Slide 1 Quantitative Risk of Linear Infrastructure on Permafrost Heather Brooks, PE Arquluk Committee Meeting November 2015 Welcome to the meeting of the committee for Arquluk s Quantitative Risk of Linear Infrastructure on Permafrost project. Thank you all for being in attendance. The goal of this meeting is three fold: 1) to provide you all with a project update, in more detail than is possible in our other meetings, 2) for me to further understand the needs of the group, who will be utilizing the end product, and 3) for you to provide me with feedback on the direction of this project. Please feel free to ask questions at any time during my presentation.
Slide 2 Project Objective Create Quantitative risk analysis method Software tool Utilizing Site conditions Engineering calculations Consequences Success Criteria Create a tool useful to practicing engineers Include engineers in project development User inputs of hazard failure criteria Focus on common hazards 2 The objective of this project is to create a quantitative risk analysis tool. This tool will take engineering equations for failure (e.g. rotational failure, settlement, bearing capacity failure, lateral embankment spreading, arching and embankment collapse), the uncertainty within each of the input parameters, and the consequences of the extent of each type of failure. For this project to be considered successful, the end product should be useful to practicing engineers. To that end, the committee of this project has input into the direction of the research and the development of the risk assessment tool. Additionally, we plan on focusing the research on common failure modes and hazards to embankment-supported infrastructure on permafrost. Thus, we need input from this group to determine the failure modes to address within this research.
Slide 3 Background, Methodology and Assumptions 3 Next, we talk about the background, methodology and assumptions that will be used in the creation of the risk assessment tool.
Slide 4 Definitions and Terminology Hazard or Failure Mode an event or process causing damage Probability of Failure the probability of a hazard s occurrence within a time frame Consequence the cost (direct, indirect, social, economic) due to or to repair the damage from a hazard Risk a combined measure of probability and consequence 4 There are more exacting definitions of terminology for risk assessment within the literature, but for the purposes of this presentation and hopefully our further discussion, these are the definitions I propose.
Slide 5 R = P x C R = Risk P = Probability of failure C = Consequence Risk Analysis Qualitative Assigned scalar values Rubrics for P and C Quantitative P from past experience or uncertainty calculation C calculated from expected damage 5 To complete a risk analysis of a hazard requires the assignment or quantification of two values: the likelihood or probability of failure (noted here as P) and the consequence of that failure (noted as C). These analyses can be completed in a qualitative or quantitative manner. Generally, qualitative analyses are based on rubrics of likelihood and consequence, where scalar values are assigned for P and C. These rubrics usually assign higher values to more likely events and higher consequences. Multiplying P and C results in the risk factor which is used to rank the hazards. The higher the value, the higher the risk. In a quantitative analysis, P is determined from past occurrence or calculated from the inherent uncertainty within the failure mode equations and their inputs. C is based on either the fiscal or casualty costs, respectively. There are multiple methods for determining P. If data is available from past occurrences such as storms, floods and earthquakes, then a frequency distribution may be calculated. If past data is not available, P can be calculated using various methods from the engineering literature. These include First Order Second Moment (FOSM) method, First Order Reliability Method (FORM) and Monte Carlo Simulation. More information will be presented on the differences between these methods later in the presentation. It is this quantitative analysis methodology that will be used in this research.
Slide 6 Methodology 6 As we discussed briefly on the last slide, various values must be calculated for each hazard analyzed within this project. The diagram above shows how these prices of information are aggregated together to calculate a risk. Starting from the top of the diagram, the uncertainties from two sources, geotechnical and climate, are combined within an engineering calculation to create the combined uncertainty of the failure mode. Because each infrastructure is different and can tolerate different failure limits, the final determination of failure limit is dependent on the definition of the user. The user s failure limit input will then be used to determine the probability of failure. An example of this type of uncertainty aggregation is presented later in this presentation. One calculates the consequences for a hazard, by determining the damages caused by the hazard s occurrence and determining the impact to budgets (direct costs) and communities (indirect costs). Additional parameters can also be used in the consequence calculation. In my previous presentations to this group, the consequence calculation was only briefly discussed. This is largely due to how little is written in the engineering literature. I will discuss the consequence calculation in further detail later.
Slide 7 Hazard Identification 7 This figure presents a fault tree for embankment-supported infrastructure on permafrost. These hazards are, based on the literature, the greatest potential hazards to existing and new infrastructure. The hazards have been classified by the general consequence. The hazards highlighted in yellow are the focus of this project.
