Research Journal of Applied Sciences, Engineering and Technology 4(24): 5591-5601, 2012 ISSN: 2040-7467 © Maxwell Scientific Organization, 2012 Submitted: June 07, 2012 Accepted: June 09, 2012 Published: December 15, 2012 Fatigue Generation Mechanism in Touchdown Area of Steel Catenary Risers in Non-Linear Hysteretic Seabed 1 1 Kosar Rezazadeh, 2Hodjat Shiri , 1Liang Zhang and 1Yong Bai Ship Building College, Harbin Engineering University, Harbin, Heilongjiang 150001, China 2 Civil Engineering Department, Urmia University of Technology, Urmia, Iran Abstract: The complex nature of seabed interaction with Steel Catenary Risers (SCR) in Touch Down Zone (TDZ) and its vital impact on fatigue performance of SCRs makes serious difficulties against proposing simplified and robust solutions for engineering design industry where the fatigue in touch down zone is still considered as one the most challenging issues in riser design. In this study, authors have tried to explore in deep the mechanism of fatigue generation in touchdown area with sophisticated numerical simulations capturing the stress variation along the riser under complex load conditions in non-linear hysteretic seabed. The results show interesting unknown stress variation trends which is believed to be considerably useful in providing robust and simple solution for design industry. Keywords: Fatigue, non-linear hysteretic seabed, Steel Catenary Riser (SCR), Touch Down Zone (TDZ) embedment of the riser into the seabed and fatigue damage generation, the area which is believed to be the main root of the subject and needs to be further understood. Various non-linear models have been presented in literature for pipeline-seabed interaction (Bridge and Howels, 2007; Randolph and Quiggin 2009) but the model proposed by Randolph and Quiggin (2009) is the model simulating gradual seabed soil stiffness degradation which in turn models the gradual riser embedment into the seabed and trench formation due to soil softening under cyclic loading. The study has been conducted through numerical simulations in which the complex non-linear hysteretic riser-seabed interaction modeling the gradual soil stiffness degradation and soil suction has been coupled with a full riser structural model connected to a generic floating vessel. The vessel is excited by a generic wave spectrum throughout the displacement-controlled time domain analysis and then the fluctuations of riser in touchdown area and its impact on stress variation along the riser is captured for detailed study. The seabed interactions and the gradual variation of boundary conditions in floating vessel has been coded in Fortran and linked to ABAQUS. Post processing Excel macros have been developed to calculate the cumulative fatigue damage and variation of von Mises stress range. INTRODUCTION The complex riser-seabed interaction in touchdown area is accepted today through ROV surveys where trenches with several diameters depth have been observed (Bridge and Howels, 2007). Various researches presented in literature have tried to investigate the effect of trench formation on fatigue performance of SCRs, but the results show interesting contradictions. Some authors report an increase in fatigue damage due to trench creation (Giertsen et al., 2004; Karunakaran et al., 2004) while others suggest fatigue damage reduction (Clukey et al., 2007; Langner 2003; Nakhaee and Zhang 2008). Shiri and Randolph (2010) have performed numerical simulations and concluded that the source of contradiction is getting back to the methodology undertaken for study. They have proposed a study methodology letting the trench to be gradually formed using a non-linear hysteretic seabed interaction model. The final conclusion was showing the increasing of peak fatigue damage for deeper trenches. This totally different with findings of Rezazadeh et al. (2012) where they showed that implementing the effects of vessel slow drifts changes the story to an unpredictable nature. Rezazadeh et al. (2012) showed