16
ESTIMATION OF BURIAL DEPTHS FOR PIPELINES IN ARCTIC REGIONS By Luc E. Chouinard' ABSTRACT: Ice scouring poses a significant threat to underwater pipelines for offshore oil production facilities in ice-infestcd waters. For most locations, theonly options against this hazard are to protect the pipeline by trenching, burial, or creative alignment. The optimal burial depths along the length of a pipeline are usually selected on the basis of a hazard model that describes the recurrence rate and severity of scouring along its length. Although sufficient data at a specific site are rarely available to accurately estimate the hazard model, several thousand scours scouring hazards at preliminary stages of design. The main features of the proposed have been documented over extended regions and can provide an estimate of depth and exposure to the ice environment, and the propagation of uncertainties model are a parametrization of the scouring hazard model as a function of water due to model incompleteness and sample size. The proposed model can be validated or readjusted at later stages of the project as moresite-specific data become avail- of the optimal burial depth for a hypotheticalpipeline route. able. The application of the proposed model is demonstrated for the determination INTRODUCTION Many oil prospects in the Arctic are located in offshore waters, sometimes several kilometers from the coastline. This location requires the design and construction of pipelines, sometimes tens of kilometers long, and can rep- resent a significant obstacle both technically and financially. The main source of hazards is scouring from ice ridges or rubble fields. Protective measures against scouring include burial, multiple branching systems, and regularly spaced closing mechanisms, as well as careful alignment. A preliminary step in the selection and design of these protective measures is the estimation of risks of ice scouring. A model is presented for the estimation of scouring hazards expressed in the form of a recurrence rate of scour exceeding given depths. Such a model can then be used to determine the optimal burial depth of a pipeline for a given return period. Scours in the Arctic have been recorded in water depths up to 60 m. However, this upper limit is not well defined and these features may be relict scours that have no relation to the present ice regime. Ice scours as deep as 5.4 m have been measured in the Beaufort Sea, with intense scouring in water depths between 15 and 40 m corresponding to the ice shear zone. Data in the Beaufort Sea off the coast of Canada consist of approximately 66,000 scour records (scour length, width, orientation, form, morphology, etc.) as measured from side-scan sonar data, and 24,000 records (scour depth and bathymetry) as measured from echo-sounder or high-resolution profiler data. Limited repetitive mapping (3000 scours for the Beaufort Sea off the coast of Canada) has also been conducted over the last few years in order to estimate the age of scours, scouring rates, and infill thickness (Shearer 1988). 'Asst. Prof., Dept. of Civ. Engrg. and Appl. Mech., McGill Univ., 817 Sherbrooke St. West, Montreal, Quebec, Canada, H3A 2K6. Note. Editor: John P. Dempsey. Discussion open until May 1, 1996. To extend the closing date one month, a written request must be filed with the ASCEManager of Journals. The manuscript for this paper was submitted for review and possible publication on February 10, 1995. This paper is part of the Journal of CoM Regions Engineering, Vol. 9, No. 4, December, 1995. OASCE, ISSN 0887-381)3/95/0004- 0167-0182/$2.00 + $.25 per page. Paper No. 10093. JOURNAL OF COLD REGIONS ENGINEERING / DECEMBER 1995 / 167 ESTIMATION OF BURIAL DEPTHS FOR PIPELINES IN ARCTIC REGIONS By Luc E. Chouinard) ABSTRACT: Ice scouring poses a significant threat to underwater pipelines for offshore oil production facilities in ice-infested waters. For most locations, the only options against this hazard are to protect the pipeline by trenching, burial, or creative alignment. The optimal burial depths along the length of a pipeline are usually selected on the basis of a hazard model that describes the recurrence rate and severity of scouring along its length. Although sufficient data at a specific site are rarely available to accurately estimate the hazard model, several thousand scours have been documented over extended regions and can provide an estimate of scouring hazards at preliminary stages of design. The main features of the proposed model are a parametrization of the scouring hazard model as a function of water depth and exposure to the ice environment, and the propagation of uncertainties due to model incompleteness and sample size. The proposed model can be validated or readjusted at later stages of the project as more site-specific data become avail- able. The application of the proposed model is demonstrated for the determination of the optimal burial depth for a hypothetical pipeline route. INTRODUCTION Many oil prospects in the Arctic are located in offshore waters, sometimes several kilometers from the coastline. This location requires the design and construction of pipelines, sometimes tens of kilometers long, and can rep- resent a significant obstacle both technically and financially. The main source of hazards is scouring from ice ridges or rubble fields. Protective measures against scouring include burial, multiple branching systems, and regularly spaced closing mechanisms, as well as careful alignment. A preliminary step in the selection and design of these protective measures is the estimation of risks of ice scouring. A model is presented for the estimation of scouring hazards expressed in the form of a recurrence rate of scour exceeding given depths. Such a model can then be used to determine the optimal burial depth of a pipeline for a given return period. Scours in the Arctic have been recorded in water depths up to 60 m. However, this upper limit is not well defined and these features may be relict scours that have no relation to the present ice regime. Ice scours as deep as 5.4 m have been measured in the Beaufort Sea, with intense scouring in water depths between 15 and 40 m corresponding to the ice shear zone. Data in the Beaufort Sea off the coast of Canada consist of approximately 66,000 scour records (scour length, width, orientation, form, morphology, etc.) as measured from side-scan sonar data, and 24,000 records (scour depth and bathymetry) as measured from echo-sounder or high-resolution profiler data. Limited repetitive mapping (3000 scours for the Beaufort Sea off the coast of Canada) has also been conducted over the last few years in order to estimate the age of scours, scouring rates, and infill thickness (Shearer 1988). I Asst. Prof., Dept. of Civ. Engrg. and Appl. Mech., McGill Univ., 817 Sherbrooke St. West, Montreal, Quebec, Canada, H3A 2K6. Note. Editor: John P. Dempsey. Discussion open until May 1, 1996. To extend the closing date one month, a written request must be filed with the ASCE Manager of Journals. The manuscript for this paper was submitted for review and possible publication on February 10, 1995. This paper is part of the Journal of Cold Regions Engineering, Vol. 9, No.4, December, 1995. ©ASCE, ISSN 0887-381X/95/0004- 0167-0182/$2.00 + $.25 per page. Paper No. 10093. JOURNAL OF COLD REGIONS ENGINEERING / DECEMBER 1995/167 Journal of Cold Regions Engineering 1995.9:167-182. Downloaded from ascelibrary.org by The University of Queensland Library on 05/07/13. Copyright ASCE. For personal use only; all rights reserved.

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ESTIMATION OF BURIAL DEPTHS FOR PIPELINES IN ARCTIC REGIONS

By Luc E. Chouinard'

ABSTRACT: Ice scouring poses a significant threat to underwater pipelines for offshore oil production facilities in ice-infestcd waters. For most locations, the only options against this hazard are to protect the pipeline by trenching, burial, or creative alignment. The optimal burial depths along the length of a pipeline are usually selected on the basis of a hazard model that describes the recurrence rate and severity of scouring along its length. Although sufficient data at a specific site are rarely available to accurately estimate the hazard model, several thousand scours

scouring hazards at preliminary stages of design. The main features of the proposed have been documented over extended regions and can provide an estimate of

depth and exposure to the ice environment, and the propagation of uncertainties model are a parametrization of the scouring hazard model as a function of water

due to model incompleteness and sample size. The proposed model can be validated or readjusted at later stages of the project as more site-specific data become avail-

of the optimal burial depth for a hypothetical pipeline route. able. The application of the proposed model is demonstrated for the determination

INTRODUCTION

Many oil prospects in the Arctic are located in offshore waters, sometimes several kilometers from the coastline. This location requires the design and construction of pipelines, sometimes tens of kilometers long, and can rep- resent a significant obstacle both technically and financially. The main source of hazards is scouring from ice ridges or rubble fields. Protective measures against scouring include burial, multiple branching systems, and regularly spaced closing mechanisms, as well as careful alignment. A preliminary step in the selection and design of these protective measures is the estimation of risks of ice scouring. A model is presented for the estimation of scouring hazards expressed in the form of a recurrence rate of scour exceeding given depths. Such a model can then be used to determine the optimal burial depth of a pipeline for a given return period.

Scours in the Arctic have been recorded in water depths up to 60 m. However, this upper limit is not well defined and these features may be relict scours that have no relation to the present ice regime. Ice scours as deep as 5.4 m have been measured in the Beaufort Sea, with intense scouring in water depths between 15 and 40 m corresponding to the ice shear zone. Data in the Beaufort Sea off the coast of Canada consist of approximately 66,000 scour records (scour length, width, orientation, form, morphology, etc.) as measured from side-scan sonar data, and 24,000 records (scour depth and bathymetry) as measured from echo-sounder or high-resolution profiler data. Limited repetitive mapping (3000 scours for the Beaufort Sea off the coast of Canada) has also been conducted over the last few years in order to estimate the age of scours, scouring rates, and infill thickness (Shearer 1988).

'Asst. Prof., Dept. of Civ. Engrg. and Appl. Mech., McGill Univ., 817 Sherbrooke St. West, Montreal, Quebec, Canada, H3A 2K6.

