15:37, 27/03/2022 Experimental and numerical investigation on reserve strength of jackets with single diagonal and X brace configurations SHIPS AND OFFSHORE STRUCTURES 2022, AHEAD-OF-PRINT, 1-15 https://elkssl0a75e822c6f3334851117f8769a30e1csfdafs.casb.nju.edu.cn:4443/10.1080/17445302.2022.2052481 Experimental and numerical investigation on reserve strength of jackets with single diagonal and X brace configurations A Renugadevi a , S Nallayarasu b, and S Karunanithi b a Department of Ocean Engineering, IIT Madras, Chennai, India b Institute of Engineering & Ocean Technology, ONGC, Navy Mumbai, India ABSTRACT Jacket framing arrangement X, K, V and single bracing systems used in jackets influence the ultimate strength and redundancy in the system Experimental investigation was conducted on a 2D frame (1:20) with two different bracing patterns (2D-1 and 2D-2) the results are compared with that obtained from nonlinear pushover analysis Parametric assessment of Reserve Strength Ratio has been carried out on three bracing patterns, namely 3D-A, 3D-B and 3D-C using non-linear pushover analysis including pile-soil interaction It is observed that RSR increases by 15% for X brace configuration (2D-2) compared to single brace configuration (2D-1) The RSR for 3D-B is found to be higher by be 35 % and 12% compared to bracing patterns 3D-A and 3D-C respectively The brace pattern 3D-C exhibits similar strength to 3D-B, illustrating the insignificance of the brace at the top bay and this leads to reduction in wave loads on the system ARTICLE HISTORY Received November 2021 Accepted March 2022 KEYWORDS Push over analysis, ultimate strength, reserve strength ratio, redundancy, design capacity CONTACT S Nallayarasu nallay@iitm.ac.in Department of Ocean Engineering, Indian Institute of Technology Madras, Chennai, India - 600 036 © 2022 Informa UK Limited, trading as Taylor & Francis Group Introduction 1.1 Background Jacket structures have been regularly constructed for supporting offshore oil and gas facilities at shallow to moderate water depths More than 300 offshore oil and gas exploration platforms exist in the Indian Western offshore India, with more than half of them outlived their design lives The need to extend the life of these platforms has arisen because of the continuation of oil and gas production In several cases, design level analysis was carried out in conjunction with ultimate strength assessments, and life extension was offered The evaluation of reserve strength is essential for permitting structures to operate beyond their design life, especially in offshore The structural arrangement and framing pattern have a significant impact on post-yield behaviour and reserve capacity In traditional offshore structure design, only the elastic capacity is considered, resulting in considerable margin in capacity As a result, the jacket structure could sustain additional loads before collapse or failure The reserve capacity or excess margin available is not only due to strain hardening but also because of redundant framing patter resulting load redistribution Redundant frames such as X braces have higher reserves strength than non-redundant frames The ultimate strength of two-dimensional single brace (2D-1) and X brace (2D-2) frames was obtained by conducting an experiment in a structural testing lab The numerical model of the same was solved and compared The results of https://elksslsfdafs.casb.nju.edu.cn:4443/doi/epub/10.1080/17445302.2022.2052481?needAccess=true 1/25 15:37, 27/03/2022 Experimental and numerical investigation on reserve strength of jackets with single diagonal and X brace configurations numerical simulations for a few jackets with varied bracing configurations (3D-A, 3D-B, and 3D-C) are presented and discussed 1.2 Literature review API RP 2A (2007) has certain guiding principles of bracing pattern on the ultimate capacity of the jacket and suggests that diagonal bracing in vertical frames transfers shear forces between horizontal frames or that vertical runs between legs are distributed approximately equally to tension and diagonal compression braces K bracing is not recommended because of panel failure due to failure of brace in compression The above principles are generally adopted in jacket design in most cases However, there are situations wherein modified bracing pattern is used Billington et al (1993) used nonlinear analytical approaches to explain the reserve, residual, and ultimate strength of offshore structures Bolt et al (1996) used experimental and numerical techniques to investigate the ultimate strength of tubular framed structures Brown et al (1997) conducted a pushover analysis to compare the RSR of two old and new North Sea platforms developed using different codes and proposed that higher wave height be used in the future to estimate the RSR of a new structure Lloyd and Clawson (1984) evaluated the reserve and residual strength of piled offshore structures and presented a method