Quantitative risk analysis for linear infrastructure supported by permafrost : methodology and computer program

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© Heather Brooks, 2019

Quantitative Risk Analysis for Linear Infrastructure

Supported by Permafrost: Methodology and Computer

Program

Thèse

Heather Brooks

Doctorat en génie civil

Philosophiæ doctor (Ph. D.)

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Quantitative Risk Analysis of Linear

Infrastructure Supported by Permafrost:

Methodology and Computer program

Thesis

Heather Margaret Brooks

Under the direction of:

Guy Doré, Ph.D., P.ing. Ariane Locat, Ph.D.

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RÉSUMÉ

Le pergélisol est omniprésent dans l’Arctique et l’Antarctique, et il est présent en haute altitude partout dans le monde. Les communautés et le développement industriel des régions pergélisolées ont besoin d’infrastructures de transport (routes, aéroports, chemins de fer, etc.), sachant que le transport y revêt une importance vitale au niveau social, économique et politique (Regehr, Milligan et Alfaro 2013). Toutefois, les changements climatiques auront des répercussions sur les infrastructures de transport existantes et futures en Alaska de l’ordre de 282 à 550 M$ (2015 USD), selon les scénarios d’émissions (Melvin et al. 2016). Vu ces conditions, des outils sont nécessaires pour aider les décideurs à prioriser l’entretien, le remplacement et la construction des infrastructures, et potentiellement justifier l’utilisation des stratégies de mitigation pour les remblais sur pergélisol. Des méthodes d’analyse de risque peuvent être utilisées, mais leur application en ingénierie du pergélisol est actuellement limitée.

Le risque est un produit du hasard, de la conséquence et de la vulnérabilité pour chacun des dangers considérés. La probabilité et le coût de l’occurrence d’un danger sont respectivement un hasard et une conséquence, tandis que la vulnérabilité corrèle le dommage possible avec la conséquence. Comme il existe peu de données de défaillance pour les installations sur pergélisol, le risque doit être déterminé à l’aide des méthodes d’analyse de fiabilité (premier-ordre deuxième-moment ou simulations de Monte Carlo), qui intègrent les incertitudes des paramètres d’entrée pour déterminer la variabilité des résultats. Ces méthodes exigent la caractérisation de l’incertitude des variables aléatoires, ce qui peut être difficile en l’absence de données suffisantes, souvent plus que nécessaire dans la pratique actuelle. En outre, ces méthodes d’analyse de fiabilité exigent une fonction d’état limite pour que le danger soit analysé.

Les dangers communs qui affectent les remblais sur pergélisol incluent : le tassement, la fissuration, la rupture soudaine, le déplacement latéral du remblai, le drainage et l’accumulation d’eau en pied de remblai, et les glissements de la couche

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active. Parmi ces dangers, seuls quelques-uns ont des fonctions d’état limite déterminées ou qui peuvent être approfondies par l’auteure. Les dangers associés à ces fonctions d’état limite ou de hasard comprennent : les tassements totaux et différentiels au dégel, la formation d’arche par le positionnement de particules au-dessus de cavité, les glissements de la couche active, la rupture de la pente du ponceau et l’affaissement de la structure du ponceau.

Un programme a été créé sur le logiciel Excel pour calculer le risque des installations linéaires construites sur un remblai de pergélisol en utilisant les méthodes statistiques appliquées aux fonctions d’état limite afin de déterminer les dangers communs aux infrastructures sur pergélisol, ainsi que d'estimer les coûts directs de réparation et les facteurs d’échelle permettant de tenir compte des coûts indirects des dommages causés aux utilisateurs de l’infrastructure et aux communautés concernées. Les calculs des risques sont basés sur les propriétés géotechniques et l’incertitude climatique, telles que caractérisées par des fonctions de densité de probabilité, en utilisant les méthodes statistiques de simulations de Monte Carlo. Une analyse de la fragilité du réchauffement climatique permet de recalculer les dangers à partir des variations des températures de l’air. Les analyses répétées le long de l’infrastructure fournissent un profil de risque actuel ainsi qu'un profil tenant compte du réchauffement climatique. Le programme a servi à déterminer les dangers pour la route d’accès à l’aéroport de Salluit, et l'évaluation des dangers, des risques et de la rentabilité a été effectuée pour l’aéroport international d’Iqaluit.

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ABSTRACT

Permafrost is ubiquitous in the Arctic and Antarctic, and present in high elevation regions throughout the world. The communities and industrial development in permafrost regions require transportation infrastructures (roadways, airports, railways, etc.) and, in these regions, transportation is of vital social, economic, and political importance (Regehr, Milligan, and Alfaro 2013). However, warming climate conditions will endanger existing and future transportation infrastructure in Alaska to the tune of $282 to $550 million (2015 USD) depending on future emission scenarios (Melvin et al. 2016). Given these conditions, tools are required to aid decision-makers in prioritizing infrastructure maintenance, replacement, and construction, and potentially justifying the use of mitigation strategies of permafrost embankments. Risk analysis methods can be used but their existing application to permafrost engineering is limited.

Risk is a product of hazard, consequence and vulnerability for each of the dangers under consideration. The probability and costs of a danger’s occurrence is a hazard and the consequence, respectively, while vulnerability correlated the damage with the consequence. Since little failure data is available for permafrost infrastructure, the hazard must be determined from reliability analysis methods (First-Order Second-Moment or Monte Carlo Simulation), which aggregate the uncertainty of input parameters to determine the result’s variation. These methods require the characterization of random variable uncertainty, which can be difficult without sufficient data, often more than the current standard-of-practice. Additionally, the method requires a limit state function for the danger to be analyzed.

Common dangers effecting permafrost embankment infrastructure included: settlement, cracking, sudden collapse, lateral embankment spreading, drainage and ponding water, and active layer detachment landslides. Of these dangers, only a few have existing limit state functions or have limit state functions that can be developed by the author. The dangers with limit state functions or hazard functions include: total

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and differential thaw settlement, particle position bridging over voids, active layer detachment landslides, and culvert gradient and structural failure.