that depending on the load condition the peak fatigue damage in touchdown area can be increased or decreased for deeper trench depths proving more complexity of the subject. In this study, authors have tried to take a basic step and deeply explore the nature of the relationship between the gradual Global configuration of the model: The global configuration of the numerical model which has been constructed in ABAQUS is shown below in Fig. 1.The Corresponding Author: Kosar Rezazadeh, Ship Building College, Harbin Engineering University, Harbin, Heilongjiang 150001, China 5591 Res. J. Appl. Sci. Eng. Technol., 4(24): 5591-5601, 2012 The riser is fixed at the anchor end in the seabed and is attached to Spar vessel in a point which is lower than center of gravity. The riser-seabed interaction has been considered from an area beyond the Touchdown Point (TDP) until the anchor point throughout the riser lay down on the seabed. The numerical model has been constructed in ABAQUS finite element software considering simple beam elements for riser. The riserseabed interaction has been modeled via User Defined Elements (UEL) with the behavior coded inside the Fortran which has been suitably coupled with main model. In this example, the Spar has been perturbed by 10 regular sinusoidal cycles and the responses show a number of features such as suction force mobilization, gradual increasing penetration depth, and gradually reducing mobilization of soil resistance at maximum penetration. The seabed model parameters and the characteristics of the SCR are presented in Table 1 and 2. The manipulated wave scatter diagram applied in analysis is based on typical conditions in the Gulf of Mexico shown in Table 3. Fig. 1: Global configuration of modeled SCR Table 1: non-linear model parameters Parameter Mudline shear strength Shear strength gradient Power law parameter Power law parameter Normalized maximum stiffness Suction ratio Suction decay parameter Repenetration parameter Table 2: Riser pipe parameters Parameter Outer diameter, Do Wall thickness, t Bending stiffness Submerged unit mass Fatigue S-N curve Symbol su0 ρ a b Kmax fsuc λsuc λrep Value 0.65 kPa 1.5 kPa/m 6 0.25 200 0.3 0.5 0.5 Value 0.324 m (123/4 “) 0.0205 m 4.67×107 Nm2 100 kg/m DNV(2008), E Class: SCF = 1.15, = 3.0 a = 1.05×10-12 , m floating vessel type, the overall model dimensions and hydrocarbon field location (Gulf of Mexico) have been selected as such to enable comparison with published results in the literature if required. The Mechanism of fatigue generation in TDZ: It is believed that fatigue damage is mostly derived in seabed trench mouth but still further explorations are required. It is worth mentioning that in this paper, since the main question is the fatigue derivation mechanism, therefore the accurate estimation of the fatigue damage itself is not a focus point. Hence for the cases that fatigue damage has been calculated some simplifications have been applied to facilitate the study. As an instance, in non-linear plastic seabed since the hierarchy of the sea states can affect themagnitude of the ultimate cumulative damage, so the validity of utilizing Miner’s rule for linear superposition of the damages caused by various sea states is under question. Shiri and Randolph (2010) showed that applying a wave with higher significant height flatten the variation of the von Mises stress range for the waves with less height. This means if the biggest sea state hits to Table 3: Manipulated wave scatter diagram for a 30 year service life in Gulf of Mexico Sea State ID Hs (m) Tz (s) N applied Sea State ID 1 0.5 4.2 18011291 16 2 1.0 4.6 71370445 17 3 1.5 5.0 4844608 18 4 2.0 5.4 25187856 19 5 2.5 5.8 13529335 20 6 3.0 6.1 7473660 21 7 3.5 6.5 3080495 22 8 4.0 6.9 1631014 23 9 4.5 7.3 583770 24 10 5.0 7.7 363725 25 11 5.5 8.0 114700 26 12 6.0 8.4 33676 27 13 6.5 8.5 16907 28 14 7.0 8.7 10864 29 15 7.5 8.9 5421 30 5592 Hs (m) 8.0 8.5 9.0 9.5 10.0 10.5 11.0 11.5 12.0 12.5 13.0 13.5 14.0 14.5 15.0 Tz (s) 9.1 9.3 9.5 9.7 