribution on the replaced structure can also be further obtained by the calib- rated FEM model above, which will be helpful for the longterm stress monitoring and analysis on the new main bracket.

Monitoring principles
In reality, it is very difficult to measure the stress directly. The stress is always derived from the measured strain. The failed main bracket and associated structures are in a plane stress state, and the strains can be measured by a rectangular rosette composed of three strain gauges with the included angle of 45° between each other and one temperature compensation strain gauge (James and Tatam, 2003;Chan et al., 2006), as shown in Fig. 3. The three strain gauges are fixed on the steel plate by the spot welding technique, and the center of the circle passing through the center of the three strain sensors is the position of the monitoring spot. The temperature compensation strain gauge is attached to the steel plate by silicon rubber, only responding to the temperature change, which can effectively correct the measured error of the strain gauge caused by the temperature change during the cutting operation.
Before the cutting operation, the strain gauge rosette is installed on the monitoring spot. During the cutting process, the time varying strains measured by the gauges are defined as , , and , where represents the time varying strain due to the change of temperature. It can be seen that the strains in different directions caused by the change of structural force during the cutting operation is: The initial strains of the monitoring spot in different directions are unknowns before the cutting, thus are defined as , and for the x, y and u axis, respectively. Therefore, the absolute strains of the structure in different directions during the cutting operation are: After the cutting operation is completed, when the intensified nonlinear effect induced by the welding high heat is dissipated and the measured values of the strain gauges are stable, the field measurement can be stopped, where the end time is recorded as t ∞ . It is assumed that the stress at each monitoring spot is completely released at this time, and the absolute strain of the monitoring spot in different directions should be zero, since the corresponding structure has been cut out and separated from the platform. Therefore, the initial strain of the monitoring spot in different directions can be obtained as follows: Substitute it into Eq. (2), the absolute strain of the structure in different directions during the cutting operation is: According to the theory of Material Mechanics and the measurement principle of rectangular rosette, the principal strains , , and the principal strain direction can be obtained: For steel material, the modulus of elasticity E = 206 GPa and the Poisson's ratio = 0.3. Based on the Generalized Hooke's Law, the maximum normal stress and the minimum normal stress can be derived: The structure strength can be evaluated by the Mises yield criterion. The equivalent Von Mises stress is:

Monitoring program
Based on the site survey and numerical analysis of the failed main bracket, eight structural stress monitoring spots were identified, as shown in Fig. 4. Nos. 1−2 monitoring spots are located on the outer pontoon plate near the lower toe of the main bracket, Nos. 3−4 monitoring spots are located on the main bracket, while Nos. 5−6 monitoring spots are located on the outer plate of column near the upper toe of the main bracket. It is noted that the lower and upper toes of the main bracket belong to high stress zones together with the two ends of the strengthening component on the main bracket, so Nos. 1−6 monitoring spots are determined. In addition, Nos. 7−8 monitoring spots are located on the outer plate of the column above the cutting route.
In order to facilitate the safety requirements of field stress monitoring, a cutting scheme dedicated to quick release stress is proposed as presented in Fig. 4, instead of cutting out all the old structures. The oxyacetylene flame is applied in this cutting process. Firstly, the connection of the main bracket with the column and the pontoon is cut off with the exception of the lower toe. Secondly, at the periphery of measuring spots Nos. 7 and 8, an 'm' type slit is cut along the predetermined cutting route of the outer plate of column. Finally, an 'n' type slit is cut on the outer plate of pontoon surrounding the measuring spots Nos. 1 and 2. The structural strains of the above eight monitoring spots were monitored throughout the cutting operation. A local coordinate system O-XYZ is defined in Fig. 4. The X and Y axes are all located on the surface of the pontoon, and the Z axis is perpendicular to the surface of the pontoon. The arrow notation '*→*' describes the implementation sequence of the cutting operation scheme. The coordinates of the position of each monitoring spot in the coordinate system O-XYZ are given in Table 1. The actual cutting operation schedule is shown in Table 2. It can be divided into five stages, i.e., initial stage, Stage I, Stage II, Stage III and final stage.