A Microsoft Excel-based program was created to calculate the risk for permafrost embankment linear infrastructure, using statistical methods applied to limit state functions to determine hazards for common permafrost dangers, estimated direct costs for the repair of a hazard’s occurrence, and scaling factors to account for the indirect costs of damage to the infrastructure’s users and connected communities. Hazard calculations are based on geotechnical property and climate uncertainty, as characterized by probability density functions, using Monte Carlo Simulation methods. A climate change fragility analysis recalculates the hazard with warming air temperatures. Repeated analyses along the infrastructure provide a risk profile of the infrastructure, now and with a warming climate. The program is used to determine hazard for the Airport Access Road in Salluit, and hazard, risk and cost/benefit assessments were conducted using this program for the Iqaluit International Airport.

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LIST OF FIGURES

Figure 1.1. Northern Hemisphere Permafrost Map ... 1 Figure 1.2. Schematic of an embankment over permafrost; thermally designed to

aggrade the permafrost into the embankment fill. ... 4 Figure 1.3. The Public Safety Canada process for developing a risk event scenario

(adapted from Figure 4 from Public Safety Canada 2011). ... 7 Figure 2.1. Photos of embankments experiencing settlement in permafrost regions:

thaw settlement on (A) Tasiujaq Airport Access Road, Northern Quebec, Canada (Photo by G. Doré) and (B) the Alaska Railroad, USA (Photo by T. Brooks). ... 20 Figure 2.2. Creep settlements of the Alaska Highway in the Takhini Valley (Figure

14 from Malenfant-Lepage (2015) and original photos from G. Doré). ... 22 Figure 2.3. Aerial Photo of Iqaluit Airport where thermal crack locations are green

(Photo from Figure 99 of Mathon-Dufour (2014) using satellite images from Worldview-1, August 19, 2008, all rights reserved)... 22 Figure 2.4. Photos of A) a small sinkhole present in at the shoulder of the

embankment of the Dempster Highway, YT from June 2014 (photo by the author) and B) surface distortion from an underlying sinkhole at the Inuvik Airport, NWT (Photo by R. Burns from

https://www.flickr.com/photos/leoalaska/10416454796, all rights reserved). .. 24 Figure 2.5. Lateral embankment spreading mechanics diagram. ... 26 Figure 2.6. Longitudinal cracking due to lateral embankment spreading on the

Alaska Highway embankment between Beaver Creek, YT and Haines

Junction, YT during the summer of 2014 (Photo by the author). ... 27 Figure 2.7. Graphical representation of culvert structural collapse due to pure pipe

bending. Note that at the margin of safety limit S equals dTS. ... 30 Figure 2.8. Photo of the Salluit 2005 active layer detachment landslide (Photo from

Figure 1 in Boucher et al. (2012)). ... 32 Figure 2.9. Aerial photo from the 2007 Anaktuvuk River fire, North Slope of Alaska

(Photo from the Alaska Fire Service, Rosen (2017)). ... 33 Figure 2.10. Photo of a frozen debris lobe (outlined in yellow) approaching the

Dalton Highway, Alaska (Photo by Todd Paris from

(Photo from https://nsidc.org/cryosphere/glaciers/gallery/rock.html )... 34 Figure 2.12. Photo of a retrogressive thaw slump in northwest Alaska on the

Selawik River (Photo by Kenji Yoshikawa, University of Alaska Fairbanks from Williams and Ferrigno (2012), Chapter A-5, Figure 27, all rights reserved). ... 34 Figure 2.13. Fault tree of dangers to embankment-supported linear permafrost

infrastructure. Note the dangers in bold can be included in a quantitative

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Figure 2.14. Insulation placement during construction of a roadway embankment along the Qinghai-Tibet Railway, China (photo from Professor F. Niu). ... 39 Figure 2.15. High albedo surface treatment (3 types) for a test section in Salluit,

Northern Quebec, Canada (Photo from G. Doré). ... 40 Figure 2.16. Air convection embankments (ACE) along the embankment shoulder

of (A) Thompson Dr. in Fairbanks, AK, USA (Photo by G. Doré) and (B) the Beaver Creek Test Section, YT, Canada (Photo by the author). ... 41 Figure 2.17. Heat drain under construction in the Salluit Airport Access Road,

Northern Quebec, Canada (Photo by G. Doré). ... 42 Figure 2.18. Air ducts used within embankments placed to take advantage of (A)

chimney effects at the Beaver Creek Test Section, Alaska Highway, YT (Photo by G. Doré) and (B) prevailing wind direction along the Qinghai-Tibet Railway, China (Photo by F. Niu). ... 42 Figure 2.19. Thermosyphons used along the Qinghai-Tibet Railway, China (Photo

from F. Niu). ... 44 Figure 2.20. Placement and construction of geotextiles (A), and the exposed

geotextiles on test section side slopes along the Inuvik-Tuktoyaktuk Hwy (Photos by De Guzman from De Guzman et al. (2016) as Figure 2). ... 45 Figure 2.21. Sun-sheds constructed at (A) Beaver Creek Test Section, Alaska

Highway, YT, Canada, and (B) Qinghai-Tibet Railway, China (Photo from F. Niu). ... 46 Figure 3.1. Examples of F-N diagrams as presented in Lacasse, Nadim and Høeg

(2012) from other authors, where (A) shows general risk curves for dangers, and (B) defines the different risk analysis regions. ... 53 Figure 3.2. Semivariogram (G) example for various lag distances (A-F), assuming

an isotropic soil state. Note, point color is the same for each lag distance figure (A-F) and the semivariogram (G), and the number of data pairs (N) is noted for each lag. ... 63 Figure 4.1. Outline of hazard calculation with user inputs in orange, statistical steps

in gray, engineering calculations in green and outputs in teal. Note Ave and SD signify the average and standard deviation of the random variable input parameters. ... 78 Figure 4.2. Outline of consequence calculation with user inputs in orange,

calculations in gray, outputs of other calculations in blue, and outputs in teal. ... 79 Figure 4.3. Outline of the climate fragility assessment where increases in mean

annual air temperature (MAAT) are used to determine the changing hazard and risk. ... 79 Figure 4.4. Average (solid lines) and variation (dashed lines ±3 standard

deviations) of the soil layers in an Iqaluit borehole are shown for (A)

gravimetric moisture content and (B) dry density. The overall depth-weighted averages and their variation, for the Stefan Equation analysis, are shown in

