SAER-5711

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Engineering Report

SAER-5711 July 2000 Submarine Pipeline Engineering Guidelines

Saudi Aramco Engineering Report Table of Contents 1 INTRODUCTION.............................................. 2 2 DEFINITIONS AND NOMENCLATURE............ 2 3 ENGINEERING ACTIVITIES............................ 4 Appendix 1 – Design Handbook Appendix 2 – Protection and Stabilization Guideline Appendix 3 – References Appendix 4 – Calculation Examples

Issue Date: July 2000 SAER-5711 Submarine Pipeline Engineering Guidelines

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1 INTRODUCTION

The "Submarine Pipeline Engineering Guidelines" have been developed to assist in the rational assessment and design of submarine pipelines. The Guidelines pertain to all pipelines used for transportation of fluids and/or gases, and installed on or below the seabed.

The guidelines apply to areas outside the surf zone. Within the surf zone more detailed engineering studies are required.

The “Submarine Pipeline Engineering Guidelines” consists of a general guideline section and four supporting appendices, giving more specific information. The general guideline sections present engineering methods and requirements to be applied when evaluating or designing submarine pipeline projects.

Appendix 1 is closely connected to the Guidelines and presents specific methods and calculation routines for various pipeline engineering assessments.

Appendix 2 describes methods for protection and stabilization of pipelines after installation. The appendix includes calculation methods for three specific stabilization methods.

Appendix 3 includes references used in the Guidelines and the appendices.

Appendix 4 presents a number of calculation examples using methods described in the Guideline.

The Guidelines are not presented as formal specifications or standards but should be regarded as a supplement to the general Saudi Aramco Engineering Reports and Standards. The prime intent is to present methods which are easily applicable and which may give a fast and reliable solution to a specific pipeline problem.

This Saudi Aramco Engineering Report replaces Saudi Aramco Engineering Report SAER-1337.

2 DEFINITIONS AND NOMENCLATURE

Submarine Pipelines: All lines used for the transportation of fluids and /or gases, installed on or below the seabed between an offshore facility and the demarcation point onshore or another offshore facility.

Demarcation Point: A point along the onshore portion of the line, established in the Project Proposal, to mark the location at which the submarine pipeline ends as referenced in the installation contract.


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Riser: That part of a submarine pipeline that is situated between the connecting flange at the mudline nearest to the platform and the first flange above water level.

Pipeline End Manifold (PLEM) Piping: All piping components between the end flange of a submarine loading line and the connection to underbuoy hoses of a single point mooring.

Open Water: Area at the sea where no depth limited wave breaking takes place.

Surf Zone: The area between the shoreline and the outermost breaking wave, which occurs when the water depth equals 130% of the 100-year maximum wave height.

B buoyancy C characteristic fatigue strength constant defined as the mean minus two-

standard-deviation curve (MPa)m

D pipeline outer diameter Dfat accumulated fatigue damage Ds, max maximum pipe diameter Ds, min minimum pipe diameter Ds average outside pipe diameter (steel) F usage or design factor fn natural frequency Ks stability parameter m Fatigue exponent (the inverse slope of the S-N curve) me effective mass per unit length of the pipe N Number of cycles to failure at stress range S S stress range based on peak-to-peak response amplitudes S0 cut-off (threshold) stress range SCF Stress Concentration Factor due to potential geometrical imperfections in

the welded area not implemented in the applied S-N curve St Strouhal number (fsD/U) SMYS specified minimum yield strength t wall thickness U time dependent flow velocity Vr reduced velocity (U/fnD) ζT total damping ratio δ eccentricity, logarithmic damping ρ density of sea water σe equivalent stress based on von Mises yield criterion σH hoop stress from internal and external pressure σL longitudinal stress from axial force and bending


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σy steel yield stress τ tangential shear stress

3 ENGINEERING ACTIVITIES

3.1 Diameter Selection

The sizing of submarine pipelines is essentially a Process function. The diameter of the lines is chosen such that, with or without pumping facilities, the resulting pressure gradients will accommodate the desired flow rate.

The relatively shallow water depths in the Saudi Aramco operating areas, combined with the state of the art in laying, permits the installation of line sizes up to around 1.5 m (5 ft).

In the past, changes in trunkline diameter have been introduced at locations where branch connections were made. Although in long lines this may be economically attractive with regard to material savings, consideration should be given to requirements regarding cleaning and/or hatching with scrapers and surveys with instrumented scraper tools. Also, axial pipeline movement should be anticipated due to the unbalanced thrust force.

3.2 Steel Grade Selection

The selection of the steel grade for submarine lines is influenced by stock availability, lead-time and purchase cost. The primary technical factors, which govern steel grade selection, are the required wall thickness and the carbon equivalent of the steel. The carbon equivalent is kept within the limits specified in 01-SAMSS-035 "API Line Pipe" to avoid the need for applying preheat for welding on the pipelaying barge. Similarly, post heat treatment on the pipelaying barge is obviously also undesirable because of the reduction in lay rates.

3.3 Wall Thickness Selection

The wall thickness selection is done in accordance with paragraph 5.1 of SAES-L-021. Figure 3.1 illustrates how pipeline wall thickness may be determined in a practical case.

Figure 3.2 gives a ready reference to determine the minimum required wall


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thickness for given water depths and may be used for all sections without significant bending movements. The Ds/t relation presented on the figure is based on buckling considerations under external pressure.

Small diameter flow and test lines often do not require weight coating for stability purposes because the required submerged weight is obtained through the weight of steel alone. When this condition applies, the line pipe may be coated with Fusion Bonded Epoxy or Polyethylene.

Due consideration should be given, however, to the fact that the concrete coating gives additional protection to external influences (impact damage by anchor wires etc) and that the absence of this protection should be compensated in additional steel. A slightly heavier pipe wall than normal would probably be required anyway, to obtain the required submerged weight. Special attention should be given to the anode design to prevent them from getting disbanded during installation.


Figure 3.1 Wall thickness selection

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Allowable Water Depth

0

50

100

150

200

0 50 100Ds/t Ratio

Max

imum

Wat

er D

epth

(m)

150

Elastic Approach

SMYS 450 Mpa

Allowable Water Depth

0

100

200

300

400

500

600

0 50 100Ds/t Ratio

Max

imum

Wat

er D

epth

(ft)

150

Elastic Approach

SMYS 65000 psi

Figure 3.2 Relation between water depth and maximum allowable Ds/t ratio (Buckling criterion). (Timoshenko & Gere (1961) Chapter 7)

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3.4 Concrete Weight Coating Selection.

3.4.1 Objective

The on-bottom stability is generally obtained by increasing the submerged weight of the pipeline by adding concrete coating. Other methods may be applied such as increased wall thickness or anchors.

Concrete coating requirements should be determined on the basis of a lateral stability analysis. The stability analysis should be carried out to ensure the integrity of the pipeline with regard to on-bottom stability when exposed to environmental loads. Reference is made to 01-SAMSS-012, Submarine Pipe Weight Coating Specifications and to Appendix 1.

3.4.2 Methodologies

Two basically different types of analyses can be used in the design, either a static analysis or a dynamic analysis.

The static analysis is based on a two-dimensional quasi-static force balance between the hydrodynamic loads acting on the pipe and the soil resistance on the pipe. The result of the static analysis is the required weight coating. The method has been implemented in a computer program COATING.

The static analysis may be carried out as a significant static analysis or as a maximum load analysis. The significant static analysis applies significant wave parameters when calculating hydrodynamic loads whereas the maximum load analysis applies the peak hydrodynamic loads in the stability check. The significant analysis implies that certain limited pipe displacements occur in the design situation (less than 20 m (65 ft)) and the design methods should only be used when such displacements are acceptable. This will normally be the case if the seabed consists of loose sediments or clayey material. In case of hard seabed (rock or hard clay with boulders) damage of the pipeline or coating may occur in case of pipe movement and a maximum load design should be applied.

A dynamic analysis involves a full dynamic simulation of a pipeline section resting on the seabed. The results of a dynamic analysis are the movements of the pipe and the pipe wall stresses. This analysis normally requires a sophisticated computer program. Veritec (1988) presents a method, which uses a set of non-dimensional parameters to calculate accumulated lateral displacements of a pipeline exposed to wave and current actions. The procedures in Veritec (1988) are presented in a


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graphical format (Figs 5.1 to 5.8 of Veritec (1988)) but are based on a large number of dynamic pipeline simulations. PRCI (1993) has developed design procedures for on-bottom stability based on static as well as dynamic approaches.

The static on-bottom stability analysis procedures are described in Appendix 1.

3.4.3 Design Conditions and Requirements

The following design conditions should be analyzed

• Pipeline during installation • Pipeline during operation For each condition the stability analysis should be carried out for the most unfavorable pipe contents.

According to SAES-L-021, paragraph 5.3.1, the minimum required submerged weight of the pipe is 0.1B where B is the buoyancy. This requirement applies for the weight of the displaced water when averaged over a length of two pipe joints or 24 m (79 ft). In areas exposed to wave and current action the minimum submerged weight has to be determined by an on-bottom stability analysis.

For the static design a factor of safety of 1.10 shall be adopted when assessing the stability, (SAES-L-021). If a dynamic analysis is carried out the lateral pipe displacements and pipe wall stresses should be checked against the allowable criteria. Unless other restrictions exist, the maximum allowable lateral displacement is equal to half the width of the surveyed corridor implying that the pipeline should not move beyond this corridor. This lateral displacement criterion is only applicable if a dynamic analysis is carried out. Design based on the significant static approach operates on a “no displacement” criterion but accepts implicitly up to 20 m (65 ft) in the design situation.

The design water depth used in conjunction with the wave analysis should in general be the algebraic sum of the chart depth (Saudi Aramco Bathymetric Charts), corrected for LAT and the height of the storm surge corresponding to the design wave predicted in SAER-5679 Arabian Gulf Hindcast Study or SAER-5565 Red Sea Hindcast Study. However, the joint probability of the extreme wave height and the extreme storm surge is generally not known. A conservative approach would be to use the lowest storm surge (i.e. negative) combined with the lowest astronomical tide, which would result in the largest bottom velocities and thereby the


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largest hydrodynamic forces.

The design waves and the design currents are readily available in SAER-5679 Arabian Gulf Hindcast Study and SAER-5565 Red Sea Hindcast Study for all of Saudi Aramco's offshore operational areas. For larger pipelines or for pipelines in shallow waters with complex bathymetry, it is recommended to take current measurements over a period of at least one lunar cycle, preferably at several strategic locations at the surface and at mid-depth, and interpret the results for use in the design.

For on-bottom stability assessment one of the following load combinations should be considered:

In areas covered by SAER-5679 the 100-year return period “extreme” wave conditions should be combined with the 100-year return period “joint extreme” current.

In areas covered by SAER-5565 or in areas not covered by SAER-5679 and where no information on the joint probability of waves and current is available the following applies:

• If waves dominate the hydrodynamic forces the 100 year wave condition should be used in combination with the 10 year current condition

• If current dominate the hydrodynamic forces the 10 year wave condition should be used combined with the 100 year current condition

If joint probability of waves and current is available, the 100-year wave and associated current or the 100-year current and associated wave should be used which ever give rise to the highest loads. For temporary phases (e.g. installation) the following should be considered:

For duration less than 3 days the environmental parameters can be established based on weather forecasts.

For duration exceeding 3 days a recurrence period of 1 year for waves and currents (for the relevant season) can be applied if there is no risk of loss of human lives. If there is a risk of loss of human lives a recurrence period of 100 years (for the relevant season) should be applied - see above for combination of waves and current. In no cases the season should be taken less than two months.


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3.5 Corrosion Protection Selection

All submarine pipelines in carbon steel shall be protected against corrosion by an external coating and a corrosion protection system using galvanic or impressed current cathodic protection. The function of the corrosion protection coating is to prevent direct contact between seawater and the steel pipe. In practice the coating will not be 100% impermeable and the steel need additional corrosion protection in the form of anodes. The anticorrosion coating reduces the amount of anodes required. An efficient anti-corrosion coating is a 3-layer coating composed of fusion bonded epoxy (FBE) primer a polypropylene (PP) adhesive and an outer PP coating. General requirements to corrosion protection are given in the Saudi Aramco Engineering Standard SAES-L-033, “Corrosion Protection Requirements for Pipelines/Piping”.

3.5.1 Design of Cathodic Protection using Sacrificial Anodes

An anode design shall meet the following criteria:

• Sufficient anode material weight to provide the required protection during the design lifetime of the pipeline

• Sufficient anode surface area to deliver the required protective current output at any time during the pipeline design life.

For an anti-corrosion coated structure like a pipeline, the necessary anode surface is determined by the current requirement in the final (end-of-life) situation whereas the necessary anode weight is determined by the mean current requirement over the lifetime.

Indium activated aluminum anodes are recommended for the cathodic protection of the pipeline.

Bracelet anodes will be mounted offshore by welding protruding reinforcement strips to doubler plates on the pipeline thus providing maximum rigidity, durability, and minimum circuit resistance. With regard to the dimensional tolerances, the anodes have been designed to fit the pipeline, including the corrosion protection coating. The anodes shall be manufactured to the specified weight and dimensions.

3.5.2 Design Parameters

The anode design is based on the following parameters:


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Seawater resistivity Sea mud resistivity Seawater temperature Pipeline or product temperature Coating breakdown factors Anode potential Anode capacity

System Life, L, is the design life for your pipeline. The cathodic protection system should be designed to be efficient without maintenance for the entire operating lifetime.

Seawater resistivity is one of the parameters determining the current density.

Sea mud resistivity is one of the parameters determining the current density in areas where the pipeline is buried.

Seawater temperature influences the resistivity and the anode temperature, which has an impact on the protective current density.

Pipeline or product temperature influences the anode temperature and the protective current density.

Coating breakdown factor gives the damage ratio of the protective coating. The breakdown factor normally increases over the lifetime of the pipeline. The breakdown factor has direct impact on the protective current density.

Anode potential is measured against a reference cell and depends on the chemical composition of the anode.

Anode capacity depends on the anode material.

3.6 Allowable unsupported free spans

3.6.1 Objective

When unsupported spans cannot be avoided proper free span design shall be performed. The analysis shall demonstrate that the stresses in the pipeline wall are within acceptable limits and that no significant fatigue damage occurs.

The route of a submarine pipeline should be chosen such that sharp changes in the slope of the seabottom are avoided. Continuous contact


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between the pipe and the seabed should be maintained as far as possible over the entire length of the line. Obstacles, which would cause unsupported spans, should be removed if feasible. Seabed preparation or presweeping may also be applied to avoid free spans.

3.6.2 Analysis of free spans

Free span analysis should be based on generally accepted static and dynamic calculation methods including non-linear structural modeling, soil reaction description, and deflection induced axial forces.

The analysis of free spans normally requires:

• Static analysis for determining pipeline configuration, sectional forces, and stress under functional loads

• Eigenvalue analysis for determining natural frequencies and modal shapes

• Dynamic analysis for determining pipeline deflection, sectional forces, and stress under combined functional and environmental loads or accidental loading

• Fatigue analysis for determining accumulated fatigue damage due to cyclic loads from wave action and vortex shedding

Dynamic analysis may be avoided if the free span length is limited in length so dynamic amplification of loads from wave action and vortex shedding are avoided. Appendix 1 presents simplified methods for calculation of natural frequency and mode shape.

3.6.3 Free span classification

Analyses of free spans are normally initiated by a classification in order to perform the most appropriate analysis. The classification will give the user information on the complexity of the analysis required and how to perform the analysis. The results of an analysis may well justify that a more complex method is used subsequently. A more complex analysis will generally provide a more reliable result and thereby longer span lengths may be accepted.

Free spans may be classified as isolated or interacting. Two spans are isolated if the intermediate support length is such that the static and dynamic behavior of each span is unaffected by the presence of the other. In all other cases free spans are interacting.

Furthermore, in order to obtain a realistic application of load in free span evaluation it is necessary to distinguish between free spans, which are caused by irregularities of the seabed, and free spans, which develop


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after pipeline installation due to some scouring action on the seabed.

‘Unevenness induced free spans’ are free spans existing since the installation caused by irregularities of the seabed only changing marginally in length during the pipeline lifetime (excluding the effect of intervention works). In this case the as-laid pipeline configuration is to be determined prior to applying the remaining functional loads.

‘Scour induced free spans’ are generated by scour or other seabed instabilities and may change in position and length throughout the pipeline lifetime.

The evaluation of the possibility of erosion and seabed instabilities is usually a specific project activity aiming at determining the maximum expected free span lengths and exposure period, while the actual location of the free span in most cases is unpredictable.

Figure 3.3 illustrates the free span classification. The common case is an isolated span on an even seabed with no other spans near by. In case two free spans are close to each other and the deflection of one span influences the deflection and stresses in the other, calculation of the deflection and stress requires that both spans be modeled.


Figure 3.3 Free span classification

Scour induced free spans occur some time after installation and they may be isolated or interacting. They are generally characterized by a small and almost constant clearance to the seabed. Unevenness induced free spans are created by irregularities of the seabed bathymetry. The figure illustrates the results of a sudden dip in the seabed. Unevenness induced free spans may be isolated or interacting.

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Free Span Classification Implication

Isolated Interacting Unevenness induced Scour induced

Simple structural model Complex structural model Loading sequence in steps All loads applied in one step

3.6.4 Static Analysis

The static analysis includes only functional loads which may give rise to insignificant dynamic amplification of the response The analysis should at minimum include the effect of the following phenomena and conditions:

• Soil-pipe interaction • Non-linear relationship between lateral deflection and axial force • Correct sequence of loading • Presence of adjacent spans when interacting The loading sequence depends on whether the span is classified as scour induced or unevenness induced.

In case of scour induced free span, the equilibrium configuration has to be determined under application of all the loads, starting from a rectilinear configuration.

In case of unevenness induced free span, an intermediate equilibrium configuration (as-laid configuration) has to be determined using loads corresponding to empty pipe conditions, a constant axial force equal to the laying tension (effective), and no axial restraint. The final equilibrium configuration is to be determined starting from the intermediate one, under application of the remaining loads and the actual axial restraint.

3.6.5 Dynamic Analysis

The suspended free span is a flexible structure having well defined natural modes and frequencies. The dynamic analysis includes all loads, which may give rise to significant dynamic amplification of the response. The loads, which should be treated in a dynamic analysis, are loads from wave action, vortex shedding, and impact loads.

Dynamic analysis requires an eigenvalue analysis of the free span for determination of natural frequencies and modal shapes.


Eigenvalue analysis

An eigenvalue analysis is a linear analysis, and a consistent linearization of the problem must be made. The eigenvalue analysis should account for the static equilibrium configuration.

The linearized stiffness of the soil shall take into account the correct properties of the soil.

Special care must be paid to the definition of the axial stiffness of the soil, as the results of the eigenvalue analysis in the vertical plane are very much affected by this axial stiffness.

In case only the suspended span is modeled, the boundary conditions to impose at the ends of the pipeline section shall represent the correct pipe-soil interaction and the continuity of the whole pipe length.

Damping

The damping of a free span is one of the parameters determining the maximum response to hydrodynamic loads. The damping is expressed by the stability parameter for each natural mode or eigenvector:

2Te

s Dm4

K⋅ρ

ζπ= (3.6.5.1)

Where:

D = pipeline outer diameter

ρ = water density

ζT = total damping ratio from pipeline, soil and surrounding water

me = effective mass per unit length of the pipe

Damping ratio and effective mass relate to the individual natural modes. Normally it is sufficient to consider the first 1 to 3 modes having the lowest frequencies.

3.6.6 Fatigue Analysis

Dynamic loads from wave action, vortex shedding, or other may give rise to cyclic stresses, which may cause fatigue damage to the pipe wall and ultimately lead to failure.

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Fatigue calculations should only be applied to the pipeline conditions being of such duration that noticeable damage may occur. Fatigue calculations are therefore normally neglected for the hydrotesting conditions.

The fatigue damage shall be calculated including as a minimum:

• Dynamic effects when determining stress ranges • Calculation of the number of cycles in a representative number of

stress ranges • Calculation of the accumulated damage according to the Palmgren-

Miner’s rule, where the number of cycles to failure for each stress range is to be predicted by means of a suitable S-N curve

The stress ranges to be used in the fatigue analysis may be found using two different methods:

• The stress ranges are found by a dynamic analysis applying an external load to the free span (load model)

• The stress ranges are determined using the normalized response amplitudes for a given flow situation (response model), appropriately scaled to the real free span.

Both methods may be applied to a wide range of flow conditions and the use of one particular method is primarily determined by practical reasons or by the quality of the appropriate model for the actual case.

The fatigue analysis should cover a period, which is representative for the free span exposure period.

S-N curves

The S-N curve is on the form:

N = C ⋅ (S ⋅ SCF)-m (3.6.5.2)

Where:

N = Number of cycles to failure at stress range S

S = Stress range based on peak-to-peak response amplitudes

SCF = Stress Concentration Factor due to potential geometrical imperfections in the welded area not implemented in the applied S-N curve

m = Fatigue exponent (the inverse slope of the S-N curve)


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C = Characteristic fatigue strength constant defined as the mean-minus-two-standard-deviation curve (MPa)m

The S-N curves (material constant m and C) may be determined from:

• Dedicated laboratory test data • Fracture mechanics theory • Accepted literature references If detailed information is not available, the S-N curves given by Appendix C, Steel Structures of DNV (1977), may be used, corresponding to carbon steel pipelines protected by anodes.

The weld root in pipes made from one side is normally classified as F2, ref. Appendix C, Steel Structures of DNV (1977). This requires a good workmanship during the construction to assure that full penetration welds are performed and that this is controlled by non-destructive examination. The F2 curve can be considered to account for some lack of penetration, but it should be noted that a major part of the fatigue life is associated with the initial crack growth while the defects are small. This may be evaluated by fracture mechanics.

The transition of the weld to base material on the outside of the pipe can normally be classified as E, see, Appendix C, Steel Structures of DNV (1977).