for performing progressive collapse analysis by systematically removing failed components to determine the structure collapse capacity Paulo and Jacobb (2005) described the nonlinear formulation for global collapse analysis for three-dimensional framed structures, including the material and geometric nonlinearity Westlake et al (2006) investigated the role of ultimate strength assessments in Structural Integrity Management (SIM) of offshore structures and provided an overview of the structure behaviour under extreme load conditions Frangopol et al (1992) investigated the redundancy of structural systems The deterministic and probabilistic methods were demonstrated through examples Starossek and Haberland (2011) investigated robustness of structures using a quantified measure The recommended prerequisites and prospective applications were explored and some simple formulations of stiffness, damage, or energy-based robustness metrics Matlock (1970) investigated the capacity of laterally loaded piles in soft clay The experiment considered three loading conditions, and their force–deformation characteristics were closely matched with numerical simulations Reese et al (1974) investigated the capacity of laterally loaded piles in sand The pile was tested under static and cyclic loads, and a method of simulating p-y curves was devised where p is the lateral load and y is the lateral displacement of pile Reese et al (1975) conducted field testing on laterally loaded piles on stiff clay Based on this, a procedure for predicting the p-y relationship of stiff clay was developed Gebara et al (1988) used pushover analyses on platforms in the North Sea to investigate the effect of framing configuration on the robustness of offshore structures, concluding that X brace configurations increase the robustness of the jacket structure without increasing the cost or constructability El-Din and Kim (2014) assessed the effects of retrofit approaches on the seismic performance of jacket structures using non-linear static and dynamic loading methods Tabeshpour et al (2019) examined the ultimate capacity of offshore jacket platforms considering the effects of global and local buckling of the elements Marshall et al (1977) investigated the inelastic dynamic analysis of offshore tubular structures and discussed structural factors such as inelastic stretch, brace postbuckling behaviour, and ductility limitation at plastic hinges Zayas et al (1981) examined the inelastic structural behaviour of braced jacket platforms under seismic loading Gates et al (1977) evaluated the ultimate seismic resistance of fixed offshore structures Riks (1979) described a numerical scheme to solve the structure deformation problems involving snapping and buckling The rapid incremental/iterative solution approach that handles ‘snap-through’ was described by Crisfield (1981) https://elksslsfdafs.casb.nju.edu.cn:4443/doi/epub/10.1080/17445302.2022.2052481?needAccess=true 2/25 15:37, 27/03/2022 Experimental and numerical investigation on reserve strength of jackets with single diagonal and X brace configurations Blume’s ‘Reserve Energy Technique’, published in 1960, developed the concept of reserve strength, which defines reserve capacity as the square root ratio of energy capacity to energy demand The reserve strength was defined as the additional strength given by redistribution of stresses within the cross-section and frame due to redundancy in the system, rather than the margin available through design approaches incorporating the factor of safety Ultimate strength can be expressed as Reserve Strength Ratio (RSR), defined by Titus and Banon (1988) as: (1) The ultimate strength of offshore structures has been evaluated using analysis techniques involving nonlinear material properties including geometric nonlinearity in the past successfully However, experiments considering the effect of framing patterns on ultimate strength and directional loading is sparse, especially for jackets Hence a detailed investigation using 3D nonlinear soil-structure interaction analysis with different bracing patterns has been carried out using Ultimate Strength of Offshore Structures (USFOS) software developed and maintained by Det Norke Veritas (DNV), Norway The validation of the numerical scheme has been carried out by conducting experiments on the 2D frame with single and X brace configuration of a 1: 20 scale model Because of the experimental setup limitations and the magnitude of loading, the 2D frame was chosen Three bracing patterns (3D-A, 3D-B, and 3D-C) were explored to derive an optimal bracing configuration from obtaining the highest RSR, and the findings are given and discussed Numerical investigation 2.1 Ultimate strength formulation The ultimate load-carrying capacity depends on the steel material nonlinearity, non-linear soil behaviour, joint flexibility and geometric nonlinearity Potential energy considerations are used to generate the stiffness formulation