Experimental and numerical investigation on reserve strength of jackets with single diagonal and x brace configurations

Karunanithib a Department of Ocean Engineering, IIT Madras, Chennai, India b Institute of Engineering & Ocean Technology, ONGC, Navy Mumbai, India ABSTRACT Jacket framing arrangement X,

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 Renugadevia , S Nallayarasu b , and S Karunanithib

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.

in a structural testing lab The numerical model of the same was solved and compared The results of

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

numerical simulations for a few jackets with varied bracing configurations (3D-A, 3D-B, and 3D-C) arepresented and discussed.

1.2 Literature review

API RP 2A (2007) has certain guiding principles of bracing pattern on the ultimate capacity of the jacketand suggests that diagonal bracing in vertical frames transfers shear forces between horizontal frames or thatvertical 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 aboveprinciples are generally adopted in jacket design in most cases However, there are situations whereinmodified bracing pattern is used

Billington et al (1993) used nonlinear analytical approaches to explain the reserve, residual, and ultimatestrength of offshore structures Bolt et al (1996) used experimental and numerical techniques to investigatethe ultimate strength of tubular framed structures Brown et al (1997) conducted a pushover analysis tocompare the RSR of two old and new North Sea platforms developed using different codes and proposedthat 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 andpresented a method for performing progressive collapse analysis by systematically removing failedcomponents to determine the structure collapse capacity Paulo and Jacobb (2005) described the nonlinearformulation for global collapse analysis for three-dimensional framed structures, including the material andgeometric nonlinearity Westlake et al (2006) investigated the role of ultimate strength assessments inStructural Integrity Management (SIM) of offshore structures and provided an overview of the structurebehaviour under extreme load conditions Frangopol et al (1992) investigated the redundancy of structuralsystems The deterministic and probabilistic methods were demonstrated through examples Starossek andHaberland (2011) investigated robustness of structures using a quantified measure The recommendedprerequisites 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 consideredthree loading conditions, and their force–deformation characteristics were closely matched with numericalsimulations Reese et al (1974) investigated the capacity of laterally loaded piles in sand The pile wastested under static and cyclic loads, and a method of simulating p-y curves was devised where p is the lateralload and y is the lateral displacement of pile Reese et al (1975) conducted field testing on laterally loadedpiles 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 offraming configuration on the robustness of offshore structures, concluding that X brace configurationsincrease the robustness of the jacket structure without increasing the cost or constructability El-Din andKim (2014) assessed the effects of retrofit approaches on the seismic performance of jacket structures usingnon-linear static and dynamic loading methods

Tabeshpour et al (2019) examined the ultimate capacity of offshore jacket platforms considering theeffects of global and local buckling of the elements Marshall et al (1977) investigated the inelastic dynamicanalysis of offshore tubular structures and discussed structural factors such as inelastic stretch, brace post-buckling behaviour, and ductility limitation at plastic hinges Zayas et al (1981) examined the inelasticstructural behaviour of braced jacket platforms under seismic loading Gates et al (1977) evaluated theultimate seismic resistance of fixed offshore structures Riks (1979) described a numerical scheme to solvethe structure deformation problems involving snapping and buckling The rapid incremental/iterativesolution approach that handles ‘snap-through’ was described by Crisfield (1981)

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 reservestrength was defined as the additional strength given by redistribution of stresses within the cross-sectionand frame due to redundancy in the system, rather than the margin available through design approachesincorporating 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 involvingnonlinear 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 analysiswith 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 numericalscheme has been carried out by conducting experiments on the 2D frame with single and X braceconfiguration of a 1: 20 scale model Because of the experimental setup limitations and the magnitude ofloading, 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

2 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 stiffnessformulation The structure stiffness matrix is built using element stiffness matrices estimated using updatedgeometry 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 maximumcapacity This process continues until the system becomes unstable and collapses due to the formation of afull mechanism The formulation of the numerical scheme used for the nonlinear simulation is explained inthis section A finite beam element with two nodes is shown in Figure 1

The elastic stiffness matrix of the beam element K L is defined as (2):

(2)

Figure 1 Beam element with two nodes.

