The number of offshore structures is in continuous increment; the application of offshore structures varies depending on the purpose. There are estimated to be more than 9000 offshore oil and gas structures [1,2]. Out of 7000 existing offshore platforms, 93% are fixed platforms in shallow waters [3]. Offshore structures are considered one of the most challenging tasks to be designed and constructed by engineering [4]. The ageing of offshore platforms is a constant and continuous challenge. Several offshore platforms globally have reached their designed span [5–11]. It is estimated that more than 50% of offshore structures are operating beyond their service span in all of the United Kingdom Continental Shelf (UKCS), Norwegian Continental Shelf (NCS) and the Gulf of Mexico Shelf (CMS) [12,13]. The same is in the Middle East, where more than 70% of 800 platforms have exceeded their design span [14]. Out of 200 offshore operating installations in Malaysia, more than 90% have exceeded their design life [15]. Some alterations may have taken place since the first time the structure was designed and built. The loading pattern (e.g., due to subsidence), the environmental load (e.g., due to waves), and the metrological and oceanographic (metocean) data may have changed since the original design, and the structure may have deteriorated to an unknown extent during decades of harsh weather [16].

Despite the rapid growth in oil and gas for deep water technology, a big production cut comes from relatively old and mostly shallow-water platforms, which are still vital to countries with offshore products. The replacement option of these aged structures entails both operational and technical challenges and expensive solutions [17–19]. Operators and stakeholders are bound by factors about the continuous service of these aged offshore installations, such as enhanced oil recovery production, falling profit margins imposed by the drop in oil prices and uneconomical small field discoveries [3,20]. In common, proper safety could be achieved by implementing the latest compliances rules and regulations in the respective field of expansion. However, it is ambiguous to perform such safety compliance regarding life extension [1,21,22]. A method such as documentation of which structure has reached its design life is not possible using design regulations, even if no cracks have been detected. Hence, it is vital to form a future scheme to present the minimum work to be done to achieve proper structure safety beyond its original design age based on the residual strength the structure presents after the failure of key components [23].

There has been extensive research work to propose recommendations for assessing existing offshore platforms [1,24–31]. Several assessment criteria, such as target reliability levels, consequences of failures, and wave loads, have been addressed. Different analysis levels are proposed within the aforementioned guidelines, such as linear with component check, linear with redundancy, structural reliability, and finally non-linear pushover analysis [26,29,30,32]. Sensitivity analysis is required to address problems about which parameter is most significant for probabilistic analysis [33,34]. This paper aims to investigate three different parameters to evaluate structural integrity through non-linear pushover analysis. These parameters selected are wave height, gravity load and corrosion allowance (thickness reduction) on primary members.

Ultimate strength assessment for offshore platforms, obtained by non-linear pushover analysis, is recognized by higher redundancy since it is built up by components [21,35]. Ultimate strength is dependent on the parameters chosen to be assessed against, which come from technology awareness and industry experience. For instance, Sunder [36] carried out numerical models to assess two platforms sensitivity to variation in wave height, wave period and hydrodynamic force coefficients (Cd & Cm) within the north sea environment. Ultimate strength is also influenced by strength degradation [37], which is led by stiffness loss, differential settlement due to unbalanced loads such as heavy drilling campaigns, fabrication quality, weld failure due to fatigue loads [38] and inadequate structural inspection and maintenance [39]. In regard to the previous investigations, the effect of foundation modelling has been neglected in the response of jacket reserved strength against wave loads. The foundation models were assumed to be rigid, which this study will aim to fulfill. Platforms’ dynamic responses when subjected to variations in soil parameters and pile bottom tip conditions showed a very sensitive relationship with the platform’s natural frequency [40]. A significant increase in deck lateral displacement is witnessed for the ductile jacket inclusive of the non-linear pile-soil interaction. However, the effect on the capacity to carry further lateral load is small [41]. Furthermore, the previous studies defined the top mass as a lumped model. In this paper, the top decks are modelled as per real drawings with exact load applications as per obtained details from a local firm, further discussed in Sections 2 and 3.

