otc 20197 templeton fea of conductor seafloor interaction

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Finite Element Analysis of Conductor/Seafloor Interaction J. S. Templeton, III, SAGE USA, Inc.

Copyright 2009, Offshore Technology Conference This paper was prepared for presentation at the 2009 Offshore Technology Conference held in Houston, Texas, USA, 4–7 May 2009. This paper was selected for presentation by an OTC program committee following review of information contained in an abstract submitted by the author(s). Contents of the paper have not been reviewed by the Offshore Technology Conference and are subject to correction by the author(s). The material does not necessarily reflect any position of the Offshore Technology Conference, its officers, or members. Electronic reproduction, distribution, or storage of any part of this paper without the written consent of the Offshore Technology Conference is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 300 words; illustrations may not be copied. The abstract must contain conspicuous acknowledgment of OTC copyright.

Abstract

This paper presents results of finite element analysis of the lateral interaction of well conductors with soil. Nonlinear, 3-D finite element analyses were performed for the site conditions at an actual deep water production system location as well as for comparison to results from centrifuge model tests. Both static and cyclic analyses are reported. The analyses incorporated elastic-plastic, work hardening models of soil behavior. The model of soil behavior included in these analyses was an elastic-plastic, work hardening model tied precisely to the site specific stress-strain soil behavior exhibited in high quality advanced soil test data or to model soil properties, as appropriate. The soil behavior modeling replicated both static and dynamic behavior of the site soils including both low level stiffness response and also the damping provided by soil hysteresis. The product of the analyses reported in this paper produced fundamentally-based p-y curves to represent the equivalent lateral soil reactions on the conductor. These equivalent p-y curves were appropriate for use in nonlinear dynamic analyses of soil-conductor interaction of the entire riser and conductor system. The results published in this paper achieve a new level for realism and accuracy in the characterization of lateral soil/conductor interaction. This is demonstrated through fundamentally based analysis by achieving simultaneously analyses accurately tied to high quality soil test data, producing and results more consistent with centrifuge test data than have previously been published. Introduction

The finite element method is experiencing increased use in offshore foundation engineering. The finite element method is a technique for solution of mathematical problems governed by systems of partial differential equations. It can produce close approximate solutions to problems with highly complex geometries, material behaviors and boundaries which would result in highly complex feildwise variations in the solution variables. With respect to the true solution to a properly posed boundary value problem in solid mechanics, taken as an ideal, one can generally obtain a finite element solution that is as close to the ideal as is desired, so long as one can work the problem within program capabilities and pay the required attention to minimizing any unavoidable errors. (See Templeton, 2002.)

The objective of the work reported here was to provide, via finite element analysis, fundamentally-based numerical results for the lateral interaction of well conductors with their surrounding soil. The work is important because the conventional methods for assessment of conductor lateral performance, i.e. the application of “p-y” curves as formulated in API RP2A (2000) for pile performance, may underestimate the stiffness of the soil-conductor interaction. The determination of more realistic p-y relations can enable elimination of undesirable over-conservatism in fatigue analyses of the riser/conductor systems for deep water . Jeanjean (2009) discusses the importance of a realistic and accurate assessment of this interaction. Figure 1 (from Jeanjean, 2009) shows a diagram of the arrangement of vessel, risers, conductors and soil in a deepwater floating production system. The finite element analysis techniques and results described in this paper have been applied to four deep water offshore development projects. This paper discusses the applications to two offshore sites as well as comparison to experimental results from centrifuge model testing.

