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Shell UK Exploration & Production Sub-sea Conductor Study LS-DYNA Three dimensional modelling of conductors under combined axial, bending and torsion loading
February 1999
Ove Arup & Partners Arup Geotechnics 13 Fitzroy Street London W1 P 6BQ Telephone +44 (0)171 636 1531 Facsimile +44 (0)171 465 2121 Job number 50169-08
POve Arup & Partners
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Document Verification
Arup Geotechnics
P
Job title
Sub-sea Conductor Study
Job number
50169-08
Document title Document reference
LS-DYNA Three dimensional modelling of conductors under combined axial, bending and torsion loading
Prepared by
Chris Humpheson
Signed Date
L2./ L/ 4C4
Chris Humpheson
Checked by
C.
Signed
LL>
Date
tl
c
Q
David Clare
Approved by Signed
*
Date
Z
HvLc
Revision record Revision
Date
Description/Filename
Prepared
Checked
Approved
1/97
07/11/97
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CH
CH
DGC
1/99
22/2/99
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CH
CH
DGC
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Ove Arup Partnership F8.5 Rev 1/99 22 February 1999
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Job title
Revisions
Ove Arup & Partners Arup Geotechnics
Sub-sea Conductor Study
Page 1 of ?
Job number
50169-08 Document title Document reference
LS-DYNA Three dimensional modelling of conductors under combined axial, bending and torsion loading
Revision
Date of issue
1/97
.07/11/97
1/99
22/02/99
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Description
First draft. Issued for comment.
Final
Ove Armp & Partners Rev 1/99 22 February 1999
Shell UK Exploration & Production
Sub-sea Conductor Study
CONTENTS SUMMARY 1.
INTRODUCTION
2.
PREVIOUS STUDIES BY SHELL
3. 3.1 3.2
STUDY DATA Soil Conditions Loads 3.2.1 Trawler Net 3.2.2 Thermal Loads Conductor Strings Connector Properties Pipe Properties
3.3 3.4 3.5 4. 4.1 4.2 4.3 4.4 4.5
METHODS OF ANALYSIS General Assumptions Analysis Procedures ALP Analyses LS-DYNA Analyses 4.4.1 Description of Program LS-DYNA Continuum Model 4.5.1 Geometry 4.5.2 Casings 4.5.3 Conductor 4.5.4 Connectors 4.5.5 Grout
4.5.6
4.6
5. 5.1 5.2
5.3
4.5.7 4.5.8 4.5.9 4.5.10 4.5.11 LS-DYNA 4.6.1 4.6.2 4.6.3 4.6.4 4.6.5
Soil Boundary Conditions Material Properties Soil-grout interface Loading Damage Identification Beam and Spring Model Conductor Casing Lateral Load Behaviour p-y Springs Skin Friction t-z Spring Loads Modelling Inaccuracies
STUDY RESULTS Analysis Strategy Lateral and Moment Loading Only 5.2.1 ALP p-y Analyses 5.2.2 ALP Elastic-Plastic Soil Model 5.2.3 LS-DYNA Beam and Spring Model 5.2.4 ALP and LS-DYNA Comparisons Combined Lateral, Moment, Vertical and Torsion Loading 5.3.1 Analyses Carried Out 5.3.2 Design Case HT1A-HB (API) 5.3.3 Results of LS-DYNA Beam and Spring Model Analyses 5.3.4 Results for Hard Soil Profile 5.3.5 Results for Medium Soil Profile
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Shell UK Exploration & Production
Sub-sea Conductor Study
5.3.6 Results for Soft Soil Profile 5.3.7 Axial and Bending Stresses 5.3.8 Comparison of Results for first ST-2RB Connector 5.3.9 Grout to Casing Shear Stresses Review of Results 5.4.1 Spalling of Grout 5.4.2 Axial Thermal Loads
5.4
6.
TEMPERATURE EFFECTS
7. 7.1
CONCLUSIONS Conductors in Hard Soil Conductor String HT1A Conductor String HT2A Conductors in Medium Soil Conductor String HT2B Conductor Strings HT3B and HT4B Conductors in Soft Soil Conductor Strings HT3B and HT4B Grout to Casing Shear Stresses Effects of Heating on Geotechnical Properties
7.2
7.3 7.4 7.5 8. 8.1 8.2
REVIEW OF ANALYTICAL METHODS Assessment of Results Improvements to Modelling Techniques 8.2.1 Detailed Modelling of Conductor and Grout 8.2.2 Improved Continuum Model 8.2.3 Improved Grout to Soil Interface
9.
RECOMMENDATIONS FOR FURTHER WORK
10.
REFERENCES
FIGURES Figure Figure Figure Figure Figure Figure Figure Figure Figure
3.1 3.2 3.3 4.1 4.2 5.1 5.2 5.3 5.4
Figure 5.5 Figure 5.6 Figure 5.7 Figure 5.8 Figure 5.9
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Undrained Shear Strength. Hard Soil Profile Undrained Shear Strength. Medium Soil Profile Undrained Shear Strength. Soft Soil Profile Cut Section Through LS-DYNA Continuum Model Skin Friction Model for LS-DYNA Beam and Spring Analyses ALP p-y Results for Hard Soil Profile ALP p-y Results for Medium Soil Profile ALP p-y Results for Soft Soil Profile Hard Soil Profile. Comparison of Computed Displacements from ALP p-y and ElasticPlastic Models Hard Soil Profile. Comparison of Computed Bending Moments from ALP p-y and Elastic-Plastic Models Medium Soil Profile. Comparison of Computed Displacements from ALP p-y and Elastic-Plastic Models Medium Soil Profile. Comparison of Computed Bending Moments from ALP p-y and Elastic-Plastic Models Soft Soil Profile. Comparison of Computed Displacements from ALP p-y and ElasticPlastic Models Soft Soil Profile. Comparison of Computed Bending Moments from ALP p-y and Elastic-Plastic Models
Ove Arup & Partners 1/99 22 February 1999
Shell UK Exploration & Production
Sub-sea Conductor Study
Figure 5.10 Hard Soil Profile. LS-DYNA Results for Lateral and Moment Loading Figure 5.11 Medium Soil Profile. LS-DYNA Results for Lateral and Moment Loading Figure 5.12 Soft Soil Profile. LS-DYNA Results for Lateral and Moment Loading Figure 5.13 API and Shell t-z Springs Figure 5.14 LS-DYNA Continuum Model. Conductor Force and Moment Profiles Figure 5.15 LS-DYNA Continuum Model. Horizontal Displacement at Top of Conductor Figure 5.16 LS-DYNA Continuum Model. Cutaway indicating Horizontal Displacement Figure 5.17 LS-DYNA Continuum Model. Cutaway Indicating Horizontal Movement Within the Soil Figure 5.18 LS-DYNA Continuum Model. Relative movement between conductor and soil Figure 5.19 LS-DYNA Continuum Model. Maximum shear stress within soil Figure 5.20 LS-DYNA Continuum Model. Stress in x-direction within soil continuum Figure 5.21 LS-DYNA Beam and Spring Model. Force/Moment for HT1A-HB(API) Figure 5.22 LS-DYNA Beam and Spring Model. Force/Moment for HT2A-HC(API) Figure 5.23 LS-DYNA Beam and Spring Model. Force/Moment for HT1A-HB(Shell) Figure 5.24 LS-DYNA Beam and Spring Model. Force/Moment for HT2A-HC(Shell) Figure 5.25 LS-DYNA Beam and Spring Model. Force/Moment for HT2B-MA(API) Figure 5.26 LS-DYNA Beam and Spring Model. Force/Moment for HT3B-MB(API) Figure 5.27 LS-DYNA Beam and Spring Model. Force/Moment for HT4B-MC(API) Figure 5.28 LS-DYNA Beam and Spring Model. Force/Moment for HT2B-MA(Shell) Figure 5.29 LS-DYNA Beam and Spring Model. Force/Moment for HT3B-MB(Shell) Figure 5.30 LS-DYNA Beam and Spring Model. Force/Moment for HT4B-MC(Shell) Figure 5.31 LS-DYNA Beam and Spring Model. Force/Moment for HT3B-SA(API) Figure 5.32 LS-DYNA Beam and Spring Model. Force/Moment for HT4B-SB(API) Figure 5.33 LS-DYNA Beam and Spring Model. Force/Moment for HT3B-SA(Shell) Figure 5.34 LS-DYNA Beam and Spring Model. Force/Moment for HT4B-SB(Shell) Figure 5.35 Comparison of Torque at First Standard Connector (API) Figure 5.36 Comparison of Torque at First Standard Connector (Shell) Figure 5.37 Torque at First Standard Connector for HT1A-HB Continuum Model Figure 5.38 Shear Stress at Conductor/Grout interface for HT1A-HB Continuum Model Figure 5.39 Frictional Resistance of Debonded Grout DRAWINGS A210990-2 A210990-3 A210990-4 A210990-5
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Rev. A Rev. A Rev. A Rev. A
30" x 30` x 30" x 30" x
1" Conductor 1" Conductor 1" Conductor 1` Conductor
String String String String
with with with with
Resistance to Torque Type Resistance to Torque Type Resistance to Torque Type Resistance to Torque Type
HT1A HT2A HT3A HT4A
& & & &
HT1B HT2B HT3B HT4B
Ove Arup & Partners 1/99 22 February 1999
Shell UK Exploration &Production
Sub-sea Conductor Study
SUMMARY Shell Expro have developed detailed proposals for conductor designs for a range of ground conditions representative of those in the UK sector of the Central North Sea. The make-up of the proposed casing strings consists of a 40ft or 60ft length of 35" outer diameter by 2" wall thickness casing, followed by 50ft lengths of 30" outer diameter 1" wall thickness casing. There are 4 or 5 lengths of 30" casing, depending on the assumed ground conditions. The 35" casing is connected to the 30" casing using a high torque connector. The lengths of 30" casing are connected using either high or standard torque connectors. The principal objective of the current study was to assess the adequacy of the proposed casing string make-up for the assumed ground conditions, and in particular whether the proposed number of high torque connectors in each of the casing strings is justifiable. The study has been carried out using the program LS-DYNA to assess the behaviour of conductors when subjected to combined axial, bending and torsion loads. Shell have prepared casing designs for three idealised soil profiles covering a range of ground conditions varying from normally consolidated to heavily overconsolidated clay. The three profiles are identified as 'hard', 'medium' and 'soft'. The hard profile represents very stiff overconsolidated clay and dense sand sites, comparable to conditions at Nelson. The medium profile is formed of firm to stiff clay and medium dense sand, similar to those at Kittiwake. Normally consolidated sites, similar to conditions at Gannet, are represented by the soft profile. The axial loads to which the conductor strings are subjected are upward forces due to thermal expansion of the inner well casing. Three axial loads are specified by Shell to cover a range of temperatures of the hydrocarbons passing through the inner casing. Lateral, moment and torsion loading is due to trawler nets snagging on the Christmas tree assembly installed on the well head. For hard soil sites the current proposal is to use one high torque connector for the design case with the lowest hydrocarbon temperature, but two high torque connector for other load cases. The analyses show that the proposed conductor strings for hard soil conditions are adequate if t-z springs normally used by Shell are adopted. However, if t-z springs recommended by API are used then two high torque connectors are required for all conductor strings in hard soil conditions. For medium soil sites the current proposal is to use 2, 3 or 4 high torque connectors depending on the temperature of the hyrocarbon. The LS-DYNA analyses show that three high torque connectors are required for the lowest temperature load case instead of the two currently proposed. The other two design proposals are adequate. The proposed arrangement of high torque connectors for soft soil sites is adequate. The analyses indicate, however, that combined stresses in the top of the 30" conductor exceed recommended values and therefore some local yielding may occur if all the design loads act simultaneously.
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1.
Sub-sea Conductor Study
INTRODUCTION Shell Expro want to rationalise the design of well conductors so that all exploration and appraisal wells with the potential to become producers can be developed as sub-sea production wells if required. To achieve this aim it is necessary that the conductors used on these wells are strong enough to withstand all loads which may be applied to the conductor through the sub-sea wellhead assembly. Attenuation of loads occurs with depth below mudline, but one aspect of particular concern is that connections within the casing string have adequate capacity to resist the torque applied to the joint. Loads that affect the design and performance of the conductors are: *
Axial tensile force due to the conductor restraining the thermal expansion of the inner well casing;
*
Environmental loading transmitted to the conductor from a sub-sea wellhead tree;
*
Accidental loads due to snagging of trawler nets or trawl boards on the wellhead tree.
These loads can act individually, or in any combination, subjecting the conductor to a combination of axial, bending and torsion loading. Calculations already carried out by Shell have resulted in detailed proposals for conductor designs for a range the ground conditions anticipated for the UK Sector of the Central North Sea where Shell own exploration licences. The methods of analysis used by Shell were not, however, able to analyse the behaviour of the conductors under the combined effects of axial, bending and torsion loading and Shell are seeking independent validation of their design proposals. Arup Geotechnics were appointed by Shell to undertake a study to investigate the adequacy of the proposed casing string make-ups for specified ground conditions and load combinations. The analyses were to be undertaken using the program LS-DYNA to develop 3-D finite element models of casing and grout configurations for three soil types. The Scope of Work required: *
Model the combined soil resistance to axial, torsion and bending stress;
*
Determine axial, bending and torsion stress profiles in casing and joints for given bending and torsional loads and various axial loads;
*
Investigate grout/casing shear stress;
*
Investigate soil and grout behaviour at high temperatures (150 to 330 degs F) and modify soil model as necessary.
Details of the work carried out to complete this study are presented in this report.
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2.
Sub-sea Conductor Study
PREVIOUS STUDIES BY SHELL Analytical studies have been carried out by Shell to study the behaviour of subsea conductors when subjected to lateral and moment loading, and also to investigate stresses within the conductors due to the application of torque and tensile axial loads. The analyses have been performed for three soil types, identified as 'hard','medium' and 'soft', which are representative of soil conditions in the Nelson, Kittiwake and Gannet fields. The Shell studies were carried out in three phases as follows: *
Early studies, carried out using the SPLICE program, considered lateral and moment loading only. The results of this study are reported in Shell Engineering Report Number E93005, dated June 1993.
*
Later studies, also using the SPLICE program, looked at the behaviour of conductors under axial and torsion loading. The purpose of these studies was to investigate the stress profile down the conductor, particularly the attenuation of torsion, so that the depth to which high torque connectors are needed could be assessed. Full details of the analyses carried out are not known but, because of the limitations of the software available to Shell, it was not possible to analyse the conductors under combined axial and torsion loading. It is understood that in the analyses carried out by Shell the skin friction mobilised by the axial load was calculated first, and it was then assumed that the remaining skin friction between mobilised and ultimate was available to resist torsion.
*
Independent studies were also carried out by Shell to assess the axial loads applied to the conductor by thermal expansion of the inner casing.
Based upon the results of these studies various conductor string make-ups have been devised by Shell for each of the reference soil conditions for various axial loads representing thermal expansion of the inner well casing due to hydrocarbons of differing temperatures.
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3.
STUDY DATA
3.1
Soil Conditions Shell have provided details for three soil profiles which characterise ground conditions in the UK sector of the Central North Sea where the majority of their exploration licences are located. The idealised soil profiles are based upon data from three Shell Expro Oil Field geotechnical boreholes and represent ground conditions varying from normally consolidated to heavily over consolidated clay. Undrained shear strength profiles for the three soil types, subsequently referred to as 'hard', 'medium' and 'soft', are shown on Figures 3.1 to 3.3. Details of the soil profiles are given in Table 1. The 'hard' profile is also representative of ground conditions in the Northern North Sea sites operated by Shell.
Profile
Field
Formation
Description
Hard (H)
Nelson
Fisher
Very stiff over consolidated silty clays and dense sands.
Medium(M)
Kittiwake
Coal Pit
Firm to stiff silty clays and medium dense sands.
Soft (S)
Gannet
Forth
Very soft to firm normally consolidated clay. Table 1. Soil Profiles
3.2
Loads 3.2.1
Trawler Net
Studies have been carried out for Shell to assess loads applied to the conductor due to trawler nets snagging on the Christmas tree assembly installed on the wellhead. Snagging loads used by Shell, and adopted as design loads for the current study, are as follows: *
lateral force of 650 kN;
*
bending moment of 3575 kNm;
*
torque applied about the vertical axis of 1820 kNm.
It is assumed that these loads are applied to the conductor 1m above seabed level. 3.2.2
Thermal Loads
Hot hydrocarbons are transmitted through the inner well casing to the wellhead. Thermal expansion of the inner well casing is restrained by the outer conductor. For the conditions of a rigid connection between the inner well casing and the outer conductor, and no upward movement of the outer conductor, Shell have provided details of the upward loads to be resisted by the conductor. Upward loads assumed for the current study are summarised in Table 2.
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Load Case
Sub-sea Conductor Study
Temperature Range
Net Upward Load
Degs. F
Degs. C
lbs
kN
A
<150
<66
500,000
2240
B
>>150 <260
>66 <127
1,500,000
6672
C
>260 <330
>127 <166
2,700,000
12010
Table 2. Thermal Loads
3.3
Conductor Strings A typical well consists of a 20" outer diameter by 0.625" wall thickness inner well casing, with a 240ft to 320ft long outer conductor casing. The conductor string consists of a 40ft or 60ft top length of 35" outer diameter by 2" wall thickness casing, which stands Im proud of the seabed, followed by 5Oft lengths of 30" outer diameter by 1" wall thickness casing. Individual lengths of casing are joined by box and pin connectors. The conductor is grouted into a 36" diameter drillhole. The annulus between the 20" well casing and the conductor is also grouted. Details of conductor strings proposed by Shell have been taken from ABB Vetco Gray drawing numbers A210990-2 to -5, which were supplied by Shell. Copies of these drawing are contained in Appendix A. The make up of conductor strings used in the current study are summarised in Table 3 (see tables following references).
3.4
Connector Properties Details of the box and pin connectors used in the conductor strings have been taken from ABB Vetco Gray data sheets TDS/1041 and TDS/1017. Yield capacities of connectors relevant to the current study are summarised in Table 4.
Connector Capacity
ALT-2HT ( high torque)
ST-2RB ( standard torque)
Tension
6200 kips
27585 kN
2430 kips
10809 kN
Compression
8650 kips
38475 kN
4549 kips
20234 kN
Bending
4200 kip-ft
5691 kN-m
1810 kip-ft
1810 kN-m
Torsion
1500 kip-ft
2033 kN-m
39 kip-ft
53 kN-m
Table 4. Connector Properties
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3.5
Sub-sea Conductor Study
Pipe Properties The conductor pipes are manufactured of grade X52 (52 ksi) steel. Yield capacities for the two sizes of pipes used in the conductor strings are summarised in Table 5 for axial tension and compression, torsion and bending.
Yield Capacity
30" x 1"
35" x 2"
Tension
4738 kips
21070 kN
10780 kips
47950 kN
Compression
4738 kips
21070 kN
10780 kips
47950 kN
Bending
2770 kip-ft
3753 kN-m
7015 kip-ft
9505 kN-m
| Torsion
3197 kip-ft
4332 kN-m
8094 kip-ft
10967 kN-m
Table 5. Pipe Properties
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Sub-sea Conductor Study
4.
METHODS OF ANALYSIS
4.1
General Assumptions All of the analyses were carried out with the following general assumptions:
4.2
*
The 20" casing inside the conductor, and the grout between the casing and the conductor, has been ignored.
*
Local scour around the conductor to a depth of 1.5m below seabed level.
*
The top surface of the grout around the outside of the conductor is at a depth of 1.5m below seabed level.
*
The conductor is placed centrally within the predrilled hole and the annulus between the conductor and the predrilled holed is completely filled with grout.
*
No restraint is applied to the conductor by the well head and Christmas tree assembly, ie free head conditions apply
*
Young's Modulus Este, = 210 x 106 kPa, Egrout
=
5 x 10 kPa
Analysis Procedures Analysis of the conductors under the combined effect of axial, bending and torsion loading was to be carried out using the 3D program LS-DYNA. This program had not been used for this particular application before and therefore the initial stage of the analyses consisted of validating LS-DYNA for 2D loading calculations against the results from a conventional 2D analysis. The program used to provide 2D results against which LS-DYNA was compared was ALP.
4.3
ALP Analyses ALP is an OASYS program for the analysis of vertical piles subjected to lateral loads, bending moments and imposed soil displacements. ALP cannot take account of vertical or torsion loading. ALP analyses were carried out in order to provide data against which LSDYNA results could be compared. ALP analyses were initially carried out using standard p-y data to represent the load deflection behaviour of the soil. The p-y curves were generated by ALP using the method proposed by Matlock (1970) for static loading conditions. Values of e.0 , the axial strain at a stress level of one-half of the ultimate resistance, used to calculate the p-y curves are given in Table 6 and follow the recommendations of Sullivan et al. (1980) Soil Profile
Eso
Hard
.004
Medium
.01
Soft
.02
Table 6. E,, values for p-y curves
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Sub-sea Conductor Study
The conductor and surrounding grout was modelled as a 36" (0.914m) diameter, 78m long, pile of variable flexural stiffness (El). No allowance was made for the increased El at the joints. In subsequent ALP analyses the soil was modelled as an elastic-plastic material. The soil stiffness was adjusted until the conductor deflection profile from the elastic-plastic model matched that obtained previously from the p-y model. The soil stiffness profile obtained in this manner was subsequently used in the LS-DYNA continuum model.
4.4
LS-DYNA Analyses 4.4.1
Description of Program
LS-DYNA is an explicit finite element program which enables the solution of three dimensional problems involving a high degree of geometric and material non-linearity.
4.5
LS-DYNA Continuum Model In this model the soil surrounding the conductor is modelled as an elastic-plastic continuum. The conductor, grout and pipe connectors are modelled as individual components with appropriate material properties. Figure 4.1 shows a cut-section through the model. The model has a total of 100,000 elements. 4.5.1
Geometry
No symmetry has been used in the model representing the subsea conductor pile. This is because it was deemed that the loading (combination of axial/torque/lateral/bending) would force the pile to behave eccentrically. Any boundary conditions used to force symmetry behaviour would also be resisting the movement of the pile and hence would be detrimental to the analysis. 4.5.2
Casings
The 20" casings and surrounding grout inside the conductor have been ignored for the purpose of this analysis. These elements are assumed to be non-load bearing, and therefore have no effect on the result - except to complicate the analysis further. 4.5.3
Conductor
The conductor is represented by 2D shell elements of the correct thickness. In the LS-DYNA model, the shell element position is located in the centre of the conductor wall, ensuring that the correct flexural stiffness is calculated. 4.5.4
Connectors
The lengths of conductor are connected together using joints which represent the high torque and standard torque connectors. These joints form a box and pin arrangement and are modelled as non-deformable materials. The pin and box are connected via non-linear springs which allow the yield criterion/capacity to be specified according to the data supplied and tabulated in Section 3.4 of this report. 4.5.5 J:\5O 69-08\15'P\R\OOOSCH. REP
Grout Page 8
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Shell UK Exploration & Production
The grout is modelled using eight node solid elements. The external diameter of the grout is 36" (0.9144 m). The grout is meshed to the conductor shell elements, so that the internal diameter of the grout is on the centre-line of the conductor wall, hence the grout is marginally thicker than specified in the drawings. Due to the weakness of the grout, this extra thickness will have very little effect on the overall stiffness of the steel-grout composite. No facility has been included to allow the grout to become detached from the steel conductor.
4.5.6
Soil
The soil is modelled using eight node solid elements. The top layers of soil (down to 5.0 m below the surface) are modelled using 'fully integrated solids'. These elements are computationally expensive, but do allow greater accuracy in calculations where large deformations are expected. The soil extends out to a radius of five diameters beyond the grout at the top of the model (eleven diameters across in total), where the deformation is expected to be the largest. This tapers to just two diameters beyond the grout (five diameters across) at a level below the bottom of the conductor. In order to model the local failure of the soil around the conductor, small elements (1" in size) are used adjacent to the conductor with increasing element size away from the conductor. A region of scour is modelled down a to depth of 1.5 m below the surface level, at a gradient of 45 degrees. The grout starts below this level.
