Vid underhållsarbeten av trafikerade tunnlar stängs trafiken av. Därav sker dessa arbeten oftast nattetid. För att kunna släppa på trafiken igen så snabbt som möjligt eftersträvas effektiva förstärkningsarbeten. Av säkerhetsskäl kan utökade hållfasthetskrav förekomma för sprutbetong som förstärkningsmetod. Om betongen hinner uppnå det krav som ställs för hållfastheten snabbare kan antal nätter som tillägnas förstärkningsarbeten reduceras. Detta examensarbete ska undersöka hur olika tillsatser av typen acceleratorer kan påskynda den tidiga hållfasthetsutvecklingen för sprutbetong. Utav de acceleratorer som utreds ska en slutsats kunna dras om dessa typer av tillsatser lämpar sig för förstärkningsmetoden våt sprutbetong. För att utreda acceleratorernas påverkan på sprutbetong har fullskaliga tester utförts. Vid testning sprutades olika betongrecept i testlådor. På lådorna kunde sedan hållfasthetstester utföras enligt gällande standarder. Testerna undersöker endast betongens tidiga hållfasthet, vilket blir en av arbetets avgränsningar. Resultatet av testerna visas i form av grafer och diagram. Därefter diskuteras metodernas osäkerhet och hur skiljande parametrar påverkar resultatet. Ur graferna kan en positiv effekt utläsas för recepten med tillsatt hållfasthetsaccelerator jämfört med recepten där endast sprutbetongaccelerator användes. Den positiva trenden syns tydligast inom de första fyra timmarna, efter detta framträder osäkerheten i mätvärdena. Slutsatser om acceleratorernas verkan för hela testet kan inte dras utan en statistisk hypotesprövning mellan de olika recepten. En sådan prövning utesluter om det statistiskt går att skilja resultaten åt. Dessutom rekommenderas företaget utföra mindre kompletterande tester på provkroppar i laborativ miljö, där skiljande parametrar kan elimineras och säkrare utdata erhållas. / During maintenance work in trafficked tunnels, the traffic must be halted. Therefore, such efforts often take place night-time. In order to enable a quick release of traffic again, it is crucial to have an effective reinforcement work. Due to the safety risks of using shotcrete as a reinforce method, there is a chance of adding additional strength-requirement can exist due to safety risks. If the concrete achieves the strength requirements sooner than expected, the number of nights dedicated to maintenance work can be reduced. This study intends to investigate how different types of admixtures, so called accelerators, can expedite the shotcrete’s initial strength development. Furthermore, the study will include a conclusion of the suitability for the accelerators that have been applied in the shotcrete. To investigate the effects of these accelerators, extensive tests has taken place. During these tests, shotcretes with different recipes were sprinkled into test boxes. Thereafter, tests of strength development could be performed on these boxes in agreement with prevailing standards. To delimitate the study, the selected methods only show the early strength-development of shotcrete. The results from these tests will be presented in graphs. Uncertainties regarding measurement data and how separated physical parameters affect the test results will be discussed as well. By reading the data presented in the graphs, a positive development can be identified in recipes with added hardening accelerators compared to recipes containing only shotcrete accelerators within the first four hours. Following the first four hours, a significant uncertainty in measurements will be noticed. Finally, due to high irregularity in measured values, conclusions of the accelerators’ effect cannot be confirmed solely by the results from these tests. Therefore, a hypothesis trial is necessary as it would exclude if the recipes statically can be separated. Furthermore, the company recommends performing additional small-scale tests in a laboratory environment. Through laboratory tests, a more certain result can be received.

