Ce travail de thèse porte sur l'étude et la réalisation de Lasers à Emission par la Surface à Cavité Verticale pompés électriquement (EP-VCSELs) à base d'antimoniures émettant dans le moyen-infrarouge au-delà de 2 µm. Ces VCSELs proposent des caractéristiques intéressantes pour la détection de gaz tel qu'une émission monomode et une large accordabilité sans saut de mode. L'objectif de ce travail était de développer de tels composants. La première partie de ce mémoire présente les propriétés des couches qui seront empilés pour former la structure VCSEL. La seconde partie traite des différentes conditions pour obtenir une source laser monomode. La troisième partie présente les procédés de fabrication qui ont étés mis en place. Notamment de la sous-gravure sélective de la Jonction Tunnel (JT), qui est une technique de confinement originale dans le système GaSb. Celle-ci permet de réduire le diamètre de la JT jusqu'à 6 µm, ce qui est la condition pour obtenir une émission monomode.La dernière partie de ce manuscrit présente les caractérisations menées sur les structures monolithiques à JT sous-gravées. La sous-gravure sélective nous a ainsi permis d'obtenir le premier EP-VCSEL monolithique monomode. Ce composant fonctionne au-delà de la température ambiante et en régime continu. Avec des courants de seuils aussi bas que 1,9 mA et un fonctionnement jusqu'à 70°C. Le développement des structures monolithique à zone active (ZA) en cascade a également permis d'augmenter les puissances optiques en sortie de ces composants. Celles-ci sont passées de 300 µW @ 20°C à 950 µW pour la première structure citée classique et la structure à ZA en cascades respectivement. / This thesis deals with study and conception of GaSb-based electrically pumped Vertical Cavity Surface Emitting Lasers (EP-VCSELs) emitting in the mid-infrared range above 2 µm. This VCSELs exhibits suitable characteristics for gas analysis like single-mode emission and a large current tunability without mode-hopping. The objective of this work was to develop such devices. The first part of this work is about properties of the epitaxial stack layers used to form the VCSEL structure. The second parts deal with characteristics and the confinement system to design a single mode cavity. The third part presents manufacturing process which has been set up, like Tunnel Junction (TJ) under-etching, which is an innovate approach on the GaSb system. It allows reducing TJ diameter down to 6 µm, which is a necessary point to demonstrate single-mode operation.The final part of this manuscript presents the characterisations purchased on the under-etched TJ monolithic-VCSELs. Selective under-etching of the TJ allowed the first demonstration of the first single-mode monolithic EP-VCSEL. This device emits around 2.3 µm in continuous regime above room temperature. This device exhibits threshold currents as low as 1.9 mA and operate up to 70°C. The development of bipolar cascaded VCSELs has also allowed increasing the optical power on large diameter multimode, with a maximum output power of 300 µW and 950 µW@20°C for the classic and the bipolar cascaded VCSEL respectively.

