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

It is essential to understand the mechanics of ice load and how it affects concrete dams located in a cold climate, such as Sweden, where the temperature becomes sufficiently cold to freeze the surface of the reservoir. The purpose of this thesis is to study ice load distribution along concrete dams, and its response during the application of an ice load. Two types of concrete dams were analysed, an arch dam and a buttress dam. For these dams, the influence from different parameters on the ice load distribution along the dams is studied. In addition to this, a study on how the ice load affects dam stability had also been performed. Stability analyses based on the finite element method were performed using both linear and nonlinear formulation of the interaction behaviour between the base of the dam and the underlying rock. A parametric study of ice sheet expansion on different dam types and geometries were performed. The expansion of the ice sheet was assumed to either be caused by a constant temperature 15 ˚C uniformly distributed over the ice thickness, or by a temperature gradient from 15 ˚C at the top surface of the ice sheet and 0 ˚C at the bottom. The parametric study also includes an investigation about influence of the shape of the reservoir beaches, where it either had a perpendicular shape towards the surface of the dam, or it had an angle of 30˚ with the dam surface. In the linear stability analysis, the structure continued to deform with increasing of the resultant pressure until it reached nonlinearity. The dam deflection had a linear relation with the applied ice load force until it reached the point when structure behaviour was nonlinear. The structure failed due to sliding, overturning or combination of both sliding and overturning. A material failure can also occur if the nonlinear material behaviour is considered, however this was not considered in this study. The parametric study showed that the ice load distribution was less near the beaches, and the distribution of the load on the concrete dam was higher near the top surface of the ice sheet. It was also shown in the study that the distribution of the ice load along the dam was as a cosine function where it had the maximum value at the buttress and the minimum at monolith connections. The result also showed that the load distribution over the thickness of the ice sheet was the same along the dam, regardless of the shape of the beaches or the length of the ice sheet. / Det är viktigt att förstå hur islasten beter sig och hur den påverkar betongdammar som är belägna i kallt klimat, som t.ex. Sverige, där temperaturen blir tillräckligt låg för att frysa ytvattnet i en flod. Syftet med detta examensarbete är att studera isbelastningsfördelningen längs en betongdamm och dess respons under en belastningen. Två olika typer av betongdammar har analyserats, vilka är valvdamm samt lamelldamm. För dessa, studerades det hur olika parametrar påverkar lastfördelningen från istrycket längsmed dessa dammar. Slutligen har det studerats hur islasten påverkar dammsäkerheten och risken för dammbrott. Inverkan från interaktionen mellan dammen och det underliggande berget som linjär eller olinjärt har studerats i stabilitetsanalyser baserade på finita elementmetoden. En parameterstudie har också genomförts för olika dammtyper och geometrier där islasten orsakades av en expansion av isytan. Denna expansion antogs vara orsakad av antingen av en jämn fördelad temperatur över istjockleken på 15 ˚C, eller en temperaturgradient över istjockleken med +15 ˚C på den övre ytan och 0 °C vid isens bottenyta. Den parametriska studien beaktar även inverkan från utformningen av stränderna, där den har definierats som antingen vinkelrät mot dammen eller med en lutande vinkel på 30 grader. I fallet med linjära stabilitetsanalyser kommer konstruktionen att fortsätta att deformeras som ett resultat av ökande resulterande tryckkraft. Dammens deformation har ett linjärt förhållande med den applicerade islasten till dess att den når en punkt då strukturens beteende övergå till olinjärt. Strukturens brottmod kan uppstå på grund av glidning, stjälpning eller i en kombination av både glidning och stjälpning. materialbrott kan uppstå om icke-lineariteterna beaktas. Dammen gick till brott på grund av glidning, vältning eller i kombinationen av dessa då. Materialbrott kan uppstå om icke-linjära materialmodeller inkluderas, men detta beaktades dock ej i denna studie. Den parametriska studien visar att isbelastningen är mindre nära stränderna och att belastningen på betongdammen är högre vid isens ovanyta. Studien visar att islastfördelningen längsmed dammen liknar en cosinusfunktion som når sitt maximum vid stödskivan och sitt minimum vid monolitanslutningen. Resultatet visar även att islastfördelningen genom islastens tjocklek har samma form längsmed dammen oavsett utformningen av stränder eller istäckets längd.