The structure stiffness matrix is built using element stiffness matrices estimated using updated geometry and plastic hinge construction When the element cross-section reaches its maximum capacity, plastic hinges are inserted, and the load is increased until the next cross-section achieves its maximum capacity This process continues until the system becomes unstable and collapses due to the formation of a full mechanism The formulation of the numerical scheme used for the nonlinear simulation is explained in this section A finite beam element with two nodes is shown in Figure Figure Beam element with two nodes The elastic stiffness matrix of the beam element KL is defined as (2): (2) https://elksslsfdafs.casb.nju.edu.cn:4443/doi/epub/10.1080/17445302.2022.2052481?needAccess=true 3/25 15:37, 27/03/2022 Experimental and numerical investigation on reserve strength of jackets with single diagonal and X brace configurations The plastic hinge can occur either at the node ‘i’ or node ‘j’, and the corresponding stiffness matrices (Ki and Kj) is given by equation (3): (3) To achieve the smooth transition between the initial elastic and the final fully plastic configurations, the third node ‘k’ is introduced at the middle of the element, avoiding discontinuities representing the element stiffness The beam element with three nodes is shown in Figure Figure Beam element with three nodes (This figure is available in colour online) The stiffness matrix for intermediate node KE, has been calculated by the following expression (4) (4) where ΔKi is the matrix defined by the subtraction of the matrices of KL of (2) and Ki of (3), the gradual reduction of the element stiffness matrix is accomplished by defining φi as a parabolic function of force state parameters (5) & (6) (5) (6) The parameter α0 and α1 defines the plastic strength surface and a similar procedure is adopted for subelement The geometric nonlinearity has been computed by the arc-length method Arc length is defined as the length of the vector that connects the last known equilibrium configuration to the following unknown configuration on the equilibrium path Still, if the above does not yield a new stable configuration of the https://elksslsfdafs.casb.nju.edu.cn:4443/doi/epub/10.1080/17445302.2022.2052481?needAccess=true 4/25 15:37, 27/03/2022 Experimental and numerical investigation on reserve strength of jackets with single diagonal and X brace configurations system, the constraint equation is added to the original equilibrium equations to balance the number of equations and unknowns The general form of constraint equation is given by (7) (7) Δu, Δλ, f, and Δl are incremental displacement vector, load parameter, reference load vector and arc-length respectively and k1 and k2 are adjustable scalar factors 2.2 Buckling mechanism Beam finite elements have been used to model the elastic, elastic-plastic, and strut like behaviour during the loading and unloading of the structure While the elastic response is modelled using Euler-Bernoulli beam theory whereas the elastic-plastic response is simulated using the nonlinear kinematic hardening plasticity concentrated at the element ends, simulating the development of plastic hinges Marshal Strut Theory is used to simulate the buckling reaction using a simplified method of nonlinear sectional failure Figure depicts the buckling envelope used by Marshall strut theory for circular hollow sections The dotted lines in the interior of the envelope indicate the damaged-elastic modulus defining the loading-unloading force versus strain path Figure Marshall strut response envelope (Reference: Abaqus user manual) The value of Pcr and seven variables defines the Marshall envelope The expression for Pcr and the variables are given below The value of Pcr is calculated using Euler’s buckling theory Euler buckling stress (8) Critical buckling force https://elksslsfdafs.casb.nju.edu.cn:4443/doi/epub/10.1080/17445302.2022.2052481?needAccess=true 5/25 15:37, 27/03/2022 Experimental and numerical investigation on reserve strength of jackets with single diagonal and X brace configurations (9) E, K, L, A and r are elastic modulus, effective length factor, length, cross-sectional area and radius of gyration of the member, respectively The coefficients that define the buckling envelope are described below Elastic limit force γEA Isotropic hardening slope (γ = 0.02) αEA Slope on the buckling envelope (α0 = 0.03, α1 = 0.004) κ Pcr Corner on the buckling envelope (κ = 0.28) βEA Slope on the buckling envelope (β = 0.02) ζPy Corner on the buckling envelope The elastic limiting coefficient ξ is taken as 0.95, α, β, κ and γ are the slope of buckling envelopes and strain hardening slope respectively defined by Marshal strut theory and D and t are the diameter and wall thickness of the tubular members, respectively 2.3 Pile soil interaction (PSI) model The nonlinear soil behaviour has been modelled based on the load-displacement relationship