Note. Editor: John P. Dempsey. Discussion open until May 1, 1996. To extend the closing date one month, a written request must be filed with the ASCE Manager of Journals. The manuscript for this paper was submitted for review and possible publication on February 10, 1995. This paper is part of the Journal of CoM Regions Engineering, Vol. 9, No. 4, December, 1995. OASCE, ISSN 0887-381)3/95/0004- 0167-0182/$2.00 + $.25 per page. Paper No. 10093.

JOURNAL OF COLD REGIONS ENGINEERING / DECEMBER 1995 / 167

ESTIMATION OF BURIAL DEPTHS FOR PIPELINES IN

ARCTIC REGIONS

By Luc E. Chouinard)

ABSTRACT: Ice scouring poses a significant threat to underwater pipelines foroffshore oil production facilities in ice-infested waters. For most locations, the onlyoptions against this hazard are to protect the pipeline by trenching, burial, orcreative alignment. The optimal burial depths along the length of a pipeline areusually selected on the basis of a hazard model that describes the recurrence rateand severity of scouring along its length. Although sufficient data at a specific siteare rarely available to accurately estimate the hazard model, several thousand scourshave been documented over extended regions and can provide an estimate ofscouring hazards at preliminary stages of design. The main features of the proposedmodel are a parametrization of the scouring hazard model as a function of waterdepth and exposure to the ice environment, and the propagation of uncertaintiesdue to model incompleteness and sample size. The proposed model can be validatedor readjusted at later stages of the project as more site-specific data become avail­able. The application of the proposed model is demonstrated for the determinationof the optimal burial depth for a hypothetical pipeline route.

INTRODUCTION

Many oil prospects in the Arctic are located in offshore waters, sometimesseveral kilometers from the coastline. This location requires the design andconstruction of pipelines, sometimes tens of kilometers long, and can rep­resent a significant obstacle both technically and financially. The main sourceof hazards is scouring from ice ridges or rubble fields. Protective measuresagainst scouring include burial, multiple branching systems, and regularlyspaced closing mechanisms, as well as careful alignment. A preliminary stepin the selection and design of these protective measures is the estimationof risks of ice scouring. A model is presented for the estimation of scouringhazards expressed in the form of a recurrence rate of scour exceeding givendepths. Such a model can then be used to determine the optimal burialdepth of a pipeline for a given return period.

Scours in the Arctic have been recorded in water depths up to 60 m.However, this upper limit is not well defined and these features may berelict scours that have no relation to the present ice regime. Ice scours asdeep as 5.4 m have been measured in the Beaufort Sea, with intense scouringin water depths between 15 and 40 m corresponding to the ice shear zone.Data in the Beaufort Sea off the coast of Canada consist of approximately66,000 scour records (scour length, width, orientation, form, morphology,etc.) as measured from side-scan sonar data, and 24,000 records (scour depthand bathymetry) as measured from echo-sounder or high-resolution profilerdata. Limited repetitive mapping (3000 scours for the Beaufort Sea off thecoast of Canada) has also been conducted over the last few years in orderto estimate the age of scours, scouring rates, and infill thickness (Shearer1988).

I Asst. Prof., Dept. of Civ. Engrg. and Appl. Mech., McGill Univ., 817 SherbrookeSt. West, Montreal, Quebec, Canada, H3A 2K6.

Note. Editor: John P. Dempsey. Discussion open until May 1, 1996. To extendthe closing date one month, a written request must be filed with the ASCE Managerof Journals. The manuscript for this paper was submitted for review and possiblepublication on February 10, 1995. This paper is part of the Journal of Cold RegionsEngineering, Vol. 9, No.4, December, 1995. ©ASCE, ISSN 0887-381X/95/0004­0167-0182/$2.00 + $.25 per page. Paper No. 10093.

JOURNAL OF COLD REGIONS ENGINEERING / DECEMBER 1995/167

Journal of Cold Regions Engineering 1995.9:167-182.

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Several models have been proposed to estimate the optimal burial depth of pipelines (Comfort et al. 1990; Murray et al. 1990; Nessim 1986, 1988; Pilkington and Marcellus 1981; Wadhams 1983; Wang 1989; Weeks et al. 1983). These can be classified under two distinct classes: one is statistical in nature and requires some field investigations over several winters; the other is based on mechanistic models of ice gouging to calculate scour depths for given soil properties and ice environments. A site-specific statistical model is unbiased for properly defined estimators and a representatiave data set. Bias can be introduced if censoring or infilling of scours is present and not accounted for in the estimation. Bias can also be introduced when pooling scour data from regions representing different populations of scours. However, repetitive mapping is very expensive and requires several surveys in order to obtain a sample that is representative of the long-term trends required for design purposes. Accurate data is also difficult to obtain. There is controversy over a universally accepted definition of scour depth, and it is not always possible to accurately correct measurements to account for sedimentation (infilling). Finally, the soil types are typically broadly clas- sified during a survey as either sand, clay, or clayey sand, which makes it difficult to develop a correlation between scour depth, ice feature, and soil type. Most recent models are based on a statistical analysis of available seabed scour data. The models do not require any characterization of the scouring process and implicitly assume that all possible interaction scenarios are included in the database. Another difficulty that engineers have had is the reconciliation of the episodic nature of the scouring process with the assumption of a Poisson process (Nessim 1988). Repetitive surveys have shown that some regions of the seabed can go for years without any scours, and suddenly receive significant scouring in the space of a single season. The nature of the process can lead to nonconservative designs if based on a few repetitive surveys where none of these episodes occurred.

The mechanistic method relies on parameters such as statistics on ice features, ice and soil mechanical properties, the annual frequency of ice features, and an ice/soil/pipeline interaction model. Several difficulties can also arise in the application of a mechanistic approach. First, there is usually a lot of uncertainty with respect to soil properties at any particular location, and mechanical properties of the submerged portion of ice features. Second, there is a lot of uncertainty on the formulation of the model itself, and on the representative values to be used in the numerical simulation. The mech- anistic approach has the advantage that it can be used to investigate ice- soil interaction scenarios not present in the historic database, to estimate an upper limit on scour depth, to study the effect of soil types on scour depths, and to estimate subscour stresses associated with different ice fea- tures and soil conditions. A hybrid model obtained by combining the two approaches is optimal for most locations in the Arctic.

Several procedures can be used to improve scour depth estimates from a statistical model. Pooling of data is based on the premise that the sample of observations at a site can be increased by pooling data from regions where the gouging process (ice environment and seabed conditions) are similar. Pooling of data has been used by Weeks et al. (1983) and Lewis (1978) to estimate the parameters for the distribution of scour depths at different water depths, respectively, in the Beaufort Sea off the coasts of Canada and the United States.

An alternative procedure, which is used here, is based on a parametri- zation of the statistical model as a function of a set of predictors. The

168 / JOURNAL OF COLD REGIONS ENGINEERING / DECEMBER 1995

Several models have been proposed to estimate the optimal burial depthof pipelines (Comfort et al. 1990; Murray et al. 1990; Nessim 1986, 1988;Pilkington and Marcellus 1981; Wadhams 1983; Wang 1989; Weeks et al.1983). These can be classified under two distinct classes: one is statisticalin nature and requires some field investigations over several winters; theother is based on mechanistic models of ice gouging to calculate scour depthsfor given soil properties and ice environments. A site-specific statisticalmodel is unbiased for properly defined estimators and a representatiavedata set. Bias can be introduced if censoring or infilling of scours is presentand not accounted for in the estimation. Bias can also be introduced whenpooling scour data from regions representing different populations of scours.However, repetitive mapping is very expensive and requires several surveysin order to obtain a sample that is representative of the long-term trendsrequired for design purposes. Accurate data is also difficult to obtain. Thereis controversy over a universally accepted definition of scour depth, and itis not always possible to accurately correct measurements to account forsedimentation (infilling). Finally, the soil types are typically broadly clas­sified during a survey as either sand, clay, or clayey sand, which makes itdifficult to develop a correlation between scour depth, ice feature, and soiltype. Most recent models are based on a statistical analysis of availableseabed scour data. The models do not require any characterization of thescouring process and implicitly assume that all possible interaction scenariosare included in the database. Another difficulty that engineers have had isthe reconciliation of the episodic nature of the scouring process with theassumption of a Poisson process (Nessim 1988). Repetitive surveys haveshown that some regions of the seabed can go for years without any scours,and suddenly receive significant scouring in the space of a single season.The nature of the process can lead to nonconservative designs if based ona few repetitive surveys where none of these episodes occurred.

The mechanistic method relies on parameters such as statistics on icefeatures, ice and soil mechanical properties, the annual frequency of icefeatures, and an ice/soil/pipeline interaction model. Several difficulties canalso arise in the application of a mechanistic approach. First, there is usuallya lot of uncertainty with respect to soil properties at any particular location,and mechanical properties of the submerged portion of ice features. Second,there is a lot of uncertainty on the formulation of the model itself, and onthe representative values to be used in the numerical simulation. The mech­anistic approach has the advantage that it can be used to investigate ice­soil interaction scenarios not present in the historic database, to estimatean upper limit on scour depth, to study the effect of soil types on scourdepths, and to estimate subscour stresses associated with different ice fea­tures and soil conditions. A hybrid model obtained by combining the twoapproaches is optimal for most locations in the Arctic.