Moreover, previous studies showed very little details on the impact of varying topside loads with real non-linear foundation model to the platform’s reserved strength represented by RSR. Furthermore, very limited details showed the impact of the maximum corrosion allowance applied to the primary members impacting the structure’s reserved strength with non-linear foundation model and distributed topside masses. This led to three main motivations for this study: (i) Conduct a sensitivity analysis of a jacket type platform against wave height using a pile-soil interaction (PSI) model, (ii) conduct a sensitivity analysis of a jacket type platform with varying topside loads, and (iii) conduct a sensitivity analysis of a jacket type platform with a reduction in primary members wall thickness representing the minimum corrosion allowances presented in design codes [26,42]. A comprehensive flowchart of this work is summarized in Fig. 1.

A detailed flow chart for each task is presented in Fig. 2, which each step is further discussed in Sections 2–5.

The applied loads varied between permanent loads, variable live loads, environmental loads, and dynamic loads. Permanent loads include the self-weight and equipment weights, while environmental loads include wave, current and wind. Table 2 summarizes the static load cases with the contingency factors applied to the platform, which are obtained from the existing structure in Malaysia [44].

The applied environmental loads are included in the analysis based on real data that was provided by an external source. The details of the data include sea wave parameters, sea current speeds, wind speeds, marine growth, salinity of water for corrosion allowance calculation, water depth of the area, and the sea-bed elevation and Metocean Criteria [43].

A single SACS PSI was used to model the piles and surrounding soil. SACS [45] software developed by Bentley has the package of PSI (Pile Structure Interaction), which analyzes the behavior of a pile supported structure subject to one or more static load conditions. Finite deflection of the piles (“P-Delta” effect) and non-linear soil behavior both along and transverse to the pile axis are accounted for. The pile model below the pile head will include geometry, sectional and material properties, and length. A pile head joint is defined at the boundary where the linear elastic structure ends, and the elastic pile surrounded by non-linear soil starts. Pile head joints are modeled at mudline elevations. Soil is modeled as non-linear springs unmodeled soil data for the P-Y lateral stiffness, Q-Z bearing capacity, and T-Z friction capacity. The curves for P-Y, Q-Z and T-Z are obtained from the soil report for the proposed platform. The platform is supported on Grids A1, A2, B1, and B2 as shown in Fig. 3 below.

The details of the soil data are obtained from the geotechnical report for the engineering assessment for the platform, which was provided by an external party to depict the actual properties of the soil where the platform is to be constructed.

The soil profile for the site consists of calcareous clay with intercalated layers of sand and silt. Eleven soil units have been identified to a depth of 100 m. The division into units is derived from a geotechnical perspective for foundation engineering purposes. Soil profile is described as per As-Built Survey [48] as below:

USFOS [46] is used for this task since it is suited for indeterminate prismatic structures such as substructure as it is designed to handle a large number of plastic hinges developed in structural and pile members. The solution strategy deployed for the pushover analysis is to use one finite element per structural element. This allows the use of the FE mesh from the linear analysis, i.e., beam-element formulation but valid for large displacements and restricted to small strains. Material non-linearity is described by means of a lumped plastic formulation at the member ends and mid span.

As elaborated in Section 2.2, the model is originally obtained from SACS software, from which both the geometry and foundation model are converted to USFOS using a third converter software (STRUMAN). A check was conducted to ensure the conversion was correct by running a static analysis in USFOS and checking the resulted loads and reactions and comparing them with the original model from SACS prior to proceeding to wave non-linear pushover analysis. The wave pushover analysis is conducted for several wave attack directions, which are postulated in Fig. 4. The load combination consists of the applied static (gravity) load associated with the wave, current, and wind loads. The maximum wave height used for the analysis is 9.8 m for 1-year operating and 15.8 m for 100-year storm conditions.

The study considered eight (8) directions for two reasons. The first is to investigate which direction results in the maximum base shear depending on the platform configuration and weakest axis of the structure, while the second reason is due to the provided metocean data with different wave height and period at each direction. Table 3 below lists the platform direction with corresponding extreme environmental data. The dynamic behavior of the structure was also considered by running a simplified dynamic analysis in order to generate the platform dynamic amplification factor for the wave and current inertia loads on the structure.

