There are many old dams in Sweden and, since few dams are constructed today, the main task in risk assessment on the existing dams is often to reduce the risk of failure. RIDAS (Swedish Guidelines on Dam Safety) is used when designing new dams and assess the existing ones. The guidelines include stability requirements for different failure modes, e.g. overturning and sliding, which imply that the load effect from e.g. uplift and ice load need to be less than the resisting loads or moments. The ice load in RIDAS is given as a deter­ministic value depending on where in Sweden the dam is located. For many years, ice and ice load have been researched, but there is still a lack of knowledge regarding the magni­tude of the ice load and how it affects the probability of failure for dams. More knowledge about the actual ice load would result in a lower calculated probability of failure for the dam which could be used to design slender dams or avoid unnecessary reinforcement of existing dams. Dam safety evaluation is often performed with deterministic methods based on safety factors. In recent years, the use of probabilistic methods in dam design has increased. The method has an advantage compared to deterministic methods in safety evaluations of existing dams, since probabilistic methods provide an answer to which parameters that have the greatest impact on the stability of the dam and take into account the variations in each parameter. I this master thesis, a statistical distribution for the variation of the ice load’s annual maxi­mum value was calculated. This was used in the analysis of the probability of failure for solid gravity concrete dams and buttress concrete dams. The probability of failure was cal­culated for dams of different sizes for overturning and sliding failure modes, and also for three different load cases; without ice load, with a truncated ice load distribution and with an ice load distribution that has not been truncated. The probabilistic stability analysis was conducted in Comrel with ice load as one of the stochastic variables. It was found which sizes of the dams that have the largest impact from the ice load; also what effect extreme values on the ice load has on the failure probability of the dam. The results indicated that the probability of failure for dams lower than 15 m is more affected by the ice load, for both failure modes analyzed. The probability of failure is reduced for all dam types when eliminating extreme values of the ice load, particularly for dams lower than 15 m. In several cases, truncation of the ice load distribution is the differ­ence between an accepted and a non-accepted level of the probability of failure. It is also shown that reduced coefficient of variance for the ice load results in a decreased probability of failure. The conclusion is that solid gravity dams and buttress dams lower than 15 m, with a high consequence class, should be risk assessed with the ice load as a stochastic vari­able. The statistical distribution of the ice load is still uncertain and the distribution used in this report should not be used globally, rather in areas with a climate similar to northern Sweden. The reason for this is that the measurements that were used to derive the global distribution were mainly performed in areas with conditions similar to those in northern Sweden. A recommendation for further research is to focus on determining statistical distributions for the ice load for southern, central and northern Sweden. An alternative is to use differ­ent ice load distributions for the different areas. Another alternative could be to use the same statistical distribution for southern, central and northern Sweden but with different values for where the ice load distribution is truncated, depending on the maximal ice thick­ness in each area. The recommendation is also to develop a reliable method for measuring the ice load. In addition, attempts should be made to determine whether extreme values on the ice load really exist or if they are effects of measurement errors. Key words: concrete dams, ice load, probabilistic stability analysis, probability of failure

En av de sannolikhetsbaserade metoderna som kan användas för dimensionering av tunnlar är partialkoefficientmetoden. Denna metod ökar eller reducerar variabler med hjälp av partialkoefficienter, vilka kan kalibreras sannolikhetsteoretiskt. Eurokod tillhandahåller sådana partialkoefficienter för till exempel armerad betong. Problemet med partialkoefficienterna i Eurokod är dock att ingen skillnad görs med avseende på vad betongen skall användas till. Detta examensarbete har därför syftat till att undersöka möjligheten att ta fram nya partialkoefficienter specifikt för sprutbetongförstärkning då den dimensionerande brottsmekanismen är böjbrott, detta med hjälp av tillförlitlighetsteori, FORM/FOSM. Böjbrott i sprutbetongen kan uppkomma då vidhäftningen mellan berg och sprutbetong är låg, och sprutbetongen måste bära eventuella bergblock med sin momentupptagande förmåga. För att ta fram partialkoefficienterna har uppmätt data på sprutbetongtjockleken och böjdraghållfastheten i en av Citybanans tunnlar, Norrströmstunneln, varit grunden. Statistiska fördelningar har tagits fram för att beskriva dessa data, för att möjliggöra användandet av dem i sannolikhetsanalysen. Resultaten visade att en lognormalfördelning passade observerad data bäst för sprutbetongtjockleken, och en betafördelning passade bäst för böjdraghållfastheten. Vidare visade resultaten att sannolikhetsbaserade metoder vid dimensionering för denna brottsmekanism ännu inte kan rekommenderas, då de visade på en kraftig överdimensionering jämfört med hur det idag dimensioneras. Osäkerheterna kring vissa av de modeller och variabler som använts behöver först reduceras. / One of the probability based methods that may be used when designing a tunnel is the partial factor method. This method adjusts the value of variables with the help of partial factors, which may be calibrated using a reliability-based approach. The Eurocodes provide these partial factors for different materials and structures, such as reinforced concrete. A limitation with the provided partial factors from Eurocode is the lack of consideration for the usage of the concrete. This thesis aims to investigate the possibility to derive new partial factors specifically for shotcrete reinforcement, for the failure mechanism of flexural failure. This has been done by means of reliability theory,FORM/FOSM. Flexural failure in shotcrete may occur when the adhesion between the rock and shotcrete is low. Further, the shotcrete has to have the capacity to withstand bending moments from the rocks. To derive the new partial factors, the measured data of thickness and flexural strength of shotcrete in one of Citybanan's tunnels, Norrströmstunneln, in central Stockholm have been used as the basis for the analysis. The data was described by a statistical distribution which enabled the usage of them in the reliability analysis. The results showed that a lognormal distribution best described the shotcrete thickness while flexural strength was best fitted by a beta distribution. The results also showed that it is not recommended to use probabilistic methods in design for this failure mechanism unless uncertainties, arising from some of the models and variables used, are reduced. It clearly shows that it would lead to oversizing compared with the design methods used today.