Several procedures can be used to improve scour depth estimates froma statistical model. Pooling of data is based on the premise that the sampleof observations at a site can be increased by pooling data from regions wherethe gouging process (ice environment and seabed conditions) are similar.Pooling of data has been used by Weeks et al. (1983) and Lewis (1978) toestimate the parameters for the distribution of scour depths at differentwater depths, respectively, in the Beaufort Sea off the coasts of Canada andthe United States.

An alternative procedure, which is used here, is based on a parametri­zation of the statistical model as a function of a set of predictors. The

168/ JOURNAL OF COLD REGIONS ENGINEERING / DECEMBER 1995

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procedure is based on a decomposition of the scouring process into its main components and on the identification of the main factors affecting the spatial variability of each component. The model consists of four elements: the probability distribution function for scour depths as a function of water depth, the annual probability of an ice incursion at a given location, an estimate of the rate of scouring as a function of water depth during a winter with ice incursions, and an estimate of the recurrence rate of scouring as a function of water depth during a winter with no ice incursion (i.e., the background rate of scouring). Ice incursions denote mainly incursions of multiyear ice (pack ice invasion), but may also include exposure to first- year ridges (Shearer 1991). In the following, each of the four elements of the model are reviewed, followed by an example for an offshore site in the Beaufort Sea. Note that this procedure addresses only the estimation of the probability distribution function of scour depths and does not consider haz- ards due to subscour stresses or distinguish between single and multiple keel features.

Water depth is one of the most important factors accounting for the spatial variation of scouring activity and of the probability distribution function of scour depths. Another important factor for the scouring rate is the exposure to pack invasions at a particular location. In general, depth of scouring and subscour stresses will also be greatly influenced by the sea-bottom soil type and strength (Shearer 1990; Dickins et al. 1991). Scours are thought to be rare in stronger soils; however, when they occur, the stresses transmitted to a pipeline will be much greater (Golder 1990). Unfortunately, there is very little information to quantify these variations at the present time, but these effects should be included in future developments of the model as more data become available. Note that the statistical database used in this study implicitly includes various combinations of ice and soil characteristics encountered across the Beaufort Sea.

DISTRIBUTION OF SCOUR DEPTHS

Different types of distributions (lognormal, negative exponential, and gamma) can be fitted to scour depth data depending on the region and water depth (Nessim 1988). For the purposes of this paper, only the negative exponential distributions will be discussed for illustrative purposes; however, the proposed procedure remains general and applicable with other types of distributions. Compilations of fitted negative exponential distribution func- tions to scour depth data can be found in Weeks et al. (1983), Lewis (1978), Shearer (1991), Barnes et al. (1978, 1982), and Marcellus and Roth (1991) for the Beaufort Sea off the coasts of the United States and Canada. In both cases, the distributions are fitted to scours grouped as a function of water depth (Fig. 1). The exponential distribution is completely specified by a single parameter, B , which has dimensions of m-l.

The variables that influence the distribution of scour depths are water depth, the type of ice feature (first-year ice or multiyear ice, single keel, multiple keel), the distribution of keel sizes (depth and width), the mag- nitude of the driving forces (free drift of individual floes versus a pack ice invasion), and the type of soil. Very rarely have all of these conditions been documented at the time of repetitive mapping. In actuality, most of the data collected historically were not from repetitive mapping, thus complicating the interpretation of the data given the impossibility of determining the age or infill for these scours. Nonetheless, it can be safely assumed that some processes affecting the scour depth distribution, such as keel depth distri-

JOURNAL OF COLD REGIONS ENGINEERING / DECEMBER 1995 / 169

procedure is based on a decomposition of the scouring process into its maincomponents and on the identification of the main factors affecting the spatialvariability of each component. The model consists of four elements: theprobability distribution function for scour depths as a function of waterdepth, the annual probability of an ice incursion at a given location, anestimate of the rate of scouring as a function of water depth during a winterwith ice incursions, and an estimate of the recurrence rate of scouring as afunction of water depth during a winter with no ice incursion (i.e., thebackground rate of scouring). Ice incursions denote mainly incursions ofmultiyear ice (pack ice invasion), but may also include exposure to first­year ridges (Shearer 1991). In the following, each of the four elements ofthe model are reviewed, followed by an example for an offshore site in theBeaufort Sea. Note that this procedure addresses only the estimation of theprobability distribution function of scour depths and does not consider haz­ards due to subscour stresses or distinguish between single and multiple keelfeatures.

Water depth is one of the most important factors accounting for the spatialvariation of scouring activity and of the probability distribution function ofscour depths. Another important factor for the scouring rate is the exposureto pack invasions at a particular location. In general, depth of scouring andsubscour stresses will also be greatly influenced by the sea-bottom soil typeand strength (Shearer 1990; Dickins et al. 1991). Scours are thought to berare in stronger soils; however, when they occur, the stresses transmittedto a pipeline will be much greater (Golder 1990). Unfortunately, there isvery little information to quantify these variations at the present time, butthese effects should be included in future developments of the model asmore data become available. Note that the statistical database used in thisstudy implicitly includes various combinations of ice and soil characteristicsencountered across the Beaufort Sea.

DISTRIBUTION OF SCOUR DEPTHS

Different types of distributions (lognormal, negative exponential, andgamma) can be fitted to scour depth data depending on the region and waterdepth (Nessim 1988). For the purposes of this paper, only the negativeexponential distributions will be discussed for illustrative purposes; however,the proposed procedure remains general and applicable with other types ofdistributions. Compilations of fitted negative exponential distribution func­tions to scour depth data can be found in Weeks et al. (1983), Lewis (1978),Shearer (1991), Barnes et al. (1978, 1982), and Marcellus and Roth (1991)for the Beaufort Sea off the coasts of the United States and Canada. Inboth cases, the distributions are fitted to scours grouped as a function ofwater depth (Fig. 1). The exponential distribution is completely specifiedby a single parameter, B, which has dimensions of m- l.

The variables that influence the distribution of scour depths are waterdepth, the type of ice feature (first-year ice or multiyear ice, single keel,multiple keel), the distribution of keel sizes (depth and width), the mag­nitude of the driving forces (free drift of individual floes versus a pack iceinvasion), and the type of soil. Very rarely have all of these conditions beendocumented at the time of repetitive mapping. In actuality, most of the datacollected historically were not from repetitive mapping, thus complicatingthe interpretation of the data given the impossibility of determining the ageor infill for these scours. Nonetheless, it can be safely assumed that someprocesses affecting the scour depth distribution, such as keel depth distri-

JOURNAL OF COLD REGIONS ENGINEERING / DECEMBER 1995/169

Journal of Cold Regions Engineering 1995.9:167-182.

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e Shearer 1992

5 Marcellus and Roth (POAC 1992)

FIG. 1. Parameter of Exponential Probability Distribution Function for Gouge Depths as Function of Water Depth (Marcellus and Roth 1991)

butions, ice strength properties, and driving forces, are homogeneous over fairly large regions, justifying the pooling of survey information to obtain a single distribution for large regions. The latter appears to be validated when comparing distributions of scours depth for similar water depths at different sites across the Beaufort Sea off Canada (Shearer 1991) (Fig. 2). In the latter case, the hypothesis that scour depths are from the same distribution could not be rejected for sites at similar water depths but with different degrees of exposure to ice incursions, and with different soil con- ditions.

Estimates of the parameters of scour depth distributions from different sources exhibit a lot of scatter (Fig. 1). Some scatter may be attributed to the variability in soil conditions for the different survey locations. This cannot, however, totally explain the apparent bias from one source to an- other. The main sources of bias may be related to different assumptions used in deriving the data and in estimating the parameters of the probability distribution function. The first relates to the definition of the scour depth and the second relates to the existence of upper and lower bounds on the values of the observations. This issue is most critical for shallow water depths

170 /JOURNAL OF COLD REGIONS ENGINEERING / DECEMBER 1995

_8

g

•\\\\. Weeks et.al. (1983)\ Alaskan Beaufort Sea

!. \/'5 \g • "\z \.~ 4 , Lewis (1977). Canadian.':E ~,e.;.. '{leaufortSea

~ "'-~!'. ." . E[BJffi ........ "-I-, \~ -:» .., "-

2 l'e ~"-- ...... _. _E~ + o[B],... -c..... ..._

E[B].~o+--r--.--.--,--,-...,..--r-r~~--,--,--,,....,r-'

o 10 20 3'0 40 50 60 70

WATER DEPTH (m)

• Shearer 1992

+ Marcellus and Roth (POAC 1992)

FIG. 1. Parameter of Exponential Probability Distribution Function for Gouge Depthsas Function of Water Depth (Marcellus and Roth 1991)

butions, ice strength properties, and driving forces, are homogeneous overfairly large regions, justifying the pooling of survey information to obtaina single distribution for large regions. The latter appears to be validatedwhen comparing distributions of scours depth for similar water depths atdifferent sites across the Beaufort Sea off Canada (Shearer 1991) (Fig. 2).In the latter case, the hypothesis that scour depths are from the samedistribution could not be rejected for sites at similar water depths but withdifferent degrees of exposure to ice incursions, and with different soil con­ditions.