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black. Note the soil profile consists of asphalt layers (dark gray), fill layers (light gray), clean sand layers (dark brown), and silty sand (light brown). ... 81 Figure 4.5. Comparison of normalized probability density function results for Stefan

and Modified Berggren Equations and First-Order Second-Moment (FOSM) and Monte Carlo Simulation (MCS) methods. ... 84 Figure 4.6. Selection process for soil property random variables for each soil layer

within a soil profile of L layers in a single Monte Carlo simulation. Note: the choice of the normal or lognormal probability density function for gravimetric moisture content is up to the user. ... 86 Figure 4.7. Dry density value selection process to ensure values do not exceed

saturated conditions given the other selected properties. ... 87 Figure 4.8. Selection of all random variable values for a single Monte Carlo

simulation. ... 88 Figure 4.9. Schematic of the values chosen for Monte Carlo simulations 1 to j with

the Excel program. Note: all the values selected within a simulation are used in evaluating the outputs of the simulation (e.g. the simulation’s thaw depth, thaw settlement, danger limit state functions, etc.). ... 88 Figure 4.10. Comparison of program used parameter values (histogram in blue)

and input parameter probability density functions (black line). Normal

distributions were used for all parameters except for moisture content where a lognormal distribution was used. Note, two soils, sand (A) and silt (B), are presented for moisture content and dry density. ... 90 Figure 4.11. Thermal property histograms (orange and blue), and normal (solid

line) and lognormal (dashed line) probability density functions are presented for frozen and unfrozen thermal properties of two soils; sand (A) and silt (B). Note: Côté and Konrad’s (2005) method was used for the thermal conductivity calculations. ... 92 Figure 4.12. The calculation process to determine the estimated thaw settlement,

which outlines input parameters (white), intermediate calculations (orange) and output parameters (blue). ... 94 Figure 4.13. Graphical definition of the total thaw settlement hazard. ... 95 Figure 4.14. The user’s soil profile and the automatically generated ice wedge soil

profile. ... 96 Figure 4.15. Ice wedge trough and wavelength of surface distortion. ... 97 Figure 4.16. Distortion amplitude, speed and wavelength chart for 30%

roadway/tire adherence for front and rear vehicle axles (redrawn from Fradette (2005)). ... 97 Figure 4.17. Thaw depth (left) and settlement (right) result variation with complete

and detail graphs on the upper and lower graphs, respectively. ... 99 Figure 4.18. The calculation process to determine the margin of safety for culvert

structural collapse, which outlines input parameters (white), intermediate calculations (orange) and output parameters (blue). ... 100

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Figure 4.19. Graphical definition of the margin of safety of culvert structural failure hazard. ... 100 Figure 4.20. Parametric study results for culvert gradient factors of safety. ... 101 Figure 4.21. The calculation process to determine the Factor of Safety for culvert

gradient failure, which outlines input parameters (white), user defined infrastructure limits (yellow), intermediate calculations (orange) and output parameters (blue). ... 101 Figure 4.22. Graphical definition of the hazard for a factor of safety (FS) limit state

function. ... 102 Figure 4.23. Parametric study results for the culvert gradient factor of safety. .... 102 Figure 4.24. The Active Layer Detachment Landslide (ALDS) calculation process

with input parameters (white), intermediate calculations (orange), and the output parameter (blue). ... 104 Figure 4.25. Active Layer Detachment Landslide (ALDS) factor of safety parametric study results. ... 105 Figure 4.26. Analysis of thaw settlement deviation from the analysis compared to

the number of MC simulations. Note: the colors denote various geological settings (A is alluvial, L is lacustrine, and GM, GM_IW and GM_IW-Insul are glaciomarine, glaciomarine ice wedge and insulated glaciomarine ice wedge profiles, respectively). ... 106 Figure 4.27. Analysis of hazard deviation from the analysis average compared to

the number of MC simulations. Note: IQA denotes an Iqaluit soil profile; SAL denotes a Salluit soil profile; TS, ALDS, CGF and CSF denote thaw

settlement, ALDS, and culvert gradient and structural failure dangers,

respectively; and, the final letters show geological settings as noted in Figure 4.26. ... 106 Figure 4.28. Surficial geology maps for (A) the Iqaluit International Airport (gray

outline) and (B) the Alaska Highway near Beaver Creek, YT. Note: for Iqaluit, the teal (GM), yellow (A) and purple (L) are glaciomarine, alluvial and

lacustrine deposits, respectively, and the dots are borehole locations from three investigations. Additionally, approximately 20 km of the Alaska Highway is presented in (B)... 117 Figure 4.29. Active layer thickness semivariogram from GPR data collected August

2010 along the centerline of the Iqaluit International Airport Runway with a linear regression from 1 to 40 m lags. ... 118 Figure 5.1. A) Aerial photo and B) subsurface ice map of Salluit, Nunavik, QC with

the location of analysis highlighted by the red circle. Note: dark blue, light blue and white areas are ice-rich, somewhat ice-rich and ice-poor permafrost

regions (Figure 2 from Périer et al. (2016)). ... 123 Figure 5.2. Simulation result histograms (blue, red) for thaw settlement, ALDS, and

culvert gradient and structural collapse with normal (orange) and lognormal (black) probability density functions. Passing simulations are in blue and simulations above the limit are red. Note: arrows and adjacent values denote

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the number of simulations above the graphs' limits; ALDS histograms are shown for each slope angle and have up to 150 simulations with values

greater than presented on the graphs. ... 128 Figure 5.3. Climate warming fragility assessment for total settlement (TS-Emb),

culvert structural (CFS-Emb) and gradient (CFG-Emb) failure and ALDS for the various slope angles. ... 129 Figure 5.4. Frost cracks (A: green), ice wedge fissures (A; red) and sinkhole (B)

locations at YFB. (Figures 99 (A) and 101 (B) from Mathon-Dufour (2014) using satellite images from Worldview-1, August 19, 2008, all rights reserved). ... 131 Figure 5.5. Borehole locations and surficial geology map for the Iqaluit airport: blue,

red and yellow boreholes note air track, chilled diamond core, and portable handheld drilling, respectively. Note: A (yellow) is the material of alluvial, GM (teal) is of glaciomarine, M (blue) is of marine, and L (purple) is of lacustrine origin and these are the primary geologic settings for the airport. ... 132 Figure 5.6. Historical Air Thawing Index (ATI) with an average (solid line) and ±3

standard deviations (dashed lines). ... 133 Figure 5.7. Historical thaw season duration (ts) with an average (solid line) and ±3

standard deviations (dashed lines). ... 133 Figure 5.8. Air Thawing Index (ATI) and thaw season duration (ts), as forecast