for each soil layer using p-y, t-z and q-z curves as per API RP 2A (2007), recommended empirical model where t is the skin friction, q is the end bearing and z is the vertical displacement The governing equation to be solved the pile-soil interaction is given by equation (10) (10) where y = Lateral deflection of the pile; Ep Ip = Bending stiffness of the pile; P = Axial load on the pile; Es = Soil reaction modulus; w = Distributed load along the length of the pile The lateral displacement (y) can be determined using the non-linear force (p) and displacement relationship of soil (p-y) The lateral load-displacement relationship (p-y curve) for soft clay soil is shown in Figure in which the ultimate lateral capacity (pu) for soft clay (Cu PEuler*pereul pereul Level of transition from 3rd-degree polynomial shape function to sine/cosine shape function Specified as a factor of the Euler buckling load Max number recalculations of one load step due to element unloading Ktrmax Values 1 × 10−20 0.1 2.0 0.05 5.0 2.5 Different bracing patterns The ultimate strength assessment and influence of bracing patterns have been investigated for two typical jackets with different water depths of 76.5 and 59.7 m with three different bracing patterns, as listed below • Single brace (3D-A) • X brace (3D-B) • X brace + Single brace (3D-C) Bracing patterns, 3D-A and 3D-B are formed by rearranging the braces in all four bays of the jacket, as shown in Figure 7(a) and (b), respectively Bracing pattern 3D-C is formed by rearranging the braces in the top two bays of the jacket with a single diagonal brace and X brace on the bottom two bays, as shown in Figure 7(c) It is to be noted that the environmental load is less for 3D-C as the member in the splash zone is removed Figure Bracing patterns commonly adopted in offshore jackets (This figure is available in colour online) 2.6 Platform data https://elksslsfdafs.casb.nju.edu.cn:4443/doi/epub/10.1080/17445302.2022.2052481?needAccess=true 10/25 15:37, 27/03/2022 Experimental and numerical investigation on reserve strength of jackets with single diagonal and X brace configurations Two typical wellhead platforms with different water depths have been selected for this investigation These platforms have been in use for more than two decades with no structural related issues The details for the platforms are summarised in Table Table Structural details of platforms (Table view) Platform Field Mumbai high Field (South) Heera field Water depth (m) No of bays 76.5 59.7 No of piles main piles + 2 skirt piles skirt piles Pile diameter (mm) Pile penetration (m) 1219 91 2438 114 2.7 Soil data The nonlinear soil stiffness is defined by the p-y, t-z and q-z curves Layers of soil are defined up to a depth of target penetration below the mudline The soil data for Mumbai high field (South) and Heera field is summarised in Tables and 5, respectively The load-displacement soil curves are shown in Figure Figure Load displacement curves for soil (t-z, q-z and p-y) (This figure is available in colour online) Table Soil data (Mumbai high field – South) (Table view) Soil type Clay Depth (m) 0.00 to 5.00 ϕ (Deg) Average Cu (kPa) γ (kN/m3) flim (kPa) qlim (MPa) ε50 (%) 6.5 1.5 https://elksslsfdafs.casb.nju.edu.cn:4443/doi/epub/10.1080/17445302.2022.2052481?needAccess=true 11/25 15:37, 27/03/2022 Soil type Sand Clay Silt Sand Clay Sand Clay Sand Clay Sand Clay Sand Clay Sand Clay Experimental and numerical investigation on reserve strength of jackets with single diagonal and X brace configurations Depth (m) ϕ (Deg) Average Cu (kPa) γ (kN/m3) flim (kPa) qlim (MPa) ε50 (%) 25 25 25 28 30 32 30 30 80 88 92 190 275 190 248 9.0 8.0 8.5 10.0 9.0 9.0 9.0 10.0 8.5 10.0 9.0 10.0 9.5 10.0 9.0 20 20 20 20 20 20 20 20 1.0 1.0 0.5 0.5 0.5 0.5 0.5 ϕ (Deg) Average Cu (kPa) γ (kN/m3) flim (kPa) qlim (MPa) ε50 (%) 16 93 120 6.6 9.0 7.8 9.5 8.0 9.0 8.0 9.5 8.5 10.0 9.0 10.0 8.0 9.5 9.0 1.5 1.0 0.5 5.00 to 8.00 8.00 to 12.00 12.00 to 18.00 18.00 to 24.50 24.50 to 34.30 34.30 to 43.00 43.00 to 54.00 54.00 to 58.50 58.50 to 74.00 74.00 to 93.00 93.00 to 98.50 98.50 to 103.00 103.00 to 104.00 104.00 to 105.50 105.50 to 125.30 Table Soil data (Heera field) (Table view) Soil type Clay Clay Clay Sand Clay Sand Clay Sand Clay Sand Clay Sand Clay Sand Clay Depth (m) 0.00 to 9.70 9.70 to 20.00 20.00 to 27.70 27.70 to 29.90 29.90 to 46.80 46.80 to 49.60 49.60 to 51.80 51.80 to 58.90 58.90 to 70.80 70.80 to 75.00 75.00 to 77.60 77.60 to 92.80 92.80 to 100.40 100.40 to 102.80 102.80 to 125.20 30 30 100 30 150 35 150 35 180 30 200 230 20 20 20 20 20 35 1.0 0.5 0.5 0.5 0.5 0.5 2.8 Environmental data The total base shear was obtained for combined effect of 100-year storm wind, wave and current Wave and current force are computed by the Morison equation Stokes’s 5th order wave theory was used to calculate the water particle kinematics and wave kinematic factor as per API RP 2A (2007) has been used The drag and inertia coefficient of 0.65 and 1.6 