The main objective of this study is to investigate the effect of the environmental loads on the platform’s RSR. The environmental effects and gravity loads are the main parameters whose effects on platform RSR are being investigated. The analysis was conducted using two software packages, SACS & USFOS where the analysis procedure is discussed in Sections 2–4 of this study. Upon obtaining the converted model in USFOS, the topside weight effect is studied by incrementing the weight in several trials and recording the platform RSR by running a wave non-linear pushover analysis for each trial. For this study, only operating waves are used to record the RSR as the aim of the study is to determine the effect of loading on the platform’s reserved capacity.

The other parameter, which is the main parameter, is the wave height and period effect on the platform RSR. The wave height is increased by 10% for several trials until the platform collapses, where the operating wave is used as the bench starting parameter to record several RSR before collapsing. The third parameter that was investigated is the corrosion effect on the platform. The corrosion was modelled as a reduction in the main legs’ thickness. Only primary legs and diagonal members were selected for this parameter. The consequence of the analysis in the summary is obtaining the platform RSR by running several runs for wave non-linear pushover analysis. The analysis for the wave height and period effect is studied for each direction (total 8) to determine the weakest jacket response to each direction and based on that, the other parameters were done only for the direction that results in the minimum RSR.

The number of wave non-linear pushover analyses conducted is 96 analyses for the wave height and period, 21 for topside, 8 for corrosion allowance, for a total of 106. As a preliminary test, the model was generated from the structural drawings based on the sizes and configurations specified. A simple static analysis was conducted in order to ensure the platform was intact before running the non-linear analysis. The static analysis was based on AISC 360-10 (2010) [3], as recommended in API RP 2A WSD [26] for the specification of steel structures. Other details for the loading or the design of offshore structures are determined from ISO 2394 (1998), ISO 13822 (2000), ISO 1990 (2002), ISO 19902 (2004), and ISO 19902 (2007) [29,30,49–51].

The static wave analysis is obtained as per the applicability of the apparent wave period Tapp, specific wave height H and storm water depth d in reference to API RP 2A [26]. The wave load is calculated based on Stokes wave theory as per API RP 2A [26]. Stoke’s second-order wave components (1^st & 2^nd) are adopted to provide the steeper and shallower trough. The following formulas represent different components for Stoke’s second order wave theory. The dynamic wave pressure adopted as per API RP 2A [26] adopts member wave pressure as follows:

1^st Order component:

p=ρg Hcosh⁡ky2cosh⁡kdcos⁡[k(x−ct)]

2^nd Order component:

p=34ρg πH2L1sinh⁡2kd[cosh⁡2kssinh2 kd−13]cos⁡2(kx−ωt)−14ρgπH2L1sinh⁡kd[cosh⁡2ks−1]

where:

ρ = fluid density.

g = gravitational accleratin.

H = wave height (crest to trough).

k=2πλ .

y = Y, certical co-ordinate in frame fixed in bed.

d = crest depth.

x = hoizaontal co-oridnate in frame moving with wave crest.

c = wave speed.

t = timen = water depth.

s = momentum flux per unit span perpendiculr t flow.

ω=z2k , Dummy variable.

The wave height and wave period are increased by 10% of the original value taken from metocean data. The analysis is run until the RSR value for at least one direction reaches a value smaller than 1. This indicates that the structure collapsed before applying the 100% load. Table 4 summarizes the wave input data for the platform’s RSR response due to wave effect. The maximum increment is 250% of the original input where a value of less than one (1) is spotted from the direction of 0°. Fig. 4 demonstrates the value of the RSR at each direction with different wave and current input.

Table 3 is represented by a spider plot where each corner represents the direction considered for the wave height and period. The vertical is the platform RSR. Each direction has the resultant RSR value from the conducted pushover analysis at each specified direction as discussed in Section 4. The results are for all the increments from 0% (with normal environmental loads) until 150% of the applied loads. Increments started with 10% increment until 100%, then the range was increased to 50%, where at the first trial, the minimum RSR value was spotted. The minimum RSR value is 0.956, which hits at 0° direction.