(2.5°C mean annual air temperature increase from 2010 to 2050) for the

climate fragility analysis. ... 134 Figure 5.9. Design profile for IRI and total settlement danger with a 3.5-cm

depression. ... 138 Figure 5.10. Climate fragility assessment hazard results. Note, TS and DS denote

the total and differential thaw settlement dangers, respectively, and A, L, G, GIW and GIW-In denote the alluvial, lacustrine, glaciomarine and glaciomarine with ice wedges and insulated glaciomarine with ice wedges, respectively. . 140 Figure 5.11. Cumulative thaw settlement results from the fragility assessment for

the alluvial (A), glaciomarine (G), glaciomarine with ice wedges (GIW), insulated glaciomarine with ice wedges (GIW In), and lacustrine (L) geologic settings. ... 140 Figure 5.12. Current and future risk results, in probable cost per a fissure in the

runway, from fragility assessment results. Note, TS and DS denote the total and differential thaw settlement dangers, respectively, and A, L, G, GIW and GIW-In denote the alluvial, lacustrine, glaciomarine and glaciomarine with ice wedges and insulated glaciomarine with ice wedges, respectively. ... 146 Figure 5.13. Present cost of repair through time from the climate fragility

assessment for the alluvial (A), glaciomarine (G), glaciomarine with ice wedges (GIW), insulated glaciomarine with ice wedges (GIW In), and

lacustrine (L) geologic settings. ... 147 Figure A.1. Thermal regions of permafrost, also known as the trumpet curve. .... 187

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Figure A.2. Examples of an ice-wedge (A) in a drainage ditch on the northern Alaska Highway and segregated ice (B) from a permafrost soil sample in

Glennallen, Alaska. ... 188

Figure A.3. Graphical description of the sinusoidal temperature model. ... 193

Figure A.4. Graphical description of the symmetry of the sinusoidal temperature model. ... 194

Figure B.1. Typical embankment section on permafrost. ... 198

Figure B.2. Schematic diagrams of an embankment with an underlying A) ice wedge, where degradation creates a void, and B) void due to a sinkhole. ... 199

Figure B.3. Typical bridges during testing, A) 5 mm material with 2 cm wedge, B) 10/5 mm material with 4 cm wedge, and C) 14 mm material with 6 cm wedge. Note the frosted area in the foreground is a drain carved in the Plexiglas box for ice wedge drainage. ... 201

Figure B.4. Occurrence (probability and observations) of bridging with bridging ratio: a logarithmic regression of the probability data is also presented with its accuracy. ... 202

Figure B.5. Schematic of flexural bridging over a sinkhole, assuming a pin and roller beam. ... 204

Figure B.6. Calculated bridge length (L) with a factor of safety of 1 for various soils and cover soil thicknesses (1.0, 0.5, and 0.2 m) for A, B and C, respectively. ... 205

Figure B.7. Beam loading (A), shear (B), and Moment (C) conditions for Case 1 and Case 2. ... 207

Figure B.8. Case 1 design chart for 1 (A), 2 (B) and 5 (C) ESAL point loads... 208

Figure B.9. Case 2 design chart without a point load for equivalent uniform loads to 4 (A), 2 (B) and 1 (C) meter thawed soil thicknesses. ... 209

Figure B.10. Case 2 design chart with a point load for 1 (A), 2 (B) and 5 (C) ESAL point loads and uniform loads equivalent to 1 (solid line) and 4 meter (dashed line) thawed soil thicknesses. ... 209

Figure C.1. The user’s soil profile and the automatically generated ice wedge soil profile. ... 214

Figure C.2. Input tab of Arquluk-RISK(SS) ... 216

Figure C.3. (SS) Program Setup Box ... 216

Figure C.4. (SS) Dangers to Analyze Box... 217

Figure C.5. (SS) Danger Limits Box ... 218

Figure C.6. (SS) Climate Conditions – Current and Model Box ... 218

Figure C.7. (SS) Other Analysis Inputs Box ... 219

Figure C.8. (SS) Text File Output Box ... 219

Figure C.9. (SS) Site Condition Variables Inputs ... 220

Figure C.10. (SS) Soil Profile Inputs for the embankment (A and B) and extra variables for the natural ground profile (C). ... 221

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Figure C.11. Inputs sheet for Arquluk-RISK(LI). ... 222

Figure C.12. (LI) Program Setup Box ... 223

Figure C.13. (LI) Dangers to Analyze and Infrastructure Analysis Data ... 224

Figure C.14. (LI) Indirect Consequences Box ... 224

Figure C.15. (LI) Hazard Analysis Limits and Climate Data in the Fragility Assessment ... 225

Figure C.16. (LI) Initial Section Sheet, and Shading for Hazard and Risk Reporting ... 225

Figure C.17. (LI) Climate Conditions Box... 226

Figure C.18. (LI) Section Direct Consequence Data ... 226

Figure C.19. (LI) Other Analysis Inputs ... 227

Figure C.20. (LI) Other Analysis Inputs 2 – Data for Next Section ... 227

Figure C.21. (LI) Site Condition Variables Inputs ... 228

Figure C.22. (LI) Soil Profile Inputs for the embankment (A and B) and extra variables for the natural ground profile (C). ... 229

Figure C.23. (LI) Current Climate Condition Hazard Result Reporting ... 230

Figure C.24. (LI) Fragility Assessment Hazard ... 230

Figure D.1. Arquluk-RISK(LI) hazard and risk calculation map showing the names of subroutines used in the program. Note: the colors of the boxes denote intermediate calculations (green), hazards (blue), consequence (yellow), outputs (orange) and risk (gray)... 231

Figure D.2. Arquluk-RISK(SS) Hazard calculation map showing the names of subroutines used in the program. Note: the colors of the boxes denote intermediate calculations (green), hazards (blue) and outputs (orange). ... 232