The S-N curves may be determined from a fracture mechanics approach using an accepted crack growth model with an adequate (presumably conservative) initial defect hypothesis and relevant stress state in the girth welds. Considerations should be given to the applied welding and NDT specifications.

A stress concentration factor (SCF) may be defined as the ratio of hot spot stress range over nominal stress range. The hot spot stress is to be used together with the nominated S-N curve.

Stress concentrations in pipelines are due to eccentricities resulting from different sources. These may be classified as:

• Concentricity, i.e. difference in pipe diameters • Difference in thickness of joined pipes • Out of roundness and center eccentricity The resulting eccentricity, δ, may conservatively be evaluated by a direct summation of the contribution from the different sources.

The eccentricity, δ, should be accounted for in the calculation of stress


concentration factor. The following conservative formula applies for a pipe butt weld with a large radius:

SCFt

= +⋅1 3 δ (3.6.5.3)

A cut-off (threshold) stress range, S0, may be specified below which no significant crack growth or fatigue damage occurs. For adequately cathodic protected joint S0 is the cut-off level at 2 ⋅ 108 cycles:

SC

m

0

81

2 10=

⋅⎛⎝⎜

⎞⎠⎟

−

(3.6.5.4)

Stress ranges S smaller than S0 may be ignored when calculating the accumulated fatigue damage.

3.6.7 Acceptance criteria

The pipeline free span shall have adequate safety against the following failure modes and deformations:

• Yielding • Fatigue • Cross flow vibrations • Buckling • Ovalization The strength criteria are based on a maximum allowable stress or fatigue damage and some usage factors, which assure that the required safety is present.

Yielding

It shall be documented that pipeline spans have an acceptable safety margin against excessive yielding during installation, hydrostatic tests, and in the operational condition. The equivalent stress criterion is to be used as a measure for safety against excessive yielding as follows:

SMYSFe ≤σ (3.6.7.1)

SMYS = specified minimum yield strength

F = usage or design factor

σe is the equivalent stress based on von Mises yield criterion, defined as:

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2HL

2H

2Le 3τ+σσ−σ+σ=σ (3.6.7.2)

σL = longitudinal stress from axial force and bending

σH = hoop stress from internal and external pressure

τ = tangential shear stress

The above equation gives the formulae for combining stress in two perpendicular directions (main stress directions). Longitudinal stress is the combined effect of bending and axial force. Hoop stress is the effect of external and internal pressure and possible soil or mattress weight on the pipe.

Table 3. 1 Usage or design factor to be applied for different operational load combinations

Operational Loads Operational and

Environmental Loads

Operational and Accidental Loads

Usage Factor

0.72

0.96

1.0

Fatigue

The fatigue criterion is given by:

Dfat ≤ F (3.6.7.3)

Where Dfat is theoretical accumulated fatigue damage.

The usage factor for fatigue, F, depends on location, accessibility for inspection and repair, inspection strategy, and consequences of failure. The following usage factors are recommended:

No access: F = 0.1 at all locations

Access: F = 0.3 below water and in splash zones. Higher usage factors may be accepted above the splash zone, dependent on the inspection strategy and consequences of fatigue failure.

Cross Flow Vibrations

Resonant cross flow vibrations of the free span due to vortex shedding

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may give an important contribution to fatigue damage. Cross flow vibrations may be avoided if the free span natural frequency is outside the region where lock-in with vortex shedding takes place. The no cross flow criterion is normally expressed by a requirement to the reduced flow velocity.

Vr ≤ 4.0 (3.6.7.4)

Vr = Df

U

n (3.6.7.5)

U = undisturbed flow velocity (combined wave and current flow)

fn = natural frequency

D = outer diameter

The requirement to Vr may be expressed by a requirement to the natural frequency

DU25.0f n ≥ (3.6.7.6)

The vortex shedding frequency for a fixed pipe is given by:

fs = St DU (3.6.7.7)

St = Strouhal number (St ≅ 0.2)

Combination of Eq. 3.6.7.6 and Eq. 3.6.7.7 gives:

fn ≥ 1.25 fs (3.6.7.8)

Buckling

The possible local buckling of the pipe due to external pressure, axial tension, or compression bending and torsion or a combination of these loads shall be considered. Local buckling of a pipeline section due to external pressure is presented in Fig 3.2. Local buckling under the combined effects of external pressure, bending, and axial force including possible ovalization is far more complex and cannot be analyzed using approximate methods only. DNV (1996), Section 5, C 300 treats local buckling in a detailed manner.

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Ovalization

The pipe is not to be subjected to excessive ovalisation. The flattening due to bending together with the out of roundness tolerance from fabrication of the pipe is not to exceed 3%, based on the following definition:

03.0D

DD

s

min,smax,s ≤−

(3.6.7.9)

Where

Ds = average outside pipe diameter (steel)

Reference is made to DNV (1996) Section 5.

3.7 Expansion stress analysis

As a result of installation alignment, hydrotest pressures, and subsequent operating temperatures and pressures, submarine pipelines may experience significant changes in configuration and incur peak stress zones.

An expansion stress analysis should be made during the design phase to predict line movement anchor forces and stress levels taking account of assumed or predicted curvatures, misalignment features, various temperatures and pressure gradients and the various types of end restraint.

Similar expansion stress analysis will be required for pipeline repair procedures, extensions or increments to existing systems and changes in operating mode.

In such cases, marine survey or aerial photography techniques should be used to determine actual pipeline alignment.

3.8 Pipeline crossings

Pipeline crossings should be avoided when minor rerouting is practical. When a crossover is required, it should be executed either by trenching the lower line into the seabed so that the top of pipe at the point of crossing is at least 0.5 meter (20 inch) below the mud line or by bridging over the lower pipe. An approach, which combines the two methods, should not be specified. Trenching the lower line is the more conservative approach and usually the more costly unless trenching equipment is otherwise required in the mobilization.

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Bridging, when employed, should be designated to suit the specific case. It should normally be a prefabricated frame of tubular members, which is placed down over the lower pipe in advance of laying the upper pipe. This minimizes the underwater work and constraints on the movement of the lower line.

Bridging may also be accomplished by placing grout or sandbags under the upper pipeline in the area of the crossing. Care must be taken to assure that this type of bridging results in a minimum of 0.3 m (12 inch) of clearance and a favorable final profile of the upper pipe.

Provisions are to be made for connecting both crossing lines by means of a cable so that any electrical potential difference of the two lines is eliminated. This is usually done by lugs, which are welded to the pipe and protrude from the concrete coating.

3.9 Branch Connections, gathering methods

a) General

Branch connections are typically employed to introduce production from independent offshore platforms into the main trunkline (or conversely to distribute fluids or gases from the main trunkline to individual injection platforms). Three general approaches may be considered and evaluated in the design of any new offshore system:

Underwater branch connections Over-the-platform branch connections (jump overs) Independent tie-in platform connections

In weighing the advantages and disadvantages of each approach the following factors should be considered:

Total installed cost Time to install initial operating network for earliest production Operational reliability Initial investment vs. deferred investment Ease of inspection and maintenance Future flexibility Requirements for pipeline scraping

b) Underwater Branch Connections

Underwater branch connections have often been specified in Saudi Aramco offshore field development. They have the usual advantage of minimum materials cost plus favorable isolation of production in the


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event of a shut-in at any individual platform. Underwater connections, however, are costly to install and represent a possible liability during the operational life of the system from damage, leakage or valve malfunction.

Underwater branch connections should be provided with shut-off provisions to permit isolation of the individual platforms and with expansion provisions to avoid overstressing of the connections.

The underwater connection should usually contain both block valves and check valves. Where large lateral movement of the main pipeline can occur it can be advantageous to restrict this lateral movement of the trunkline by installing straddle piles in the area of the connection to permit and accommodate longitudinal movement of the trunkline.

It is common practice to incorporate a reducer (increaser) just upstream from the branch connection to provide for favorable hydraulics, and improved section modulus in this high stress concentration location.

To accommodate the relative movements of the trunkline at the tie-in point and the end of the branch the latter should have a horizontal offset running parallel to the trunkline. The direction of this offset should be in the same direction as the expected movement of the trunkline upon start-up. If the direction of trunkline movement cannot be predicted, the offset should be in opposite direction of the flow in the trunkline.

Structural bracing should be applied between trunkline and the parallel branch offset close to the tie-in point and valves in order to protect valves, flanges and the tee from large expansion forces.

Sleepers on the sea bottom may be installed to avoid unwanted reduction in expansion flexibility due to bottom friction or resistance or due to an undulating seabed.

It should be noted that this type of gathering system is the least preferred and that, in fact, the installation of valves under water is against the intent of paragraph 6.2 of SAES-L-021.

Underwater branch connections are included as an option to allow extension of existing systems and other cases with possible strong justifications not to select other alternatives.

c) Tie-in Platforms

Recent Saudi Aramco practice has been to install tie-in platforms ( TP's) to gather production from several wellhead platforms for shipping to a


Page 26 of 31

GOSP through a trunkline. The increased cost of installing a dedicated platform is offset against the disadvantages of other tie-in and gathering methods and systems.

3.10 Riser and riser connections

Risers are normally installed before the jacket is loaded out at the fabrication yard. It is good practice to install them on the inboard side of the jacket to give them maximum protection against impact damage. Adequate provision should be made to protect the riser and its flanges and clamps during load-out, transportation and installation of the jacket. If the risers are installed when the jacket is already in place, the installation Contractor should submit a fully detailed installation procedure and particular attention should be given to the tie-in procedure, which should normally include the use of spools.

The connection between pipeline and riser should be made using flanges as described in SAES-L-021 to allow riser change-out. Risers and their fittings and clamps must be designed to withstand the environmental forces referenced in paragraph 5.1.4 of SAES-L-021.

3.11 Installation stress analysis

The normal technique for the installation of Saudi Aramco submarine pipelines employs conventional lay barges. Should other techniques such as the bottom pull or reel barge method be employed, they should be controlled by an appropriate separate analysis.

a) Allowable stress limits

Allowable stresses during installation are given in SAES-L-021. In the stress calculations the position of the neutral axis of a concrete coated line should be determined for a cross-section containing the pipe wall and that half of the concrete weight coating, which is in compression.

b) Factors Influencing Installation Stresses

Except for pipe diameter, wall thickness, yield strength and weight coating characteristics (which are defined prior to the installation analysis), a number of factors influence the combined stress level that will be reached in the pipeline over its profile from the deck of the lay barge to the touch down point at the seabed. The following factors control the static axial stress:


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Water depth. Effective stinger length and stinger configuration. Stinger angle. Effective tension on the pipeline (pipeline tensioning applied on deck

may not exceed forward anchor holding capacity). Radius of curvature of ramp profile. Deck height.

In the addition to the static axial stress, the following factors tend to increase the combined laying stress.

Barge motion due to waves. Strong lateral (tidal) currents during laying. External pressure as a function of water depth. Circumferential bending stress caused by pipe ovality under external

pressure. A computer analysis should be conducted in the design phase to ensure that it is feasible to install the coated pipeline without exceeding the stress limitations and to establish general requirements for pipe tensioning (and anchor capacity), stinger length and stinger departure angle. A satisfactory solution would not normally require a degree of pipe tensioning or a stinger length that is not readily available from Contractors on site. A tension of 500 kN (100 kips) in conjunction with a 90 m (300 foot) stinger is considered practical.

A computer analysis check should also be made following the selection of the low Bidder, and prior to award of the pipeline installation work, if there is any doubt that the Contractor can safely install the pipeline with the equipment he has designated for use or the procedure he plans to follow.

Designers should pay special attention to the stress levels that may arise in flanges, reducers, tees, elbows, valves and other accessories, which are installed in such a manner that they are subjected to significant axial or bending stresses during installation. If required, extra strength accessories should be specified.

3.12 Trenching and Burial

3.12.1 General Requirements

Except in shore approaches or other shallow water areas or areas with unfavorable soil condition where local conditions dictate otherwise, pipelines should be installed resting on the seabed and trenching should not be specified.


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Trenching requirements are determined upon careful consideration of the balance between economics and safe operation and acceptable risk.

In this respect proper assessment must be made of the following factors:

The degree of the pipeline's exposure to external loading due to waves and currents.

Potential hazards due to marine activities. The pipeline's own properties and type of service. Soil properties, possible floatation of the line in back filled trench,

seabed scour, etc. It is impossible to give hard and firm rules for trenching requirements, which will cover all possible combinations of location and pipeline properties in conjunction with route direction and external loading.

Hence, the parameters set out below serve as guidelines only. Each pipeline route should be evaluated on its own merits and it is the responsibility of the Project Engineer to ensure that the final pipeline configuration represents the best possible combination of the above requirements.

3.12.2 Shore Approach and Shallow Water Areas

A shore approach is defined by that part of the pipeline route, which extends from open water onto the beach through the surf zone.

The following conditions should be satisfied with respect to trenching in shore approaches and other shallow water areas along the pipeline route:

Pipelines must be trenched in surf zones where wave-slamming action would dangerously impair their safety.

Pipelines must be trenched if the height of the column of water over the coated pipe is less than the minimum value derived from the curve in Figure 3.4.


Minimum Water Column above Pipeline

00.5

11.5

22.5

33.5

44.5

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Pipeline Diameter (m)

Wat

er C

olum

n (m

)

Minimum Water Column above Pipeline

0

2

4

6

8

10

12

14

0 1 2 3 4 5 6

Pipeline Diameter (ft)

Wat

er C

olum

n (ft

)

Figure 3.4 Minimum required water depth above pipeline dependent on pipeline outer diameter.

Page 29 of 31


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3.12.3 Other Locations

Trenching may be required in locations other than shore approaches for one or more of the following reasons:

Marine or other offshore activities. Avoidance of congestion due to other existing or future facilities in

the same area. Stability requirements.

Shallow water areas such as sandbanks and coral reefs should, if at all possible, be avoided.

3.12.4 Routing of Trenches

The proposed pipeline route through shore approaches should be chosen such that the length of the trench is as short as possible. The trench must, however, have sufficient length to allow friction between the pipeline and surrounding soil to build up such that the pipelines becomes fully restrained and the minimum amount of cover on the line should be calculated accordingly. The need for end-anchors must also be evaluated in this regard, particularly at the offshore/onshore interface where the line may be brought above grade.

If natural backfill of the trench cannot be expected to occur within a reasonable period of time, the trench should be backfilled with selected materials.

Economics dictate that trenching be kept to the minimum required to assure the integrity of the system. In offshore areas and depending on soil conditions, trenching may be specified without backfill, or alternatively partial trenching can be specified, (e.g. to half the pipeline diameter).

In such cases the pipeline would be subjected to environmental influences to a lesser degree through move favorable force coefficients and trenching cost would be minimized.

3.12.5 Trenching Methods

Trenching methods will largely depend on soil characteristics in combination with Contractor capabilities.

Rock areas may require blasting and subsequently a significant amount of trench bottom preparation. Such practices should be avoided if minor re-rerouting is possible.


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Sands and clays may be jetted or plowed. Other methods are available, such as fluidization or permeable soils, which are technically acceptable but probably economically unattractive. When pre-trenching is specified, it should be executed immediately prior to installation. The trench dimensions for width, depth and side slope shall be determined by soil and pipe properties in conjunction with the installation technique to be used. Post trenching, when specified, should be executed immediately upon the acceptance of the hydrotest.

3.12.6 Backfill

Backfilling of trenched pipelines are in most cases required for protection or stabilization purposes. Backfilling may occur due to natural sediment transport on the seabed. In case the time scale for backfilling is too long artificial backfilling may be applied. For shorter lengths sand or grout bags or concrete mattresses may be applied. If longer lengths are to be covered sand-, gravel- or rock fill are to be preferred. Methods for pipeline stabilization and protection are described in Appendix 2 to this Guideline.

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Engineering Report

Appendix 1 - Submarine Pipeline Engineering Handbook SAER-5711 July 2000

Appendix 1 Table of Contents

1 INTRODUCTION 2 2 DEFINITIONS AND NOMENCLATURE 3 3 PIPELINE DESIGN CONDITIONS 7 4 WALL THICKNESS SELECTION 10 5 PIPELINE STABILITY AND CONCRETE

WEIGHT COATING REQUIREMENTS 12 6 UNSUPPORTED FREE SPANS 34 7 EXPANSION ANALYSIS 51 8 RISER AND RISER CONNECTIONS 56 9 INSTALLATION STRESS ANALYSIS 58 10 PIPELINE REPAIR 61

Issue Date: July 2000 Submarine Pipeline Engineering Handbook Appendix No. 1 to SAER-5711

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1 INTRODUCTION

The "Submarine Pipeline Engineering Handbook" has been developed to supplement the “Submarine Pipeline Engineering Guidelines” with specific design and calculation procedures. The Guidelines pertain to all pipelines used for transportation of fluids and /or gases, and installed on or below the seabed.






The calculation methods presented in Appendix 1 should be regarded as a supplement to the general Saudi Aramco Engineering Reports and Standards. Some of these procedures are relatively simple, explicit expressions which can be solved directly. Others have a more complex format which requires computer based tools. The prime intent is to present methods which may give a fast and reliable answer to a specific pipeline problem. The answer may well dictate that more advanced methods are applied to further analyze the problem and investigate various solutions.


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2 DEFINITIONS AND NOMENCLATURE a, a(t) time varying acceleration aw acceleration amplitude As pipe sectional area Ca added mass coefficient CD drag coefficient CL lift coefficient CM inertia coefficient Cu undrained shear strength for soil D pipeline outer diameter Dfat accumulated fatigue damage Di internal pipe diameter Ds outside pipe diameter (steel) e pipeline clearance of the seabed e/D non-dimensional gap E modulus of elasticity f wave frequency fo natural frequency FH in-line force fp peak frequency fs shedding frequency, safety factor F design or usage factor FA anchor force Ff friction force FD drag force FL lift force FM inertia force g acceleration of gravity Huη spectral transfer function h water depth

H distance from the top of the pipe to the surface of the soil, wave height Hmax maximum wave height Hs significant wave height h water depth I moment of inertia IB number of stress blocks ks soil spring stiffness, or constant k/D non-dimensional pipe roughness k pipe roughness including marine growth, wave number kb seabed roughness KC Keulegan Carpenter number (UwT/D) Ko pressure coefficient for soil at rest Ks stability parameter


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L wave length, sagbend length L1 stinger length Li distance along pipeline Lo wave length for deep water wave, pipe length m2u second moment of velocity spectrum me effective mass per unit length of the pipe mou zeroth moment of velocity spectrum Mb bending moment Mmax maximum moment N number of forces Ni number of cycles to failure at stress range S(Un) defined by the S-N curve Nγ soil bearing capacity factor Nq soil bearing capacity factor Nc soil bearing capacity factor ni number of equivalent stress cycles with stress range S(Un) in block i P force pi internal pressure pe external pressure Pi force for lifting pipe r radius of curvature rf axial friction force per unit length RV vertical reaction force RH horizontal reaction force s specific density S stress range based on peak-to-peak response amplitudes Sη (f) unidirectional wave power spectrum S0 cut-off (threshold) stress range Su(f) velocity spectrum at the pipe level SMYS specified minimum yield strength t pipe steel wall thickness, time tc weight coating thickness te external anti-corrosion coating thickness T wave period, tension

Tθ thermal induced axial force Tcr buckling load

Te total effective axial force Tν hoop stress induced axial force

Tn Euler force Tnl displacement induced axial force (non-linear)

Tp wave spectral peak period, or pressure induced axial force Tres residual force from installation

Tz , T02 average zero-crossing wave period U, U(t) time dependent flow velocity

cU mean flow velocity over pipe diameter


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Ufc shear or friction velocity Umo significant velocity at the pipe level Un flow velocity normal to the pipe Uw wave velocity amplitude Vr reduced velocity (U/fiD) Ws submerged weight of pipeline z cross-flow response, distance from the seabed Z section modulus zu height of sand in front of the pipe Zmax pipeline deflection θ rotation at pipe end θ1 angle

θa ambient temperature θi internal temperature

κ von Karmans constant (=0.4) ϕ(x) mode shape ϕs angle of friction for soil ψmod mode shape parameter accounting for the flexibility of the span νs Poisson’s ratio for soil ζT total damping ratio α current to wave ratio (Uc/Uw), coefficient of temperature expansion,

generalized Phillips’ constant, support conditions coefficient β empirical constant, soil parameter γ peak enhancement factor γs submerged unit weight for soil λL frequency parameter λpeak factor transforming standard deviations of vibrations to average peak-to-

peak response. Normally λpeak = 2 2 ΔL pipe elongation ΔT temperature increase μ friction coefficient μa axial friction coefficient ν Poisson’s ratio of steel ρ density of sea water ρb maximum stress due to bending moment ρs density of steel ρc density of concrete ρe density of corrosion coating ρi density of pipeline content σ spectral width parameter, stress σb maximum stress due to bending moment σe equivalent stress based on von Mises yield criterion


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σH hoop stress from internal and external pressure σL longitudinal stress from axial force and bending τ tangential shear stress ω cyclic frequency (ω = 2π ⋅ f)


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3 PIPELINE DESIGN CONDITIONS

Submarine pipeline must be designed for:

1. Construction Phase (Pipe laying)

2. Hydrostatic Testing

3. Operating Conditions

4. Special Conditions (hydrostatic collapse)

3.1 Construction

The most critical phase during construction is the pipelaying. Pipelines are normally installed from a dedicated laybarge provided with a ramp or stinger, which provides support for the first part of the pipeline leaving the barge. The free hanging section from the tip of the stinger to the landing point on the seabed is controlled by the tension provided by the tensioner on the barge. 12 m (39.4 ft) or 24 m (78.7 ft) long pipesections are welded into a continuous pipestring leaves the barge over the stinger, while the barge is moving forward. Pipelines are normally installed in empty conditions. See also SAER 5711, Submarine Pipeline Engineering Guidelines, section 3.11.