Estimates of the parameters of scour depth distributions from differentsources exhibit a lot of scatter (Fig. 1). Some scatter may be attributed tothe variability in soil conditions for the different survey locations. Thiscannot, however, totally explain the apparent bias from one source to an­other. The main sources of bias may be related to different assumptionsused in deriving the data and in estimating the parameters of the probabilitydistribution function. The first relates to the definition of the scour depthand the second relates to the existence of upper and lower bounds on thevalues of the observations. This issue is most critical for shallow water depths

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Journal of Cold Regions Engineering 1995.9:167-182.

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1

1.4

1.2.

1.0

0.8

0.6

0.4

0.2

0.0

0.1 0.3 0.5 0.7 0.9 1.1 1.3 1.5 1.7 1.9 2.1 2.3

FIG. 2. Scour Depth I ada (Shearer 1991)

Is

0.90

B /B* 0.60

tribution fol

Scout-Depth(m)

r Different Sites across Beaufort Sea off Can-

‘** Luc pLmc!cr ’ B = estimated paramctf

FIG. 3. Effect of Lower Truncation of Estimate of Parameter of Exponential Prob- ability Distribution Function

JOURNAL OF COLD REGIONS ENGINEERING / DECEMBER 1995 / 171

Torsiut-Nektorolik ~1979-1981.22-25 mjTorsiut-Nektorolik 1979-1981.25-28 mTorsiut-Nektorolik 1983-1984.22-25 mPullen (1974-1978,14-18 mlPullen (1 978-1984, 14-18 mMinuk (1983-1984. 14-17 m)Atkinson !'984-1986. 13-15 mjAtkinson 1984-1986,15-20 mAtkinson 1984-1986,20-25 mKoubvik (1983-1984, 18-21 m)

--····0···._..- ..···fr··- -._ .--~_.

--9--.....+.....~

0.2

1.6

1.4

1.2

1.0

a 0.8~-

0.6

0.4

0.0L.-'----'t...-.___i____'___..L--'--l..~...L..__'_...I__'__...l__"'__.l..._........J__'___i____'___..L_J

0.1 0.3 0.5 0.7 0.9 1.1 1.3 1.5 1.7 1.9 2.1 2.3

Scour Depth (m)

FIG. 2. Scour Depth Distribution for Different Sites across Beaufort Sea off Can­ada (Shearer 1991)

1.80 2.00

I I I IB* = true parameter

B = estimated parameter0.90--H~,*-+--+----t--t---+-":""'-+---t--+--

1.00

0.60-l---l--\+~~--4:--"c-l-~I-----:.l--<'=~+---l--+--

0.70 +--~r\--\-+--\-----+<c--+~--1I--+----+--+---l---

0.50 -!---j---f.:...;....---'-f-----'-----'--f----j---'-----f--I---+----t------,0.00 0.20 0.40 0.80 0.80 LOa 1.20 1.40

B/B* 0.80

FIG. 3. Effect of Lower Truncation of Estimate of Parameter of Exponential Prob­ability Distribution Function

JOURNAL OF COLD REGIONS ENGINEERING / DECEMBER 1995 / 171

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10.00 - I

B no lower truncation

10

FIG. 4. Effect of Upper Truncation of Estimate of Parameter of Exponential Prob- ability Distribution Function

where the scatter is greatest, and the estimates are most sensitive to these two limits. The distribution of scour depths is important in shallow waters due to the long distances usually involved and problems associated with shore crossing for the pipeline. Lower truncations are artifical and occur due to limitations in the resolution of the surveying instruments, and upper truncation limits are due to physical limitations associated with the maximum ice feature that can reach given water depths and the strength of the surface deposits. Figs. 3 and 4 illustrate, respectively, the effect of neglecting lower and upper bounds on the parameter of an exponential distribution function fitted to scour depth data. The effect of neglecting a lower truncation limit results in an underestimation of the distribution parameter. For example, in water depths of 10 m, assuming that the true distribution parameter ( B * ) is equal to 2.1 m- and that the lower truncation is equal to 0.2 m, neglecting the lower truncation results in an estimate equal to 80% of the true value. The effect of the lower truncation decreases for smaller values of the true distribution parameter; for a true parameter equal to 0.5 and a lower trun- cation of 0.2, the estimate is equal to 90% of the true value. The effect of neglecting an upper-bound limit on scour depth can lead to an overesti- mation of the parameter of the distribution. Fig. 4 indicates that the effect is probably negligible for water depths between 10 and 40 m, considering that for the specified range of water depths, the upper limit of scour depths is greater than 3 m for most soils. For shallow waters (< lo m), the effect of an upper limit on scour depths is only significant when the upper limit is below 1.5 m. Data from Lewis (1978) suggest that the parameter for scour depth distribution in 15 m water depth is between 2 and 3.5 m-' (or average scour depth of 0.33-0.5 m), and data from Weeks et al. (1983) suggest

172 /JOURNAL OF COLD REGIONS ENGINEERING / DECEMBER 1995

10.00.---~----,--~--,---~-----,-----------~

B no lower truncation

8.00 +--+--+----+--f--+----+----+---I---+---+---IB* =true parameter

B =estimated parameter

6.00 +--a+----+--f---+---+---j'---+----+---+----l

<.00~~,1------l---+--+---+--,------+---l--+---1B*=2.0

,~- ------ --- ---- -----' --------2.00L-L-~~t~;§....~.._..i..~..::~.::.::~.::::~.:.::~::::~.::::~.::.:~::.:.=..:::.~..::.:~::::f..:.~..~.....f.....~_...~......~...§~

B*=lA

0.00 I .. I Upper truncation point (m)

0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00 4.50 5.00

FIG. 4. Effect of Upper Truncation of Estimate of Parameter of Exponential Prob­ability Distribution Function

where the scatter is greatest, and the estimates are most sensitive to thesetwo limits. The distribution of scour depths is important in shallow watersdue to the long distances usually involved and problems associated withshore crossing for the pipeline. Lower truncations are artifical and occurdue to limitations in the resolution of the surveying instruments, and uppertruncation limits are due to physical limitations associated with the maximumice feature that can reach given water depths and the strength of the surfacedeposits. Figs. 3 and 4 illustrate, respectively, the effect of neglecting lowerand upper bounds on the parameter of an exponential distribution functionfitted to scour depth data. The effect of neglecting a lower truncation limitresults in an underestimation of the distribution parameter. For example,in water depths of 10 m, assuming that the true distribution parameter (B*)is equal to 2.1 m-[ and that the lower truncation is equal to 0.2 m, neglectingthe lower truncation results in an estimate equal to 80% of the true value.The effect of the lower truncation decreases for smaller values of the truedistribution parameter; for a true parameter equal to 0.5 and a lower trun­cation of 0.2, the estimate is equal to 90% of the true value. The effect ofneglecting an upper-bound limit on scour depth can lead to an overesti­mation of the parameter of the distribution. Fig. 4 indicates that the effectis probably negligible for water depths between 10 and 40 m, consideringthat for the specified range of water depths, the upper limit of scour depthsis greater than 3 m for most soils. For shallow waters «10 m), the effectof an upper limit on scour depths is only significant when the upper limitis below 1.5 m. Data from Lewis (1978) suggest that the parameter for scourdepth distribution in 15 m water depth is between 2 and 3.5 m -[ (or averagescour depth of 0.33-0.5 m), and data from Weeks et al. (1983) suggest

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values close to 5 m-l. Marcellus and Roth (1991) revised the data collected by Weeks et al. (1983) with a definition of scour consistent with Canadian practice, and obtained estimates in the range of 3.0 m-l. Estimates of the parameters of the scour depth distribution should consider an upper-bound or maximum scour depth as a function of water depth in different soils due to physical limitations (i.e. available driving force, grounding of large ridges in deeper water, etc.) and a lower truncation or censoring corresponding to the resolution of the measuring devices.

To account for the scatter in scour data and the factors not explicitly included in the model, a doubly stochastic model is proposed for the scour depth distribution. In this model, scour depth is assumed to be exponentially distributed, and the uncertainty in the parameter of the exponential distri- bution is modelled as a normally distributed random variable with mean value E[Blwater depth] and standard deviation a[BI water depth]. The es- timate of the standard deviation is obtained from an analysis of the residuals of the parameters after accounting for water depth effects.

For preliminary design, it is assumed that the distribution of Fig. 1 is representative of general conditions in the Beaufort Sea. Information on local sea-bottom conditions is rarely available at the preliminary stage of an offshore project and available data seem to indicate that site effects due to different types of soils may be secondary with respect to water depth effects. Any variability arising from these secondary sources is assumed to be included in the standard deviation a[B I depth] assigned to the distribution parameters for scour depth. More accurate estimates may be obtained by parametrizing the distribution parameters as a function of these variables as more data become available.

