Drying shrinkage of concrete is often estimated using a phenomenological approach where it is assumed that shrinkage is proportional to the change in internal humidity. In this study, a mechanistic approach was used which instead aims to mathematically describe the physical processes of drying shrinkage. Simulations of two laboratory tests were made and compared to results from two models based on the phenomenological approach. The results show that the developed model can describe drying shrinkage of concrete equally well as the phenomenological models but without the need to specify the final drying shrinkage strain.

The purpose of this study is to show the influence and significance of including water filling of air pores when studying moisture conditions in concrete structures cast with air-entrained concrete and in contact with free water. Especially if the aim is to assess the risk for frost damages in different regions of the structure, based on a critical degree of saturation, in order to ultimately perform a service life prediction. A hygro-thermo-mechanical multiphase model that includes the effect of water filling in air pores, recently presented by the authors, is briefly described and applied in two numerical examples. The results show moisture distributions that would not be possible to capture without the air pore filling included in the model. More importantly, the general shape of these distributions complies well with measured distributions in real concrete structures as well as with distributions obtained in laboratory measurements.

Many concrete structures located in cold climates and in contact with free water are cast with air-entrained concrete. The presence of air pores significantly affects the absorption of water in the concrete, and it might take decades before these are fully saturated. This generally improves the long-term performance of such structures and in particular their frost resistance. To study the long-term moisture conditions in air-entrained concrete, a hygro-thermo-mechanical multiphase model is presented, where the rate of water filling of air pores is described as a separate diffusion process. The driving potential is the concentration of dissolved air, obtained using an averaging procedure with the air pore size distribution as the weighting function. The model is derived using the Thermodynamically Constrained Averaging Theory (TCAT) as a starting point. Two examples are presented to demonstrate the capabilities and performance of the proposed model. These show that the model is capable of describing the complete absorption process of water in air-entrained concrete, and yield results that comply with laboratory and in situ measurements.

Many concrete structures located in cold climates and in contact with free water are cast with air-entrained concrete. The presence of air pores significantly affects the absorption of water into the concrete, and it may take decades before these are fully saturated. This generally improves the long-term performance of such structures and in particular their frost resistance. To study the long-term moisture conditions in air-entrained concrete, a hygro-thermo-mechanical multiphase model is presented, where the rate of filling of air pores with water is described as a separate diffusion process. The driving potential is the concentration of dissolved air, obtained using an averaging procedure with the air pore size distribution as the weighting function. The model is derived using the thermodynamically constrained averaging theory as a starting point. Two examples are presented to demonstrate the capabilities and performance of the proposed model. These show that the model is capable of describing the complete absorption process of water in air-entrained concrete and yields results that comply with laboratory and in situ measurements.

Even though air-entrained concrete is usually used for concrete structures located in cold climates that are exposed to wet environments, frost damages are frequently detected during inspections. However, it is often hard to assess the extent and severity of these damages and, thus, there is a need for better tools and aids that can complement already established assessment methods. Several studies have successfully shown that models based on poromechanics and a multiphase approach can be used to describe the freezing behaviour of air-entrained concrete. However, these models are often limited to the scale of the air pore system and, hence, hard to use in applications involving real structures. This study proposes a hygro-thermo-mechanical multiphase model which describes the freezing behaviour of partially saturated air-entrained concrete on the structural scale. The model is implemented in a general FE-code and two numerical examples are presented to validate and show the capabilities of the model. The first concerns a series of experimental tests of air-entrained cement pastes, whereas the second aims to show the capability of the model to account for an initial non-uniform distribution of moisture. The results show that the model can reproduce the freezing behaviour observed in the experimental tests on a structural scale as well as being capable of describing freezing induced deformations caused by non-uniform moisture distributions.

Even though air-entrained concrete is usually used for concrete structures located in cold climates that are exposed to wet environments, frost damage is frequently detected during inspections. However, it is often hard to assess the extent and severity of the damage and, thus, there is a need for better tools and aids that can complement already established assessment methods. Several studies have successfully shown that models based on poromechanics and a multiphase approach can be used to describe the freezing behaviour of air-entrained concrete. However, these models are often limited to the scale of the air pore system and, hence, hard to use in applications involving real structures. This study proposes a hygro-thermo-mechanical multiphase model which describes the freezing behaviour of partially saturated air-entrained concrete on the structural scale. The model is implemented in a general FE-code and two numerical examples are presented to validate and show the capabilities of the model. The first concerns a series of experimental tests of air-entrained cement pastes, whereas the second aims to show the capability of the model to account for an initial non-uniform distribution of moisture. While the model predictions underestimate the magnitude of the measured strains, the results still show that the model can capture the general freezing behaviour observed in the experimental tests on the structural scale. Furthermore, the results demonstrate that the model is capable of describing freezing induced deformations caused by non-uniform moisture distributions.

During its lifetime, a concrete structure is subjected to many different actions, ranging from mechanical loads to environmental actions. To accurately predict its integrity from casting and throughout its service life, a modelling strategy is required that considers mechanical loading but also implicitly accounts for physical effects such as temperature and moisture variations. This is especially true for large concrete structures found in many infrastructure applications such as bridges, nuclear power plants and dams. Modelling concrete as a multi-physical material is becoming an increasingly used approach for which large research efforts are being made, including the development of more refined mathematical and numerical methods as well as considering more physical and chemical variables in the coupled model.

The research project, of which this licentiate thesis is the first phase, aims at investigating aging concrete structures at hydro power facilities, with focus on the internal structures of the power plants. This thesis presents a review of advanced mathematical methods and concepts for modelling aging concrete found in the literature which can later be applied to study such structures. The focus is on models that describe the deformational behaviour of concrete where aspects such as aging, cracking, creep and shrinkage are investigated. However, in order to accurately describe such phenomena, a multi-physical approach is adopted where moisture and temperature variations in the concrete are studied. Also, models that describe the chemical behaviour related to hydration and thus in extension aging, are also reviewed and introduced in the multi-physical framework. The use of such models are discussed in the context of the finite element method (FEM), in which coupled models are implemented, verified and applied in the appended papers using two different FE codes.

