1 Introduction

Offshore platforms are form-dominant steel structures deployed in the deep sea for exploratory drilling, natural gasses, and oil [1,2,3]. The topside comprises several facilities to support such operations and is subjected to accidental loads, which include impact and blast loads, developing higher stress concentration on structural elements [4,5,6]. Functionally graded materials (FGM) are suggested for topside application due to their increased strength and performance criteria [7]. The current study examines the capacity of offshore topside under accidental loads using pushover analysis while comparing the response behaviour using FGM and X52 steel. The topside view and details of several components contributing to the load during operation are shown in Fig. 1. Numerical studies carried out using pushover analysis on buildings showed that the response spectrum method underestimates the building's response compared to the model-pushover analysis [8, 9]. Steel structures under lateral loads are examined to study the effect of concentric bracings on different seismic zones, base shear, roof displacement, and hinge formations [10]. Steel moment-resisting frames with reduced beam section, reduced web section, and fully fixed moment connection are compared to highlight the superiority of the reduced web section. [11]. Braced steel frames showed higher shear capacity [12], but irregularity in the plan shall result in torsional coupling [13]. Offshore topside, as seen in the figure, exhibits a lot of vertical and horizontal irregularities due to the electro-mechanical layout of equipment and pipelines; detailed investigations under accidental loads make the study more important to arrive at a safe design.

Fig.1
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Typical view of offshore platforms topside

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Pushover analysis is discussed as an alternate to inelastic seismic analysis. The effect of higher mode contributions and a continuous change in the structure's resistance distribution are elements of uncertainty in the pushover analysis [14]. Modal pushover showed improvement while retaining simplicity over the response spectrum analysis [15,16,17]. It also contains material nonlinearity under a combined stress state [18]. Ant colony optimization (ACO) is an alternate to estimate the seismic performance of steel frames, which compares well with the genetic algorithm [19]. It is interesting to examine offshore topside under blast loads as the high-temperature effects increase the damage potential, initiating a buckling failure in columns [20,21,22]. In comparison, the dynamic-based pushover analysis of steel moment-resisting frames shall include higher modes' nonlinear behaviour [23, 24], an improved version of the first mode's participation to yield higher modes, and reported to be more efficient [25,26,27]. The steel frame's capacity and height affect the behaviour factor (BF) [28, 29], which is also a major concern in offshore topside structures. Further, it is also observed that a lumped plasticity model underestimates the shear demand compared to the shell and frame element model [30,31,32]. While fire can cause a significant reduction in the mechanical properties of steel at higher temperatures (> 500 °C) [33], a combination of impact and blast loads makes the platform highly vulnerable during installation and operational stages [34]. Blast load raises the temperature in structural members and degrades the beam-column connections. In the presence of accidental loads, waves and wind force combination cause excessive deformation and plastic hinge formations [35]. The present study compares the response behaviour of the topside using pushover analysis under such critical combinations using two different materials, namely X52 steel and FGM. During the blast, the temperature may rise beyond 1000 °C in lesser than 10 min, causing high thermal stresses [36]. As it is evident that conventional structural steel cannot withstand such high temperatures, the current study examines the use of FGM to model structural members in the region vulnerable to hydrocarbon explosion. FGM constitutes carbon-manganese steel and duplex stainless steel with high resistance to temperature, corrosion, and second-order vibrations, in addition to higher ultimate and yield strength values. A comparative analysis is made between the X52 steel and FGM to show the superiority of FGM under the combination of lateral loads and special loads, which is novel.

2 Geometric Configuration

The topside comprises a multi-tier deck useful for several functional needs. Figures 2 and 3 show the topside plan and elevation; long-span beams and increased storey heights are inevitable to facilitate the drilling activities of the topside. The geometry of the Bullwinkle platform deployed in the Gulf of Mexico region at 412 m water depth is taken for reference. A preliminary design is carried out under wave, wind, and mechanical loads; details of the members are summarised in Tables 1 and 2 [35] (Figs. 4 and 5).