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LIST OF TABLES

Table 2.1. Summary of Published Permafrost Embankment Infrastructure Dangers

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Table 2.2. Location of Mitigation Methods for Full-Scale Implementation and Test Sections ... 38

Table 4.1. Climate and Stefan Analysis Soil Random Variables from the Iqaluit Airport Site. ... 82

Table 4.2. Equation References and Methodologies for Intermediate Thermal Property Calculations. ... 91

Table 4.3. Surface distortion wavelengths for safety and comfort limits at different speeds (translated from OCDE (1984) Table 3.1). ... 98

Table 4.4. Casualty Consequence Impact Factors (Ih)... 108

Table 4.5. Societal Consequence Impact Factors (Is) ... 108

Table 4.6. Multiplier for estimating a normally distributed standard deviation from a sample range. ... 114

Table 5.1. Salluit hazard analysis embankment soil profile. ... 126

Table 5.2. Salluit hazard analysis in-situ soil profile. ... 126

Table 5.3. Assumed culvert parameters for the Salluit culvert hazard analysis. .. 127

Table 5.4. Alluvial Geologic Setting Soil Profile ... 136

Table 5.5. Glaciomarine Geologic Setting Soil Profile ... 136

Table 5.6. Lacustrine Geologic Setting Soil Profile ... 137

Table 5.7. Hazard for the analyzed dangers. ... 138

Table 5.8. YFB Construction Areas ... 142

Table 5.9. YFB Construction Actions for Sections ... 143

Table A.1. Parameters for calculating thermal conductivity from Côté and Konrad (2005). ... 191

Table A.2. Thermal properties of non-soil embankment or permafrost materials. 192 Table B.1. Testing Matrix with average grain size, bridging ratios and the number of observations. ... 201

Table C.1. Danger Abbreviations ... 213

Table C.2. Differences between (SS) and (LI) Arquluk-RISK versions. ... 215

Table C.3. (SS) Program Setup Variable Values ... 216

Table C.4. (SS) Variables Output in Each Text File. ... 219

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GLOSSARY OF TERMS

Critical Infrastructure “An infrastructure is termed critical if its incapacity or destruction has a significant impact on health, safety, security, economics and social well-being” (Zio 2014)

Cumulative Probability Function

The function describing the integral of the probability density function, generally, resulting in the probability of occurrence of a value equal to or less than the value of interest (Baecher and Christian 2003a)

Danger

Natural phenomenon that could lead to damage (Lacasse and Nadim 2011) or a feature or situation which can negatively impact the life, health, property and environment of humans if an event or significant change occurs (Haeberli and Whiteman 2015)

Disaster A serious disruption of a community or society causing widespread loss exceeding the community’s or society’s ability to cope using its own resources (Lacasse and Nadim 2011) Exposure The circumstances of being exposed to a danger (Lacasse and _{Nadim 2011)} Failure Undesirable and unanticipated outcomes in or compromises to

the quality of the engineered system (Bea 2006)

Geohazard A geotechnical failure which represents a major threat to human life, constructed facilities, infrastructure and natural environment (Lacasse and Nadim 2011)

Hazard The probability that a danger occurs within a given period of _{time (Lacasse and Nadim 2011)} Population Statistics Average, standard deviation and other statistical properties generated over all possible observations (Ching and Phoon

2015) Probability Density

Function

A continuous mathematical function which models the

probability space of a random variable (Baecher and Christian 2003a)

Random Variable A variable that is uncertain where its value can be a range of _{probable values (Baecher and Christian 2003a)}

Reliability

The probability that a given level of quality will be achieved during the primary life-cycle activities associated with an engineered system (Bea 2006) or the probability that capacity exceeds demand (Whitman 2000)

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Measure of probability and severity of an adverse effect to life, health, property and/or environment; mathematically, the hazard times the potential worth of loss (consequences) of a dangers occurrence (Haeberli and Whiteman 2015; Lacasse and Nadim 2011)

Sample Statistics Average, standard deviation and other statistical properties generated from a finite number of measurements (Ching and Phoon 2015)

Vulnerability (Climate Change Definition)

“The degree to which a system is susceptible to, or unable to cope with, adverse effects of climate change… a function of the character, magnitude, and rate of climate variation to which a system is exposed, its severity and its adaptive capacity” (IPCC 2001 pg 995 as reported in Brooks (2003)); “the shortfall in the ability of public infrastructure to absorb the negative effects, and benefit from the positive effects, of changes in the climate conditions used to design and operate infrastructure”

(Nodelcorp Consulting, Inc. 2010) Vulnerability (Risk

Assessment Definition)

Degree of loss to a given element or set of elements within the area affected by the hazard (Lacasse and Nadim 2011) or an estimation of the extent and severity of damage due to a danger’s occurrence (Uddin and Ang 2011)

Vulnerability (Social Science Definition)

A measure of the factors determining the ability of the analyzed system to cope with the occurrence of dangers and their

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GLOSSARY OF ABBREVIATIONS AND SYMBOLS

A Convective heat transfer contact area, Alluvial geologic setting Ao Amplitude of the sinusoidal climate temperature model

ACE Air Convection Embankment

AD Air Ducts

AK Alaska

ALARP As Low As Reasonably Possible

ALD Active Layer Depth

ALDepth Active Layer Depth

ALDS Active Layer Detachment Landslides

AMAP Arctic Monitoring and Assessment Programme

ATI Air Thawing Index

ATIFA Air thawing index used in the climate fragility analysis

AVE Average of a parameter

b Permafrost creep parameter

B Width along the void

BR Bridging Ratio

C Consequence, Climate scenario

𝑐" _{Effective soil cohesion}

Cd Direct consequence

Cf Frozen heat capacity

ci Specific heat of ice

cs Specific heat of the soil solids

Ct Thawed heat capacity, total consequence cv coefficient of consolidation

cvw Volumetric heat capacity of water CALM Circumpolar Active Layer Monitoring CEN Centre for Norther Studies

CFSlimit Culvert ring strain at failure CGF Culvert Gradient Failure

cm centimeter

COV Coefficient of Variation

COVLSF Limit State Function Coefficient of Variation CSF Culvert Structural Failure

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xxiv CulLength Culvert length