A forte polarisation (V >1V), une jonction tunnel planaire peut émettre de la lumière dans le domaine optique à des fréquences f<eV/h ~ 10¹⁴Hz. Cette émission résulte du rayonnement de plasmons-polariton de surface, générés par le bruit de grenaille dans la jonction. La densité spectrale de rayonnement dP/df est alors directement reliée à la densité spectrale des fluctuations du courant SII via une simple impédance de rayonnement: dP/df = R × SII. De la même manière, la densité spectrale de rayonnement du corps noir est reliée aux fluctuations thermiques du courant dans un conducteur ohmique via le théorème fluctuation-dissipation (TFD). Il semble alors naturel de décrire le rayonnement d'une jonction tunnel par la relation fluctuation-dissipation, dérivée par Scalapino et Rogovin [Annals of Physics 1974], généralisant le TFD aux conducteurs hors équilibre (V≠0). Nous avons étudié cette relation dans un régime où la jonction tunnel est fortement hors équilibre, lorsque eV ~1eV est de l'ordre de la hauteur de la barrière tunnel. La RFD est vérifiée à fréquence nulle (MHz), mais est violée de manière flagrante à fréquence finie (10¹⁴Hz). Nous attribuons cette violation à la non linéarité intrinsèque de la jonction. Nous dérivons une nouvelle expression pour la puissance émise, à partir de l'approche quantique de Landaueur-Büttiker du transport électronique. L'émission est alors interprétée en terme de recombinaison électron-trou dans les électrodes et rend compte d'une accumulation de charges dans la barrière. L'efficacité du couplage électron-photon est évaluée quantitativement via l'impédance de rayonnement de la jonction. Ce travail de thèse s'adresse à deux communautés, celle de la physique mésoscopique étudiant les mécanismes du transport électronique, et celle des opticiens voulant comprendre et optimiser l'émission de lumière dans ces systèmes. / In a strongly voltaged biased tunnel junction, optical photon emission occurs at frequencies below the threshold f<eV/h ~ 10¹⁴Hz, mediated by the shot-noise-generated surface plasmon-polaritons. The spectral power density dP/df depends only on the current fluctuation spectral density SII and a radiation impedance: dP/df = R × SII . This expression is analogous to the relation between the power spectral density of a black body and thermal current fluctuations in a ohmic conductor, via the fluctuation-dissipation theorem (FDT). Therefore, it seems natural that the optical power emitted by a tunnel junction be given by the fluctuation-dissipation relation (FDR) derived by Scalapino and Rogovin [Annals of Physics 1974], which extends the FDT to out-of-equilibrium conductors (V≠0). When the junction is far-from-equilibrium, i.e. when eV ~1eV is of the order of magnitude of the tunnel barrier height, our experiments show that the FDR holds at zero frequency (MHz), but breaks down at finite frequency (10¹⁴Hz). We attribute the discrepancy between the FDR and our measurements to the junction's intrinsic current-voltage non-linearity. We derive a new expression for emitted optical power, based on the Landauer-Büttiker formalism for quantum electronic transport. Light emission from the junction can then be interpreted as due to electron-hole recombination processes in the electrodes. This expression also account for charge accumulation in the tunnel barrier. The resulting estimate of the junction's radiation impedance is a measure of the electron-photon coupling e_ciency in our device. This work should be of interest to both mesoscopic physicists studying electronic transport mechanisms, and those of optics community studying light emission in microstructures.

Tunnel safety – an inventory of accidents in four road tunnels in Stockholm This report investigates traffic accidents in four road tunnels in Stockholm. The tunnels investigated are Klaratunneln, Söderledstunneln, Törnskogstunneln and Häggvikstunneln. The main purpose of this project was to work with a delimited part of the project TUFS (Tunnel Framkomlighet och Säkerhet, Tunnel practicability and safety, my translation) that is going to build a knowledge bank for Swedish road tunnel accidents. The goal of this project was to investigate if the forecasts for accident rates in the tunnels calculated from empirical data differ from the forecasts of the road network made by the forecast program used by Trafikverket, Lill-EVA, for the observed tunnels. Another goal was to determine where accidents occur in the tunnels. In addition, two different tunnel types were compared in terms of accident rates. The tunnel types are located in: countryside (high speed, low traffic flows, no on- and off ramps) or urban center (low speed, high traffic flows, on- and off ramps). Accident data has been collected from the data bases STRADA and NTS and compiled in histograms displaying accident type, light conditions, the seriousness of the accident and number of accidents/year. The results showed that there are no differences in accident rates calculated by Lill-EVA and empirical data for accident rate, serious accident rate and death rate. However, there was a difference in the results concerning light injuries. No difference was found regarding the two tunnel types. Rear-end collision was the most common accident type in Söderledstunneln and serial vehicle crashes in Törnskogstunneln and Häggvikstunneln. Vehicles that got stuck in the tunnel entrance dominated the accident type in Klaratunneln. The majority of the accidents occurred in daylight. The coordinate positions for the accidents showed that there was a concentration of accidents near the tunnel entrance in Klaratunneln, Söderledstunneln and Häggvikstunneln. This is not the case for Törnskogstunneln where accidents have occurred in the tunnel center.