was used for smooth cylinders while 1.05 and 1.2 was used for rough cylinders (with marine growth) The current blockage factor of 0.80 for end-on and broadside direction and 0.85 for diagonal direction has been used in the load calculation Wind pressure is calculated using the drag formula and applied to the deck structure The environmental data used for the load calculation are https://elksslsfdafs.casb.nju.edu.cn:4443/doi/epub/10.1080/17445302.2022.2052481?needAccess=true 12/25 15:37, 27/03/2022 Experimental and numerical investigation on reserve strength of jackets with single diagonal and X brace configurations summarised in Tables and for Mumbai high field (South) and Heera field, respectively These typical data are pertaining to offshore platforms located in western offshore India Table Environmental data for Mumbai high field (South) (Table view) Direction Wave height (m) Wave period (Sec) Current speed (m/s) Wind speed (m/sec) 14.33 17.38 17.07 17.68 18.29 16.77 14.94 16.16 12.50 14.00 13.90 14.20 14.40 13.70 12.80 13.40 1.40 1.22 1.13 1.22 1.37 1.16 1.07 1.16 41.57 41.64 43.41 44.83 44.83 44.83 44.42 43.02 N N 45 W W S 45 W S S 45 E E N 45 E Table Environmental data for Heera field (Table view) Direction Wave height (m) Wave period (Sec) Current speed (m/s) Wind speed (m/sec) 15.32 11.03 9.51 11.64 17.71 17.10 16.50 15.88 13.70 12.20 11.50 12.70 14.30 13.90 13.50 13.45 1.56 1.25 1.16 1.28 1.62 1.25 1.13 1.25 43.71 41.84 41.09 42.59 44.83 44.83 44.83 44.83 N N 45 W W S 45 W S S 45 E E N 45 E Experimental investigation 3.1 Scale model A typical jacket structure is selected and the same is used to design the scale model for experimental investigation The scale model has been chosen based on the availability of small-size pipes on the market The scale model of in 20 has been used to derive the sizes from a typical jacket in 60 m water depth and the member sizes used in the field The slenderness of the model and prototype is maintained as the geometry and sections are scaled linearly It is noted that the EI is not scaled appropriately Hence, the scale model results are only compared with the numerical model corresponding to the scale model for validation and verification of the results The extension or scaling of scale model results to prototype has not been used in this paper The geometric properties are summarised in Table The structural arrangement of frames and their loading direction is shown in Figure https://elksslsfdafs.casb.nju.edu.cn:4443/doi/epub/10.1080/17445302.2022.2052481?needAccess=true 13/25 15:37, 27/03/2022 Experimental and numerical investigation on reserve strength of jackets with single diagonal and X brace configurations Figure Structural arrangement of 2D frames (This figure is available in colour online) Table Geometric properties (Table view) S No Description Frame height Leg Brace Brace Scale model (1:20) 3.6 m 76 mm × 4 mm 42 mm × 3 mm 25 mm × 3 mm Prototype 72 m 1520 mm × 80 mm 840 mm × 60 mm 500 mm × 60 mm 3.2 Material properties The mechanical properties of the steel tube were tested as per ASTM E8/E8M-2016 Three coupon specimens were taken from each tube and the tests were performed in the MTS tension testing machine, which had a displacement control mechanism with a testing capacity of 1000 kN The displacement rate is set at 0.05 and 0.1 mm/s between strain ranges of 0–0.2% and 0.2% up to fracture, respectively Strain gauges were pasted on each specimen to measure the strain Typical coupon specimen test arrangement is shown in Figure 10(a) and the stress–strain curve obtained from the coupon test is shown in Figure 10(b) The material property for the test specimen is summarised in Table https://elksslsfdafs.casb.nju.edu.cn:4443/doi/epub/10.1080/17445302.2022.2052481?needAccess=true 14/25 15:37, 27/03/2022 Experimental and numerical investigation on reserve strength of jackets with single diagonal and X brace configurations Figure 10 Material characteristics from coupon test (This figure is available in colour online) Table Steel material properties (Table view) S No Specimen type Leg Brace Brace Yield stress Fy (MPa) 252 241 235 Young’s modulus (E) (MPa) 203,541 200,102 218,987 3.3 Test setup The lateral load test was carried out to determine the ultimate strength of the test frames The twodimensional frames were arranged horizontally with a fixed support at the bottom of the frame using bolted connections as shown in Figure 11 The test load was applied to the top frame using a hydraulic jack that is fully controlled by a computer The applied load was monitored using an inbuilt load cell with a resolution of 0.01 kN The lateral displacement of the frame was measured by Linear Variable Displacement Transducers (LVDT) which has a stroke length of 100 mm and a resolution of 0.001 mm Hydraulic pressure for jack was increased gradually to obtain the load-displacement relationship for the frame until the lateral displacement was large or the failure of the frame and