9.9 10.1 10.2 10.4 10.6 10.7 10.9 11.0 11.2 11.3 11.5 N applied 3389 3011 1822 1395 1070 1246 566 928 544 813 712 8.77 262 343 420 Res. J. Appl. Sci. Eng. Technol., 4(24): 5591-5601, 2012 8 0.000040 Fatigue Shear far 6 0.000030 Peak fatigue location Shear near 0.000020 Trench bottum point 2 0.000010 0 0.000000 -2 Fatigue damage Shear Force kN 4 -0.000010 Scaled trench profile TDP -4 -0.000020 -370 -360 -350 -340 -330 -320 -310 -300 -290 -280 Horizontal coordinate (m) Fig. 2: Peak fatigue position relative to trench and shear profile of near and far offsets 0.000040 7 wave 15 6 wave 10 5 Shear Force kN 0.000035 0.000030 0.000025 wave 5 4 0.000020 3 0.000015 2 0.000010 1 0.000005 0 0.000000 Fatigue damage wave 20 -0.000005 -1 -370 -360 -350 Horizontal coordinate (m) -340 -330 Fig. 3: Near and far offset shear profile compare with fatigure damage for various waves the vessel first, for the rest of the sea states the von Mises stress range will not be varied which in turn means the application of Miner’s rule is allowed. In this paper the described hypothesis has been undertaken simplifying the calculation of the cumulative fatigue damage and enabling authors to focus on subtle mechanisms rather than the value of ultimate damage. As apparently shown in Fig. 5 for a sample analysis, the peak fatigue damage is interestingly located at the point at which the shear force profiles of near and far offsets are crossing each other. This is exactly in agreement with basic mechanical rule, where the bending moment is the gradient of shear force which reaches its maximum value when the gradient becomes zero. The bending moment itself is the main component making the von Mises stress for riser tubular section which in turn produce the fatigue damage by its variation range. Comparing the location of peak fatigue damage with riser profile ( Fig. 2) shows that the fatigue is 5593 Res. J. Appl. Sci. Eng. Technol., 4(24): 5591-5601, 2012 120 0.000040 wave 20 0.000035 100 wave 15 0.000030 Bending Moment kN.m 80 60 Fatigue damage 0.000025 0.000020 wave 10 40 0.000015 0.000010 wave 5 20 0.000005 0 0.000000 -20 -0.000005 -370 -360 -350 -340 Horizontal coordinate (m) -330 Fig. 4: Near and far offset bending moment profiles compared with fatigue damage for various waves 0.00004 4.5 wave 20 4 0.000035 0.00003 wave 15 3 0.000025 2.5 0.00002 2 wave 10 1.5 1 Fatigue damage Contact envelope, kPa 3.5 0.000015 wave 5 0.00001 0.5 0.000005 0 0 -0.5 -0.00000 -1 -370 -360 -350 -340 Horizontal coordinate (m) -330 Fig. 5: Contact envelope compared with fatigue damage for various waves study was performed and a wide range of parameters mostly derived in trench mouth where the TDP has are examined. As expected, the wave characteristics, longest travel courses. seabed stiffness and the trench depth were found having As will be shown in coming section, the shear considerable impacts on fatigue performance which will force crossing points of the near and far offsets are be briefly reviewed in coming sections. gradually moved toward the vessel end by increasing the number of load cycles but then stabilized for higher Influence of sea state characteristics: The sea states number of cycles and it is due to stabilization of trench No. 5, 10, 15 and 20 were selected and the initial profile, a fact that will be used for some evaluations analysis was repeated under selected loads. For easier later in this study. comparison of the results, only the near and far offset This starting analysis encouraged authors to deeply profiles at cycle 20 (end of the analyses) where plotted explore the parameters affecting the shear force, against the fatigue damage profiles ( Fig. 3, 4 and 5). As bending moment, riser and contact profile etc., in the seen, the wave characteristics is directly affecting the proximity of trench mouth over the various profile with a regular trend. representative load cycles. Comprehensive parametric 5594 Res. J. Appl. Sci. Eng. Technol., 4(24): 5591-5601, 2012 7 0.000025 Far offset shear Su0 = 1.0 kPa 