No description available.

This project began with me joining in on a safety tour. This safety tour spanned across a neighborhood called Andersberg, in my hometown of Gävle. By talking to the participants of the safety tour, I started to realize the scope of the problem that presented itself there. These individuals, mostly consisting of residents of the area and neighboring areas, disclosed that they felt a constant insecurity while they were out and about in Gävle, especially during late nights. This piqued my interest. I wanted to enable these individuals to feel safe in their own hometown. I carried out interviews with residents of Gävle to fully understand their feelings of insecurity. The interviews and analysis of research that had been done within the subject, also gave me a more specific target group. A target group that experienced insecurity to further extents than other groups; women between the ages of 20 to 24. A survey was created for me to get a better understanding of what causes and elements there was for the experiences. The survey was sent to several young women, who shared the survey link with other members of the target group. The respondents’ answers painted a picture of the true scale of the problem and made me realize that the problem was too immense for me to solve completely. Thereby I found, amongst the survey answers, a part of the problem where I could do the most good. Which turned out to be loneliness and the thought of not being able to get out of a dangerous situation. Further exploration of the locations where the insecurity was experienced made it apparent that the tunnel was the structure where change was needed the most. The design that contributes to solving the problem is as follows; a system of speakers that play the sound of women talking and walking. These systems are used in tunnels to give the impression that the individual that passes through is surrounded by other women. This explains the name given to the concept; “Aldrig ensam” (Never alone). / Projektet tog sin början i att jag deltog i en trygghetsvandring i området Andersberg i min hemstad Gävle. Efter att ha pratat med de andra deltagarna, började jag förstå storleken av det problem som fanns där. Dessa individer, som mestadels bestod av områdets och närliggande områdens invånare, hävdade att de kände en konstant känsla av otrygghet då de befann sig i staden, speciellt under nattetid. Detta fångade mitt intresse. Jag ville hjälpa dessa individer att känna sig trygga i sin egen hemstad. Jag utförde intervjuer med några av Gävles invånare för att tydligare förstå deras känslor av otrygghet. Intervjuerna, tillsammans med analyser av forskning i ämnet gav mig även en mer specifik målgrupp. En målgrupp som upplevde otrygghet i större utsträckning än andra grupper; kvinnor i åldrarna 20 till 24. En enkät skapades för att ge mig en bättre förståelse för orsakerna till den upplevda otryggheten. Enkäten skickades ut till flera unga kvinnor, som i sin tur delade med sig av enkätens länk till andra individer inom målgruppen. Respondenternas svar målade upp en bild av problemets sanna storlek, och fick mig att inse att det var för stort för att jag skulle kunna lösa det helt och hållet. Därför hittade jag, bland enkätens svar, en del av problemet där jag kunde göra mest nytta. Detta visade sig vara känslan av ensamhet och tron om att man inte kan ta sig ifrån en farlig situation. Vidare utforskning av de platser där otrygghet upplevdes tydliggjorde att gångtunneln var platsen där förändring behövdes som mest. Designen som bidrar till lösningen av problemet är som följande; ett högtalarsystem som spelar upp ljudet av kvinnor som pratar och går. Systemet används i tunnlar för att ge intrycket av att individen som passerar genom tunneln är omgiven av andra kvinnor. Därav namnet givet till designen, ”Aldrig ensam”