Several verification examples are presented covering different aspects of the implemented models, both in isolation and coupled in a multi-physical setting. By comparing the numerical results with experimental data from the literature it can be shown that it is possible to predict most aspects of aging concrete that have been of interest here. While these examples are all on a laboratory scale, numerical examples and case studies are also provided that exemplify how the models can be applied on a structural scale. By using the developed analysis tools, valuable information and insights can be gained on aging concrete structures and these tools will in the next phase of the research project be applied to large concrete structures at hydro power facilities.

With the societal demand for sustainability and the increasing age of infrastructure, a crucial task for the civil engineering community is to improve the durability of concrete structures. This thesis aims to contribute to such development through theoretical studies using mathematical modelling and numerical simulations. During its service life, a concrete structure is subjected to many different actions, ranging from mechanical loads to chemical and physical processes. Hence, a sound modelling strategy requires multiphysics and the inclusion of coupled chemical and physical fields (e.g. temperature, moisture and cement hydration) in addition to methods that describe mechanical integrity of the material. Conditions and phenomena critical for concrete structures at hydropower facilities have been of particular interest to study.

The thesis presents several mathematical models of various complexity to describe the multiphysical behaviour of concrete using a material point description. A significant focus is on models that describe the mechanical behaviour of concrete where aspects such as ageing, cracking, creep and shrinkage are investigated. For the creep behaviour, a state-of-the-art model based on the Microprestress–Solidification (MPS) theory is reviewed and further developed. The appended papers (III to IV) presents a mathematical framework for the modelling of durability aspects of concrete based on multiphase porous media theory. The governing equations are derived with the Thermodynamically Constrained Averaging Theory (TCAT) as a starting point. It is demonstrated how this framework can be applied to a broad variety of phenomena related to durability; from the casting and hardening of concrete to the long-term absorption of water into air-entrained concrete. The Finite Element Methods (FEM) is used to solve the proposed mathematical models, and their capabilities are verified using experimental data from the literature.

The main research contribution is the development and evaluation of theoretical models that advance the understanding and improve knowledge of the ageing and durability of concrete and concrete structures. More precisely, it is shown how multiphysical models and the developed multiphase framework can be used to gain insights on the material behaviour of concrete at smaller scales while they are also applicable to structural-scale simulations. During all model development, the efficient solution of structural problems has been fundamental. Through case studies and several examples from the literature, it is exemplified how these models can be used to enhance the performance and thereby increase the durability of concrete structures.

Nuclear concrete containment buildings typically consist of pre-stressed concrete. The pre-stressing tendons are utilized to enforce a compressive state of stress to ensure that cracks do not occur in the containment structure. The tendons are thereby an important part of the containment building and important for its structural integrity. In many cases, these tendons are grouted with cement grout to prevent corrosion. This results however in that it is not possible to directly assess the tendons or re-tension these if significant long term losses occurs. The drawback with cement grouted tendons is, thereby, that it is not possible to directly measure the current tendon force. One conventional method to assess the status of the containment building, and thereby indirectly the tendons, is to perform pressure tests. The pressure tests are performed where the pressure in the containment building is increased. The response of the containment can after this be determined based on measurements of displacements and strains. The purpose of this project is to perform simulations of a pressure test of a Boiling Water Reactor (BWR) that is common in Sweden and Finland. Based on these simulations, the response of the containment building is determined and suggestions are made regarding suitable placement of measuring sensors. The suggested instrumentation has been divided into different types of sensors defined as detectors and support sensors. The detectors are needed to monitor the structural response of the containment while the support sensors are needed to give sufficient input to numerical analyses. It is suggested that detector sensors are placed at four vertical positions and at three points along the perimeter. At these locations, it is recommended that displacement sensors, strain gauges and temperature sensors are installed. In addition, it is also recommended that the relative radial displacement between the intermediate slab and the cylinder wall is monitored. As support sensors, it is recommended that the ambient temperature and relative humidity is measured since these constitute important boundary conditions for numerical analyses and thereby prediction of the structural behaviour.

An extension of the Solid mechanics interface in Comsol Multiphysics is presented to analyse localized deformations of quasi-brittle materials, for example cracking in concrete. This is achieved by implementing an isotropic damage mechanics constitutive law, which is combined with both a local and a non-local regularization technique to ensure mesh objectivity. The implementation is made using equation based modelling and modification of built-in features. To facilitate easier use of the model, a custom user interface is constructed using the Physics Builder. Lastly, the implemented model is validated using examples of both plain and reinforced concrete, with two examples taken form the literature. Overall the simulation results are in good agreement with the experimental observations.

Time-dependent deformations, such as creep and shrinkage, are important when dealing with durability aspects of concrete. In the current study, a multi-field analysis method is described, verified and used in a numerical study to investigate the influence of short and long term variations in temperature and relative humidity. It is found that especially the creep behaviour is significantly influenced by the seasonal variations in climate conditions and also to a lesser extent the daily variations.

The design and maintenance of concrete dams in cold regions is a challenging task, in large due to the temperature difference between summer and winter. In order to enhance the knowledge of this, theme A of the 14th International Benchmark Workshop on Numerical Analysis of Dams is dedicated to the prediction of the extent of cracking in a concrete arch dam due to temperature variations. The current study proposes a solution to this using the finite element software COMSOL Multiphysics. A global model is set up to analyze the transient temperature variations as well as the displacements given the assumption of a linear material behavior. To predict the extent of cracking, a rate-dependent isotropic damage model is implemented as an extension of the built-in functionality of COMSOL Multiphysics. Furthermore, a submodel is created to allow for a higher mesh resolution in the non-linear analysis. The results indicate that the considered arch dam suffers a large risk of cracking due to temperature variations, especially on the downstream side. Most cracks propagate during the winter, although some cracks appear already when static loads are applied.

Understanding the early-age behaviour of concrete is of importance for designing durable concrete structures. To contribute to the improvement of this, a hygro-thermo-chemo-mechanical model is presented that accounts for phenomena such as hydration, external and internal drying, self-heating, creep, shrinkage and fracture. The model is based on a multiphase porous media framework, using the Thermodynamically Constrained Averaging Theory (TCAT) as starting point to derive the governing equations of the system. This allows for a systematic treatment of the multiscale properties of concrete and how these develop during hydration, e.g. chemical and physical fixation of water. The proposed mathematical model is implemented within the context of the Finite Element Method (FEM), where all physical fields are solved in a fully-coupled manner. Chosen properties of the model are demonstrated and validated using three experimental results from the literature. Generally, the simulated results are in good agreement with the measurements.