RATE OF SCOURING

In the Beaufort Sea off Canada about 3,000 of the reported scours are from repetitive surveys, as compared with approximately 66,000 undated or old scours. The traditional approach used to model the process of scouring in time and space is to assume that it follows a Poisson process (Nessim 1988; Weeks et al. 1983). However, this hypothesis appears to be invalid given that scouring events are episodic. Repetitive surveys have shown that some regions of the seabed can go for years without any scours, and suddenly undergo significant scouring in the space of a single season. This nature of the process can lead to very unconservative designs if based on a sample of a few repetitive surveys where none of these episodes have occurred. In consequence, small sampling surveys in space or time can lead to inaccurate estimates.

A review of available data on scouring rates reveals large variations in the observed recurrence rate as a function of water depth, as well as a function of geographical location (Shearer 1992). In the proposed model, it is assumed that the primary sources of spatial variability in the rate of scouring are the relative mobility of the winter ice cover and water depth. In shallow waters, fast ice prevents ice movement during the winter and few first-year or multiyear ice ridges are present. Most of the scouring events occur during the summer breakup and are caused by drifting ice floes. These will generally cause only superficial or shallow scours due to the relatively small mass of the floes and weaker driving forces. As water depth increases, the mobility of the winter ice cover and ice ridging activity both increase, especially in the shear zone. The average size and frequency of ridges and available driving forces increases which accounts for large rates of scouring

JOURNAL OF COLD REGIONS ENGINEERING / DECEMBER 1995 / 173

values close to 5 m -1. Marcellus and Roth (1991) revised the data collectedby Weeks et al. (1983) with a definition of scour consistent with Canadianpractice, and obtained estimates in the range of 3.0 m -1. Estimates of theparameters of the scour depth distribution should consider an upper-boundor maximum scour depth as a function of water depth in different soils dueto physical limitations (i.e. available driving force, grounding of large ridgesin deeper water, etc.) and a lower truncation or censoring correspondingto the resolution of the measuring devices.

To account for the scatter in scour data and the factors not explicitlyincluded in the model, a doubly stochastic model is proposed for the scourdepth distribution. In this model, scour depth is assumed to be exponentiallydistributed, and the uncertainty in the parameter of the exponential distri­bution is modelled as a normally distributed random variable with meanvalue E[Blwater depth] and standard deviation a[B Iwater depth]. The es­timate of the standard deviation is obtained from an analysis of the residualsof the parameters after accounting for water depth effects.

For preliminary design, it is assumed that the distribution of Fig. 1 isrepresentative of general conditions in the Beaufort Sea. Information onlocal sea-bottom conditions is rarely available at the preliminary stage ofan offshore project and available data seem to indicate that site effects dueto different types of soils may be secondary with respect to water deptheffects. Any variability arising from these secondary sources is assumed tobe included in the standard deviation a[B Idepth] assigned to the distributionparameters for scour depth. More accurate estimates may be obtained byparametrizing the distribution parameters as a function of these variablesas more data become available.

RATE OF SCOURING

In the Beaufort Sea off Canada about 3,000 of the reported scours arefrom repetitive surveys, as compared with approximately 66,000 undatedor old scours. The traditional approach used to model the process of scouringin time and space is to assume that it follows a Poisson process (Nessim1988; Weeks et al. 1983). However, this hypothesis appears to be invalidgiven that scouring events are episodic. Repetitive surveys have shown thatsome regions of the seabed can go for years without any scours, and suddenlyundergo significant scouring in the space of a single season. This nature ofthe process can lead to very unconservative designs if based on a sample ofa few repetitive surveys where none of these episodes have occurred. Inconsequence, small sampling surveys in space or time can lead to inaccurateestimates.

A review of available data on scouring rates reveals large variations inthe observed recurrence rate as a function of water depth, as well as afunction of geographical location (Shearer 1992). In the proposed model,it is assumed that the primary sources of spatial variability in the rate ofscouring are the relative mobility of the winter ice cover and water depth.In shallow waters, fast ice prevents ice movement during the winter andfew first-year or multiyear ice ridges are present. Most of the scouring eventsoccur during the summer breakup and are caused by drifting ice floes. Thesewill generally cause only superficial or shallow scours due to the relativelysmall mass of the floes and weaker driving forces. As water depth increases,the mobility of the winter ice cover and ice ridging activity both increase,especially in the shear zone. The average size and frequency of ridges andavailable driving forces increases which accounts for large rates of scouring

JOURNAL OF COLD REGIONS ENGINEERING / DECEMBER 1995/173

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2.00

1.80

1.80

i.40

F: 1.20

1.00 ,h 0.80 E

?5 aa 0.60

L

c 5 0.40

g 0.20 V

L 8 .-0.00

0, -0.20 %

al L v

-.I -0.40

-0.60

-0.80

-1.00 0.00 5.00 10.00 15.00 20.00 25.00 30.00 35.00 40.00 45.00 51 00

water depth (m)

FIG. 5. Recurrence Rate of Scours as Function of Water Depth (Shearer 1991)

and more severe scours (Figs. 1 and 5). As water depth increases even further, fewer ridges are large enough to ground and the scouring rate gradually decreases to zero.

Shearer (1992) presents data on scouring rates as a function of water depth for the Beaufort Sea (Fig. 5). The scouring rates were obtained from repetitive line surveys at different locations across the Beaufort Sea (in- cluding the Yukon shelf) and over different periods of time. A careful review of the original data set indicates that it can be divided into two groups. The first group consists of observations following winters when there was almost no ice movement, most of the scouring having occurred during breakup and the summer season. The rate of scouring associated with these years is denoted as the background rate (Ahack) in Fig. 5. The second population of observations follows winters during which there was significant movement of the ice cover or ice invasions. The rate of scouring associated with these years is denoted as the ice invasion rate (Ainv) (Fig. 5 ) and is approximately one order of magnitude greater than the breakground rate. There is a lot of uncertainty on the estimates of these rates and their relevance to any specific location. This uncertainty is modelled by assuming that the rate of scouring is a random variable that is lognormally distributed with the pa- rameters (mean value and standard deviation) indicated in Fig. 5. The recurrence rates are expressed in a logarithmic scale and a set of three curves is shown for each of the two regimes. In each, the middle curve corresponds to the expected value of the logarithm of the recurrence rate

174 /JOURNAL OF COLD REGIONS ENGINEERING / DECEMBER 1995

E[loglo""'.l + o(logloAmv1

IE[I~l'...... -."L 1/ I I

E[logloAmv1 - a[Iog1oAmv1 _

/ ......... V // "/ /~ ;'- \/ , /\

/'./ \ ;

~ - ,~

/ 1/V ....... ..", : ~I' \

'J '/ ...... •1/ y/ ,/ 'i. 1\ \ \ \J r.l' /' \

/jv/ / ~ \ \ ~./ V E[logl~ .... f1 \

~f// I I '/ '1" .\ ,\ 1\v E[logl~ - a[Iog1~ / - \ \ \ \I I I V

I E[logl~ + o(logl~\ \ ' \\\I ," I I

,\ \\\'!'

2.00

1.80

1.60

i.40

,-. 1.20'i:'~~ 1.00~E 0.80~'-"

0.60~-~... 0.40~Colc

0.20~......= ·-0.00Col~...'-" -0.20eemoS -0.40

-0.60

-0.80

-1.000.00 5.00 10.00 15.00 20.00 25.00 30.00 35.00 40.00 45.00 50.00

water depth (m)

FIG. 5. Recurrence Rate of Scours as Function of Water Depth (Shearer 1991)

and more severe scours (Figs. 1 and 5). As water depth increases evenfurther, fewer ridges are large enough to ground and the scouring rategradually decreases to zero.

Shearer (1992) presents data on scouring rates as a function of waterdepth for the Beaufort Sea (Fig. 5). The scouring rates were obtained fromrepetitive line surveys at different locations across the Beaufort Sea (in­cluding the Yukon shelf) and over different periods of time. A careful reviewof the original data set indicates that it can be divided into two groups. Thefirst group consists of observations following winters when there was almostno ice movement, most of the scouring having occurred during breakup andthe summer season. The rate of scouring associated with these years isdenoted as the background rate (Aback) in Fig. 5. The second population ofobservations follows winters during which there was significant movementof the ice cover or ice invasions. The rate of scouring associated with theseyears is denoted as the ice invasion rate (Ainv) (Fig. 5) and is approximatelyone order of magnitude greater than the breakground rate. There is a lotof uncertainty on the estimates of these rates and their relevance to anyspecific location. This uncertainty is modelled by assuming that the rate ofscouring is a random variable that is lognormally distributed with the pa­rameters (mean value and standard deviation) indicated in Fig. 5. Therecurrence rates are expressed in a logarithmic scale and a set of threecurves is shown for each of the two regimes. In each, the middle curvecorresponds to the expected value of the logarithm of the recurrence rate

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and the two accompanying curves represent the same curve plus or minus one standard deviation. The spatial variability in the observed scouring rate is assumed to be mainly related to the variation in the mobility of the winter ice cover, which affects the relative contribution of the background and invasion rates given that ice pack characteristics are fairly uniform across the Arctic. As more site-specific data becomes available, these estimates can be refined by including additional site-specific effects besides water depth and the relative frequency of pack ice invasions. The last element in the model is the site-specific annual probability of ice invasions (pin"). In the present formulation, this is the only factor that contributes to the spatial variation of scouring hazards for a given water depth. The mean annual rate of scouring is then

h(d, x) = h(d1bac-k. [1 - p i n v V ) I + h(d)rnv.pinv(x) (1)

where d = water depth; and R = spatial coordinates of a given location. Note that the background and invasion rates are associated with mutually exclusive events in this expression.