Spin-torque nano-oscillators (STNOs) are prospective successors of transistor-based emitters and receivers of radio-frequency signals in commonly used remote communication systems. In comparison to the conventional electronic oscillators, STNOs offer the advantage of being tunable over a wide range of frequencies simply by adjusting the applied current, the smaller lateral size (up to 50 times) and the lower power consumption as the lateral size of the device is reduced. It has already been demonstrated that the output signal characteristics of STNOs are compatible with the requirements for applications: they can provide output powers in the µW range, frequencies of the order of GHz, quality factors Q (equal to df/f, where f is the frequency, and df is the linewidth) up to several thousands (e.g., 3 200), and can be integrated into Phase-Locked Loop (PLL) circuits. The most promising type of spin-torque oscillators is the hybrid geometry STNOs utilizing an in-plane magnetized fixed layer, an out-of-plane magnetized free layer and the MgO tunnel barrier as a spacer. This geometry maximizes the output power, since the full parallel-to-antiparallel resistance variation can be exploited in the limit of large magnetization precession angle (i.e., when the magnetization oscillates fully within the plane of the STNO stack). Moreover, the considered hybrid geometry allows for the reduction of the critical currents, enables functionality regardless of the applied magnetic or current history and requires a simplified fabrication process in comparison to the opposite hybrid geometry, consisting of an in-plane magnetized free layer and an out-of-plane reference layer, which requires an additional read-out layer. Simultaneously, the choice of the spacer material in considered STNOs is motivated by the increase of both the output power (via large magnetoresistance ratios) and the power conversion rate ('output power to input power' ratio), compared to their fully metallic counterparts. Despite the many advantages of MgO-based hybrid geometry STNOs, unexplained issues related to the physics behind their principle of operation remained. In this thesis, the main focus is put on the two key aspects related to the out-of-plane steady-state precession in hybrid STNOs: the precession mechanism (combined with the analysis of the influence of the bias dependence of the tunnel magnetoresistance) and the zero-field oscillations stabilized by an in-plane shape anisotropy. State-of-the-art theoretical studies demonstrated that stable precession in hybrid geometry STNOs can only be sustained if the in-plane component of the spin-transfer torque (STT) exhibits an asymmetric dependence on the angle between the free and the polarizing layer (which is true for fully metallic devices, but not for the MgO-based magnetic tunnel junctions (MTJs)). Nevertheless, recent experimental reports showed that spin-transfer driven dynamics can also be sustained in MgO-based STNOs with this particular configuration. In this thesis, a phenomenological and straightforward mechanism responsible for sustaining the dynamics in considered system is suggested. The mechanism is based on the fact that, in MgO-based MTJs, the strong cosine-type angular dependence of the tunnel magnetoresistance, at constant applied current, translates into an angle-dependent voltage component, which results in an angle-dependent spin-transfer torque giving a rise to the angular asymmetry of the in-plane STT and, thus, enabling steady-state precession to be sustained. Subsequently, the bias dependence of the tunnel magnetoresistance (TMR), which has been so far neglected in similar calculations, is taken into account. According to the results of analytical and numerical studies, the TMR bias dependence brings about a gradual quenching of the dynamics at large applied currents. The theoretical model yields trends confirming our experimental results. The most important conclusion regarding to this part of the thesis is that, while the angular dependence of the tunnel magnetoresistance introduces an angular asymmetry for the in-plane spin transfer torque parameter (which helps maintain steady-state precession), the bias dependence of the resistance works to reduce this asymmetry. Thus, these two mechanisms allow us to tune the asymmetry of the in-plane STT as function of current and to control the dynamical response of the actual device. Except for the precession mechanism, the thesis is also focused on the issue of zero-field oscillations, which would be especially desirable from the point of view of potential applications. According to the state-of-the-art theoretical studies, for hybrid geometry devices with circular cross-section (i.e., exhibiting no other anisotropy terms), current-driven dynamics cannot be excited at zero applied field. Indeed, zero-field oscillations have only been experimentally observed for systems having the free layer magnetization slightly tilted from the normal to the