CulSlope Current culver slope

CulSlopeMin Minimum allowable culvert slope CulThickness Culvert wall thickness

d soil layer thickness

D Culvert diameter, Damage

D50 Particle Size at 50% passing by weight

Dt, dthaw Thaw depth, thaw displacement in thaw strain tests DS Differential thaw settlement danger

𝐸[ ] Expected value

Emb Embankment Profile

ESAL Equivalent single axle load

EVR Earned Value Report

FHWA Federal Highway Administration

F-N Frequency-Number

FMEA Failure Mode and Effects Analysis FORM First-Order Reliability Method FOSM First-Order Second-Moment

FS Factor of Safety

FSCGF Culvert gradient failure factor of safety FSALDS Factor of safety for active layer detachment G Glaciomarine geologic setting

Gd Dry density

GCM Global Climate Model

GM Glaciomarine geologic setting GPR Ground Penetrating Radar

GR Geosynthetic Reinforcement

GSS Gentle Side Slopes

H Hazard, total beam thickness

h Vertical drop across a culvert’s length, semivariogram lag, distance _{from the edge to the neutral axis of the beam} hc beam thickness in compression

hmin Minimum vertical drop across a culvert’s length Ho Thaw strain sample height

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xxv ht beam thickness in tension

HAS High Albedo Surfacing

HD Heat Drain

Hwy highway

i Slope angle

Ih Casualty indirect consequence factor Is Social indirect consequence factor

Insul Insulation

IPCC International Panel on Climate Change

IQA Iqaluit

IRI International Roughness Index

IW Ice wedge

j # of user defined simulations kf Frozen thermal conductivity ks Soil particle thermal conductivity kt Thawed thermal conductivity

km Kilometer

L Soil’s latent heat, Culvert length, Loss if full damage occurs, _{Lacustrine geologic setting, # of layers in soil profile, beam length} Lf Latent heat of fusion of water

LES Lateral Embankment Spreading LRFD Load and Resistance Factor Design LSF Limit State Function

m meter

M beam moment

MAAT Mean Annual Air Temperature

MAATC Current mean annual air temperature

MAATEODL End-of-design-life mean annual air temperature

MAATFA Mean annual air temperature values used in climate fragility _analysis MAATStep step increase in MAAT

MB Manitoba

MCS Monte Carlo Simulation

MS Margin of Safety

MSTS Thaw settlement margin of safety

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xxvi

Nn Sample to population standard deviation correction factor

n n-factor, permafrost creep parameter, # of semivariogram data pairs, # of random variables, # of samples in a data set, Soil Water Characteristic Curve parameter, porosity

nc creep parameter in compression nt creep parameter in tension

NG Natural ground profile

NU Nunavut

NWT Northwest Territories

P applied point load

𝑃(𝐶) Climate scenario probability of occurrence 𝑃(𝐻|𝐶) Hazard conditional on the climate scenario 𝑃(𝐷|𝐻) Damage probability conditional upon the hazard 𝑃(𝐿|𝐷) Loss probability conditional upon the damage

PIEVC Public Infrastructure Engineering Vulnerability Committee

ppt parts per thousand

Q heat transferred via convection

QC Quebec

R Risk, culvert radius due to bending forces

RCI Riding Comfort Index

RCMP Royal Canadian Mounted Police

RSmax Maximum allowable culvert ring deflection

S Culvert deflection due to bending, soil saturation, beam section _modulus Sallowable Minimum allowable culvert gradient

Se effective soil saturation Sr residual saturation of the soil STS Culvert slope after thaw settlement

SAL Salluit

SD Standard deviation of a parameter SLLSF Limit State Function's Safe Limit SORM Second-Order Reliability Method

SpG Specific gravity

SS Sun-Sheds

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xxvii

t Convective heat transfer duration, culvert wall thickness, time in _{sinusoidal climate temperature model} 𝑡[ ] Regression function

ts Thaw season duration

ts,FA Thaw season duration used in climate fragility analysis

ThawD Thaw depth

ThawS Thaw settlement

TS Thermosyphons, Total thaw settlement danger 𝑢[ ] Stochastic function

USA United States of America USACE US Army Corps of Engineers USD United States Dollar

V Vulnerability

VBA Visual Basic for Applications

vo Temperature difference between MAAT and 0°C vs Summer equivalent step temperature

w total moisture content (gravimetric) wi moisture content as ice

wu moisture content from unfrozen water X thickness of soil above the frozen beam 𝑥̅ Average of the likelihood function

𝑥₂ Random variable

𝑥4₃ Random variable's average

xmax Minimum value in a sample data set xmin Maximum value in a sample data set YFB Iqaluit International Airport designation

YT Yukon Territories

Z Modified Berggren Eqn. Factor, data value for variogram data pair

°C Degrees Celsius

°F Degrees Fahrenheit

𝛼 Modified Berggren Eqn. Factor, convective heat transfer coefficient, _{Soil Water Characteristic Curve parameter}

𝛽 Reliability Index

𝛾 unit weight of soil

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xxviii 𝛾8(ℎ) Semivariogram value

gd Dry density

gt Total soil density

gw Density of water

DT Temperature difference in convective heat transfer Dy Culvert ring deflection

𝛿_;<<=>;?<@ Settlement limit 𝛿_A;<AB<;C@D Calculated settlement 𝛿_EFG;H Differential settlement limit 𝛿_IF Calculated thaw settlement

𝛿_IF,KLM Calculated thaw settlement from the Ice Wedge Profile 𝛿_IF,G;H Total Settlement Limit

𝛿_IF,NEM Calculated thaw settlement from the User Defined Profile

𝜀̇ Strain rate

𝜀_CQ;> Thaw strain

𝜂 Thermal conductivity calculation parameter

𝜃 Permafrost temperature

𝜃_B Volumetric unfrozen moisture content 𝜅 Thermal conductivity calculation parameter 𝜆 Modified Berggren Eqn. Correction factor 𝜇 Modified Berggren Eqn. Factor

𝜇′ Prior distribution average 𝜇′′ Posterior distribution average

𝜎 Stress, standard deviation, standard deviation of the likelihood _function 𝜎′ Prior distribution standard deviation

𝜎′′ Posterior distribution standard deviation 𝜎_@YC Estimated population standard deviation 𝜎_ZC ultimate tensile stress of the frozen soil 𝜎_C uniaxial tensile strength

𝜎[_C beam tensile stress

𝜙" _{Effective friction angle}

𝜙_C internal friction angle at low normal stress 𝜒 Thermal conductivity calculation parameter #ClimateSteps # of climate fragility analysis steps

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xxix

#Sfail # of simulations exceeding danger limits #STotal Total # of simulations

1D One dimensional

2D Two dimensional

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xxx

ACKNOWLEDGEMENTS

To my family: Thanks for supporting my crazy idea to move across the continent to another country and learn another language to achieve a dream. Thanks for the mid-thesis writing Hawaii trip, the constant phone calls and knowing I have your backing in any choice I make in life. Your quiet presence means more than you know.