COMPUTATION OF SCOURING HAZARDS

The scouring hazard function is defined as the rate of occurrence of scours with depth greater than D' at a given location 2 (Murray et al. 1990; Green et al. 1983; Pilkington and Marcellus 1981),

where X(d, X) = rate of scouring at water depth d . Uncertainties on the distribution parameters of scour depth, the recurrence rate of scouring, and the annual probability of an ice invasion are propagated into the estimates of the hazard function by assuming that the three random variables are mutually independent for a given water depth.

DESIGN BURIAL DEPTHS

Design burial depths are obtained for a specified return period. Several strategies can be used for selecting the burial depth along different segments of the pipeline. For example, the rate of failure may be allowed to be higher in regions that are easily accessible during the whole year. Assuming that the designer specifies that the rate of failure should be the same along the full length of the pipeline, burial depths are selected such that the expected rate of a damaging scour anywhere along the pipeline (assumed to be a scour that contacts the pipeline; subscour stresses are neglected) is equal to one occurrence during a period of T years. The design burial depths (Di) for a pipeline composed of N segments is such that

where T = return period; X,; = hazard function along segment i of the pipeline [(l)]; Di = design burial depth for segment i; Lj = length of segment i; and dj = average water depth for segment i. A burial strategy could be to select burial depths such that failure is equally likely along the length of the pipeline (Asj = A: for all i)

JOURNAL OF COLD REGIONS ENGINEERING / DECEMBER 1995 / 175

and the two accompanying curves represent the same curve plus or minusone standard deviation. The spatial variability in the observed scouring rateis assumed to be mainly related to the variation in the mobility of the winterice cover, which affects the relative contribution of the background andinvasion rates given that ice pack characteristics are fairly uniform acrossthe Arctic. As more site-specific data becomes available, these estimatescan be refined by including additional site-specific effects besides waterdepth and the relative frequency of pack ice invasions. The last element inthe model is the site-specific annual probability of ice invasions (Pinv)' Inthe present formulation, this is the only factor that contributes to the spatialvariation of scouring hazards for a given water depth. The mean annualrate of scouring is then

(1)

where d = water depth; and i = spatial coordinates of a given location.Note that the background and invasion rates are associated with mutuallyexclusive events in this expression.

COMPUTATION OF SCOURING HAZARDS

The scouring hazard function is defined as the rate of occurrence ofscours with depth greater than D' at a given location i (Murray et al. 1990;Green et al. 1983; Pilkington and Marcellus 1981),

As[D > D'ld, x] = A(d, x)'P[D > D'ld] (2)

where "A(d, x) = rate of scouring at water depth d. Uncertainties on thedistribution parameters of scour depth, the recurrence rate of scouring, andthe annual probability of an ice invasion are propagated into the estimatesof the hazard function by assuming that the three random variables aremutually independent for a given water depth.

DESIGN BURIAL DEPTHS

Design burial depths are obtained for a specified return period. Severalstrategies can be used for selecting the burial depth along different segmentsof the pipeline. For example, the rate of failure may be allowed to be higherin regions that are easily accessible during the whole year. Assuming thatthe designer specifies that the rate of failure should be the same along thefull length of the pipeline, burial depths are selected such that the expectedrate of a damaging scour anywhere along the pipeline (assumed to be ascour that contacts the pipeline; subscour stresses are neglected) is equalto one occurrence during a period of T years. The design burial depths (Di )

for a pipeline composed of N segments is such that

(3)

where T = return period; "ASi = hazard function along segment i of thepipeline [(1)]; Di = design burial depth for segment i; L i = length of segmenti; and di = average water depth for segment i. A burial strategy could beto select burial depths such that failure is equally likely along the length ofthe pipeline ("Asi = "A: for all i)

JOURNAL OF COLD REGIONS ENGINEERING / DECEMBER 1995 / 175

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- fl .2? -

Y

s-

b

- E

x-

-

rm

Y

b

Nb

0

iD

Nv

lv

lv

l

00

00

00

00

00

9

93

11

NN

NN

N

00

00

00

00

00

00

00

00

00

00

N

NN

NN

NN

NN

N

wwwwwwwwww

176 /JOU

RN

AL OF C

OLD

RE

GIO

NS

EN

GIN

EE

RIN

G / D

EC

EM

BE

R 1995

ai-c...oC:IIZ:>ro"T1()orCl:IIm(j)

ozUlmz(j)

Zmm:IIZ(j)-Clm()ms::Olm:II

~01

TABLE 1. Parameters for Discretized Pipeline Route

Mean waterL depth Distribution B aa Elln A;nv) Elln AbaCk)

Segment (km) (m) type (m- 1 ) (m- 1 ) (number/km/yr) alln A;nv) (number/km/yr) alln Aback)(1 ) (2) (3) (4) (5) (6) (7) (8) (9) (10)

1 3.16 3.05 E 3.5 0.20 -0.35 0.05 -0.48 0.022 3.16 6.1 E 3.3 0.20 -0.25 0.07 -0.40 0.043 3.16 12.2 E 2.9 0.20 0.3 0.18 0.02 0.104 3.16 18.3 E 2.5 0.20 0.77 0.2 0.32 0.15 3.16 22.9 E 2.25 0.20 0.93 0.2 0.28 0.166 3.16 27.4 E 2.05 0.20 0.65 0.3 -0.1 0.27 3.16 28.4 E 2.0 0.20 0.54 0.3 -0.2 0.228 3.16 29.9 E 1.9 0.20 0.27 0.3 -0.4 0.259 3.16 31.1 E 1.8 0.20 0.10 0.29 -0.58 0.25

10 1.58 32.9 E 1.75 0.20 -0.16 0.27 -0.83 0.25

Note: aB = standard deviation on the estimates of B; E[ln Ainv] = logarithm (base 10) of the recurrence rate of scouring during ice invasions(expected value); a[ln Ainv ] = standard deviation on the logarithm (base 10) of the recurrence rate of scouring during ice invasions; E[ln Ahack] =logarithm (base 10) of the background recurrence rate of scouring (expected value); and a[ln Aback] = standard deviation on the logarithm (base 10)of the background recurrence rate of scouring.

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Scour depth (m)

Scow depth (m)

FIG. 6. Scouring Hazards for Each Segment of Pipeline

JOURNAL OF COLD REGIONS ENGINEERING / DECEMBER 1995 / 177

-6.00. 0

0.00

-0.50

-1.00

~ -1.50"..i' -2.00

g-2.50

.!I".. -3.00flI:~ -3.50..=u..

-4.00.:.coi.5! -4.50

-5.00

-5.50

~ 5 (~l E[logl~

~ 6~

~"" 7.~~~1/ 8,.~~/''\

.~ ',,~~"~ "3 ~~ . ~ .

"\f'-.

""~~

1~2 ~ ~~~

"~ " '4 ~Pipeline segment 1

'\ '" "" """"'\ ""'.""", "".00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00 4.50 ~ o

Scour depth (m)

~(b) E[loglO"J·0[I0g10.1.]

~~~ 6

~~~J

~7

~~~ l0... 1--8

~ I~V,

"\k\,,~

~~3,

~ /,10

'2 '" ~~'-\

I . "\f\ "" '"~~Pipeline segment - 1 \\ 4-

'" .""-~ '" """\"" ~.

-6.000.00 0.50 1.00 1.50 2.00 2.50 3.00 3.\l0 4.00 4.5Il 5.00

0.00

-0.50

~-1.00

".. -1.50

f -2.00:!..!I -2.50"..fl

-3.00I:......2 -3.50

.:.coi -4.00

.5!-4.50

-5.00

-5.50

Scour depth (m)

FIG. 6. Scouring Hazards for Each Segment of Pipeline

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Scorn depth (m)

FIG. 6. (Continued)

1 - = h, Li = h,L, (4) T r = l

N

where L , = total length of the pipeline; A: = As(Di(di), for all segments i = 1 , n; and Di = design burial depth for segment i.

APPLICATION

The following example illustrates the application of the model to an offshore site in the Beaufort Sea. The pipeline route is discretized into 10 segments with the characteristics listed in Table 1. The parameters for the scour depth distribution and the rate of scouring were obtained respectively from Figs. 1 and 5. The annual probability of an ice invasion was estimated as 0.20 (one year out of five on average). Estimates for the expected hazard function and its uncertainty for each of the 10 segments of the pipeline are shown in Fig. 6 . Design burial depths are obtained for four return periods: 10,20,50, and 100 yr and equal probabilities of damaging scours anywhere along the pipeline. Fig. 7 shows the estimates of the burial depths as a function of water depth for the four return periods. A damaging scour is defined as an ice scour that actually contacts the pipeline. These burial depths need to be adjusted to account for the type of soil and subscour stresses. Fig. 7 shows that for a given return period, burial depths increase steadily with water depth up to a depth of 23 m, and then decrease due to the smaller rate of scouring. Uncertainty on design burial depths increases both with water depth and the return period.

178 I JOURNAL OF COLD REGIONS ENGINEERING / DECEMBER 1995

, ". ... .. ..

~5 I (t) I E[logloAJ + o(IogloAJ6

~~~l~ ~~~\ 9

'\~ ~~~

~ "",-'~~.~ '3 ~~.,

'\~'I .."'\ "~>~.~ !!o... ..