Monitoring results σ ei
It is noted that the stress at each monitoring spot is assumed to be completely released after the cutting operation. The principal stress and its direction for each measuring spot can be calculated by the monitoring principles described in Section 3. Finally, the Von Mises stresses of the measuring spots are obtained, which are denoted as , where i=1−8, representing the 8 different measuring spots. The stress variations of each measuring spot during the releasing-stress cutting scheme are shown in Fig. 5   ally declined, although a rapid rise is observed due to the considerably high temperature of the cutting flame. When the cutting operation of the main bracket is completed, the stress drops rapidly. The measured stress of No. 4 spot increases firstly and then decreases, and finally increases rapidly due to the notably high temperature of the flame. The measured stresses of Nos. 5 and 6 spots on the outer plate of the column and near the upper toe of the bracket decrease during the cutting operation. The measured stresses of Nos. 7 and 8 spots on the outer plate of the column above the removal structures are not obviously varied. At Stage II (3060−6300 s), the cutting operation of the outer plate of the column was performed. The measured stresses of Nos. 1−4 spots are not obviously changed. The measured stresses of Nos. 5−8 spots are fluctuated by the state change of the structure due to the cutting operation and the considerably high temperature of flame.
At Stage III (8760−10500 s), the cutting operation of the outer plate of the pontoon was performed. The measured stresses of Nos. 1−2 spots of the outer plate of pontoon near the lower toe of the main bracket are generally reduced, and increased at some moments (9000 s, 9800 s and 10200 s for instance) due to the high temperature of the cutting flame. The measured stresses of the other spots are not obviously varied.
At the final stage (10500 s−the end of measurement), the local cutting operations are completed. While the measurement continues until the temperature of all the spots decreases to the same as the ambient temperature. As can be seen from Fig. 5, the measured stresses of Nos. 1 and 2 still decrease notably after the measurement, i.e., the measured stresses still include the effects of temperature. However, the measured stresses of Nos. 3−8 are more or less stable before the end of the measurement, i.e., the temperature effects are negligible.
During the cutting operation, the measured stresses variations are caused by structural changes due to the cutting operation as well as the considerably high and fast varying temperature of the cutting flame. In the analysis of the measured stress, from the structural safety point of view, the temperature effects should be essentially eliminated. It can be seen from Fig. 5 that the measured stresses of all spots are not generally significant, where the maximum value is smaller than 350 MPa except for No. 4 spot that it reaches 600 MPa due to the influence of flame. After the cutting operation is completed, the stresses of Nos. 7 and 8 spots outside the cutting area are notably lower than their initial stresses before the cutting operation.