4.5.7
Boundary Conditions
The free field boundaries of the soil elements are fully fixed against translation. While there is likely to be some interaction between the pile and the outside boundary, it is not considered to be enough to affect the failure mechanisms of the pile against the soil.
4.5.8
Material Properties Steel
The steel material has an elasto-plastic behaviour allowing the maximum stress to be limited. The pipe work is made of grade X52 steel having a yield stress of 52 ksi (361 N/mnr). When this stress level is exceeded, the material deforms plastically, maintaining the yield stress with no plastic hardening. The ability for the steel to deform plastically will allow the steel tube to buckle under extreme load conditions. Connectors As mentioned above, the connectors are modelled as non-deformable materials. The non-linear springs connecting the pin and box allow elastic-perfectly-plastic behaviour. A displacement criterion has been used to define the yield of the joints. In axial compression and tension the joint can deform by 0.1 mm elastically, beyond which the plastic deformation occurs. The elastic stiffness is calculated assuming that the full yield capacity is developed at 0.1mm displacement. Similarly in bending and torque the maximum elastic rotation allowed is 2.5 x 10O' radians. Grout The grout material behaves elastically at a fraction of the stiffness of concrete approximately 5 MPa. This is an approximation, because grout can resist limited tensile forces. While it is possible to model the grout such that it behaves as in reality, this would require the correct confining stresses to be present in the soil surrounding the pile. Since the strength of the grout is small in comparison with the steel, it is considered sufficient to ignore the tensile failure.
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Soil The soil material uses a Modified Drucker Prager failure criterion (similar to Mohr-Coulomb but applicable to three dimensional analysis). This allows the soil to yield once a given deviatoric stress or shear stress is achieved within the soil. In this case, for all three soil profiles (hard, medium and soft) a simple undrained shear strength is used to define the yield, varying with depth. The elastic Young's Modulus of the soil is assumed to be directly proportional to the undrained shear strength, ie. for the 'hard' profile E = 150C to 4.5m, E = 250cu below 4.5m. To model undrained (incompressible) behaviour it is assumed that Poisson's Ratio = 0.49. In this study the failure criteria of the soil is dependent only on the undrained shear strength, cu. The initial state of stress in the soil prior to installation of the conductor is therefore not critical in this study. The current model does not consider the following:*
the pre-analysis stress history,
*
the effect of the drilling of the pile bore,
*
the effect of thermal cycling on the soil.
The soil is assumed to be homogenous across the horizontal plane (not varying with temperature gradients), and varying strength with depth.
4.5.9
Soil-grout interface
In the continuum model the soil is not meshed directly to the grout. A 'contact surface' is used between the grout and the soil which prevents the grout from penetrating into the soil when the conductor pushes into the soil, but allows the grout to pull away from the soil so that tension cannot be transferred from the grout to the soil. The drawback of this arrangement is that shear can only be transferred across a contact surface by friction. (ie. the shear transfer depends on the normal stress and the angle of friction between the two surfaces.) There is currently no facility within LS-DYNA for adhesion contact surfaces on which the shear transfer depends on the contact area and some proportion of the undrained shear strength of the soil. Although shear due to torque or axial loading of the conductor could be modelled using the frictional characteristics of the grout-soil interface (which would require the correct confining pressures to be known in the soil), for piles in clay the limiting 'skin friction' is usually assumed to be a function of the undrained shear strength. In offshore pile design it is common practice to use t-z curves to define the relationship between pile movement and mobilised skin friction. To overcome the uncertainty associated with using a friction model for the grout-pile interface, and to be compatible with conventional offshore pile design methods, a series of non-linear t-z springs are used to model the skin friction on the grout-soil interface (assuming that the 'contact surface' is frictionless). These springs connect the outer surface of the grout to the soil continuum and are oriented so that they work in the plane tangential to the surface of the grout. The springs are linear elastic/plastic and it is assumed that full friction is mobilised at a relative displacement between grout and soil of 1% of the diameter of the pile. Ultimate skin friction values are calculated as acd using a values recommended API RP 2A (1993), Section 6.4.2. This failure mechanism was tested by analysing the conductor being pulled directly out of the ground until the full shear force was mobilised. The force to cause failure compares well with the force calculated by integrating acd over the entire length of the pile.
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4.5.10
Sub-sea Conductor Study
Loading Thermal
A constant vertical force is applied to the top of the conductor where it is attached to the wellhead tree. The magnitude of this force varies with hydrocarbon temperature according to the data shown in Table 2 of this report. The vertical force is applied prior to the other loads so that the model is in equilibrium under the thermal loading condition.
Trawler net The loading from the trawler net is applied to a non-deformable collar at the top of the steel tube. The collar distributes the load over the entire circumference of the tube, although only one point load is defined for each loading type. The loads applied to the top of the pipe are: *
a lateral force in the x-direction of the model, magnitude 650 kN,
*
a bending moment applied about the y-axis of the model, magnitude 3575 kNm,
*
a torque applied about the (vertical) z-axis of the model, magnitude 1820 kNm.
These loads are applied to the model, allowing the pipe to deform and load the soil until an equilibrium state is achieved where the trawler net forces are resisted by the soil stress. 4.5.11
Damage Identification
It is assumed that the pile/conductor is considered to fail the test if either the steel tube becomes plastic, or any of the non-linear springs in the connectors have an excursion into the plastic range. Localised soil failure is not considered to be sufficient to warrant the failure of the pile/conductor combination.
4.6
LS-DYNA Beam and Spring Model Difficulties were experienced when using the continuum model in obtaining solutions to the analysis. The contact surface allows load to be transferred from the conductor onto adjacent soil elements. At the top of the conductor these elements fail due to localised yielding of the soil and became numerically unstable due to the large plastic deformations associated with squeezing of the soil. In soft and medium soil conditions, where the lateral displacements of the conductor are greater, these instability problems were amplified. To progress the study an alternative model was developed to overcome the computational difficulties associated with the continuum model Two major changes were made to the modelling technique: The lateral load is resisted by a series of p-y springs instead of the solid element mesh using the modified Drucker-Prager soil model The conductor and grout have been reduced to beam elements of the correct equivalent stiffness and cross section 4.6.1
Conductor Casing
The conductor casings are subdivided into beam elements. 50 elements are used in the first 40' section of casing (or 75 elements for the 60' casing). The second casing (50' length) is split into 30 elements, with all further sections of casing using 15 elements.
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The conductor casings are connected to each other using non-linear springs using an identical method to the previous model. The capacity of these 'connector' springs is as defined in Table 4. These non-linear springs will enable the force/moment to be monitored in the joints. 4.6.2
Lateral Load Behaviour p-y Springs
The lateral load is resisted at each node below 1.Sm depth (where the top level of grout begins) by non-linear springs which behave as p-y springs. The method used to define the properties of these springs is identical to the OASYS ALP geotechnical program described in Section 4.2 of this report. 4.6.3
Skin Friction t-z Spring
The skin friction on the outer surface of the grout is modelled in a similar way to the previous LS-DYNA model using non-linear t-z springs. One set of springs is used to resist combinations of torsional moment and axial forces. As for the continuum model, the springs work in the plane tangential to the surface of the grout. Skin friction at any point is mobilised in the direction of the resultant force, but is limited to the maximum available skin friction. The procedures adopted to implement the skin friction springs is described below, and illustrated in Figure 4.2. Two non-deformable rings are defined at each node level below the top of the grout. These rings are of the same diameter as the external diameter of the grout. Twenty non-linear t-z springs, equally spaced around the rings, are used to join the two rings together. One of the rings represents the surface of the grout, and the other the surface of the soil. Both rings are constrained to move translationally with the central node on the conductor beam, but the plane through the rings and the conductor beam node remains normal to the axis of the beam at the node location. The ring representing the soil is restrained so that it cannot rotate about the axis of the pile, and the plane through the conductor beam node cannot move vertically in the axial direction at the node position. With this arrangement the p-y curve springs only resist horizontal movement, and the skin friction springs only resist axial movement and/or rotation of the conductor. The model is best illustrated by reference to Figure 4.2. For the case of pure bending lateral forces are resisted by the p-y springs and the two non-deformable rings move with the pile. No forces are generated in the skin friction springs (see 'Bending' sketch on Figure 4.2). Under axial loading the t-z springs stretch/compress by the relative movement at the node position, thereby generating skin friction forces. Similarly a rotation a causes a relative movement aD/2 at the grout/soil interface and generates skin friction. Under combined axial and torsion loading the skin friction acts in the direction of the resultant force at the node and the combined skin friction is limited to the maximum permissible skin friction compatible with the total resultant relative movement. 4.6.4
Loads
The loading applied to the top of the conductor casing is sequenced. The axial (thermal) load is applied first, and the model is allowed to reach an equilibrium state. Once the thermal load is in equilibrium, the trawler net loading is applied, and equilibrium state found again for the combined load. This loading mechanism is identical to that used in the continuum model. With this loading sequence skin friction is first mobilised in the vertical direction to oppose the axial thermal loads. When torque is applied the orientation of the skin friction vector changes. If full skin friction is mobilised by the axial thermal load, then as torque is applied J \50169-0S\WP\R\0005cOHREP
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the vertical component of skin friction reduces as the component opposing the torque increases. In this manner skin friction is mobilised to greater depths to maintain overall equilibrium. 4.6.5
Modelling Inaccuracies
The modifications to the LS-DYNA model have introduced some inaccuracies into the results due to the simplifications. When applying load to the pile axially, or torsionally, the soil surrounding the pile will deform to some extent. This is not the case with the simplified model described here. The non-deformable ring representing the soil is prevented from ANY rotation about the axis of the pile and is also prevented from any axial movement relative to a plane normal to the pile. If movement of the soil is allowed, there will be a small reduction in the relative displacement between the grout and the soil with a consequent reduction is mobilised skin friction. This implies that the simplified model is over working the interface, and would give a conservative answer. The converse is the case for bending. With the simplified model no skin friction is developed by bending under lateral loading. In practice bending will cause some movement of the pile relative to the soil and so generate skin friction. The lack of movement in the soil does not compromise the position where the failure surface occurs. The pile will always fail on the interface, not in the soil. This is because even if the interface strength was not less than the soil strength, the force will be concentrated (higher stress) the closer to the centre of the pile that the failure surface occurs.
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5.
STUDY RESULTS
5.1
Analysis Strategy
Sub-sea Conductor Study
Various methods of analysis and modelling techniques have been used during the course of the study. The various methods are described in Section 4 of this report. The strategy adopted for this study is as follows:
5.2
*
Carry out conventional 2D lateral pile analyses with ALP using standard p-y curves
*
Carry out 2D lateral pile analyses using the elastic-plastic soil model in ALP. Determine elastic soil stiffness parameters to give comparable results to the previous p-y analyses
*
Carry out equivalent 2D analysis using LS-DYNA using a continuum soil model with elastic soil stiffness parameters derived from ALP elastic-plastic analyses
*
Carry out 3D analysis using LS-DYNA continuum model
*
Develop LS-DYNA beam and spring model for 3D loading and compare against LSDYNA continuum results
*
Analyse all load design cases using LS-DYNA beam and spring model
Lateral and Moment Loading Only 5.2.1
ALP p-y Analyses
The results of conventional laterally loaded pile analyses, using standard Matlock p-y data, are shown on Figures 5.1 to 5.3 for hard, medium and soft soil profiles respectively. The figures show profiles of displacement, bending moment, shear force and soil pressures when the lateral load and moment components of the trawler snagging loads are applied to the top of the conductor (ie. no axial load or torque). Maximum displacements vary from 60mm for the hard soil profile to 703mm for the soft soil profile. 5.2.2
ALP Elastic-Plastic Soil Model
ALP analyses using an elastic-plastic soil model were carried out to determine the stiffness profile for an elastic/plastic material which gives conductor displacement and bending moment profiles comparable to those obtained using the p-y approach. The stiffness profile derived frcm these ALP analyses were subsequently used in the LS-DYNA continuum model analyses. This procedure was adopted so that LS-DYNA results could be compared directly against previous analyses carried out using p-y analyses. The ultimate soil resistance was calculated using the method proposed by Brirch Hansen(1961), and it was assumed that Young's Modulus of the soil was proportional to the undrained shear strength c,. Starting from the initial assumption E'=250q,, the stiffness profiles were modified by trial and error until an acceptable match was achieved with the p-y predictions of displacement and bending moment. Figures 5.4 to 5.9 show the final comparisons achieved between the p-y and elastic-plastic soil models, and gives details of the soil stiffness profile derived for the elastic-plastic model.
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5.2.3
Sub-sea Conductor Study
LS-DYNA Beam and Spring Model
For lateral load analyses the LS-DYNA beam and spring model is in principle the same as used by ALP, but the method of solution is different. The modelling of the conductor pipes and connectors is more detailed in the LS-DYNA model, and consequently the analysiswill be more precise than corresponding ALP analyses. In the ALP analyses, for example, the conductor and surrounding soil is represented by 39 beam elements and 39 p-y springs. The corresponding number for the LS-DYNA model is 125 beam elements and 120 p-y springs. Pipe connectors are modelled in LS-DYNA and therefore force and moment components within the joint can be determined directly. Joints cannot be modelled in ALP, and forces and moments can only be determined by interpolation. Results from the LS-DYNA beam and spring model for hard, medium and soft soil profiles are shown on Figures 5.10 to 5.12. (These results are directly comparable to the ALP results shown on Figure 5.1 to 5.3.) 5.2.4
ALP and LS-DYNA Comparisons
Displacements and bending moments calculated using ALP and LS-DYNA are summarised in Table 7. Maximum bending moments are given for the top section of 35" x 2" pipe, the first high torque connector, and the first length of 30" x 1" pipe. For all of the analyses bending moments on the second connector are relatively small and are therefore not reported in Table 7.
Soil Profile
Method of Analysis
Maximum Displacement
Report Fig. No.
(mm) Hard
Medium
Soft
Maximum Bending Moment (kNm)
RCm@U-
35"9 X2"' Pipe
Joint 1
30" x1" Pipe
Rac Fax N6.
ALP
60
5.1
5525
0
150
;, 1
LS-DYNA
60
5.10
5601
99
125.3
T, lD
ALP
200
5.2
6685
429
160
LS-DYNA
212
5.11
6891
212
136
b.11
ALP
703
5.3
8373
4738
4492
6.3
LS-DYNA
718
5.12
8470
4821
4827
5 1
9505
5691
3753
Yield Capacity Moment (kNm)
Table 7. Comparison of ALP and LS-DYNA Results for Lateral Loading Only Case There is good correlation between the two sets of results. The maximum difference in lateral displacement at the top of the conductor is 6% (medium soil profile) and bending moments are generally with 7% of each other. Higher differences in bending moment occur when the bending moment are small in comparison to the yield moment, but these differences are of no significance to the overall results. For analyses using the soft soil profile both sets of results calculate bending moment in the 30" x 1" pipe greater than the yield moment capacity of this element. Maximum bending moment in the 35" x 2" pipe and the top connector are also high in comparison to their
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ultimate moments. Maximum moments in the 35" x 2" pipe are 88% to 89% of yield capacity, whilst moments in the top high torque connector are 83% to 85% of yield capacity.
5.3
Combined Lateral, Moment, Vertical and Torsion Loading 5.3.1
Analyses Carried Out
All the analyses for combined lateral, moment, vertical and torsion loading have been carried out using LS-DYNA. Analyses have been carried out for seven design cases as detailed in Table 8. Design Case
Conductor String
Soil Profile
Thermal Load Case
HTIA-HB
HTIA
Hard
B (1,500.000 Ibs)
HT2A-HC
HT2A
t'Hard
C (2,700,000 Ibs)
HT2B-MA
HT2B
6o'
Medium
A (500,000 Ibs)
HT3B-MB
HT3B
(0'
Medium
B (1,500,000 Ibs)
HT4B-MC
HT4B
6g'
Medium
C (2,700,000 Ibs)
HT3B-SA
HT3B
66'
Soft
A (500,000 Ibs)
HT4B-SB
HT4B
6O'
4
Soft Table 8. LS-DYNA Design Cases
B (1,500,000 Ibs)
As described in Sections 4.4.9, t-z springs have been used to model the transfer of shear across the soil-grout interface. Two forms of t-z springs have been used. The two types of tz springs, referred to as API and Shell, are defined on Figure 5.13. The API t-z springs assume linear elastic/plastic behaviour with the maximum skin friction, t mobilised at a relative movement between grout and soil of 1% of the grout diameter, i.e. 9.14mm. It is assumed that tmax = acu and that a values are as defined in Section 6.4.2 of API RP 2A (1993). The Shell t-z spring is the same as currently by Shell Expro for piles installed in clay. The shape of the t-z curve is as proposed by Vijayvergiya (1977) and tmax values are calculated using a values defined in API RP 2A (1993), Section C6.4. Figure 5.13 shows that for the hard soil profile the Shell t.nax values are greater than the API tmax values. Figure 5.13 also shows that smaller movements are required to mobilise skin friction with the Shell t-z springs. The suffix 'Shell' or 'API' is appended to the design case reference to define which type of tz spring has been used for a particular analysis, ie HTIA-HA (Shell). The continuum model has been used for only one design case ( HTIA-HB (API) ), and the beam and spring model has been used for 14 design cases (7 design cases x 2 types of t-z springs). 5.3.2
Design Case HT1A-HB (API)
5.3.2.1
Continuum Model Results
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Results obtained using the LS-DYNA continuum model are shown on Figures 5.14 to 5.20. Figure 5.14 shows profiles of forces and moments within the conductor when all the specified design loads are acting. Figures 5.15 to 5.20 show contours of horizontal displacement, shear stress and horizontal stress. 5.3.2.2
Beam and Spring Model
Profiles of forces and moments within the conductor calculated using the beam and spring model are shown on Figure 5.21. 5.3.2.3
Comparison of Continuum and Beam and Spring Models
For comparative purposes maximum values of axial force, shear force, bending moment and torque derived from the continuum and beam and spring models, are summarised in Table 9. The beam and spring model calculates a horizontal displacement at the top of the conductor of 53.6mm. The average horizontal displacement at the top of the conductor calculated by the continuum model is 52.5mm. The difference between the two horizontal displacement is only 2%, confirming compatibility between the p-y springs used in the beam and spring model and the elastic-plastic soil model used in the continuum analysis. 5.3.3
Results of LS-DYNA Beam and Spring Model Analyses
Results of LS-DYNA beam and spring analyses are shown on Figure 5.21 to 5.36 and summarised in Tables 1 1 to 15. Figures 5.2 Ia to 5.36a each show plots of axial force, shear force, bending moments and torsion moment versus depth below seabed level. Figures 5.21b to 5.36b show plots of maximum available and mobilised skin friction, rotation, axial displacement and lateral displacement versus depth below seabed level. Table 10 shows results for hard soil profile design cases, Table 11 shows results for medium soil profile design cases, and Table 12 shows results for soft soil profile design cases. Each of these tables gives the maximum calculated value of axial force, shear force, bending moment and torque in the 35" x 2" pipe, the top ALT-2HT high torque connector, the 30" x 1" pipe, and the top ST-2RB standard connector. Table 13 summarises the calculated maximum axial loads in the conductor elements due to thermal axial loading only, and under the combined effects of axial, bending and torsion loading. For each design case, Table 14 summarises the calculated lateral movement, upward movement and rotation of the conductor, at a depth of 1.5m below seabed level (ie base of scour depth), under the combined effects of axial, bending and torsion loading. From the results summarised in Tables 10 to 14 a number of general observations can be made: when torque is applied the axial loads in the elements below the top length of 35" x 2" pipe increase (see Table 13); as the axial thermal load increases, but the applied moment and torque remains constant(see Tables 10,11 and 12):
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(i)
bending moments in the 35" x 2" pipe reduce
(ii)
torque in the first high torque connector and the 30" x 1" pipe increase
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(iii)
Sub-sea Conductor Study
rotation of the conductor head, and upward movement of the conductor, increase, but the lateral displacement reduces (see Table 14).