Methods to describe the interaction between fluids and solids has been one of the biggest focus points for the research within the field of computationalengineering for the recent years. This area is of interest to a variety ofengineering problems, ranging from flow in blood vessels, aerodynamics andof course the interaction between water and civil engineering structures. Thetypical civil engineering application of fluid-structure interaction (FSI)encountered in a nuclear facilities is obtained at seismic loading, where the nuclear facilities consists of water filled pools of various sizes, for example the spent fuel and condensation pools. These water filled pools contribute with added mass to the structure, which lowers the natural frequency of thestructure as well as hydrostatic and hydrodynamic pressure that acts on thewalls of the pool due to wave propagation in the fluid. In addition, as the pools also have a free water surface towards the environment of thestructure, free surface wave propagation also has to be accounted for; i.e.sloshing. This introduces extra non-linearity to the problem, since a freesurface constitutes a boundary condition with an unknown location.

The main part of this report constitutes as a state-of-the-art summary whereconcepts important for FSI analyses are presented and important differencesare discussed. Due to the different interests of the numerous disciplinesengaged in this research area, a large number of methods have been developed, where each has different strengths and weaknesses suited for the problem in mind when developing the method. The focus of this report havebeen to describe the most important numerical techniques and the categories of methods that or of most interest for civil engineering problems, such as simplified analytical or mass-spring models, Acoustic Elements, ArbitraryLagrangian-Eulerian (ALE) and coupled Eulerian-Lagrangian (CEL).

Thereafter two benchmark examples are presented, intended to highlightdifferences between the different methods. In the first study, sloshing of aliquid tank is studied where the numerical methods are compared toexperimental results, regarding the movement of the free water surface. In addition, the hydrodynamic (fluid) pressures on the walls of the tanks arecompared between the different numerical methods. It was shown that mostanalysis methods give accurate results for the sloshing wave height whencompared with the experimental data. It should however be mentioned that the tank was only excited by a simple harmonic motion with a frequency thatdo not give rise to any resonance waves in the water body.

Also when it comes to fluid pressure good agreement between the differentanalysis methods was found, although no experimental data was available forthis parameter. It was also noticed that for the sloshing tank, most of the change in pressure occurred close to the free surface of the water, which indicates that it mainly consists of a convective pressure, i.e. from the sloshing. Thereby, finite element programs that account the impulsive mass incivil engineering FSI problems should not be used for this type of analysis. In the second study, the numerical methods are compared based on differenttypes of seismic input, such as a large earthquake with mainly low frequencycontent typically like an earthquake on the US west coast and one smallerearthquake with relatively higher degree of high frequency content typicallylike a Swedish type of earthquake. One important observation was that the relative increase in induced stresses in the structure, with and withoutconsideration of the water was significantly larger for the Swedish earthquakethan for the US earthquake. One possible reason for this may be that the Swedish earthquake is not large enough to excite the relatively stiff structurewithout any water, but it will induce significant dynamic effects in the waterwhich give rise to higher stresses in the concrete as well. However, this shows that it is very important to include water in seismic analyses.

In earlier times, the generators of the hydropower plants ran more or less continuously, while nowadays there are many planned starts and stops. The hydropower stations are thereby, due to the new pattern of operation, subjected to loads that they were not originally designed for. The aim of this study is to understand the complex interaction between the power generating system and the supporting concrete structure, during this new operational pattern.

During inspections, cracks were discovered in the concrete structure of the power house, near the stator and rotor spider supports, at several hydropower stations in Sweden. In a previous phase of this project it was shown that these cracks initiated due to the combined effect of drying shrinkage, mechanical loads and variations in temperature due to starts and stops. Cracking of the concrete structure reduces its stiffness, which may result in larger loads acting on the structure and vibrations exceeding the unit’s strict tolerance limits.

In this part of the study, the behaviour of a concrete support structure subjected to rotor dynamic loads during normal operation has been studied. A detailed 3D numerical model has been developed which include hydropower unit. The results of this study show that a reduced structural stiffness of the concrete support structure, due to cracking, influences the behaviour of the rotating system.

At many of the Swedish hydropower plants, cracks have been observed in the concrete power station. Although the presence of cracks in these massive concrete structures does not pose an immediate threat to the structural safety, it of course affects its durability. Besides this, and perhaps as important in this application, the presence of cracks reduces the structural stiffness which affects the operation of the machinery.A case study is presented, where cracks have been found in the concrete support. Furthermore, analysis methods to evaluate the status of the concrete support; mainly through the use of finite element analysis are proposed.

It is necessary to consider coupled analysis methods for a simulation to accurately predict the long-term deformations of concrete structures. Among other physical fields that can be considered, both temperature and moisture have a significant influence on the deformations. Variations of these fields must therefore be included implicitly in an analysis. This paper presents a coupled hygro-thermo-mechanical model for hardened concrete based on the framework of the Microprestress-Solidification theory. The model accounts for important features of concrete such as ageing, creep, shrinkage, thermal dilation and cracking; all of these under variable temperatures and moisture conditions. It is discussed how to implement the proposed model in a flexible numerical framework that is especially suitable for multi-physics analyses. The capabilities of the model are shown through the analysis of three experimental data sets from the literature, with focus on creep and shrinkage. Overall, the agreement between the analysis and experimental results is good. Finally, a numerical example of a concrete gravity dam with dimensions and loads typical to northern Sweden is analysed to show the capabilities of the model on a structural scale.