no further loading was possible https://elksslsfdafs.casb.nju.edu.cn:4443/doi/epub/10.1080/17445302.2022.2052481?needAccess=true 15/25 15:37, 27/03/2022 Experimental and numerical investigation on reserve strength of jackets with single diagonal and X brace configurations Figure 11 Experimental setup for X-brace frame (2D-2) (This figure is available in colour online) Results and discussion 4.1 Load–displacement relationship of 2D frames The displacement/failure pattern obtained from the numerical simulation and experiment for 2D-1 (Single brace) is shown in Figure 12 It can be observed that the failure pattern obtained from numerical simulation and the experiment matches closely as seen from buckling failure of the brace connecting legs at the top Further, the lateral displacement of legs including bending at the bottom is noticed in a similar pattern to the numerical model The measured and simulated load-displacement relationship for the single brace (2D-1) frame is shown in Figure 13 The ultimate failure load of 53kN and 50kN has been obtained from numerical simulation and experiment respectively for a lateral displacement of 5.6 and 7.0 mm, respectively The results obtained from the experiment and simulation match reasonably with a maximum difference of less than 10% https://elksslsfdafs.casb.nju.edu.cn:4443/doi/epub/10.1080/17445302.2022.2052481?needAccess=true 16/25 15:37, 27/03/2022 Experimental and numerical investigation on reserve strength of jackets with single diagonal and X brace configurations Figure 12 Failure pattern for single brace (2D-1) (This figure is available in colour online) Figure 13 Load displacement relationship for single brace (2D-1) (This figure is available in colour online) Beyond ultimate load, the experiment model exhibited ductile behaviour compared to the numerical model and this may be due to variation in characteristics of steel material used for the fabrication The unloading process depicted by the reduction indicates that the first member has failed but no further load https://elksslsfdafs.casb.nju.edu.cn:4443/doi/epub/10.1080/17445302.2022.2052481?needAccess=true 17/25 15:37, 27/03/2022 Experimental and numerical investigation on reserve strength of jackets with single diagonal and X brace configurations increase is possible due to the unavailability of the second load path However, the experiment could not be continued due to limitations on the stroke of hydraulic jack, reaction frame design and the unloading of load, the experiment was stopped The displacement/failure pattern obtained from the numerical simulation and experiment for 2D-2 (Single brace) is shown in Figure 14 A similar comparison of measured and simulated load-displacement relationship for the X-brace frame (2D-2) is shown in Figure 15 The ultimate failure load of 60 kN and 59 kN has been obtained from numerical simulation and experiment respectively for a lateral displacement of 10 mm The results obtained from the experiment and simulation matches very well a maximum difference is less than 1% The failure due to local joint rotation for the X brace (bottom) deforms the leg, introducing load distribution and increasing failure load This is not visible from the single brace pattern and the top brace fails without additional deformation of the leg This might be useful in comparing single and X brace failure mechanisms while comparing ultimate load and the lateral displacement of the overall structure Figure 14 Failure Pattern for X brace (2D-2) (This figure is available in colour online) https://elksslsfdafs.casb.nju.edu.cn:4443/doi/epub/10.1080/17445302.2022.2052481?needAccess=true 18/25 15:37, 27/03/2022 Experimental and numerical investigation on reserve strength of jackets with single diagonal and X brace configurations Figure 15 Load displacement relationship for X brace (2D-2) (This figure is available in colour online) 4.2 Comparison between single and X brace frames The comparison of the load-displacement relationship of single and X brace framings is shown in Figure 16 It can be observed that the X brace frame has a higher failure load compared to that of a single brace by 15% The lateral deflection at ultimate load for single and X brace is noted to be 5.6 and 10 mm respectively and the X brace has ductile deformation than the single brace frame Figure 16 Load-displacement relationship of 2D-1 and 2D-2 obtained from experiment (This figure is available in colour online) The load step and the displacement pattern for the single brace and X brace framings are shown in Figure 17(a) and (b), respectively It can be seen from the figure that the X brace frame exhibits a ductile bending of legs before the brace at the top starts a change in load path resulting in local buckling failure compared to https://elksslsfdafs.casb.nju.edu.cn:4443/doi/epub/10.1080/17445302.2022.2052481?needAccess=true 19/25 15:37, 27/03/2022 Experimental and numerical investigation on reserve strength of jackets with