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Wind and waves forces

cause vessel motions Some current conditions

cause hull VIM Hull Figure 1. Vessel, risers conductors, and soil Figure 2. Finite element mesh for conductor and surrounding soil Static Analysis for Offshore Site

Finite element analyses were performed for the lateral performance of a 3-ft diameter, 2-inch wall thickness well conductor in clay soil with properties based on soil conditions for a deep water offshore site (Figuree 1). The objective was to provide analysis of the performance of well conductors under lateral loading including the effects of rate, cyclic loading and strain range. The work was undertaken because the conventional methods for assessment of conductor lateral performance (application of “p-y” curves as formulated in API RP2A for pile perormance) could underestimate the stiffness of the soil-conductor interaction. The development of more realistic p-y relations could allow elimination of undesirable over-conservatism in fatigue analyses of the riser/conducter systems. Since the interest in this problem included both low level stiffness response and also the damping provided by soil hysteresis, analyses were planned for both static and cyclic loading conditions. This section covers the static analysis. The approach taken to the static problem included 3-D nonlinear total stres analysis with the ABAQUS program. For the soil behavior an elastic-plastic, work hardening model with Mises yield was used. Soil properties were based on direct simple shear and resonant column test data. The basic geometry of the model used is shown on Figure 2. Symmetry conditions permitted use of a half-space model (180 degrees about the conductor axis). The model included finite elements out to a diameter of 120 ft (40 times the conductor diameter) and infinite elements beyond that diameter. The solid continuum elements used to represent the soil were 8-node brick elements. The conductor was modeled with 4-node shell elements, 2 inches thick, using an elastic-perfectly plastic behavior and properties of 60 ksi steel. The conductor was modeled down to a depth of 200 ft, at which depth its displacement was fixed. The soil was modeled as an elastic-plastic, work hardening material with Mises yield.

Figure 3 shows a plot of Gmax/Su (ratio of maximum shear modulus to undrained shear strength) vs. depth (from mudline) for the subject site. The shear moduli presented here are based on resonant column test data plus allowances for overburden, over-consolidation, void ratio, rate of loading and time effects. The two curves presented reflect the application of two alternate available correlations of Gmax to void ratio. Figure 4 shows these same data plus an additional simplified plot of interpreted values for use in the finite element analyses. The plot of interpreted values approximates the two plots of calculated values to a degree consistent with the difference between the two calculated plots. All of these plots are based upon undrained shear strengths, Su, equal to 8 psf per foot of penetration. This 8 psf per foot strength distribution approximates the offshore strength interpretation – without any correction for rate of loading. Application of a rate of loading correction (appropriate to vortex induced vibration of the riser) results in an interpreted undrained shear strength of approximately 10 psf per foot.

Current forces cause riser VIV

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Figure 3. Gmax/Su profile Figure 4. Gmax/Su profile plus straight line interpretation

Figure 5 shows the same plots as Figure 4 plus an additional plot for the interpreted Gmax/Su values based on this rate adjusted strength interpretation. Figure 6 presents a comparison of normalized stress strain data between results of direct simple shear test and the elastic-plastic work hardening model used in the static finite element analysis. In the model, purely elastic behavior was taken up to 10 percent of the ultimate strength. The stress strain curvature beyond this initial yield point was provided by the (isotropic) plastic work hardening behavior. Distinct stress strain behavior was used for each soil element layer in the finite element model. For each soil layer the rate adjusted ultimate shear strength was taken from the 10 psf per foot rate adjusted interpretation. The Gmax was then formed by combination of this strength with the Gmax/Su interpretation plotted in Figure 5. The stress strain behavior was taken as elastic with slope given by this Gmax, up to the initial yield point. Beyond the initial yield point, the stress strain behavior was given at each stress by additive combination of the elastic strain and a plastic strain based on the particular ultimate strength and the plastic part of the normalized stress strain curve of Figure 6.

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Figure 5. Gmax/Su profile plus rate corrected interpretation Figure 6. Stress-strain data (1_44b_NF) compared to elastic- plastic work hardening model (linear piece fit)

The static loading applied to the conductor was a lateral load with no moment restraint at the mudline. This applied lateral load was increased until very large lateral displacements were achieved. The results of the static analysis are presented graphically in Figures 7 through 9. Figure 7 presents the lateral load vs. displacement curve at the mudline. Figures 8 and 9 present p-y curves for various stations along the depth of the conductor. Figure 8 shows the most representative p-y result. This slide shows a comparison at the 23.3-ft depth between a p-y curve based on lateral soil reaction results from the finite element analysis and p-y data based on API RP2A formulae. At this depth the soil reactions in both the API calculations and

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the finite element results have fully transitioned from the shallow type to the deep type of lateral soil reaction. At shallower depths the finite element results may reflect a different rate of deep-to-shallow transition that that prescribed by API formulations. At greater depths the comparison is complicated by a softening phenomenon apparent in the finite element results. This softening may result from interaction of displacement and rotation of the conductor. Such softening is observed in experimental results but not provided in the API formulations.