The durability of concrete structures is in no small degree determined by the quality and integrity of the concrete, where structural damages such as cracks negatively affect many of the functions of the structure. Often cracks are formed due to restrained thermal and hygral deformations, where the risk is exceptionally high during the early stages after casting. This study presents a hygro-thermo-chemo-mechanical model that accounts for phenomena such as hydration, external and internal drying, self-heating, creep, shrinkage and fracture. The model is derived as a modified version of a fully-coupled multiphase model recently proposed by Gasch et al. (Cem Concrete Res 116:202–216, 2019. https://doi.org/10.1016/j.cemconres.2018.09.009) and implemented in the Finite Element Method. Here the governing equations are simplified, and a more efficient solution method is proposed. These modifications are made with the intention to obtain a model more suitable for structural scale simulations. To validate the model, one of the end-restrained beams tested within the French research project CEOS.fr is analyzed. Laboratory data on the concrete is used to calibrate to model and recordings of ambient conditions makes it possible to define accurate boundary conditions. Results from the simulation are compared to measured temperatures and deformations from the first 60 days after casting and are found to generally be in good agreement. Compared to the fully-coupled model by Gasch et al. (2019), the modifications proposed in this study reduce the computational cost by a factor five; without any noticeable differences to the structural results.

The durability of concrete structures is in no small degree determined by the quality and integrity of the concrete, where structural damages such as cracks negatively affect many of the functions of the structure. Often cracks are formed due to restrained thermal and hygral deformations, where the risk is exceptionally high during the early stages after casting. This study presents a hygro-thermo-chemo-mechanical model that accounts for phenomena such as hydration, external and internal drying, self-heating, creep, shrinkage and fracture. The model is derived as a modified version of a fully-coupled multiphase model recently proposed by Gasch et al. (2019) and implemented in the Finite Element Method. Here the governing equations are simplified, and a more efficient solution method is proposed. These modifications are made with the intention to obtain a model more suitable for structural scale simulations. To validate the model, one of the end-restrained beams tested within the French research project CEOS.fr is analyzed. Laboratory data on the concrete is used to calibrate to model and recordings of ambient conditions makes it possible to define accurate boundary conditions. Results from the simulation are compared to measured temperatures and deformations from the first 60 days after casting and are found to generally be in good agreement. Compared to the fully-coupled model by Gasch et al. (2019), the modifications proposed in this study reduce the computational cost by a factor five; without any noticeable differences to the structural results.

Several concrete buttress dams in northern Sweden have been found to be subjected to, more or less severe, cracks according to recent assessments and investigations. Theoretical analyses and field measurements have shown that most of these cracks have developed or propagated as a result of the seasonal temperature variations. Most dams in Sweden were built for more than 50 years ago and it is therefore important to also consider the influence of long-term effects and degradation to assess the dam. The ordinary sliding and overturning stability analyses may not be sufficient when the supporting structure is cracked, since the cracks may comprise the integrity and the homogeneity of the structure.

The work presented in this report is a continuation of the work on advanced numerical methods for studying crack propagation in concrete dams presented in Björnström et al. (2006), Ansell et al. (2008), Ansell et al. (2010) and Malm et al. (2013). In the latter parts of the project the main focus has been on the development of probabilistic analysis methods for studying crack propagation, mainly with respect to the stochastic variation of material properties of concrete but also with regard to loading conditions. The concepts of the used probabilistic analysis methods were introduced in a previous part of the project, (Malm et al. 2013).  In the previous part, stochastic spatial distribution of material properties was only studied within local areas where a crack was expected to be developed. In the work presented in this report, this concept has been expanded to cover stochastic spatial distribution of material properties within an entire buttress wall of one monolith. A sensitivity study is also presented regarding variations in the assumed temperatures of the seasonal temperature loading.

To increase the accuracy of the numerical model a new FE-model was developed with a refined mesh compared to previously used meshes. The new mesh size was chosen with respect to the smallest characteristic crack length of a concrete sample in the stochastic population. All other aspects of the model were defined equally as in previous models.

The results of the probabilistic analyses with respect to variation in material properties showed a significant increase in developed cracks, compared to a deterministic analysis. The main crack patterns were, however, similar, but additional cracks were developed adjacent to previous cracks and the inclination of some cracks was changed. These findings should be included when assessing different dam stability failure modes of buttress dams. The sensitivity study of the assumed temperatures showed that it was mainly the low temperatures in combination with temperature differences that initiate cracking in the monolith.

The concrete structures at Swedish hydro power facilities were built during the early to mid-20th century and many of them are starting to exhibit age related wear and deterioration. It isimportant to ensure the integrity of these concrete structures from a dam safety perspectiveand also to secure a safe operation of the power facility in the future. With the latter in mind,this paper aims to study the concrete structures that house the power generating machinery ofthe facility, especially the parts close to the generator where the loads from the power unit aresupported. Cracks observed in these structures will reduce its stiffness, which affects theoperation of the rotating machinery. This paper presents and discusses some generalconsiderations and loads that are of importance for this type of structures and highlights sometypical cracks that have been observed in Swedish hydro power facilities. To complement thisdiscussion, a case study is presented of a hydro power facility where cracks have been foundin the concrete support structure of the power unit, especially at the interconnections betweenthe unit and the concrete. The most likely cause of these cracks are investigated through nonlinearfinite element analysis considering mechanical loads as well as physical loads such asdrying shrinkage and temperature variations. It is concluded that the long-term physicalloading is the most probable cause of the observed cracks. However, the operation of thepower unit and changes in its operational pattern can cause further propagation of thesecracks. Finally, suggestions on possible enhancement of the analysis methods used in the casestudy are proposed and discussed for further studies of this type of concrete structures.

The concrete structures at Swedish hydro power facilities were built during the early to mid-20th century and many of them are starting to exhibit age related wear and deterioration. It isimportant to ensure the integrity of these concrete structures from a dam safety perspectiveand also to secure a safe operation of the power facility in the future. With the latter in mind,this paper aims to study the concrete structures that house the power generating machinery ofthe facility, especially the parts close to the generator where the loads from the power unit aresupported. Cracks observed in these structures will reduce its stiffness, which affects theoperation of the rotating machinery. This paper presents and discusses some generalconsiderations and loads that are of importance for this type of structures and highlights sometypical cracks that have been observed in Swedish hydro power facilities. To complement thisdiscussion, a case study is presented of a hydro power facility where cracks have been foundin the concrete support structure of the power unit, especially at the interconnections betweenthe unit and the concrete. The most likely cause of these cracks are investigated through nonlinearfinite element analysis considering mechanical loads as well as physical loads such asdrying shrinkage and temperature variations. It is concluded that the long-term physicalloading is the most probable cause of the observed cracks. However, the operation of thepower unit and changes in its operational pattern can cause further propagation of thesecracks. Finally, suggestions on possible enhancement of the analysis methods used in the casestudy are proposed and discussed for further studies of this type of concrete structures.