Fig. 2
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Plan of topside

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Fig. 3
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Elevation of topside

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Table 1 Topside details [35]
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Table 2 Cross-sectional dimensions of structural members [35]
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Fig. 4
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Functionally graded materials at normal stress conditions [36, 37]

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Fig. 5
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Stress–strain plot of X52 steel and FGM samples [36, 37]

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3 Materials

Accidental loads occur from a hydrocarbon explosion or high-velocity impact; the strain rate increases rapidly over a finite time, causing a permanent deformation or distortion of the material. Hence, topside material should possess adequate strength, higher resistance to impact loads, good weldability, durability, and toughness. While X52 is the conventional material preferred for topside, the present study explores an alternate material, FGM. Functionally graded materials (FGM) have limited application in offshore platforms but are successful in biomaterials, optics, and energy conversion. FGM possesses improved resistance to second-order vibrations, buckling, and bending, which are demonstrated through three samples; namely, (i) carbon-manganese steel and duplex stainless steel, (ii) Nickle, carbon-manganese steel, and duplex stainless steel, and (iii) titanium, carbon-manganese steel, Nickle, and duplex stainless steel [36, 37]. The material constituents used for fabricating FGM samples in the current study are given in Table 3, while the individual properties of FGM and X52 steel are given in Table 4. The structural members prone to fire accidents are proposed to use FGM, whose section properties are shown in Fig. 6.

Table 3 Materials properties used for FGM [36, 37]
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Table 4 Mechanical properties of X52 steel and FGM [36, 37]
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Fig. 6
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Structural components proposed for topside using FGM

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4 Wind, Blast, and Impact Load

Wind loads are computed on the topside at every storey level using the gust factor method (GFM). For the mean wind speed of 55 m/s (Gulf of Mexico), wind force variation on the topside is shown in Fig. 7. Wind force on the XZ plane is lesser due to the reduced exposure area, as shown in Fig. 8. Under the payloads recommended by the code [38], the deformation of beams and columns due to the hydrocarbon explosion is computed using ABAQUS explicit. The explosion caused by a blast load is idealized as a linearised triangular impulse, as shown in Fig. 9. The blast pressure is applied on the beams and column surfaces, as shown in Fig. 10. The displacement contour of the beams and columns using X52 steel and FGM are illustrated in Fig. 11, while Figs. 12 and 13 show the beam and column tip displacements. It can be seen from the plots that structural members made of FGM showed reduced displacement in comparison to that of X52 steel due to the improved mechanical properties of FGM.

Fig. 7
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Variation of wind force on the topside [35]

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Fig. 8
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View of Topside

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Fig. 9
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Triangular blast pressure impulse

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Fig. 10
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Direction of blast load and boundary conditions

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Fig. 11
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Displacement contour of beams and columns: a X52 steel b FGM [35]

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Fig. 12
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Beam tip displacement comparison at 0.25 MPa [35]

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Fig. 13
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Column tip displacement comparison at 0.25 MPa [35]

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Impact loads on the topside arise from the fall of machinery, crane hook, equipment, drill pipes, and tools. The fall of objects from a considerable height shall lead to permanent deformation or distortion of the topside deck [39,40,41,42]. Figures 14 and 15 show the details of stiffeners used on the topside. In the current study, impact load is generated using the free fall of a square block from a height of about 20 m. The deck plate and stiffeners are shown in Figs. 16 and 17, while Figs. 18 and 19 show a typical offshore crane and the impactor model.

Fig. 14
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Typical view of deck plate

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Fig. 15
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Stiffeners details

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Fig. 16
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Model of topside deck plate

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Fig. 17
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Model of stiffener

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Fig. 18
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Typical offshore topside crane

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Fig. 19
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Model of an impactor

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Four-node shell elements are used to model the deck as a 3-D deformable member, while eight are used for the stiffeners. Figure 20 shows the boundary conditions of the topside plate and impactor. Mesh size is optimized for the stiffeners and the deck by following the re-meshing rule. The impactor is modelled as a discrete rigid body, dropped from 20 m height. Numerical analysis is performed by ABAQUS explicit for the time duration of 1000 ms. Figures 21 and 22 show the deck’s maximum central deflection for various time steps using FGM and X52 steel under impact load, while Fig. 23 compares their central deflection.