Målet med det här examensarbetet var att undersöka hur väl dagens partialkoefficienter för sprutbetong tar hänsyn till samhällets normer och säkerhetskrav vid dimensionering enligt partialkoefficientmetoden. Det brottfall som har undersökts för dimensionering av sprutbetong är vidhäftningsbrott vid god vidhäftning. Vidhäftningsbrottet har undersökts med hjälp av en sannolikhetsbaserad metod benämnd ”First-Order Reliability Method”, FORM. Metoden förutsätter kännedom om sannolikhetsfördelningar för ingående variabler i brottgränstillståndet som i det här arbetet till stor del baserats på provtagningar från projektet Norrströmstunneln i Citybanan. Resultatet av undersökningen visar att partialkoefficienterna antar otillåtna värden för dimensionering av sprutbetong på grund av den stora spridningen som råder i framförallt vidhäftningsparametern. Vidhäftningsparametern antog en normalfördelning med medelvärde 0.808 MPa och standardavvikelse 0.319 MPa vid analys av samtliga vidhäftningsmätningar. Spridningen för vidhäftningsparametern har reducerats genom att undersöka gnejs och granit var för sig och genom att ta bort mätningar där dålig vidhäftning i förväg kunnat antas. För granit fick vidhäftningsparametern ett medelvärde på 0.759 MPa och en standardavvikelse på 0.264 MPa. För gnejs fick vidhäftningsparametern ett medelvärde på 0.820 MPa och en standardavvikelse på 0.279 MPa. I den här fallstudien resultera en reducerad spridning för vidhäftningsdata inte i någon avgörande skillnad för beräknade partialkoefficienter. Modellen för vidhäftningsbrottet verkar tillsynes inte vara för komplicerad men det existerar samtidigt stora osäkerheter i modellen och ingående variabler gällande laster och bärförmågor. Framförallt okunskapen gällande lastvariabeln gör det svårt att kalibrera relevanta partialkoefficienter med FORM.