P - Y Curves at 23.3 ft PenetrationElastic-Plastic Isotropic Hardening Soil

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Figure 9 presents similar p-y curve comparisons for a selection of depths ranging from 2 ft to 30 ft. The comparisons in all of these slides show that although the finite element results and API formulation give the same general shape of p-y curve, the finite element results in this case are substantially stiffer and stronger. We believe that the finite element results are the more realistic because they are fundamentally based and they are more consistent with the published results of more recent experimental studies including centrifuge tests.

Cyclic Analysis for Offshore Site

Finite element analyses were also performed to investigte the cyclic lateral performance of well conductors at the offshore site. The cyclic analyses were performed using the same mesh as was used in the static analyses. Symmetry conditions again permitted use of a half-space model (180 degrees about the conductor axis). The model included finite elements out to a diameter of 120 ft (40 times the conductor diameter) and infinite elements beyond that diameter. The solid continuum elements used to represent the soil were 8-node brick elements.

As in the case of the previous static analysis we used an elastic-plastic, work hardening, soil behavior model with Mises yield. Soil properties were based on direct simple shear and resonant column test data. The static analyses had been performed using an isotropic hardening model, but for the cyclic analysis, the need to model properly the hysteretic soil behavior indicated the use of a kinematic hardening model. The kinematic hardening model available did not permit quite as precise a fit to the soil stress-strain data as had been possible with the isotropic harening model, but the fitting errors incurred due to this limitation were small compared to the data uncertainties, and the effects on the overall model performance were not significant. Figure 10 shows stress-strain plots for the models used in comparison to the data. The upper plot on this figure shows 4 work hardening models in comparison to the available site data. The stresses plotted are all normalized by peak strength values. In addition to the isotropic hardening model used in the prior analyses, three kinematic hardening models are shown, a stiff case, medium case and a soft case. The data shown here include 4 samples with apparent data quality problems, as labeled. The plot of Figure 11 includes only the data judged best. The range of the 3 kinematic hardening models encompases reasonably well the range of these best data. The isotropic hardening model lies generally within the range of the 3 kinematic hardening models.

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P - Y Curves at 4 ft PenetrationElastic-Plastic Isotropic Hardening Soil

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elastic - plastic exponential kinematic hardening, upper stiff caseelastic - plastic exponential kinematic hardening, medium caseelastic - plastic exponential kinematic hardening, lower soft caseelastic - plastic isotropic hardening, piecewise linear fit to best dataData, Holstein sample 1_31e: Apparatus stuck up to ~ 40% of tau max?Data, Holstein sample 1_31b: No data below ~ 75% of tau maxData, Holstein sample 1_44bData, Holstein sample 1_23bData, Holstein sample 1_50b: Possible minor slip up to 0.3% strain?Data, Holstein sample C3_2b: Premature slip below 2% strain ?

Figure 10. Stress-strain models for soil behavior compared to site data

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Monotonic (static) loading analyses were performed with all 3 kinematic hardening models. Load vs. displacement results from these analyses were compared to corresponding results for the isotopic hardening model. Figure 12 shows the results of this comparison. The isotropic hardening results were typically within the range of the kinematic hardening results. Moreover, the range of differences amoung all four cases was judged inconsequentially small. On this basis, the medium kinematic hardening model was accepted for use in the cyclic analyses. Using the medium stiff kinematic hardening model, we performed pseudo-static cyclic analyses at 9 different load levels. In these analyses, completely reversed cyclic lateral loading was applied to the conductor with no moment restraint at the mudline.