plane, which has usually been achieved by introducing an in-plane shape anisotropy. In the thesis, the influence of the in-plane shape anisotropy of the MTJ on zero-field dynamics in the hybrid geometry MgO-based STNOs is analytically and numerically investigated. In agreement with the previous reports, no zero-field dynamics for circular nano-pillars is observed; however, according to the numerical data, an additional in-plane anisotropy smaller than the effective out-of-plane anisotropy of the free layer enables zero-field steady-state precession. Accordingly, the lack of an in-plane anisotropy component (e.g., for circular cross-section nano-pillars), or the presence of an in-plane shape anisotropy equal or greater than the out-of-plane effective anisotropy, inhibits the stabilization of dynamics in the free layer at zero field. The results of analytical and numerical studies and the general trends identified in the corresponding experimental data are found to be in excellent qualitative agreement.:1. Introduction 1.1. Short history of magnetotransport applications 1.2. Spin-transfer torque induced effects and devices 1.3. Goals of the thesis 2. Fundamentals 2.1. Electronic transport in single transition metal layers 2.2. Tunnel magnetoresistance (TMR) 2.2.1. Electronic transport in magnetic tunnel junctions 2.2.2. Tunnel magnetoresistance versus structural properties of the multilayer 2.2.3. Bias voltage and temperature dependence of tunnel magnetoresistance 2.2.4. Angular dependence of tunnel magnetoresistance 2.3. Spin-transfer torque in GMR/TMR structures 2.3.1. Spin-transfer torque 2.3.2. Landau-Lifshitz-Gilbert (LLG) equation 2.3.3. LLG equation and spin-transfer torques 2.3.4. Bias voltage dependence of spin-transfer torques in MTJs 2.3.5. Angular dependence of spin-transfer torque 2.4. Spin-torque-based phenomena 2.4.1. Current-induced switching 2.4.2. Current-induced dynamics 3. Experimental 3.1. General characteristics of MgO-based magnetic tunnel junctions 3.2. STNO samples 3.2.1. Samples by AIST (Tsukuba, Japan) 3.2.2. Samples by HZDR / SINGULUS (Dresden / Kahl am Main, Germany) 3.3. Magnetotransport measurements 3.3.1. Experimental setup and data analysis 3.3.2. Experimental results 3.4. Aspects to be explained 4 Numerical and analytical calculations 4.1 Out-of-plane steady-state precession in hybrid geometry STNO 4.1.1 Angular dependence of tunnel magnetoresistance as a mechanism of stable precession 4.1.2. Influence of the bias dependence of tunnel magnetoresistance 4.1.3. Comparison with the experimental data 4.1.4. Comparison with the GMR-type counterpart 4.1.5. Summary 4.2. Zero-field dynamics in hybrid geometry STNO stabilized by in-plane shape anisotropy 4.2.1. Effect of the in-plane shape anisotropy 4.2.2. Zero-field dynamics 4.2.3. Summary 5. Conclusions 6. Outlook Appendix Bibliography

When creating cavities below ground, movements occur in the surrounding soil due to disrupted equilibrium. In tunnel constructions these displacements are referred to as tunnel convergence. This report compares four dierent methods for monitoring tunnel convergence with regards to both measurement precision and method cost. Three of the methods are based on displacement measurements of optical targets placed at regular intervals in the tunnel. Presented is also a method using a combination of wireless tilt and distance sensors to monitor tunnel convergence. The overall conclusion is that measurement precision and cost are well correlated. However, important to consider is that tunnel convergence monitoring cost is faceted and not only the obvious cost of equipment and labour, but also the indirect cost from interfering with other activities in the tunnel. Measurement precision of the dierent methods was determined by applying the methods in a lab environment, congured to eliminate any possible movements, and analysing the distribution of the displacement demonstrated by each method. In addition, information regarding the labour eort required to prepare and perform the measurements was also collected. Based on the experiments and literature studies, the report discusses the criteria to consider when selecting a tunnel convergence monitoring method and presents a comparison of the four methods included in the study. / Vid skapandet av underjordiska hålrum uppträder rörelser i den omgivande marken på grund av att jämvikten upphävs. I tunnelkonstruktioner kallas