After a pipeline has been installed on the seabed there is theoretically still the lay-tension in the pipe. This tension is in case of shallow water depth small but becomes larger at increasing water depth. Close to laydown points or pipeline ends the lay-tension will be released at the completion of the installation. It is, in general, very difficult to document the presence and magnitude of the residual lay-tension and therefore it is often neglected.

The pipeline has been laid more or less straight, but will have its horizontal deviations (because of barge movement, currents, etc during laying) and its vertical deviations because of non-horizontal seabed (humps, pockets, ridges, crossovers, etc). This may result in free spanning sections, which shall be properly investigated.

3.2 Hydrostatic Testing

Before going into operation a pipeline is pressure tested using water. Hydrostatic testing is normally made by a pressure not less than 1.25 times the internal design pressure unless limited by other criteria (see ASME B 31.4, § 437.4.1). Hydrostatic testing is carried out with water having the same temperature as the


Page 8 of 63

surrounding water, so no temperature difference is present.

3.3 Operating Condition

During operation the pipe is subject to all kinds of influences causing circumferential (hoop) and longitudinal stresses in the pipe wall.

Main influences are the temperature differential (between the pipe content and the surrounding water) and the pressure differential (between the internal pressure and the water pressure).

For transmission and transportation lines, the design temperature and design pressure are dictated by the process design conditions.

For flowlines and trunklines running from a producing oil or gas well to the first processing plant (normally the Gas Oil Separator Plant, GOSP) the design temperature and pressure are dictated by the reservoir conditions, see SAES-L-022.

These lines are normally designed for the maximum shut-in wellhead pressure (SIWHP).

Other influences causing stresses in the pipe wall are:

Bearing pressure of seafloor

Bending due to unevenness of seafloor and free spans (pockets, ridges, etc) horizontal curves in pipeline (change in direction)

Offsets, branch connections, crossovers wave and current action

In addition to the stress design, submarine pipelines must be checked for hydrodynamic stability (only for lines installed on the seabed). Furthermore, pipes must be checked for vortex shedding for unsupported spans (pipes spanning valleys, risers, etc).

3.4 Special Conditions (Hydrostatic Collapse)

The pipeline must be checked for a number of special conditions such as hydrostatic collapse (empty conditions). This is particularly relevant during installation where the installation method may induce supplementary bending in the pipe.


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3.5 Design Conditions and Maximum Allowable Stress

3.5.1 The longitudinal stress (combined stress for restrained lines or equivalent tensile stress for unrestrained lines) must be calculated according to ASME B 31.4, § 419.6.4 for liquid lines and ASME B 31.8 Section A 842-223 for gas lines.

3.5.2 Flow lines and trunk lines

Design is governed by SAES-L-022 which refers to ASME B 31.4 and ASME B 31.8.

3.5.3 Offshore Gas Transmission Lines

Design is governed by SAES-L-021, which refers to ASME B 31.8.

However, the two following exceptions exist:

(1) For gas pipelines on trestles above water and in tidal flats the design factor shall be 0.60 max, see AES-L-021, § 4.2.1 (c).

(2) For gas piping in fabricated assemblies (spool pieces, etc.) in submarine pipelines the design factor F shall be 0.60 max.

3.5.4 Liquid Petroleum Transportation Lines (crude, naphta, NGL, etc.)

Design stress criteria are governed by SAES-L-003, which refers to ASME B 31.4, §5.2.7.

The same exceptions on design factor as given by § 3.5.3 apply.

Furthermore, the nominal hoop stress due to vapor pressure of NGL at flowing conditions shall not exceed 0.25 SMYS. This is required to provide crack arrest capability in accordance with SAES-L-031.

3.5.5 Water Injection Lines

Design is governed by SAES-L-020.

General design of water injection lines is the same as explained above for liquid petroleum transportation lines.


Page 10 of 63

4 WALL THICKNESS SELECTION

The wall thickness for a given pipeline shall be such that the stresses in the pipe wall resulting from the most unfavorable expected loading conditions are within the permissible limits. Reference is made to SAES-L-021.

Loading conditions comprise:

• Functional loads

• Environmental loads

• Construction loads

• Accidental loads

The wall thickness is checked for a number of pipeline conditions, e.g.:

• Pipeline installation, see Section 9

• Pressure containment, see Section 4.1

• Unsupported spans, See section 6

• Pipeline expansion, see Section 7

• On-bottom stability, see Section 5

The requirements to analysis are project specific and are given in Saudi Aramco’s Engineering Reports and Standards. The methods presented in this document are developed to provide fast and reliable answers to the most common situations. The general case of submarine pipeline design requires more extensive methods and investigations than presented in this document.

4.1 Pressure Containment

The hoop stress is calculated as:

t2tD

)pp( seiH

−−=σ (4.1.1)

pi = internal pressure

pe = external pressure

Ds = nominal outside diameter of pipe


Page 11 of 63

t = wall thickness

The hoop stress is to fulfill the condition:

σH ≤ F SMYS (4.1.2)

F = usage factor or design factor

SMYS = specified minimum yield strength

The design factor is given in SAES-L-003.


Page 12 of 63

5 PIPELINE STABILITY AND CONCRETE WEIGHT COATING REQUIREMENTS

5.1 On-bottom Stability

General

On-bottom stability analysis should be performed to ensure the stability of the pipeline, when exposed to wave and current forces and other loads (e.g. buckling loads in curved pipeline sections). This may be ensured either by requiring no movements at all or by allowing certain limited movements that do not cause interference with adjacent objects or over-stressing of the pipe.

On-bottom stability is generally obtained by increasing the submerged weight of the pipe by concrete coating. Concrete coating requirements should be determined through a stability analysis based on design criteria, which represent realistic values of the environmental conditions to which the pipeline is subjected.

Other means may, however, be applied such as increased wall thickness or anchors.

A pipeline on the seabed forms a structural unit where displacements in one area are resisted by incurred bending and tensile stresses. Residual stresses from the laying process may also provide resistance against displacement. Although the term "on the seabed" is applied, the real situation most probably involves a great variety of pipeline-seabed interface conditions. Some sections of a pipeline may be embedded to a substantially larger degree than determined by touchdown forces and parts may even be fully buried. The embedment is influenced by soil characteristics as well as phenomena like scour, sediment transport, and other seabed instabilities. In other sections, the pipe may be slightly elevated above the seabed due to seabed undulations or scour processes. For both conditions (embedded/buried or elevated pipe), the hydrodynamic forces are reduced relatively to the idealized on-bottom condition. Soil resistance forces will also be heavily affected by embedded/buried (or elevated) pipe sections. In general, the actual soil resistance is a function of the load history and it is larger for cyclic loading than for static, unidirectional loading. The soil resistance may be made up of frictional forces determined by the effective weight of the pipeline (submerged weight minus lift force) and a passive soil resistance due to embedment. The soil resistance varies along the pipeline and in case of lateral pipe displacements longitudinal soil resistance will also develop.

The design procedures for on-bottom stability includes in principle the following steps:


Page 13 of 63

• Determination of near seabed kinematics.

• Determination of hydrodynamic forces and soil reaction forces.

• Hydrodynamic stability check.

A number of projects, studies, and guidelines are available to be used in connection with on-bottom stability assessment. SAER-5679, Arabian Gulf Hindcast Study, and SAER-5565, Red Sea Hindcast Study, provide wave, current, and water level information to be used in on-bottom stability calculations. The PRCI report, Submarine Pipeline On-bottom Stability Volumes 1 and 2 provides calculation procedures and software to perform the calculations, reference PRCI (1993). DHI’s project, Stability of Marine Pipelines, was partly sponsored by Saudi Aramco and describes on-bottom stability design procedures. The program “Coating” was developed as part of this project.

5.2 Near Seabed Flow Kinematics

5.2.1 Single Wave Transfer

Linear (1st order) or Stokes 5th order wave theory can normally be applied for transferring the wave data into near bed velocity (and acceleration).

Inter-comparison of several wave theories and field and laboratory data have demonstrated that linear wave theory provides good prediction of near bottom kinematics for a fairly wide range of relative water depth and wave steepness. One reason for this relatively good agreement is that the influence of non-linearity is attenuated with depth below the free surface. The sinusoidal theory is not capable of describing the near seabed kinematics under breaking waves. In this situation a transportation of mass is initiated, and the phase relation between the velocity and acceleration is no longer π/2 due to the modified wave profile. In case of shallow water close to the breaking zone other theories should be applied, e.g. higher order Stokes or Stream Function theory. The importance of an accurate assessment of the wave induced bottom kinematics under breaking waves may be less significant in connection with e.g. shore approach perpendicular to a straight coastline. In this situation the wave induced bottom velocity will be almost parallel to the pipeline as a result of wave refraction.


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Wave data:

Height: H

Period: T

Wave length: L

Water depth: h

Wave number: k = 2π/L

Near bed water velocity amplitude:

)khsinh(1

THU W

⋅π= (5.2.1.1)

Near bed water acceleration amplitude:

w2

2

W UT2

)khsinh(1

TH2a ⋅

π=⋅

π= (5.2.1.2)

Velocity and acceleration vary as sine functions:

U(t) = UW ⋅ sin 2πt/T (5.2.1.3)

a(t) = aW ⋅ cos 2πt/T (5.2.1.4)

The wavelength, L, has to be determined for the specific water depth. The following equation may be used to determine L (iteratively):

Lh2tanh

LL

0

π= (5.2.1.5)

Where π

=2

gTL2

0 (= 1.561 T2 in SI units) (5.2.1.6)

is the wave length in deep water.

Note:

Although the maximum wave and associated period generally will produce the critical near bed design flow kinematics, there may be situations where other combinations of wave height and period lead to more severe near bed flow situations and associated hydrodynamic forces. Generally, the combination of wave height and period that


Page 15 of 63

produces the maximum near bed flow velocity/acceleration should be applied.

Fig 5.2.1 shows the relation between the dimensionless near bed velocity, Uw ⋅ T/H, versus the dimensionless water depth, h/gT2 (H is the local wave height). With known values of the above listed data, the wave induced bottom velocity can then easily be found by entering this diagram.

Wave induced Seabed Velocity

0

5

10

15

20

0.001 0.01 0.1Non-dimensional depth h/(gT2)

Non

-dim

ensi

onal

vel

ocity

UwT/

H

Fig 5.2.1 Diagram for the computation of wave induced seabed velocity


Page 16 of 63

Table 5.1 below (from Technical University of Denmark) may be used to calculate wave induced flow velocity and accelerations. The entry is h/Lo (Eq. 5.2.1.6) and h/L and sinh (kh) can be read.

Table 5.1 Sinusoidal wave functions for calculating near bed velocities and accelerations. Entry parameter to table is h/L0

5.2.2 Spectral Transfer of Waves

Sea states may be described by a wave spectrum, e.g. by the distribution of wave energy on frequencies (and directions for three-dimensional waves).


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Wave spectra may be produced from wave measurements or they may be defined by an analytical expression, such as the Pierson-Moscovitz (PM) spectrum:

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛−= −

η

4p54

p2s f

f45.expffH

165)f(S (5.2.2.1)

Which represents a spectrum for fully developed waves in deep water, e.g. no fetch or duration limitations.

Or the JONSWAP spectrum:

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛−γα= −

η

4pa5

ff

45expf)f(S (5.2.2.2)

( )⎟⎟⎠

⎞⎜⎜⎝

⎛

⋅σ

−−= 2

p2

2p

f2

ffexpa (5.2.2.3)

Hs = significant wave height

f = wave frequency

fp = peak frequency

g = acceleration of gravity

α = generalized Phillips’ constant

= ( )( ))ln(287.01g/)f2(H165 24

p2s γ−π

σ = spectral width parameter

σ = 0.07 if f ≤ fp (5.2.2.4)

σ = 0.09 if f ≥ fp (5.2.2.5)

γ = JONSWAP peak enhancement factor

The JONSWAP spectrum is applicable to areas where the wave height is limited by the free fetch of the wind. For γ = 1, being the lowest value, the spectrum becomes identical to the PM spectrum.

Each frequency component of the wave spectrum is transferred to the


Page 18 of 63

seabed analogous to the single wave transfer. In the frequency domain the transfer function is given by:

Huη (f) = 2π ⋅ f/sinh (k(f) ⋅ h) (5.2.2.6)

and the near bed velocity spectrum is found as:

)f(S)f(H)f(S 2uu ηη ⋅= (5.2.2.7)

The near seabed kinematics characterizing the spectrum are:

Significant Velocity:

oumo m2U ⋅= (5.2.2.8)

mou = ∫ Su (f) df (5.2.2.9)

(ie mou is the total energy of the velocity spectrum).

Maximum Velocity Amplitude:

Umax ≅ 1.86 ⋅ Umo (5.2.2.10)

Mean Zero-crossing Period:

( )½u2ou02 m/mT = ( )z02 TT ≅ (5.2.2.11)

m2u = ∫ f2 ⋅ Su (f) df (5.2.2.12)

Peak Period

Tp ∼ 1.4 ⋅ T02 (5.2.2.13)

The significant bottom velocity and mean zero-crossing period can be determined graphically from Fig 5.2.2.


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Near Seabed Significant Velocity, Um0

0

0.1

0.2

0.3

0.4

0.5

0 0.1 0.2 0.3 0.4 0.5Non-dimensional Peak Period, Tn/Tp

Non

-dim

ensi

onal

Vel

ocity

, U

m0T

n/Hs

γ=3.3γ=1.0γ=5.0

Near Seabed Zero-Up-Crossing Period, T02

0.7

0.8

0.9

1

1.1

1.2

1.3

1.4

1.5

0 0.1 0.2 0.3 0.4 0.5Non-dimensional Peak Period, Tn/Tp

Non

-dim

ensi

onal

Per

iod,

T 02/T

p

γ=3.3γ=1.0γ=5.0

Fig 5.2.2 Significant water velocity, Umo and zero up-crossing period, T02.

(Wave directionality and spreading not accounted for) Tn = g/h h = water depth g = gravity constant γ = Jonswap peak enhancement factor


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5.2.3 Steady Current

In the stability calculations the steady current averaged over the pipe diameter is used. The velocity profile is described by the logarithmic expression:

( )bfc k/z30lnU1)z(U ⋅⋅κ

= (5.2.3.1)

κ = 0.4 (von Karmans constant)

Ufc = shear velocity

kb = seabed roughness

z = distance from seabed

The mean current velocity over the pipe diameter is then:

bfc

D

0c

k72.2D30lnU1~

dz)z(UD1U

⋅⋅κ

= ∫ (5.2.3.2)

This velocity may easily be found for the following two situations:

• The velocity Uc(z*) is known at a height z* above seabed:

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛⋅=

bbcc k

*z30ln/k72.2D30ln*)z(UU (5.2.3.3)

• The mean velocity over the entire depth, ),h(Uc is known:

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛⋅=

bbcc k72.2

h30ln/k72.2D30ln)h(UU (5.2.3.4)


Page 21 of 63

Fig 5.2.3 Calculation of steady current velocity for different current profiles

5.2.4 Combined Wave and Current Velocity

Wave and current velocities must be vectorially added. It is only the components perpendicular to the pipeline, which are used when calculating the hydrodynamic forces. If no information is available regarding wave or current direction it is assumed that wave and current act perpendicular to the pipeline.

The total velocity is calculated according to the following expression:

Utot(t) = U(t) + Uc (5.2.4.1)

The wave induced flow, U(t), is calculated according to Eq. 5.2.1.3. In case the near seabed flow velocity has been found using spectral transfer of waves (Section 5.2.2) the velocity amplitude, Uw, is replaced by the significant velocity, Umo (Eq. 5.2.2.8).

The current velocity, Uc, is calculated according to Section 5.2.3. cU is used for on-bottom stability calculation.


Page 22 of 63

5.3 Hydrodynamic forces from Waves and Current

A pipeline near the seabed exposed to wave and current flow will experience a time varying hydrodynamic force. This force can be expressed by two components, one horizontal in-line with the flow, in-line force, and one vertical perpendicular to the flow, the lift force.

The hydrodynamic forces may in general be found as:

In-line: aCD4

UUCD21FFF M

2DMDH ρ

π+ρ=+= (5.3.1)

(Morison Equation)

Lift: 2LL UCD

21F ρ= (5.3.2)

Where:

FD: Drag force

FM: Inertia force

FH: In-line force

FL: Lift force

ρ: Density of sea water

U: Water particle velocity, i.e. sum of wave and current induced velocity cU)t(U +

a: Wave induced water particle acceleration, a (t)

CD: Drag coefficient

CM: Inertia coefficient

CL: Lift coefficient

The three force coefficients, CD, CM, and CL depend on a number of parameters, e.g. the relative pipe roughness, k/D, the relative amplitude of water motion (or the Keulegan-Carpenter Number, KC), and the ratio between the steady current and the wave velocity. The values of CD, CM, and CL cannot be found using analytical methods only but model tests are required. In the next section CD and CL are given in the form of graphs. The coefficients presented give the best overall fit between forces measured in experiments and forces calculated using


Page 23 of 63

equation 5.3.1 and 5.3.2. Practical experience has shown that the use of the theoretical value for CM = 3.29 gives an adequate accuracy in the force calculations. Therefore, it is recommended to use CM = 3.29 for all pipelines resting on the seabed.

Fig 5.2.4 Forces on a submarine pipeline exposed to wave and current action

5.3.1 Force Coefficients

The force coefficients have been found through experimental investigations as presented in PRCI (1993). The force coefficients are presented dependent on:

KC = Keulegan Carpenter number α = current to wave ratio (Uc/Uw) k/D = non-dimensional pipe roughness


Page 24 of 63

Fig 5.3.1 Drag coefficient against KC-number - pure wave flow


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Fig 5.3.2 Lift coefficient against KC-number - pure wave flow


Page 26 of 63

Fig 5.3.3 Drag coefficient against current ratio, combined wave and current flow


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Fig 5.3.4 Lift coefficient against current ratio, combined wave and current flow


Page 28 of 63

5.4 Soil Reaction Forces

5.4.1 Coulomb Friction

The lateral soil resistance that can be mobilized against sliding may be described by the Coulomb friction model:

RH = μRV, (5.4.1.1)

Where:

μ: Friction coefficient (static) RV: Vertical soil reaction on the pipe RH: Lateral soil resistance on the pipe

For the very common design case: a pipeline resting directly on a sandy seabed, the Coulomb friction model is reasonable. However, for partly buried pipelines and pipelines on soft clayey soil the soil force model is more complex and cannot be described accurately by the simple Coulomb friction.

Recommended values for friction coefficients are given in the table below.

Table 5.4.1 Typical soil parameters

USCS Symbol

Soil Description

SubmergedWeight

γs (kN/m3)

Peak FrictionAngle ϕ (°)

Coulomb Friction Model

μ

Soil Parameter

β

SW Well graded sands, little or no fines

8.5-11.5 34-41 0.65-0.90 3-10

SP Poorly graded sands, little or no fines

7.5-10.5 34-39 0.65-0.80 5-15

SM Silty sands, poorly graded

8.0-11.5 31-37 0.55-0.75 *)

SC Clayey sands, poorly graded

8.0-11.0 29-35 0.55-0.70 *)

ML Silts and clayey silts 8.0-11.0 26-33 0.50-0.65 *)

CL Clays of low to medium plasticity

8.0-11.0 - 0.2 (for cu >25 kN/m2)

*)

CH Clays of high plasticity

7.0-9.0 - 0.4 (for cu <25 kN/m2)

*)

*) Not available


Page 29 of 63

5.4.2 Refined Soil Modeling

Lateral soil resistance can be modeled using an empirical approach, which separates the total lateral soil resistance into a dynamic Coulomb frictional component and a passive soil resistance component. This approach is particularly relevant to pipelines being partly buried either during trenching operations or through sediment movements on the seabed. The approach should not be used for pipelines with low submerged weight, which may become buoyant due to hydrodynamic lift from waves and current action.

The Coulomb component depends on RV and a dynamic friction coefficient, μ'. The dynamic friction coefficient is smaller than the static. If no other value is available the dynamic friction coefficient may be taken as 0.9 times the static friction coefficient. The passive component depends on the submerged unit weight of the sand, γs, on the actual value of the settlement, z, and possibly also on the loading history, reflected in the number of cycles and loading level, since the start of loading at the initial embedment, z0.

The limiting total lateral soil resistance may be described as:

RH = μ'RV + βγsA (5.4.2.1)

Where A is a characteristic area (here taken as half the area of the vertical cross-section of the soil displaced by the pipe itself), and β is an empirical soil resistance coefficient, see table 5.4.1.

The first term is the Coulomb component and it will dominate when the settlement, z, is small. The second term becomes more important as z increases, and provides a finite lateral soil resistance even if the actual value of RV is zero.

For small values of z:

22/3 D)D/z(32A ≅ (5.4.2.2)

Which transforms equation 5.4.2.1 into:

2/32sVH )D/z(D

32R'R γβ+μ= (5.4.2.3)

In order to simplify the use of the force description, the actual pipe settlement, z, may be replaced by the ultimate asymptotic value, zu.


Page 30 of 63

zu depend on the initial vertical reaction, of the loading history and also of the sand properties. Data for zu are not generally available but for poorly graded sands with little or no fines zu = 0.2D may be applied.

5.5 Hydrodynamic Stability Requirements

5.5.1 General Comments

The stability against wave and current forces may be calculated using either a static or a dynamic approach.

The static stability design is based on the following main assumptions:

• Pipe movements are not allowed, requiring equilibrium between loads (hydrodynamic forces) and reactions (soil resistance forces).

• Near bed wave flow is oscillating and uni-directional.

• Soil resistance is based on 2-dimensional assumptions, but may include simple friction as well as passive soil resistance.

The dynamic stability design is based on the following main assumptions:

• Pipe movement is allowed, and restrictions on total movements or maximum stresses form the design criteria.

• The pipeline is viewed as a structural unit (long section used in the analysis), where bending and tensile stresses act as restoring forces.

• The wave flow is modeled as three-dimensional with a mean direction and an energy spreading.

• The effect of pipe movements on the hydrodynamic forces is included.