5 0.000020 Su0 = 1.5 kPa 4 0.000015 3 0.000010 2 1 0.000005 Fatigue damage 6 Shear force kN Fatigue Near offset shear Su0 = 0.65 kPa 0 0.000000 -1 -2 -0.000005 -370 -360 -350 -340 -330 Horizontal coordinate (m) Fig. 5: Near and offset shear profiles compared with fatigue damage for different seabed stiffness 0.000025 120 Near offset bending Fatigue 0.000020 Su0 = 1.5 kPa 80 0.000015 Su0 = 1.0 kPa 60 Fatigue damage Bending Moment, kN.m 100 Far offset bending 0.000010 40 Su0 = 0.65 kPa 20 0.000005 0.000000 0 -20 -0.000005 -370 -360 -350 -340 -330 Horizontal coordinate (m) Fig. 7: Near and offset bending moment profile comared with fatigure damage for various seabed stiffness The contact envelope shown in Fig. 5 is in quite For all of the sea states the peak fatigue damage is agreement with results above. An important point is that about the location at which the shear profile of far and the TDP location is gradually moved towards the vessel near offsets are crossing. It is also interestingly seen end by increasing the wave height. It means, the trench that the variation of the peak shear force in near and far mouth is still the most indicative area in which the offsets are following opposite trends, but the average fatigue damage is derived, this is in absolute correlation shear in initial position is gradually changing parallel to with Fig. 2 where the peak fatigue position is shown to fatigue damage variation. This means though the near be somewhere between the TDP and trench bottom and far offset profiles are varying in relatively irregular point. scheme but the initial average can still be considered as It is accepted that the fatigue damage is increased a reference index for fatigue damage estimation which for seabed with higher stiffness. This has been will be further discussed in later sections. Illustration of examined here to explore the effect of stiffness the bending moment variation in far and near vessel variation on fatigue derivation mechanism for seabed offset over load cycles relative to fatigue damage in with stiffness in range of 0.65 to 1.5 kPa for undrained Fig. 4 shows logic correlation with shear force profiles shear strength. As illustrated in Fig. 6, the peak values as explained before in the current section. 5595 Res. J. Appl. Sci. Eng. Technol., 4(24): 5591-5601, 2012 of near and far offset shear forces are increased for stiffer seabed soil and this is same for fatigue damage itself. This in turn explains the main reason for such ascending trend. The contact pressure is increased for higher seabed stiffness which causes the increasing of shear force as seen above. This makes inverse change in bending moment particularly for near offset (Fig. 7) and the results is wider clearance between far and near bending moment profiles which means higher von Mises variation over load cycles and higher fatigue damage accordingly. Influence of trench depth: ROV surveys proves trench formation beneath the riser with couple of times of riser diameter (Bridge and Howells, 2007). This has been examined hear using extreme soil model parameters to make a trench in initial stages of fatigue analysis. Two trench depths have been examined here, 3D and 5D and the results are shown in Fig. 8 to 10. It is interestingly seen that insertion of deep trenches stabilize the variation of shear force and bending moment profiles keeping the peak fatigue position still at the point that near and far shear offsets are crossing. For the cases with presence of deep trenches most serious variations occur in near offset profiles and this is getting back to the high contact pressure of the riser with seabed in this course. As a common trend in all of these analysis the peak fatigue point is moved towards the vessel for 0.000035 10 Fatigue 8 Far offset shear 5D Trench 0.000030 Shear force kN 3D Trench 4 0.000020 2 0.000015 0 0.000010 -2 Fatigue damage 0.000025 6 0.000005 Near offset shear 0.000000 -4 -400 -380 -360 -340 -320 -300 Horizontal coordinate(m) -280 Fig. 8: Near and for