Observationsmetoden utgör sedan lång tid tillbaka en central princip för dimensioner­ing av undermarksanläggningar i berg, eftersom det anses fördelaktigt att under bygg­tiden utnyttja observationer av geotekniska och geologiska förhållanden, samt kon­struktionens beteende, i bedömningen av den färdiga konstruktionens säkerhet. Det sak­nas dock riktlinjer för hur denna säkerhetsbedömning med observationsmetoden ska gå till i praktiken. Denna artikel presenterar översiktligt resultatet av ett forskningsprojekt som drivits på KTH Jord- och bergmekanik, finansierat av BeFo, och som tagit sig an denna fråga. Resultaten visar hur man kan använda sannolikhetsbaserade metoder i ett ramverk för att ta fram gränser för acceptabelt beteende, baserat på en fastställd tillåten brottsannolikhet. Dessa larmgränser visar när konstruktionens säkerhetsmarginal mot brott blir för liten. Vi har använt ramverket på ett tunneltvärsnitt inspirerat av Förbifart Stockholm. Erfarenheterna av detta arbete diskuteras utförligt i artikeln.

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.

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.

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.

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.

I och med samhällets krav på hållbarhet och den ökande åldern på infrastrukturkonstruktioner är en avgörande uppgift för byggindustrin att förbättra betongkonstruktioners beständighet. Syftet med denna avhandling är att bidra till en sådan utveckling genom teoretiska studier med hjälp av matematisk modellering och numeriska simuleringar. En betongkonstruktion utsätts under sin livslängd för många olika mekaniska laster samt fysikaliska och kemiska processer. Ett sunt tillvägagångsätt gällande modellering kräver därför multifysik och kopplade fysikaliska och kemiska fält (t.ex. temperatur, fukt och cementhydratisering) beaktas utöver de metoder som beskriver materialets mekaniska hållfasthet. Sådana förutsättningar och fenomen som är kritiska för betongkonstruktioner vid vattenkraftsanläggningar är av särskilt intresse att studera.

Avhandling presenterar ett flertal matematiska modeller av varierande komplexitet baserade på en materialpunktsbeskrivning av betongens multifysikaliska beteende. En tonvikt ligger på modeller som beskriver betongens mekaniska beteende där aspekter som åldrande, sprickbildning, krypning och krympning undersöks. Gällande krypning har en state-of-the-art modell baserad på  “Microprestress–Solidification (MPS )” teorin studerats och vidareutvecklats. I de bilagda artiklarna (III till V) presenteras ett matematiskt ramverk för att beskriva fenomen relaterade till betongens beständighet. Detta ramverk baseras på en multifas beskrivning av porösa material, där de styrande ekvationerna är härledda utifrån “Thermodynamically Constrained Averaging Theory (TCAT)”. Det exemplifieras hur detta ramverk kan tillämpas på en rad olika fenomen relaterade till beständighet. Dessa sträcker sig från gjutning och hårdnande av betong till absorption av vatten till lufttillsatt betong. För att lösa de presenterade matematiska modellerna tillämpas den finita elementmetoden (FEM) och de numeriska lösningarna verifieras med hjälp av experimentella resultat från litteraturen.

Avhandlingens huvudsakliga forskningsbidrag är utveckling och utvärdering av teoretiska modeller som ökar förståelsen och förbättrar kunskapen om betong- och betongkonstruktioners åldrande och beständighet. Mer specifikt visas hur multifysiska modeller och det utvecklade multifas modellerna kan användas till att studera betongmaterialets beteende samtidigt som de också är användbara för simuleringar på strukturskala. En effektiv lösning av strukturproblem har varit viktig under all modellutveckling. I olika fallstudier och experiment från litteraturen exemplifieras hur dessa modeller kan användas för att förbättra betongkonstruktioners funktion och därigenom öka dess beständighet.

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.

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 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.

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.

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.

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.