The plastic hinge can occur either at the node ‘i’ or node ‘j’, and the corresponding stiffness matrices (K i and K j) is given by equation (3):

(3)

To achieve the smooth transition between the initial elastic and the final fully plastic configurations, thethird node ‘k’ is introduced at the middle of the element, avoiding discontinuities representing the elementstiffness The beam element with three nodes is shown in Figure 2

The stiffness matrix for intermediate node K E, has been calculated by the following expression (4)

(4)

where ΔK i is the matrix defined by the subtraction of the matrices of K L of (2) and K i of (3), the gradual

reduction of the element stiffness matrix is accomplished by defining φ i as a parabolic function of force stateparameters (5) & (6)

(5)(6)

The parameter α0 and α1 defines the plastic strength surface and a similar procedure is adopted for element 2

sub-The geometric nonlinearity has been computed by the arc-length method Arc length is defined as thelength of the vector that connects the last known equilibrium configuration to the following unknownconfiguration on the equilibrium path Still, if the above does not yield a new stable configuration of the

Figure 2 Beam element with three nodes (This figure is available in colour online).

system, the constraint equation is added to the original equilibrium equations to balance the number ofequations and unknowns The general form of constraint equation is given by (7).

depicts the buckling envelope used by Marshall strut theory for circular hollow sections The dotted lines inthe interior of the envelope indicate the damaged-elastic modulus defining the loading-unloading forceversus strain path

The value of P cr and seven variables defines the Marshall envelope The expression for P cr and the

variables are given below The value of P cr is calculated using Euler’s buckling theory

Euler buckling stress

(8)Critical buckling force

Figure 3 Marshall strut response envelope (Reference: Abaqus user manual).

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 describedbelow

Elastic limit force

γEA Isotropic hardening slope (γ = 0.02)

αEA Slope on the buckling envelope

(α0 = 0.03, α1 = 0.004)

κ P cr Corner on the buckling envelope (κ = 0.28)

βEA Slope on the buckling envelope (β = 0.02)

ζP y 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 andstrain hardening slope respectively defined by Marshal strut theory and D and t are the diameter and wallthickness 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 soillayer 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; E p I p  = Bending stiffness of the pile; P = Axial load on the pile; E s = 

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 4 in which the ultimate lateral capacity (p u ) for soft clay (C u < 96 kPa) is given by:

(11)(12)where

The limiting distance is defined by the expression

d = Depth below seabed (m); p u  = Ultimate lateral resistance (kPa); γ s = Effective unit weight of soil(kN/m3); C u  = Undrained shear strength (kPa); J = Dimensionless empirical constant (usually to be taken as 0.5); D = Pile diameter (m); y c  = Critical lateral displacement given by 2.5ϵ50D in which ϵ50 is the strain at50% deviator stress in unconsolidated and unconfined compression test of soil sample

The p-y curve for sand is shown in Figure 5 in non-dimensional form and the lateral capacity (p) values

shall be calculated using the empirical relationship in equation (13)

(13)

where, A = 0.9 for cyclic loading; (3-0.8(d/D)) ≥ 0.9 for static loading; k h = Initial modulus of subgradereaction(kN/m3); p u is taken as the lesser of p us at shallow water depths and p ud at large water depths

(14)(15)

where C1, C2 and C3 are coefficients given by the following expression

Figure 4 Lateral load–displacement (p-y) curve for soft clay (API RP 2A-2007) (This figure is available in colour

online).

And ϕ, Ko, Ka and K p are angle internal friction of sand, earth pressure coefficient at rest, active and

passive states, respectively β, α, K a and K p are determined using the following expressions

The numerical model for the foundation is automated by dividing the total length of the pile into segments based on number of soil strata provided The pile-soil model is attached to the structural model atthe pile head usually at the seabed level The jacket structure with pile/soil springs is shown in Figure 6

sub-Figure 5 Lateral load–displacement (p-y) curve for sand (API RP 2A-2007) (This figure is available in colour

online).