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The pseudo-static cyclic analyses capture the effects of energy dissipation due to hysteretic soil behavior, but they do not include effects of inertial dynamics in the soil. At wave frequencies we would generally expect the former to be more important, but the latter may also be significant. In order to make a preliminary investigation of the possible importance of soil inertial dynamics, we also performed a few approximate analyses including inertial dynamic effects in the soil.

The results of the cyclic analysis are presented graphically in Figures 13 through 18. Figure 13 presents cyclic load vs. displacement results for 6 different levels of completely reversed cyclic loading with load amplitudes ranging from 20 kips to 500 kips. In these plots, the hysteretic nature of the cyclic soil behavior is clearly reflected in the resulting hysteresis in the load vs. displacement loops. It is also clear in these results that the significance of the system hysteresis (from the standpoint of the amount of energy dissipated) increases dramatically with cyclic load level.

The hysteretic nature of the cyclic soil behavior is also reflected in the lateral soil reactions, or P-Y, curves. Figure 14 shows a typical example. This plate presents p-y curve loops for the 11-ft penetration resulting from three different levels of cyclic loading. In the cyclic p-y results it is again clear that the significance of the hysteresis increases dramatically with cyclic load level.

It is further evident both in the load vs. deflection results and in the p-y results that the monotonic loading results effectively form “backbone” curves for the cyclic behavior. This, in turn, suggests that the monotonic loading results could be used to construct accurate approximations to the cyclic behavior via the “Masing rules.” We tested this by developing equivalent linear stiffness and energy dissipation parameters both from the cyclic analysis results and (via. Masing rules) from the monotonic loading results. We did this for the load vs. deflection results and also for the p-y results.

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CYCLIC P-Y RESPONSE AT 11-FT PENETRATION

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Figure 15 shows the equivalent linear stiffness and energy dissipation parameters developed from the load vs. deflection results. The parameters displayed here include the equivalent stiffness, Ksecant, the energy dissipation ratio and the damping ratio. The normalized equivalent stiffness, K_bar, also displayed, is the secant stiffness divided by it’s maximum value. The energy dissipation ratio is the energy dissipated per cycle divided by the energy that would be dissipated per cycle by a perfect Coulomb damper operating over the same range of load and displacement. The equivalent damping ratio is the fraction of critical damping required for a resonant single-degree-of-freedom system with the same equivalent stiffness to dissipate the same amount of energy per cycle. The stiffnesses, the energy dissipation ratio and the damping ratio are all plotted vs. double amplitude cyclic displacement. Cross plots are also provided for the energy dissipation ratio and the damping ratio vs. the normalized stiffness. The equivalent stiffness and damping ratio are also plotted vs. the double amplitude displacement on log as well as linear scales. In all of these plots, the discrete data points are based on the cyclic analyses, and the continuous lines are based on the monotonic loading analyses.

Figure 16 shows the equivalent linear stiffness and energy dissipation parameters developed from the p-y results. The plots presented in Figure 16 are for the same variables as those in Plate 5, except that the stiffness is plotted on a per unit area basis and the damping ratio (which does not have a clear interpretation on a per unit area basis) is not presented. On both Figure 15 and Figure 16, all of the data points based on cyclic analyses compare favorably with values on the corresponding lines based on monotonic analyses.

Figure 17 presents results from the analyses including inertial dynamics effects for the soil. This plate includes plots of conductor head load vs. displacement results from inertial dynamic analyses for three different cyclic periods compared to corresponding results from pseudo-static cyclic analysis. Over a range of periods from 0.1 second to 10 seconds, the inertial dynamic effects vary from dominant to insignificant. The dynamic analysis results for a 10 second period are essentially equivalent to the pseudo-static cycling results. With a period of 1 second, the inertial effects contribute significant additional damping. With a period of 0.1 second, the inertial effects dominate the response. The additional damping apparent in the inertial dynamic analyses is the consequence of an energy dispersion phenomenon, commonly called “radiation damping,” in

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which energy is removed from the vicinity via wave propagation. These results suggest that soil radiation damping effects may be significant to the conductor dynamics.