La investigación realizada es no experimental y de enfoque cualitativo en su mayor parte y cuantitativo en lo que resta, con alcances descriptivos y explicativos. El enfoque principal de nuestra investigación fue el problema del deficiente lanzado de Shotcrete en túneles, producto de una inadecuada gestión de la calidad, teniendo como fundamental objetivo elaborar una propuesta de gestión de calidad con la finalidad de optimizar el proceso de lanzado de Shotcrete en túneles, usando la conocida guía para la gestión de proyectos PMBOK a través de esta podemos deducir que siguiendo el área de conocimiento de gestión de la calidad alinearemos los procedimientos aprobados con el control respectivo en las distintas áreas o frentes de trabajo, además de realizar un continuo seguimiento de estos procesos con auditorías internas y externas. Se adoptó una metodología de recopilación de información, estudio y aplicación del área de conocimiento del PMBoK, determinación de cantidades de Shotcrete usado en el caso de estudio donde se analizó los costos y tiempos, y se evaluó los diferentes procesos que están relacionados con el sistema de Shotcreteado. Concluyéndose que el uso del sistema de gestión de calidad bajo los lineamientos del PMBoK es una guía de gran importancia para la aplicación en procedimientos constructivos debido a que nos señala las pautas adecuadas para la planificación, seguimiento y control de cada proceso con la finalidad de retroalimentarlo continuamente y mejorarlo si fuera el caso necesario. The investigation is a non-experimental research, mostly qualitative and quantitative in the rest with descriptive and explanatory scopes. The main theme of our investigation was the problem of the deficient Shotcrete spraying in tunnels, product of an inadequate management of the quality, having as principal scope the elaboration of a proposal for Quality Management with the purpose of optimizing the process of Shotcrete spraying in tunnels, with the known guide for the project management PMBOK. Using this guide, we can determinate that following the Quality area of knowledge we will align the procedures approved with the respective control in the different areas or fronts of work, moreover, monitoring of these processes with internal and external audits. There was adopted a methodology of summary of information, study and application of the area of knowledge of the PMBoK, determination of Shotcrete quantities used in case of study where the costs and schedules were analyzed, and there were evaluated the different processes that are related to Shotcreting System. Concluding that Quality Management of the PMBoK is a guide of great importance for the application in constructive procedures due to the fact that indicates the guidelines for planning, assurance and control of every process with the purpose of control and improvement if it was necessary.

The subject of the diploma thesis is the stress analysis of the circular and elliptical shaft from material jet grouting. A new advanced constitutive Shotcrete model will be applied on the material jet grouting. In the thesis, the shaft tensile strength factor and the size of the ground pressures will be primarily examined. The practical part of the diploma thesis is completed by the comparison of the analytical and numerical calculation of the normal force of the circular and elliptical shafts.

Concreto projetado é aquele pneumaticamente transportado e projetado a alta velocidade, sobre uma superficie, sendo auto-compactado. Assim, denota-se que suas propriedades são dependentes do processo de projeção utilizado. Desta forma, para se estudar o material, é importante ter-se o conhecimento do seu processo de produção (se por via seca ou úmida, equipamentos e mão-de-obra utilizados, etc.) e das propriedades especificas do concreto projetado (como a reflexão, o desplacamento e a liberação de poeira ou névoa) e as respectivas formas de controle. Foi executado o estudo experimental do concreto projetado via seca, onde foi possivel caracterizar algumas diferenças de comportamento em relação ao concreto convencional. Entre elas está o fato de que a maior compactação e resistência mecânica é obtida com o teor ótimo da mistura e não com a menor relação água/cimento. Constatou-se o fato da projeção do concreto no teto fornecer um material de melhor qualidade que aquele projetado na parede. Finalmente, para a obtenção de um material boa qualidade, é fundamental o controle rigoroso do teor de aditivo acelerador, a utilização de bicos afunilados, pressão de ar comprimido adequada, pré-umidificação com injeção de água sob pressão e seguir as recomendações para o controle da qualidade do processo de projeção como um todo. / Shotcrete is concrete pneumatically conveyed and projected at high speed onto a surface, compacting itself. Thus its properties depend on the shooting process. It is important to know the shooting process (wet ou dry-mix process, equipaments and working crew, etc.), the specific properties of shotcrete (rebound, sloughing and dust generation) and respective mean of controlo An experimental study was made using dry-mix shotcrete, where it was possible to point out some differences of the plain concrete analysis. One of these is the high compaction and stregth achieved with the optimum waterIdry materiaIs ratio and not the minimum water/cement ratio. Shotcrete, gunned in overhead, generates a better material compared to the vertical walls. Finally, to obtain a good quality material, it\'s very important to make a rigorous control of the accelerator admixture contento AIso, it is recommended to use a funnelshaped nozzle, adequate compressed air pressure, hidromix with high water pressure and to follow the recommendations on alI shotcreting process quality control.

