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

I Sverige finns det idag ett stort antal dammar och nära hälften av Sveriges elproduktion kommer ifrån vattenkraft. Höga säkerhetskrav ställs på dammarna då konsekvenserna av ett dammbrott kan orsaka stor ekonomisk skada både i form av minskad produktion och som uppbyggnadskostnader. Dammbrott kan även utgöra risk för skador på människor och omkringliggande miljö samt byggnader. Det finns flera dimensioneringsmetoder för att uppfylla gällande säkerhetskrav på konstruktioner. De tillämpningsvägledningar som används vid stabilitetsanalys av betongdammar baseras på gamla deterministiska metoder med säkerhetsfaktorer. Det arbetas med att ta fram nya tillämpningsvägledningar baserat på sannolikhetsbaserade metoder. De sannolikhetsbaserade metoderna tar hänsyn till osäkerheterna i enskilda variabler, vilket förväntas ge effektivare konstruktioner. Stabilitetsanalys med sannolikhetsbaserade metoder i varje enskilt fall är förmodligen det bästa ur säkerhetssynpunkt, men det kan vara väldigt tidskrävande. Ett sett att underlätta stabilitetsberäkningarna, i vanligt förekommande konstruktioner, är användandet av partialkoefficienter. Partialkoefficienter är en semi-probabilistisk metod som kan kalibreras med hjälp av tillförlitlighetsanalysen och appliceras på systemets olika variabler och parametrar. På så vis beaktas osäkerheten i enskilda variabler och parametrar bättre än i deterministiska metoder med säkerhetsfaktorer. Målet med det här examensarbetet var att undersöka om stabilitetsanalys av betongdammar med partialkoefficienter kan vara ett alternativ till de metoder som redan finns. Rapporten kan delas in i tre delar. Den första delen av rapporten beskriver teorin bakom kalibrering av partialkoefficienter med hjälp av tillförlitlighetsteori, FORM. I den andra delen beskrivs metoder och tillämpningsvägledning för stabilitetsanalys av betongdammar med probabilistiska metoder. I den tredje delen används kunskaperna från de två första delarna för att beräkna tillförlitligheten på 15 utav Sveriges dammar. Beräkningarna används sedan för att kalibrera partialkoefficienter. En del kraftiga avgränsningar har gjorts i arbetet, bland annat har beräkningarna utförts för ett statiskt lastfall och bara fokuserat på stabilitetsvillkoret för glidning. Resultatet visar att det inte är rekommenderat att använda sig av partialkoefficienter vid stabilitetsanalys, åtminstone inte med den information och kunskap som idag finns tillgänglig. Osäkerheterna kring vissa modeller och variabler behöver minskas för att partialkoefficienter skall vara ett alternativ. Teorin kring partialkoefficienter kräver även en viss likhet i konstruktioner och konstruktionselement. De dammar som användes i denna studie kan ha varit för olika för att erhålla tillfredsställande resultat med avseende på likartade partialkoefficienter. / In Sweden today there are a large number of dams and nearly half of Sweden's electricity is produced from hydropower. The safety requirements on the dams are high due to the consequences that a dam failure can cause. There are several design methods to achieve the expected safety requirements. The design guidelines used in the stability analysis of concrete dams in Sweden is based on the deterministic methods with safety factors. However, a new proposition for design guidelines based on probabilistic methods is being developed. Compared to the deterministic approach the probabilistic method takes into account the uncertainties in individual variables, which are expected to provide more efficient structures. One problem with stability analysis using probabilistic methods is that it can be very time consuming. Another method which combines the simplicity of the deterministic approach with the effectiveness of the probabilistic method is the use of partial factors. The use of partial factors is a semi-probabilistic method that can be calibrated from the reliability analysis in the probabilistic method and applied to the individual variables and parameters in the system similar to the safety factor. The aim of this thesis was to investigate if stability analysis of concrete dams with partial factors can be an alternative to the methods already available. The report can be divided into three parts. The first part of the report describes the theory behind the calibration process of partial factors using the first order reliability method, FORM. The second part describes existing Swedish methods and application guidelines for stability analysis of concrete dams. The knowledge from the first two parts is then used in order to calculate the reliability of 15 of Sweden's dams. It should be observed that the work contains some limitations, for instance only the sliding stability is studied using one static load case. The results from the calculation of this load case are then used to calibrate the partial factors. The result shows that it is not recommended to use the partial factors for stability analysis of concrete dams, at least not with the information and knowledge available today in the field. The uncertainties surrounding certain models and variables need to be reduced in order for partial factors to be an option. The theory behind partial factors requires a certain degree of uniformness when it comes to the structure or elements used. The difference among the dams analyzed in this study may have impacted the results negatively.

The purpose of this thesis is to evaluate the contribution of grouted rock bolts on the stability of concrete dams. The load capacity of the grouted rock bolts are assessed considering eventual deteriorating processes. An additional objective was to compare the resulting load capacity with the prevailing regulations in RIDAS (the power companies’ guidelines on dam safety) and possibly suggest new guideline values. The literature study consists of two parts; concrete dams and grouted rock bolts. In the first part concrete dams are discussed and especially the inherent forces and aspects when controlling their stability. The second part treats grouted rock bolts and the theoretical focus is on their function and possible failure modes as well as on the degrading processes (primarily corrosion) that are affecting the rock bolts.  Subsequently, the theory was applied on the Swedish concrete buttress dam Storfinnforsen, which is the largest concrete dam in Sweden. The dam was selected for this study mainly because its shape is archetypical for buttress dams. In addition, a digitalized model of the dam was obtainable from previous research projects.  A numerical analysis with the finite element analysis software ABAQUS was performed in order to evaluate the stability of the dam and to support the analytical analysis. The load capacity of the grouted rock bolts was analytically evaluated with consideration to eventual degradation. Assuming a corrosion rate of 60 μm/year, the grouted rock bolts in Storfinnforsen could after 100 years be trusted with a load capacity of approximately 180 MPa. That load capacity is due to shear failure, which constitutes the most plausible failure mode for rock bolts in buttress dams. The value 180 MPa is to be seen in contrast to the current limitation of 140 MPa that is defined in RIDAS (2011). The conclusion of this thesis is accordingly, that the maximum allowed load capacity that can be assigned the grouted rock bolts in the stability calculations of concrete dams can be increased from todays 140 MPa. This conclusion is substantiated by the analytical analyses with the numerical calculations as support.

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