To Isaac: For many years, you were my anchor, especially when I first arrived in Québec. We survived 5,000 miles of road trip and too much stress on my part. We supported each other through a lot. Thank you.

To Guy: Thank you for your direction and guidance throughout my studies. Thanks for teaching me what it is like to be professor. I’ve enjoyed having you as a mentor throughout the last 5 years. I hope, we collaborate in future.

To the Arquluk and i3c Research Team: You all have been nothing but supportive and welcoming. Chantal, stopping by your desk was invaluable in helping me think through ideas, complain when I was feeling overwhelmed, and deal with all things Université Laval. J-P, your support with articles and the thoughts you put into research team dynamics are refreshing. Pauline and Damien, your encouragement was appreciated. To the other students: Thanks for your friendship and putting up with my French.

To my friends, the knitters and dancers: You celebrate my successes and get me to relax and laugh. Heather, Julie, Rachel, and Liz: Thanks for the great food, and conversations over the last few years. Drew: for talking books and life. The Québec's swing dancers for conversation and dances.

Finally, thanks to Transport Canada, ArcticNet and the Arquluk Program funding partners for their financial support of this work; John Hawkins for his aid in Iqaluit; my committee for providing thoughtful conversation and comments; and all the others, whom I have forgotten to mention by name. Thank you all.

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Introduction

Continuous and discontinuous permafrost areas are ubiquitous in the Arctic and are also present in high elevation regions throughout the world and Antarctica (Figure 0.1). Specifically, in the Arctic, communities are rural, and business interests (oil, gas, mineral exploration activities, and tourism) are increasing (Allard et al. 2012). Future development in the arctic regions of the United States of America (USA) and Canada is focused on extractive industries and will require improved or additional infrastructure (Conley 2013).

Figure 0.1. Northern Hemisphere Permafrost Map

These communities and business interests require transportation of goods and people to and from these areas; thus, transportation infrastructures are necessary in the form of roads, ports, airports, and railways. Dalziell and Nicholson (2001) noted that of the lifeline infrastructure systems (water, sewage, communication, etc.), transportation is the most important because it is required to restore all the other

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systems after a disaster. In rural permafrost regions of Alaska and Canada, a significant number of rural communities are solely connected to large population centers via their airports (transport of people and perishable goods), waterways (transport of durable goods), or, in areas of industry or communities of close proximity, winter roads, generally constructed of ice or snow (Allard et al. 2012; Beaulac and Doré 2006b). Due to the sparse infrastructure, “transportation infrastructure(s) are of vital social, economic, and political importance in cold regions” (Regehr, Milligan, and Alfaro 2013).

Year-round transportation infrastructure in permafrost regions consists of roadways, railways, and airports, constructed of regional granular fill. In North America and China, there are major roadways constructed on permafrost. In Canada, these include: Northwest Territories (NWT) Highway 3 linking Yellowknife, NWT to the Canadian Highway network; Dempster Highway connecting Inuvik and Tuktoyaktuk, NWT to Dawson City, Yukon Territory (YT); and the Alaska Highway— the only year-round ground transportation link between Alaska and the contiguous USA lower forty-eight states. In Alaska, including the Dalton Highway linking Fairbanks and Prudhoe Bay, AK, approximately 2680-km of roadway are within continuous and discontinuous permafrost regions (US Arctic Research Commission 2003). The Qinghai-Tibet Highway crosses the Tibetan Plateau in China (Tai et al. 2015). After the construction of the Qinghai-Tibet Railroad in China in 2007, approximately 9,000 km of railroad were operational in the permafrost regions of Alaska, Canada, China and Russia (Cheng 2005; Kondratiev 2013). Besides the road and railways of Alaska and Canada, approximately 250 airstrips and airports are within permafrost regions, and 200 of their connected communities rely solely on the airport for year-round access (US Arctic Research Commission 2003; Office of the Auditor General of Canada 2017).

1.1 Current Permafrost Embankment Design Practice

Modern permafrost engineering began with the construction of the Alaska Highway during World War II (Stephani 2013), was expanded in the 1970’s with the

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construction of the Trans-Alaska Pipeline and resulted in the understanding that thermal and mechanical design must be interwoven, as thermal instability will result in mechanical instability. In current practice, infrastructure supported by permafrost must be analyzed and designed for current and future thermal and mechanical stability. To ensure embankment thermal stability, current and future climate conditions must be analyzed (Doré, Niu, and Brooks 2016; Andersland and Ladanyi 2004; Buteau, Fortier, and Allard 2010; Doré and Zubeck 2009; Gaumond, Doré, and Guimond 2012).

Infrastructure on permafrost is supported in a manner bypassing compression of the active layer, burial, or through compression of the active layer. Construction methods, which do not compress the active layer, are largely used for buildings and include piles (driven, adfreeze or helical), “post and pad” foundations, etc. These methods require a clear space between the base of the structure and the ground surface to cool the ground during the winter months (author experience, Rice 1984). Burial can be used for pipelines and cables, generally causing large surficial disturbances in the construction process. Methods that compress the active layer are used for road, rail, airport and some building construction; these require the construction of a fill section, in the form of a pad or embankment, on the ground surface.

As embankment-supported linear infrastructure on permafrost, including roadways, railways, and airports, largely falls within the latter category, it is the focus of this work. These infrastructures are designed and with practices aiming to preserve or aggrade the elevation of the permafrost underlying the embankment via a thermal design (Vinson 1995). The general permafrost profile within an embankment section is presented in Figure 0.2 with compression of the organic material due to the embankment’s presence. The dip in the permafrost surface at the shoulder of the embankment is commonly observed.