An extensive program for improvement of the hydropower plants in Sweden is currently on-going. The aims are to secure future production and to maintain and further develop an already high dam safety.

During inspection, cracks were discovered in the concrete foundation, near the stator and rotor spider supports, at some hydropower stations in Sweden. The cracks were believed to be related to new patterns for generator operation, thereby changing the dynamic loading of the stator and rotor spider supports. Previously the generators ran continuously, while nowadays there are an increased number of stops and starts, sometimes even several times during one day. Increased dynamic forces due to runaways, and also other dynamic events such as emergency stops, may also contribute to increased stress levels and cracking of the foundation. Furthermore, although extreme loads such as short circuits of the generator seldom occurs, the influence on the dynamic forces acting on the supporting structure and concrete foundation may be strongly influenced during such events.

The objective of this study is to understand the complex interaction between the power generating system (stator, rotor, turbine, etc.) and its supporting concrete structure. It is important from a dam safety perspective to determine the causes of existing structural cracks in the foundation. Furthermore, to be able to predict further crack propagation of the concrete foundation will help to determine future maintenance requirements.

A three dimensional non-linear finite element model developed earlier was used to evaluate a methodology for analyses of the interaction between the generator and the concrete foundation. The influence of cracks in the concrete foundation was investigated by including the fracture pattern obtained in earlier FE analyses of time-dependent thermal and moisture gradients. These analyses showed that the drying shrinkage induced cracking inside the concrete foundation and especially close to the supports of the stator and the rotor spider. The obtained fracture pattern for the previous analysis was used as input for this study, with the concrete foundation’s changed structural properties and their influence on the interaction with the generator considered in the analyses. Furthermore, deadweight and operational load were also included in the analyses.

The study show that FE models with a cracked concrete foundation can be used to analyse structural interaction betwee foundation and generator components during operation of a hydro power generator. The crack pattern can be determined by FE analyses, or by in-situ measurements of existing concrete cracks for a specific concrete foundation. The analyses show that further studies are needed regarding the combined effects from thermo-mechanical loads, drying shrinkage, creep and dynamical loads caused by the generator. The combined effects may further increase the stress levels for the concrete foundation, especially locally near perforations, and stator and rotor spider supports. These analyses should be performed with an increased numerical resolution for both the concrete foundation and the supporting structure for the generator, with an increased accuracy for the local stress variations near perforations of the foundation and also at the supports for the generator. This research area will be further investigated within a recently started research project at KTH, financed by the Swedish Hydropower Centre.

The behaviour of concrete at early-age is complex and involves several physical fieldssuch as temperature, moisture and deformations. In this paper a hygro-thermo-chemo-mechanicalmodel for the analysis of early-age concrete based on a combination of models from the literature ispresented. The chemical model is based on the reaction degree concept, also used to define internal actions such as self-desiccation and ageing of mechanical properties. A mechanical model based on the Microprestress-Solidification theory for concrete creep is used, that in a simplified manner alsoconsiders concrete fracture. The model has been implemented in a numerical framework suitable for coupled multi-physics problems. It is here applied to a case study of an un-reinforced concrete tunnel plug made of a low-pH self-compacting concrete. Good agreement is generally obtained with measurements and hypotheses previously made on the behaviour of the plug are verified.

The aim of this study is to investigate how Fluid-Structure interaction may beincluded in numerical earthquake analyses of dams. The basis for this project is theme Afrom ICOLDs 12th international benchmark workshop on numerical analysis of dams,which was held in October 2013. The focus of theme A was on how to account for fluidstructure interaction in numerical earthquake analyses of dams. In this study, parametricnumerical analyses have been performed where the purpose was to isolate someimportant parameters and investigate how these influence the results in seismic analysesof dams. These analyses were performed through the use of the finite element methodare the choice of Rayleigh damping parameters, reservoir boundaries and waveabsorption in the foundation-reservoir interface. The use of acoustic elements has proven to be a powerful approach for FSI analyses of adam-reservoir-computation time, while allowing for more advanced features such as bottom absorptionand non-be a challenging task, where it has a significant impact on the results. The methodproposed by Spears and Jensen has a physical meaning in the sense that this methodexcites the same e ective mass for the Rayleigh damped case as for the modal dampedcase. If a constant modal damping is desired or prescribed in a standard, this methodprovides a reasonable and sound method to choose the Rayleigh damping parameters fora complex structure. A more straightforward method is to choose the two frequencies insuch a way that the span between the frequencies covers about 80% of the e ective mass.The choice of reservoir boundary conditionsparameter showed to be the one that least a ected the results in the time-history analysis.results and this coe cient should be used carefully.

The aim of this study is to investigate how Fluid-Structure interaction may be included in numerical earthquake analyses of dams. The basis for this project is theme A from ICOLDs 12th international benchmark workshop on numerical analysis of dams, which was held in October 2013. The focus of theme A was on how to account for fluid structure interaction in numerical earthquake analyses of dams. In this study, parametric numerical analyses have been performed where the purpose was to isolate some important parameters and investigate how these influence the results in seismic analyses of dams. These analyses were performed through the use of the finite element methodare the choice of Rayleigh damping parameters, reservoir boundaries and wave absorption in the foundation-reservoir interface. The use of acoustic elements has proven to be a powerful approach for FSI analyses of adam-reservoir-computation time, while allowing for more advanced features such as bottom absorption and non- be a challenging task, where it has a significant impact on the results. The method proposed by Spears and Jensen has a physical meaning in the sense that this method excites the same e ective mass for the Rayleigh damped case as for the modal damped case. If a constant modal damping is desired or prescribed in a standard, this method provides a reasonable and sound method to choose the Rayleigh damping parameters for a complex structure. A more straightforward method is to choose the two frequencies in such a way that the span between the frequencies covers about 80% of the e ective mass. The choice of reservoir boundary conditionsparameter showed to be the one that least a ected the results in the time-history analysis. results and this coe cient should be used carefully.