Initial stress of measuring spots
According to the equivalent stress variations of each measuring spot during the cutting operation shown in Fig. 5, the initial stress of each measuring spot before the cutting operation can be obtained. However, it should be noted that the initial stress is obtained based on the assumption that the stress at each measuring point has been completely released after the measurement. Therefore, it is necessary to analyze the actual stress state of each measuring spot after the cutting is completed, in order to obtain the actual initial stress of each measuring spot.
(1) After the cutting operation is completed, the No. 1 measuring spot of the outer plate of pontoon is connected with the vertical bulkhead of the pontoon. Since the structural deformation of the column cannot be directly transmitted to the No. 1 spot, the structural stress can be regarded as partly released. The No. 2 measuring spot of the outer plate of pontoon is in a state of 'two sides constrained, two sides free', i.e., two sides of the surrounding plate have been cut off and the other two sides are still connected to the platform structure. Thus, its structural stress can also be considered as completely released. However, as can be seen from Fig. 5, the measured stresses of the Nos. 1 and 2 spots are still in a downward trend at the end of the measurement. Therefore, the initial stresses of the Nos. 1 and 2 spots are larger than 70 MPa and 80 MPa, respectively.
(2) After the cutting operation is completed, there is only a small part of the lower toe of the main bracket that is connected with the outer plate of pontoon. Thus, the main bracket is in a state of free. By ignoring the influence of the gravity of the main bracket itself, the structural stresses of Nos. 3 and 4 spots are completely released. As can be seen from Fig. 5, the structural stresses at the spots Nos. 3 and 4 tend to be stable at the end of the measurement. Therefore, the initial stresses of the spots Nos. 3 and 4 on the main bracket are both about 150 MPa.
(3) After the cutting operation is completed, the No. 5 spot of the outer plate of the column is still connected with the longitudinal bulkhead of the column. The longitudinal bulkhead of the column is the main force-bearing component, whose structural stress is incompletely released. The No. 6 spot of the outer plate of column is in a state of 'two sides constrained, two sides free', as the same with the No. 2 spot. Thus, its structural stress can be regarded as completely released. As can be seen from Fig.5, the structural stress of the No. 6 spot tends to be stable at the end of the measurement. Therefore, the initial stress of the No. 6 spot on the main bracket is about 80 MPa.
(4) After the cutting operation is completed, the No. 7 spot of the outer plate of the column is in a state of 'three sides constrained and one side free', i.e., only one side of the surrounding plate has been cut off and the other three sides are still connected to the platform structure. While No. 8 spot of the outer plate of the column is still connected with the longitudinal bulkhead of the column. Thus, the structural stresses of Nos. 7 and 8 spots are incompletely released. As revealed in Fig. 5, the initial stresses of Nos. 7 and 8 spots are only about 60 MPa and 20 MPa, respectively.
As analyzed above, the initial stresses of all measuring spots are shown in Table 3. These field-measurement results can be used as a benchmark to calibrate the numerical FEM model.

Description of the FEM model
To verify the feasibility of the scheme for cutting operation of the failed main bracket and associated structrues, Finite Element Method (FEM) is employed to calculate the stress distribution of the structures during the cutting operation. Software SESAM is used to create the structural model in which variation of local structure caused by cutting operation is taken into account. The overall structural model of the semi-submersible platform is shown in Fig. 6. This model gives a detailed description of the columns, pontoons and braces, as well as the main bracket to be cut off. Refined meshes are applied to the bracket and its adjacent structures to obtain the accurate stress states in these local areas, as shown in Fig. 6. Except the structural model, external load distribution and boundary conditions of the platform are also required to be included in the FEM model. The first external load is caused by the temporarily installed structures on the pontoon such as the staircase for maintenance and life uses in the period of repair. These loads are simulated by a set of 45 mass points located at about 3 times length of the bracket away from the column, as given in Fig.7a. The average mass of these mass points is denoted as m 1 . Like the loads on the pontoons, there are also some temporarily installed structures on the column such as supporting and protective structures. These loads are also represented by a set of 225 mass points and Fig. 7b illustrates the distribution of points on the outer plates of the column. The average mass of the latter set is denoted as m 2 . The platform is supported by the slipway during the cutting operation performed in a dry dock. In this paper, the support by the slipway on the bottom plates of the pontoon is simulated by a set of 8262 linear spring elements which only allow the relative vertical displacements. The stiffness k s of these spring elements (Fig. 8) is deemed as a regulable constant to represent the relation between the displacement and support force.