Slide 8 Probability of Failure - Inputs 8 This image shows some of the input parameters required for completing the probability of failure section of the analysis. These parameters include climate conditions both current and future projections, geotechnical properties and permafrost temperatures. Additionally, haul distances and material costs will vary dependent upon the position along the infrastructure which will be properties used within a direct consequence analysis. The majority of these parameters are very site specific. Linear infrastructure crosses different conditions throughout its length thus
Slide 9 Probability of Failure - Landforms 9 I propose to create the risk analysis tool which analyzes the risks within a section or a landform. Since the soil profiles within landform areas formed under similar geologic conditions and were exposed to similar freezing conditions, the variability within the general soil, ice and temperature conditions should be less than between landforms. Depending on the needs and resources of the user and the stage of the project (planning requires less detail than design), the analysis can be refined with shorter or longer sections. The figure above is a coloured landform map of the Alaska Hwy in the vicinity of Beaver Creek.
Slide 10 Probability of Failure - Calculation First Order Second Moment (FOSM) Methodology Taylor series expansion of the failure equation partial derivatives for each input variable Result average calculated from input averages Result variation summation of evaluated partial derivatives Monte Carlo Simulation Methodology Varies all uncertain input parameters simultaneously probability density functions Each calculation is a simulation Repeated simulations define average standard deviation Greater accuracy with more simulations 10 As I discussed earlier, the probability of failure can be calculated from past events or from engineering calculation and parameter uncertainties. Since little is presented within the literature discussing the rates of past failure occurrence of different hazards within the permafrost literature, this project must rely on probability calculation from engineering calculations and input parameter uncertainty. There are multiple methods used to make this analysis; however, First Order Second Moment and Monte Carlo Simulation will be used in the probability of failure calculations within this project. FOSM requires an equation for failure be able to be derived with respect to each of the uncertain parameters. This is not possible for some of the calculations used in permafrost engineering; for example, Modified Berggren Equation which calculates freeze and thaw depths within soils, is iterative and includes a transcendental function. Since an iterative function is unsolvable through algebraic methods, it cannot be derived. In this case, Monte Carlo Simulation must be used. An example of Monte Carlo Simulation is presented later in this presentation.
Slide 11 Risk Literature Fatalities Monetary Consequence Consequence Calculation This Project Requires consequences Fatality Social Monetary Tool will likely have qualitative adjustment factors Christian 2004 39 th Terzaghi Lecture Geotechnical Engineering Reliability: How well do we know what we are doing? 11 Within the geotechnical engineering risk analysis literature, the risk and the tolerance to risk is presented in terms of either monetary or casualty losses. As shown in the F-N diagram on the right of the slide. These diagrams are often presented within codes and laws. In these codes if a project is outside the risk tolerance zone, the project team must either reduce the probability of occurrence or the potential hazards until the risk comes within tolerable levels. In this project, most of the failure modes are unlikely to result in consequences which impact human health. However, if infrastructure is closed and the closure indirectly results in consequences to the community, this project must include these impacts. The largest problem is how does one combine the monetary consequences that will results from most of the hazards with the potential human impacts. Additionally, the indirect economic and social impacts to communities must be analyzed. One paper, looking at the impacts to tax revenues following hurricanes and earthquakes in Florida and California, respectively, showed impacts but did not review the economic impacts to local businesses. This paper did point out that what information is available is largely a review of post natural disaster data, which may not be applicable to the small communities impacted in this project. I plan on continuing to review the literature of economics and other social science to see in other methods have been used in this regard. It is likely that the analysis of consequences will require additional qualitative factors for the infrastructure importance and the indirect social impacts due to the failure.
Slide 12 Programming & Future Work 12 So where does the project stand to date and where are we headed
Slide 13 Excel Spreadsheet Tool - Beginnings Thaw Depth Calculation Mod Berg. Monte Carlo Climate & Soil Property Variation Soil Data from Iqaluit Airport VBA Program in Excel 13 I have begun working on the computer program, it consists of an Excel spreadsheet for the user to input the required data and a VBA code for completing the calculation and outputting the results. To date, this program includes statistical thaw depth calculation using Monte Carlo Simulation and Modified Berggren Equation. I verified the program using a hand calculation and data from a project by Michel Allard and Valerie Mathon-Dufour for the Center for Northern Studies at the Iqaluit Airport in Iqaluit, Nunavut.
Slide 14 Thaw Depth Monte Carlo Results 14 Here is an example of the output, it includes a histogram of the Monte Carlo Simulation results, where the number of simulations for a depth range is presented vs. the ranges of depths. The table also shows a brief statistical analysis of the MC data. This includes the average thaw depth calculated from all the average input parameters, the MC average thaw depth, the standard deviation of the MC data, the number of iterations, and the minimum and maximum depths calculated. There is a slight difference between the thaw depth calculated from all of the average values and the average of the Monte Carlo Simulation. I am working on determining the source of this error.