dessa förskjutningar för tunnelkonvergens. Denna rapport jämför, med avseende både på precision och kostnad, fyra metoder för mätning av tunnelkonvergens. Tre av metoderna baseras på förskjutningsmätningar av optiska mål placerade på regelbundna avstånd längs tunneln. Rapporten presenterar även en metod där en kombination av trådlösa tilt- och distanssensorer används för att monitorera tunnelkonvergens. Den övergripande slutsatsen är att mätprecision och kostnad är väl korrelerade. Viktigt är dock att beakta de olika delarna i den totala kostnaden, som inte bara består av kostnader för arbetskraft och utrustning utan även indirekta kostnader på grund av att annan verksamhet hindras under mätaktiviteter. Mätprecisionen för de olika metoderna uppskattades genom att analysera fördelningen av mätvärden uppmätta i en lab-miljö beskaffad så att inga rörelser förväntades. Från labmätningarna noterades även omfattningen av den arbetsinsats som krävs för att förbereda och utföra mätningarna. Med mätningarna och litteraturstudier som bakgrund diskuteras kriterier att beakta när man väler metod för konvergensmätning. Baserat på dessa kriterier jämförs de fyra metoderna.

This master thesis has investigated the performance of a deep excavation with a jet grout bottom plug used to prevent bottom heave and hydraulic uplift failure. The concept of a jet grout plug as a structural and sealing component in a specific case was studied, namely one of the tunnel sections of The West Link tunnel project in Gothenburg. The section was to be built as a cut-and-cover tunnel with the excavation shaft consisting of secant pile walls, struts and a jet grout bottom plug. It is to be established where there are a lot of sensitive buildings and constructions close to the excavation site. This makes it important not to disturb the surroundings during construction with, for example, settlements.The study was carried out by doing a literature study, analytical calculations and numerical simulations in the finite element software PLAXIS 2D. More specifically, the checks evaluated were uplift equilibrium of the jet grout plug and of the whole structure, structural performance of the jet grouted plug and hydraulic conductivity of the jet grouted mass.The results show a design of a jet grout plug that together with the additional structures works sufficiently enough to make a secure construction for a deep excavation below the ground water table. The structural performance of the jet grouted plug to function as a strut level is fulfilled even if the jet grout is not perfectly performed. To work as a sealing component the jet grout column pattern and the centre-to-centre distance between the columns are important factors together with the alignment and diameter of the jet grout columns. To make a completely watertight construction is however almost impossible in this case since the jet grout plug is located at a large depth (around 20 m). To work properly against failure by uplift it does not need to be completely watertight. Instead, the use of relief wells makes sure that the pore water pressure is not larger than the vertical stress from the soil, otherwise failure by uplift is a real danger. Furthermore, to work properly against settlements it is not only the water tightness of the jet grout plug that decides whether it will work properly. Instead, it is also the pumping and infiltration system together with the, in this case, sensitivity of the lower aquifer that decides the risk of settlements.

As technology for manufacturing small scale prototypes of aeroplanes has become cheaper and more easily viable, the process of Rapid Prototyping has become more common. Rapid Prototyping allows for the fundamental aerodynamic qualities of a geometric body to be tested in a wind tunnel using a small scale prototype. This means smaller prototypes of aircraft can be manufactured more rapidly and at a lower cost, allowing for more extensive testing of a design’s final aerodynamic qualities before any actual full-size production. In order to gain a better insight in the behaviours of the full-sized aircraft itself, a downscaled version of the KTH project UAV ALPHA has been deigned for testing in a low speed wind tunnel. The design will be used in further testing to help confirm simulations and estimations done on the ALPHA of its aerodynamic performance.

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