offset profiled compared with fatigue damage for various trench depths 0.000035 140 Fatigue 120 Far offset shear 0.000030 0.000025 5D Trench 80 0.000020 3D Trench 60 40 0.000015 20 0.000010 Fatigue damage Bending Moment kN.m 100 0 0.000005 -20 Near offset shear -40 -400 -380 -360 -340 -320 -300 Horizontal coordinate (m) 0.000000 -280 Fig. 9: Near and far offset bending moment profiles compared with fatigue damage for various trench depths 5596 Res. J. Appl. Sci. Eng. Technol., 4(24): 5591-5601, 2012 0.000035 8 Far offset shear 0.000030 5D Trench 0.000025 4 0.000020 2 0.000015 3D Trench 0 Fatigue damage Contact pressure envelope kPa Fatigue 6 0.000010 -2 0.000005 Near offset shear -4 0.000000 -400 -380 -360 -340 -320 Horizontal coordinate(m) -300 -280 Fig. 10: Contact envelope compared with fatigue damage for various trench depths deeper trenches, stiffer seabed soil and more severe sea states. It is worth reminding hear that this for the cases having no slow drift and only the wave action is implemented. Figure 10shows contact pressure envelope in which by increasing the trench depth, the TDP moves towards the vessel end whilst the trench surface point in anchor side dose not considerably changes. Since the nature of fatigue is governed by changing in stress profiles, the fatigue damage is derived in trench mouth where we have the maximum variations. Rough estimation of fatigue damage on non-linear seabed without fatigue analysis: In a standard fatigue calculation, for an operating life that incorporates many millions of cycles of various stress ranges, the accumulated fatigue damage can be calculated using a linear cumulative damage, according to the well-known Miner’s rule. The fatigue analysis itself is considered as a time consuming process with extensive number of analysis for various load conditions. In the early stages of a project, designers usually wish to have a rough estimation of riser fatigue life in TDZ as a red line of riser projects based on seabed soil characteristics, because, the seabed stiffness governs the bed response to riser through contact pressure, which in turn makes the shear force distribution. The shear force itself is the gradient of bending moment, the key parameter to calculate von Mises stress range which in turn produce the fatigue damage and fatigue life accordingly. Since the mechanism of fatigue derivation in TDZ was relatively explored in the previous section, we are going to propose an approximation methodology enabling a rough estimation of peak fatigue damage of the riser in TDP on a non-linear hysteretic seabed, which can be quite valuable for designers in early stages of projects. As described by Barltrop et al. (1991) a standard form of S-N curves for marine structures to be used for fatigue calculations is: N = a .∆σ f −m (1) where, N = Is the number of cycles to failure a = Is an empirical coefficient ∆σ f = Is the factored stress variation range in MPa M = Is the inverse slope of the S-N curve For tubular elements as pipelines under bending moments, stress range variation is calculated in terms of von Mises stress. For SCRs the maximum von Mises stress can be written as follows: σ f − Max = H M TDP . D + As 2I (2) where, H = As = D = I = MTDP = Is tension force in riser Is riser section area Is riser diameter Is section moment of inertia Is bending moment in TDP The fatigue damage is calculated using the von Mises stress range ∆σ f within a load cycle, i.e., a cycle of vessel perturbation. Ignoring the minor changes in horizontal force in the Touchdown Zone 5597 Res. J. Appl. Sci. Eng. Technol., 4(24): 5591-5601, 2012 (TDZ) due to relocation of the touchdown point, ∆σ f can be approximated by the following relation: ∆σ f − Max ≈ ∆M TDP .D 2I (3) This equation can be simplified in terms of bending gradient, i.e., the product of average shear force and the TDP relocation, as: ∆σ f − Max ≈ V TDP − ave .