Slide 15 Thaw Depth Monte Carlo Results 15 In an early version of the MC program, I varied all of the parameters individually. This plot shows the correlation between the variation of the parameter and the resulting variation in thaw depth. Any parameters near the x-axis do not have a large impact on the thaw depth variation. At this site, the factors which impact the depth of thaw to the greatest extent are Air thawing index, moisture content and dry unit weight of the gravel layer between the two asphalt layers of this site s profile and the moisture content of the frozen sand layer at the base of previously placed fill.
Slide 16 Failure Mode Definitions Lateral Embankment Spreading Common hazard Failure modes not well defined Arching Effects Previous fatality (1985 Dempster Hwy) Failure mode not well understood 16 In addition to continuing to work on programming, the literature review revealed that some failure modes require further analysis before a engineering calculation can be defined. These include lateral embankment spreading and arching effects. Lateral embankment spreading is a commonly observed hazard which effects embankments in permafrost; however, the mechanics of failure are little understood. I will continue to work with another student, Anne-Gabrielle Nolet, on this problem. Arching effects are also a hazard effecting permafrost areas with subsurface ice-wedges. In 1985, a fatality occurred along the Dempster Highway. Subsequent investigations discovered that the cause of the accident was due to convective heat transfer from flowing water, rapidly thawing an ice-wedge, where an arch formed within the embankment fill. This arch collapsed under the weight of a vehicle causing a fatality. However, the mechanics and theory of arching has not been significantly advance since Terzaghi s initial experiments in 1943. I discuss this further in a few slides.
Slide 17 Embankment Spreading - Problem 17 The failure mechanics of embankment spreading may be due to three failure modes. When the thaw depth at the shoulder of the roadway descends below the initial active layer thickness, the settlement that results, steepens the side slopes of the embankment which either ravels once the angle of repose of the embankment fill is reached, or the triangular wedge of embankment fill rotates as a block into the settled area. The thawing processes reduces the effective stress in the thawed area and slope failures occur. The curved permafrost surface at the side slopes causes a lateral frost jacking effect. Heave occurs in the in-situ soils perpendicular to the surface of the permafrost, but thaws and settles vertically in the summer relocating the material away from the center of the roadway. Repeated freezing and thawing moves these materials further away form the roadway.
Slide 18 Arching - Problem 18 In the case of arching, an arch may form over an ice wedge as it thaws.
Slide 19 Arching Current Work Simplified Model Tests: B/D50 from 4-8.5 Centrifuge Model (1/30 Scale): B/D50 from 40-95 19 However, little laboratory experimentation has explained the phenomena. Observations made during laboratory testing of model materials tested in the trap-door problem. A door of width B is lowered and the material allowed to form an arch or flow. During these models tests, stable arches were observed at B to average grain-size ratios of 4 to 8.5. One set of experiments conducted in a centrifuge, looked at arch formation and infilling due to melting ice wedges. The ratios observed ranged from 40 to 95. This increase in ratio may have been caused by the observed pore water pressure, which was less than hydrostatic during a portion of the thawing process. Possibly increasing the effective stress at the arch face.
Slide 20 Arching Laboratory Ratio Testing 20 We propose to conduct some laboratory testing to determine a quantitative ratio at which arching effects are likely to occur. The tests will consist of freezing a triangular wedge of ice within a concrete form, levelling the concrete surface, placing cover soil, and allowing the ice to thaw form the surface down. Various ice wedge widths and depths and cover soils will be used to cover a range of arching ratios (2 to ~160). This testing will hopefully provide a ratio at which arching is possible and will provide a baseline value for use in the probability of failure calculation. We are currently designing the testing apparatus and testing is likely to begin in January.
Slide 21 Future Work Statistical analysis of failure modes Continue programing and tool creation Validation with field sites Proposed locations (Iqaluit Airport, Dempster Hwy, etc.) 21 I will continue to define the limit state equations for the remaining hazards. I will begin to integrate these failure modes into the computer program. I also plan on validating the program using field research sites such as the Iqaluit Airport and the Dempster Hwy. Any necessary field work will occur summer 2016. After an initial validation, the project committee should meet to review the results and provide direction.
Slide 22 www.arquluk.gci.ulaval.ca Thank you all for your input and collaboration! Thank you all. I would like to open the meeting for additional questions and discussion.