Bending moments reduce as the axial load increases because higher axial tensile loads results in lower horizontal movement and so reduced curvature of the conductor. The increase in upward movement and rotation is attributed to the redistribution of shear stress (skin friction) on the grout/soil interface as either the torque or the axial load is applied or increased. 5.3.4
Results for Hard Soil Profile
Results of LS-DYNA beam and spring analyses for the hard soils profile are summarised on Figures 5.21 to 5.24 and in Table 10. Figures 5.21 and 5.22 shown results obtained using API t-z springs while Figures 5.23 and 5.24 show corresponding results if Shell t-z springs are used. Table 10 shows that the torque capacity of the first standard torque connector is exceeded for design case HTIA-HB if API t-z springs are used, but not if Shell t-z springs are used. For design case HT2A-HC the capacity of the standard torque connector is adequate for both API ans Shell t-z springs. Ultimate values of axial force, shear force and bending moment are not exceeded in any of the conductor elements for the two load cases considered. The higher torque applied to the ST-2RB connector when API springs are used are due to the lower a values, and softer initial stiffness, which result in lower values of skin friction being mobilised to a greater depth. This can be seen by comparing the plots of mobilised skin friction on Figures 5.21 b and 5.23b. The reduction of axial load and torque within the conductor with depth below seabed is therefore less for the API t-z springs than for the Shell springs. This can be seen by comparing axial force components on Figures 5.21 and 5.23. With the API t-z springs the axial force becomes zero at a depth of about 65m below mudline, but when using Shell t-z springs the axial force becomes zero at a depth of about 45m below mudline. When the thermal axial load is increased, higher values of skin friction are mobilised but the depth at which the axial force in the conductor becomes zero does not change significantly. The distribution of torque is different for the higher axial load case, particularly for the API t-z spring case. 5.3.5
Results for Medium Soil Profile
Results of analyses for the medium soil profile are shown on Figures 5.25 to 5.30 and summarised in Table 11. For this soil profile there is little difference between the results obtained using API and Shell t-z springs. All of the design cases show the axial force reducing to zero at the base of the conductor, indicating that skin friction is mobilised over the full length if the conductor. Upward movement of the base of the conductor is of the order of 0.5mm. The plots of mobilised skin friction show that using API t-z springs full skin friction is mobilised to a depth of 20m below seabed level for design case HT2B-MA (ref Fig 5.25b). The depth of full mobilisation of skin friction increases to about 30m for HT2B-MB (Fig 5.26b) and 47m for HT2B-MC (Fig 5.27b). The use of Shell t-z springs allows higher values of skin friction at shallow depths with the consequence that for design case HT2B-MA full skin friction is only mobilised to a depth of about 6m (Fig 5.28b). For higher axial loads, however, skin friction is fully mobilised to depths comparable to those obtained using API springs. Both the API and Shell t-z spring models show the first standard ST-2RB connector failing in torque for design case HT2B-MA. For design cases HT3B-MB and HT4B-MC the torque in
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the first ST-2RB connector is less than the joint capacity for both the API and Shell t-z spring models. 5.3.6
Results for Soft Soil Profile
Results of analyses carried out for the soft soil profile are shown on Figures 5.31 to 5.34 and in Table 12. There are no significant differences between results obtained using API and Shell t-z spring. Skin friction is fully mobilised to slightly greater depths when API t-z springs are used, but for all the soft soil profile design cases full skin friction is not mobilised below a depth greater than about 40m. For all of the soft soil profile analyses non of the standard ST-2RB connectors fail in torque. Without any axial load Table 7 shows a maximum bending moment in the 30" x 1" pipe of 4827 kNm. Table 12 shows that this bending moment reduces to 2799 kNm, a reduction of 42%, when the axial load is 1.5 x 106 lbs and API t-z springs are used. Table 12 also shows that when Shell t-z springs are used the bending moment in the 30` x 1" pipe is greater than the yield moment when the axial thermal load is less than 5 x 1( lbs. 5.3.7
Axial and Bending Stresses
Tables 15 and 16 show calculated values of axial and bending tensile stresses in the 35" x 2" and 30" x 1" conductors for each of the design cases considered. Axial stresses in the 35" x 2" pipes, shown in Table 15, are a maximum of 41% of the allowable tensile stress of 0.6FY defined in API RP2A, while the tensile bending stresses exceed the allowable of 0.75FY for design case HT3A-SA. Table 16 also shows the combined axial tension and bending stress. API RP2A requires for cylindrical structural member that
A-f 0.6F1, where
+_fb_ < 1.0 0.75F,
fa = axial tensile stress fb = tensile bending stress
FY = yield stress Table 16 shows that none of the design cases except HTIA-HB(Shell and API) and HT2B-MA(API) meet this requirement. API RP2A permits allowable stresses to be increased by one third when the stresses are due in part to lateral and vertical forces imposed by design environmental conditions. The trawler snagging loads represent an accidental limit state, and although the imposed conductor loads are not environmental loads it is considered appropriate to allow a 33% overstress when assessing combined stress effects. The combined stress check inequality therefore becomes -f,_ +_fb_ 0.6FY
< 1.33
0.75FY
Table 15 shows that this relationship is satisfied in the 35" x 2" pipe for all design cases. Also shown in Table 15 are bending stresses resulting from analyses in which lateral load and moment components of the snagging loads were considered, but torque and axial thermal
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loads were ignored. The results show that for the soft soil profile this load combination results in higher stresses within the conductor than the full load analyses. Axial and bending stresses in the 30" x 1" pipe are shown in Table 16. This table shows that, after allowing a 33% overstress, the stresses exceed allowable stresses for all soft soil design cases. For the soft soil design cases the stresses due to lateral and moment loading only are significantly higher than those resulting for combined loading. 5.3.8
Comparison of Results for first ST-2RB Connector
Figures 5.35 and 5.36 summarise calculated values of torque at the first standard connector. Figure 5.35 shows results obtained using API t-z springs, and Figure 5.36 shows results obtained using Shell t-z springs. These two figures show torque plotted against time. 'Time' in this instance is a consequence of the LS-DYNA iterative procedure and has no direct relevance to the problem. The increase of torque with time shown on these figures merely illustrates convergence to an equilibrium solution. The only significant difference between the two sets of results is for design case HTIA-HB. When API t-z springs are used the analyses shows the torque capacity of the connector (53 kNm) has been reached, while the corresponding analysis using Shell t-z springs shows that the maximum torque at the first connector is 18 kNm. Figure 5.37 is a similar plot of results obtained using the LS-DYNA continuum model with API t-z springs. This Figure shows the same result as the beam and spring model, ie failure of the first standard connector in torque. Both sets of results show that the torque at the first standard connector exceed the joint torque capacity for design case HT2B-MA. All other analyses show that the proposed conductor strings are adequate. 5.3.9
Grout to Casing Shear Stresses
The 35" and 30" conductor casings are grouted into a 36" diameter drillhole. In principle the 35" conductor casing is therefore surrounded by a l/2" thick annulus of grout, and the 30" conductor casing is surrounded by a 3" thick annulus of grout. Grout to casing shear stresses can only be determined from the continuum model results since this is the only analysis in which the casing and grout are modelled separately. Shear stresses determined from the hard profile continuum model analysis are shown on Figure 5.38. Maximum values of grout to casing shear stress for the top section of 35" x 2" pipe range from 0 to 3.35 MPa. Corresponding values for the top section of 30" x 1" pipe are about 0.25 to 1.5 MPa. Shear stresses due to the axial load and torque components of applied load will be limited by the grout/soil skin friction. Within lOim of mudline Figure 5.13 shows that for API t-z springs the maximum skin friction is in the range 0.05 to 0.1 MPa. The results shown on Figure 5.38 therefore indicate that most of the grout to casing shear stress is due to bending of the conductor. No analyses have been carried out for medium and soft soil profiles from which the grout to conductor shear stresses can be determined. It is evident, however, that the larger displacements and higher bending moments associated with these weaker soils will result in higher grout to conductor shear stresses.
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5.4
Sub-sea Conductor Study
Review of Results The results of the LS-DYNA analyses indicate that some of the model features result in nonconservative estimates of forces and stresses in the conductor casings and connectors. Two major factors which could affect the solutions are discussed in the following sections. 5.4.1
Spalling of Grout
In the LS-DYNA model the grout is modelled as an elastic material, fully bonded to the conductor. This is an oversimplification since bending of the conductor will cause cracking of the grout, and the magnitude of the calculated shear stresses indicates that local debonding of the grout from the conductor may occur. If debonding does occur, it is possible there could be reduced transfer of load from the conductor into the soil over the depth of the debonding, resulting in increased loads in the conductors and connectors below the depth of spalling. The current calculations could therefore underestimate the forces to be resisted by the connectors. Debonding will occur if the local shear stresses between grout and steel exceed the ultimate bond stress. API RP2A recommends an allowable axial load transfer shear stress of 0.185 MPa for grouted annulus connections between plain steel pipe piles and jacket legs, but does not give any recommendations for grouted connections subject to shear, bending or torque, other than to state these effects should be considered by appropriate analytical or testing procedures. The API recommended allowable bond stress value is significantly lower than the calculated shear stresses, but data contained in the Commentary of API RP2A shows that ultimate values of grout to steel bond stresses can be much higher. The grout around the conductor casing is reported to have a 24 hour compressive strength in excess of 17 MPa. Based upon published data, the equivalent 28 day compressive strength is expected to be in excess of 80 MPa. Data in the API RP2A Commentary shows ultimate grout to steel bond strengths in the range 0.5 to 5 MPa for a grout of this strength. Neville (1981 ) reports an ultimate axial bond stress, determined by pull-out tests, of about 3.5 MPa for plain bars in concrete with a compressive strength greater than 40 MPa. BS 8110 (1997) states thet the ultimate bond stress for reinforcement bars in concrete can be determined using the equation: fb. D V flu where fbU is the ultimate bond stress, 3is a coefficient dependent on the bar type and f. is the compressive strength of the concrete. Taking fu = 80 MPa the resulting values of ultimate bond stress are 2.5 MPa for plain bars in tension and 3.1 MPa for plain bars in compression. It is evident from the foregoing that although ultimate bond strengths are considerably greater than the allowable shear stresses recommended by API RP2A, the grout to steel shear stresses calculated by LS-DYNA are comparable to published values of ultimate bond strengths . Neville (1981) also reports that a rise in temperature reduces the bond strength of concrete. At temperatures of 200 to 300C he reports that there may be a loss of one-half of the bond strength at room temperature. It is therefore very likely that grout to steel shear stresses will locally exceed the ultimate bond strength and that some spalling of the grout will occur. The grout to steel shear stresses shown on Figure 5.38 suggest that for the hard soil profile local spalling may occur on one side of the conductor to a depth of about 5m to 6m below mudline. Intuitively it is expected that spalling would occur to a greater depth for medium and soft soil profiles. If cracking and debonding of grout does occur the transfer of shear from the conductor into the surrounding soil will be governed by friction between the de-bonded grout and the steel
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conductor casing. Laboratory tests reported by Rabbat and Russell (1984) show an interface friction angle between de-bonded grout and steel of 350 at a normal stress of 140 kPa, reducing to 33° at a normal stress of 690 kPa. Assuming an interface friction angle of 330, Figure 5.39 shows the shear that could be transferred through a debonded grout interface for various values of K (lateral earth pressure coefficient). Also shown on Figure 5.39 is the maximum skin friction on the grout-soil interface based upon Shell t-z springs. This figure suggests that shear on the grout/steel interface is likely to be governing for hard soil conditions, but is not likely to be the governing criteria for medium and soft soil profiles.
5.4.2
Axial Thermal Loads
In the current analyses the axial load due to thermal expansion of the inner casing is modelled as a constant vertical load. The analyses show bending moments, and associated bending stresses, in the conductor casing casings reduce as the vertical load increases. In practice it is probable that the axial load applied to the conductor will reduce as the inner casing expands. Assuming the load remains constant as the casing expands will result in lower bending moments and bending stresses in the conductors. It is therefore possible that combined stresses could be higher if the axial load reduces as expansion takes place.
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6.
Sub-sea Conductor Study
TEMPERATURE EFFECTS The hot hydrocarbons flowing through the well casing will cause a rise in temperature in the conductor casing, the grout around the conductor casing, and the surrounding soil. The effects of temperature on the geotechnical properties of the soil has been investigated by a number of researchers but published data relevant to the design of conductors in heated soil is scarce and inconclusive. Results of field and laboratory testing by the Swedish Geotechnical Institute into the effects of heating on the properties of clay are reported by Moritz (1995) and Gabrielsson, Lehtmets, Moritz and Bergdahl (1997). Results of triaxial testing reported by Moritz (1995) show that the undrained shear strength of samples taken from 6m depth reduce by about 30%, from about 27 kPa to 18 kPa, as the temperature of the specimens increases from Soc to 70WC. Tests on samples taken from 9m depth, however, show no consistent relationship between temperature and undrained shear strength. In situ measurements of undrained shear strength taken within a field heat store, reported by Gabrielsson et al (1997), show that the undrained shear strength temporarily reduces by about 30% on first heating, but subsequently increases to about the initial values as the excess porewater pressures associated with the initial heating dissipate. The triaxial tests reported by Moritz were consolidated undrained tests in which consolidation of the heated sample was allowed prior to undrained testing. No explanation is offered by SGI as to why fully consolidated heated samples show a reduction in undrained shear strength, but fully consolidated field tests do not. Based upon the results of the laboratory and field tests, over the temperature range 8 0C to 70WC, SGI conclude that the undrained shear strength will temporarily decrease by about 0.5 % per 'C at first heating, but will return to its original strength with time. Similar laboratory triaxial testing reported by Towhata and Kuntiwattanakul (1994) appear to show the opposite trend. Their test results show that as the consolidation temperature increases from 21 'C to 90WC the undrained shear strength increases from about 37 kPa to 48 kPa, an increase of 30% due to a 69WC temperature rise. Both sets of triaxial tests were consolidated undrained tests in which consolidation of the heated sample was allowed prior to undrained shearing. The differences are that the SGI tests were carried out on undisturbed samples of natural clay which were anisotropically consolidated to ar, = 48 kPa, ah' = 33.6 kPa or cr' = 70 kPa, ah' = 42 kPa, whilst Towhata et al tested specimens of 'MC Clay' prepared from a slurry and isotropically consolidated to q' = 196 kPa. No analyses have been carried out to assess whether these differences in the consolidation stages could account for the difference in response to heating. No data has been identified for samples heated to temperatures higher than 90°C. Constant rate of settlement (CRS tests) consolidation tests carried out by SGI indicate that both the preconsolidation pressure and the compressibility modulus reduce as the temperature increases. There is no data to indicate whether or not this is a temporary phenomenon. Considering the uncertainty of the effects of heating on the geotechnical properties of clay it is considered that further analyses to study the effects of soil heating on the performance of the conductors is not justified at this stage. An indication of the potential effects of reductions of undrained strength and compressibility modulus can be obtained from the existing results. Assuming as an extreme case that the SGI findings can be extrapolated to a temperature rise of 160°C, their recommendation of a temporary decrease of undrained shear strength of 0.5 % per 'C corresponds to an 80% reduction of undrained shear strength. With this degree of strength reduction the hard soil shear strength profile approximates to the medium soil shear strength profile, and within about lOm of mudline the medium soil profile
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approximates the soft soil strength profile. The medium soil results could therefore be considered as representative of the extreme worst case for the hard soil condition, and the soft soil results could be taken as the extreme worst case for medium soil conditions. If more detailed analyses are required the first stage would be a conduction analysis to determine the maximum temperature rise of the soil. As previously reported in Section 5.4.1 the grout to steel bond strength is also affected by temperature.
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7.
Sub-sea Conductor Study
CONCLUSIONS Theoretical analyses have been carried out to investigate the adequacy of proposed conductor string make-ups for specified ground conditions and load combinations. The principal findings of this study are as follows.
7.1
Conductors in Hard Soil Conductor String HT1A The analyses show that the proposed string make-up is adequate if the t-z springs normally used by Shell are used to represent mobilisation of skin friction on the grout/soil interface, but that the torque capacity of the first ST-2RB connector is exceeded if t-z springs based upon API recommendations are adopted. Using two ALT-2HT high torque connectors in place of the one currently proposed would result in an acceptable design for both types of t-z springs Conductor String HT2A The proposed torque connectors are adequate, but combined stresses in the top length of 35" x 2" conductor pipe exceed the API recommendations for allowable combined axial tension and bending stresses. Stresses are acceptable if a 33% overstress is permissible.
7.2
Conductors in Medium Soil Conductor String HT2B The torque capacity of the first ST-2RB connector is exceeded and therefore three ALT-2HT high torque connectors are required on this conductor string. Other components of the string are adequate. Conductor Strings HT3B and HT4B The proposed arrangement of torque connectors is adequate. Combined axial and bending stresses in the top length of 35" x 2" conductor pipe exceed the API recommendations, but are acceptable if a 33% overstress is permitted.
7.3
Conductors in Soft Soil Conductor Strings HT3B and HT4B The proposed arrangement of torque connectors is adequate. Combined axial and bending stresses in the top length of 35" x 2" conductor pipe exceed the API recommendations, but are acceptable if a 33% overstress is permitted. Combined axial and bending stresses in the top length of 30" x 1" conductor pipe are more than 33% greater than the API recommended stresses in the section of pipe directly beneath the top connector. The bending moment reduces rapidly with depth, but immediately beneath the top connector the combined stresses are slightly greater than the yield strength of the pipe material. Some local yielding of the conductor pipe could therefore occur within this zone.
7.4
Grout to Casing Shear Stresses The analyses predict high shear stresses between the 35" x 2" conductor pipe and the surrounding grout. Shear stresses up to 3.3 MPa are calculated for hard soil conditions. The maximum shear stresses occur within a depth of about 5m below seabed level in the zone of
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maximum bending moment. It therefore appears that these shear stresses are predominantly due to bending of the pipe. Shear stresses have not been calculated for the medium and soft soil conditions, but high shear stresses are anticipated for these design cases. The maximum shear stresses are comparable in magnitude to reported values of ultimate bond strength between grout and plain steel. Bending will cause cracking of the grout, and in the zones of maximum shear stress it is possible that local debonding of the grout may occur. If debonding does occur it will still be possible for skin friction to be mobilised by friction between the debonded grout and the conductor. For hard soil conditions the skin friction between debonded grout and steel is likely to be less than the skin friction between soil and grout over the debonded depth. This could lead to higher loads on the conductor pipes and connectors than predicted by the current analyses. It is anticipated that this redistribution of skin friction would not result in overstress of the conductor pipe or the ALT-2HT connector, but could result in the torque capacity of the top ST-2RB connector being reached for design cases other than HT1 A-HB (see section 7.1 above). For medium and soft soil conditions the friction between debonded grout and steel is likely to be comparable to the skin friction between soil and grout. The effect of grout debonding on the overall performance of the conductor string is likely to be marginal.
7.5
Effects of Heating on Geotechnical Properties Published data on the effect of heating on the strength and stiffness of clay soil is inconsistent. Data from large scale field trials reported by the Swedish Geotechnical Institute indicates a temporary reduction in undrained shear strength on first heating, followed by a return to pre-heating strengths as excess porewater pressures generated by initial heating dissipate. Extrapolation of the SGI data indicates heating to 160CC could result in a temporary reduction in undrained shear strength to 20% of the original value.
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8.
REVIEW OF ANALYTICAL METHODS At the start of this study the intention was to use a detailed three dimensional finite element continuum model to analyse the behaviour of conductors under combined axial, bending and torsion loading. Detailed numerical modelling of this complex soil structure interaction problem proved to be more difficult than originally anticipated and it was necessary to modify the numerical model in order to complete the full scope of work required. The modifications concerned the way in which the skin between the grout around the outside of the conductor and the soil was modelled. LS-DYNA is able to model frictional contact surfaces, but does not have a facility for modelling adhesive contact surfaces in which the shear stress between two surfaces is assumed to be a function of the undrained shear strength of the contacting materials. To overcome this deficiency a continuum model was developed which had a frictionless contact surface between the. grout and the soil, but included t-z springs connecting the grout to the soil to model the mobilisation of skin friction due to relative movement between the surface of the gout and the surrounding soil. This model was generally satisfactory for the hard soil profile but some numerical instability occurred at the top of the conductor due to large plastic strains associated with local yielding and squeezing of the soil around the conductor. The numerical instability became more pronounced for the medium and soft soil analyses. Work continued throughout the contract period.on developing the continuum model, but at the same time an alternative model, more able to cope with large deformations, was developed in parallel with the continuum model in order to provide solutions for all of the specified design cases. The alternative model developed was a simpler beam and spring model which uses conventional p-y springs to represent lateral load displacement behaviour and t-z springs to model development of skin friction. One set of t-z springs is used to account for combined axial and torsional loading, with skin friction mobilised in the direction of the resultant force at any point and limited to specified ultimate skin friction values. The results from the beam and spring model were validated by comparing them against those obtained using the continuum model for the hard soil profile. The results presented in this report are predominantly those obtained using the beam and spring model, although limited results from a continuum model are presented for comparative purposes.
8.1
Assessment of Results It is believed that the methods and models developed to carry out the analyses provide an acceptable means of assessing the behaviour of the conductor under three dimensional loading. The procedures consider the development of skin friction under both axial and torsion loading, and successfully limit skin friction to pre-defined ultimate values taking account of the sequence of loading and directionality of resultant forces. The modelling techniques used in this study employed a number of simplifying assumptions. Some of the assumptions lead to conservatism in the results, others are not conservative. The principal conservative assumptions are: *
the stiffness of the inner 20" casing and the grout between the inner casing and the conductors has been ignored
*
local scour has been assumed to depth of 1.5m, and the grout on the outside of the conductor to I .5m depth has been ignored
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the steel forming the conductor has been modelled as an elastic/plastic material with a yield stress of 361 N/mm 2 . No allowance has been made for post yield strain hardening. The first of these assumptions is likely to be the most significant. Allowing for the 20" casing and the grout between the inner casing and the conductor will give a higher bending, axial and torsional stiffness with a consequent reduction in displacements and stresses within the conductor and connectors. The principal non conservative assumptions are: *
the axial load due to thermal expansion remains constant
*
in the beam and spring model the soil movement at the grout/soil interface due to continuum movement is not allowed for
*
in all the models the grout is assumed to be an integral part of the conductor
The analyses show that a constant axial tensile load is beneficial as the upward pull reduces the curvature of the conductor with a consequent reduction in bending moment. The bending moments could therefore increase if the axial thermal load reduces as the conductor moves upwards. Neglecting continuum movement is likely to result in an underestimate of the movement required to mobilise sufficient skin friction to oppose axial and torsional loads. This could result in an underestimate of the torque applied to the connectors. Assuming that the grout is integral with the conductor does not allow for the effects of grout debonding. This could also result in an underestimate of the torque applied to the connectors, particularly for the hard soil profiles.
8.2
Improvements to Modelling Techniques The experience gained to date, together with an improved understanding of the factors affecting the design analyses, leads us to believe that there are modifications which could be made to the existing LS-DYNA models to improve the analysis procedures and provide greater confidence in the design of the conductors. In order of increasing complexity, and increasing risk of successful implementation, modifications which could be made to the LSDYNA models are detailed below. 8.2.1
Detailed Modelling of Conductor and Grout
In the existing beam and spring model the conductor and surrounding grout are modelled as composite elastic beam elements. The soil is represented by p-y and t-z springs. The beam. elements could be replaced by a detailed finite element model where the conductor, connectors and grout are modelled using shell and solid elements, as done previously for the continuum model. The p-y and t-z springs representing the soil would be retained. This approach would provide more detailed information on the stress conditions within the conductor, connectors and grout and would identify whether or not local yielding occurs in the conductor pipes. The grout could be modelled as a non-linear material which cracks, and it may be possible to specify limiting grout to steel shear stresses to model debonding. 8.2.2
Improved Continuum Model
Initial analyses using the continuum model experienced numerical instability and convergence problems. Most of these problems were eventually overcome by modifying the analytical procedures used by LS-DYNA to model the contact surface between the grout and
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the soil. Continuum model analyses for medium and soft soil profiles have not been run since this modification was implemented. It may now be possible to obtain continuum model solutions for medium and soft soil profiles, but in view of the number of elements and the magnitude of the displacements expected considerable run time will be required to reach a converged solution. Run times could be reduced by using an option to re-generate new meshes as the material deforms, or by using a hybrid between a continuum and a spring model. With this latter option a continuum model would be used for say the top 15m of soil, but p-y and t-z springs would be used below this depth.
8.2.3
Improved Grout to Soil Interface
Skin friction at the grout to soil contact surface in the continuum model is currently modelled using t-z springs. Although the contact surface allows peel away for lateral load behaviour, the t-z springs ensure that peel away does not result in a reduction in the contact area over which skin friction is mobilised. The t-z springs could be eliminated by introducing a friction/adhesion contact surface. The simplest procedure would be a friction contact surface, but this would require that skin friction is calculated in effective stress terms rather than total stress as at present. The results would depend upon stress history and it very likely that the results would be different from those obtained previously using t-z springs. It may be possible to adapt one of the hysteretic model within LS-DYNA, or develop an interface element, to replace the t-z springs. If this could be done it may be possible to increase the size of the elements and reduce run times.
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9.
Sub-sea Conductor Study
RECOMMENDATIONS FOR FURTHER WORK To progress design of the well conductors it is recommended that the following work is carried out. *
.
Modify the LS-DYNA beam and spring model to replace the composite beam elements by a detailed finite element model of the conductor and grout in order to investigate cracking and spalling of the grout and the implications of this on the loads transferred to the connectors and the stresses within the pipe elements.
*
Undertake a thermal conduction analysis to determine temperature rises within the ground, thermal expansion of the well casing and the outer conductor, and axial loads generated by thermal expansion.
*
Stress analysis of the conductor string and surrounding ground to determine how the axial load applied to the conductor casing varies with thermal expansion of the well and conductor casings.
*
Carry out preliminary tests of LS-DYNA continuum model using the soft soil profile.
*
Investigate methods and carry out preliminary analyses to assess feasibility of developing friction/adhesion contact surface between grout and soil.
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10.
Sub-sea Conductor Study
REFERENCES API RP 2A (1993). Recommended Practice for Planning, Designing and Constructing Fixed Offshore Platforms - Working Stress Design, Twentieth Edition. Brinch-Hansen J (1961). The Ultimate Resistance of Rigid Piles against Transversal Forces. Danish Geotechnical Institute, Bulletin No. 12, Copenhagen, pp. 5-9. British Standards Institution BS 8110: Part 1: (1997). Structural use of concrete. Part 1. Code of practice for design and construction. Gabrielsson A, Lehtmets M, Moritz L and Bergdahl U (1997). Heat Storage in Soft Clay. Field Tests with Heating (70 0 C) and Freezing of the Soil. Swedish Geotechnical Institute, Report No. 53, Linktiping. Matlock H (1970). Correlations for Design of Laterally Loaded Piles in Soft Clay. OTC 1204, Offshore Technology Conference, Houston. Moritz L (1995). Geotechnical Properties of Clay at Elevated Temperatures. Swedish Geotechnical Institute, Report No. 47, Linkdping. Neville A M (1981). Properties of Concrete, 3rd Edition, Pitman. Rabbat B G and Russell H G (1985). Friction Coefficient of Steel on Concrete or Grout. ASCE Journal of Structural Engineering, Vol. 111, No. 3, pp 505-515. Shell Expro (1993). Geotechnical Report. Sub-Sea Wellhead Study Central North Sea Soil Profiles. Engineering Report No. E93005. Sullivan W R, Reese L C and Fenske C W (1980). Unified Method for Analysis of Laterally Loaded Piles in Clay. Conference on Numerical Methods in Offshore Piling, ICE, London pp. 135-146. Towhata I and Kuntiwattanakul P (1994). Behaviour of Clays Undergoing Elevated Temperatures. X111 ICSMFE, Vol 1 pp. 85-88, New Delhi, India. Vijayvergiya V N (1977). Load Movement Characteristics of Piles. Proceedings of Ports '77 Conference, ASCE, Vol. II pp. 269-284.