5.5.2 Static Stability Design

The design format is expressed by:

Hs

H Rf1F ≤ Where (5.5.2.1)

FH = in-line hydrodynamic force component


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RH = available horizontal soil reaction

= μ(Ws-FL)

fs = safety factor against sliding

The lateral stability check is performed using the expressions for wave and current forces and soil reaction forces from previous chapters and the requirements to submerged weight is:

LHs

s FFf

W +μ

≥ (5.5.2.2)

The minimum allowable factor of safety is 1.10.

5.5.3 Dynamic Stability Design

The design format is either expressed through a maximum allowable lateral displacement or by the general stress criteria for the pipeline design.

5.5.4 Other Horizontal Loads

Pipelines having a curvature in the horizontal plane or a bend may experience lateral forces imposed by the axial force in the pipeline. Exceeding the lateral stability in this case will result in lateral pipeline displacements and a reduction of the axial force. When limited lateral movements are acceptable the axial force induced lateral load may be neglected in the lateral stability design.

Axial loads in heated pipelines need special attention because of the potential risk of lateral buckling including large displacements and high bending moments.

5.5.5 Vertical Stability

If the seabed is very weak the pipe will sink into the seafloor till the soil reaction can balance the downward forces. The stability of the pipeline (in vertical direction) is checked by establishing the force equilibrium of all relevant forces, see Eq. 5.6.1. Fig 5.6.1 illustrates the force equilibrium.


Page 32 of 63

Fig 5.5.5.1 Vertical equilibrium for a buried pipe

VfSLVS RF2FFFW ≤⋅−+−+ (5.5.5.1)

WS submerged weight

FV vertical force due to pipe curvature in the vertical plane

FS weight of soil on top of pipe Ff friction along shear planes (if Ff > ½Fs then Ff = ½Fs)

FL hydrodynamic lift force (if any)

RV bearing capacity of the soil

FV = Te/r effective axial force divided by radius of curvature

Ff = s2

S tand21

ϕγ (if Ff > ½Fs then Ff = ½Fs) (5.5.5.2)

FL = 2L UDC

21 (5.5.5.3)

CL = lift coefficient, dependent on the exposure of the pipe. The lift coefficient given in Section 5.3.1 is valid for a fully exposed pipe. The lift coefficient for a partly exposed pipe is smaller.

RV = DNCNdDN21

cuqss ⎟⎠⎞

⎜⎝⎛ +γ+γ γ (5.5.5.4)


Page 33 of 63

Nγ, Nq, Nc = bearing capacity factors

Cu = undrained shear strength


Page 34 of 63

6 UNSUPPORTED FREE SPANS

6.1 Description of Free Spans

Unsupported submarine pipeline sections - free spans - may occur due to a number of reasons; they may be constructed intentionally, they may occur due to unforeseen conditions on the seabed or they may develop due to seabed instability or sediment transport on the seabed. Free spans represent critical section in the pipeline system because high bending stress may develop and in combination with the hoop stress from the internal pressure, and temperature induced stresses an increased risk for yielding or local buckling of the pipeline wall exists. Furthermore, the free span is an elastic structure, which may undergo large amplitude oscillations if exposed to dynamic cyclic loads having a frequency near the natural frequency of the span.

The following sections present methodologies to the assessment of free spans. The methodologies presented are simplified and yields conservative results.

Free spans shall be checked for hydrotesting and during operational conditions.

6.2 Main Definitions, Span Analysis Sequence

Pipeline free span analysis comprises a number of activities dealing with the pipeline and free span structural and geometrical properties and with the environmental and soil conditions. The main elements in a free span analysis are listed below. The specific calculations and analysis required are described in the following sections.

Pipe System Data: Basic geometrical and physical data describing the pipe system and its contents are given as input. Additional quantities and parameters based on this data are calculated for use in the succeeding calculations.

Span Configuration Data: Simple geometrical data describing the pipeline span are required as input. The main parameters are span length, height above seabed and burial depth. The span length, L, should be assessed as accurately as possible (for existing spans) as this has a dominating influence on the resonance frequency. The characteristic gap, e, is defined as the average gap in the middle one-third of the span. The burial depth, d, is the distance from the underside of the pipe to the seabed. If the burial depth varies the characteristic burial depth is defined as the average burial depth over a length corresponding to 1/4 of the free span length.


Page 35 of 63

Hydrographic Data: The Wave and current parameters required for the description of the wave and current conditions during the calculation period considered (e.g. 1 year) are given. Extreme wave parameters are required for maximum load considerations. The waves and currents are transferred to the seabed and parameters describing the wave and current induced water velocities perpendicular to the pipe axis are calculated.

Soil Parameters: Soil stiffness parameter and friction coefficients are established on the basis of soil information available.

Structural Model: The structural model calculates the static configuration (deflection and moments) the resonance frequency and the dynamic moments based on the pipe and span data and the soil parameters.

Static Analysis: Static Analysis includes determination of deflected shape, sectional forces and maximum stress. The static configuration is the starting point for any dynamic analysis.

Dynamic Analysis: Dynamic analysis consists of an eigen value analysis for determining natural frequencies and mode shapes. The eigen value analysis si followed by a dynamic response analysis forming the basis for a fatigue analysis.

Damping Parameters: The structural damping is entered. Based on the pipe, span and soil data, three soil damping components (hysteretic and radiation, axial friction and transverse friction damping) are calculated. The total damping is thereby determined.

Fatigue Analysis: Parameters describing SN-curves are given. The most appropriate curve is selected for the specific calculation.

Pipe Orientation (θp): The pipe is oriented relatively to geographical North.

Pipeline System and Span Configuration Data are illustrated by Fig 6.2.1.


Page 36 of 63

Te

Ws

Te

Mb Mm Mb

ks ks

L

otd1.00/50302-3

Fig 6.2.1 Definition of span configuration data

A cross-section in the pipe is shown below

Fig 6.2.2 Cross-section in pipe

The relevant physical properties of the pipe and coatings are described by the following expressions:

External diameter of pipeline: ces t2t2DD ++= (6.2.1)

Moment of inertia: ( )( )4s

4s t2DD

64I −−

π= (6.2.2)

Internal area: ( )2si t2D

4A −

π= (6.2.3)


Page 37 of 63

Steel area: ( )( )2s

2ss t2DD

4A −−

π= (6.2.4)

External coating area: ( )( )2s

2ese Dt2D

4−+

π=Α (6.2.5)

Concrete coating area: ( ) )(( )2es

2ecsc t2Dt2t2D

4+−++

π=Α (6.2.6)

Mass of pipe and content: cceessii Am ρΑ+ρΑ+ρ+ρΑ= (6.2.7)

Effective mass: a2

e CD4

mm ρπ

+= (6.2.8)

Specific density: 2D

4

msρ

π= (6.2.9)

Submerged weight of pipeline per unit length:

gD4

mgW 2S ρ

π−= (6.2.10)

( )1sgD4

W 2S −ρ

π= (6.2.11)

The following nomenclature is used

Ca = added mass coefficient (Ca = Cm – 1)

Ds = outside pipe diameter (steel pipe)

d = burial depth

e = characteristic gap

ks = soil reaction coefficient

t = nominal pipe wall thickness

tc = weight coating thickness

te = external anti-corrosion coating thickness

ρs = density of steel

ρc = density of weight coating


Page 38 of 63

ρe = density of external corrosion coating

ρi = density of contents of pipe

ρ = density of sea water

The effective mass includes added mass and is relevant for dynamic analysis. The added mass can intuitively be explained considering acceleration of the pipeline. Not only the pipeline has to be accelerated but also part of the surrounding water. The pipeline will therefore react as having an increased mass. The added mass depends on the gap below the pipeline. For a pipeline resting on the seabed the added mass coefficient is Ca = 2.29. For a free pipe the added mass coefficient is Ca = 1.0. Values for the added mass coefficient Ca can be obtained from the literature e.g. DNV (1988) Fig 3-1. In most cases it is adequate to use Ca = 1.0.

6.3 Simplified Structural Model

The static configuration and sectional forces of a free span can be calculated using explicit expressions and an iterative procedure. The simplified procedure is based on the assumption that the pipeline originally has a rectilinear configuration, that the seabed the pipeline act as an elastic foundation, and that the pipeline is fully restrained at some distance on the seabed.

Fig 6.2.1 illustrates the simplified structural system. The following expressions give the bending moment at the support (Mb) and in the center of the span (Mm) and the settlement at the support (zb) and midspan (zmax). Different expressions are obtained when the effective axial is positive (tension) and negative (compression).

Tension, Te>0 and Te < 2 EIks

⎟⎟⎠

⎞⎜⎜⎝

⎛+

−⎟⎟⎠

⎞⎜⎜⎝

⎛ −−

−=

u2utanh

ba3L/a2/

u4utanhu

ba3L/1LW

21M 22322

22

sb (6.3.1)

ucosh1M

u1ucosh

ucosh1LW

41M b2

2sm +

−= (6.3.2)

( ) ⎟⎟⎠

⎞⎜⎜⎝

⎛−+

−=

EIM

abak

LWba3

1z b22

s

s22b (6.3.3)

ucoshucosh1

TM

1u21

ucosh1

TEIWzz

e

b22e

sbmax−

−⎟⎠⎞

⎜⎝⎛ −++= (6.3.4)


Page 39 of 63

EIT

2Lu e= (6.3.5)

EI4T

EI4k

a es += (6.3.6)

EI4T

EI4k

b es −= (6.3.7)

Compression Te<0, Te> -2 EIks and Te > 22

lEI4π−

⎟⎟⎠

⎞⎜⎜⎝

⎛+

−⎟⎟⎠

⎞⎜⎜⎝

⎛ −−

−=

u2utan

ab3L/b2/

u4uutan

ab3L/1LW

21M 22322

22

sb (6.3.8)

ucos1M

uucos1

ucos1LW

41M b2

2sm +

−= (6.3.9)

( ) ⎟⎟⎠

⎞⎜⎜⎝

⎛−+

−=

EIM

bbak

LWab3

1z b22

s

s22b (6.3.10)

ucosucos1

TM

1u21

ucos1

TEIWzz

e

b22e

sbmax−

−⎟⎠⎞

⎜⎝⎛ −−+= (6.3.11)

EIT

2Lu e−

= (6.3.12)

akEI

TEI

s e= −4 4

(6.3.13)

bkEI

TEI

s e= +4 4

(6.3.14)

The expressions for calculating moments and deflections include the effective axial force, Te, the submerged weight, Ws, and the soil reaction coefficient, ks.

The axial force is calculated according to Section 6.6, the soil reaction coefficient is available from the literature, e.g. Hetényi (1976).


Page 40 of 63

6.4 Simplified Dynamic Analysis

The free span may be designed using a no cross flow vibration criteria or fatigue caused by cross flow vibrations may be accounted for. In both cases the natural frequency of the free span has to be determined.

Calculation of the dynamic response of a free span requires an eigen-value analysis for determination of modal shapes and natural frequencies, unless the response is calculated using direct simulation and complex structural dynamic simulation.

Eigenvalue Analysis: An eigen-value analysis is a linear analysis, and a consistent linearization of the problem must be made. The eigen-value analysis should account for the static equilibrium configuration.

The linearized stiffness of the soil shall take into account the correct properties of the soil. In particular the axial stiffness of the soil should be modeled correctly because this affects the results of the eigen-value analysis in the vertical plane.

The boundary conditions to impose at the ends of the pipeline section shall be such as not to alter the simulation of the pipe-soil interaction and to take care of the actual continuity of the whole pipe length.

Natural Frequencies and Mode Shapes: In order to perform a fatigue analysis the natural frequencies and the mode shapes of the pipeline are required. For this purpose a simplified procedure is given below. Only the first symmetrical mode is considered.

Natural Frequencies: For a linear elastic beam the natural frequency, f0, of the first symmetrical vibration mode is given by:

⎟⎟⎠

⎞⎜⎜⎝

⎛−

λπ

=cr

e

e2

2

0 TT1

mEI

L)L(

21f (6.4.1)

f0 = natural frequency

λL = parameter depending on the support conditions i.e. the soil parameter )EI/Lk 4

s=β

ks = soil reaction coefficient

EI = bending stiffness


Page 41 of 63

me = effective mass per unit length (incl. added mass)

Te = effective axial force (tension or compression)

Tcr = buckling load (Tcr<0).

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11

Log(β)

λL

4.734.73

Fig 6.4.1 Free span frequency parameter, λL, presented as a function of the soil parameter, β = ks L4/EI. Reference is given to Hobbs (1986)

The buckling load Tcr is found in Hetenyi (1976) and it is expressed by following equation:

⎟⎠⎞

⎜⎝⎛ π

+

π=β

ncr

ncr2

T/T2

cos1

T/T (6.4.2)

Tn = π 2EI/L2 Euler force (6.4.3)

The equation for determining Tcr can by solved iteratively. Fig 6.4.1 shows the relation between log10β and Tcr/Tn.


Page 42 of 63

0

1

2

3

4

0 1 2 3 4 5 6 7 8 9 10 11Log(β)

T cr/T

n

Fig.6.4.2 Relation Tcr/Tn presented as function of the soil parameter, β = ksL4/EI

Due to the static deflection of the pipeline (in-plane deflection) the in-plane and the out-of-plane natural frequencies are not equal. In order to determine the in-plane natural frequency the frequency given above is modified according to Bruschi (1991) using a semi-empirical methodology.

Assuming that the pipeline oscillates symmetrically round the initially deflected shape the first natural frequency f1 (vibration in the vertical plane) can be estimated by:

( ) ( ) 2432

smax,2

02

1 az2f2f2 α+α+π=π (6.4.4)

Where zmax,s is the static midspan deflection of the pipe, a is the amplitude of vibration, and α is a coefficient which accounts for the support conditions. According to Bruschi (1991) this equation overestimates the frequency with up to 25 %. Therefore α is conservatively determined with the assumption of a pinned-pinned mode shape:

απ

=⎛⎝⎜

⎞⎠⎟⎛⎝⎜

⎞⎠⎟

EAm L L

L

e

' 4

4 (6.4.5)

Where A' is the effective area considering support flexibility given by:


Page 43 of 63

A

AEL k k

' =+ +

⎛⎝⎜

⎞⎠⎟

11 1 1

1 2

(6.4.6)

Where k1 and k2 are the axial spring stiffness of the two supports.

The initial deflection does not influence significantly the out-of-plane natural frequency, hence the expression for f0 (eq. 6.4.1) given above is valid.

Mode Shapes: The mode shape of the first symmetrical mode is determined according to Hobbs (1986). He presents a method where a full analysis of the vibrations of the pipeline embedded in the foundations is linked to the analysis of the free span.

The general form of the mode shape of the free span for the first symmetrical mode is given by:

v x B x D x( ) cos cosh= +λ λ (x=0 at midspan) (6.4.7)

While the mode shape on the seabed is given by:

v x x C x C xB B B( ) exp( )( cos sin )= − +λ λ λ3 4 (x=0 at boundary) (6.4.8)

Where:

λω

=⎛⎝⎜

⎞⎠⎟

mEIe

2 0 25.

(6.4.9)

And

λλ

Bsk

EI= −

⎛⎝⎜

⎞⎠⎟

4 4

4 0 25.

(6.4.10)

f2 ⋅π=ω cyclic frequency

Matching v(x) and its first three derivatives at the interface four equations are obtained for the determination of B, D, C3, and C4, however, only B/D can be determined. Reference is made to Hobbs (1986).

The calculation is performed in a series of steps:

When f1 has been determined a new value of λL is determined and used to calculate λ and λB. B/D, C3, and C4 are determined using equations 6.4.9 and 6.5.10 which are fitted at the boundary.


Page 44 of 63

The normalized mode shapes in the free span and on the seabed are given by:

1xcoshxcos

)x(DB

DB

+λ+λ

=Φ (x=0 at midspan) (6.4.11)

1)xsinxcos)(xexp(

)x(DB

BDC

BDC

B43

+λ+λλ−

=Φ (x=0 at boundary) (6.4.12)

The normalized stress can be determined by:

σ∂

∂( ) ( )x x

xE

Ds= −2

2 2Φ (6.4.13)

Where Ds is the outside pipe diameter. The normalized stress is determined at midspan and at the support.

Damping: The damping of a free span is one of the parameters determining the maximum response to hydrodynamic loads. The damping is expressed by the stability parameter for each natural mode or eigenvector:

2Te

s Dm4

K⋅ρ

ζπ= (6.4.14)

Where:


ρ = water density

ζT = total damping ratio from pipeline, soil and surrounding water

me = effective mass per unit length of the pipe

6.5 Axial Force

The axial force contributes to the pipe wall stress and may have a dominant influence on the deflections in areas where transversal pipeline movements occur.

The following elements contribute:

• Residual force from installation Tres


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• Thermal induced axial force Tθ

• Pressure induced axial force Tp

• Hoop stress induced axial force Tν

• Deflection induced axial force (non-linear) Tnl

The value of the various axial force components may vary from project to project, however, the following general considerations are valid:

• The residual axial force from construction installation activities is in general small and may be neglected in most cases

• Thermal induced axial force may occur if the content of the pipeline has a different temperature than the environment. In most cases the content will have a temperature close to ambient and this force component can be neglected. The force can be calculated by Tθ = -α (θi - θa) π (D-t) t E (6.5.1) θi = temperature of internal medium θa = temperature of ambient water

• The pipeline operates generally on high pressure and the pressure induced as well as the hoop stress induced axial force components need to be considered. The effect of external pressure on the effective axial force may be neglected. The force can be calculated by

i2i

i

ip pD

DtD5.0

2TT ⎟⎟

⎠

⎞⎜⎜⎝

⎛ +ν−

π−=+ ν (6.5.2)

• The deflection induced axial tension is the force generated by the lateral movements and is a priori unknown but can be found through an iterative scheme

• The total effective axial force is made up by the above contributions. Te = Tres + Tθ + Tp + Tν + Tnl (6.5.3)

6.6 Simplified Formulations for Free Spans

The maximum bending stress can be calculated using simplified formulations for a number of free span configurations, neglecting the influence of the axial force. This is not correct in the general case because pressure and temperature


Page 46 of 63

induce large axial forces. It may be an acceptable approach for a first assessment, near expansion loops or at other locations where the axial force is released.

A. Pipeline Crossing Pocket in Seafloor

For a pocket with length L is;

Maximum bending moment Mb = 141 Ws L2 (6.6.1)

Maximum bending stress σb = Mb/Z (6.6.2)

Midspan deflection Zmax = 0.06 (Mb/EI) L2 (6.6.3)

This is for very rigid edges of the pocket. Normally the edges are softer and the expression below can be used:


Fig 6.6.2 Pipeline crossing a pocket in the seabed

B. Pipeline Crossing a Ridge

Free span length L = 4

sWEId913.2 (6.6.5)


Page 47 of 63


Maximum bending stress σb = Mb/Z

= 1.414 ZEIdWs (6.6.7)

d is the height of the ridge

Fig 6.6.3 Pipeline crossing a ridge on the seabed

C. Pipeline Crossing a Sudden Dip in Seabed

Free span length L2 = 4

sWEId6833.2 (6.6.8)

L1 is calculated using equation 6.7.10 and ϕ = d/L2

Maximum bending stress σb = EIdWZ96.0

s (6.6.9)


Page 48 of 63

Fig 6.6.4 Pipeline crossing a sudden dip in the seabed

D. Pipeline Crossing a Sudden Change in Seabed Slope

Free span length L1 = 3

sWEI12 ϕ (6.6.10)

Maximum bending stress σb = 3/23/1s )EI12()W(

Z41

⋅ (6.6.11)

Fig 6.6.5 Pipeline crossing a sudden change in seabed slope

E. Crossing of two pipelines

For cross-over the formulas for pipe on a ridge can be used. The minimum distance between the two pipes is 0.3 m (12 inches).

The nomenclature in the above equations is explained on the figures and below

EI = bending stiffness Ws = submerged weight


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Z = section modulus (2I/Ds) Zmax = mid span deflection

Acceptance criteria for stresses are given in the Submarine Pipeline Engineering Guidelines, section 3.6.7. Bending stress is combined with other stress components according to von Mises yield criterion.

6.7 Fatigue Damage Calculation

Reference is made to DNV (1998).

The fatigue damage shall be based on the accumulation law by Palmgren-Miner:

DnNfat

i

ii

IB

==∑

1

(6.7.1)

Where:

Dfat = accumulated fatigue damage

IB = number of stress blocks

ni = number of equivalent stress cycles with stress range S(Un) in block i

Ni = number of cycles to failure at stress range S(Un) defined by the S-N curve

Un = flow velocity normal to the pipe

The number of stress blocks, IB, is to be large enough to ensure reasonable numerical accuracy, i.e. a change of stress blocks should not result in a significantly different result.

The number of stress cycles, ni, corresponding to the stress range block, S(Un) to be used in the analysis equals the number of load cycles when the load model is applied. In case a response model is applied the total number of cycles can be found multiplying the natural frequency of the span with the exposure time.

The stress ranges, S(Un), may be calculated using the load model, through integration of the equation of motion, or the stress ranges may be found using the response model.


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Application of the response models can be performed according to the following equation:

( ) ( ) modpeaknmn D/UaUS ψ⋅λ⋅⋅σΔ= (6.7.2)

Where:

a(Un)/D = response model for in-line or cross-flow amplitudes (standard deviation)

Δσm = maximum stress range for actual vibration mode for maximum amplitude of 1 diameter

ψmod = mode shape parameter accounting for the flexibility of the span

λpeak = factor transforming standard deviations of vibrations to average peak-to-peak response. Normally λpeak = 2 2


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7 EXPANSION ANALYSIS

7.1 Restrained and Unrestrained Pipelines

There are fundamental differences in loading conditions for restrained sections of a pipeline and for the unrestrained sections. Therefore, different limits on allowable longitudinal stresses are applicable.

A pipeline or a section thereof is considered restrained when it possesses substantial axial restraint (due to anchors or axial friction), so that axial elongation or contraction is zero or minimal.