Fig. 20
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Boundary conditions of the deck plate and Impactor model

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Fig. 21
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Deformed shape of the deck with X52 steel

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Fig. 22
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Deformed shape of the deck using FGM

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Fig. 23
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Comparison of central deflection of the deck

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5 Design of Topside Under Conventional and Accidental Loads

The structural members are chosen based on the topside ultimate load-carrying capacity by considering all the modules and facilities. Loads on the topside are increased by load factors, complying with the appropriate design codes. IS-800 (2007) and Eurocode 3 (1993) are used for structural member design, and IS-875 (Part 3) is used for wind load calculations. The topside is modelled using SAP 2000 nonlinear. Shell elements are used for modelling the deck plate, while link elements are used for modelling beam-column connections. All support connections are considered rigid connections, while von-mises stress failure criteria are used for the model [35]. The offshore platform's topside is prone to wind and accidental loads. The accidental load includes the impact and blast from the hydrocarbon explosion. Figure 24 shows the topside's deformed shape using X52 steel and FGM on selected members in the prone region. Figure 25 shows the deformed shape of the topside using X52 steel. The topside is designed to withstand accidental load and wind combined, while the connections are analysed using ABAQUS. Figure 26 shows the design check carried out on the topside. The revised cross-sectional dimensions of the members based on the design check are shown in Table 5. The topside design satisfies gravity, wind, blast, and impact loads requirements. Further, the topside is investigated by pushover analysis using SAP 2000 nonlinear.

Fig. 24
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Topside deformed shape using X52 steel and FGM in a prone region

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Fig. 25
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Topside deformed shape using X52 steel

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Fig. 26
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Design check of the topside: a X52 steel and FGM in the prone region; b X52 steel

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Table 5 Cross-sectional dimensions of members for accidental loads
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Table 6 shows the dynamic characteristics of the topside for cases 1 and 2. It is seen from the table that natural frequencies for case-1 are marginally higher, indicating higher stiffness of the topside; a higher contribution (about 90%) from the first mode indicates an acceptable design. Figures 27 and 28 show the collapse patterns of the topside for case 1 and 2. The first two modes are subjected to lateral vibration, and the third mode shows lateral and torsional vibrations.

Table 6 Dynamic characteristics of the topside
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Fig. 27
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Collapse pattern of the topside for case-1 (X-52 steel and FGM, used in prone areas)

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Fig. 28
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Collapse pattern of the topside for case-2 (X-52 steel for complete topside)

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Pushover analysis is capable of analysing the topside under lateral forces. A typical topside model is shown in Fig. 29, subjected to gravity loads and predefined lateral load combinations. The lateral forces are distributed along with the height and increased until the yielding of structural members. The structural system is modified to account for a reduced stiffness caused due to the yielding; lateral forces are increased until successive members yield. The process is continued until the structure becomes unstable. The static pushover curve is obtained by plotting the displacement against the base shear. The displacement-controlled pushover analysis (FEMA-356) is used to compute the topside capacity, position of plastic hinge formation, and failure modes. The nonlinear behaviour of the elements is modelled using plastic hinges based on the moment–curvature relationship as described in FEMA 356 guidelines; P-M2-M3 hinges are used for each structural member. The moment-rotation curve of a P-M2-M3 hinge is a monotonic backbone relationship, which describes the post-yield behaviour of a beam-column element under the combined axial and biaxial-bending conditions. Base shear vs. roof displacement curves are obtained from pushover analysis, as shown in Fig. 31. The intersection of these curves with the seismic demand curve indicates the performance point. It is observed that the lateral displacement under wind and wave is significant in comparison to that of seismic forces. The target displacement was considered based on the topside's maximum roof displacement under combined wave and wind forces [35].