Pi' "'1" ""i"'.~

peline segment· '\.'\

'" "'"~"" ~'\~. f"'\.'\'"-6.00

0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00 4.,50 5.00

Scour depth (m)

FIG. 6. (Continued)

-4.00

-4.50

-3.00

-2.50

-3.50

-2.00

~... -1.50

t~

~Ij

-5.50

O.OD

-5.00

-1.00

-0.50

1T

N

~s 2: L j = ~sLTi=l

(4)

where L T = total length of the pipeline; A~ = A,(D;ld;), for all segmentsi = 1, n; and D; = design burial depth for segment i.

APPLICATION

The following example illustrates the application of the model to anoffshore site in the Beaufort Sea. The pipeline route is discretized into 10segments with the characteristics listed in Table 1. The parameters for thescour depth distribution and the rate of scouring were obtained respectivelyfrom Figs. 1 and 5. The annual probability of an ice invasion was estimatedas 0.20 (one year out of five on average). Estimates for the expected hazardfunction and its uncertainty for each of the 10 segments of the pipeline areshown in Fig. 6. Design burial depths are obtained for four return periods:10, 20, 50, and 100 yr and equal probabilities of damaging scours anywherealong the pipeline. Fig. 7 shows the estimates of the burial depths as afunction of water depth for the four return periods. A damaging scour isdefined as an ice scour that actually contacts the pipeline. These burialdepths need to be adjusted to account for the type of soil and subscourstresses. Fig. 7 shows that for a given return period, burial depths increasesteadily with water depth up to a depth of 23 m, and then decrease due tothe smaller rate of scouring. Uncertainty on design burial depths increasesboth with water depth and the return period.

178/ JOURNAL OF COLD REGIONS ENGINEERING / DECEMBER 1995

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FIG.

00

A

E

WATER DEPTH (m)

7. Burial Depth as Function of Water Depth and Return Period

JOURNAL OF COLD REGIONS ENGINEERING I DECEMBER 1995 I179

-2.00

-3.00

-2.50

0.00

-0.50

-1.00

! -1.50

;!

-3.50

-4.00

-4.50

(a) RETURN PERIOD =10 YEARSI

, .

:::::: b--.. . E[D] + o[D]

~~J E[D]

.~li i[D]. olD] V~~l-/V

./

~

"" l/-.7"

-5.000.00 5.00 10.00 15.00 20.00 25.00 30.00 35.00

0.00

-0.50

-1.00

-1.50

! -2.00

t -2.50

~~ -3.00

"l -3.50

-4.00

-.4.50

(b) RETURN PERIOD =20 YEARS

..

~

:::::::~I

E[D]+o[D]