The aim of this study is to investigate how fluid-structure interaction (FSI) may be included in numerical earthquake analyses of dams. The basis for this project is Theme A from ICOLD’s 12th International Benchmark Workshop on Numerical Analysis of Dams[5], which was held in October 2013 in Austria. The focus of Theme A was on how to account for fluid-structure interaction in numerical earthquake analyses of dams. In this study, parametric numerical analyses have been performed, where the purpose was to isolate some important parameters and investigate how these influence the results in seismic analyses of dams. These analyses were performed through the use of the finite element method, where the reservoir was modelled with acoustic finite elements. The studied parameters are the choice of Rayleigh damping parameters, reservoir boundaries, and wave absorption in the foundation-reservoir interface.

The use of acoustic elements has proven to be a powerful approach for FSI analyses of a dam-reservoir-foundation system. The acoustic finite elements provide reasonable computation time, while allowing for more advanced features such as bottom absorption and non-reflecting boundaries. The choice of Rayleigh damping coefficients has proven to be a challenging task,

where it has a significant impact on the results. The method proposed by Spears & Jensen[1] has a physical meaning in the sense that this method excites the same effective mass for the Rayleigh damped case as for the modal damped case. If a constant modal damping is desired, or prescribed in a standard, this method provides a reasonable and sound method to choose the Rayleigh damping parameters for a complex structure. A more straightforward method is to choose the two frequencies in such a way that the span between the frequencies covers about 80% of the effective mass. The choice of reservoir boundary conditions was based on the assumption of an infinite reservoir. A conservative approach is to use a fixed boundary condition, where the pressure waves are reflected at the upstream boundary of the reservoir. However, this parameter proved to be the one that least affected the results in the time-history analysis. The reflection coefficient describing bottom absorption showed to greatly influence the results, and this coefficient should be used  carefully.

Recent assessments and investigations of buttress dams in northern Sweden reveal several types of cracks. The theoretical analysis and field measurements have showed that the most of the cracks are either developed or propagated as a result of the seasonal temperature variations. Cracks influence the behaviour of the dams in different ways, such as reducing the tightness of the dam and increasing the hydraulic pressure within the material/structure. Furthermore, cracks may have an impact on the stiffness and stability of the dam. The ordinary sliding and overturning stability analyses are not sufficient when the supporting structure is cracked. The cracks may comprise the integrity and the homogeneity of the structure. A cracked, and for that matter even repaired structure, can’t be regarded as a homogenous structure and should be treated accordingly. Consequently, other types of models instead of the conventional design models should be utilized for the stability analyses of the cracked and repaired dams.

The mode of the failure is one of the decisive elements considering determination of the probability of the failure. The conditions for crack initiation and the trajectory of the crack propagation are the decisive factors which govern the failure mode. Ordinary design methods and advanced numerical models which are based on the elastic behaviour of the structure can’t be utilized, since these models are not able to describe the non-linear behaviour and to predict the failure mode of the structure.

A finite-element model based on non-linear fracture mechanics is being utilized to study crack development in a buttress dam. The aim of the study was to reveal crack trajectories and different probable failure modes, and moreover to determine the influences of the cracks on the overall behaviour of the structure. In a real structure the loading (mechanical and environmental) and boundary conditions are decisive factors regarding initiation, propagation and trajectory of the cracks. Furthermore, the material properties and their statistical distribution may influence the formation of cracks and the mode of failure.

A concrete arch dam subjected to seismic ground accelerations has been analysed using the finite element method. The response of the concrete structure is calculated through dynamic implicit analyses using two different modelling approaches, the Westergaard added mass approach with hydrodynamic inertia forces from a finite water volume and a model based on acoustic elements. The models show high tensile stresses near the base of the dam which indicate a risk for cracking. The study demonstrate that the choice of damping, the type of seismic excitation and use of quiet boundaries have a significant influence on the result.

Several concrete buttress dams in northern Sweden have been found to be subjected to, more or less severe, cracks according to recent assessments and investigations. Theoretical analyses and field measurements have shown that most of these cracks have developed or propagated as a result of the seasonal temperature variations. Most dams in Sweden were built for more than 50 years ago and it is therefore important to also consider the influence of long-term effects and degradation to assess the condition of the dam. In this paper, simulations have been performed with detailed 3D nonlinear numerical analyses in order to study crack initiation and crack propagation due to stochastic variation in material properties, which represent concrete degradation. The structural response due to loads from gravity, hydrostatic water pressure and thermal seasonal effects have been considered in the studies. It was shown that weak material properties near the crack-tip will govern the trajectory of the crack. According to the analyses, significant amount of cracking can occur in the front-plate and buttress if the strength of the concrete is reduced, which lead to new potential failure modes. In addition, the extent of cracking in the buttress dam is largely governed by the induced cracking in the front-plate since these cracks have a tendency to propagate into the concrete buttress. Based on the calculated extent of cracking in the dam body, different failure modes can be assessed in order to determine the dam stability failure.

Several concrete buttress dams in northern Sweden have been found to be subjected to, more or less severe, cracks according to recent assessments and investigations. Theoretical analyses and field measurements have shown that most of these cracks have developed or propagated as a result of the seasonal temperature variations. Most dams in Sweden were built for more than 50 years ago and it is therefore important to also consider the influence of long-term effects and degradation to assess the dam. The ordinary sliding and overturning stability analyses may not be sufficient when the supporting structure is cracked, since the cracks may comprise the integrity and the homogeneity of the structure.

This project is a continuation from previous projects presented by Björnström et al. (2006), Ansell et al. (2008) and Ansell et al. (2010). In these previous projects, Storfinnforsen hydropower dam located in northern part of Sweden was studied and the purpose of the projects was to explain the cause for cracking found in situ. In the present project, the previously developed numerical model was verified against measured variations in crest displacement and crack width due to temperature variations during one year. The results showed that the numerical model, which was used, could predict both variations in displacements and crack width with good accuracy compared to the measurements on the actual dam.