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Pipe Combination
HT1A
HT2A
HT2B
HT3B
HT4B
Section 1
35" x 2"
35" x 2"
35" x 2"
35" x 2"
35" x 2"1
Length
40 ft
40 ft
60 ft
60 ft
60 ft
Joint
ALT-2HT
ALT-2HT
ALT-2HT
ALT-2HT
.ALT-2HT
Section 2
30" x 1"
30" x 1"
30" x1"
30" x 1"
30" x1"
Length
50 ft
50 ft
50 ft
50 ft
50 ft
Joint
ST-2RB
ALT-2HT
ALT-2HT
ALT-2HT
ALT-2HT
Section 3
30" x 1"
30" x I "
30" x I1"
30" x Iv"
30" x I"
Length
50 ft
50 ft
50 ft
50 ft
50 ft
Joint
ST-2RB
ST-2RB
ST-2RB
ALT-2HT
ALT-2HT
Section 4
30" xI"
30" xI"
30" xI"
x0" xI"
30" xI"
Length
50 ft
50 ft
50 ft
50 ft
50 ft
Joint
ST-2RB
ST-2RB
ST-2RB
ST-2RB
ALT-2HT
Section 5
30" x 1"
30" x
0" x1"
30" x1"
30" x1"
Length
50 ft
50 ft
50 ft
50 ft
50 ft
Joint
Shoe
Shoe
Shoe
Shoe
ST-2RB
Section 6
n/a
n/a
n/a
n/a
30" x 1"
Length
50 ft
Joint
Shoe Table 3. Conductor Strings
C')
et
b~JAl
S-)1
tt)5~xfTse
t& CI
gt
)
StIf
XI.S Xc
@e
A-,et-P W^<
STER
3K
hiyrc~j), LO A)t1MG MAY
so X
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6
w eLL4
X
(Xf)
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Conductor Element
Force /Moment
Continuum Model
Beam and Spring Model
Yield Capacity
35" x 2" Pipe
Axial Force (kN)
6675
6680
47950
Shear Force (kN)
1038
1073
Bending Moment (kNm)
5084
5200
9505
Torque (kNm)
1830
1820
109678
Axial Force (kN) Shear Force (kN)
5230 66.1
5021 32.8
27585
Bending Moment (kNm)
86.8
104.5
5691
Torque (kNm)
935
1026
2033
Axial Force (kN)
4828
5021
21070
Shear Force (kN)
34.8
42.0
Bending Moment (kNm)
96.2
120.7
3753
Torque (kNm)
815
1026
4332
Axial Force (kN)
2753
2145
10890
Shear Force (kN)
Z
Bending Moment (kNm)
Z0
ZO
52.9
52.9
ALT-2HT Connector
30"xl" Pipe
ST-2RB Connector
Torque (kNm)
° 1810% 53
Table 9. Comparison of LS-DYNA Continuum and Beam and Spring Models
1V610 IS$ COAf~CKTY
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Conductor Element
Sub-sea Conductor Study
Force /Moment
Yield Capacity
API t-z Springs
Shell t-z Springs
Axial Thermal Load (Ibs)
35"x2" Pipe
Axial Force (kN)
47950
Shear Force (kN)
ALT-2HT Connector @-2
2.2tkn't (HT IA) i)-41.
p~rm)
1,500,000 HTIA-HB(Shell) (Ref. Fig. 5.23)
2,700,000 HT2A-HC(Shell) (Ref. Fig. 5.41)
6680
12020
6680
12020
1073
1034
1079
1028
5200
5018
5230
4986
Torque (kNm)
10967
1820
1819
1820
1820
Axial Force (kN)
27585
5021
10393
4162
8484
32.8
30.2
36.1
26.7
Bending Moment (kNm)
5691
104.5
101.0
102.5
103.0
Torque (kNm)
2033
1026
1276
735
902
Axial Force (kN)
21070
5021
10390
4162
8484
42.0
40.1
41.7
40.5
Bending Moment (kNm)
3753
120.7
115.5
120.4
116.2
Torque (kNm)
4332
1026
1276
735
902
Axial Force (kN)
10890
2145
1938
767
276
0
=0
Z0
Z0
O0
=0
Zo0
Shear Force (kN)
("TBending _
2,700,000 HT2A-HC(API) (Ref. Fig. 5.22)
9505
Shear Force (kN)
ST-2RB Connector
1,500,000 HTI-A-I-IB(API) (Ref. Fig. 5.21)
Bending Moment (kNm)
Shear Force (kN)
30"xI" Pipe
Axial Thermal Load (Ibs)
_Torque
Moment (kNm) (kNmT
1810 53
RFF -Nce hFic-Nc
52.9
.2I 21_.2
33.1
[_ __ 12
18.1
=0
'523_
Table 10 LS-DYNA Beam and Spring Model Results for Hard Soil Profile
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Conductor
Sub-sea Conductor Study
Force /Moment
Element
35"x2` Pipe
Axial Force (kN)
Yield
API t-z Springs
Shell t-z Springs
Capacity
Axial Thermal Load (Ibs)
Axial Thermal Load (Ibs)
500,000
1,500,000
2,700,000
500,000
1,500,000
2,700,000
HT2B-MA
HT3B-MB
HT4B-MC
HT2B-MA
HT3B-MB
HT4B-MC
(Ref. Fig. 5.25)
(Ref. Fig. 5.26)
(Ref. Fig. 5.27)
(Ref. Fig. 5.28)
(Ref. Fig. 5.29)
(Ref. Fig. 5.30)
2241
6686
12020
2241
6686
12020
829
767
712
830
768
771
47950
Shear Force (kN)
ALT-2HT Connector
0
(
30"xI" Pipe
Bending Moment (kNm)
9505
6286
5817
5443
6287
5819
5427
Torque (kNm)
10967
1819
1820
1820
1820
1820
1820
Axial Force (kN) Shear Force (kN)
27585
1781 120.0
5666 106.4
-10742 87.8
1744 120.8
5495 106.5
10358 102.5
Bending Moment (kNm)
5691
48.4
35.1
13.2
48.4
35.3
41.3
Torque (kNm)
2033
1141
1283
1400
1068
1193
1307
Axial Force (kN)
21070
1759
5660
10850
1744
5498
10360
22.3
126.6
117.2
118.7
102.8
96.3
Shear Force (kN)
ST-2RB Connector
)
.e@-butom Mrz )-+.2e(HT41
Bending Moment (kNm)
3753
120.8
108.9
96.6
120.9
109.1
97.7
Torque (kNm)
4332
1137
1300
1434
1068
1193
1307
Axial Force (kN) Shear Force (kN)
10890
1938 =0
606 =0
987 =0
933 =°
1125 =0
2096 =0
Bending Moment (kNm)
1810
=0
Z0
=0
=0
=0
=0
52.9
44.6
bTorque (kNm)
53
|REFF~CE Hi. No0|
35524
g.2.9 |
S.k
t~2+
|
T. 25 |
C . 29
41.6
|
301
Table 11 LS-DYNA Beam and Spring Model Results for Medium Soil Profile
J:\50169-08\WII\R\0005C1 .REP
Ove Arup & Partners Page 35
1/99
22 February 1999
Shell UK Exploration & Production
Conductor Element
Sub-sea Conductor Study
Force /Moment
Yield Capacity
API t-z Springs
Shell t-z Springs
Axial Thermal Load (Ibs)
35"x2' Pipe
Axial Force (kN)
500,000
1,500,000
500,000
1,500,000
HT3B-SA(API)
HT4B-SB(API)
HT3B-SA(Shell)
HT4B-SB (Shell)
(Ref. Fig. 5.31)
(Ref. Fig. 5.32)
(Ref. Fig. 5.33)
(Ref. Fig. 5.34)
2253
6695
2255
6696
856
711
784
646
47950
Shear Force (kN)
ALT-2HT Connector
Bending Moment (kNm)
9505
7385
6228
7345
6127
Torque (kNm)
10967
1819
1819
1819
1819
Axial Force (kN)
27585
2074
6212
2102
6199
838
669
766
608
Shear Force (kN)
30"xl" Pipe
Axial Thermal Load (Ibs)
Bending Moment (kNm)
5691
3200
2457
3860
2999
Torque (kNm)
2033
1466
1526
1458
1506
Axial Force (kN)
21070
2079
6245
2096
5072
836
710
784
646
Shear Force (kN) Bending Moment (kNm)
3753
3405
2799
3854
Torque (kNm)
4332
1481
1547
1458
1506
ST-2RB Connector
Axial Force (kN)
10890
319.4
481
308
605
e-63.Of (WF3a)
Shear Force (kN)
=0
Z0
=0
1810
=O
=O0
53
14.8
-XR .2
(Hk4/3)
Bending Moment (kNm) Torque (kNm)
| QF2E*CS FIC- N6:[
5,31
8.1
|______
-K
2997
|
|0 30.1
12.1
_________I________
Table 12 LS-DYNA Beam and Spring Model Results for Soft Soil Profile
J:50169-08\WlI\R\0005CI-I.REP
Ove Arup & Partners Plage 36
1/99 22 February 1999
Shell UK Exploration &Production
Design Case
Sub-sea Conductor Study
35" x 2" Pipe
ALT-2HT Connector
30" x 1" Pipe
First ST-2RB Connector
Axial Only
Combined Loading
Axial Only
Combined Loading
Axial Only
Combined Loading
Axial Only
Combined Loading
HTIA-HB
6711
6680
3740
4102
3733
4162
637
767
HT2A-HC
12010
12020
7968 .
8484
8009
8484
232
276
HT2B-MA
2224
2224
1154
1744
1165
1744
234
533
HT31B-MB
6672
6686
4937
5498
4915
5498
662
1125
HT4B-MC
12010
12020
9974
10358
10010
10360
1611
2096
HT3B-SA
2224
2255
1660
2102
1669
2096
1320
3079
HT4B-SB
6674
6696
5817
6199
5832
5072
365
605
Table 13 Axial Loads in Conductor Elements Due to Thermal Axial Loading Only, and Due to Combined Loading (Results for Shell t-z Springs)
Design Case
API t-z Springs Upward Movement
Lateral Movement
(mm)
(mm)
HTIA-HB
8.5
8.0
HT2A-HC
19.2
HT2B-MA
Shell t-z Springs Rotation (degs)
Upward Movement
Lateral Movement
(mm)
(mm)
1.06
5.0
24
0.67
22.0
1.41
11.3
22
0.82
4.2
104
1.81
2.9
56
1.70
HT3B-MB
14.3
95
2.09
15.3
96
2.18
HT4B-MC
32.7
90
2.70
37.3
90
2.88
HT3B-SA
5.0
380
2.42
5.3
460
2.56
HT4B-SB
13.5
310
2.64
12.7
360
2.78
Rotation (degs)
Table 14 Displacements at Conductor Head
J:\50169-08\IP',\ROOOSCH.REP
Page 37
Ove Arup & Partners
1/99
22 February 1999
Sub-sea Conductor Study
Shell UK Exploration & Production
Combined Stress Check
Axial Tension
Bending
Allowable Tensile Stress
Allowable Bending Stress
Ft = 0.6 FY = 217MPa
Fb = 0.75 FY = 271MPa
Design Case
Force
Stress
Fa (MN)
fa (MPa)
Moment
Stress
Axial and
Mb
fb (MPa)
Bending fa+fb (MPa)
(MNm)
ja- +fb 0.6F.
0.75F, : 1.33
Shell t-z Spring Results HTIA-HB
6.68
49.9
5.23
196.5
246.4
0.96
HT2A-HC
12.02
89.8
4.99
187.5
277.3
1.11
HT2B-MA
2.24
16.7
6.29
236.3
253.0
1.01
HT3B-MB
6.68
49.9
5.82
218.6
268.5
1.04
HT4B-MC
12.02
89.8
5.43
204.0
293.6
1.17
HT3A-SA
2.25
16.8
7.35
276.1
292.9
1.10
HT4B-SB
6.70
50.1
6.13
230.3
280.4
1.08
195.4
245.3
0.95
API t-z Spring Results HT1A-HB
6.68
49.9
5.20
HT2A-HC
12.02
89.8
5.02
188.6
278.4
1.11
HT2B-MA
2.24
16.7
6.29
236.3
253.0
0.95
HT3B-MB
6.69
49.9
5.82
218.6
268.5
1.04
HT4B-MC
12.02
89.8
5.44
204.4
294.2
1.17
HT3B-SA
2.25
16.8
7.39
277.6
294.4
1.10
HT4B-SB
284.2 234.1 6.23 50.1 6.70 a). Combined Axial, Moment, Shear and Torque Loading
Soil Profile
.
1.09
Allowable Bending Stress Fb = 0.75 FY =
Moment Mb (M)
27
1 MPa
Stress fb (MPa)
fb-
0.75FY
(kI~m) Hard
5601
210.4
0.78
Medium
6891
258.9
0.96
318.2 8470 b). Moment and Shear Loading Only
1.17
Soft
Table 15 Axial and Bending Stresses in 35" x 2" Pipe
J:\50169-08\WS'P\R\OOOSCH.REP
Page 38
Ove Arup &Partners 1/99 22 February 1999
Shell UK Exploration &Production
Design Case
Sub-sea Conductor Study
Axial Tension
Bending
Allowable Tensile Stress
Allowable Bending Stress
F, = 0.6 FY Force Fa
(MN)
217MPa
Combined Stress Check
Fb =0.75 FY = 271MPa
Stress
Moment
fa (MPa)
Mb
Stress fb
Axial and
(MPa)
(MNm)
-fa
+ fb_
Bending fa+fb (MPa)
0.6FY 0.75FY <1.33
Shell t-z Spring Results HTIA-HB
4.16
70.8
0.12
11.5
82.3
0.37
HT2A-HC
8.48
144.2
0.12
11.5
155.7
0.71
HT2B-MA
1.74
29.6
0.12
11.5
41.1
0.18
HT3B-MB
5.50
93.6
0.11
10.5
104.1
0.47
HT4B-MC
10.36
176.2
0.1
9.5
185.7
0.85
HT3A-SA
2.10
35.7
3.86
368.6
404.3
1.53 4
HT4B-SB
5.07
86.2
3.0
286.5
372.7
1.46 3
API t-z Spring Results HTIA-HB
5.02
85.4
0.13
12.4
97.8
0.44
HT2A-HC
10.39
176.7
0.12
11.5
188.2
0.86
HT2B-MA
1.76
29.9
0.12
11.5
41.4
0.18
HT3B-MB
5.66
96.3
0.11
10.5
106.8
0.48
HT4B-MC
10.85
184.6
0.10
9.5
194.1
0.8
HT3B-SA
2.08
35.4
3.45
329.4
364.8
1.38
HT4B-SB
6.25 106.3 2.80 267.4 373.7 a). Combined Axial, Moment, Shear and Torque Loading
Soil Profile
1.48 s
Allowable Bending Stress Fb =0. 7 5 FY Moment
Mb
(kNm)
271
MPa
Stress
fb
fb_
(MPa)
0.75FY
Hard
125
11.9
0.04
Medium
136
13.0
0.05
4827 460.9 b). Moment and Shear Loading Only
1.70
Soft
(fggLaw .5t
s Page 39
P PE
5&F
Table 16 Axial and Bending Stresses in 30" x 1" Pipe
JA\50169-08\5\'P\R\0005CHREP
(
f-,
Fe tY AtiPLg
Ove Arup &Partners 1/99 22 February 1999
Sub-sea Conductor Study
Shell UK Exploration &Production
FIGURES
J \50169-OS\WP\R\OOOSCH.REP
Page 40
Ove Arup &Partners 1/99 22 February 1999
SHEAR STRENGTH (kN/m 2) 0
100
200
500
400
300
700
600
0
2
4
6
8
-10
I CL
W
12
*
0
14
16
DESIGN
PROFILE
@
18
20
.
UNDRAINED SHEAR STRENGTH HARD SOIL PROFILE 50169/08 Oct.'97
n
50169108
F
FIGURE J.
0
20
SHEAR STRENGTH (kN/m2 ) 60 80
40
100
120
140
W~~~~
14
0
0
10
*
12
16
20
*
*
*
~~~~DESIGN.
_ Note: Design profile follows the normally consolidated soft soil design profile below 30m depth
UNDRAINED SHEAR STRENGTH MEDIUM SOIL PROFILE 50169/08.
Oct. '97
50169/08
FIGURE1{-
40
20
0
SHEAR STRENGTH (kPa) 80 60
100
120
140
0
5
1
00
15
X
___
20~~~
20 10
*
M 30~~~~
25
40~~~~ I~~~~~~~~~~~~~DSG
50
UNDRAINED SHEAR STRENGTH SOFT SOIL PROFILE 50169/08 Oct. '97
50169/08
FIGURE
3.
~~~~~~~~~~~~~~~~~~~~~~~~~~~Soil surface
-
00= 0
-I1
Rigid collar
_____Scour
-I
to -1.5m
0
UI)
Top of grout
.
z o
~~~~~~~~~~~~~~~~~~~~~~~~~~Far-field boundary
C Lx CD
Pipe connector CD
CD~~~~~~~~~~~~~~~~.
X
D
t - z Springs
l
p - y Springs D= diameter of grout / soil interface
Bending
Schematic Model T
Fv
Axial Loading
Torsion Loading
T
LA
to l 3
tsa
Skin friction opposing axial loads
fst
Skin friction opposing torsion loads
.0~~~~~~~~~
FI
fst
/ atmax =Maximum available skin fsa~~~axfriction Axial
Axial and Torsion 50169/08 JAN. 99
Loading
SKIN FRICTION MODEL FOR LS-DYNA BEAM AND SPRING ANALYSES 0
50169/08
F
FIGURE'
Results for Increment -1000.0 1000.0 l
l
IShear force (kN) Pressure (kN/m2) 0
1000.0 1000.0
I
-3575.0 kNm
0~~~~~~~~~~~~~~~~~~~10
3~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~32 -10
-20
-30 CD
CD-4o
U
50
--
-60
-70
-78.00 -80 Shear F.___Disp.
----. P eff . -50.0 -5000.0
-~. B. Mom. 0
50.0
Displacement (mm) Bending moment (kNm)
5000.0
SUBSEA CONDUCTOR STUDY ALP P-Y RESULTS FOR HARD SOIL PROFILE 50169-08
FIGURE
5.1
Results for Increment -1000.0
1Shear force (kN) Pressure (kN/m2)
1000.0
I
0
_
I
=V
1000.0
0 I
1000.0
I
I
I
-3575.0 k0m 650 .0 kd
V._ °
1.00
2
2
3
3
-10
-20
-30
> -40-
CD
CD
a5-50
-60
-70
-78.00 -80 Shear F.____Disp.
P~wp.---250.0 -10000.0
P eff.
-
-B
Mom.
0 Displacement (mm) Bending moment (kNm)
250.0 10000.0
SUBSEA CONDUCTOR STUDY ALP P-Y RESULTS FOR MEDIUM SOIL PROFILE 50169-08
FIGURE
5.2
Results for Increment -1000.0 1000.0 I
lShear force (kN) Pressure (kN/m2) 0
1000.0 1000.0
I
-3575.0 kNm 0
V0
5
0k
_
2
_10
_
2
-10
I
Isr
Scir
__________.__
-20 LocAL -30
>-40_
w-50 -J~~_
.
-60
-70
-78.00
-80
....... P.w.p.-1000.0 -10000.0
-----_ P eff.
Shear F. - - - B. Mom.
0 Displacement (mm) Bending moment (kNm)
Disp.
1000.0. 10000.0
SUBSEA CONDUCTOR STUDY ALP P-Y RESULTS FOR SOFT SOIL PROFILE 50169-08
FIGURE
5.3
Subsea Conductor Study
HARD SOIL
5
0
-10
~-15
-20l -80
-40
0
40
80
Displacement (mm)
P-Y curve
---
250cu
--------- E= 150 to 250 cu
HARD SOIL PROFILE COMPARISON OF COMPUTED DISPLACEMENTS FROM ALP P-Y AND ELASTIC-PLASTIC MODELS 50169-08 J:\501 69-08\WP\Z\QPROFILE.WB2
FIGURE
5.4
Printed on 02/02199 13:29
Subsea Conductor Study
5
HARD SOIL
________
0
-5
0
-10
-15
-20
_
L 1
-6000
~
L
-4000
-2000
_
L
0
_
_
~
2000
_
_
_
4000
_
_
6000
Bending moment (kNm)
-
P-Y curve
--
E= 250cu
--------E= 150 to 250cu
HARD SOIL PROFILE COMPARISON OF COMPUTED BENDING MOMENTS FROM ALP P-Y AND ELASTIC-PLASTIC MODELS 50169-08 J:X50169-08\WPRZ\QPROFILEWB2
FIGURE
5.5
Printed on 02/02199 13:30
Subsea Conductor Study
MEDIUM SOIL
-5
_
_
_
_
-10
-15
-1
-20 -5
l___
ll
0
-30 -35 -40
-45
__
L
L
-350 -300 -250 -200 -150 -100
-50
0
50
Displacement (mm)
P-Y curve
--------- E'= 75 to 100 cu
MEDIUM SOIL PROFILE COMPARISON OF COMPUTED DISPLACEMENTS FROM ALP P-Y AND ELASTIC-PLASTIC MODELS 50169-08 J:\501 69-08\WP\Z\QPROFILE.WB2
FIGURE
5.6
Printed on 02/02/99 13:31
Subsea Conductor Study
5
_______
MEDIUM SOIL
________
0 0)
:S-0
-15
-4000
-2000
0
2000
4000
6000
8000
Bending moment (kNm)
P-Y curve
E' = 75 to 100 cu
MEDIUM SOIL PROFILE COMPARISON OF COMPUTED BENDING MOMENTS FROM ALP P-Y AND ELASTIC-PLASTIC MODELS 50169-08 J\501 69-08\WP\Z\QPROFl LI
B2
FIGURE
5.7
Printed on 02/02/99 13:31
Subsea Conductor Study
SOFT SOIL
5
-5
_
-10
-15__ :
20,
0,
CL
-20 30
~-35 -40
COMPARISON OF COMPUTED DISPLACEMENTS FROM ALP P-Y AND ELASTIC-PLASTIC MODELS 50169-08 OIL J:501 69-08\WVPZ\QPROF IL1 .WB2
5.8 Printed on 02/02/99 13:32
Subsea Conductor Study
5
SOFT SOIL
________
-5 -10__
_
_
_
_
_
~-15 -20
0
0
.5 -25 -30 -35 -40
-2000
0
2000
4000
8000
6000
10000
Bending moment (kNm)
P-Y curve ----
=
250cu
SOFT SOIL PROFILE COMPARISON OF COMPUTED BENDING MOMENTS FROM ALP P-Y AND ELASTIC-PLASTIC MODELS 50169-08 J:\50169-08\WvrZ\OPROFIL1.WB2
FIGURE
5ig
Printed on 02/02/99 13:33
z-. -(0 (D O
LS-DYNA Beam and Spring Model ;
800 600 --
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Shell UK Exploration &Production
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DRAWINGS
JASO169-08S\kP\R\OOOSCH. REP
Page 41
Ove Arup & Partners 1/99 22 February 1999
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February 1999
Ove Arup & Partners Arup Geotechnics 13 Fitzroy Street London W1 P 6BQ Telephone +44 (0)171 636 1531 Facsimile +44 (0)171 465 2121 Job number 50169-08
POve Arup & Partners
A]RJJ 1t j1
Document Verification
Arup Geotechnics
P
Job title
Sub-sea Conductor Study
Job number
50169-08
Document title Document reference
LS-DYNA Three dimensional modelling of conductors under combined axial, bending and torsion loading
Prepared by
Chris Humpheson
Signed Date
L2./ L/ 4C4
Chris Humpheson
Checked by
C.