Many dams existing today were constructed around fifty years ago. Condition monitoring is essential for maintaining high safety and determining the current level of safety and stability for these dams. There is a need for new monitoring techniques and finite element coupled monitoring could be one of these techniques. A concrete arch dam located in Sweden is modelled and calibrated with respect to concrete temperature measurements. The temperature distribution is then defined as a prescribed strain in a structural mechanical model in which a parametric study is performed. The results from the parametric study are compared to measurements of the crest deformation and a combination of parameters is found giving the lowest difference between measurements and model results for the mid-section. The results show that the finite element model can be used to predict the behavior of the dam with acceptable deviation. The parametric study indicates that the reference temperature of the concrete has little effect on the amplitude of the deformation and that the governing factor is the coefficient of thermal expansion. / Många av de dammar som finns idag byggdes för omkring femtio år sedan. Tillståndsövervakning är avgörande för att kunna bestämma nivån av säkerhet och stabilitet för dessa dammar. Det finns ett behov av ny övervakningsteknik och finita element-kopplad övervakning kan vara en av dessa tekniker. En betongvalvdamm modelleras och kalibreras med avseende på uppmätt betongtemperatur. Den beräknade temperaturfördelningen definieras sedan som en föreskriven töjning en strukturmekanisk modell i vilken en parametrisk studie utförs. Resultaten från parameterstudien jämförs med mätningar av kröndeformation och en kombination av parametrar identifieras som ger lägsta skillnad mellan mätningar och modellresultat för mittsektionen. Resultaten visar att modellen kan användas för att förutsäga dammens beteende med acceptabel avvikelse. Parameterstudien indikerar att referenstemperaturen för betongen har liten inverkan på amplituden för deformationen och att den styrande faktorn är längdutvidgningskoefficienten.

En damm används i huvudsak för att magasinera vatten i energiutvinningssyfte. Dammen rör sig fram och tillbaka i ett säsongsmönster mestadels beroende på skillnader i utomhustemperatur och vattentemperaturen i magasinet. Det nordiska klimatet innebär risk för isläggning i magasinet, för vilken lasten är relativt outforskad. Denna rapport syftar till ett med multipla linjära regressionsmodeller samt dynamiska regressionsmodeller avgöra vilka variabler som förklarar en specifik svensk dammkonstruktions rörelse. Dammens rörelse mäts genom att mäta dammens förflyttning kontra berggrunden med data från dammens inverterade pendlar. Av särskilt intresse är att avgöra islastens påverkan på rörelsen. Resultaten visar att multipla linjära regressions-modeller inte fullständigt lyckas modellera dammens rörelse, då de har problem med autokorrelerade residualer. Detta hanteras med hjälp av autoregressiva regressionsmodeller där de initiala förklarande variablerna inkluderas, kallat dynamisk regression. Denna rapports resultat visar att de autoregressiva parametrarna fungerar mycket väl för att förklara pendlarna, men att även tid, temperatur, det hydrostatiska trycket samt istjocklek är användbara förklarande variabler. Istjockleken visar signifikant påverkan på 5 % signifikansnivå på två av de undersökta pendlarna, vilket är ett noterbart resultat. Författarna menar att rapportens resultat indikerar att det finns anledning att fortsätta forska kring islastens påverkan på dammkonstruktioner. / A dam is a structure mainly used for storing water and generating electricity. The structure of a dam moves in a season-based pattern, mainly because of the difference in temperature between the air on outside of the dam and the water on the inside. Due to the Nordic climate, occurrences of icing on the water in the basin is fairly frequent. The effects of ice on the structural load of the dam are relatively unexplored and are the subject to this bachelor’s thesis. The goal of this project is to evaluate which predictors are significant to the movement of the dam with multiple linear regression models and dynamic regressions. The movement is measured by inverted pendulums that register the dam’s movement compared to the foundation. It is of particular interest to determine if the ice load influences the movement of the dam. The multiple regression models used to explain the dam’s movement were all discarded due to autocorrelation in the residuals. This falsifies the models, since autocorrelation means that they don’t meet the needed assumptions. To counteract the autocorrelation, dynamic models with autoregressive terms were fitted. These models showed no problem with autocorrelation. The result from the dynamic models were successful and managed to significantly explain the movement of the dam. The autoregressive terms proved to be efficient explanatory variables. The dynamic regression models also show that the time, temperature, hydrostatic pressure and ice thickness variables are also useful explanatory variables. The ice thickness shows a significant effect at the 5 % significance level on two of the investigated pendulums. The report's results indicate that there is reason to continue research on the ice load impact on dam constructions.