The studies of this project which are presented in this report are focused on the crack propagation due to stochastic variations in material properties. This was performed with probabilistic analyses based on a local model of an inclined crack in the supporting buttress. Monte-Carlo simulations were performed where each element was randomly assigned a concrete strength according to an assumed material distribution. It was shown that weak material properties near the crack-tip will govern the propagation and the trajectory of the crack. The results also showed that the average crack propagation from the probabilistic analyses differed both regarding inclination and length compared to the deterministic analysis which was based on mean values. In addition to the local analyses, global analyses were also performed, where stochastic variations in material properties were assigned to the whole monolith. The analyses showed that using design values or characteristic values of the material strength may give a different failure mode compared to the case where mean values of the material properties are used. When considering nonlinear properties for verification analyses, it is important to base the material properties on as accurate material properties as possible. In addition, the extent of cracking in the buttress dam is largely governed by the induced cracking in the front-plate since these cracks have a tendency to propagate into the concrete buttress. The results also showed that if the dam have been subjected to degradation and thereby has reduced concrete strength, the thermal stresses could induce significant cracking in the monolith which could lead to new failure modes. Based on the calculated extent of cracking in the dam body, different failure modes should be assessed in order to determine the dam stability failure.

Buttress dams located in cold areas are often subjected to severe environmental conditions. Recent assessments and investigations of buttress dams in northern Sweden reveal several types of cracks. Theoretical analysis and field measurements have showed that the most of the cracks are either developed or propagated as a result of the seasonal temperature variations.

Cracks influence the behaviour of the dams in different ways, such as reducing the tightness of the dam and increasing the hydraulic pressure within the cracks. Furthermore, cracks may have impact on the stiffness and stability of the dam. The ordinary sliding and overturning stability analyses are not sufficient when the supporting structure is cracked. The cracks may comprise the integrity and the homogeneity of the structure. A cracked, and for that matter even repaired structure, can’t be regarded as a homogenous structure and should be treated accordingly. Consequently other types of models instead of the conventional design models should be utilized for the stability analyses of the cracked and repaired dams.

There are at least two major aspects which must be considered when a cracked or repaired structure is being analysed. The first aspect is the principle of superposition and the second aspect is probability of the failure. It is well known that a cracked structure does not behave linearly, consequently the principle of superposition can’t be applied to determine the overall effects of the several simultaneously acting events.

The mode of failure is one of the decisive elements considering determination of the probability of the failure. The condition for crack initiation and the trajectory of the crack propagation are the decisive factors which govern the failure mode. Ordinary design methods and advanced numerical models which are based on the elastic behaviour of the structure can’t be utilized, since these models are not able to describe the non-linear behaviour and to predict the failure mode of the structure.

A finite-element model based on the non-linear fracture mechanics has been utilized to study crack development in a buttress dam. The aim of the project was to study crack trajectories and to determine the influences of cracks on the overall behaviour of the structure, for instance in the global stiffness of the structure and possible failure modes. The paper will present the structure, the numerical model and the results.

An extensive program for improvement of the hydropower plants in Sweden is currently on-going. The aims are to secure future production and to maintain and further develop an already high dam safety.

During inspection, cracks were discovered in the concrete foundation, near the stator and rotor spider supports, at some hydropower stations in Sweden. The cracks were believed to be related to the function of the stator supports and to new patterns of generator operation. In earlier times, the generators ran continuously, while nowadays there are many stops and starts, sometimes even several times during one day. The objective of this study is to understand the complex interaction between the power generating system (stator, rotor, turbine, etc.) and the supporting concrete structure. It is important from a dam safety perspective to determine the causes of the structural cracks that have been found in-situ.

A three dimensional non-linear finite element model has been developed in order to analyse formation and propagation of the cracks. Several different load effects have been studied in this project in addition to the mechanical loads during operation. The new pattern of generator operation with several starts and stops lead for instance to variations in temperature which have been studied. Besides this, the uneven drying shrinkage of concrete has also been studied in this project. Thereby, the structural behaviour of a concrete foundation for the power generating system has been analysed taking into account the transient thermal and moisture gradients in combination with dead loads and some of the operational loads imposed to the foundation.

The analyses shows that reinforced concrete structure that constitute a support to the generator is subjected to cracking due to the loads considered in this study, where the cracks near the supports are caused by a combination of mechanical loads, long-term drying shrinkage and temperature variations. The analyses showed that even after 20 years, the moisture content in the centre of the thicker part in the concrete foundation still had a high relative humidity. At the same time the concrete close to the free surfaces and the slender parts of the concrete foundation had reached the same relative humidity as the environment. Thereby, a large difference in drying shrinkage is obtained between different parts of the concrete foundation and thereby large forces due to restrain. The analyses showed that the drying shrinkage induced cracking inside the concrete foundation and especially close to the supports of the stator and the rotor spider which coincides with location of the cracks found in-situ.

The results show that the cracks found in-situ can be simulated and explained with advanced numerical methods. The results also indicate that the dynamic effect from the loads caused by the power generating system have to be studied further, since a reduced structural stiffness due to cracking may result in larger loads imposed on the structure from the magnetic eccentricity and turbine imperfections or alternatively lead to a fatigue failure of for instance the reinforcement.

A concrete arch dam have been analyzed during seismic loading with a model based on acoustic elements to describe the water and infinite elements as quiet boundaries to prevent wave reflection. The results have also been compared with a simplified model based on Westergaards added mass approach. The simplified model is only used, in this study, for comparison with the more advanced model with acoustic elements. Therefore the results from this simplified model are just used as a rough estimate of the induced stresses and displacements. Despite this, the simplified Westergaard model gives similar results compared to the more advanced model with acoustic elements for the water and infinite elements for the boundaries. The largest difference between the models often occurs at the nodes in the base of the arch dam, which may be due to poor discretization. Generally, the Westergaard added mass gives higher maximum principal stresses at the base on the upstream side than the acoustic model, while often underestimating the min principal stresses at the base on the downstream side. Both models show high tensile stresses near the base of the arch dam that would result in cracks.