The 0° direction is therefore considered the direction that will impose the maximum wave forces on the structure. Fig. 4 illustrates the results of the RSR due to the wave loading effect for each direction. While Fig. 5 shows the relationship between the increase in the wave height and the period against the platform RSR. The collapse wave height (150%) observed in the final step is not realistic, as the wave-in deck would occur on topside modules, which will be another design criterion to be considered in the earlier design stage. It can be seen in Fig. 5 that the direction of 0 degree is the most severe direction that will impose the maximum wave loading on the platform.

As shown in Fig. 6, once the wave height increases, the loading imposed on the structure from the wave will be more. When the wave height increases, the lateral loads and wave dynamic forces on the structure increase significantly, leading to a larger base shear and overturning moment, where platform RSR is dependent on the platform base shear during damaged conditions relative to the normal base shear. The increment has reached 2.5 times the height of operating waves, categorized as a breaking wave per API RP 2A. However, it was assumed to happen to maximize the forces on the structure for the severity study. The overall platform depth is 58.77 m, indicating that not a major wave load is applied at the normal wave height, and that is why it required several load steps (until 250% increment) to reach a significant failure. The 250% wave height is 25.50 m which is very high and impossible to happen as the provided metocean data for 1000-year return wave data is smaller than this value. The maximum 1000-year return period wave height is 15.90 m which is smaller than the 25.50 m wave height unless a non-expected natural event such as a hurricane has occurred.

The results above show that the platform’s RSR behaves inversely with the applied environmental waves, where the larger the wave height, the lower the platform’s reserved strength ratio (RSR). Based on this conclusion, the structure showed a very stiff response to wave height increment and has collapsed at a very high wave height such that the probability of it happening is very small. Moreover, the figures above prove the theory of the contradictory relationship between the environmental load and platform RSR, where once the wave height increases, the platform RSR decreases. Fig. 7 shows the structure’s overall member plastic utilization during the 150% increment in the 0° direction.

Through visual inspection of the plastic plots, the platform was witnessed to be overstressed in soil, as the soil is represented by a non-linear spring with the soil properties from the soil report and represented in Fig. 7 by discs with different diameters (the larger the diameter, the stiffer the soil properties at that depth), followed by major structural failure at the members in the lower part of the jacket. The red color in the figure indicates a full utilization of the member cross-section. The graph at Fig. 6 illustrates the structure’s load-displacement relationship when subjected to the incremented wave height. The figure shown is only for the latest increment where the structure achieved the minimum RST of 0.96, which is lower than 1.0. The failure of the structure is determined by the drop of the curve in the load-displacement graph, as the curve shows the elastic and plastic behavior of the structure and stops at the rupture point where the USFOS software terminates the analysis automatically. The rupture point is achieved when several key components of the structure are fully plastic, and no further residual strength has remained.

On the other hand, and apart from environmental loads, another investigation was conducted on the platform RSR concerning topside weight. Topside weight is defined separately in the analysis by defining it in a separate load combination. The details of the topside weight are shown in Table 5 below. The methodology in this analysis is to increase the factor times the load combination designated for the topside until the platform RSR reaches a value below one (1). The analysis was done with environmental loads (wave, current, and wind) only from one direction, which is the 0° direction, as it was seen in Section 6 that the environmental loads from this direction produce the minimum platform RSR. The total topside weight is 62410.23 kN (6362 MT), including operating and live load, which was assumed to be active during the wave non-linear pushover analysis.

Figs. 8–10 below illustrate the graph for the jacket RSR response to the topside weight increment. The increments started with the original applied load as detailed in Table 2 and were incremented by 10% at each run, then wave non-linear pushover analysis was performed. The analysis showed that as long as the topside or gravity weight increases, the structure’s RSR is not affected much as the RSR mainly depends on the lateral forces. Though the RSR has decreased significantly when the increment has reached 200% of the initial load, the reason for that is the high member failures and stresses from the gravity load where these members are primary members and play a significant role in the structure’s stability.