When a pipeline or section thereof does not possess sufficient axial restraint, so that it will experience appreciable movement (elongation or contraction) it is considered unrestrained. One of the main differences is, that a restrained line is usually subject to a very large axial compressive force at elevated temperature and an unrestrained line to a large axial tensile stress due to internal pressure, plus bending stresses.

Fig 7.1 illustrates the conditions for a fully unrestrained pipeline

Fig 7.1.1 Fully unrestrained pipeline

For a fully unrestrained line subject to an internal pressure, pi , and a positive temperature differential of ΔΤ the following can be calculated

Hoop stress Hσ = t2

)tD(p si − (tension) (7.1.1)

Longitudinal stress Lσ = ( )( )

( )H

si

s

2si 5.0

t4t2Dp

tDt4t2Dp

σ≅−

≅−

−⋅ (tension) (7.1.2)

Axial movement ΔL = E

L50.0E

LTL HH ⋅σ

+⋅νσ

−Δα (7.1.3)


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= )20.0TE(EL

Hσ+Δα (7.1.4)

Fig 7.2 illustrates the conditions for a restrained pipeline. The situation is derived from Fig 7.1 by adding the anchor force FA which magnitude is determined so the axial movement is zero

Fig 7.1.2 Restrained pipeline

For fully restrained lines, subject to an internal pressure, pi , and a positive temperature differential Δt

Hoop stress σH = ( )t2

tDp si − (tension) (7.1.5)

Longitudinal stress Lσ = -(ΕαΔΤ + 0.20σH) + 0.50 σH (7.1.6)

= -ΕαΔΤ+0.30 σH (7.1.7)

Axial force LF = As·σL = As(-ΕαΔT + 0.30 σH) (steel pipe) (7.1.8)

Anchor force FA = )20.0TE(A Hs σ+Δα (effective force) (7.1.9)

Axial movement ΔL = 0

α = temperature expansion coefficient of pipe material ( for steel α=12 10-6 °C-1 )

ν = Poisson’s ratio

Normally, pipes are not completely restrained or totally unrestrained. However, the exact conditions of a pipeline cannot be predicted except close to expansion loops where pipeline expansion can be monitored. The pipeline should therefore in the general case be considered either fully unrestrained or restrained which ever conditions yields the worst stress.


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7.2 Expansion Calculation

At pipeline ends (platform approach) the internal pressure and possible elevated temperature will result in pipeline expansion, which often is relieved through an expansion. Calculation of the pipeline expansion is important for the proper design of expansion loop and similar structures.

Fig 7.2.1 Build-up of friction at pipe end. P is the effective axial force at the point where

the pipeline expansion is calculated

At L the pipe has built up so much friction that the total friction force equals the required anchor force for fully restrained lines:

rfL = (FA-P)

= )20.0TE(A Hs σ+Δα -P (7.2.1)

L = (As/rf) fH r/P)20.0TE( −σ+Δα

Expansion at pipe end

ΔL = 2

A

A

fs

2A

fs

2A

FPF

rEA2F

rEA2)PF(

⎟⎟⎠

⎞⎜⎜⎝

⎛ −⋅=

− (7.2.2)


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For P = 0, is ΔL = s

2f

fs

2A

EA2Lr

rEA2F

= (7.2.3)

P = effective axial force at the point where the pipeline expansion is calculated

FA = axial force in fully restrained pipeline

μa = axial friction coefficient. If no other information is available, μa = tan ϕs in sand

rf = axial friction force per unit length of pipeline

The axial friction coefficient depends on the soil conditions and the pipeline surface. Typical values are in the range 0.3< μa<0.7 for sandy soils. The unit friction force rf can be found multiplying the submerged pipe weight including content with the friction coefficient.

In case of buried or part buried pipe the axial friction force is increased. An approximate expression for the axial friction force is in this case

rf = πDγs ⋅ (H+D/2) tanϕs + Ws tanϕs (7.2.4) H = height of soil cover γs = submerged soil density ϕs = friction angle of soil Ws = submerged weight including content

It is important to select the axial friction coefficient with care and due consideration to the problem. A too high friction coefficient will result in expansion lengths, which are too small. This may result in inadequate design of expansion loops. On the other hand too low friction coefficients may result in a underestimation of the axial compression force and pipeline buckling may occur.

7.3 Pressure and Temperature Cycles

When the line is depressurized the pipe will contract again and try to regain its original position. Due to the movement back the friction forces act now in the opposite direction thus reducing the pipes contracting capability.

The pipe will move back till the friction forces along the pipe is in balance. The remaining elongation (for P = 0) is

s

2f

L½

0s

2fL½

0s

f

EA4Lr

EAxr

EAxdxr

2L =⎥⎦

⎤⎢⎣

⎡==Δ ∫ (7.3.1)


Page 55 of 63

The pipe contracts over 50 per cent of its initial elongation. The remaining elongation after a temperature cycle is therefore 50% of its initial value.

It is clear that large portions of submarine pipelines are normally restrained. Only the end sections over a certain length can be considered unrestrained or partially restrained. The previous pages gave the method to determine the location where pipelines can be considered restrained.

Except for local effects such as cross-overs, there are few other conditions that could change a restrained line into an unrestrained one e.g. if a pipe is laid in a horizontal curve and the radius of curvature is small, so that the lateral friction forces are not capable of holding the pipe in place.


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8 RISER AND RISER CONNECTIONS

Flexibility of Unrestrained Lines

The flexibility of unrestrained submarine pipelines on seabed is complicated due to the nature of the friction forces that resists the movement of the pipe. The friction force acts against movements but the magnitude depends on the instantaneous reaction force.

A number of commercially available computer programs includes fairly accurate description of friction forces and may be applied to cases where the friction force has importance. It should, however, be noted that the actual conditions of the pipeline on the seabed to great extend are unknown and may vary significantly in time. This will add to the uncertainty of the description of friction forces.

Risers

The riser is a prefabricated assembly with a flange at the top connecting to the platform deck piping, with splash zone protection and ending in a swivel joint flange near seabed which will, through a special spool piece, be connected to the end of the submarine pipeline.

Normally the pipeline is laid with the lay barge at some distance of the platform. The lay barge moves out and a crane barge comes in and picks the pipeline end up and brings it in line with the riser. The distance between the pipeline end flange and the bottom flange of the riser is measured and a special spool piece is made and installed by divers.

This is only one typical installation method, but there are a number of alternatives.

Usually there is some space left between bottom of riser and seabed to account for the expansion of the riser during operation. The riser is normally fixed at deck level by means of a heavy clamp. The other clamps from riser top to riser bend are not to resist weight, temperature or pressure movement, but only to resist wave and current forces.

The riser must be designed for dead weight, content weight, temperature differential, pressure differential and wave and current loads. For risers at well platforms the possibility of slugs must be investigated because they cause high impact forces in the elbows.

The wave and current loads are normally determined already by the platform designer because it causes additional loads on the platform through the clamps. The riser and the riser clamps have to be designed to resist the 100-year design wave and current.


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The Stokes fifth order wave theory should be used. The riser and clamp spacing should be designed with due consideration to vortex shedding and to the possibility of vibrations induced by vortex shedding.

The connecting part of the submarine pipeline that is supported by the soil can be analyzed as an elastic supported beam.

For offshore risers the design factor, F, for hoop stress shall not exceed F = 0.5 per SAES-L-003.


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9 INSTALLATION STRESS ANALYSIS

Pipeline installation is normally performed using dedicated laybarges.

The laybarge requirements to install a particular pipeline installation depends on various factors, the most important being:

- Pipe size and weight - Length of pipeline - Maximum water depth - Environmental conditions such as waves and currents - Construction period - Available space for construction in platform areas - Availability of laybarges

Tensioning equipment on lay barges in the Arabian Gulf has normally a capacity of approximately 400-500 kN (90-100 kips). The stinger can be either straight, articulated or curved. Typical lengths are 60-250 m (200-400 ft). The stinger hinges around a support at the stern of the lay barge and its angle with the horizon can be controlled by means of emptying or flooding buoyancy tanks in the stinger. Typical ramp angle is from 4 to 12 degrees.

Pipe stress analysis during laying is relatively complicated and is normally done by means of dedicated computer programs.

These computer programs are usually very sophisticated and account for barge movements, wave and current influences, elastic properties of seabed, slope of seabed, position of rollers, moment-curvature relation for pipe, etc. Computer programs are based on the finite element method (FEM) combining the elastic characteristics of catenaries with beam columns. Catenaries are particularly important for deeper waters. For the shallow Arabian Gulf a beam-column analysis only can be considered satisfactory.

In preliminary design stage (feasibility study, project proposal, etc.) the analysis can be simplified assuming no barge movement and no wave or current action.

For the consolidated soils in the Arabian Gulf (except parts of Safaniya and Berri) it can be assumed that the seabed is horizontal and incompressible. If the point of counter-flexure is assumed at the end of the stinger (conservative assumption).

The sagbend moment and the required tension can be estimated using theory based on a tensioned beam. Figure 9.1 defines the system and the required parameters. The formulas are presented in Roark and Young (1985), Table 11.


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Fig 9.1 Definition sketch

θ = 3

31

uutanhu

EI8LW −

⋅ (9.1)

Mmax = ( )ucoshu1ucosh2

8LW

2

21 − (max. sagbend moment) (9.2)

Zmax = ucoshu

ucosh2ucoshu2EI

LW321

4

241 −+ (deflection of sagbend) (9.3)

u2 = EI4

TL2

(9.4)

W1 = θcosWs (9.5)

θ1 = 22 θ−θ (9.6)

Ws = submerged weight

W1 = projection of submerged weight

h = θ+θ sinLsinL 11 (9.7)

h = water depth


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L1 = stinger length

θ2 = built-in offset angle of the pipeline at stinger tip

EI = bending stiffness

As = cross sectional steel area

L = length of the sagbend

The calculations are performed the following way

Step 1 The sagbend length L is estimated together with a reasonable tension

Step 2 θ, Mmax, Zmax are calculated

Step 3 θ1 and h are calculated and h is compared to the real water depth (Eqs. 9.6 and 9.7)

Step 4 Tension or sagbend length are adjusted and step 1, 2 and 3 repeated until the right water depth is calculated

The maximum stress is calculated by:

ZM

AT max

smax +=σ (9.8)

This maximum stress should be limited to 80% of the SMYS.

The stress can be optimized by changing either the initial stinger angle, the tension, the stinger length or the stinger curvature. The above analysis assumes that the seabed at the pipe landing point is very stiff and can resist the reaction without appreciable deformation. This is more or less true for compacted sands and stiff clays. For softer soils the pipe will penetrate into the seabed under the influence of the reactive force.

In preliminary design stage, it is normally sufficient to increase the water depth with 0.3 m-0.6 m (1-2 ft) to account for the influence of a soft seabed.


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10 PIPELINE REPAIR

Pipelines can be damaged by anchors, trawl boards, dropped debris or due to abrasion caused by pipes moving over hard spots, when the on-bottom stability is not adequate enough. A repair can be carried out either underwater using a hyperbaric chamber or above water, when the damaged pipe ends are lifted above water.

10.1 Hyperbaric Chamber

The state of the art in hyperbaric welding has made significant progress in recent years and Saudi Aramco has made use of this technique on several occasions for submarine pipeline repair.

Typically, a damaged section of the line is removed and replaced by a spool piece.

Whereas the connection between the spool piece and the line pipe may be made mechanically, a welded connection offers a more permanent solution. (Note that mechanical devices have been used for many years and have built a good track record). The welded connection can be made by using weld balls when misalignment is expected to be significant or by butt weld (full penetration).

Before the habitat is lowered over the pipe, a pit has to be dug underneath it, or the line has to be raised, to give divers access. Once in place and sealed, the habitat is made free of water by means of air. Sealing is checked and when found acceptable; the air is replaced with an inert gas.

Possible water in the line is prevented from getting to the weld area by means of inflatable seals placed in the open ends of the line.

The welding technique employed is either Gas Tungsten Arch Welding (GTAW) or Gas Metal Arch Welding (GMAW) or a combination of both. The wire feed to the weld nozzle is automatic and regulated from deck similar to the gas feed to the torch.

10.2 Pipeline Lifting

When a pipeline repair is carried out above water, the damaged pipe ends are lifted above water. Normally a barge (like the ARB-1) would move in and be positioned close to and along the line. The damaged pipe would be cut under water and one end would be lifted above water. The pipe end would be repaired, beveled and a flange would be welded to it. Then the pipe end would be


Page 62 of 63

lowered onto the seabed again. The same procedure would be carried out for the other pipe end. When both pipe ends are back on seabed, very accurate measurements are taken and a snug fitting spool piece prepared. The spool piece would be lowered in place and divers would tighten the bolts on the flanges. This would complete the repair procedure.

Stress analysis of Pipelines during lifting can be done by treating the pipeline as a beam of length Lo cantilevering from the landing point (where M = 0, Rotation = 0). However, Lo varies with the applied forces (either barge lift forces or buoyancy tank forces). Lo can be determined as follows:

s

N

1

N

1 iiN

1 s2

iio W

)LP(W2)P(PL

∑ ∑∑ ⋅−+=

(10.2.1)

Where

N = number of applied forces.

Pi = magnitude of force i.

Li = distance of force i to pipe end

Ws = submerged pipe, unit weight

The formula applies to vertical forces and when the pipe is completely submerged.

However, it can be used if part of the pipe is above water.

For one force at the end, we get

oL = 4

sWEIh24

(10.2.2)

P = 2LW os ⋅

(10.2.3)

h = pipe end height above seabed


Page 63 of 63

Fig 10.2.1 Pipeline lifting

Page 1 of 36

Engineering Report

Appendix 2 - Submarine Pipeline Protection and Stabilization Guideline SAER-5711 July 2000


1 INTRODUCTION 2 2 DEFINITIONS AND NOMENCLATURE 3 3 PIPELINE PROTECTION AND

STABILIZATION METHODS 7 4 SELECTION OF PROTECTION AND

STABILIZATION METHOD 10 5 PROTECTIVE MATTRESSES 15 6 RIVER WEIGHTS 23 7 ROCK DUMPING 28

Issue Date: July 2000 Submarine Pipeline Protection and Stabilization Guideline Appendix No 2 to SAER-5711

Page 2 of 36

1 INTRODUCTION

The Submarine Pipeline Protection and Stabilization Guideline has been developed to supplement the “Submarine Pipeline Engineering Guidelines” with methods for stabilization and protection of pipelines. The Guidelines pertain to all pipeline used for transportation of fluids and/or gases and installed on or below the seabed.






The focus of the Protection and Stabilization Guideline is put on situations where the need arises for assessing and planning of rectification work for stabilization and protection of an already installed submarine pipeline.

Submarine pipelines are normally designed to remain stable in their permanent condition on the seabed. They may be buried, left in an open trench or remain exposed on the seabed. Over time the pipeline may become unstable due to a number of reasons. Sediment movements on the seabed may increase pipeline exposure, concrete coating may be damaged and lost on sections, the product in the pipeline may change density, wave and current conditions may be more severe than anticipated at the design stage or a combination of the above factors may be present.

In these cases remedial work is required to establish adequate pipeline stability. The Protection and Stabilization Guideline presents the conclusions of a study for finding the optimal solution for post-stabilization of submarine pipelines.

The conclusions presented in the Guideline provide guidance for selection of the most appropriate concept for stabilization and protection of a pipeline. Further, the Guideline includes detailed calculation procedures for three specific methods well suited for Saudi Aramco operational areas. The three methods considered are stabilization by

a. Flexible mattresses


Page 3 of 36

b. River weights

c. Rock dumping

These methods together are applicable for the most common cases of pipeline instability, and a technical optimal solution can be found among these three methods. However, it cannot be excluded that economical, safety or operational considerations dictate a different solution to a specific problem.

The calculation of current and wave induced water particle kinematics is based on flow conditions which are valid outside the surf zone. In the surf zone wave breaking and varying seabed contours makes it impossible to use simple expressions for calculation of flow velocity and acceleration. Calculation of hydrodynamic forces is in general based on Morison’s Equation and this is not valid for structures placed in the surf zone or at very shallow areas. In these cases model tests should be applied to determine the force on structures.

The detailed calculation procedures include guidance on selecting appropriate hydrodynamic coefficients for the different concepts. However, these coefficients are associated with uncertainty as only sparse literature is available on the subject. It is therefore recommended that model tests be carried out to provide a safe, cost-efficient design.

2 DEFINITIONS AND NOMENCLATURE

Submarine Pipelines: All lines used for the transportation of fluids and/or gases, installed on or below the seabed between an offshore facility and the demarcation point onshore or another facility.

Demarcation Point: A point along the onshore portion of the line, established in the Project Proposal, to mark the location at which the submarine ends as referenced in the installation contract.

a acceleration, half of rock berm width Am characteristic area ARW area of river weight b rock berm height Ca added mass coefficient CD drag coefficient CL lift coefficient CLE lift coefficient on edge of mattress CM inertia coefficient

RWMC inertia coefficient for river weight RWLC lift coefficient on river weight RWDC drag coefficient on river weight


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Cu undrained shear strength for soil d burial depth, rock berm height D pipeline outer diameter Ds pipe diameter (steel), stone size ea active soil pressure ep passive soil pressure f friction coefficient for the pure steady current case fϕ skin friction factor for sand (wall factor) fb reduction factor fc skin friction factor for clay fcw friction coefficient for the combined flow condition fs safety factor Fexcess hydrodynamic force on exposed pipeline FH in-line force FH,tot total in-line force on mattress FL lift force FL,tot total lift force on mattress FLE lift force on edge of mattress FM inertia force

RWHF horizontal (in-line) force on river weight RWLF lift force of river weight

g acceleration of gravity h water depth h1 height of pipeline and mattress above undisturbed seabed h2 thickness of mattress href reference height, href = 0.5 ⋅ h1 hRW height of river weight k pipe roughness including marine growth Ka active soil pressure coefficient kb seabed roughness (kb = 2.5 Ds), Nikuradse equivalent sand roughness

(ks=2.5Ds) KC Keulegan Carpenter number

KCm Keulegan Carpenter number for mattress system, KCm = 1

max,w

wTU

Ko pressure coefficient for soil at rest Kp passive soil pressure coefficient Lb length of rock berm ℓ distance from the leading edge of the berm to the center of the berm Lm length of mattress along pipeline lRW length of river weight Rb horizontal reaction from rock berm per unit length Re Reynolds number (=UD/ν) Rfriction friction force


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RH horizontal reaction force Rm reaction force from mattress Rmax maximum stabilization force from river weight Rpassive passive soil pressure Rpipe soil reaction RV vertical reaction force s specific gravity of the stone S distance between mattresses Sb free distances between rock berms T wave period U total velocity, U = Uw + Uc U(z) flow velocity in height z Uf friction velocity in steady current Ufcw friction velocity in the combined flow Umax maximum flow velocity (steady current) Umo significant velocity at the pipe level Un flow velocity normal to pipe Uw wave velocity amplitude at seabed or in reference height Uc steady current velocity Uw,max wave velocity amplitude U (b) mean flow velocity over height b Vol characteristic volume Volm characteristic volume w1 horizontal distance between touch-down points at seabed perpendicular to

pipeline axis w2 length of upstream or downstream section of mattress in contact with seabed

(perpendicular to pipeline) wb half width of rock berm wm total width mattress wRW width of river weight Ws submerged weight of pipeline WSE submerged weight of edge block of mattress Wsm submerged weight of mattress Wsm,eff effective weight of mattress z distance from seabed zo distance from seabed α current ratio, flow amplification β seabed slope in degrees κ von Karmans constant (=0.4) ρ sea water density θ Shields parameter ν viscosity μ friction coefficient μ1 friction coefficient


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μm mattress to soil friction coefficient μRW river weight to soil friction coefficient ϕs angle of friction for soil or stone material γs submerged unit weight of soil θcr critical Shields parameter for movement of stones θcro critical Shields parameters for movement of stones on horizontal bed


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3 PIPELINE PROTECTION AND STABILIZATION METHODS

3.1 General

Three main methods applicable for protection and stabilization of an already installed marine pipeline are dealt with in this guideline, namely:

• Protective mattresses

• River weights

• Rock dumping

In the following a general outline of the characteristics for each of the protection and stabilization systems is given.

3.2 Protective Mattresses

Various types of mattresses exist, including mattresses consisting of “tapered or rectangular cubes” filled with concrete and interconnected by woven fabric or fiber ropes, to obtain flexibility as well as coherence and continuity. Examples of brand names are “LINKLOK”, “FLEXMAT”, “SUBMAR”, and “C-SAC/Sea-Struct”. Certain types of mattresses, eg LINKLOK, can be filled with concrete after subsea installation (which subsequently hardens), thus limiting the requirement to crane lift capacity. As a special application “FLEXMAT” also manufactures the “concrete block mat”-system, consisting of a single row of concrete block sleepers at each side of the pipeline, providing ballast weight to the pipeline by means of woven polypropylene loop-matting. The loop matting is extended over the top of the pipeline, and fastened below the concrete ballast blocks.

“SARMAC” mattresses consist of a composite built-up type flexible mattress, where the main constituent is sand asphalt mastic, which is contained within various layers of wire mesh reinforcement and geotextile lining and covering.

The flexible mattress method has the advantage that it is possible to re-cover the mattresses at a later stage for re-use. Similarly the mattresses can be used for temporary conditions, e.g. for protection at a pipeline free end later to be tied in to a riser or a pipeline spool piece.

The placing of protective mattresses at the pipeline basically involves the use of a dedicated installation frame of a vessel with a suitable crane capacity, and it should also be capable of providing diving support to the extent required. The protective mattresses are typically installed over the pipeline to provide ballast to stabilize the pipeline, and in addition to provide protection against external


Page 8 of 36

impact to the pipeline.

The use of mattresses in relation to free spans is less obvious. The mattress placed across the pipeline adds weight to the free span and may result in overstressing. However, free span supports may be constructed using Dura bags or similar and mattresses may subsequently be placed across the overall structure for protection.