This paper presents a study on water filled pools within nuclear facilities subjected to seismic loads. The type of structure studied is an elevated rectangular concrete tank, supported by the reactor containment, which is a high cylindrical concrete structure. Seismic analysis is performed using finite element models, accounting for fluid-structure interaction (FSI) between the water and the concrete structure. The stresses in a concrete pool are calculated, also investigating the changes in stresses as additional cross-walls are added. The effects from earthquakes dominated by low and high frequencies are evaluated, representative for conditions at the West coast of North America and Northern Europe, respectively. It is shown that the coupled fluid-structure systems have more significant modes in the high frequency range compared to the models without water, that is, for frequencies at which the Northern European type earthquake has significant energy compared to the Western North American earthquake. The seismic analyses show that the relative increase of hydrodynamic pressure is higher when the outer walls of the pool are stiffened due to the inclusion of additional cross-walls. With the inclusion of additional cross-walls, modes with lower natural frequencies, although still relatively high, become more important for the hydrodynamic pressure response. Leading to a higher stress response in the outer walls of the pool for models including the additional cross-walls compared to models without cross-walls. The study indicates that the effect from fluid-structure interaction is of great importance also for seismic loads with relatively high-frequency content.

The objective of this paper is to evaluate different approaches to account for fluid-structure interaction (FSI) in seismic analyses of nuclear facilities. Different methods to account for FSI, from simplified to highly advanced numerical methods, are briefly reviewed and some important concepts are discussed. A benchmark example of a simple tank sloshing problem is included to evaluate the use of different FSI methods.

The main conclusion from the study is that it is of great significance to first of all include the effect of FSI. When considering the response of a tank subjected to a load of periodic nature, as in the benchmark example, the hydrodynamic effects are very important, since they increase the load effect on the structure. It is also observed that the simplified methods, in which the hydrodynamic effects are included as a mass-spring system, results in much higher stresses in the structure than if the fluid is included as continuum elements. However, the more advanced methods lead to extra computational time and also require more from the analyst. With the focus of this project being the global response of the structure, most methods describe the fluid unnecessarily complicated and phenomena such as splashing and turbulence are of little interest. The main aspects that influence the structure are the mass and inertia of the fluid along with the surface waves, the sloshing. Considering this, simplified methods such as elements with acoustic equations, and even mass-spring systems, to represent the fluid, often give results that are accurate enough.

Shotcrete (sprayed concrete) is commonly used to support tunnels in good quality hard rock. Including a drainage system often results in end-restrained sections of shotcrete, which have created problems with shrinkage induced cracking. In this paper a multi-physical material model with coupled behaviour between thermal actions, moisture transportation and mechanical strain has been used to model and describe the complex behaviour and effects of shrinkage of such a structure. The model was first calibrated against a free shrinkage test and then used to simulate an experimental set-up for testing of end-restrained shrinkage. The first results lead to a need of tuning of the parameters controlling the drying of the shotcrete to accurately describe the experimental results. This tuning could be an indication that the shrinkage behaviour differs between a restrained and an un-restrained sample. However, further research about possible changes in the pore structure as well as more detailed measurements of the early shrinkage behaviour is needed before any such conclusions can be drawn.

The restrained ring test under constant temperature is used for estimating cracking tendency of pastes, mortar or concrete. This test induces hygro-mechanical interactions, with intricate interplay of several phenomena such as autogenous shrinkage, drying shrinkage, basic and drying creep, as well as evolution of tensile strength and fracture energy. The benchmark described in this paper relies on extensive experimental data sets obtained through the extended Round Robin Testing programme (RRT+) of COST Action TU1404. Five teams took part with their simulation models. A series of outputs were produced, starting from mass loss of a prism through its axial deformation up to stress/strain evolution in the ring. Three teams quantified also damage due to drying and stress concentration around a ring’s notch. All models showed excellent performance on mass loss while strain validation showed higher scatter and influence of several other factors. The benchmark demonstrated high capability of used models and emphasized strong role of calibration with regards to available experimental data.

Civil engineering structures are commonly monitored to assess their structural behaviour, using alarm thresholds to indicate when contingency actions are needed to improve safety. However, there is a need for guidelines on how to establish thresholds that ensure sufficient safety. This paper therefore proposes a general computational algorithm for establishment of reliability-based alarm thresholds for civil engineering structures. The algorithm is based on Subset simulation with independent-component Markov chain Monte Carlo simulation and applicable with both analytical structural models and finite element models. The reliability-based alarm thresholds can straightforwardly be used in the monitoring plans that are developed in the design phase of a construction project, in particular for sequentially loaded structures such as staged construction of embankments. With the reliability-based alarm thresholds, contingency actions will only be implemented when they are needed to satisfy the target probability of failure.

The observational method has for a long time been key to design of underground rock engineering structures, as observations of geotechnical and geological conditions and structural behaviour can be useful in assessments of the structural safety. There is today a lack of guidelines on how this safety assessment should be carried out in practice. This article presents the results of a research project that addressed this issue. The project was conducted by KTH Royal Institute of Technology and funded by the Rock Engineering Research Foundation. The results show how a reliability framework can be used to derive limits of acceptable behaviour for the structure, based on a target probability of failure. These thresholds indicate when the safety margin against failure becomes too small. The framework was applied to analyse a cross section inspired by a part of the Stockholm Bypass project. The experiences of this work are thoroughly discussed.

This study presents a multiphysics model developed to predict the internal temperature and moisture development in a concrete reactor containment at an early age. The work is a part of the benchmark study, VeRCoR, provided by EDF. The model was applied on an experimental reactor containment mock-up erected in the vicinity of Paris. The 3D geometry was provided from VeRCoRs. The model includes concrete hydration, heat release, chemical moisture binding, and a moisture transport model with relative humidity as a driving potential. Results from the simulation was compared with temperature sensors located in the mock-up. The model was found to be able to predict the temperature development at early age. There was no possibility to compare the relative humidity because of lack of humidity sensors.

The restrained ring test belongs to a traditional method for estimating cracking tendency of a paste, mortar or concrete mix. The test involves hygro-mechanical interactions with intricate interplay of several phenomena, such as autogenous shrinkage, drying shrinkage, basic and drying creep, together with evolution of tensile strength and fracture energy. The benchmark described in this paper relies on extensive experimental data sets obtained through the extended Round Robin Testing programme (RRT+) of COST Action TU1404. Six teams took part with their simulation models. A series of outputs were produced, starting from mass loss of a prism through its axial deformation up to hoop stress/strain evolution in the ring. Four teams quantified also damage due to drying and strain concentrations. All models showed excellent performance on mass loss while strain validation showed higher scatter and influence of several factors. The benchmark demonstrated high capability of used models and emphasized strong role of calibration with regards to available experimental data.