∆ x TDP . D 2I (4) Fig. 6: Schematic view of vessel relocation and curve variation where, ∆xTDP =is the maximum TDP relocation under a si = zi vessel perturbation cycle V = is the initial/static maximum shear force in the sin θ i 1 − cos θ i (5) max TDZ ds i = To avoid complex finite element analysis we would need to propose closed form solutions for quick calculation of the main parameters defined in equation above. This can be done by combination of classical catenary equations for estimation of TDP relocation and an efficient boundary layer method for rough calculation of average shear force in TDP. TDP Relocation: Every change in vessel position due to load cycles applied by sea states will cause cyclic relocation of the touchdown point, which will in turn affect the SCR profile and stress distribution at the seabed. In a 2-Dimensional (2D) planar system, the vessel can have vertical (heave) and horizontal (surge) motion and the vessel rotation (pitch) can be converted into equivalent vertical and horizontal displacements taking into account the position of the attachment point of the riser, relative to the centre of gravity of the vessel. Figure 11 shows a schematic configuration of the SCR as the vessel moves from its initial position (denoted by subscript i) to a new relocated position (denoted by subscript r) under environmental loading. The positive and negative sign of the heave and surge offsets (a, b) are determined based on the designated coordinate system. The catenary length of the SCR hanging part, the horizontal distance of the TDP from vessel and the distance of the vessel from the seabed are taken to be always positive. According to traditional catenary equations the horizontal offset and the arc length in initial position are the functions of depth and hang off angle, so the TDP relocation can be expressed based on changes of these 2 parameters: si zi dz i − dθ i zi 1 − cos θ i x TDPi = z i dx TDPi = arcsin h (tan θ i ) cos θ i 1 − cos θ i x TDPi z − x TDPi tan θ i dz i + i dθ i zi 1 − cos θ i (6) (7) (8) The change in hang-off angle can be written as below using catenary equations: ∆θ = θ r − θ i = 1 − cos θ i 2 z i − x TDPi tan θ i ⎛ x − s i ⎞ (9) ⎜⎜ b − TDPi a ⎟⎟ z i ⎝ ⎠ substituting the change in vessel vertical and horizontal position, the TDP relocation can be written as below: ⎛s ⎞ xTDPi− si ⎞ ⎛ zi ⎟⎟a + ⎜⎜ ⎟⎟b ∆xTDP = sr − si = ⎜⎜ i + ⎝ zi 2zi − xTDPitanθi ⎠ ⎝ 2zi − xTDPitanθi ⎠ (10) TDZ peak shear force in initial configuration: Thus far, a range of different boundary layer methodologies have been to predict the analytical riser-seabed interaction overcoming the discontinuity of shear force and bending moment along the riser in the touchdown area (Palmer et al., 1974; Pesce et al., 1998; Croll, 2000; Lenci and Callegari, 2005). Such models are aimed to precisely evaluate SCR curvature in the touchdown zone, and also to ensure continuity of displacement gradient and shear force. As an example 5598 Res. J. Appl. Sci. Eng. Technol., 4(24): 5591-5601, 2012 of these methods, the model presented by Pesce et al. (1998) is selected and used in this work to find the analytical stress distribution in touchdown area. They applied a standard boundary layer technique to construct local consistent analytical solutions for the static/dynamic curvature problems, with the aim of smooth matching of the corresponding ‘outer’ ideal cable solution. A non-dimensional soil rigidity parameter is defined as: K = k λ 4 / EI = k λ 2 / H = kEI / H 2 (11) where, ݇= Is the soil rigidity per unit area E= Is the SCR Young’s Modulus I= Is the SCR second moment of inertia =ܪ Is the horizontal tension force at the TDP ߣ is a flexural length parameter that provides the boundary layer length scale, with a significant role in local solution. Its value is also interpreted as the distance between the actual and ideal cable TDP - given by: EI H λ = (12) Pesce et al. (1998) gives the following equations for the shear force distribution in the TDZ: V = ⎞⎫ ⎞ ⎛ K 0.25 ⎞ ⎧ ⎛ K 0.25 ⎛ K 0.25 ms gλ .K 0.25 exp ⎜⎜ (ξ − ξ f ) ⎟⎟ × ⎨cos ⎜⎜ (ξ − ξ f ) ⎟⎟ − sin ⎜⎜ (ξ − ξ f ) ⎟⎟ ⎬ 2 + K 0.25 ⎠⎭ ⎠ ⎝ 2 ⎠ ⎩ ⎝ 2 ⎝ 2 (13) if ξ < ξ f or m g λ . K 0 .25 V = s exp( − (ξ − ξ f )) 2 + K 0 .25 if ξ ≥ ξ (14) f f = 1 2 + K 0 . 