Fig 3.2.1 Concrete mattress on a pipeline

3.3 River Weights

River weights are U-shaped concrete blocks which are dimensioned to fit across a pipeline. The inner diameter of the river weight is larger than the pipeline outer diameter, leaving room for placing grout bags between the pipeline and the river weight. The function of the grout bags is to protect the pipeline coating and to lock the river weight relative to the pipeline. Fig 3.3.1 illustrates a river weight adapted for use on a 1.20 m (48") pipeline.

Fig 3.3.1 River weight on 1.20 m (48") pipeline

Stabilization of a submarine pipeline by river weights involves the placing of these across the pipeline at suitable intervals. The river weights normally rest


Page 9 of 36

directly on the seabed increasing the lateral resistance against pipe movement. The river weight may also be designed to be supported by the pipeline. In this case the pipeline wall and concrete coating should have sufficient strength to carry this additional weight.

One advantage of this method is that there are relatively limited requirements to the size of crane- and support vessels, and other applicable installation equipment. In some cases this will imply a potential for savings compared to other more equipment intensive types of rectification methodology.

Thus, if a diving support vessel fitted with crane capacity suitable for lifting single river weights is applied, then this vessel alone can basically do the rectification work, and a separate crane vessel would not be needed.

The feasibility of the application of U-type river weights depends amongst other on the problem type to be rectified. The method may be advantageous at shallow water areas where heavy vessels (e.g. for rock dumping or lifting heavy mattresses) would have difficulties to access. The pipeline would still be possible to inspect, except where covered by individual river weights.

It should be noted that soft and loose seabed materials could pose problems, due to low bearing capacity and relatively high scour potential. For instance, scouring at a pipeline stabilized with river weights could cause destabilization and cause the weights to come off (fully or partially), or to ”hang” on the pipeline in case of a pipeline free span.

Ballasting the pipeline with river weights will typically be relevant if the pipeline stabilization is to be carried out over a certain limited length and for large diameter pipelines. If longer sections of the pipelines are to be stabilized it may be advantageous to use methods, which are less sensitive to variations along the pipeline. The application of river weights to stabilize a pipeline has a fairly substantial application record in areas of relatively stable seabed (low potential for scour and free span development).

3.4 Rock Dumping

Two main types of rock dump layout are used to stabilize pipelines. The rock berm may be continuous along the pipeline or it may be composed of isolated rock fill berms, positioned at certain distances along the pipeline. Such “Spot rock dumping” may also be applied to reduce pipeline free spans to keep these within allowable lengths.


Page 10 of 36

Fig 3.4.1 Rock dumping for pipeline stabilization

Dependent on factors such as water depth, required accuracy, and available equipment and economy, various rock dumping installation methods are relevant, such as fall pipe vessel, side dump vessel or split barge, or placing with grab, clamshell bucket, or dumping hopper.

A worldwide extensive experience record exists for pipeline stabilization and protection by means of rock dumping, whereby the pipeline is fully or partially buried by means of rock dumping. The general advantages of this method are mainly associated with the flexibility in terms of adaptability to given pipeline and seabed configuration, including pipeline free span rectification, soil conditions, and a fairly high possibility of local provision of rock dump material. Also, repair and maintenance of a rock berm can typically be done by performing additional rock dumping.

4 SELECTION OF PROTECTION AND STABILIZATION METHOD

4.1 Optimization Method

The general principles for the selection and optimization of pipeline stabilization method are illustrated in the flow chart in Fig 4.1. The flow chart relates to the three methods suited for Saudi Aramco operational areas:

• Protective mattresses • River weights • Rock dumping


Page 11 of 36

In order to proceed with pipeline stabilization it is required to perform an identification of the problem and a full analysis of the situation. Pipeline free spans may develop on an erodible seabed and increase in length over time, or loss of stability may occur due to deterioration and loss of concrete coating, due to change in density of the transported product, or because of unexpected severe environmental loadings. The analysis of the situation shall describe how critical the situation is with regard to pipeline conditions, stress and deformation-wise as well as possible damages to coatings or denting of the pipe.

The conclusions of the examination will lead to the most feasible rectification method and give a measure of how urgently the intervention is required. The conclusions may imply that the pipeline should be operated at reduced flow or maybe shut down. In such situations other parameters than purely technical may dictate solutions not included in the Guideline.


Page 12 of 36

Fig 4.1.1 Selection of protection or stabilization method

The first step in selection of protection or stabilization method is identification and analysis of the pipeline problem. It is normally through inspection that pipeline instability is observed in the form of loss of concrete coating, laterally displaced pipeline, free spans etc.

In the further evaluations it is required to distinguish between instability problems and free spans, although free spans may be generated as the result of


Page 13 of 36

pipeline instability. The analysis of the problem and the rectification procedure is dependent on whether the pipeline is in contact with the seabed or not. Actions and stabilization measures can result in overstressing of a free span, whereas an on-bottom pipeline in most cases is a very robust structure.

4.2 Insufficient Pipeline Stability

In the case of pipeline instability, this may be either in the form of vertical instability or horizontal instability. Vertical instability is defined as cases where the pipeline becomes buoyant and lifts from the seabed. Vertical instability occurs due to loss of weight coating or in cases where the density of the product is becoming lighter.

In the case of vertical instability, rock dumping is excluded due to the relatively poor ability of a rock berm to keep the pipeline from floating, compared to the two other methods.

Horizontal instability may also be caused by loss of concrete which reduces the submerged weight to a level where lateral movements may occur caused by external or functional loads.

In the case of horizontal instability associated with functional loads, river weights are not recommended. This is mainly due to the fact that functional loads such as temperature and pressure give rise to axial compressive forces which can be released in a buckling mode. The point anchoring provided by river weights may be less optimal to prevent lateral buckling unless spaced very tight. Furthermore, sudden movement would imply a risk of capsizing the river weights, thereby losing their stabilizing function. Opposite to this, a rock berm or mattresses being properly designed can allow for some (limited) movement within the berm or under the mattress, without losing their stabilizing effect. The longitudinal section of the pipeline being covered by rocks or mattresses is normally substantially longer than the river weight length.

For horizontal stability problems caused by hydrodynamic loads, all three methods can be relevant without any of the methods being excluded beforehand.

River weights, and to some degree also mattresses, are sensitive to nearby scour development, which may destabilize the river weight base and cause rotation and loss of stabilizing effect on the pipeline. Furthermore, an erodible seabed with an inherent scour potential implies a risk of free span development and associated risk that the river weights (alternatively the mattresses) may hang onto a pipeline free span. The situation can cause an unacceptable loading, or the river weights may simply rotate and come off the pipeline.

The seabed scour potential depends on the seabed soil properties and the wave and current climate at the site. Also, the dimensions and shape of the pipeline


Page 14 of 36

with river weights or the mattress configuration will influence a scour development.

Obviously, for hard seabed such as coral reef, scour development is not an issue, and similarly, areas of hard clay will often have an erosion rate that is negligible in this context.

4.3 Free Spans

In the case of free spanning, mattresses and river weights can be excluded, as placing either of these devices on top of a pipeline free span would mean additional loading to the pipeline and associated increased pipe wall stresses.

The additional weight problem can be eliminated by placing intermediate supports in the form of grout bags (Dura bags) or other. Grout bags alone may be applied in free span rectification but the solution is sensitive to wave and current actions and seabed scour may undermine the grout bags. Free span correction using grout bags is therefore used in combination with other protection systems and the grout bags alone are not analyzed further within this Guideline.

That leaves rock dumping as the optional free span rectification method. The rock dumping has of course to be performed so that sufficient material is placed below the span to generate support and preventing additional loads from rock on top of the pipeline. Rock dumping may be performed only in the form of local supports or the overall span may be covered.

Free span correction using river weights or mattresses is seldom the optimal method because intermediate supports should be constructed and this complicates the solution.

4.4 Design of Stabilization Method

Having completed the activities outlined above, the final step is then to move on to the design assessment for the candidate method(s). Calculation procedures for the three methods are described in the following sections.

A preliminary design may be carried out of the relevant options in order to compare the methods using the most recent cost and equipment data.


Page 15 of 36

5 PROTECTIVE MATTRESSES

The analysis of mattresses in the following sections apply primarily to blankets composed of individual concrete blocks linked through wires or rope. Mattress composed of asphalt mastic or similar can be analyzed according to the principles outlined. However, the manufacturer should specify that the strength and homogeneity of the mattress are at least equivalent to that of concrete block mattresses.

Applying protective mattresses for pipeline stabilization or protection can be made in a continuous manner, or as isolated individual mattresses placed at certain spacing along the pipeline.

In general terms, continuous coverage of the pipeline is relevant if the key issue is protection of the pipeline against external impact or other interference with third party activities, whereas stabilization of the pipeline to resist hydrodynamic action in many cases can be accomplished by the isolated mattress method.

There are in principle three failure scenarios, which the mattresses should be designed to resist:

a) Mattress dislodging: the mattress should be designed to resist hydrodynamic lift and drag forces trying to dislodge the mattress from the pipeline

b) Pipeline pull-out resistance: the mattress should be designed to prevent pipeline pullout beneath the mattress, in case of lateral pipeline forcing relative to the mattress

c) Total stability: the mattress should be designed to prevent lateral movement of the combined mattress-pipeline system

Pipeline stabilization with the isolated method involves mattresses placed at certain spacing along the pipeline, thus leaving the pipeline exposed in between.

The structural bearing principle is that the excess hydrodynamic forcing on the exposed pipeline sections is transferred to the pipeline sections stabilized with mattresses (basically by the pipeline acting as a laterally loaded beam), and that the mattresses are designed to accommodate this excess lateral force. The excess lateral force to be accommodated at the mattress-covered section is equal to the maximum lateral hydrodynamic force in the design situation, reduced by the available lateral soil friction force in this situation. In case of continuous application of mattresses pipeline pullout is not feasible and it is only required to check mattress dislodging and total stability.

The specific failure modes to be considered for each of the application cases, isolated versus continuous application, are highlighted in Table 5.1.1 below.

It is noted that at certain pipeline sections, such as at expansion offsets, it may be a requirement that the pipeline is not fully restrained against lateral movement beneath


Page 16 of 36

the mattress, however, such special cases must be considered under special investigations, which are not covered herein.

Table 5.1.1 Mattress failure modes and analysis

Failure Mode

Mattress Application Mode

Mattress Dislodging

Pipeline Pull-out

Total Stability

Isolated Mattresses

X X X

Continuous Coverage

X X

The mattress-covered pipeline represents a relatively complex fluid-structure interaction system and the hydrodynamic forces acting on the system cannot be predicted accurately using analytical methods only. Physical model tests are a safe and reliable design avenue, but simplified and conservative calculation methods may be applied as presented below.

5.1 Mattress Dislodging from Pipeline

The hydrodynamic forces acting on the mattress are illustrated on Fig 5.1.1. The mattress is exposed to a horizontal force composed of a drag and inertia term and a vertical lift force. The lift force is distributed over the mattress but it will have maximum intensity over the pipeline and at the mattress edge. The mattress may be dislodged from the pipeline in two ways:

a1) The mattress is washed sideways off the pipeline under the combined drag and lift force

a2) The mattress is lifted at the edge and rolled off the pipeline

Fig 5.1.1 Mattress on the pipeline. Definition of parameters


Page 17 of 36

The following parameters are defined based on Fig 5.1.1 and Fig 5.2.4:

a = flow acceleration in reference level

Am = typical area, Am = h1 ⋅ lm

CD = drag coefficient

CL = lift coefficient

CLE = lift coefficient for edge of mattress


fexcess = horizontal hydrodynamic force exceeding the friction force per unit length of pipeline

fs = safety factor (typical value, fs=1.1)

h1 = height of pipeline and mattress above undisturbed seabed

h2 = height of mattress (height of concrete blocks)

href = reference height, href = 0.5 ⋅ h1

KC = Keulegan Carpenter number for pipeline

KCm = Keulegan Carpenter number for mattress system, KCm = 1

max,w

wTU ⋅

lm = length of mattress along pipeline

U = total velocity, U = Uw + Uc

Uc = steady current velocity in reference height

Uw = wave induced flow velocity in reference height

Uw,max = wave induced velocity amplitude in reference height

Volm = typical volume, Volm = h1 ⋅ w1 ⋅ lm

w1 = horizontal distance between touch-down points at seabed perpendicular to pipeline axis

w2 = length of upstream or downstream section of mattress in contact with seabed (perpendicular to pipeline)


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wm = width of mattress

Ws = submerged weight of pipeline per unit length

Wsm = submerged weight of mattress per unit length

μ = pipeline to soil friction coefficient

μ1 = mattress to pipeline friction coefficient

μm = mattress to soil friction coefficient, also refer to Table 5.3.1

The forces on the total mattress are described by a horizontal force in the direction of the flow and a vertical lift force:

Horizontal force:

aCVolUUAC½F MmmDtot,H ρ+ρ= (5.1.1)

Lift force:

FL,tot = ½ ρ CL Am U2 (5.1.2)

A two-dimensional approach is feasible if the pipeline is covered over a length comparable to the total width of the mattress. The hydrodynamic forces can then be expressed per unit length of mattress:

aChwUUhC½F M111DH ρ+ρ= (5.1.3)

21LL UhC½F ρ= (5.1.4)

The forces on the edge of the mattress are described by a lift force and a drag force. Only the lift force is of interest. If the lift force exceeds the submerged weight of the outer blocks there is a risk of the mattress being lifted and rolled or folded on to the mattress itself.

FLE = ½ ρ CLE h2 U2 (5.1.5)

The requirement to the overall mattress stability is expressed by:

( )Lsms

mH FW

fF −

μ≤ (5.1.6)

This should be valid for the worst combination of FH and FL.

The requirement to the stability of the mattress edge is expressed by:


Page 19 of 36

SEs

LE Wf1F ≤ (5.1.7)

WSE is the submerged weight of the first set of blocks along the mattress edge.

In case of a continuous mattress, the risk of lifting the edge is smaller. However, the stability should be checked assuming the presence of edge blocks having a width equal to 3 times the mattress height.

The force coefficients to be used in the mattress stability evaluation are presented below.

0

0.5

1

1.5

2

0 10 20 30KC-Number

Dra

g C

oeffi

cien

t, C

D

0

0.2

0.4

0.6

0.8

1

1.2

0 0.5 1Current Ratio Uc/Uw

Red

uctio

n Fa

ctor

on

Dra

g C

oeffi

cien

t

Fig 5.1.2 Drag coefficient for mattress, CD, presented against KC number for mattress system and current ratio

0

0.5

1

1.5

2

2.5

3

0 10 20 30

KC-Number

Lift

Coe

ffici

ent,

CL

0

0.2

0.4

0.6

0.8

1

1.2

0 0.5 1Current Ratio Uc/Uw

Red

uctio

n Fa

ctor

on

Lift

Coe

ffici

ent

Fig 5.1.3 Lift coefficient for mattress, CL, presented against KC number for mattress system and current ratio


Page 20 of 36

Lift coefficient for edge of mattress

0

0.5

1

1.5

0 1 2 3 4 5

Block length-height ratio

Lift

coef

ficie

nt C

LE

Fig 5.1.4 Lift coefficient for edge of mattress (CLE).

5.2 Pipeline Pullout Resistance

The nomenclature and parameters used in this section are given in Section 5.1.

The mattresses should prevent the pipeline from being pulled out from below. This is theoretically possible when the mattresses are placed in an isolated formation and the excess loads on the free sections of the pipelines exceed the possible reaction force exerted by the mattresses. Figs 5.2.4 and 5.2.5 illustrate the situation. In this situation the excess forces on the free pipeline is transferred to the pipeline section covered by the mattress. The excess force is equal to the maximum lateral hydrodynamic and functional force in the design situation, reduced by the available lateral soil friction force in this situation.

Fig 5.2.4 Top view of pipeline stabilized with isolated mattresses


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Fig 5.2.5 Force equilibrium preventing the pipe from being pulled out

Fig 5.2.5 illustrates the force equilibrium for pullout check. Hydrodynamic forces on the mattress itself are neglected in this situation because it is implicitly assumed that the mattress remains in place and only the pipeline is pulled. The active force is Fexcess = S/Lm ⋅ fexcess per unit length of mattress covered pipeline and the stabilizing forces are friction between the mattress and the pipe and between the pipe and the seabed.

The excess force on the exposed part of the pipeline, fexcess, can be calculated using the approach given in Appendix 1, Equations 5.3.1 and 5.3.2:

( )pipeLs

pipeHexcess FWFf −μ−=

=pipeHF horizontal hydrodynamic force, Appendix 1, Equation 5.3.1

=pipeLF lift force, Appendix 1, Equation 5.3.2

The stabilizing forces depend on the weight of mattress resting on the pipeline. The length of the mattress, (wm – 2 w2) actually resting on an on-bottom pipeline varies dependent on block design. A typical value is in the range of 2D to 4D. A reasonable value to use in design when no specific information on the mattress construction exists is 2.5 D.

Rpipe = (Ws + Wsm,eff) μ (5.2.1)

Rm = Wsm,eff ⋅ μ1 (5.2.2)

Wsm,eff = Wsm mwD5.2 (5.2.3)

Fexcess ≤ sf

1 (Rpipe + Rm) (5.2.4)


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The stabilizing force, Rm, is a friction force between the mattress and the pipeline. To be efficient, it is a requirement that part of the mattress rests on the seabed so that the force can be transferred through the mattress to the seabed. It is assumed that the force to be transformed through one side of mattress. A requirement is:

mm

sm2m w

WwR μ≤ (5.2.5)

This requirement can be transformed into:

D5.2wm

12 μ

μ≥ (5.2.6)

5.3 Total Stability of Pipeline-Mattress System

The nomenclature and parameters used in this section are defined in Section 5.1.

The objective of placing mattresses is that the total system composed of free pipeline sections, pipeline sections covered by mattresses, and the mattresses are stable.

The total stability check of the pipeline-mattress system is performed to ensure that this system does not laterally slide across the seabed in a failure mode where the pipeline and the mattress move more or less jointly together. Pipelines placed in curved sections where temperature and pressure induced axial forces may give rise to large lateral forces are not covered by the present methodology.

The global stability check is in principle performed for both continuous and isolated application of mattresses.

In case of continuous covered pipeline, the total stability is adequate when the stability of the mattress is satisfactory according to Section 5.1.

In case of isolated application of mattresses, the total stability check can be performed by combining the mattress stability check and the load on the free pipeline sections between mattresses. Using the nomenclature from Sections 5.1 and 5.2 the total stability check is expressed:

( )[ ]sLsmms

Hexcess WFWf1FF μ+−μ≤+ (5.3.1)


Page 23 of 36

Friction Coefficients

The following friction coefficients may be applied for the mattress design investigations:

Table 5.3.1 Friction coefficients between mattress and seabed and pipeline and seabed (μm and μ)

Friction Coefficient Sand Clay Graded Rock Bed(without Marine

Growth)

Ungraded Rock Bed (without Marine

Growth)

Friction between mattress and seabed (dependent on mattress type and branch, the manufacturer can normally supply detailed data), μm

1.0 0.4 0.6 1.0

Friction between pipe and seabed, steel pipe surface, μ

0.7 0.4 0.4 0.6

Friction between pipe and seabed, concrete coated pipe, μ

0.7 0.4 0.7 1.0

Table 5.3.2 Friction coefficients between mattress and pipeline, μ1

Friction Coefficient Concrete Coated Pipeline Anti-corrosion Coated Pipeline

Friction between mattress and pipeline, μ1

0.4 0.3

6 RIVER WEIGHTS

River weights are U-shaped concrete structures placed across a pipeline. The structure is to be designed with small tolerances giving a relatively tight fit to the pipeline. The structure shall not rest directly on the pipeline but stand on the seabed. The two “concrete legs” of the river weight resting on the seabed prevent lateral movements of the pipeline.

If the river weight looses contact with the seabed (e.g. because of local erosion) the river weight may tilt under wave and current action and loose its stabilizing effect.

The stabilizing effect of a river weight equals the lateral soil resistance required for moving the river weight sideways. This friction force shall of course be reduced for the direct wave and current forces on the river weight.

River weights may be designed to provide additional weight to the pipeline directly. In this situation the river weight rests on top of the pipeline and in principle has no direct


Page 24 of 36

contact with the seabed. This solution requires that the river weight is stable under loads from waves and current, and that the pipeline and weight coating can support the additional weight. The stabilizing effect equals the weight added to the pipeline, however reduced for the local increase in wave and current forces from the river weight it self.

6.1 River Weight Calculation

The river weight provides an additional horizontal stabilization force to the pipeline. The stabilization force is the difference between the available soil reaction and the hydrodynamic load on the river weight.

Definition of the most important parameters used in design of river weight is given in Fig 6.1.1.

Fig 6.1.1 Definition of river weight parameters and data

The lateral soil resistance acting on river weigh can be calculated using formulation from foundation engineering

RH = R friction+ Rpassive horizontal soil reaction

Rfriction = frictional resistance from sliding of the river weight footing

Rpassive = passive soil resistance from any part-burial of the river weight

Rfriction = μRW ⋅ RV

μRW = friction coefficient, μRW = tan (fϕ⋅ϕs) (on sand)

μRW = fc (on clay)

fc = wall friction factor on clay

RV = vertical reaction


Page 25 of 36

ϕs = internal soil friction angle

fϕ = wall friction factor for sand

Rpassive = ½ γs KP lRW d2 (6.1.1)

γs = submerged unit weight of soil

KP = passive soil pressure coefficient

lRW = length of the river weight

d = burial depth

Cu = undrained shear strength for soil


Page 26 of 36

Table 6.1.1 Recommended Values of Key Parameters and coefficients for typical offshore soils.