Signed
LL>
Date
tl
c
Q
David Clare
Approved by Signed
*
Date
Z
HvLc
Revision record Revision
Date
Description/Filename
Prepared
Checked
Approved
1/97
07/11/97
G:\50169-08\R\0004CH.REP
CH
CH
DGC
1/99
22/2/99
J:\50169-08\WP\R\OOO5CH.REP
CH
CH
DGC
J:\50169-O8\WP\R\OOO5CH.REP
Ove Arup Partnership F8.5 Rev 1/99 22 February 1999
AJ~
T
U T iD Ji
Job title
Revisions
Ove Arup & Partners Arup Geotechnics
Sub-sea Conductor Study
Page 1 of ?
Job number
50169-08 Document title Document reference
LS-DYNA Three dimensional modelling of conductors under combined axial, bending and torsion loading
Revision
Date of issue
1/97
.07/11/97
1/99
22/02/99
J:\50169-OS\WP\R\OOOSCH.REP
Description
First draft. Issued for comment.
Final
Ove Armp & Partners Rev 1/99 22 February 1999
Shell UK Exploration & Production
Sub-sea Conductor Study
CONTENTS SUMMARY 1.
INTRODUCTION
2.
PREVIOUS STUDIES BY SHELL
3. 3.1 3.2
STUDY DATA Soil Conditions Loads 3.2.1 Trawler Net 3.2.2 Thermal Loads Conductor Strings Connector Properties Pipe Properties
3.3 3.4 3.5 4. 4.1 4.2 4.3 4.4 4.5
METHODS OF ANALYSIS General Assumptions Analysis Procedures ALP Analyses LS-DYNA Analyses 4.4.1 Description of Program LS-DYNA Continuum Model 4.5.1 Geometry 4.5.2 Casings 4.5.3 Conductor 4.5.4 Connectors 4.5.5 Grout
4.5.6
4.6
5. 5.1 5.2
5.3
4.5.7 4.5.8 4.5.9 4.5.10 4.5.11 LS-DYNA 4.6.1 4.6.2 4.6.3 4.6.4 4.6.5
Soil Boundary Conditions Material Properties Soil-grout interface Loading Damage Identification Beam and Spring Model Conductor Casing Lateral Load Behaviour p-y Springs Skin Friction t-z Spring Loads Modelling Inaccuracies
STUDY RESULTS Analysis Strategy Lateral and Moment Loading Only 5.2.1 ALP p-y Analyses 5.2.2 ALP Elastic-Plastic Soil Model 5.2.3 LS-DYNA Beam and Spring Model 5.2.4 ALP and LS-DYNA Comparisons Combined Lateral, Moment, Vertical and Torsion Loading 5.3.1 Analyses Carried Out 5.3.2 Design Case HT1A-HB (API) 5.3.3 Results of LS-DYNA Beam and Spring Model Analyses 5.3.4 Results for Hard Soil Profile 5.3.5 Results for Medium Soil Profile
J:\SO169-OS\0VP\R\OOOSCH.REP
Ove Armp & Partners 1/99 22 February 1999
Shell UK Exploration & Production
Sub-sea Conductor Study
5.3.6 Results for Soft Soil Profile 5.3.7 Axial and Bending Stresses 5.3.8 Comparison of Results for first ST-2RB Connector 5.3.9 Grout to Casing Shear Stresses Review of Results 5.4.1 Spalling of Grout 5.4.2 Axial Thermal Loads
5.4
6.
TEMPERATURE EFFECTS
7. 7.1
CONCLUSIONS Conductors in Hard Soil Conductor String HT1A Conductor String HT2A Conductors in Medium Soil Conductor String HT2B Conductor Strings HT3B and HT4B Conductors in Soft Soil Conductor Strings HT3B and HT4B Grout to Casing Shear Stresses Effects of Heating on Geotechnical Properties
7.2
7.3 7.4 7.5 8. 8.1 8.2
REVIEW OF ANALYTICAL METHODS Assessment of Results Improvements to Modelling Techniques 8.2.1 Detailed Modelling of Conductor and Grout 8.2.2 Improved Continuum Model 8.2.3 Improved Grout to Soil Interface
9.
RECOMMENDATIONS FOR FURTHER WORK
10.
REFERENCES
FIGURES Figure Figure Figure Figure Figure Figure Figure Figure Figure
3.1 3.2 3.3 4.1 4.2 5.1 5.2 5.3 5.4
Figure 5.5 Figure 5.6 Figure 5.7 Figure 5.8 Figure 5.9
J:\50169-08\W\'P\R\OOO5CH.REP
Undrained Shear Strength. Hard Soil Profile Undrained Shear Strength. Medium Soil Profile Undrained Shear Strength. Soft Soil Profile Cut Section Through LS-DYNA Continuum Model Skin Friction Model for LS-DYNA Beam and Spring Analyses ALP p-y Results for Hard Soil Profile ALP p-y Results for Medium Soil Profile ALP p-y Results for Soft Soil Profile Hard Soil Profile. Comparison of Computed Displacements from ALP p-y and ElasticPlastic Models Hard Soil Profile. Comparison of Computed Bending Moments from ALP p-y and Elastic-Plastic Models Medium Soil Profile. Comparison of Computed Displacements from ALP p-y and Elastic-Plastic Models Medium Soil Profile. Comparison of Computed Bending Moments from ALP p-y and Elastic-Plastic Models Soft Soil Profile. Comparison of Computed Displacements from ALP p-y and ElasticPlastic Models Soft Soil Profile. Comparison of Computed Bending Moments from ALP p-y and Elastic-Plastic Models
Ove Arup & Partners 1/99 22 February 1999
Shell UK Exploration & Production
Sub-sea Conductor Study
Figure 5.10 Hard Soil Profile. LS-DYNA Results for Lateral and Moment Loading Figure 5.11 Medium Soil Profile. LS-DYNA Results for Lateral and Moment Loading Figure 5.12 Soft Soil Profile. LS-DYNA Results for Lateral and Moment Loading Figure 5.13 API and Shell t-z Springs Figure 5.14 LS-DYNA Continuum Model. Conductor Force and Moment Profiles Figure 5.15 LS-DYNA Continuum Model. Horizontal Displacement at Top of Conductor Figure 5.16 LS-DYNA Continuum Model. Cutaway indicating Horizontal Displacement Figure 5.17 LS-DYNA Continuum Model. Cutaway Indicating Horizontal Movement Within the Soil Figure 5.18 LS-DYNA Continuum Model. Relative movement between conductor and soil Figure 5.19 LS-DYNA Continuum Model. Maximum shear stress within soil Figure 5.20 LS-DYNA Continuum Model. Stress in x-direction within soil continuum Figure 5.21 LS-DYNA Beam and Spring Model. Force/Moment for HT1A-HB(API) Figure 5.22 LS-DYNA Beam and Spring Model. Force/Moment for HT2A-HC(API) Figure 5.23 LS-DYNA Beam and Spring Model. Force/Moment for HT1A-HB(Shell) Figure 5.24 LS-DYNA Beam and Spring Model. Force/Moment for HT2A-HC(Shell) Figure 5.25 LS-DYNA Beam and Spring Model. Force/Moment for HT2B-MA(API) Figure 5.26 LS-DYNA Beam and Spring Model. Force/Moment for HT3B-MB(API) Figure 5.27 LS-DYNA Beam and Spring Model. Force/Moment for HT4B-MC(API) Figure 5.28 LS-DYNA Beam and Spring Model. Force/Moment for HT2B-MA(Shell) Figure 5.29 LS-DYNA Beam and Spring Model. Force/Moment for HT3B-MB(Shell) Figure 5.30 LS-DYNA Beam and Spring Model. Force/Moment for HT4B-MC(Shell) Figure 5.31 LS-DYNA Beam and Spring Model. Force/Moment for HT3B-SA(API) Figure 5.32 LS-DYNA Beam and Spring Model. Force/Moment for HT4B-SB(API) Figure 5.33 LS-DYNA Beam and Spring Model. Force/Moment for HT3B-SA(Shell) Figure 5.34 LS-DYNA Beam and Spring Model. Force/Moment for HT4B-SB(Shell) Figure 5.35 Comparison of Torque at First Standard Connector (API) Figure 5.36 Comparison of Torque at First Standard Connector (Shell) Figure 5.37 Torque at First Standard Connector for HT1A-HB Continuum Model Figure 5.38 Shear Stress at Conductor/Grout interface for HT1A-HB Continuum Model Figure 5.39 Frictional Resistance of Debonded Grout DRAWINGS A210990-2 A210990-3 A210990-4 A210990-5
J \50169-08\WP\R\OOOSCH.REP
Rev. A Rev. A Rev. A Rev. A
30" x 30` x 30" x 30" x
1" Conductor 1" Conductor 1" Conductor 1` Conductor
String String String String
with with with with
Resistance to Torque Type Resistance to Torque Type Resistance to Torque Type Resistance to Torque Type
HT1A HT2A HT3A HT4A
& & & &
HT1B HT2B HT3B HT4B
Ove Arup & Partners 1/99 22 February 1999
Shell UK Exploration &Production
Sub-sea Conductor Study
SUMMARY Shell Expro have developed detailed proposals for conductor designs for a range of ground conditions representative of those in the UK sector of the Central North Sea. The make-up of the proposed casing strings consists of a 40ft or 60ft length of 35" outer diameter by 2" wall thickness casing, followed by 50ft lengths of 30" outer diameter 1" wall thickness casing. There are 4 or 5 lengths of 30" casing, depending on the assumed ground conditions. The 35" casing is connected to the 30" casing using a high torque connector. The lengths of 30" casing are connected using either high or standard torque connectors. The principal objective of the current study was to assess the adequacy of the proposed casing string make-up for the assumed ground conditions, and in particular whether the proposed number of high torque connectors in each of the casing strings is justifiable. The study has been carried out using the program LS-DYNA to assess the behaviour of conductors when subjected to combined axial, bending and torsion loads. Shell have prepared casing designs for three idealised soil profiles covering a range of ground conditions varying from normally consolidated to heavily overconsolidated clay. The three profiles are identified as 'hard', 'medium' and 'soft'. The hard profile represents very stiff overconsolidated clay and dense sand sites, comparable to conditions at Nelson. The medium profile is formed of firm to stiff clay and medium dense sand, similar to those at Kittiwake. Normally consolidated sites, similar to conditions at Gannet, are represented by the soft profile. The axial loads to which the conductor strings are subjected are upward forces due to thermal expansion of the inner well casing. Three axial loads are specified by Shell to cover a range of temperatures of the hydrocarbons passing through the inner casing. Lateral, moment and torsion loading is due to trawler nets snagging on the Christmas tree assembly installed on the well head. For hard soil sites the current proposal is to use one high torque connector for the design case with the lowest hydrocarbon temperature, but two high torque connector for other load cases. The analyses show that the proposed conductor strings for hard soil conditions are adequate if t-z springs normally used by Shell are adopted. However, if t-z springs recommended by API are used then two high torque connectors are required for all conductor strings in hard soil conditions. For medium soil sites the current proposal is to use 2, 3 or 4 high torque connectors depending on the temperature of the hyrocarbon. The LS-DYNA analyses show that three high torque connectors are required for the lowest temperature load case instead of the two currently proposed. The other two design proposals are adequate. The proposed arrangement of high torque connectors for soft soil sites is adequate. The analyses indicate, however, that combined stresses in the top of the 30" conductor exceed recommended values and therefore some local yielding may occur if all the design loads act simultaneously.
J\SO169-o8\
PaR\0005CH REP
Ove Arup &Partners 1/99 22 February 1999
Shell UK Exploration & Production
1.
Sub-sea Conductor Study
INTRODUCTION Shell Expro want to rationalise the design of well conductors so that all exploration and appraisal wells with the potential to become producers can be developed as sub-sea production wells if required. To achieve this aim it is necessary that the conductors used on these wells are strong enough to withstand all loads which may be applied to the conductor through the sub-sea wellhead assembly. Attenuation of loads occurs with depth below mudline, but one aspect of particular concern is that connections within the casing string have adequate capacity to resist the torque applied to the joint. Loads that affect the design and performance of the conductors are: *
Axial tensile force due to the conductor restraining the thermal expansion of the inner well casing;
*
Environmental loading transmitted to the conductor from a sub-sea wellhead tree;
*
Accidental loads due to snagging of trawler nets or trawl boards on the wellhead tree.
These loads can act individually, or in any combination, subjecting the conductor to a combination of axial, bending and torsion loading. Calculations already carried out by Shell have resulted in detailed proposals for conductor designs for a range the ground conditions anticipated for the UK Sector of the Central North Sea where Shell own exploration licences. The methods of analysis used by Shell were not, however, able to analyse the behaviour of the conductors under the combined effects of axial, bending and torsion loading and Shell are seeking independent validation of their design proposals. Arup Geotechnics were appointed by Shell to undertake a study to investigate the adequacy of the proposed casing string make-ups for specified ground conditions and load combinations. The analyses were to be undertaken using the program LS-DYNA to develop 3-D finite element models of casing and grout configurations for three soil types. The Scope of Work required: *
Model the combined soil resistance to axial, torsion and bending stress;
*
Determine axial, bending and torsion stress profiles in casing and joints for given bending and torsional loads and various axial loads;
*
Investigate grout/casing shear stress;
*
Investigate soil and grout behaviour at high temperatures (150 to 330 degs F) and modify soil model as necessary.
Details of the work carried out to complete this study are presented in this report.
J:\50169-OS\X'P\R\OOOSCH.REP
Page 2
Ove Arup & Partners 1/99 22 February 1999
Shell UK Exploration & Production
2.
Sub-sea Conductor Study
PREVIOUS STUDIES BY SHELL Analytical studies have been carried out by Shell to study the behaviour of subsea conductors when subjected to lateral and moment loading, and also to investigate stresses within the conductors due to the application of torque and tensile axial loads. The analyses have been performed for three soil types, identified as 'hard','medium' and 'soft', which are representative of soil conditions in the Nelson, Kittiwake and Gannet fields. The Shell studies were carried out in three phases as follows: *
Early studies, carried out using the SPLICE program, considered lateral and moment loading only. The results of this study are reported in Shell Engineering Report Number E93005, dated June 1993.
*
Later studies, also using the SPLICE program, looked at the behaviour of conductors under axial and torsion loading. The purpose of these studies was to investigate the stress profile down the conductor, particularly the attenuation of torsion, so that the depth to which high torque connectors are needed could be assessed. Full details of the analyses carried out are not known but, because of the limitations of the software available to Shell, it was not possible to analyse the conductors under combined axial and torsion loading. It is understood that in the analyses carried out by Shell the skin friction mobilised by the axial load was calculated first, and it was then assumed that the remaining skin friction between mobilised and ultimate was available to resist torsion.
*
Independent studies were also carried out by Shell to assess the axial loads applied to the conductor by thermal expansion of the inner casing.
Based upon the results of these studies various conductor string make-ups have been devised by Shell for each of the reference soil conditions for various axial loads representing thermal expansion of the inner well casing due to hydrocarbons of differing temperatures.
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3.
STUDY DATA
3.1
Soil Conditions Shell have provided details for three soil profiles which characterise ground conditions in the UK sector of the Central North Sea where the majority of their exploration licences are located. The idealised soil profiles are based upon data from three Shell Expro Oil Field geotechnical boreholes and represent ground conditions varying from normally consolidated to heavily over consolidated clay. Undrained shear strength profiles for the three soil types, subsequently referred to as 'hard', 'medium' and 'soft', are shown on Figures 3.1 to 3.3. Details of the soil profiles are given in Table 1. The 'hard' profile is also representative of ground conditions in the Northern North Sea sites operated by Shell.
Profile
Field
Formation
Description
Hard (H)
Nelson
Fisher
Very stiff over consolidated silty clays and dense sands.
Medium(M)
Kittiwake
Coal Pit
Firm to stiff silty clays and medium dense sands.
Soft (S)
Gannet
Forth
Very soft to firm normally consolidated clay. Table 1. Soil Profiles
3.2
Loads 3.2.1
Trawler Net
Studies have been carried out for Shell to assess loads applied to the conductor due to trawler nets snagging on the Christmas tree assembly installed on the wellhead. Snagging loads used by Shell, and adopted as design loads for the current study, are as follows: *
lateral force of 650 kN;
*
bending moment of 3575 kNm;
*
torque applied about the vertical axis of 1820 kNm.
It is assumed that these loads are applied to the conductor 1m above seabed level. 3.2.2
Thermal Loads
Hot hydrocarbons are transmitted through the inner well casing to the wellhead. Thermal expansion of the inner well casing is restrained by the outer conductor. For the conditions of a rigid connection between the inner well casing and the outer conductor, and no upward movement of the outer conductor, Shell have provided details of the upward loads to be resisted by the conductor. Upward loads assumed for the current study are summarised in Table 2.
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Load Case
Sub-sea Conductor Study
Temperature Range
Net Upward Load
Degs. F
Degs. C
lbs
kN
A
<150
<66
500,000
2240
B
>>150 <260
>66 <127
1,500,000
6672
C
>260 <330
>127 <166
2,700,000
12010
Table 2. Thermal Loads
3.3
Conductor Strings A typical well consists of a 20" outer diameter by 0.625" wall thickness inner well casing, with a 240ft to 320ft long outer conductor casing. The conductor string consists of a 40ft or 60ft top length of 35" outer diameter by 2" wall thickness casing, which stands Im proud of the seabed, followed by 5Oft lengths of 30" outer diameter by 1" wall thickness casing. Individual lengths of casing are joined by box and pin connectors. The conductor is grouted into a 36" diameter drillhole. The annulus between the 20" well casing and the conductor is also grouted. Details of conductor strings proposed by Shell have been taken from ABB Vetco Gray drawing numbers A210990-2 to -5, which were supplied by Shell. Copies of these drawing are contained in Appendix A. The make up of conductor strings used in the current study are summarised in Table 3 (see tables following references).
3.4
Connector Properties Details of the box and pin connectors used in the conductor strings have been taken from ABB Vetco Gray data sheets TDS/1041 and TDS/1017. Yield capacities of connectors relevant to the current study are summarised in Table 4.
Connector Capacity
ALT-2HT ( high torque)
ST-2RB ( standard torque)
Tension
6200 kips
27585 kN
2430 kips
10809 kN
Compression
8650 kips
38475 kN
4549 kips
20234 kN
Bending
4200 kip-ft
5691 kN-m
1810 kip-ft
1810 kN-m
Torsion
1500 kip-ft
2033 kN-m
39 kip-ft
53 kN-m
Table 4. Connector Properties
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3.5
Sub-sea Conductor Study
Pipe Properties The conductor pipes are manufactured of grade X52 (52 ksi) steel. Yield capacities for the two sizes of pipes used in the conductor strings are summarised in Table 5 for axial tension and compression, torsion and bending.
Yield Capacity
30" x 1"
35" x 2"
Tension
4738 kips
21070 kN
10780 kips
47950 kN
Compression
4738 kips
21070 kN
10780 kips
47950 kN
Bending
2770 kip-ft
3753 kN-m
7015 kip-ft
9505 kN-m
| Torsion
3197 kip-ft
4332 kN-m
8094 kip-ft
10967 kN-m
Table 5. Pipe Properties
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4.
METHODS OF ANALYSIS
4.1
General Assumptions All of the analyses were carried out with the following general assumptions:
4.2
*
The 20" casing inside the conductor, and the grout between the casing and the conductor, has been ignored.
*
Local scour around the conductor to a depth of 1.5m below seabed level.
*
The top surface of the grout around the outside of the conductor is at a depth of 1.5m below seabed level.
*
The conductor is placed centrally within the predrilled hole and the annulus between the conductor and the predrilled holed is completely filled with grout.
*
No restraint is applied to the conductor by the well head and Christmas tree assembly, ie free head conditions apply
*
Young's Modulus Este, = 210 x 106 kPa, Egrout
=
5 x 10 kPa
Analysis Procedures Analysis of the conductors under the combined effect of axial, bending and torsion loading was to be carried out using the 3D program LS-DYNA. This program had not been used for this particular application before and therefore the initial stage of the analyses consisted of validating LS-DYNA for 2D loading calculations against the results from a conventional 2D analysis. The program used to provide 2D results against which LS-DYNA was compared was ALP.
4.3
ALP Analyses ALP is an OASYS program for the analysis of vertical piles subjected to lateral loads, bending moments and imposed soil displacements. ALP cannot take account of vertical or torsion loading. ALP analyses were carried out in order to provide data against which LSDYNA results could be compared. ALP analyses were initially carried out using standard p-y data to represent the load deflection behaviour of the soil. The p-y curves were generated by ALP using the method proposed by Matlock (1970) for static loading conditions. Values of e.0 , the axial strain at a stress level of one-half of the ultimate resistance, used to calculate the p-y curves are given in Table 6 and follow the recommendations of Sullivan et al. (1980) Soil Profile
Eso
Hard
.004
Medium
.01
Soft
.02
Table 6. E,, values for p-y curves
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The conductor and surrounding grout was modelled as a 36" (0.914m) diameter, 78m long, pile of variable flexural stiffness (El). No allowance was made for the increased El at the joints. In subsequent ALP analyses the soil was modelled as an elastic-plastic material. The soil stiffness was adjusted until the conductor deflection profile from the elastic-plastic model matched that obtained previously from the p-y model. The soil stiffness profile obtained in this manner was subsequently used in the LS-DYNA continuum model.
4.4
LS-DYNA Analyses 4.4.1
Description of Program
LS-DYNA is an explicit finite element program which enables the solution of three dimensional problems involving a high degree of geometric and material non-linearity.
4.5
LS-DYNA Continuum Model In this model the soil surrounding the conductor is modelled as an elastic-plastic continuum. The conductor, grout and pipe connectors are modelled as individual components with appropriate material properties. Figure 4.1 shows a cut-section through the model. The model has a total of 100,000 elements. 4.5.1
Geometry
No symmetry has been used in the model representing the subsea conductor pile. This is because it was deemed that the loading (combination of axial/torque/lateral/bending) would force the pile to behave eccentrically. Any boundary conditions used to force symmetry behaviour would also be resisting the movement of the pile and hence would be detrimental to the analysis. 4.5.2
Casings
The 20" casings and surrounding grout inside the conductor have been ignored for the purpose of this analysis. These elements are assumed to be non-load bearing, and therefore have no effect on the result - except to complicate the analysis further. 4.5.3
Conductor
The conductor is represented by 2D shell elements of the correct thickness. In the LS-DYNA model, the shell element position is located in the centre of the conductor wall, ensuring that the correct flexural stiffness is calculated. 4.5.4
Connectors
The lengths of conductor are connected together using joints which represent the high torque and standard torque connectors. These joints form a box and pin arrangement and are modelled as non-deformable materials. The pin and box are connected via non-linear springs which allow the yield criterion/capacity to be specified according to the data supplied and tabulated in Section 3.4 of this report. 4.5.5 J:\5O 69-08\15'P\R\OOOSCH. REP
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The grout is modelled using eight node solid elements. The external diameter of the grout is 36" (0.9144 m). The grout is meshed to the conductor shell elements, so that the internal diameter of the grout is on the centre-line of the conductor wall, hence the grout is marginally thicker than specified in the drawings. Due to the weakness of the grout, this extra thickness will have very little effect on the overall stiffness of the steel-grout composite. No facility has been included to allow the grout to become detached from the steel conductor.