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Figure 0.2. Schematic of an embankment over permafrost; thermally designed to aggrade the permafrost into the embankment fill.

The construction of the fill section is completed using available local materials, which are placed and compacted in a thawed state during summer or in a frozen state during winter and, depending on the specification, re-compacted the following summer. Subsidence is common after construction, but conditions stabilize 3 to 5 years following construction under summer and winter conditions, respectively (Lingnau 1985). Adaptation methods for embankment infrastructure on permafrost have been created and tested for small and full-scale applications in light of warming climate conditions (Doré, Niu, and Brooks 2016). Further discussion of the problems observed along, and mitigation and adaptation strategies for embankment infrastructure on permafrost are presented in Chapter 2.

1.2 Climate Warming and Permafrost Infrastructure

Global warming is “unequivocal and unprecedented” with substantial evidence of the influence that greenhouse gases released from human activity are affecting global temperatures (IPCC 2013)—the average air temperature has increased 0.78°C between data sets from 1850-1900 and 2003-2012. The Arctic Monitoring and Assessment Program (AMAP 2012) summarized studies of global warming’s

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estimated effects on the Arctic, and it notes preferential warming in the arctic at rates two times higher than the rest of the world.

Currently, measured average annual air temperatures have increased when compared to historical trends. An average air temperature increase of 1.7°C has been observed in Alaska (Hong, Perkins, and Trainer 2014) and, specifically in 2016, the average air temperature was 3.3°C above the long-term average and 0.9°C above the previous record annual average air temperature in 2014 (Rosen 2017). YT has experienced a 2°C increase in annual temperature overall and 4°C increase in the average winter temperature (Rosen 2016). These warming trends are common within the North and Arctic, and warming is expected to be increased (3 to 6°C by 2050) in the autumn and winter months (AMAP 2012; Hinzman et al. 2005; Rosen 2016, 2017; Springman and Arenson 2008).

Permafrost lands are particularly sensitive to climate change (Allard et al. 2012). The current warming has moved the southern extent of permafrost northward throughout the world, 30 to 80 km in Russia and 130 km in Québec, Canada (AMAP 2012). Permafrost temperatures have increased 3°C and 2°C in some parts of northern Alaska and the European side of Russia, respectively, and active layer depths are increasing in Scandinavia, Russia and inland Alaska (AMAP 2012; IPCC 2013). Should the predicted climate change occur in the future, “permafrost will disappear partially or completely over large areas in the north” (Couture, Robinson, and Burgess 2000).

The permafrost areas of Alaska and Canada, which are “most susceptible to the adverse impacts of climate change, are also the ones most reliant on transportation infrastructure” for the movement of goods and people via year-round roadways or airports (McGregor, Hassan, and Hayley 2008). Currently, “despite spending extra money on maintenance in permafrost areas, compared to non-permafrost areas, ride quality and safety standards are compromised” along the Alaska Highway in YT (Reimchen et al. 2010). The compromise between safety and cost was also revealed by the Auditor General of Canada’s report (2017) on the state

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of rural airports in Canada, which noted that the cost of maintaining and upgrading existing airport facilities is greater than the available funding.

Melvin et al. (2016) analyzed of the “economic impacts of climate change to Alaska’s public road, building, airport, rail and pipeline infrastructures.” Excluding the costs of routine replacement and maintenance, the total future economic impacts, in 2015 USD, ranged from $5.5 to $4.2 billion for the high and low greenhouse gas emission scenarios, respectively. Using assumptions for reconstruction response, the projected reduction in costs, compared to scenarios without adaptation action, ranged from 10 to 45% for reactive and 45 to 47% for proactive adaptation strategies (Melvin et al. 2016). Their analysis also confirmed that 38% of the costs for climate change infrastructure damage resulted from near-surface permafrost thaw with projected damages, in 2015 USD, to roadway, airport and rail infrastructure ranging from $282 to $550 million for low and high emission scenarios, respectively.

1.3 Risk Assessment

Permafrost dangers, the methods by which damage may happen, occur “in dynamic and distinct environmental and social contexts, reducing vulnerability and promoting resilience requires a comprehensive approach” (Carey et al. 2015). One methodology for a comprehensive approach to assessing data uncertainties, costs, social impacts and climate change is the risk assessment.

Risk (R) from a danger is calculated from the following equation:

1.1

where H is the hazard, C is the consequence and V is the vulnerability. The hazard consists of the probability of a danger’s occurrence, such as the likelihood of a landslide occurring along a slope. If the landslide damages infrastructure or someone is killed as a result, the cost of repair for that infrastructure is the direct consequence. If the infrastructure damage impacts the surrounding community, these costs, while not often measured in dollars, are the indirect consequence of a danger’s occurrence. The vulnerability correlates the severity of the danger to the

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consequence. These analyses can be completed either qualitatively, using scalar factors from a previously defined matrix or rubric, or quantitatively, from historical trends or calculated (Ang 2011; Engineers Canada 2011). In practice, hazard can be calculated using engineering reliability theory from uncertain input properties and limit state functions.

Multiple organizations have developed risk analysis methods (Engineers Canada 2011; Public Safety Canada 2011; USACE 2003), each with their specific focus, but with a consistent analysis process, best defined in the All Hazards Risk Assessment Methodology created by Public Safety Canada (2011) and shown in Figure 0.3. While not specifically an engineering risk analysis, the steps presented for the risk analysis are apt and include: 1) identifying the dangers, 2) describing the dangers, 3) risk analysis via hazard and consequence calculation, 4) risk evaluation, and 5) risk treatment (Chowdhury and Flentje 2007; Public Safety Canada 2011). These steps are described in detail later (section 3.1), including a literature survey of two studies applying these principles to permafrost embankment infrastructure in a qualitative manner (Arenson and Seto 2011; Calmels et al. 2015) for two different purposes.

Figure 0.3. The Public Safety Canada process for developing a risk event scenario (adapted from Figure 4 from Public Safety Canada 2011).

Quantitative risk analysis for linear infrastructure supported by permafrost : methodology and computer program

© Heather Brooks, 2019