25 ⎛ 1 − K ⎜ 0 . 25 ⎝ K 0 . 25 ⎞ ⎟ ⎠ X (15) v max − in m s g λ .K 2 + K = 0 . 25 (16) 0 . 25 λ 2 + K 0 . 25 ⎛ 1 ⎜ 0 . 25 − K ⎝ K 0 . 25 ⎞ ⎟ ⎠ (17) Examination of proposed method: The vessel has been exited by one cycle of sea state No. 20 on a nonlinear seabed with undrained shear strength of 0.65 kPa at mudline and a gradient of 1.5 kPa per meter in depth. Figure 12 shows the shear force distribution for far and near offsets of the vessel comparing with vessel initial configuration, the hang-off angle and water depth is as per the configuration illustrated in Fig 1. The magnitude of TDP relocation (XTDP) for Wave No.20 based on the Equation 10 extracted from traditional catenary equations in last section is about 6.2 m. To calculate the maximum shear force by boundary layer method the linear seabed stiffness is required; for the riser not deeply penetrated into the seabed this value can be roughly taken as about ten times of undrained shear strength in mudline which is 0.65 kPa in this analysis, then the seabed stiffnes, k will be about 5.2 kPa. Using the boundary layer equation given before the magnitude of parameter K will equals to 1.4, so the maximum shear force for initial configuration can be calculated as below (Eq.16): − in = 100 × 9 . 81 × 10 . 59 × (1 . 4 ) 0 . 25 = 4 . 52 kN 1000 × ( 2 + (1 . 4 ) 0 . 25 ) The calculated value is almost equal to the peak shear force value obtained from finite element analysis shown in Fig, 12. Using the Eq. 5 the von Mises stress range can be calculated as below: ∆σ and ξ = ξ f is the non-dimensional form of actual TDP = − in As shown before in this paper in parametric study of the effect of load cycles and sea state characteristics on shear force distribution, the peak shear force in TDZ for initial vessel configuration is gradually varied for cyclic loading on non-linear seabed. These effects shall be implemented on analytical estimation of peak shear force, but before that we need to examine the accuracy of the proposed methodology for a given configuration. V max where, msg is the weight of the riser unit length, ξf is the ideal position of the TDP, defined as: ξ V max f − Max ≈ 4 . 52 × 6 . 2 × 0 . 324 1000 × 2 × 0 . 000226 = 20 . 1 MPa as shown in Fig. 13 the peak magnitude of von Mises variation is about 18 MPa. This means the closed form solution has an accuracy about 90% which is quit interesting. In another word, the fatigue life can be estimated by analytical solution without performing 5599 position (x/ λ ). The peak value of shear force and its distance for ideal TDP can be obtained by differentiation of Eq. (13) and (14) which occurs, as expected, at ξ = ξ f : Res. J. Appl. Sci. Eng. Technol., 4(24): 5591-5601, 2012 cycles. Comprehensive parametric study was performed and a wide range of parameters are examined. As expected, the wave characteristics, seabed stiffness and the trench depth were found having considerable impacts on fatigue performance. Be side that an approximation methodology was proposed to estimation of peak fatigue damage of the riser in TDP on a non-linear hysteretic seabed, which can be quite valuable for designers in early stages of projects. The fatigue life can be estimated by analytical solution without performing extensive fatigue analysis with a tolerance of about 10% which can be very appealing for design engineers. 