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Figure 16. Equivalent linear stiffness and dissipation for soil reactions at 11 ft penetration, analysis of cyclic lateral performance

Analysis for Centrifuge Test Comparison

Jeanjean (2009) describes a centrifuge test program directed at the acquisition of high quality experimental data relevant to the same problems of conductor lateral performance that are the object of the finite element studies being reported here. Using the same procedures as described for the offshore site case, finite element analyses were performed modeling the physical parameters of that centrifuge test program. These finite element analyses were performed using dimensional and material behavior data from the centrifuge tests, but the analyses were performed completely blind of the test results.

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Cyclic Load vs. Displacement Loops Effect of Inertial Dynamics

-60

-40

-20

0

20

40

60

-0.15 -0.10 -0.05 0.00 0.05 0.10 0.15

Displacement, ft

Load

, kip

s

Dynamic analysis (T=0.1sec)

Dynamic analysis (T=1sec)

Dynamic analysis (T=10sec)

Pseudo-static cycling analysis

Figure 17. Cyclic load vs. displacement, effect of inertial dynamics, analysis of conductor cyclic lateral performance The following chart shows the shear strength profile. The given data are for DSS tests. They were corrected using the following factor

⎟⎟⎠

⎞⎜⎜⎝

⎛ ××+=

RC

DSSSu T

TLogf 1.01.01 10

where: TDSS is the time period for peak shear strain, taken as 279 minutes. TRC is the time period for peak shear strain for an assumed resonance test. This is assumed to be given as 3 seconds. The factor 0.1 corresponds to the approximate fraction of strength assumed mobilized under centrifuge testing.

Figure 18 shows the (prototype scale profile of shear strength with depth. A Gmax/Su value of 550 was estimated in view of the plasticity of the site soils and the data of Andersen (2004). This resulted in the (prototype scale) Gmax profile shown in Figure 19. Using these profiles of strength and modulus, the soil was modelled with an elastic-plastic, work hardening model, and analyses of the lateral performance were performed using the same procedures as used for the offshore site analysis.

OTC 20197 13

1.25

11.25

21.25

31.25

41.25

51.25

61.25

71.25

0 0.1 0.2 0.3 0.4 0.5 0.6Su (ksf)

Dep

th (f

t)

Figure 18. Strength profile for finite element analysis of centrifuge test (prototype scale)

1.25

11.25

21.25

31.25

41.25

51.25

61.25

71.25

0 50 100 150 200 250 300 350 400

Gmax (ksf)

Dep

th (f

t)

Figure 19. Maximum shear modulus profile for finite element analysis of centrifuge test (prototype scale) The analysis results for p-y reaction curves are shown in Figure 19 and compared to corresponding calculated results based on API RP-2A and to the centrifuge test results from Jeanjean (2009). Complete details of the centrifuge test program are presented by Jeanjean (2009). The overall level of agreement between the centrifuge test data and finite element results is truly remarkable, particularly in view of the fact that the analyses were done blind of the test results. It is also extremely significant that the finite element and centrifuge test results are both substantially and similarly different from the API RP-2A recommendations for lateral pile performance. The analytical and experimental results consistently indicate much greater values of both initial stiffness and maximum reaction than do the API RP-2A recommendations. This result has significance well beyond the application to well conductors. Both the analysis and test results should apply to lateral performance of foundation piles as well. Both finite element analysis and centrifuge testing are, of course, subject to some unavoidable error. The best that one can normally do is to try to minimize the analytical and experimental errors by attention to details known to be at cause. The nature and source of errors in finite element analysis and in centrifuge testing are well known, however, and they are completely different. For the numerical analyses and physical experiments to produce entirely similar errors form distinctly different sources, would be literally incredible. Consequently, the agreement between the finite element and centrifuge test results provides strong validation for both the analyses and the experiments.