Submerged Weight γs

Cu ( )2kN/m USCS Symbol

Soil Description

(kN/m3) (lbf/ft3)

Angle of Frictionϕs (º)

(kN/m2) (lbf/in2)

Passive Soil Pressure

CoefficientKP

SW Well graded sands, little or no fines

8.5-11.5 54-73 34-41 3.5-4.8

SP Poorly graded sands little or no fines – very loose – medium dense – very dense

7.5-10.5

8.1 9.3

10.6

48-67

52 59 67

34-39

28 34 40

3.5-4.4

2.8 3.5 4.5

SM Silty sands, poorly graded – very loose – medium dense – very dense

8.0-11.5

8.9 10.1 11.4

51-73

57 64 73

31-37

27 32 38

3.1-4.0

2.7 3.2 4.1

SC Clayey sands, poorly graded

8.0-11.0 51-70 29-35 2.8-3.7

ML Silts and clayey silts 8.0-11.0 51-70 26-33 2.6-3.4

CL Clays of low to medium plasticity

8.0-11.0 51-70 - 1.0

CH Clays of high plasticity – very soft – medium stiff to stiff – stiff to very stiff

3.0-9.0 19-57 - 10-100 10 50 100

1.5-15.0 1.5 7.3

15.0

1.0

Table 6.1.2 Wall friction factors

Sand Silt Clay

Friction Factor fϕ fϕ fc

Smooth 0.8 0.87 0.4 Concrete

Rough 0.9 0.96 0.5

Steel 0.8 0.75 0.5


Page 27 of 36

The hydrodynamic loads from wave and current action on the river weight can be calculated using Morison’s formula for the in-line force and a standard force formulation for the lift force.

In-line force

aCVolUUAC½F RWMRW

RWD

RWH ρ+ρ= (6.1.2)

Lift force

2RW

RWL

RWL UAC½F ρ= (6.1.3)

ARW = area of the river weight, ARW = lRW⋅hRW RWDC = drag coefficient RWMC = inertia coefficient RWLC = lift coefficient

Vol = characteristic volume of the river weight = lRW⋅hRW⋅wRW U, a = instantaneous water particle velocity and acceleration.

The hydrodynamic force coefficients to be used in combination with river weights are given below

RWDC = 1.40 RWLC = 0.50 RWMC = 1.35

The maximum stabilization force from a river weight is

Rmax = RH - RWHF (6.1.4)

RH is calculated using the submerged weight of the river weight reduced for the hydrodynamic lift force.

passiveRWLRWRWH R)FW(R +−μ= (6.1.5)

6.2 Pipeline Stability Including River Weights

The overall stability of the pipeline-river weight system is checked by calculation of the on-bottom stability of the exposed pipe including the stabilization force from the river weight. The static design format is used expressed by Equation 5.5.2.1 of Appendix 1:


Page 28 of 36

( )RWmaxpipeH

s

pipeH S/RR

f1F +≤

The equation is expressed per unit length of pipeline and the stabilization force from the river weights has to be divided by the free distance between the river weights.

pipeHF = in-line hydrodynamic force component on pipeline (Appendix 1, Eq.

5.3.1)

pipeHR = available horizontal soil reaction on exposed pipe (Appendix 1, Eq.

5.4.1.1)

RWS = free distance between river weights

fs = safety factor (fs = 1.1)

7 ROCK DUMPING

The general use of rock dumping to stabilize pipelines is described in Section 3.4. The use of rock dumping requires careful evaluation of the suitability of the method and proper rock berm design.

7.1 Suitability of Method

The selection of pipeline stabilization methods is described in Section 5, and rock dumping is suitable in all cases, except when the pipeline has become buoyant, e.g. because of loss of concrete coating. The movements of the rock material and of the pipeline may result in gradual lifting of the pipeline through the rock berm and thereby loss of stabilization effects.

It is furthermore required that the pipeline can sustain the increased weight from the rocks. In case of an on-bottom pipeline this will be the normal case. In case of a free span, an assessment of stresses induced by the rock dumping has to be performed. If required, supports have to be constructed below the span before rock dumping is initiated.

7.2 Rock Berm Design

The function of the rock berm in relation to the pipeline stability is primarily to shield the pipeline where covered from wave and current loads (and other loads, if applicable). Secondly, the rock berm, if sufficiently large, may generate an anchoring of neighboring exposed sections of the pipeline.


Page 29 of 36

The rock berm design comprises the determination of the following elements:

a. Pipeline length to be covered

b. Length and distance of rock berms, if point stabilization is selected

c. Gradation of rock material

The design may be an iterative process. The shape of the rock berm influences the required rock gradation as well as stabilization efficiency, and rock berm cross-section is at the same time dependent on the installation method. A number of rock berm configurations may have to be designed in order to find the optimal one.

Full covering of the unstable pipeline section generates adequate pipeline stability and further investigations are only required to determine cross-section and gradation of the rock material.

If only partial rock dumping is applied, the length of rock berm should be sufficient to anchor the exposed pipeline sections. The rock berm provides an increased lateral soil resistance, which can be taken into account when calculating the on-bottom stability of the exposed pipeline sections.

7.3 Length of Rock Berm

The simplest approach is to cover the full length of pipeline requiring additional stabilization. In this situation the pipeline is shielded from external forces and is thus stable. If point stabilization is used, the lateral resistance from the rock berm has to be calculated.

Lateral Resistance from Rock Berm

The lateral resistance provided by a rock berm can in principle be calculated using a passive soil resistance model. Fig. 7.3.1 illustrates the pipeline rock berm configuration. The berm slope is normally defined as tan(v) where v is the slope angle.

Fig. 7.3.1 Passive soil resistance from rock berm


Page 30 of 36

Active and passive soil pressure ea and ep are calculated:

ep = γsKp⋅fb⋅z (7.3.1)

ea = γsKa⋅fb⋅z (7.3.2)

Kp, Ka = passive and active soil pressure coefficient

fb = reduction factor to account for rock berm slope

γs = submerged density of rock material

Development of passive soil pressure requires a geotechnical failure within the rock berm. It shall be checked that a geotechnical failure through the seabed soil is unlikely.

The resistance from the rock berm is calculated as the difference between active and passive soil pressure:

Rb = ( ) 2apbs D1

Dd2KKf

21

⎟⎠⎞

⎜⎝⎛ −−γ (7.3.3)

Rb = horizontal reaction from rock berm per unit length

The overall stability of the pipeline-rock berm system is checked by calculation of the on-bottom stability of the exposed pipeline including the stabilization force from the rock berm. The static design format is used expressed by Equation 5.5.2.1 of Appendix 1:

⎟⎟⎠

⎞⎜⎜⎝

⎛+≤

b

bb

pipeH

s

pipeH S

LRR

f1F (7.3.4)

The equation is expressed per unit length of pipeline and the stabilization force from the rock berm has been divided by the free distance between the rock berms.

pipeHF = in-line hydrodynamic force component on pipeline (Appendix 1,

Eq. 5.3.1)

pipeHR = available horizontal soil reaction on exposed pipe (Appendix 1,

Eq. 5.4.1.1)

Lb = length of rock berm

Sb = free distances between single rock berms


Page 31 of 36

fs = safety factor (fs = 1.1)

7.4 Cross-section and Gradation

Selection of cross-section and rock gradation are performed in a number of steps:

a) Determination of flow velocity. The near seabed undisturbed flow velocity is transformed to characteristic flow velocities on top of the rock berm.

b) The friction velocity at the top of the rock berm is calculated using imperical relations, which take the rock berm shape and the flow condition into account.

c) The required stone size is found using a design criterion based on Shield’s parameter, θcr = 0.04.

d) Stone sizes and rock berm shape are optimized according to installation method, equipment and rock material available.

Detailed description of the steps is given in the following paragraphs.

Rock Stability Criterion:

The Shields criterion has been adopted for the stability of the berm stones. The stones are stable if the Shields parameter, θ, satisfies the following condition:

θθ cr <

In which

1)D-g(s

U = s

f2

θ (7.4.1)

Uf = friction velocity at the surface of the berm

Ds = stone size

s = specific gravity of the stone

g = acceleration due to gravity

The critical value of θ is a function of the stone Reynolds number, DsUf/ν, where ν is the water viscosity. However, for the stone Reynolds number larger


Page 32 of 36

than 400, θcr is constant, approximately 0.06 (Fredsøe and Deigaard, 1992). The stability criterion is not absolute, because movements of stones are initiated over a certain velocity range. In practice, movements of stones may be observed when θ is in the range θ=0.03 to θ=0.06. For θ below 0.03, the stone movements are zero for all practical applications and for θ above 0.06, stones will move continuously. It is recommended to use θ cr = 0.04.

Velocity Amplification at the Top of the Berm:

The calculation of the velocity at the top of the rock berm is based on potential flow theory. Potential flow theory disregards boundary layers and flow separation, and the calculations are therefore only an approximation to the real-life situation. In case of pure wave action the approximation is reasonable in case of steady current boundary layer effect should be accounted for.

Due to the contraction of streamlines, the velocity is increased at the top of the berm. This increase can be expressed in terms of a velocity amplification coefficient:

U

U = c

maxα (7.4.2)

Umax = maximum flow velocity at the top of the berm

Uc = incoming flow (steady current)

These velocities are defined disregarding boundary layers.

The top part of the rock berm is the most critical part erosion-wise. On the upstream part, gravity increases the stability of the stones. On the downstream slope, flow separation reduces the flow velocity.


Page 33 of 36

Fig 7.4.1 Sketch of principle in flow amplification

In the present analysis, the berm cross-section has been approximated by an ellipse with a certain slenderness, a/b, of the elliptical cross-section, in which a and b are the half width and half height of the ellipse. Subsequently, the potential-flow solution for the flow around an elliptical cylinder has been adopted (Schlichting, 1979, p 218), and then the amplification coefficient has been obtained from this solution.

Schlichting’s solution to the potential flow problem has been approximated by an analytical expression through curve fitting. The velocity amplification coefficient is now:

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎠⎞

⎜⎝⎛ −−+=α

425.0

1ba5.1exp1.21 (7.4.3)

In the present potential-flow approximation, the approach velocity (Uc) is constant above the seabed. However, in reality, the approach flow is a boundary-layer flow. Therefore, the actual velocity amplification will be smaller than that found from the potential-flow approximation. To compensate for this, the approach velocity used in the calculations is the mean flow velocity over the height of the rock berm.

Boundary Layer:

b

fc k

z30lnU

)z(U ⋅κ

= (7.4.4)

ℓ


Page 34 of 36

b

o

bo

kz30

ln

k72.2b30ln )z(U

= )b(U⋅

(7.4.5)

Uc(z) = flow velocity in height z

z = distance from the seabed

Uf = friction velocity

κ = von Karman’s constant (κ = 0.4)

kb = seabed roughness (kb = 2.5 Ds)

U (b) = mean flow velocity over height b

b,zo = distances from the seabed

The velocity on the top of the berm is now calculated using equation 7.4.3.

)b(UUmax α=

The friction velocity at the top of the berm is calculated from:

U 2f = U maxf (7.4.6)

The friction coefficient, f, is calculated from the resistance relationship for the turbulent boundary layer developing over a rough flat plate (Schlichting, 1979, p 654):

))k

(log 1.58 + (2.87 = f 2.5-

b

l (7.4.7)

l = distance from the leading edge of the berm to the center of the berm

kb = Nikuradse equivalent sand roughness (kb=2.5Ds)

Ds = the stone size


Page 35 of 36

Influence of Waves:

In the case of the current with a combined wave, the friction coefficient increases with respect to that experienced in the case of the current alone. Fredsøe, Andersen and Sumer (1999) give the following empirical expression for this:

1]+ )U/(U [0.673 = f

f 0.879-wc

cw (7.4.8)

fcw = friction coefficient for the combined flow condition

f = friction coefficient for the pure steady current case

Uc = steady current flow

Uw = maximum wave-induced oscillatory flow velocity

The friction coefficient for the combined flow condition are defined by:

U2

f = U ccw

fcw (7.4.9)

The above empirical relation has been obtained for a ripple-covered flat bed, but it is estimated to be a reasonable approach for the present case with a rock berm.

The friction velocity at the top of the berm for the combined flow case has been calculated using the basic equation (7.4.5), where f is replaced by fcw:

max-0.879

w21

fcw U1]+ )U/)b(U( [0.673 = U (7.4.10)

Effect of Seabed Slope:

In case of sloping seabed, gravity will have a component parallel to the seabed. This component will act in the same plane as the fluid forces and may reduce the stability of the stones. The effect of sloping seabed is therefore in most cases incorporated in the form of a reduced Shields parameter. Two different situations are considered:

a) The flow direction is parallel to the direction of maximum slope

b) The flow direction is perpendicular to the direction of maximum slope

In both cases, the critical Shields parameter is found by vectorial addition of fluid forces and gravitational component in the plane of the gravel layer. The


Page 36 of 36

solution to the two cases is given by (Fredsøe and Deigaard, 1992):

Case a): ]tantan-[1 cos =

scrocr

ϕβ

βθθ (7.4.11)

Case b): tantan-1 cos =

s2

2

crocrϕβ

βθθ (7.4.12)

θcr = critical Shields parameter for movement of stones

θcro = critical Shields parameters for movement of stones on horizontal bed

β = the seabed slope in degrees

φs = internal friction (∼ angle of repose of the stone material)

Page 1 of 4

Engineering Report

Appendix 3 - References SAER-5711 July 2000

Appendix 3 Table of Contents 1 REFERENCES .......................................... 2

Issue Date: July 2000 References Appendix No 3 to SAER-5711

Page 2 of 4

1 REFERENCES

The selection of material and equipment, and the design, construction, maintenance, and repair of equipment and facilities covered by this Guideline shall comply with the latest edition of the references listed below, unless otherwise noted.

1.1 Saudi Aramco Standards

Saudi Aramco Engineering Standards

SAER-5679 Arabian Gulf Hindcast Study

SAER-5565 Red Sea Hindcast Study

SAES-L-003 Design Stress Criteria for Pressure Piping

SAES-L-020 Design of Transportation Piping Systems

SAES-L-021 Design of Submarine Pipelines and Risers

SAES-L-022 Design of Wellhead Piping, Flowlines and, Trunklines and Testlines

SAES-L-032 Material Selection of Piping Systems

SAES-L-033 Corrosion Protection Requirements for Pipelines/Piping

01-SAMSS-012 Submarine Pipe Weight Coating

01-SAMSS-035 API Line Pipe

1.2 Industry Codes and Standards

American Petroleum Institute

API RP 1111 Design, Construction, Operation and Maintenance of Offshore Hydrocarbon Pipelines. Third Edition

American Society of Mechanical Engineers

ASME B31.4 Pipeline Transportation Systems for Liquid, Hydrocarbons, and other Liquids

ASME B31.8 Gas Transmission and Distribution Piping System


Page 3 of 4

ASME SEC VIII D1 Boiler and Pressure Vessel Code

ASME B 31.8 Guide for Gas Transmission and Distribution Piping Systems, 1992.

Environmental Conditions and Environmental Loads, Classification Notes No. 30.5. Det Norske Veritas, March 1991.

Guidance on Methods for Assessing the Acceptability of Flaws in Fusion Welded Structures, PD 6493, British Standards Institution, 1991.

On-bottom Stability Design of Submarine Pipelines, Veritec, October 1988.

Process of Welding of Steel Pipelines on Land and Offshore, BS 4515 British Standard Institution, 1984.

Rules for Submarine Pipeline Systems, Det Norske Veritas, 1996.

Rules for the Design, Construction and Inspection of Offshore Structures - Appendix C - Steel Structures, Det Norske Veritas, 1977.

Rules for the Design, Construction and Inspection of Offshore Structures - Appendix F - Foundations, Det Norske Veritas, 1977.

Rules for the Design, Construction and Inspection of Offshore Structures - Appendix G - Dynamic Analysis, Det Norske Veritas, 1977.

Structural Reliability Analysis of Marine Structures, Det Norske Veritas Classification Notes No 30.6, July 1992.

Free Spanning Pipelines, Guidelines No. 14, Det Norske Veritas, June 1998.

Submarine Pipeline On-bottom Stability, Volume 1, Analysis and Design Guidelines, A.G.A. Project PR-178-9333, American Gas Association, PRCI, September 1993.

1.3 Other Technical Publications

Bruschi, R., Vitali, L., 1991. Large-Amplitude Oscillations of Geometrically Nonlinear Elastic Beams Subjected to Hydrodynamic Excitation. Journal of Offshore Mechanics and Arctic Engineering, Vol. 113, 1991.

Fredsøe, J. and Deigaard, R. (1992): Mechanics of Coastal Sediment Transport. World Scientific.


Page 4 of 4

Fredsøe, J., Andersen, K.H., and Sumer B.M. (1999): Wave plus current over ripple-covered bed, in print, Coastal Engineering, 1999.

Hetényi, M. Beams on Elastic Foundation, Ann Arbor: The University of Michigan Press (1976).

Hobbs, R.E., 1986. Influence of Structural Boundary Conditions on Pipeline Free Span Dynamics. Proc. of the fifth international Offshore Mechanics and Arctic Engineering (OMAE), volume III.

Roark, R.J. and Young, W.C. Formulas for Stress and Strain (1976).

Schlichting, H. (1979): Boundary Layer Theory. McGraw Hill.

Timoshenko, S.P. and Gere, J.M. Theory of Elastic Stability, second edition, McGraw-Hill Kogakusha, Ltd., 1961.

Page 1 of 27

Engineering Report

Appendix 4 – Calculation Examples SAER-5711 July 2000


1 INTRODUCTION 2 2 PIPELINE ON-BOTTOM STABILITY 3 3 PIPELINE FREE SPAN ASSESSMENT 7 4 PIPELINE INSTALLATION 13 5 PIPELINE STABILIZATION 17

Issue Date: July 2000 Calculation Examples Appendix No. 4 to SAER-5711

Page 2 of 27

1 INTRODUCTION

The “Calculation Examples” have been prepared to facilitate the use of the “Submarine Pipeline Engineering Guidelines”. The Guidelines pertain to all pipelines used for transportation of fluids and /or gases, and installed on or below the seabed.






Examples presented in Appendix 4 relate to the more complex parts of the Guideline dealing with on-bottom stability, free span evaluation, and post-stabilization of pipelines. The major part of the Guidelines is self-explanatory and does not require specific calculation examples.


Page 3 of 27

2 PIPELINE ON-BOTTOM STABILITY Reference is made to Appendix No 1 of SAER-5711, Section 5, simply by giving the figure number, equation number, or page number. Other references are given in full.

Basic Data

Pipeline Data (24” Pipeline)

Pipe diameter (steel) Ds =609.6 mm (24 in) Wall thickness t =14.3 mm (0.56 in) Anti corrosion coating thickness te =4 mm (0.16 in) Anti corrosion coating density ρe =1400 kg/m3 (87.4 lb/ft) Concrete coating thickness tc =70 mm (2.76 in) Concrete coating density ρc =3192 kg/m3 (199.3 lb/ft3) Contents density ρi =600 kg/m3 (37.5 lb/ft3)

Submerged weight Ws =3928 N/m (269 lbf/ft) Outer diameter D =757.6 mm (29.8 in) Drag coefficient CD =1.70 Lift coefficient CL =2.16 Inertia coefficient CM =3.29 The drag and lift coefficients are determined from Figs 5.3.3 and 5.3.4 based on the Keulegan-Carpenter No and current to wave ratios given below. Environmental Data Water density ρ =1025 kg/m3 (64.0 lb/ft3) Water Depth h =12.7 m (41.7 ft) Current velocity at pipe level Uc =0.5 m/s (1.64 ft/s) Significant Wave Height Hs =3.2 m (10.5 ft) Mean Period Tp =8.4 s PM spectrum used

From 1st order wave theory: Significant near seabed velocity Um0 =0.90 m/s (2.95 ft/s)


Near Seabed peak period Tpu =8.8 s Associated acceleration aw = 2π/ Tpu Um0 =0.64 m/s2 (2.10 ft/s) From Fig 5.2.2, Tp and Um0 can be calculated: Tn = 14.1g/h = Tn/Tp = 0.135 Um0Tn/Hs = 0.32 Um0 = 0.90

Non-dimensional Parameters Keulegan-Carpenter No KC =10.6 Current to wave ratio α =0.55 Current to total flow ratio Uc/(Uc+Uw)=0.36 Seabed Soil Data

Friction coefficient μ=0.7 The figure below shows the forces acting on a section of a submarine pipeline resting on the seabed.

The stability criterion is expressed by:

Page 4 of 27


( ) )F - W( fsF + F LsMD ⋅μ

≤ (5.5.2.1)

where fs is a safety factor. In the present example a safety factor of 1.1 has been applied. The equation can be rearranged to give a utilisation factor, Util:

( )( ) FW

FFfsUtilLs

MD

−μ+

=

Util < 1.0 on-bottom stability is satisfactory Util ≥ 1.0 submerged weight is insufficient By applying Morison's equation to determine the drag, lift, and inertia forces the equation above can be written as:

( )U C D 2/1 - W fs

aC D 4 + |U|U C D2/1 2

LsM2

D ρμ

≤⎟⎠⎞

⎜⎝⎛ ρ⋅

πρ

The nearbed velocities consist of a sinusoidal contribution from the waves and a steady current contribution. The nearbed accelerations are determined by differentiating the velocity.

U + T

t2 sinU = U cpu

moπ

Tt2cosU

T2 = a

upmo

up

ππ

The minimum stability (ie maximum utilisation) can now be determined by stepping though the wave and calculate the forces for each time step. For the present example the maximum utilisation is obtained for a phase angle of 72.3 deg. For this phase the following results are obtained: Util=1.0 FD=1221 N/m (83.7 lbf/ft) FL=1551 N/m (106.3 lbf/ft) FM=298 N/m (20.4 lbf/ft)

Page 5 of 27


Page 6 of 27

Therefore on-bottom stability is obtained by using a concrete coating thickness of 70 mm (2.76 in), satisfying the stability criterion using a safety factor of 1.1.


Page 7 of 27

3 PIPELINE FREE SPAN ASSESSMENT Reference is made to Appendix No 1 of SAER-5711, Section 6, simply by giving the figure number, equation number, or page number. Other references are given in full.