~~ )[D]

~~~-o{~]-~/

.~K .-/"/'

""'- ----/'

-5.000.00 5.00 10.00 15.00 20.00 25.00 30.00 35.00

WATER DEPTH (m)

FIG. 7. Burial Depth as Function of Water Depth and Return Period

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WATER DEPTH (m)

~

WATER D E m H ( m )

FIG. 7. (Continued)

180 / JOURNAL OF COLD REGIONS ENGINEERING / DECEMBER 1995

0.00

-3.00

-0.50

-1.00

-1.50

§~ -2.00

_ -2.50..J

~=-3.50

-4.00

-4.50

(c) RETURN PERIOD =50 YEARS

::::::~.~+f]

~ . EJD]

M I~ E[D] - o{D]

"-~~ ./...-/

~~ --./""- -/-

-5.000.00 5.00 10.00 15.00 20.00 25.00 30.00 35,

WATER DEPTH (m)

. (d) RETURN PERIOD =100 YEARS

--........--:::::~ E[D]+ o{D]

~~ /E[D]/'

~«~]-O{D]/

"Y< ""-... ---'

.......... /'

'" '- ----'

'"I"-- /

-5.000.00 5.00 10.00 15.00 20.00 25.00 30.00 35.00

WATERDEPTH(m)

0.00

-0.50

-1.00

~-1.50

E-2.00

~Q -2.50..J

~ -3.00

=-3.50

-4.00

-4.50

FIG. 7. (Continued)

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CONCLUSION

Site-specific data on ice scouring is very sparse for most locations in ice- infested water. The current practice to obtain preliminary estimates of scour- ing hazards is to use data that have been compiled over very large regions. To obtain more accurate estimates, a model is proposed that accounts for spatial variability by identifying the most important factors that can affect the rate and severity of scouring. In addition, uncertainty is propagated through the model to obtain an estimate of the uncertainty on the burial depths. It is assumed that the main factors controlling the spatial variability of scouring hazards are the water depth and the annual probability of an ice pack invasion. The next step in the formulation of the model is to include other major contributing factors (i.e., soil type, coastline effects, etc.) for the spatial variation of the rate and severity of scouring in order to decrease the uncertainty of design burial depths.

ACKNOWLEDGMENTS

The writer would like to acknowledge S. Blasco of the Geological Survey of Canada for providing data and contract reports on scouring in the Beau- fort Sea off Canada, and J. Allender and R. Sisodyia of Chevron Petroleum Technology Company for some thoughtful comments and the permission to publish these results. The writer would also like to acknowledge the National Science and Engineering Research Council of Canada for its financial sup- port through an operating grant.

APPENDIX 1. REFERENCES

Barnes, P. W., McDowell, D., and Reimnitz, E. (1978). “Ice gouging characteristics: their changing patterns from 1975-1977, Beaufort Sea, Alaska.” USGS Open File Rep., 78-730, U.S. Geological Survey (USGS), Menlo Park, Calif.

Barnes, P. W., Reimnitz, E., and Rearic, D. M. (1982). “Ice gouging characteristics related to sea-ice zonation, Beaufort Sea, Alaska.” Proc., Nut. Res. Council of Canada’s Ice Scour Workshop, Montebello, Quebec, Canada, 185-219.

Chouinard, L. E. (1993). “Design burial depth for pipelines in the U.S. Beaufort Sea.” Proc., Conf. on Port and Oc. Engrg. under Arctic Conditions.

Comfort, G . , Gilbert, G. , and Ferregut, C. (1990). “Analysis of subscour stresses and probability of ice scour induced damage for buried pipelines.” Volume I . data base of key ice scour parameters.” Contractor Rep. submitted by Fleet Technology Ltd. and Canadian Seabed Research Ltd. , Canada Oil and Gas Lands Admin., Energy, Mines and Resour. Indian and Northern Affairs, Ottawa, Ontario, Can- ada.

Dickins, D. F., et al. (1991). “The ice environment affecting the distribution of new scours in the Canadian Beaufort Sea.” Rep., Atlantic Geoscience Centre, Bedford Institute of Oceanography, Dartmouth, Nova Scotia, Canada.

Golder Associates Ltd. (1990). “Analysis of subscour stresses and probability of ice scour-induced damage for burial submarine pipelines. Vol. 11. deterministic model of ice-soil-pipe interaction.” Rep., Canada Oil and Gas Lands Admin., Energy, Mines and Resour. Indian and Northern Affairs, Ottawa, Ontario, Canada.

Green, H. P., Reddy, A. S. , and Chari, T. R. (1983). “Iceberg scouring and pipeline burial depth.” Proc., POAC ’83, 7th Int. Conf. on Port and Oc. Engrg. under Arctic Conditions, Vol. 1, 280-288.

Lewis, C. F. M. (1978). “The frequency and magnitude of drift ice groundings from ice scour tracks in the Canadian Beaufort Sea.” Proc., 4th Int. Conf. on Port and Oc. Engrg. under Arctic Conditions, D. B. Muggridge, ed., Memorial Univ., St- John’s, Newfoundland, Canada, Vol. 1 , 568-579.

Marcellus, R. W., and Roth, D. R. (1991). “Comparison of Canadian and Alaskan

JOURNAL OF COLD REGIONS ENGINEERING / DECEMBER 1995 / 181

CONCLUSION

Site-specific data on ice scouring is very sparse for most locations in ice­infested water. The current practice to obtain preliminary estimates of scour­ing hazards is to use data that have been compiled over very large regions.To obtain more accurate estimates, a model is proposed that accounts forspatial variability by identifying the most important factors that can affectthe rate and severity of scouring. In addition, uncertainty is propagatedthrough the model to obtain an estimate of the uncertainty on the burialdepths. It is assumed that the main factors controlling the spatial variabilityof scouring hazards are the water depth and the annual probability of anice pack invasion. The next step in the formulation of the model is to includeother major contributing factors (i.e., soil type, coastline effects, etc.) forthe spatial variation of the rate and severity of scouring in order to decreasethe uncertainty of design burial depths.

ACKNOWLEDGMENTS

The writer would like to acknowledge S. Blasco of the Geological Surveyof Canada for providing data and contract reports on scouring in the Beau­fort Sea off Canada, and J. Allender and R. Sisodyia of Chevron PetroleumTechnology Company for some thoughtful comments and the permission topublish these results. The writer would also like to acknowledge the NationalScience and Engineering Research Council of Canada for its financial sup­port through an operating grant.

APPENDIX I. REFERENCES

Barnes, P. W., McDowell, D., and Reimnitz, E. (1978). "lee gouging characteristics:their changing patterns from 1975-1977, Beaufort Sea, Alaska." USGS Open FileRep., 78-730, U.S. Geological Survey (USGS), Menlo Park, Calif.

Barnes, P. W., Reimnitz, E., and Rearic, D. M. (1982). "Ice gouging characteristicsrelated to sea-ice zonation, Beaufort Sea, Alaska." Proc., Nat. Res. Council ofCanada's lee Scour Workshop, Montebello, Quebec, Canada, 185-219.

Chouinard, L. E. (1993). "Design burial depth for pipelines in the U.S. BeaufortSea." Proc., Conf. on Port and Dc. Engrg. under Arctic Conditions.

Comfort, G., Gilbert, G., and Ferregut, C. (1990). "Analysis of subscour stressesand probability of ice scour induced damage for buried pipelines." Volume I. database of key ice scour parameters." Contractor Rep. submitted by Fleet TechnologyLtd. and Canadian Seabed Research Ltd., Canada Oil and Gas Lands Admin.,Energy, Mines and Resour. Indian and Northern Affairs, Ottawa, Ontario, Can­ada.

Dickins, D. F., et al. (1991). "The ice environment affecting the distribution of newscours in the Canadian Beaufort Sea." Rep. , Atlantic Geoscience Centre, BedfordInstitute of Oceanography, Dartmouth, Nova Scotia, Canada.

Golder Associates Ltd. (1990). "Analysis of subscour stresses and probability of icescour- induced damage for burial submarine pipelines. Vol. II. deterministic modelof ice-soil-pipe interaction." Rep., Canada Oil and Gas Lands Admin., Energy,Mines and Resour. Indian and Northern Affairs, Ottawa, Ontario, Canada.

Green, H. P., Reddy, A. S., and Chari, T. R. (1983). "Iceberg scouring and pipelineburial depth." Proc-, POAC '83, 7th Int. Conf. on Port and Oc. Engrg. underArctic Conditions, Vol. 1,280-288.

Lewis, C. F. M. (1978). "The frequency and magnitude of drift ice groundings fromice scour tracks in the Canadian Beaufort Sea." Proc., 4th Int. Conf. on Port andDc. Engrg. under Arctic Conditions, D. B. Muggridge, ed., Memorial Univ., St­John's, Newfoundland, Canada, Vol. 1,568-579.

Marcellus, R. W., and Roth, D. R. (1991). "Comparison of Canadian and Alaskan

JOURNAL OF COLD REGIONS ENGINEERING / DECEMBER 1995/181

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Beaufort Sea ice scour depth data and analysis methodologies.” Proc., 11th Conf. on Port and Oc. Engrg under Arctic Conditions, St-John’s, Canada, 1004-1016.

Murray, A, , Ferregut, C., and Ritch, R. (1990). “Analysis of subscour stresses and probability of ice scour-induced damage for buried submarine pipelines, volume 111: probabilistic modelling.” Rep. Prepared by Fleet Technology Limited for the Panel for Energy Res. and Devel. (PERD), Canada Oil and Gas Lands Admin., Energy, Mines and Resour. Indian and Northern Affairs, Ontario, Canada.

Nessim, M. A. (1988). “Statistical data analysis of new scour characteristics in the Beaufort Sea.” Contractor Rep. Submitted by Det Norske Veritas (Canada) Ltd. , Geological Survey of Canada, Dartmouth, Nova Scotia, Canada.

Nessim, M. A. (1986). “Pilot study to examine ice scour statistics for the Canadian Beaufort continental shelf.” Contractor Rep. Submitted by Det Norske Veritas (Canada) Ltd. , Geological Survey of Canada, Dartmouth, Nova Scotia, Canada.

Pilkington, G. R., and Marcellus, R. W. (1981). “Methods of determining pipeline trench depths in the Canadian Beaufort Sea.” Proc., Sixth Znt. Conf. on Port and Oc. Engrg. under Arctic Conditions, Volume 2 , 674-687.

Shearer, J. (1990). “Regional correlation of extreme scour depths with environmental factors for the Canadian Beaufort continental shelf.” Rep., Geological Survey of Canada, Dartmouth, Nova Scotia.

Shearer, J . (1991). “Observed rescouring rates by sea-ice pressure ridge keels on the Canadian Beaufort Shelf.” Draft Rep. Prepared for the Atlantic Geoscience Centre, Geological Survey of Canada, Dartmouth, Nova Scotia.

Wadhams, P. (1983). “The prediction of extreme keel depths from sea ice profile.” Cold Region Sci. and Technol., Amsterdam, The Netherlands, 6(3), 257-266.

Wang, A. T. (1989). “Numerical simulations for rare ice gouge depths.” Cold Regions Sci. and Technol., Amsterdam, The Netherlands, 19, 19-32.

Weeks, W. F., Barnes, P. W., Rearic, D. M., and Reimnitz, E. (1983). “Statistical aspects of ice gouging on the Alaskan Shelf of the Beaufort Sea.” CREEL Rep. 83-21, Hanover, N.H.

APPENDIX II. NOTATION

The following symbols are used in this paper:

= parameter for exponential probability distribution function; = scour depth (m); = expectation; = probability density function for scour depth; = length of pipeline segment (km); = number of pipeline segments; = probability of ice invasion; = return period; = background of scouring (events/year/km); = invasion rate of scouring (events/year/km); = hazard function (eventdyear); and = standard deviation.

182 /JOURNAL OF COLD REGIONS ENGINEERING / DECEMBER 1995

Beaufort Sea ice scour depth data and analysis methodologies." Proc., 11th Conf.on Port and Oc. Engrg under Arctic Conditions, St-John's, Canada, 1004-1016.

Murray, A., Ferregut, C., and Ritch, R. (1990). "Analysis of subscour stresses andprobability of ice scour-induced damage for buried submarine pipelines, volumeIII: probabilistic modelling." Rep. Prepared by Fleet Technology Limited for thePanel for Energy Res. and Devel. (PERD), Canada Oil and Gas Lands Admin.,Energy, Mines and Resour. Indian and Northern Affairs, Ontario, Canada.

Nessim, M. A. (1988). "Statistical data analysis of new scour characteristics in theBeaufort Sea." Contractor Rep. Submitted by Det Norske Veritas (Canada) Ltd.,Geological Survey of Canada, Dartmouth, Nova Scotia, Canada.

Nessim, M. A. (1986). "Pilot study to examine ice scour statistics for the CanadianBeaufort continental shelf." Contractor Rep. Submitted by Det Norske Veritas(Canada) Ltd., Geological Survey of Canada, Dartmouth, Nova Scotia, Canada.

Pilkington, G. R., and Marcellus, R. W. (1981). "Methods of determining pipelinetrench depths in the Canadian Beaufort Sea." Proc., Sixth Int. Conf. on Port andOc. Engrg. under Arctic Conditions, Volume 2,674-687.

Shearer, J. (1990). "Regional correlation of extreme scour depths with environmentalfactors for the Canadian Beaufort continental shelf." Rep., Geological Survey ofCanada, Dartmouth, Nova Scotia.

Shearer, J. (1991). "Observed rescouring rates by sea-ice pressure ridge keels onthe Canadian Beaufort Shelf." Draft Rep. Prepared for the Atlantic GeoscienceCentre, Geological Survey of Canada, Dartmouth, Nova Scotia.

Wadhams, P. (1983). "The prediction of extreme keel depths from sea ice profile."Cold Region Sci. and Technol., Amsterdam, The Netherlands, 6(3), 257-266.

Wang, A. T. (1989). "Numerical simulations for rare ice gouge depths." Cold RegionsSci. and Technol., Amsterdam, The Netherlands, 19, 19-32.

Weeks, W. F., Barnes, P. W., Rearic, D. M., and Reimnitz, E. (1983). "Statisticalaspects of ice gouging on the Alaskan Shelf of the Beaufort Sea." CREEL Rep.83-21, Hanover, N.H.

APPENDIX II. NOTATION

The following symbols are used in this paper:

BD

E( ]f[)(d)

LN

Piny

TAhack

Ainv

As(J

parameter for exponential probability distribution function;scour depth (m);expectation;probability density function for scour depth;length of pipeline segment (km);number of pipeline segments;probability of ice invasion;return period;background of scouring (events/year/km);invasion rate of scouring (events/year/km);hazard function (events/year); andstandard deviation.

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