Fig. 29
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Typical model of topside

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Two cases are considered for the analysis: Case-1, in which FGM is used only on members in regions prone to hydrocarbon explosion while the rest are X-52 steel; Case 2, where X52 steel is used to model the entire topside. Figure 30 shows the pushover curves for different states, namely immediate occupancy (IO), life safety (LS), collapse prevention (CP), and total collapse (C) as per ACT 40 and FEMA 356. A comparison of the capacity curves for cases (1 and 2) is shown in Fig. 31. It is seen that case-1 shows a higher capacity than case-2 (about 8%) because FGM possesses higher yield and ultimate strength in addition to a higher strength ratio, ductility ratio, and tensile toughness; it improved the topside performance under special loads. Bottom-storey columns experienced larger displacement due to the absence of bracings. Variations of stiffness and height resulted in the formation of plastic hinges. Tables 7 and 8 show the different hinge formations on the topside for both cases, while Figs. 32, 33, 34 and 35 show the corresponding hinge locations and topside collapse pattern.

Fig. 30
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Idealized pushover curve

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Fig. 31
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Comparison of pushover curve of Topside for Cases1 and 2

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Table 7 Hinge details for case-1
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Table 8 Hinge details for case-2
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Fig. 32
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Location of plastic hinges for case-1

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Fig. 33
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Location of plastic hinges for case-2

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Fig. 34
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Collapse pattern of the topside for case-1

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Fig. 35
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Collapse pattern of the topside Case-2

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Using FGM in a vulnerable region reduces the number of plastic hinge formations, as shown in Figs. 32 and 33. However, FGM is not recommended for the entire topside considering the complexities involved in the fabrication and economic factors. Figures 34 and 35 show the topside collapse pattern for cases 1 and 2. A comparison of the moment-rotation curve of critical beam-column connection shows that FGM possesses higher resistance to plastic rotation, as shown in Fig. 36, while the moment-rotation values are given in Table 9. It is observed that FGM offers about 21% higher resistance to plastic rotation than X52 steel. The results comparison for cases 1 and 2 are given in Table 10.

Fig. 36
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Moment-Rotation curve of the connection for Cases-1 and 2

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Table 9 Moment-rotation values for cases-1 and 2
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Table 10 Results comparison for cases 1 and 2
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In case-1, the maximum number of hinges beyond the yield limit falls within IO (please refer to Table 7), indicating the lesser danger of the topside without losing its original strength. Beam-column connection experiences minor yielding at very few locations (Fig. 32). There is no visible buckling or complete distortion of structural members. It comprises life safety (LS) hinges, topside experiences only moderate damage, retaining some residual strength. Hinges are formed in beam-column connection; however, the shear connection remains sound. Whereas in case 2, the maximum number of hinges falls under life safety (LS). The range of hinges reached Collapse prevention (CP), indicating that the topside experienced severe damage with marginal residual stiffness and strength. The topside suffered permanent deformation, and beams and columns were distorted heavily. Case-2 comprises a few critical joints that come under total collapse (C), affecting the structural integrity, as shown in Fig. 33.

6 Conclusions

The presented study discussed the FGM's superiority in offshore topside subjected to accidental loads. Topside response under blast load arising from hydrocarbon explosion and impact loads are computed using ABAQUS explicit and designed to withstand the combination of special loads using FGM and X52 steel. The design of the topside under accidental loads satisfied the code recommendations. Nonlinear static pushover analysis is performed to compute the topside capacity using SAP2000. A comparison is made for two cases, namely case-1, where the topside is modelled using FGM only in prone regions, while the rest of the members are with X52 steel. In case 2, where the complete topside is made with X52 steel.

  • Numerical analyses showed that the FGM and X52 combination experienced fewer plastic hinges, showing an improved capacity against lateral loading conditions.

  • The range of hinge formations is within immediate occupancy (IO) and life safety (LS), confirming that the topside can retain its original strength.

  • On the other hand, the topside made with X52 steel showed severe damage and could not retain residual stiffness and strength.

  • Moment-rotation curve at critical beam-column connection showed that the presence of FGM enhances resistance to plastic rotation capacity by about 21% compared to that of X52 steel.

  • Using FGM as a structural member in offshore topside proves its suitability for high-pressure and high-temperature applications.