2.4 Numerical simulation

The wave and current loads are generated based on the maximum base shear method using the parameterspecified for the simulation The stiffness of the structure and pile-soil stiffness is estimated and iterateduntil force equilibrium is achieved The simulation is carried out using generated load by incrementing theinitial value until collapse occurs Following steps are performed in the analysis during the increment ofeach load step

• Each load step, structure stiffness and displacements are computed

• Corresponding to each load step, the nonlinear soil stiffness is computed based on p-y, t-z and q-zcurves and iteration is repeated until equilibrium of forces is reached

• All the members are checked at each load step for stresses and corresponding plasticity limit and aplastic hinge is introduced by the program is case, if the condition is satisfied

• The stiffness matrix is updated to account for the hinge, and the process proceeds to the next load step.The load control parameters and the analysis control parameters considered in the numerical simulationare summarised in Tables 1 and 2, respectively

Figure 6 Pile–Soil–Structure interaction model (This figure is available in colour online).

Table 1 Load control parameters ( Table view )

npostp Number of load steps in post collapse range 5000 mxpstp Maximum load step size in the collapse range 1.0 mxpdis Max incremental displacements in the post-collapse range The suggested value is 1.0 1.0 mxld The current load vector is repeated until the accumulated load reaches the relative load

level mxld, specified as a factor of the reference load

10

2.5 Different bracing patterns

The ultimate strength assessment and influence of bracing patterns have been investigated for two typicaljackets 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, asshown in Figure 7(a) and (b), respectively Bracing pattern 3D-C is formed by rearranging the braces in thetop 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 isremoved

2.6 Platform data

nstep Both mxld and nstep may be specified at the same time; the load is incremented until

either of the conditions is satisfied.

500

Table 2 Analysis control parameters ( Table view )

epssol Numerical accuracy of the equation solver 1 × 

10−20gamstp Accepted value for overshooting the yield surface 0.1 Ifunc FEM beam shape function

1: Sine/cosine shape functions 3: 3rd degree polynomials

2:3rd degree polynomials used when P x  ≤ PEuler*pereul Sine/cosine functions used

when P x  > PEuler*pereul

2.0

pereul Level of transition from 3rd-degree polynomial shape function to sine/cosine shape

function Specified as a factor of the Euler buckling load.

0.05 Ktrmax Max number recalculations of one load step due to element unloading 5.0

Figure 7 Bracing patterns commonly adopted in offshore jackets (This figure is available in colour online).

Two typical wellhead platforms with different water depths have been selected for this investigation Theseplatforms have been in use for more than two decades with no structural related issues The details for theplatforms are summarised in Table 3.

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 issummarised in Tables 4 and 5, respectively The load-displacement soil curves are shown in Figure 8

Table 3 Structural details of platforms ( Table view )

1 Mumbai high Field

(South)

76.5 5 4 main piles + 2

skirt piles

Figure 8 Load displacement curves for soil (t-z, q-z and p-y) (This figure is available in colour online).

Table 4 Soil data (Mumbai high field – South) ( Table view )

Soil type Depth (m) ϕ

2.8 Environmental data

The total base shear was obtained for combined effect of 100-year storm wind, wave and current Wave andcurrent force are computed by the Morison equation Stokes’s 5th order wave theory was used to calculatethe water particle kinematics and wave kinematic factor as per API RP 2A (2007) has been used The dragand inertia coefficient of 0.65 and 1.6 was used for smooth cylinders while 1.05 and 1.2 was used for roughcylinders (with marine growth) The current blockage factor of 0.80 for end-on and broadside direction and0.85 for diagonal direction has been used in the load calculation Wind pressure is calculated using the dragformula and applied to the deck structure The environmental data used for the load calculation are

Soil type Depth (m) ϕ

Table 5 Soil data (Heera field) ( Table view )

Soil type Depth (m) ϕ