single diagonal and X brace configurations that in the Single brace frame The presence of X brace in all bays increases the load carrying capacity, and no local failures have been observed Figure 17 Load-displacement pattern for single and X brace frames (This figure is available in colour online) 4.3 Effect of bracing on RSR (3D frame) A design level sea state analysis was carried out to obtain the design load on the structure for 100-year storm conditions using the SACS (Structural Analysis Computer System) software developed by Bentley Systems As explained earlier, the maximum base shear is considered the design load on the structure, and it has been computed for four orthogonal and diagonal directions The base shear for each direction is summarised in Table 10 It has been observed that the maximum base shear is noted for the south direction Table 10 Base shear for 100-year storm condition (Table view) Direction 3D – A N N 45 W W S 45 W S S 45 E E N 45 E 9.74 11.81 12.27 12.31 14.55 9.03 7.48 9.59 Platform – 3D – B 14.97 12.98 13.57 13.53 15.87 9.91 8.67 10.54 3D – C 3D – A Platform – 3D – B 10.62 12.07 12.53 12.57 14.91 9.19 7.96 9.80 18.46 17.34 18.69 19.96 23.57 11.32 7.87 10.34 19.34 18.31 19.03 20.98 25.84 12.26 8.43 10.99 https://elksslsfdafs.casb.nju.edu.cn:4443/doi/epub/10.1080/17445302.2022.2052481?needAccess=true 3D – C 19.01 17.69 19.05 23.40 24.63 11.57 7.99 10.23 20/25 15:37, 27/03/2022 Experimental and numerical investigation on reserve strength of jackets with single diagonal and X brace configurations Pushover analysis was carried out for eight load directions for each platform with three bracing patterns (A, B and C) The RSR for platforms and is summarised in Table 11 The RSR for the bracing pattern 3D-B is consistently higher than the other two bracing patterns (A and C) for all load directions The maximum increase in RSR for 3D-B is found to be 35% and 12% compared to 3D-A and 3D-C, respectively A comparison between 3D-B and 3D-C indicates that the single brace at the top bay has less reduction in RSR since the wave load reduces considerably due to a smaller number of braces near the water line This is clearly understood from Table 10 that the base shear is lower than 3D-B for all load directions It has led to the increase in RSR values for the 3D-C in general for most cases Table 11 RSR value for platforms (Table view) Direction 3D – A N N 45 W W S 45 W S S 45 E E N 45 E 1.81 1.66 1.56 1.58 1.40 2.04 2.29 1.96 Platform – 3D – B 1.96 1.85 2.14 1.66 1.67 2.38 2.99 2.88 3D – C 3D – A Platform – 3D – B 1.89 1.75 1.66 1.64 1.63 2.27 2.31 2.75 1.79 1.80 2.05 1.84 1.24 2.41 2.56 2.67 2.51 2.29 3.01 2.70 1.92 3.80 3.62 2.88 3D – C 1.84 1.86 2.15 1.70 1.70 3.49 2.57 2.75 The failure pattern for platform at the south wave direction is shown in Figure 18 It can be observed that the first member failure occurred at the brace in the fourth bay for the 3D-A jacket and the brace in splash zone 3D-C However, for 3D-B brace failure did not occur due to X brace configurations while jacket legs at the bottom started yielding due to redundancy Figure 18 Failure pattern for platform (Main Pile) due to south wave (This figure is available in colour online) https://elksslsfdafs.casb.nju.edu.cn:4443/doi/epub/10.1080/17445302.2022.2052481?needAccess=true 21/25 15:37, 27/03/2022 Experimental and numerical investigation on reserve strength of jackets with single diagonal and X brace configurations The load-displacement relationship for platform for the south wave direction is shown in Figure 19 The ultimate capacity for 3D-A, 3D-B and 3D-C are noted as 20MN, 26MN and 24MN, respectively The ultimate capacity for 3D-B is higher by 23% and 8% compared to 3D-A and 3D-C, respectively However, capacity reduction for 3D-C is small compared to 3D-B indicating the insignificance of X brace at the top bay and can be concluded that the X brace at the bottom bay has more influence on the RSR Figure 19 Load–displacement relationship for platform (This figure is available in colour online) A similar failure pattern can be observed for another jacket (platform 2) subjected to waves from the south direction as shown in Figure 20 The load-displacement relationship is shown in Figure 21 The ultimate capacity for 3D-A,3D-B and 3D-C are noted as 33MN, 38MN and 36MN, respectively The ultimate capacity for 3D-B is higher by 13% and 5% compared to 3D-A and 3D-C, respectively However, capacity reduction for 3D-C is small compared to 3D-B indicating the insignificance of X brace at the top bay and can be concluded that the X brace at the bottom bay has more influence on the RSR However, the change in the main pile (platform 1) to the skirt pile (platform 2) has a significant influence on the failure pattern https://elksslsfdafs.casb.nju.edu.cn:4443/doi/epub/10.1080/17445302.2022.2052481?needAccess=true 22/25 15:37, 27/03/2022 Experimental and numerical investigation on reserve strength of jackets with single diagonal and X brace