Basic Data


Pipe diameter (steel) Ds =609.6 mm (24 in) Wall thickness t =14.3 mm (0.56 in) Steel density ρs = 7850 kg/m3 (490.1 lb/ft3) Anti corrosion coating thickness te =4 mm (0.16 in) Anti corrosion coating density ρe =1400 kg/m3 (87.4 lb/ft) Concrete coating thickness tc =125 mm (4.9 in) Concrete coating density ρc =3192 kg/m3 (199.3 lb/ft3) Contents density ρi =600 kg/m3 (37.5 lb/ft3)

Submerged weight Ws =6913 N/m (473.7 lb/ft3) Outer diameter D =867.6 mm (34.2 in) Free span length (scour induced) L =20 m (65.6 ft) Residual lay tension Tres =0 kN (0 lb) Contents temperature θi =15°C (59°F) Ambient temperature θa =15°C (59°F) Pipeline operating pressure pi =10 MPa (1450 psi) Inertia coefficient CM =Ca + 1.0 Added mass Ca =1.0 (Section 6.2) Pipe steel type API 5L X60 SMYS =413 MPa (5.99 ⋅ 104 psi) Modulus of elasticity E =2.1 ⋅ 105 MPa (3.05 ⋅ 107 psi) Free Span Data Span type Scour induced (no adjacent spans) Gap ratio e/D =0.5


Page 8 of 27

Environmental Data

Water density ρ =1025 kg/m3 (64.0 lb/ft3) Water Depth h =10 m (32.8 ft) Current velocity at pipe level Uc =0.5 m/s (1.64 ft/s) Significant Wave Height Hs =3.2 m (10.5 ft) Peak Period Tp =8.4 s Mean Period T02 =6.0 s PM spectrum used

From 1st order wave theory: Significant near seabed velocity Um0 =1.12 m/s (3.68 ft/s) Near Seabed mean period Tu02 =8.76 s Associated acceleration aw =2π/T02u Um0=0.80 m/s2 (2.62 ft/s2) Maximum near seabed wave induced velocity U =2.08 m/s (6.82 ft/s) (5.2.2.10)

Non-dimensional Parameters Keulegan-Carpenter No KC =11.3 Current to wave ratio α =0.45 Current to total flow ratio Uc/(Uc+Uw)=0.31

Seabed Soil Data

Soil type loose sand Submerged density γs=10 kN/m3 (63.7 lbf/ft3) Friction coefficient μ=0.7 Seabed reaction coefficient ks=3000 kN/m/m (435 psi) Pipe Sectional Properties Pipe bending stiffness EI = 2.49 ⋅ 108 Nm2 (8.68 ⋅ 1010 lbf ⋅ in2) Internal area Ai = 0.265 m2 (411 in2) (6.2.3) Steel area As = 2.68 ⋅ 10-2 m2 (41.5 in2) (6.2.4) Axial pipe stiffness EAs = 5.62 ⋅ 109 N (1.26 ⋅ 109 lbf) Section modulus Z = 3.88 ⋅ 10-3 m3 (237 in3) Mass of pipe and content m = 1311 kg/m (881 lb/ft) Effective mass (including added mass) me = 1917 kg/m (1290 lb/ft) (Ca = 1.0, also refer to Section 6.2 of Appendix No 1 to SAER-5711)


Submerged weight of pipeline per unit length incl. contents Ws = 6913 N/m (474 lbf/ft)

Te

Ws

Te

Mb Mm Mb

ks ks

L

otd1.00/50302-3 Fig 3.1 Free span configuration and data definition Simplified Structural Model Axial force due to functional loads Te = Tres + Tθ + Tp + Tν

Tres = 0 kN (0 lbf) Tθ = 0 kN (0 lbf)

72vPe 10581.0

581.00143.0581.030.05.0

2TTT ⋅⋅⎟⎟

⎠

⎞⎜⎜⎝

⎛ +⋅−

π−=+= (6.6.2)

Te = -1021 kN (-2.30 ⋅ 105 lbf) The structural model formulation corresponding to compression, Te < 0, is applied. The auxiliary variables u, a, and b become:

( ) 640.01049.2

1010212

20u 8

3

=⋅

⋅−−= (6.4.12)

( ) 2367.01049.24101021

1049.24103000a 8

3

8

3

=⋅⋅⋅−

−⋅⋅

⋅= (6.4.13)

( ) 2321.01049.24101021

1049.24103000b 8

3

8

3

=⋅⋅⋅−

+⋅⋅

⋅= (6.4.14)

The moment at the support, the mid-span moment, and the deflections at the support and mid-span are calculated:

Page 9 of 27


Mb = -131.1 kNm (-9.66 ⋅ 104 lb ⋅ ft) (6.4.8) Mm = 252.9 kNm (1.87 ⋅ 105 lb ⋅ ft) (6.4.9) Zb = 0.016 m (0.63 in) (6.4.10) Zmax = 0.046 m (1.81 in) (6.4.11) The mid-span moment is largest and the stress criterion is checked here. Stress from internal pressure (fully restrained pipeline): Hoop stress σH = 196.8 MPa (2.85 ⋅ 104 psi) (7.5) Longitudinal stress σLA = 59.0 MPa (8.56 ⋅ 103 psi) (7.6) Stress from bending moment:

Longitudinal stress σLB = MPa3.65ZM

±= (±9.47 ⋅ 103 psi)

Combined longitudinal stress σL = ⎩⎨⎧

−−⋅+

)psi914(MPa3.6)psi1080.1(MPa3.124 4

Equivalent stress (von Mises):

2HL

2H

2Le 3 τ+σσ−σ+σ=σ

For all practical purposes the shear stress can be neglected. σe = 200 MPa < 0.72 ⋅ 413 MPa = 297 MPa (2.90 ⋅ 104 psi < 4.31 ⋅104 psi), ie OK (Table 3.1 of SAER-5711). Simplified Expressions for Bending Moment Section 6.6 of Appendix 1 presents simplified expressions for calculating bending moments which are valid when the configuration of the free span is as illustrated in the figures and when the axial force is zero. For comparison, the free span used for the example is calculated using case A of Section 6.6.

Mm = kNm19720913.6141 2 =⋅ (6.6.1)

σLB = MPa511088.3

197Z

M3

m ±=⋅

=−

Page 10 of 27


Zb = m019.0201049.21019706.0 2

8

3

=⋅⋅⋅ (6.6.3)

The simplified formulations give results which deviate by up to 30 per cent from the results based on the more complex expressions. Natural Frequency, First Symmetrical Mode

F0 = Hz34.11061401010211

19171049.2

202.3

21

3

38

2

2

=⎟⎟⎠

⎞⎜⎜⎝

⎛⋅−⋅−

−⋅⋅

⋅⋅π

(6.5.1)

To obtain the free span frequency parameter, λL, Fig 6.4.1 of Appendix 1 to SAER-5711 is applied, where β = 3000 ⋅ 103 ⋅ 204/2.49 ⋅ 108 = 3.29 is entered, giving λL = 3.2. Tcr is the axial compression buckling force which is obtained from Fig 6.4.2 of Appendix 1 to SAER-5711 which gives the relationship Tcr/Tn = 1.9, ie:

Tcr = 1.9 ⋅ kN614020

1049.22

82

=⋅⋅π (1.38 ⋅ 106 lbf)

f1 (natural frequency for first mode in-plane vibrations) is established based on the expression:

(2π ⋅ f1)2 = 222 4.043046.02)34.12( ⋅α⋅+⋅α⋅+⋅π (6.5.2)

( ) ( ) ( ))in2.41(m1066.2

)4.5.6(20/101.2106.5/1106.5/11068.2/1

1'A

222

1110102

−

−

⋅=

⋅⋅⋅+⋅+⋅=

224211

sm4434

2020201917

1066.2101.2 −−−

⋅=⋅⎟⎠⎞

⎜⎝⎛ π

⋅⎟⎟⎠

⎞⎜⎜⎝

⎛⋅

⋅⋅⋅=α (6.87⋅105 in-2⋅s-2) (6.5.3)

( ) Hz79.14.044343046.0443234.12

21f 222

1 =⋅⋅+⋅⋅+⋅π⋅π

=

then for cross-flow (in-plane vibrations) Vr becomes:

Page 11 of 27


Vr = 34.1868.079.1

08.2=

⋅ (Eq. 3.6.7-5 of SAER-5711)

This is less than = 4 (Eq. 3.6.7-4 of SAER-5711) and hence the free span length of 20 m is OK according to a dynamic criterion, as the free span natural frequency is outside the region of lock-in with cross flow vibrations due to vortex shedding.

CRITrV

Page 12 of 27


Page 13 of 27

4 PIPELINE INSTALLATION Reference is made to Appendix No 1 to SAER-5711, Section 9, simply by giving the figure number, equation number, or page number. Other references are given in full.

Basic Data


Pipe diameter (steel) Ds =609.6 mm (24 in) Wall thickness t =14.3 mm (0.56 in) Anti corrosion coating thickness te =4 mm (0.16 in) Anti corrosion coating density ρe =1400 kg/m3 (87.4 lb/ft) Concrete coating thickness tc =125 mm (4.9 in) Concrete coating density ρc =3192 kg/m3 (199.3 lb/ft3) Contents density ρi =0 kg/m3

Mass of pipe m =1151 kg/m (773 lb/ft) (6.2.7)

Submerged weight Ws =5352 N/m (367 lbf/ft) (6.2.10) Outer diameter D =867.6 mm (34.2 in) Bending stiffness EI =249.05MNm2 (603 lbf ⋅ ft2) Section area As = 0.0267m2 (41.4 in2) Section modulus Z =3.89 10-3 m3 (0.153 in) Steel strength SMYS =413 MPa (60000 psi) Environmental Data

Water density ρ =1025 kg/m3 (64.0 lb/ft3) Water Depth h =12.7 m (41.7 ft)


Pipeline Sagbend Calculation

Stinger Data

Ramp start angle θ (depends on stinger radius and stinger angle)

Stinger Radius R =200 m (656 ft)

Stinger Length L1 = 35m (115 ft)

Stinger tip offset angle θ2 = 5 degree (pipeline angle relative to stinger)

Stinger angle θ1 (to be calculated)

Installation Data

Tension T =1000kN (2.25 ⋅ 105 lbf)

Sagbend length (first estimate) L = 75m (246 ft)

Sagbend angle (first estimate) θ = 6 degrees

Page 14 of 27


Page 15 of 27

Calculation of Sagbend Stress

u2 = TL2/(4EI) = 5.646 (9.4)

u = 2.376

W1 = Ws cos(θ)=5287 N/m (362 lbf/ft) (9.5)

θ = 0.1162 Rad= 6.7 degrees (9.1)

Mmax = 1074 kNm (7.92 ⋅ 105 lbf ⋅ ft) (9.2)

Zmax = 2.64 m (8.66 ft) (9.3)

θ1 = 2 θ-θ2 = 8.4 degrees (9.6)

Calculated water depth h = L1 sin(θ1) + L sin(θ) (9.7)

h = 35 sin(8.4) + 75 sin(6.7)

h = 13.8 m (45.3 ft)

Sagbend length (second estimate) L = 72 m (36 ft) (9.4)

u2 =TL2/(4EI) = 5.239

u = 2.2898

W1 =Ws cos(6.7 ο)=5352 N/m (367 lbf/ft)

(9.5)

θ = 0.1106 Rad= 6.3 degrees (9.1)

Mmax = 1065 kNm (7.86 ⋅ 105 lbf ⋅ ft) (9.2)

Zmax = 2.64 m (8.66 ft) (9.3)

θ1 = 2 θ-θ2 = 7.7 degrees (9.6)

Calculated water depth h = L1 sin(θ1) + L sin(θ) (9.7)

h = 35 sin(7.7) + 72 sin(6.3)

h = 12.65 m (41.5 ft)

The calculated water depth is close to the real and the sagbend moment and


Page 16 of 27

tension can be used for a stress check.

Max stress σ = T/As + M/Z (9.8)

σ = 1/0.0236+1.065/0.00389 = 316 MPa (4.58 ⋅ 104 psi)

The allowable stress for pipeline installation is given in SAES-L-021 and should not exceed 80 per cent of SMYS, equal to 330 MPa. The calculation shows that the installation stress is within the acceptable limit.


Page 17 of 27

5 PIPELINE STABILIZATION Reference is made to Appendix No 2 of SAER-5711, simply by giving the figure number, equation number, or page number. Other references are given in full.

Basic Data (24” Pipeline)

Pipeline Data Pipe diameter (steel) Ds =609.6 mm (24 in) Wall thickness t =14.3 mm (0.56 in) Anti corrosion coating thickness te =4 mm (0.16 in) Anti corrosion coating density ρe =1400 kg/m3 (87.4 lb/ft3) Concrete coating thickness tc =125 mm (4.9 in) Concrete coating density ρc =3192 kg/m3 (199.3 lb/ft3) Contents density ρi =600 kg/m3 (37.5 lb/ft3)

Submerged weight Ws =6913 N/m (473.7 lbf/ft) Outer diameter D =867.6 mm (34.16 in) Drag coefficient CD =1.85 (Appendix 1 Lift coefficient CL =2.3 Figs 5.3.3 and 5.3.4) Inertia coefficient CM =3.29 Environmental Data Water density ρw =1025 kg/m3 (64.0 lb/ft3) Water Depth h =12.7 m (41.7 ft) Current velocity at pipe level Uc =0.5 m/s (1.6 ft/s) Maximum Wave height H =6.0 m (19.7 ft) Wave Period T =7.0 s Significant Wave Height Hs =3.2 m (10.5 ft)

From 1st order wave theory: Bottom max orbital velocity Uw =1.71 m/s (5.61 ft/s) Bottom max orbital acceleration aw =1.53 m/s2 (5.02 ft/s2)


Page 18 of 27

Nondimensional Parameters Keulegan-Carpenter No KC =13.8 Current to wave ratio α =0.29 Current to total flow ratio Uc/(Uc+Uw)=0.23 Seabed Soil Data Submerged density γs=10 kN/m3 (63.7 lbf/ft3) Passive earth pressure coef Kp=3.7 Passive earth pressure coef Ka=0.4 Angle of friction φ=35 deg Friction coefficient μ=0.7


Pipeline stabilization by means of River Weights

River Weight Parameters Height hRW=1.3 m (4.3 ft) Width wRW=1.9 m (6.2 ft) Length lRW=2.0 m (6.6 ft) Characteristic area ARW=2.6 m2 (28.0 ft2) Characteristic volume VolRW=4.94 m3 (174.5 ft3) Volume VRW=1.96 m3 (69.2 ft3) Concrete density ρRW=3000 kg/m3 (187.3 lb/ft3) Submerged Weight WRW=37.98 kN (8538 lbf)

Drag coefficient =1.4 RWDC

Lift coefficient =0.5 (page 25) RWLC

Inertia coefficient =1.35 RWMC

Soil Parameters Wall friction factor fφ=0.88 Friction coefficient (river weight) μ=tan(fφφ)=0.60 Assuming a burial depth of d=0.1 m (3.9 in) the passive soil resistance is determined to

2RWPs2

1passive dlKR γ= [N] (6.1.1)

The stabilizing force on the pipeline from one river weight is determined by:

Page 19 of 27


RWHHmax FRR −= (6.1.4)

RWHpassive

RWLRWmax FR)FW(R −+−μ= (6.1.4)

Where is the horizontal hydrodynamic force on the river weight and s the lift force.

RWHF RW

LF i

This additional friction force is distributed evenly over the free distance between each river weight, sRW. If the distance from center to center of the river weights is denoted dRW then sRW=dRW-lRW. The calculations are only performed for the exposed pipeline sections. Forces on the pipeline covered by river weights are neglected. This is justified because the hydrodynamic forces on the river weights are calculated including the presence of the pipeline. The stability of the pipeline is calculated by:

( )( RWmaxLsH s/RFWfs1F +−μ≤ ) (Appendix 1, Eq. 5.5.2.1)

In terms of a utilization factor the stability is expressed by:

RWmaxLs

H

s/R)FW(FfsUtil

+−μ=

where FH and FL are the horizontal hydrodynamic force and the lift force on the pipeline per unit length. The maximum utilization factor is now determined for a given river weight configuration by stepping through the wave and calculating the hydrodynamic forces using Morison's equation. The forces on the pipeline are determined from equations 5.3.1 and 5.3.2 of Appendix 1. A maximum utilization of 1.0 is obtained for a river weight distance (center to center) of 4.7 m (15.4 ft). The following values of basic parameters in this situation are: FH=4716 N/m (323 lbf/ft) (Appendix 1, Eq. 5.3.1) FL=4467 N/m (306 lbf/ft) (Appendix 1, Eq. 5.3.2)

RWLF =2910 N (654 lbf) (6.1.3)

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RWHF =11998 N (2697 lbf) (6.1.2)

Rpassive=370 N (83 lbf) (6.1.1) Rmax=9274 N (2085 lbf) (6.1.4)

Pipeline stabilization by means of Mattresses

Mattress Parameters Height (above seabed) h1=1.17 m (3.84 ft) Thickness h2=0.30 m (0.98 ft) Length lm=6.0 m (19.7 ft) Dist. between touch down points w1=2.5 m (8.2 ft) Length of downstream mattress w2=2.0 m (6.6 ft) Width of mattress wM=6.1 m (20.0 ft) Characteristic area Am=7.0 m2 (75.3 ft2) Characteristic volume Volm=17.0 m3 (600 ft3) Submerged Weight Wsm=44.2kN/m (3029 lbf/ft) Submerged Weight of 1st set of blocks along mattress Wse=2.3 kN/m (158 lbf/ft)

Drag coefficient CD=1.28 Lift coefficient CL=2.0 Edge lift coefficient CLE=1.0 (figs 5.1.2 through 5.1.4) Inertia coefficient CM=1.5

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Soil Parameters Friction coefficient mattress-soil μm=0.7 Friction coefficient mattress-pipe μ1=0.5 Mattress dislodging failure Overall failure:

( Lsmm

H FWfs

F −μ

≤ ) [N/m] (5.1.6)

By rearranging the equation it is possible to calculate a utilization factor, Util.

)FW(FfsUtil

Lsmm

H

−μ=

Stability of mattress edge

SE

LE

WFfsUtil =

The horizontal force FH, and the lift force FL on the mattress and the lift force on the mattress edge FLE are determined by Morisons equation (5.1.3 to 5.1.5). Pipeline Pullout failure

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The following condition is considered

( )mpipeexcess RRfs1F +≤ (5.2.4)

mpipe

excess

RRFfsUtil

+=

The excess hydrodynamic force on the exposed pipeline is distributed over the mattress length

[ ]m

LsHexcess LS)FW(FF ⋅−μ−= [N/m]

where FH is the horizontal hydrodynamic force, FL is the lift force, and Ws is the submerged weight of the pipeline. FH and FL are determined from equations 5.3.1 and 5.3.2 of Appendix 1. S is the free distance along the pipeline between mattresses.

The friction between the pipe and the seabed is determined by:

( )seff,smpipe WWR +μ= [N/m] (5.2.1) where Wsm,eff is the effective submerged weight per unit length of the mattress

resting on the pipe (Wsm,eff = Wsm mWD5.2 ).

Friction between mattress and pipe:

eff,sm1m WR μ= [N/m] (5.2.2)

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Overall stability failure This failure occurs when pipeline and mattress move together:

( )( sLsmmHexcess WFWfs1FF μ+−μ≤+ ) (5.3.1)

Expressed in the form of a utilization factor:

( )( ) sLsmm

excessH

WFWFFfsUtil

μ+−μ+

=

Considering these four failure modes, the maximum utilization is determined for each mode by stepping through the wave and calculating the forces on the pipe and the mattress using Morison's equation. For a distance between the mattresses (center to center) of 48 m (157 ft) the following results are obtained (the values listed are the maximum utilization factor for each failure mode, hence the values are not in phase): Dislodging

• Overall failure: Util=0.28 • Mattress edge stability Util=0.36

Pipeline pullout resistance Util=1.00 Overall stability Util=0.93 The pipeline pullout resistance is the most critical case having Util = 1.0 including a safety factor of 1.1. Util = 1.0 is calculated based on the following forces:

m/N21509Fexcess = (1474 lbf/ft) FL=5565 N/m (381 lbf/ft) (5.1.4) FLE=715 N/m (49.0 lbf/ft) (5.1.5) FH=5269 N/m (361 lbf/ft) (5.1.3) Rpipe=15885 N/m (1088 lbf/ft) (5.2.1) Rm=7890 N/m (541 lbf/ft) (5.2.2)

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The overall stability is less critical corresponding to Util = 0.93 including the safety factor fs = 1.1.


Pipeline stabilization by means of Rock Dumping

Rock parameters Height d=1.3 m (4.3 ft) Length L=6.0 m (19.7 ft) Rock density ρ=2600 kg/m3 (162.3 lb/ft3) Submerged density γs=15.45 kN/m3 (98.4 lbf/ft3) Passive earth pressure coef Kp=3.7 Active earth pressure coef Ka=0.4 Berm slope tan(α)=0.333 Slope reduction factor fb=0.5 Angle of friction φ=42 deg The resistance from the berm per unit length is given by:

( ) 2apbs2

1b D1

Dd2KKfR ⎟

⎠⎞

⎜⎝⎛ −−⋅γ=

The stability criterion is given by:

⎟⎟⎠

⎞⎜⎜⎝

⎛+≤

b

bbHH S

LRRfs1F

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where Sb is the exposed length of the pipeline between each rock dumping section and Lb is the length of the rock berm. The stability criterion may be expressed by a utilization factor:

b

bbH

H

SLRR

fsFUtil+

⋅=

The maximum utilization is determined by stepping through the wave and calculating the forces on the pipe using Morison's equation. A utilization factor of 1.00 is obtained with a distance between the rock sections (center to center) of 38.5 m (126 ft) and a safety factor of 1.1. In this case the forces are: FH=4583 N/m (314 lbf/ft) (Appendix 1, Eq. 5.3.1) FL=4755 N/m (326 lbf/ft) (Appendix 1, Eq. 5.3.2) Rb=19159 N/m (1313 lbf/ft)

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SAER-5711