14 OTC 20197

Figure 20. Normalized p-y curves for lateral soil reactions on well conductor: FEA results compared to API recommendations and to centrifuge test results, from Jeanjean (2009)

0 0.1 0.202468

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API WSD 21stAPI WSD 21st ErrataFEACentrifuge

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OTC 20197 15

Conclusions Based on the work reported here the following conclusions are made:

1. The use of finite element analysis published in this paper has demonstrated a new level for realism and accuracy in

the characterization of lateral soil/conductor interaction. This was accomplished through fundamentally based analysis by achieving simultaneously analyses accurately tied to high quality soil test data, producing and results more consistent with centrifuge test data than have previously been published.

2. The analytical and experimental results consistently indicate much greater values of both initial stiffness and maximum reaction than do the API RP-2A recommendations. This result has significance well beyond the application to well conductors. The results should apply to lateral performance of foundation piles as well

3. The high quality geotechnical data such as were available for the offshore site soils can be modeled satisfactorily with elastic-plastic, work hardening models of soil behavior.

4. In analyses with monotonic (static) loading, the kinematic hardening soil behavior models employed here produced results which very closely approximated the results from analyses performed using the isotropic hardening model used previously in this study.

5. In analyses with cyclic loading, the kinematic hardening soil behavior models employed here produced results which satisfactorily embodied the expected hysteretic nature of cyclic soil-conductor interaction.

6. Equivalent linear stiffness and hysteretic damping (or energy dissipation) parameters for the conductor head reactions as well as for the lateral (p-y) soil reactions were successfully derived from results of both the cyclic and the monotonic analyses.

7. Additional damping from inertial dynamic effects may also be significant particularly in the case of cyclic loading with periods of one second or less. For periods on the order of fractions of seconds, it could be a dominant effect.

Acknowledgements The author acknowledges the owners of the data herein, BP America Inc. and Shell Exploration & Production Co., and is

grateful for their permission to publish. The author also specifically acknowledges the important contributions to the work that were made by Edward C. Clukey, Ph.D., Philippe Jeanjean, Ph.D. and Eric Liedtke, Ph.D. of BP. These engineers all provided valuable guidance throughout the course of the work. They had the vision to see that valuable results could be obtained from an advanced engineering approach to better assessment of the lateral interaction of well conductors with their supporting soil than is possible with conventional methods. The author wishes to acknowledge the contributions of other SAGE engineers who made important contributions to the work. F. B. Biegler, Z. M. Oden Duffy, Ph.D. and A. A. Rahim, Ph.D. contributed to the work via construction of finite element models, characterization of material behavior, conduct of analyses and organization of results. The finite element analyses were performed with the ABAQUS program (Versions 6.4 through 6.6) from Hibbitt, Karlsson and Sorensen Inc., ABAQUS Inc. and Dassault Systemes SIMULIA. References Andersen, K. H.(2004), “Cyclic Clay Data For Foundation Design of Structures Subjected to Wave Loading,” Proc.

International Conference on Cyclic Behaviour of Soils and Liquefaction Phenomena, Ed Th. Triantafyllidis, A. A. Balkema Publishers, Bochum, Germany, CBS04, 2004. p. 371 – 387

API RP2A (2000), “Recommended Practice for Planning, Designing and Constructing Fixed Offshore Platforms-Working Stresses Design,” 21st Edition, December 2000.

API RP2A-WSD Errata (2007), “Errata and Supplement 3 to API Recommended Practice 2A-WSD. Recommended Practice for Planning, Designing and Constructing Fixed Offshore Platforms-Working Stresses Design,” 21st Edition, December 2000.” October 2007.

Jeanjean, P. (2009): "Re-Assessment of P-Y Curves for Soft Clays from Centrifuge Testing and Finite Element Modeling," Proceedings, Offshore Technology Conference, Houston, TX, Paper Number 20158.

Templeton, J. S. (2002), “The role of finite element analysis suction foundation design,” Proceedings Offshore Technology Conference, Houston, TX, Paper Number 14235.

otc 20197 templeton fea of conductor seafloor interaction

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