4.5.6
Soil
The soil is modelled using eight node solid elements. The top layers of soil (down to 5.0 m below the surface) are modelled using 'fully integrated solids'. These elements are computationally expensive, but do allow greater accuracy in calculations where large deformations are expected. The soil extends out to a radius of five diameters beyond the grout at the top of the model (eleven diameters across in total), where the deformation is expected to be the largest. This tapers to just two diameters beyond the grout (five diameters across) at a level below the bottom of the conductor. In order to model the local failure of the soil around the conductor, small elements (1" in size) are used adjacent to the conductor with increasing element size away from the conductor. A region of scour is modelled down a to depth of 1.5 m below the surface level, at a gradient of 45 degrees. The grout starts below this level.
4.5.7
Boundary Conditions
The free field boundaries of the soil elements are fully fixed against translation. While there is likely to be some interaction between the pile and the outside boundary, it is not considered to be enough to affect the failure mechanisms of the pile against the soil.
4.5.8
Material Properties Steel
The steel material has an elasto-plastic behaviour allowing the maximum stress to be limited. The pipe work is made of grade X52 steel having a yield stress of 52 ksi (361 N/mnr). When this stress level is exceeded, the material deforms plastically, maintaining the yield stress with no plastic hardening. The ability for the steel to deform plastically will allow the steel tube to buckle under extreme load conditions. Connectors As mentioned above, the connectors are modelled as non-deformable materials. The non-linear springs connecting the pin and box allow elastic-perfectly-plastic behaviour. A displacement criterion has been used to define the yield of the joints. In axial compression and tension the joint can deform by 0.1 mm elastically, beyond which the plastic deformation occurs. The elastic stiffness is calculated assuming that the full yield capacity is developed at 0.1mm displacement. Similarly in bending and torque the maximum elastic rotation allowed is 2.5 x 10O' radians. Grout The grout material behaves elastically at a fraction of the stiffness of concrete approximately 5 MPa. This is an approximation, because grout can resist limited tensile forces. While it is possible to model the grout such that it behaves as in reality, this would require the correct confining stresses to be present in the soil surrounding the pile. Since the strength of the grout is small in comparison with the steel, it is considered sufficient to ignore the tensile failure.
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Soil The soil material uses a Modified Drucker Prager failure criterion (similar to Mohr-Coulomb but applicable to three dimensional analysis). This allows the soil to yield once a given deviatoric stress or shear stress is achieved within the soil. In this case, for all three soil profiles (hard, medium and soft) a simple undrained shear strength is used to define the yield, varying with depth. The elastic Young's Modulus of the soil is assumed to be directly proportional to the undrained shear strength, ie. for the 'hard' profile E = 150C to 4.5m, E = 250cu below 4.5m. To model undrained (incompressible) behaviour it is assumed that Poisson's Ratio = 0.49. In this study the failure criteria of the soil is dependent only on the undrained shear strength, cu. The initial state of stress in the soil prior to installation of the conductor is therefore not critical in this study. The current model does not consider the following:*
the pre-analysis stress history,
*
the effect of the drilling of the pile bore,
*
the effect of thermal cycling on the soil.
The soil is assumed to be homogenous across the horizontal plane (not varying with temperature gradients), and varying strength with depth.
4.5.9
Soil-grout interface
In the continuum model the soil is not meshed directly to the grout. A 'contact surface' is used between the grout and the soil which prevents the grout from penetrating into the soil when the conductor pushes into the soil, but allows the grout to pull away from the soil so that tension cannot be transferred from the grout to the soil. The drawback of this arrangement is that shear can only be transferred across a contact surface by friction. (ie. the shear transfer depends on the normal stress and the angle of friction between the two surfaces.) There is currently no facility within LS-DYNA for adhesion contact surfaces on which the shear transfer depends on the contact area and some proportion of the undrained shear strength of the soil. Although shear due to torque or axial loading of the conductor could be modelled using the frictional characteristics of the grout-soil interface (which would require the correct confining pressures to be known in the soil), for piles in clay the limiting 'skin friction' is usually assumed to be a function of the undrained shear strength. In offshore pile design it is common practice to use t-z curves to define the relationship between pile movement and mobilised skin friction. To overcome the uncertainty associated with using a friction model for the grout-pile interface, and to be compatible with conventional offshore pile design methods, a series of non-linear t-z springs are used to model the skin friction on the grout-soil interface (assuming that the 'contact surface' is frictionless). These springs connect the outer surface of the grout to the soil continuum and are oriented so that they work in the plane tangential to the surface of the grout. The springs are linear elastic/plastic and it is assumed that full friction is mobilised at a relative displacement between grout and soil of 1% of the diameter of the pile. Ultimate skin friction values are calculated as acd using a values recommended API RP 2A (1993), Section 6.4.2. This failure mechanism was tested by analysing the conductor being pulled directly out of the ground until the full shear force was mobilised. The force to cause failure compares well with the force calculated by integrating acd over the entire length of the pile.
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4.5.10
Sub-sea Conductor Study
Loading Thermal
A constant vertical force is applied to the top of the conductor where it is attached to the wellhead tree. The magnitude of this force varies with hydrocarbon temperature according to the data shown in Table 2 of this report. The vertical force is applied prior to the other loads so that the model is in equilibrium under the thermal loading condition.
Trawler net The loading from the trawler net is applied to a non-deformable collar at the top of the steel tube. The collar distributes the load over the entire circumference of the tube, although only one point load is defined for each loading type. The loads applied to the top of the pipe are: *
a lateral force in the x-direction of the model, magnitude 650 kN,
*
a bending moment applied about the y-axis of the model, magnitude 3575 kNm,
*
a torque applied about the (vertical) z-axis of the model, magnitude 1820 kNm.
These loads are applied to the model, allowing the pipe to deform and load the soil until an equilibrium state is achieved where the trawler net forces are resisted by the soil stress. 4.5.11
Damage Identification
It is assumed that the pile/conductor is considered to fail the test if either the steel tube becomes plastic, or any of the non-linear springs in the connectors have an excursion into the plastic range. Localised soil failure is not considered to be sufficient to warrant the failure of the pile/conductor combination.
4.6
LS-DYNA Beam and Spring Model Difficulties were experienced when using the continuum model in obtaining solutions to the analysis. The contact surface allows load to be transferred from the conductor onto adjacent soil elements. At the top of the conductor these elements fail due to localised yielding of the soil and became numerically unstable due to the large plastic deformations associated with squeezing of the soil. In soft and medium soil conditions, where the lateral displacements of the conductor are greater, these instability problems were amplified. To progress the study an alternative model was developed to overcome the computational difficulties associated with the continuum model Two major changes were made to the modelling technique: The lateral load is resisted by a series of p-y springs instead of the solid element mesh using the modified Drucker-Prager soil model The conductor and grout have been reduced to beam elements of the correct equivalent stiffness and cross section 4.6.1
Conductor Casing
The conductor casings are subdivided into beam elements. 50 elements are used in the first 40' section of casing (or 75 elements for the 60' casing). The second casing (50' length) is split into 30 elements, with all further sections of casing using 15 elements.
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The conductor casings are connected to each other using non-linear springs using an identical method to the previous model. The capacity of these 'connector' springs is as defined in Table 4. These non-linear springs will enable the force/moment to be monitored in the joints. 4.6.2
Lateral Load Behaviour p-y Springs
The lateral load is resisted at each node below 1.Sm depth (where the top level of grout begins) by non-linear springs which behave as p-y springs. The method used to define the properties of these springs is identical to the OASYS ALP geotechnical program described in Section 4.2 of this report. 4.6.3
Skin Friction t-z Spring
The skin friction on the outer surface of the grout is modelled in a similar way to the previous LS-DYNA model using non-linear t-z springs. One set of springs is used to resist combinations of torsional moment and axial forces. As for the continuum model, the springs work in the plane tangential to the surface of the grout. Skin friction at any point is mobilised in the direction of the resultant force, but is limited to the maximum available skin friction. The procedures adopted to implement the skin friction springs is described below, and illustrated in Figure 4.2. Two non-deformable rings are defined at each node level below the top of the grout. These rings are of the same diameter as the external diameter of the grout. Twenty non-linear t-z springs, equally spaced around the rings, are used to join the two rings together. One of the rings represents the surface of the grout, and the other the surface of the soil. Both rings are constrained to move translationally with the central node on the conductor beam, but the plane through the rings and the conductor beam node remains normal to the axis of the beam at the node location. The ring representing the soil is restrained so that it cannot rotate about the axis of the pile, and the plane through the conductor beam node cannot move vertically in the axial direction at the node position. With this arrangement the p-y curve springs only resist horizontal movement, and the skin friction springs only resist axial movement and/or rotation of the conductor. The model is best illustrated by reference to Figure 4.2. For the case of pure bending lateral forces are resisted by the p-y springs and the two non-deformable rings move with the pile. No forces are generated in the skin friction springs (see 'Bending' sketch on Figure 4.2). Under axial loading the t-z springs stretch/compress by the relative movement at the node position, thereby generating skin friction forces. Similarly a rotation a causes a relative movement aD/2 at the grout/soil interface and generates skin friction. Under combined axial and torsion loading the skin friction acts in the direction of the resultant force at the node and the combined skin friction is limited to the maximum permissible skin friction compatible with the total resultant relative movement. 4.6.4
Loads
The loading applied to the top of the conductor casing is sequenced. The axial (thermal) load is applied first, and the model is allowed to reach an equilibrium state. Once the thermal load is in equilibrium, the trawler net loading is applied, and equilibrium state found again for the combined load. This loading mechanism is identical to that used in the continuum model. With this loading sequence skin friction is first mobilised in the vertical direction to oppose the axial thermal loads. When torque is applied the orientation of the skin friction vector changes. If full skin friction is mobilised by the axial thermal load, then as torque is applied J \50169-0S\WP\R\0005cOHREP
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the vertical component of skin friction reduces as the component opposing the torque increases. In this manner skin friction is mobilised to greater depths to maintain overall equilibrium. 4.6.5
Modelling Inaccuracies
The modifications to the LS-DYNA model have introduced some inaccuracies into the results due to the simplifications. When applying load to the pile axially, or torsionally, the soil surrounding the pile will deform to some extent. This is not the case with the simplified model described here. The non-deformable ring representing the soil is prevented from ANY rotation about the axis of the pile and is also prevented from any axial movement relative to a plane normal to the pile. If movement of the soil is allowed, there will be a small reduction in the relative displacement between the grout and the soil with a consequent reduction is mobilised skin friction. This implies that the simplified model is over working the interface, and would give a conservative answer. The converse is the case for bending. With the simplified model no skin friction is developed by bending under lateral loading. In practice bending will cause some movement of the pile relative to the soil and so generate skin friction. The lack of movement in the soil does not compromise the position where the failure surface occurs. The pile will always fail on the interface, not in the soil. This is because even if the interface strength was not less than the soil strength, the force will be concentrated (higher stress) the closer to the centre of the pile that the failure surface occurs.
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5.
STUDY RESULTS
5.1
Analysis Strategy
Sub-sea Conductor Study
Various methods of analysis and modelling techniques have been used during the course of the study. The various methods are described in Section 4 of this report. The strategy adopted for this study is as follows:
5.2
*
Carry out conventional 2D lateral pile analyses with ALP using standard p-y curves
*
Carry out 2D lateral pile analyses using the elastic-plastic soil model in ALP. Determine elastic soil stiffness parameters to give comparable results to the previous p-y analyses
*
Carry out equivalent 2D analysis using LS-DYNA using a continuum soil model with elastic soil stiffness parameters derived from ALP elastic-plastic analyses
*
Carry out 3D analysis using LS-DYNA continuum model
*
Develop LS-DYNA beam and spring model for 3D loading and compare against LSDYNA continuum results
*
Analyse all load design cases using LS-DYNA beam and spring model
Lateral and Moment Loading Only 5.2.1
ALP p-y Analyses
The results of conventional laterally loaded pile analyses, using standard Matlock p-y data, are shown on Figures 5.1 to 5.3 for hard, medium and soft soil profiles respectively. The figures show profiles of displacement, bending moment, shear force and soil pressures when the lateral load and moment components of the trawler snagging loads are applied to the top of the conductor (ie. no axial load or torque). Maximum displacements vary from 60mm for the hard soil profile to 703mm for the soft soil profile. 5.2.2
ALP Elastic-Plastic Soil Model
ALP analyses using an elastic-plastic soil model were carried out to determine the stiffness profile for an elastic/plastic material which gives conductor displacement and bending moment profiles comparable to those obtained using the p-y approach. The stiffness profile derived frcm these ALP analyses were subsequently used in the LS-DYNA continuum model analyses. This procedure was adopted so that LS-DYNA results could be compared directly against previous analyses carried out using p-y analyses. The ultimate soil resistance was calculated using the method proposed by Brirch Hansen(1961), and it was assumed that Young's Modulus of the soil was proportional to the undrained shear strength c,. Starting from the initial assumption E'=250q,, the stiffness profiles were modified by trial and error until an acceptable match was achieved with the p-y predictions of displacement and bending moment. Figures 5.4 to 5.9 show the final comparisons achieved between the p-y and elastic-plastic soil models, and gives details of the soil stiffness profile derived for the elastic-plastic model.
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5.2.3
Sub-sea Conductor Study
LS-DYNA Beam and Spring Model
For lateral load analyses the LS-DYNA beam and spring model is in principle the same as used by ALP, but the method of solution is different. The modelling of the conductor pipes and connectors is more detailed in the LS-DYNA model, and consequently the analysiswill be more precise than corresponding ALP analyses. In the ALP analyses, for example, the conductor and surrounding soil is represented by 39 beam elements and 39 p-y springs. The corresponding number for the LS-DYNA model is 125 beam elements and 120 p-y springs. Pipe connectors are modelled in LS-DYNA and therefore force and moment components within the joint can be determined directly. Joints cannot be modelled in ALP, and forces and moments can only be determined by interpolation. Results from the LS-DYNA beam and spring model for hard, medium and soft soil profiles are shown on Figures 5.10 to 5.12. (These results are directly comparable to the ALP results shown on Figure 5.1 to 5.3.) 5.2.4
ALP and LS-DYNA Comparisons
Displacements and bending moments calculated using ALP and LS-DYNA are summarised in Table 7. Maximum bending moments are given for the top section of 35" x 2" pipe, the first high torque connector, and the first length of 30" x 1" pipe. For all of the analyses bending moments on the second connector are relatively small and are therefore not reported in Table 7.
Soil Profile
Method of Analysis
Maximum Displacement
Report Fig. No.
(mm) Hard
Medium
Soft
Maximum Bending Moment (kNm)
RCm@U-
35"9 X2"' Pipe
Joint 1
30" x1" Pipe
Rac Fax N6.
ALP
60
5.1
5525
0
150
;, 1
LS-DYNA
60
5.10
5601
99
125.3
T, lD
ALP
200
5.2
6685
429
160
LS-DYNA
212
5.11
6891
212
136
b.11
ALP
703
5.3
8373
4738
4492
6.3
LS-DYNA
718
5.12
8470
4821
4827
5 1
9505
5691
3753
Yield Capacity Moment (kNm)
Table 7. Comparison of ALP and LS-DYNA Results for Lateral Loading Only Case There is good correlation between the two sets of results. The maximum difference in lateral displacement at the top of the conductor is 6% (medium soil profile) and bending moments are generally with 7% of each other. Higher differences in bending moment occur when the bending moment are small in comparison to the yield moment, but these differences are of no significance to the overall results. For analyses using the soft soil profile both sets of results calculate bending moment in the 30" x 1" pipe greater than the yield moment capacity of this element. Maximum bending moment in the 35" x 2" pipe and the top connector are also high in comparison to their
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ultimate moments. Maximum moments in the 35" x 2" pipe are 88% to 89% of yield capacity, whilst moments in the top high torque connector are 83% to 85% of yield capacity.
5.3
Combined Lateral, Moment, Vertical and Torsion Loading 5.3.1
Analyses Carried Out
All the analyses for combined lateral, moment, vertical and torsion loading have been carried out using LS-DYNA. Analyses have been carried out for seven design cases as detailed in Table 8. Design Case
Conductor String
Soil Profile
Thermal Load Case
HTIA-HB
HTIA
Hard
B (1,500.000 Ibs)
HT2A-HC
HT2A
t'Hard
C (2,700,000 Ibs)
HT2B-MA
HT2B
6o'
Medium
A (500,000 Ibs)
HT3B-MB
HT3B
(0'
Medium
B (1,500,000 Ibs)
HT4B-MC
HT4B
6g'
Medium
C (2,700,000 Ibs)
HT3B-SA
HT3B
66'
Soft
A (500,000 Ibs)
HT4B-SB
HT4B
6O'
4
Soft Table 8. LS-DYNA Design Cases
B (1,500,000 Ibs)
As described in Sections 4.4.9, t-z springs have been used to model the transfer of shear across the soil-grout interface. Two forms of t-z springs have been used. The two types of tz springs, referred to as API and Shell, are defined on Figure 5.13. The API t-z springs assume linear elastic/plastic behaviour with the maximum skin friction, t mobilised at a relative movement between grout and soil of 1% of the grout diameter, i.e. 9.14mm. It is assumed that tmax = acu and that a values are as defined in Section 6.4.2 of API RP 2A (1993). The Shell t-z spring is the same as currently by Shell Expro for piles installed in clay. The shape of the t-z curve is as proposed by Vijayvergiya (1977) and tmax values are calculated using a values defined in API RP 2A (1993), Section C6.4. Figure 5.13 shows that for the hard soil profile the Shell t.nax values are greater than the API tmax values. Figure 5.13 also shows that smaller movements are required to mobilise skin friction with the Shell t-z springs. The suffix 'Shell' or 'API' is appended to the design case reference to define which type of tz spring has been used for a particular analysis, ie HTIA-HA (Shell). The continuum model has been used for only one design case ( HTIA-HB (API) ), and the beam and spring model has been used for 14 design cases (7 design cases x 2 types of t-z springs). 5.3.2
Design Case HT1A-HB (API)
5.3.2.1
Continuum Model Results
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Results obtained using the LS-DYNA continuum model are shown on Figures 5.14 to 5.20. Figure 5.14 shows profiles of forces and moments within the conductor when all the specified design loads are acting. Figures 5.15 to 5.20 show contours of horizontal displacement, shear stress and horizontal stress. 5.3.2.2
Beam and Spring Model
Profiles of forces and moments within the conductor calculated using the beam and spring model are shown on Figure 5.21. 5.3.2.3
Comparison of Continuum and Beam and Spring Models
For comparative purposes maximum values of axial force, shear force, bending moment and torque derived from the continuum and beam and spring models, are summarised in Table 9. The beam and spring model calculates a horizontal displacement at the top of the conductor of 53.6mm. The average horizontal displacement at the top of the conductor calculated by the continuum model is 52.5mm. The difference between the two horizontal displacement is only 2%, confirming compatibility between the p-y springs used in the beam and spring model and the elastic-plastic soil model used in the continuum analysis. 5.3.3
Results of LS-DYNA Beam and Spring Model Analyses
Results of LS-DYNA beam and spring analyses are shown on Figure 5.21 to 5.36 and summarised in Tables 1 1 to 15. Figures 5.2 Ia to 5.36a each show plots of axial force, shear force, bending moments and torsion moment versus depth below seabed level. Figures 5.21b to 5.36b show plots of maximum available and mobilised skin friction, rotation, axial displacement and lateral displacement versus depth below seabed level. Table 10 shows results for hard soil profile design cases, Table 11 shows results for medium soil profile design cases, and Table 12 shows results for soft soil profile design cases. Each of these tables gives the maximum calculated value of axial force, shear force, bending moment and torque in the 35" x 2" pipe, the top ALT-2HT high torque connector, the 30" x 1" pipe, and the top ST-2RB standard connector. Table 13 summarises the calculated maximum axial loads in the conductor elements due to thermal axial loading only, and under the combined effects of axial, bending and torsion loading. For each design case, Table 14 summarises the calculated lateral movement, upward movement and rotation of the conductor, at a depth of 1.5m below seabed level (ie base of scour depth), under the combined effects of axial, bending and torsion loading. From the results summarised in Tables 10 to 14 a number of general observations can be made: when torque is applied the axial loads in the elements below the top length of 35" x 2" pipe increase (see Table 13); as the axial thermal load increases, but the applied moment and torque remains constant(see Tables 10,11 and 12):
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(i)
bending moments in the 35" x 2" pipe reduce
(ii)
torque in the first high torque connector and the 30" x 1" pipe increase
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rotation of the conductor head, and upward movement of the conductor, increase, but the lateral displacement reduces (see Table 14).