The topside weight was increased to a maximum factor of 3, and the structure’s RSR value is 1.645, which is still above one and safe. A further increase will impose a small reduction in the structure’s RSR but significant failures in members who are not the main bones of the structure’s stability. Fig. 11 shows the structure member failure and plastic utilization due to topside weight.

Results show that the failure hits the structure before the soil. The soil has shown a very stiff response to the weight increment even though the stress is gravitational. As shown in Fig. 8, the gravity load is increased to the targeted value and released when the full load is achieved. Once the first load is removed, but its effect remains, the next load combination, which represents the environmental load from 0° direction, is applied incrementally until it is either achieved or at least one member fracture is spotted. In the maximum case (factor of 3), the structure has managed to sustain the full environmental load when three times the original topside weight is applied to it. Within this summary, the scenario of the structure’s RSR response to gravity load has met the expectations. Once the gravity load increases, the platform RSR will be decreased.

The next parameter investigated in this study is the corrosion effect on the platform reserved strength ratio (RSR). Corrosion is a fundamental parameter that is worth investigating. The best methodology for representing the corrosion phenomena is by applying for corrosion allowance in the model by introducing a reduction in the thickness of the tubular (since all the jacket members are tubular). The reduction was made in an incremental method to observe the effect on the platform RSR. Only primary members were selected for this reduction since these members are the main legs. Table 6 shows the platform RSR corresponding to the reduction percentage. The analysis was done only from the 0° direction as it was observed to generate the minimum RSR. The reduction was made consistent as it starts with a 5 mm reduction and continues with 5 mm increments until the structure shows significant instability.

The first results are almost the same since the overall loading remains the same and the stiffness is not majorly affected by the thickness reduction. Once the reduction is 25 mm in the thickness of the primary legs, the structure significantly decreases the RSR. The reason is that since most of the primary legs have a thickness of 40 mm and this reduction represents 63%, in a simple logical explanation, it will reduce the structure leg stiffness by an equivalent percentage. The structure shows great instability in the subsequent reduction, where it ended up with 35 mm and a corresponding RSR of 0.619. Fig. 11 shows the relationship of RSR with the thickness reduction in primary legs.

The graph proves the concept of the different relationships between the platform RSR and its stiffness. The drastic decrease happens when a significant reduction occurs at 20 mm and forward, as shown in the figure above. Figs. 12 and 13 show the member plastic utilization for the 25 and 35 mm reductions, respectively.

This study aims to assess the existing offshore structures through wave non-linear pushover analysis under various conditions. The study was represented by a structure modelled with supplied details from a consulting company in Malaysia in offshore engineering. The model consists of a four-legged platform with four pile sleeves connected to it.

To obtain a direct relationship, the study investigated the environmental loads on the structure’s reserved strength ratio (RSR). The study also included the platform RSR relationship with the gravity load increment that could happen over the life span of the platform. The platform RSR decreases with a significant change in the gravity load. Corrosion on steel members in harsh corrosive environments is another major environmental factor affecting platform strength degradation. The maximum wave height reported by the minimum RSR was at an increment of 150% of the original value corresponding to direction 0, with a wave height of 24 m which is unrealistic.

It is concluded that pushover analysis (global ultimate strength analysis) showed that the wave height and period are the most affecting factors in reducing the structure’s ultimate strength ratio (RSR). The greater the wave height, the lower the RSR, despite the low occurrence probability.

The structure’s topside weight had little effect on its reserved strength ratio (RSR) unless it was 200% or 300% greater than its initial value. At that point, the RSR would be significantly affected due to the structure’s stiffness loss, which only occurred during a large increase in the structure’s gravity load. In this case, the structure may experience pre-failures for major structural members before the collapse of the structure.

Corrosion on offshore structures is a significant ageing factor at a high level. The structure’s RSR is significantly reduced with high levels of corrosion. The critical amount of corrosion that leads to a major failure is spotted at 20 mm. This value is quite high as most applicable design codes call for [26,47] specifying a maximum value of 6 mm for extreme designs on primary members.

Moreover, the offshore structures are mainly affected by the wave forces more than any other parameter. The wave loads are majorly contributing to overturning the structure to the collapse position, where the RSR is majorly reduced.