FEM model calibration
In order to numerically investigate the structural safety of the platform after the main bracket and associated structures are cut off, the external loads m 1 , m 2 and the boundary Outer plate of column(near bracket) 80 MPa 7 Above the cutting route / 8 Above the cutting route / KOU Yu-feng et al. China Ocean Eng., 2019, Vol. 33, No. 6, P. 649-659 655 conditions k s should be firstly determined. However, due to complicated procedures during the cutting operation, it is difficult to correctly record these parameters. Thus, a 'calibration' procedure is performed in this section to obtain these parameters of external loading and boundary conditions.
The main procedure of the calibration is as follows: 1) collect the initial monitoring stress for the measuring spots, and set them as the calibration targets; 2) calculate the initial stress of the measuring spots by using the FEM model and finding the effect of the parameters m 1 , m 2 and k s on the initial stress; 3) keep adjusting the parameters m 1 , m 2 and k s until the FEM results and calibration targets are in a comparatively good agreement. It is noted that the effects of temperature on structural stresses are neglected since the temperature of each spot has decreased to the same as the ambient temperature at the end of the field measurement.
Through adjusting the parameters m 1 , m 2 and k s , a series of the FEM results are obtained. Here, two sets of parameters that make the FEM results have comparatively good agreements with monitoring results are obtained, and denoted as Set A and Set B, respectively, as given in Table 4. σ x σ y τ xy By using the software SESAM, stress responses of the main bracket and associated structures under the uncut state and after-cut state are calculated. The differences of the component stresses such as , and between the two states are obtained as the initial stress for each measuring spot. Comparisons of the initial stress between the FEM and monitoring results are presented in Table 5. It can be seen that the FEM results with Sets A and B parameters are in comparatively good agreements with monitoring results for all measuring spots, which indicates that the identified parameters m 1 , m 2 and k s of the two sets are adequate.

FEM analysis of cutting operation
This section predicts structural safety of the platform after the main bracket and associated structures are cut out by FEM analysis, where the two sets parameters m 1 , m 2 and k s of external loading and boundary conditions determined in the last section are adopted. As the main bracket and associated structures should be removed, some protective girders are welded around the bracket to ensure the local structure has sufficient strength during cutting operation. In the FEM model, these girders are represented by two beam elments whose sizes and locations are in accordance with the construction scheme. The local FEM model are shown in Fig. 9. With the two sets of external loading and boundary conditions achieved in Section 5, structural strength of the platform without the main bracket and its associated structures are investigated. Two cases Case A and Case B are numerically analyzed with the parameters of Set A and Set B, respectively. Since Von Mises stress distributions of Case A and Case B are similar, here only stress conditions of Case A are shown.
Figs. 10−12 respectively show the front, side and back  The right and left inflexion points of cutting routes at the outer plate of column are labeled as Inflexion 3 and Inflexion 4, respectively. It can be seen that it is due to the geometrical mutation at the inflexion point of cutting routes that stress concentration occurs. Therefore, special attention should be given to these points. The local peak stresses and corresponding element numbers for Case A and Case B are listed in Table 6. The main bracket and associated struc-       tures are made of EH36 high strength marine structural steel with the yield stress criterion of 400 MPa (Choung et al., 2012). Although Von Mises stresses at the inflexion points increase dramatically after cutting out, the amplitudes of these stresses are still below the yield strength, indicating that the cutting operation is feasible.

Conclusion
This paper combines structural stress monitoring and finite element analysis (FEA) method to evaluate the safety of the cutting operation of the main bracket which connects the column with pontoon of a semi-submersible platform in repair. Based on the site survey and theoretical analysis of the failed structures, structural stress monitoring of eight key spots was carried out. In view of the safety requirement of stress monitoring during the cutting operation, a tailored cutting scheme was proposed to release the initial stress. By analyzing the monitoring results, initial structural stress of some measuring spots were achieved. To verify the feasibility and safety of the cutting operation of the main bracket and all associated structures, FEA is employed to calculate the stress distribution after the cutting operation. The FEM model is calibrated through identifying loading parameters and boundary conditions by using the monitoring results. It can be concluded from the FEA analysis for the cutting operation of the main bracket and associated structures that although Von Mises stresses at inflexion points increase drastically after the cutting operation, the amplitudes of these stresses are still below the yield stress criterion of the main bracket steel plate, indicating that the cutting operation is feasible. In addition, the calibrated finite element model can be used to calculate the initial stress condition of the new main bracket, which will be very helpful for the long-term stress monitoring on the main bracket.