Bending moments reduce as the axial load increases because higher axial tensile loads results in lower horizontal movement and so reduced curvature of the conductor. The increase in upward movement and rotation is attributed to the redistribution of shear stress (skin friction) on the grout/soil interface as either the torque or the axial load is applied or increased. 5.3.4
Results for Hard Soil Profile
Results of LS-DYNA beam and spring analyses for the hard soils profile are summarised on Figures 5.21 to 5.24 and in Table 10. Figures 5.21 and 5.22 shown results obtained using API t-z springs while Figures 5.23 and 5.24 show corresponding results if Shell t-z springs are used. Table 10 shows that the torque capacity of the first standard torque connector is exceeded for design case HTIA-HB if API t-z springs are used, but not if Shell t-z springs are used. For design case HT2A-HC the capacity of the standard torque connector is adequate for both API ans Shell t-z springs. Ultimate values of axial force, shear force and bending moment are not exceeded in any of the conductor elements for the two load cases considered. The higher torque applied to the ST-2RB connector when API springs are used are due to the lower a values, and softer initial stiffness, which result in lower values of skin friction being mobilised to a greater depth. This can be seen by comparing the plots of mobilised skin friction on Figures 5.21 b and 5.23b. The reduction of axial load and torque within the conductor with depth below seabed is therefore less for the API t-z springs than for the Shell springs. This can be seen by comparing axial force components on Figures 5.21 and 5.23. With the API t-z springs the axial force becomes zero at a depth of about 65m below mudline, but when using Shell t-z springs the axial force becomes zero at a depth of about 45m below mudline. When the thermal axial load is increased, higher values of skin friction are mobilised but the depth at which the axial force in the conductor becomes zero does not change significantly. The distribution of torque is different for the higher axial load case, particularly for the API t-z spring case. 5.3.5
Results for Medium Soil Profile
Results of analyses for the medium soil profile are shown on Figures 5.25 to 5.30 and summarised in Table 11. For this soil profile there is little difference between the results obtained using API and Shell t-z springs. All of the design cases show the axial force reducing to zero at the base of the conductor, indicating that skin friction is mobilised over the full length if the conductor. Upward movement of the base of the conductor is of the order of 0.5mm. The plots of mobilised skin friction show that using API t-z springs full skin friction is mobilised to a depth of 20m below seabed level for design case HT2B-MA (ref Fig 5.25b). The depth of full mobilisation of skin friction increases to about 30m for HT2B-MB (Fig 5.26b) and 47m for HT2B-MC (Fig 5.27b). The use of Shell t-z springs allows higher values of skin friction at shallow depths with the consequence that for design case HT2B-MA full skin friction is only mobilised to a depth of about 6m (Fig 5.28b). For higher axial loads, however, skin friction is fully mobilised to depths comparable to those obtained using API springs. Both the API and Shell t-z spring models show the first standard ST-2RB connector failing in torque for design case HT2B-MA. For design cases HT3B-MB and HT4B-MC the torque in
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the first ST-2RB connector is less than the joint capacity for both the API and Shell t-z spring models. 5.3.6
Results for Soft Soil Profile
Results of analyses carried out for the soft soil profile are shown on Figures 5.31 to 5.34 and in Table 12. There are no significant differences between results obtained using API and Shell t-z spring. Skin friction is fully mobilised to slightly greater depths when API t-z springs are used, but for all the soft soil profile design cases full skin friction is not mobilised below a depth greater than about 40m. For all of the soft soil profile analyses non of the standard ST-2RB connectors fail in torque. Without any axial load Table 7 shows a maximum bending moment in the 30" x 1" pipe of 4827 kNm. Table 12 shows that this bending moment reduces to 2799 kNm, a reduction of 42%, when the axial load is 1.5 x 106 lbs and API t-z springs are used. Table 12 also shows that when Shell t-z springs are used the bending moment in the 30` x 1" pipe is greater than the yield moment when the axial thermal load is less than 5 x 1( lbs. 5.3.7
Axial and Bending Stresses
Tables 15 and 16 show calculated values of axial and bending tensile stresses in the 35" x 2" and 30" x 1" conductors for each of the design cases considered. Axial stresses in the 35" x 2" pipes, shown in Table 15, are a maximum of 41% of the allowable tensile stress of 0.6FY defined in API RP2A, while the tensile bending stresses exceed the allowable of 0.75FY for design case HT3A-SA. Table 16 also shows the combined axial tension and bending stress. API RP2A requires for cylindrical structural member that
A-f 0.6F1, where
+_fb_ < 1.0 0.75F,
fa = axial tensile stress fb = tensile bending stress
FY = yield stress Table 16 shows that none of the design cases except HTIA-HB(Shell and API) and HT2B-MA(API) meet this requirement. API RP2A permits allowable stresses to be increased by one third when the stresses are due in part to lateral and vertical forces imposed by design environmental conditions. The trawler snagging loads represent an accidental limit state, and although the imposed conductor loads are not environmental loads it is considered appropriate to allow a 33% overstress when assessing combined stress effects. The combined stress check inequality therefore becomes -f,_ +_fb_ 0.6FY
< 1.33
0.75FY
Table 15 shows that this relationship is satisfied in the 35" x 2" pipe for all design cases. Also shown in Table 15 are bending stresses resulting from analyses in which lateral load and moment components of the snagging loads were considered, but torque and axial thermal
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loads were ignored. The results show that for the soft soil profile this load combination results in higher stresses within the conductor than the full load analyses. Axial and bending stresses in the 30" x 1" pipe are shown in Table 16. This table shows that, after allowing a 33% overstress, the stresses exceed allowable stresses for all soft soil design cases. For the soft soil design cases the stresses due to lateral and moment loading only are significantly higher than those resulting for combined loading. 5.3.8
Comparison of Results for first ST-2RB Connector
Figures 5.35 and 5.36 summarise calculated values of torque at the first standard connector. Figure 5.35 shows results obtained using API t-z springs, and Figure 5.36 shows results obtained using Shell t-z springs. These two figures show torque plotted against time. 'Time' in this instance is a consequence of the LS-DYNA iterative procedure and has no direct relevance to the problem. The increase of torque with time shown on these figures merely illustrates convergence to an equilibrium solution. The only significant difference between the two sets of results is for design case HTIA-HB. When API t-z springs are used the analyses shows the torque capacity of the connector (53 kNm) has been reached, while the corresponding analysis using Shell t-z springs shows that the maximum torque at the first connector is 18 kNm. Figure 5.37 is a similar plot of results obtained using the LS-DYNA continuum model with API t-z springs. This Figure shows the same result as the beam and spring model, ie failure of the first standard connector in torque. Both sets of results show that the torque at the first standard connector exceed the joint torque capacity for design case HT2B-MA. All other analyses show that the proposed conductor strings are adequate. 5.3.9
Grout to Casing Shear Stresses
The 35" and 30" conductor casings are grouted into a 36" diameter drillhole. In principle the 35" conductor casing is therefore surrounded by a l/2" thick annulus of grout, and the 30" conductor casing is surrounded by a 3" thick annulus of grout. Grout to casing shear stresses can only be determined from the continuum model results since this is the only analysis in which the casing and grout are modelled separately. Shear stresses determined from the hard profile continuum model analysis are shown on Figure 5.38. Maximum values of grout to casing shear stress for the top section of 35" x 2" pipe range from 0 to 3.35 MPa. Corresponding values for the top section of 30" x 1" pipe are about 0.25 to 1.5 MPa. Shear stresses due to the axial load and torque components of applied load will be limited by the grout/soil skin friction. Within lOim of mudline Figure 5.13 shows that for API t-z springs the maximum skin friction is in the range 0.05 to 0.1 MPa. The results shown on Figure 5.38 therefore indicate that most of the grout to casing shear stress is due to bending of the conductor. No analyses have been carried out for medium and soft soil profiles from which the grout to conductor shear stresses can be determined. It is evident, however, that the larger displacements and higher bending moments associated with these weaker soils will result in higher grout to conductor shear stresses.
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5.4
Sub-sea Conductor Study
Review of Results The results of the LS-DYNA analyses indicate that some of the model features result in nonconservative estimates of forces and stresses in the conductor casings and connectors. Two major factors which could affect the solutions are discussed in the following sections. 5.4.1
Spalling of Grout
In the LS-DYNA model the grout is modelled as an elastic material, fully bonded to the conductor. This is an oversimplification since bending of the conductor will cause cracking of the grout, and the magnitude of the calculated shear stresses indicates that local debonding of the grout from the conductor may occur. If debonding does occur, it is possible there could be reduced transfer of load from the conductor into the soil over the depth of the debonding, resulting in increased loads in the conductors and connectors below the depth of spalling. The current calculations could therefore underestimate the forces to be resisted by the connectors. Debonding will occur if the local shear stresses between grout and steel exceed the ultimate bond stress. API RP2A recommends an allowable axial load transfer shear stress of 0.185 MPa for grouted annulus connections between plain steel pipe piles and jacket legs, but does not give any recommendations for grouted connections subject to shear, bending or torque, other than to state these effects should be considered by appropriate analytical or testing procedures. The API recommended allowable bond stress value is significantly lower than the calculated shear stresses, but data contained in the Commentary of API RP2A shows that ultimate values of grout to steel bond stresses can be much higher. The grout around the conductor casing is reported to have a 24 hour compressive strength in excess of 17 MPa. Based upon published data, the equivalent 28 day compressive strength is expected to be in excess of 80 MPa. Data in the API RP2A Commentary shows ultimate grout to steel bond strengths in the range 0.5 to 5 MPa for a grout of this strength. Neville (1981 ) reports an ultimate axial bond stress, determined by pull-out tests, of about 3.5 MPa for plain bars in concrete with a compressive strength greater than 40 MPa. BS 8110 (1997) states thet the ultimate bond stress for reinforcement bars in concrete can be determined using the equation: fb. D V flu where fbU is the ultimate bond stress, 3is a coefficient dependent on the bar type and f. is the compressive strength of the concrete. Taking fu = 80 MPa the resulting values of ultimate bond stress are 2.5 MPa for plain bars in tension and 3.1 MPa for plain bars in compression. It is evident from the foregoing that although ultimate bond strengths are considerably greater than the allowable shear stresses recommended by API RP2A, the grout to steel shear stresses calculated by LS-DYNA are comparable to published values of ultimate bond strengths . Neville (1981) also reports that a rise in temperature reduces the bond strength of concrete. At temperatures of 200 to 300C he reports that there may be a loss of one-half of the bond strength at room temperature. It is therefore very likely that grout to steel shear stresses will locally exceed the ultimate bond strength and that some spalling of the grout will occur. The grout to steel shear stresses shown on Figure 5.38 suggest that for the hard soil profile local spalling may occur on one side of the conductor to a depth of about 5m to 6m below mudline. Intuitively it is expected that spalling would occur to a greater depth for medium and soft soil profiles. If cracking and debonding of grout does occur the transfer of shear from the conductor into the surrounding soil will be governed by friction between the de-bonded grout and the steel
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conductor casing. Laboratory tests reported by Rabbat and Russell (1984) show an interface friction angle between de-bonded grout and steel of 350 at a normal stress of 140 kPa, reducing to 33° at a normal stress of 690 kPa. Assuming an interface friction angle of 330, Figure 5.39 shows the shear that could be transferred through a debonded grout interface for various values of K (lateral earth pressure coefficient). Also shown on Figure 5.39 is the maximum skin friction on the grout-soil interface based upon Shell t-z springs. This figure suggests that shear on the grout/steel interface is likely to be governing for hard soil conditions, but is not likely to be the governing criteria for medium and soft soil profiles.
5.4.2
Axial Thermal Loads
In the current analyses the axial load due to thermal expansion of the inner casing is modelled as a constant vertical load. The analyses show bending moments, and associated bending stresses, in the conductor casing casings reduce as the vertical load increases. In practice it is probable that the axial load applied to the conductor will reduce as the inner casing expands. Assuming the load remains constant as the casing expands will result in lower bending moments and bending stresses in the conductors. It is therefore possible that combined stresses could be higher if the axial load reduces as expansion takes place.
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TEMPERATURE EFFECTS The hot hydrocarbons flowing through the well casing will cause a rise in temperature in the conductor casing, the grout around the conductor casing, and the surrounding soil. The effects of temperature on the geotechnical properties of the soil has been investigated by a number of researchers but published data relevant to the design of conductors in heated soil is scarce and inconclusive. Results of field and laboratory testing by the Swedish Geotechnical Institute into the effects of heating on the properties of clay are reported by Moritz (1995) and Gabrielsson, Lehtmets, Moritz and Bergdahl (1997). Results of triaxial testing reported by Moritz (1995) show that the undrained shear strength of samples taken from 6m depth reduce by about 30%, from about 27 kPa to 18 kPa, as the temperature of the specimens increases from Soc to 70WC. Tests on samples taken from 9m depth, however, show no consistent relationship between temperature and undrained shear strength. In situ measurements of undrained shear strength taken within a field heat store, reported by Gabrielsson et al (1997), show that the undrained shear strength temporarily reduces by about 30% on first heating, but subsequently increases to about the initial values as the excess porewater pressures associated with the initial heating dissipate. The triaxial tests reported by Moritz were consolidated undrained tests in which consolidation of the heated sample was allowed prior to undrained testing. No explanation is offered by SGI as to why fully consolidated heated samples show a reduction in undrained shear strength, but fully consolidated field tests do not. Based upon the results of the laboratory and field tests, over the temperature range 8 0C to 70WC, SGI conclude that the undrained shear strength will temporarily decrease by about 0.5 % per 'C at first heating, but will return to its original strength with time. Similar laboratory triaxial testing reported by Towhata and Kuntiwattanakul (1994) appear to show the opposite trend. Their test results show that as the consolidation temperature increases from 21 'C to 90WC the undrained shear strength increases from about 37 kPa to 48 kPa, an increase of 30% due to a 69WC temperature rise. Both sets of triaxial tests were consolidated undrained tests in which consolidation of the heated sample was allowed prior to undrained shearing. The differences are that the SGI tests were carried out on undisturbed samples of natural clay which were anisotropically consolidated to ar, = 48 kPa, ah' = 33.6 kPa or cr' = 70 kPa, ah' = 42 kPa, whilst Towhata et al tested specimens of 'MC Clay' prepared from a slurry and isotropically consolidated to q' = 196 kPa. No analyses have been carried out to assess whether these differences in the consolidation stages could account for the difference in response to heating. No data has been identified for samples heated to temperatures higher than 90°C. Constant rate of settlement (CRS tests) consolidation tests carried out by SGI indicate that both the preconsolidation pressure and the compressibility modulus reduce as the temperature increases. There is no data to indicate whether or not this is a temporary phenomenon. Considering the uncertainty of the effects of heating on the geotechnical properties of clay it is considered that further analyses to study the effects of soil heating on the performance of the conductors is not justified at this stage. An indication of the potential effects of reductions of undrained strength and compressibility modulus can be obtained from the existing results. Assuming as an extreme case that the SGI findings can be extrapolated to a temperature rise of 160°C, their recommendation of a temporary decrease of undrained shear strength of 0.5 % per 'C corresponds to an 80% reduction of undrained shear strength. With this degree of strength reduction the hard soil shear strength profile approximates to the medium soil shear strength profile, and within about lOm of mudline the medium soil profile
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approximates the soft soil strength profile. The medium soil results could therefore be considered as representative of the extreme worst case for the hard soil condition, and the soft soil results could be taken as the extreme worst case for medium soil conditions. If more detailed analyses are required the first stage would be a conduction analysis to determine the maximum temperature rise of the soil. As previously reported in Section 5.4.1 the grout to steel bond strength is also affected by temperature.
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Sub-sea Conductor Study
CONCLUSIONS Theoretical analyses have been carried out to investigate the adequacy of proposed conductor string make-ups for specified ground conditions and load combinations. The principal findings of this study are as follows.
7.1
Conductors in Hard Soil Conductor String HT1A The analyses show that the proposed string make-up is adequate if the t-z springs normally used by Shell are used to represent mobilisation of skin friction on the grout/soil interface, but that the torque capacity of the first ST-2RB connector is exceeded if t-z springs based upon API recommendations are adopted. Using two ALT-2HT high torque connectors in place of the one currently proposed would result in an acceptable design for both types of t-z springs Conductor String HT2A The proposed torque connectors are adequate, but combined stresses in the top length of 35" x 2" conductor pipe exceed the API recommendations for allowable combined axial tension and bending stresses. Stresses are acceptable if a 33% overstress is permissible.
7.2
Conductors in Medium Soil Conductor String HT2B The torque capacity of the first ST-2RB connector is exceeded and therefore three ALT-2HT high torque connectors are required on this conductor string. Other components of the string are adequate. Conductor Strings HT3B and HT4B The proposed arrangement of torque connectors is adequate. Combined axial and bending stresses in the top length of 35" x 2" conductor pipe exceed the API recommendations, but are acceptable if a 33% overstress is permitted.
7.3
Conductors in Soft Soil Conductor Strings HT3B and HT4B The proposed arrangement of torque connectors is adequate. Combined axial and bending stresses in the top length of 35" x 2" conductor pipe exceed the API recommendations, but are acceptable if a 33% overstress is permitted. Combined axial and bending stresses in the top length of 30" x 1" conductor pipe are more than 33% greater than the API recommended stresses in the section of pipe directly beneath the top connector. The bending moment reduces rapidly with depth, but immediately beneath the top connector the combined stresses are slightly greater than the yield strength of the pipe material. Some local yielding of the conductor pipe could therefore occur within this zone.
7.4
Grout to Casing Shear Stresses The analyses predict high shear stresses between the 35" x 2" conductor pipe and the surrounding grout. Shear stresses up to 3.3 MPa are calculated for hard soil conditions. The maximum shear stresses occur within a depth of about 5m below seabed level in the zone of
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maximum bending moment. It therefore appears that these shear stresses are predominantly due to bending of the pipe. Shear stresses have not been calculated for the medium and soft soil conditions, but high shear stresses are anticipated for these design cases. The maximum shear stresses are comparable in magnitude to reported values of ultimate bond strength between grout and plain steel. Bending will cause cracking of the grout, and in the zones of maximum shear stress it is possible that local debonding of the grout may occur. If debonding does occur it will still be possible for skin friction to be mobilised by friction between the debonded grout and the conductor. For hard soil conditions the skin friction between debonded grout and steel is likely to be less than the skin friction between soil and grout over the debonded depth. This could lead to higher loads on the conductor pipes and connectors than predicted by the current analyses. It is anticipated that this redistribution of skin friction would not result in overstress of the conductor pipe or the ALT-2HT connector, but could result in the torque capacity of the top ST-2RB connector being reached for design cases other than HT1 A-HB (see section 7.1 above). For medium and soft soil conditions the friction between debonded grout and steel is likely to be comparable to the skin friction between soil and grout. The effect of grout debonding on the overall performance of the conductor string is likely to be marginal.
7.5
Effects of Heating on Geotechnical Properties Published data on the effect of heating on the strength and stiffness of clay soil is inconsistent. Data from large scale field trials reported by the Swedish Geotechnical Institute indicates a temporary reduction in undrained shear strength on first heating, followed by a return to pre-heating strengths as excess porewater pressures generated by initial heating dissipate. Extrapolation of the SGI data indicates heating to 160CC could result in a temporary reduction in undrained shear strength to 20% of the original value.
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8.
REVIEW OF ANALYTICAL METHODS At the start of this study the intention was to use a detailed three dimensional finite element continuum model to analyse the behaviour of conductors under combined axial, bending and torsion loading. Detailed numerical modelling of this complex soil structure interaction problem proved to be more difficult than originally anticipated and it was necessary to modify the numerical model in order to complete the full scope of work required. The modifications concerned the way in which the skin between the grout around the outside of the conductor and the soil was modelled. LS-DYNA is able to model frictional contact surfaces, but does not have a facility for modelling adhesive contact surfaces in which the shear stress between two surfaces is assumed to be a function of the undrained shear strength of the contacting materials. To overcome this deficiency a continuum model was developed which had a frictionless contact surface between the. grout and the soil, but included t-z springs connecting the grout to the soil to model the mobilisation of skin friction due to relative movement between the surface of the gout and the surrounding soil. This model was generally satisfactory for the hard soil profile but some numerical instability occurred at the top of the conductor due to large plastic strains associated with local yielding and squeezing of the soil around the conductor. The numerical instability became more pronounced for the medium and soft soil analyses. Work continued throughout the contract period.on developing the continuum model, but at the same time an alternative model, more able to cope with large deformations, was developed in parallel with the continuum model in order to provide solutions for all of the specified design cases. The alternative model developed was a simpler beam and spring model which uses conventional p-y springs to represent lateral load displacement behaviour and t-z springs to model development of skin friction. One set of t-z springs is used to account for combined axial and torsional loading, with skin friction mobilised in the direction of the resultant force at any point and limited to specified ultimate skin friction values. The results from the beam and spring model were validated by comparing them against those obtained using the continuum model for the hard soil profile. The results presented in this report are predominantly those obtained using the beam and spring model, although limited results from a continuum model are presented for comparative purposes.
8.1
Assessment of Results It is believed that the methods and models developed to carry out the analyses provide an acceptable means of assessing the behaviour of the conductor under three dimensional loading. The procedures consider the development of skin friction under both axial and torsion loading, and successfully limit skin friction to pre-defined ultimate values taking account of the sequence of loading and directionality of resultant forces. The modelling techniques used in this study employed a number of simplifying assumptions. Some of the assumptions lead to conservatism in the results, others are not conservative. The principal conservative assumptions are: *
the stiffness of the inner 20" casing and the grout between the inner casing and the conductors has been ignored
*
local scour has been assumed to depth of 1.5m, and the grout on the outside of the conductor to I .5m depth has been ignored
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the steel forming the conductor has been modelled as an elastic/plastic material with a yield stress of 361 N/mm 2 . No allowance has been made for post yield strain hardening. The first of these assumptions is likely to be the most significant. Allowing for the 20" casing and the grout between the inner casing and the conductor will give a higher bending, axial and torsional stiffness with a consequent reduction in displacements and stresses within the conductor and connectors. The principal non conservative assumptions are: *
the axial load due to thermal expansion remains constant
*
in the beam and spring model the soil movement at the grout/soil interface due to continuum movement is not allowed for
*
in all the models the grout is assumed to be an integral part of the conductor
The analyses show that a constant axial tensile load is beneficial as the upward pull reduces the curvature of the conductor with a consequent reduction in bending moment. The bending moments could therefore increase if the axial thermal load reduces as the conductor moves upwards. Neglecting continuum movement is likely to result in an underestimate of the movement required to mobilise sufficient skin friction to oppose axial and torsional loads. This could result in an underestimate of the torque applied to the connectors. Assuming that the grout is integral with the conductor does not allow for the effects of grout debonding. This could also result in an underestimate of the torque applied to the connectors, particularly for the hard soil profiles.
8.2
Improvements to Modelling Techniques The experience gained to date, together with an improved understanding of the factors affecting the design analyses, leads us to believe that there are modifications which could be made to the existing LS-DYNA models to improve the analysis procedures and provide greater confidence in the design of the conductors. In order of increasing complexity, and increasing risk of successful implementation, modifications which could be made to the LSDYNA models are detailed below. 8.2.1
Detailed Modelling of Conductor and Grout
In the existing beam and spring model the conductor and surrounding grout are modelled as composite elastic beam elements. The soil is represented by p-y and t-z springs. The beam. elements could be replaced by a detailed finite element model where the conductor, connectors and grout are modelled using shell and solid elements, as done previously for the continuum model. The p-y and t-z springs representing the soil would be retained. This approach would provide more detailed information on the stress conditions within the conductor, connectors and grout and would identify whether or not local yielding occurs in the conductor pipes. The grout could be modelled as a non-linear material which cracks, and it may be possible to specify limiting grout to steel shear stresses to model debonding. 8.2.2
Improved Continuum Model
Initial analyses using the continuum model experienced numerical instability and convergence problems. Most of these problems were eventually overcome by modifying the analytical procedures used by LS-DYNA to model the contact surface between the grout and
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Shell UK Exploration & Production
Sub-sea Conductor Study
the soil. Continuum model analyses for medium and soft soil profiles have not been run since this modification was implemented. It may now be possible to obtain continuum model solutions for medium and soft soil profiles, but in view of the number of elements and the magnitude of the displacements expected considerable run time will be required to reach a converged solution. Run times could be reduced by using an option to re-generate new meshes as the material deforms, or by using a hybrid between a continuum and a spring model. With this latter option a continuum model would be used for say the top 15m of soil, but p-y and t-z springs would be used below this depth.
8.2.3
Improved Grout to Soil Interface
Skin friction at the grout to soil contact surface in the continuum model is currently modelled using t-z springs. Although the contact surface allows peel away for lateral load behaviour, the t-z springs ensure that peel away does not result in a reduction in the contact area over which skin friction is mobilised. The t-z springs could be eliminated by introducing a friction/adhesion contact surface. The simplest procedure would be a friction contact surface, but this would require that skin friction is calculated in effective stress terms rather than total stress as at present. The results would depend upon stress history and it very likely that the results would be different from those obtained previously using t-z springs. It may be possible to adapt one of the hysteretic model within LS-DYNA, or develop an interface element, to replace the t-z springs. If this could be done it may be possible to increase the size of the elements and reduce run times.
J.\501 69-08\WVPaR\0005CH.REP
Page 29
Ove Arup & Partners 1199 22 February 1999
Shell UK Exploration &Production
9.
Sub-sea Conductor Study
RECOMMENDATIONS FOR FURTHER WORK To progress design of the well conductors it is recommended that the following work is carried out. *
.
Modify the LS-DYNA beam and spring model to replace the composite beam elements by a detailed finite element model of the conductor and grout in order to investigate cracking and spalling of the grout and the implications of this on the loads transferred to the connectors and the stresses within the pipe elements.
*
Undertake a thermal conduction analysis to determine temperature rises within the ground, thermal expansion of the well casing and the outer conductor, and axial loads generated by thermal expansion.
*
Stress analysis of the conductor string and surrounding ground to determine how the axial load applied to the conductor casing varies with thermal expansion of the well and conductor casings.
*
Carry out preliminary tests of LS-DYNA continuum model using the soft soil profile.
*
Investigate methods and carry out preliminary analyses to assess feasibility of developing friction/adhesion contact surface between grout and soil.
J:\S0169.OS\11'P\R\OOOSCH.REP
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Ove Arup &Partners 1/99 22 February 1999
Shell UK Exploration & Production
10.