configurations Figure 20 Failure pattern for platform (skirt pile) due to south wave (This figure is available in colour online) Figure 21 Load–displacement relationship for platform (This figure is available in colour online) Conclusions Experimental and numerical investigation was carried out to evaluate the ultimate strength of 2D frames with a single brace (2D-1) and X brace (2D-2) configurations The results obtained from 2D frame experiments were used to validate the simulation model Pushover analysis of two typical jackets with three different configurations and main & skirt pile foundations has also been carried out to evaluate bracing and pile effects on the RSR Following observations and salient conclusion can be noted a The load-displacement relationship for 2D frames obtained from the experiment matches reasonably https://elksslsfdafs.casb.nju.edu.cn:4443/doi/epub/10.1080/17445302.2022.2052481?needAccess=true 23/25 15:37, 27/03/2022 Experimental and numerical investigation on reserve strength of jackets with single diagonal and X brace configurations well with numerical simulation b A 15% increase in ultimate strength was observed for X brace configuration (2D-2) compared to single brace configuration (2D-1) and ductile failure was noted with X brace configuration c The RSR of jackets is sensitive to the wave direction and the lowest RSR was observed for bracing pattern 3D-A due to its non-redundant configuration d The jacket structures based on the X bracing pattern (3D-B) have higher redundancy than 3D-A and 3D-C The maximum increase in RSR for 3D-B is found to be 35% and 12% compared to 3D-A and 3D-C, respectively e A jacket with bracing pattern 3D-C has similar characteristics as 3D-B especially in larger water depth indicating the insignificance of X brace requirement at the top bays and the contribution of X brace at the bottom bays is influencing the RSR Disclosure statement No potential conflict of interest was reported by the author(s) References API 2007 API RP 2A Recommended practice for planning, designing and constructing fixed offshore platforms – Working stress design 21st ed American Petroleum Institute Billington CJ, Bolt HM, Keith ward J 1993 Reserve, residual and ultimate strength of offshore structures Third International offshore and engineering conference, Singapore Bolt HM, Billington CJ, WardNaser JK 1996 A review of the ultimate strength of the tubular framed structures OTH 92:365–1996 Brown and Root Ltd 1997 Comparison of reserve strength ratios of old and new platforms Offshore Technology Report OTO-97046 Crisfield MA 1981 A fast incremental/iterative solution procedure that handles “snap-through” p 55–62 El-Din MN, Kim J 2014 Seismic performance evaluation and retrofit of fixed jacket offshore platform structures J Perform Constr Facil 29:1–10 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offshore oil exploitation J Constr Steel Res 61:1147–1171 Reese LC, Cox WR, Koop FD 1974 Analysis of laterally loaded piles in sand Offshore Technology Conference Reese LC, Cox WR, Koop FD 1975 Field testing and analysis of laterally loaded piles on stiff clay Offshore Technology Conference Riks E 1979 An incremental approach to the solution of snapping and buckling problems Int J Solids Struct 15:529– 551 Starossek U, Haberland M 2011 Approaches to measures of structural robustness Struct Infrastruct Eng 7:625–631 Tabeshpour MR, Erfani MH, Sayyaadi H 2019 Study on ultimate capacity of offshore jacket platforms considering the effects of global and local buckling of the elements J Adv Solid Fluid Mech 1:9–17 Titus, PG and Banon, H 1988 Reserve strength analysis of offshore platforms (7th offshore) Singapore: Southeast Asia Conference Westlake HS, Puskar FJ, Bucknell JR 2006 The role of ultimate strength assessments in the structural integrity management (SIM) of Offshore Structures OTC 18831-2006 Zayas VA, Mahin SA, Popov EP, Shing P-SB 1981 Inelastic structural analysis of braced platforms for seismic loading Houston: Offshore Technology https://elksslsfdafs.casb.nju.edu.cn:4443/doi/epub/10.1080/17445302.2022.2052481?needAccess=true 24/25 15:37, 27/03/2022 Experimental and numerical investigation on reserve strength of jackets with single diagonal and X brace configurations https://elksslsfdafs.casb.nju.edu.cn:4443/doi/epub/10.1080/17445302.2022.2052481?needAccess=true 25/25 ... Sand Clay Silt Sand Clay Sand Clay Sand Clay Sand Clay Sand Clay Sand Clay Experimental and numerical investigation on reserve strength of jackets with single diagonal and X brace configurations. .. 27/03/2022 Experimental and numerical investigation on reserve strength of jackets with single diagonal and X brace configurations numerical simulations for a few jackets with varied bracing configurations. .. 27/03/2022 Experimental and numerical investigation on reserve strength of jackets with single diagonal and X brace configurations that in the Single brace frame The presence of X brace in all