6 Initial peak Shear force, kN 5 4 Far offset 3 Near offset 2 1 Initial 0 -1 -400-390-380-370-360-350-340-330-320-310-300-290-280 Horizontal coordinate (m) Voin Mises, MPa Fig. 12: Initial, near and far offset shear profiles 30 20 10 0 -10 -20 -30 -40 -50 -60 REFERENCES Peak von Mises Range Von Mises Range Max von Mises Min von Mises -400-390-380-370-360-350-340-330-320-310-300-290-280 Horizontal coordinate (m) Fig. 7: Von Mises stress envelope and variation range extensive fatigue analysis with a tolerance of about 10% which can be very appealing for design engineers. Now it is time to implement the influence of number of wave cycles as the parameter gradually vitiating the shear force distribution along the riser in TDZ. Combining the curve fits proposed before in parametric study the Equation 16 can be written as below: V max − var = V max − in ( 1 ) 0 .08 n c ycle (18) This equation implements the invers influence of number of wave cycles on peak shear force in initial configuration. CONCLUSION The mechanism of fatigue generation in TDZ was studied through use of the hysteretic non-linear seabed. The nature of the relationship between the gradual embedment of the riser into the seabed and fatigue damage generation was investigated and the parameters affecting the shear force, bending moment, riser and contact profile was deeply explored in the proximity of trench mouth over the various representative load Barltrop, N., A. Adams and M.G. Hallam, 1991. Dynamics of Fixed Marine Structures. Butterworth-Heinemann, London, pp: 764, ISBN: 0750610468. Bridge, C.D. and H.A. Howells, 2007. Observations and modeling of steel catenary riser trenches. Proceedings of the 17th International Offshore and Polar Engineering Conference, Lisbon, Portugal, July, 1-6, 2007, pp: 803, ISBN: 978-1-880653-685. Clukey, E., R. Ghosh, P. Mokarala and M. Dixon, 2007. Steel Catenary Riser (SCR) design issues at touch down area. Proceedings of the Seventeenth International Offshore and Polar Engineering Conference, Lisbon, Portugal, July, 1-6, 2007, pp: 814, ISBN: 978-1-880653-68-5. Croll, J.G.A., 2000. Bending boundary layers in tensioned cables and rods. Appl. Ocean Res., 22(4): 241-253. Giertsen, E., R. Verley and K. Schroder, 2004. CARISIMA a catenary riser/soil interaction model for global riser analysis. Proceedings of the International Conference on Offshore Mechanics and Arctic Engineering OMAE2004, June 20-25, Vancouver, BC, Canada, pp: 633-640. Karunakaran, D., K.A. Farnes and E. Giertsen, 2004. Analysis guidelines and application of a riser-soil interaction model including trench effects. Proceedings of the International Conference on Offshore Mechanics and Arctic Engineering OMAE2004, June 20-25, 2004, Vancouver, BC, Canada, ASME, NY, USA, pp: 955-962. Langner, C.G., 2003. Fatigue Life Improvement of Steel Catenary Risers due to Self-Trenching at the Touchdown Point. Offshore Technology Conference, Houston, Texas, USA, pp: 11, ISBN: 978-1-55563-250-2. Lenci, S. and M. Callegari, 2005. Simple analytical models for the j-lay problem. Acta Mechanica, 178(1-2): 23-39. Nakhaee, A. and J. Zhang, 2008. Effects of the interaction with the seafloor on the fatigue life of a SCR. International Offshore and Polar Engineering 5600 Res. J. Appl. Sci. Eng. Technol., 4(24): 5591-5601, 2012 Conference, Vancouver, BC, Canada, July 6-11, pp: 87, ISBN: 978-1-880653-70-8. Palmer, A.C., G. Hutchinson and J.E. Ells, 1974. Configuration of submarine pipelines during laying operation. ASME J. Engng. Indust., 96: 1112-1118. Pesce, C., J. Aranha and C. Martins, 1998. The soil rigidity effect in the touchdown boundary-layer of a catenary riser: Static problem. Proceedings of the 8th International Offshore and Polar Engineering Conference, International Society of Offshore and Polar Engineers, Montreal, Canada, No. 207. Randolph, M.F. and P. Quiggin, 2009. Non-linear hysteretic seabed modelfor catenary pipeline contact. Proceedings of the 28th International Conference on Ocean, Offshore and Arctic Engineering OMAE 2009, Honolulu, Hawaii, USA, pp: 1-10. Rezazadeh, K., H. Shiri, L. Zhang and Y. Bai, 2012. Seabed trench formation and its impact on fatigue life of steel catenary risers in touchdown area. The 22th International Offshore and Polar Engineering Conference ISOPE2012, Rhodos, Greece, pp: 20051. Shiri, H. and M. Randolph, 2010. Influence of seabed response on fatigue performance of steel catenary risers in touchdown zone. Proceeding of the 29th International Conference on Offshore, Ocean and Arctic Engineering OMAE2010, Shanghai, China, pp: 63-72. 5601