Constructing sustainable structures in rock that satisfy all predefined technical specifications requires rational and effective construction methods. When the geotechnical behaviour is hard to predict, the Euro­pean design code, Eurocode 7, suggests application of the observational method to verify that the performance is acceptable. The basic principle of the method is to accept predefined changes in the design during con­struction to comply with the actual ground conditions, if the current de­sign is found unsuitable. Even though this in theory should ensure an effective design solution, formal application of the observational method is rare. Investigating the applicability of the observational method in rock en­gineering, the aim of this thesis is to identify, highlight, and solve the aspects of the method that limit its wider application. Furthermore, the thesis aims to improve the conceptual understanding of how design deci­sions should be made when large uncertainties are present. The main research contribution is a probabilistic framework for the observational method. The suggested methodology allows comparison of the merits of the observational method with that of conventional design. Among other things, the thesis also discusses (1) the apparent contradiction between the preference for advanced probabilistic calculation methods and sound, qualitative engineering judgement, (2) how the establishment of limit states and alarm limits must be carefully considered to ensure structural safety, and (3) the applicability of the Eurocode defini­tion of the observational method and the implications of deviations from its principles. / För att kunna konstruera en anläggning i berg, som uppfyller satta tek­niska krav, krävs det en rationell och effektiv konstruktionsmetod. När konstruktionens beteende är svårt att förutsäga, erbjuder den europeiska standarden Eurokod 7 den så kallade observationsmetoden. Denna metod tillåter i förväg förberedda förändringar i designen under konstruktions­tiden, om observationer av konstruktionens beteende indikerar att så behövs. På så vis anpassas konstruktionen till de faktiska förhållandena i marken. Trots att detta tillvägagångssätt i teorin ger en rationell design, används metoden sällan i enlighet med Eurokod 7. Denna doktorsavhandling undersöker tillämpbarheten av observa-tionsmetoden när man bygger i och på berg. Målet är att belysa de aspekter som begränsar dess användning och i dessa fall föreslå förbätt­ringar som ökar tillämpbarheten. I ett vidare perspektiv syftar avhand­lingen även till att förbättra den konceptuella förståelsen för hur beslut bör fattas i designprocessen när det finns stora osäkerheter. Avhandlingen visar hur observationsmetoden kan användas i ett san­nolikhetsbaserat ramverk. Metodiken ger användaren möjlighet att jäm­föra för- och nackdelarna med observationsmetoden och konventionell dimensionering. Avhandlingen diskuterar bland annat även (1) den skenbara motsatsen mellan användandet av sannolikhetsbaserade beräkningsmetoder för att lösa komplexa dimensioneringsfrågor och kvalitativa ingenjörsmässiga bedömningar, (2) hur larmgränser och brottgränstillstånd bör definieras för att ge tillräcklig säkerhetsmarginal, samt (3) hur Eurokod 7:s strikta definition av observationsmetoden påverkar dess användbarhet. / <p>QC 20160926</p>

Tunneling involves large uncertainties. Since 2009, design of rock tunnels in European countries should be performed in accordance with the Eurocodes. The main principle in the Eurocodes is that it must be shown in all design situations that no relevant limit state is exceeded. This can be achieved with a number of different methods, where the most common one is design by calculation. To account for uncertainties in design, the Eurocode states that design by calculation should primarily be performed using limit state design methods, i.e. the partial factor method or reliability-based methods. The basic principle of the former is that it shall be assured that a structure’s resisting capacity is larger than the load acting on the structure, with high enough probability. Even if this might seem straightforward, the practical application of limit state design to rock tunnel support has only been studied to a limited extent. The aim of this licentiate thesis is to provide a review of the practical applicability of using reliability-based methods and the partial factor method in design of rock tunnel support. The review and the following discussion are based on findings from the cases studied in the appended papers. The discussion focuses on the challenges of applying fixed partial factors, as suggested by Eurocode, in design of rock tunnel support and some of the practical difficulties the engineer is faced with when applying reliability-based methods to design rock tunnel support. The main conclusions are that the partial factor method (as defined in Eurocode) is not suitable to use in design of rock tunnel support, but that reliability-based methods have the potential to account for uncertainties present in design, especially when used within the framework of the observational method. However, gathering of data for statistical quantification of input variables along with clarification of the necessary reliability levels and definition of “failure” are needed. / <p>QC 20170407</p>

Vehicles losing their GPS signal is a considerable issue for autonomous vehicles and can be a danger to people in their vicinity. To circumvent this issue, a particle filter localization technique using pre-generated offline Open Street Map (OSM) maps was investigated in a software simulation of Scania’s heavy-duty trucks. The localization technique runs in real-time and provides a way to localize the vehicle safely if the starting position is known. Access to global localization was limited, and the particle filter still succeeded in localizing the vehicle in the vicinity of the correct road segment by creating a graph of the map information and matching the trajectory to the vehicle’s sensor data. The mean error of the Particle filter localization technique in optimal conditions is 16m, which is 20% less than an optimally tuned dead reckoning solution. The mean error is about 50% larger compared to a Global Positioning System. The final product shows potential for expansion but requires more investigation to allow for real-world deployment. / Att fordon kan mista sin GPS-signal är ett stort problem för autonoma fordon och kan vara en fara för människor i dess närhet. För att undvika detta problem föreslås en icke-global lokaliseringsteknik som använder Open Street Maps-kartor (OSM) och ett partikelfilter för att lokalisera fordonet i en mjukvarusimulation. Implementering körs i realtid och anger fordonets position med en tillräcklig träffsäkerhet för att det inte ska utgöra någon fara om dess startposition är känd. Globala lokaliseringsmöjligheter var begränsade, och partikelfiltret lyckades lokalisera fordonet till rätt vägsegment genom att konstruera en graf över den kartinformation den läst in och para ihop fordonets nuvarande färdväg med denna. Resultatet ger en lösning som optimalt har ett medelfel på 16m, vilket är 20% mindre än medelfelet jämfört med optimiserad dödräkning. Lösningen har ca 50% större medelfel än positionering med GPS. Slutresultatet visar en potential att användas i verkliga situationer, men kräver mer undersökningar.