Sub-sea Conductor Study
REFERENCES API RP 2A (1993). Recommended Practice for Planning, Designing and Constructing Fixed Offshore Platforms - Working Stress Design, Twentieth Edition. Brinch-Hansen J (1961). The Ultimate Resistance of Rigid Piles against Transversal Forces. Danish Geotechnical Institute, Bulletin No. 12, Copenhagen, pp. 5-9. British Standards Institution BS 8110: Part 1: (1997). Structural use of concrete. Part 1. Code of practice for design and construction. Gabrielsson A, Lehtmets M, Moritz L and Bergdahl U (1997). Heat Storage in Soft Clay. Field Tests with Heating (70 0 C) and Freezing of the Soil. Swedish Geotechnical Institute, Report No. 53, Linktiping. Matlock H (1970). Correlations for Design of Laterally Loaded Piles in Soft Clay. OTC 1204, Offshore Technology Conference, Houston. Moritz L (1995). Geotechnical Properties of Clay at Elevated Temperatures. Swedish Geotechnical Institute, Report No. 47, Linkdping. Neville A M (1981). Properties of Concrete, 3rd Edition, Pitman. Rabbat B G and Russell H G (1985). Friction Coefficient of Steel on Concrete or Grout. ASCE Journal of Structural Engineering, Vol. 111, No. 3, pp 505-515. Shell Expro (1993). Geotechnical Report. Sub-Sea Wellhead Study Central North Sea Soil Profiles. Engineering Report No. E93005. Sullivan W R, Reese L C and Fenske C W (1980). Unified Method for Analysis of Laterally Loaded Piles in Clay. Conference on Numerical Methods in Offshore Piling, ICE, London pp. 135-146. Towhata I and Kuntiwattanakul P (1994). Behaviour of Clays Undergoing Elevated Temperatures. X111 ICSMFE, Vol 1 pp. 85-88, New Delhi, India. Vijayvergiya V N (1977). Load Movement Characteristics of Piles. Proceedings of Ports '77 Conference, ASCE, Vol. II pp. 269-284.
:\50169-08\1VP\R\OOO5CH. REP
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Ove Arup &Partners 1/99 22 February 1999
Sub-sea Conductor Study
Shell UK Exploration & Production
Pipe Combination
HT1A
HT2A
HT2B
HT3B
HT4B
Section 1
35" x 2"
35" x 2"
35" x 2"
35" x 2"
35" x 2"1
Length
40 ft
40 ft
60 ft
60 ft
60 ft
Joint
ALT-2HT
ALT-2HT
ALT-2HT
ALT-2HT
.ALT-2HT
Section 2
30" x 1"
30" x 1"
30" x1"
30" x 1"
30" x1"
Length
50 ft
50 ft
50 ft
50 ft
50 ft
Joint
ST-2RB
ALT-2HT
ALT-2HT
ALT-2HT
ALT-2HT
Section 3
30" x 1"
30" x I "
30" x I1"
30" x Iv"
30" x I"
Length
50 ft
50 ft
50 ft
50 ft
50 ft
Joint
ST-2RB
ST-2RB
ST-2RB
ALT-2HT
ALT-2HT
Section 4
30" xI"
30" xI"
30" xI"
x0" xI"
30" xI"
Length
50 ft
50 ft
50 ft
50 ft
50 ft
Joint
ST-2RB
ST-2RB
ST-2RB
ST-2RB
ALT-2HT
Section 5
30" x 1"
30" x
0" x1"
30" x1"
30" x1"
Length
50 ft
50 ft
50 ft
50 ft
50 ft
Joint
Shoe
Shoe
Shoe
Shoe
ST-2RB
Section 6
n/a
n/a
n/a
n/a
30" x 1"
Length
50 ft
Joint
Shoe Table 3. Conductor Strings
C')
et
b~JAl
S-)1
tt)5~xfTse
t& CI
gt
)
StIf
XI.S Xc
@e
A-,et-P W^<
STER
3K
hiyrc~j), LO A)t1MG MAY
so X
J:\50169-08\WP\R\OOOSCH.REP
6
w eLL4
X
(Xf)
Page 32
s
Ove Arup &Partners 1/99 22 February 1999
Sub-sea Conductor Study
Shell UK Exploration & Production
Conductor Element
Force /Moment
Continuum Model
Beam and Spring Model
Yield Capacity
35" x 2" Pipe
Axial Force (kN)
6675
6680
47950
Shear Force (kN)
1038
1073
Bending Moment (kNm)
5084
5200
9505
Torque (kNm)
1830
1820
109678
Axial Force (kN) Shear Force (kN)
5230 66.1
5021 32.8
27585
Bending Moment (kNm)
86.8
104.5
5691
Torque (kNm)
935
1026
2033
Axial Force (kN)
4828
5021
21070
Shear Force (kN)
34.8
42.0
Bending Moment (kNm)
96.2
120.7
3753
Torque (kNm)
815
1026
4332
Axial Force (kN)
2753
2145
10890
Shear Force (kN)
Z
Bending Moment (kNm)
Z0
ZO
52.9
52.9
ALT-2HT Connector
30"xl" Pipe
ST-2RB Connector
Torque (kNm)
° 1810% 53
Table 9. Comparison of LS-DYNA Continuum and Beam and Spring Models
1V610 IS$ COAf~CKTY
J:\50169-O\WPPR\OOO5CH.REP
Page 33
1
Ove Arup &Partners 1/99
22 February 1999
Shell UK Exploration & Production
Conductor Element
Sub-sea Conductor Study
Force /Moment
Yield Capacity
API t-z Springs
Shell t-z Springs
Axial Thermal Load (Ibs)
35"x2" Pipe
Axial Force (kN)
47950
Shear Force (kN)
ALT-2HT Connector @-2
2.2tkn't (HT IA) i)-41.
p~rm)
1,500,000 HTIA-HB(Shell) (Ref. Fig. 5.23)
2,700,000 HT2A-HC(Shell) (Ref. Fig. 5.41)
6680
12020
6680
12020
1073
1034
1079
1028
5200
5018
5230
4986
Torque (kNm)
10967
1820
1819
1820
1820
Axial Force (kN)
27585
5021
10393
4162
8484
32.8
30.2
36.1
26.7
Bending Moment (kNm)
5691
104.5
101.0
102.5
103.0
Torque (kNm)
2033
1026
1276
735
902
Axial Force (kN)
21070
5021
10390
4162
8484
42.0
40.1
41.7
40.5
Bending Moment (kNm)
3753
120.7
115.5
120.4
116.2
Torque (kNm)
4332
1026
1276
735
902
Axial Force (kN)
10890
2145
1938
767
276
0
=0
Z0
Z0
O0
=0
Zo0
Shear Force (kN)
("TBending _
2,700,000 HT2A-HC(API) (Ref. Fig. 5.22)
9505
Shear Force (kN)
ST-2RB Connector
1,500,000 HTI-A-I-IB(API) (Ref. Fig. 5.21)
Bending Moment (kNm)
Shear Force (kN)
30"xI" Pipe
Axial Thermal Load (Ibs)
_Torque
Moment (kNm) (kNmT
1810 53
RFF -Nce hFic-Nc
52.9
.2I 21_.2
33.1
[_ __ 12
18.1
=0
'523_
Table 10 LS-DYNA Beam and Spring Model Results for Hard Soil Profile
J:\50169-08\WI'\R\0005C[-1.REIP
Ove Arup & Partners Page 34
1/99
22 February 1999
Shell UK l xploration & Production
Conductor
Sub-sea Conductor Study
Force /Moment
Element
35"x2` Pipe
Axial Force (kN)
Yield
API t-z Springs
Shell t-z Springs
Capacity
Axial Thermal Load (Ibs)
Axial Thermal Load (Ibs)
500,000
1,500,000
2,700,000
500,000
1,500,000
2,700,000
HT2B-MA
HT3B-MB
HT4B-MC
HT2B-MA
HT3B-MB
HT4B-MC
(Ref. Fig. 5.25)
(Ref. Fig. 5.26)
(Ref. Fig. 5.27)
(Ref. Fig. 5.28)
(Ref. Fig. 5.29)
(Ref. Fig. 5.30)
2241
6686
12020
2241
6686
12020
829
767
712
830
768
771
47950
Shear Force (kN)
ALT-2HT Connector
0
(
30"xI" Pipe
Bending Moment (kNm)
9505
6286
5817
5443
6287
5819
5427
Torque (kNm)
10967
1819
1820
1820
1820
1820
1820
Axial Force (kN) Shear Force (kN)
27585
1781 120.0
5666 106.4
-10742 87.8
1744 120.8
5495 106.5
10358 102.5
Bending Moment (kNm)
5691
48.4
35.1
13.2
48.4
35.3
41.3
Torque (kNm)
2033
1141
1283
1400
1068
1193
1307
Axial Force (kN)
21070
1759
5660
10850
1744
5498
10360
22.3
126.6
117.2
118.7
102.8
96.3
Shear Force (kN)
ST-2RB Connector
)
.e@-butom Mrz )-+.2e(HT41
Bending Moment (kNm)
3753
120.8
108.9
96.6
120.9
109.1
97.7
Torque (kNm)
4332
1137
1300
1434
1068
1193
1307
Axial Force (kN) Shear Force (kN)
10890
1938 =0
606 =0
987 =0
933 =°
1125 =0
2096 =0
Bending Moment (kNm)
1810
=0
Z0
=0
=0
=0
=0
52.9
44.6
bTorque (kNm)
53
|REFF~CE Hi. No0|
35524
g.2.9 |
S.k
t~2+
|
T. 25 |
C . 29
41.6
|
301
Table 11 LS-DYNA Beam and Spring Model Results for Medium Soil Profile
J:\50169-08\WII\R\0005C1 .REP
Ove Arup & Partners Page 35
1/99
22 February 1999
Shell UK Exploration & Production
Conductor Element
Sub-sea Conductor Study
Force /Moment
Yield Capacity
API t-z Springs
Shell t-z Springs
Axial Thermal Load (Ibs)
35"x2' Pipe
Axial Force (kN)
500,000
1,500,000
500,000
1,500,000
HT3B-SA(API)
HT4B-SB(API)
HT3B-SA(Shell)
HT4B-SB (Shell)
(Ref. Fig. 5.31)
(Ref. Fig. 5.32)
(Ref. Fig. 5.33)
(Ref. Fig. 5.34)
2253
6695
2255
6696
856
711
784
646
47950
Shear Force (kN)
ALT-2HT Connector
Bending Moment (kNm)
9505
7385
6228
7345
6127
Torque (kNm)
10967
1819
1819
1819
1819
Axial Force (kN)
27585
2074
6212
2102
6199
838
669
766
608
Shear Force (kN)
30"xl" Pipe
Axial Thermal Load (Ibs)
Bending Moment (kNm)
5691
3200
2457
3860
2999
Torque (kNm)
2033
1466
1526
1458
1506
Axial Force (kN)
21070
2079
6245
2096
5072
836
710
784
646
Shear Force (kN) Bending Moment (kNm)
3753
3405
2799
3854
Torque (kNm)
4332
1481
1547
1458
1506
ST-2RB Connector
Axial Force (kN)
10890
319.4
481
308
605
e-63.Of (WF3a)
Shear Force (kN)
=0
Z0
=0
1810
=O
=O0
53
14.8
-XR .2
(Hk4/3)
Bending Moment (kNm) Torque (kNm)
| QF2E*CS FIC- N6:[
5,31
8.1
|______
-K
2997
|
|0 30.1
12.1
_________I________
Table 12 LS-DYNA Beam and Spring Model Results for Soft Soil Profile
J:50169-08\WlI\R\0005CI-I.REP
Ove Arup & Partners Plage 36
1/99 22 February 1999
Shell UK Exploration &Production
Design Case
Sub-sea Conductor Study
35" x 2" Pipe
ALT-2HT Connector
30" x 1" Pipe
First ST-2RB Connector
Axial Only
Combined Loading
Axial Only
Combined Loading
Axial Only
Combined Loading
Axial Only
Combined Loading
HTIA-HB
6711
6680
3740
4102
3733
4162
637
767
HT2A-HC
12010
12020
7968 .
8484
8009
8484
232
276
HT2B-MA
2224
2224
1154
1744
1165
1744
234
533
HT31B-MB
6672
6686
4937
5498
4915
5498
662
1125
HT4B-MC
12010
12020
9974
10358
10010
10360
1611
2096
HT3B-SA
2224
2255
1660
2102
1669
2096
1320
3079
HT4B-SB
6674
6696
5817
6199
5832
5072
365
605
Table 13 Axial Loads in Conductor Elements Due to Thermal Axial Loading Only, and Due to Combined Loading (Results for Shell t-z Springs)
Design Case
API t-z Springs Upward Movement
Lateral Movement
(mm)
(mm)
HTIA-HB
8.5
8.0
HT2A-HC
19.2
HT2B-MA
Shell t-z Springs Rotation (degs)
Upward Movement
Lateral Movement
(mm)
(mm)
1.06
5.0
24
0.67
22.0
1.41
11.3
22
0.82
4.2
104
1.81
2.9
56
1.70
HT3B-MB
14.3
95
2.09
15.3
96
2.18
HT4B-MC
32.7
90
2.70
37.3
90
2.88
HT3B-SA
5.0
380
2.42
5.3
460
2.56
HT4B-SB
13.5
310
2.64
12.7
360
2.78
Rotation (degs)
Table 14 Displacements at Conductor Head
J:\50169-08\IP',\ROOOSCH.REP
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Ove Arup & Partners
1/99
22 February 1999
Sub-sea Conductor Study
Shell UK Exploration & Production
Combined Stress Check
Axial Tension
Bending
Allowable Tensile Stress
Allowable Bending Stress
Ft = 0.6 FY = 217MPa
Fb = 0.75 FY = 271MPa
Design Case
Force
Stress
Fa (MN)
fa (MPa)
Moment
Stress
Axial and
Mb
fb (MPa)
Bending fa+fb (MPa)
(MNm)
ja- +fb 0.6F.
0.75F, : 1.33
Shell t-z Spring Results HTIA-HB
6.68
49.9
5.23
196.5
246.4
0.96
HT2A-HC
12.02
89.8
4.99
187.5
277.3
1.11
HT2B-MA
2.24
16.7
6.29
236.3
253.0
1.01
HT3B-MB
6.68
49.9
5.82
218.6
268.5
1.04
HT4B-MC
12.02
89.8
5.43
204.0
293.6
1.17
HT3A-SA
2.25
16.8
7.35
276.1
292.9
1.10
HT4B-SB
6.70
50.1
6.13
230.3
280.4
1.08
195.4
245.3
0.95
API t-z Spring Results HT1A-HB
6.68
49.9
5.20
HT2A-HC
12.02
89.8
5.02
188.6
278.4
1.11
HT2B-MA
2.24
16.7
6.29
236.3
253.0
0.95
HT3B-MB
6.69
49.9
5.82
218.6
268.5
1.04
HT4B-MC
12.02
89.8
5.44
204.4
294.2
1.17
HT3B-SA
2.25
16.8
7.39
277.6
294.4
1.10
HT4B-SB
284.2 234.1 6.23 50.1 6.70 a). Combined Axial, Moment, Shear and Torque Loading
Soil Profile
.
1.09
Allowable Bending Stress Fb = 0.75 FY =
Moment Mb (M)
27
1 MPa
Stress fb (MPa)
fb-
0.75FY
(kI~m) Hard
5601
210.4
0.78
Medium
6891
258.9
0.96
318.2 8470 b). Moment and Shear Loading Only
1.17
Soft
Table 15 Axial and Bending Stresses in 35" x 2" Pipe
J:\50169-08\WS'P\R\OOOSCH.REP
Page 38
Ove Arup &Partners 1/99 22 February 1999
Shell UK Exploration &Production
Design Case
Sub-sea Conductor Study
Axial Tension
Bending
Allowable Tensile Stress
Allowable Bending Stress
F, = 0.6 FY Force Fa
(MN)
217MPa
Combined Stress Check
Fb =0.75 FY = 271MPa
Stress
Moment
fa (MPa)
Mb
Stress fb
Axial and
(MPa)
(MNm)
-fa
+ fb_
Bending fa+fb (MPa)
0.6FY 0.75FY <1.33
Shell t-z Spring Results HTIA-HB
4.16
70.8
0.12
11.5
82.3
0.37
HT2A-HC
8.48
144.2
0.12
11.5
155.7
0.71
HT2B-MA
1.74
29.6
0.12
11.5
41.1
0.18
HT3B-MB
5.50
93.6
0.11
10.5
104.1
0.47
HT4B-MC
10.36
176.2
0.1
9.5
185.7
0.85
HT3A-SA
2.10
35.7
3.86
368.6
404.3
1.53 4
HT4B-SB
5.07
86.2
3.0
286.5
372.7
1.46 3
API t-z Spring Results HTIA-HB
5.02
85.4
0.13
12.4
97.8
0.44
HT2A-HC
10.39
176.7
0.12
11.5
188.2
0.86
HT2B-MA
1.76
29.9
0.12
11.5
41.4
0.18
HT3B-MB
5.66
96.3
0.11
10.5
106.8
0.48
HT4B-MC
10.85
184.6
0.10
9.5
194.1
0.8
HT3B-SA
2.08
35.4
3.45
329.4
364.8
1.38
HT4B-SB
6.25 106.3 2.80 267.4 373.7 a). Combined Axial, Moment, Shear and Torque Loading
Soil Profile
1.48 s
Allowable Bending Stress Fb =0. 7 5 FY Moment
Mb
(kNm)
271
MPa
Stress
fb
fb_
(MPa)
0.75FY
Hard
125
11.9
0.04
Medium
136
13.0
0.05
4827 460.9 b). Moment and Shear Loading Only
1.70
Soft
(fggLaw .5t
s Page 39
P PE
5&F
Table 16 Axial and Bending Stresses in 30" x 1" Pipe
JA\50169-08\5\'P\R\0005CHREP
(
f-,
Fe tY AtiPLg
Ove Arup &Partners 1/99 22 February 1999
Sub-sea Conductor Study
Shell UK Exploration &Production
FIGURES
J \50169-OS\WP\R\OOOSCH.REP
Page 40
Ove Arup &Partners 1/99 22 February 1999
SHEAR STRENGTH (kN/m 2) 0
100
200
500
400
300
700
600
0
2
4
6
8
-10
I CL
W
12
*
0
14
16
DESIGN
PROFILE
@
18
20
.
UNDRAINED SHEAR STRENGTH HARD SOIL PROFILE 50169/08 Oct.'97
n
50169108
F
FIGURE J.
0
20
SHEAR STRENGTH (kN/m2 ) 60 80
40
100
120
140
W~~~~
14
0
0
10
*
12
16
20
*
*
*
~~~~DESIGN.
_ Note: Design profile follows the normally consolidated soft soil design profile below 30m depth
UNDRAINED SHEAR STRENGTH MEDIUM SOIL PROFILE 50169/08.
Oct. '97
50169/08
FIGURE1{-
40
20
0
SHEAR STRENGTH (kPa) 80 60
100
120
140
0
5
1
00
15
X
___
20~~~
20 10
*
M 30~~~~
25
40~~~~ I~~~~~~~~~~~~~DSG
50
UNDRAINED SHEAR STRENGTH SOFT SOIL PROFILE 50169/08 Oct. '97
50169/08
FIGURE
3.
~~~~~~~~~~~~~~~~~~~~~~~~~~~Soil surface
-
00= 0
-I1
Rigid collar
_____Scour
-I
to -1.5m
0
UI)
Top of grout
.
z o
~~~~~~~~~~~~~~~~~~~~~~~~~~Far-field boundary
C Lx CD
Pipe connector CD
CD~~~~~~~~~~~~~~~~.
X
D
t - z Springs
l
p - y Springs D= diameter of grout / soil interface
Bending
Schematic Model T
Fv
Axial Loading
Torsion Loading
T
LA
to l 3
tsa
Skin friction opposing axial loads
fst
Skin friction opposing torsion loads
.0~~~~~~~~~
FI
fst
/ atmax =Maximum available skin fsa~~~axfriction Axial
Axial and Torsion 50169/08 JAN. 99
Loading
SKIN FRICTION MODEL FOR LS-DYNA BEAM AND SPRING ANALYSES 0
50169/08
F
FIGURE'
Results for Increment -1000.0 1000.0 l
l
IShear force (kN) Pressure (kN/m2) 0
1000.0 1000.0
I
-3575.0 kNm
0~~~~~~~~~~~~~~~~~~~10
3~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~32 -10
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-~. B. Mom. 0
50.0
Displacement (mm) Bending moment (kNm)
5000.0
SUBSEA CONDUCTOR STUDY ALP P-Y RESULTS FOR HARD SOIL PROFILE 50169-08
FIGURE
5.1
Results for Increment -1000.0
1Shear force (kN) Pressure (kN/m2)
1000.0
I
0
_
I
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1000.0
0 I
1000.0
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2
2
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3
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P~wp.---250.0 -10000.0
P eff.
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Mom.
0 Displacement (mm) Bending moment (kNm)
250.0 10000.0
SUBSEA CONDUCTOR STUDY ALP P-Y RESULTS FOR MEDIUM SOIL PROFILE 50169-08
FIGURE
5.2
Results for Increment -1000.0 1000.0 I
lShear force (kN) Pressure (kN/m2) 0
1000.0 1000.0
I
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0 Displacement (mm) Bending moment (kNm)
Disp.
1000.0. 10000.0
SUBSEA CONDUCTOR STUDY ALP P-Y RESULTS FOR SOFT SOIL PROFILE 50169-08
FIGURE
5.3
Subsea Conductor Study
HARD SOIL
5
0
-10
~-15
-20l -80
-40
0
40
80
Displacement (mm)
P-Y curve
---
250cu
--------- E= 150 to 250 cu
HARD SOIL PROFILE COMPARISON OF COMPUTED DISPLACEMENTS FROM ALP P-Y AND ELASTIC-PLASTIC MODELS 50169-08 J:\501 69-08\WP\Z\QPROFILE.WB2
FIGURE
5.4
Printed on 02/02199 13:29
Subsea Conductor Study
5
HARD SOIL
________
0
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0
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HARD SOIL PROFILE COMPARISON OF COMPUTED BENDING MOMENTS FROM ALP P-Y AND ELASTIC-PLASTIC MODELS 50169-08 J:X50169-08\WPRZ\QPROFILEWB2
FIGURE
5.5
Printed on 02/02199 13:30
Subsea Conductor Study
MEDIUM SOIL
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_
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0
50
Displacement (mm)
P-Y curve
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MEDIUM SOIL PROFILE COMPARISON OF COMPUTED DISPLACEMENTS FROM ALP P-Y AND ELASTIC-PLASTIC MODELS 50169-08 J:\501 69-08\WP\Z\QPROFILE.WB2
FIGURE
5.6
Printed on 02/02/99 13:31
Subsea Conductor Study
5
_______
MEDIUM SOIL
________
0 0)
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-15
-4000
-2000
0
2000
4000
6000
8000
Bending moment (kNm)
P-Y curve
E' = 75 to 100 cu
MEDIUM SOIL PROFILE COMPARISON OF COMPUTED BENDING MOMENTS FROM ALP P-Y AND ELASTIC-PLASTIC MODELS 50169-08 J\501 69-08\WP\Z\QPROFl LI
B2
FIGURE
5.7
Printed on 02/02/99 13:31
Subsea Conductor Study
SOFT SOIL
5
-5
_
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20,
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COMPARISON OF COMPUTED DISPLACEMENTS FROM ALP P-Y AND ELASTIC-PLASTIC MODELS 50169-08 OIL J:501 69-08\WVPZ\QPROF IL1 .WB2
5.8 Printed on 02/02/99 13:32
Subsea Conductor Study
5
SOFT SOIL
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SOFT SOIL PROFILE COMPARISON OF COMPUTED BENDING MOMENTS FROM ALP P-Y AND ELASTIC-PLASTIC MODELS 50169-08 J:\50169-08\WvrZ\OPROFIL1.WB2
FIGURE
5ig
Printed on 02/02/99 13:33
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5.39
Shell UK Exploration &Production
Sub-sea Conductor Study
DRAWINGS
JASO169-08S\kP\R\OOOSCH. REP
Page 41
Ove Arup & Partners 1/99 22 February 1999
____________
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