The strive for a time-efficient construction process naturally put focus on the possibility of reducing the time of waiting between stages of construction, thereby minimizing the construction cost. If recently placed concrete, cast or sprayed, is exposed to impact vibrations at an early age while still in the process of hardening, damage that threatens the function of the hard concrete may occur. A waiting time when the concrete remains undisturbed, or a safe distance to the vibration source, is therefore needed. However, there is little, or no, fully proven knowledge of the length of this distance or time and there are no established guidelines for practical use. Therefore, conservative vibration limits are used for young and hardening concrete exposed to vibrations from e.g. blasting. As a first step in the dynamic analysis of a structure, the dynamic loads should always be identified and characterized. Here it is concluded that impact-type loads are the most dangerous of possible dynamic loads on young and hardening concrete. Shotcrete (sprayed concrete) on hard rock exposed to blasting and cast laboratory specimens subjected to direct mechanical impact loads have been investigated using finite element models based on the same analysis principles. Stress wave propagation is described in the same way whether it is through hard rock towards a shotcrete lining or through an element of young concrete. However, the failure modes differ for the two cases where shotcrete usually is damaged through loss of bond, partly or over larger sections that may result in shotcrete downfall. Cracking in shotcrete due to vibrations only is unusual and has not been observed during previous in situ tests. The study of shotcrete is included to demonstrate the need of specialized guidelines for cases other than for mass concrete, i.e. structural elements or concrete volumes with large dimensions in all directions. Within this project, work on evaluating and proposing analytical models are made in several steps, first with a focus on describing the behaviour of shotcrete on hard rock. It is demonstrated that wave propagation through rock towards shotcrete can be described using two-dimensional elastic finite element models in a dynamic analysis. The models must include the material properties of the rock and the accuracy of these parameters will greatly affect the results. It is possible to follow the propagation of stress waves through the rock mass, from the centre of blasting to the reflection at the shotcrete-rock interface. It is acceptable to use elastic material formulations until the strains are outside the elastic range, which thus indicates imminent material failure. The higher complexity of this type of model, compared with mechanical models using mass and spring elements, makes it possible to analyse more sophisticated geometries. Comparisons are made between numerical results and measurements from experiments in mining tunnels with ejected rock mass and shotcrete bond failure, and with measurements made during blasting for tunnel construction where rock and shotcrete remained intact. The calculated results are in good correspondence with the in situ observations and measurements, and with previous numerical modelling results. Examples of preliminary recommendations for practical use are given and it is demonstrated how the developed models and suggested analytical technique can be used for further detailed investigations. The modelling concept has also been used for analysis of impact loaded beams and concrete prisms modelled with 3D solid elements. As a first analysis step, an elastic material model was used to validate laboratory experiments with hammer-loaded concrete beams. The laboratory beam remained un-cracked during the experiments, and thus it was possible to achieve a good agreement using a linear elastic material model for fully hardened concrete. The model was further developed to enable modelling of cracked specimens. For verification of the numerical results, earlier laboratory experiments with hammer impacted smaller prisms of young concrete were chosen. A comparison between results showed that the laboratory tests can be reproduced numerically and those free vibration modes and natural frequencies of the test prisms contributed to the strain concentrations that gave cracking at high loads. Furthermore, it was investigated how a test prism modified with notches at the middle section would behave during laboratory testing. Calculated results showed that all cracking would be concentrated to one crack with a width equal to the sum of the multiple cracks that develop in un-notched prisms. In laboratory testing, the modified prism will provide a more reliable indication of when the critical load level is reached. This project has been interdisciplinary, combining structural dynamics, finite element modelling, concrete material technology, construction technology and rock support technology. It is a continuation from previous investigations of the effect on young shotcrete from blasting vibrations but this perspective has been widened to also include young, cast concrete. The outcome is a recommendation for how dynamic analysis of young concrete, cast and sprayed, can be carried out with an accurate description of the effect from impact-type loads. The type of numerical models presented and evaluated will provide an important tool for the work towards guidelines for practical use in civil engineering and concrete construction work. Some recommendations on safe distances and concrete ages are given, for newly cast concrete elements or mass concrete and for newly sprayed shotcrete on hard rock. / <p>QC 20150529</p>

abstract: Concrete design has recently seen a shift in focus from prescriptive specifications to performance based specifications with increasing demands for sustainable products. Fiber reinforced composites (FRC) provides unique properties to a material that is very weak under tensile loads. The addition of fibers to a concrete mix provides additional ductility and reduces the propagation of cracks in the concrete structure. It is the fibers that bridge the crack and dissipate the incurred strain energy in the form of a fiber-pullout mechanism. The addition of fibers plays an important role in tunnel lining systems and in reducing shrinkage cracking in high performance concretes. The interest in most design situations is the load where cracking first takes place. Typically the post crack response will exhibit either a load bearing increase as deflection continues, or a load bearing decrease as deflection continues. These behaviors are referred to as strain hardening and strain softening respectively. A strain softening or hardening response is used to model the behavior of different types of fiber reinforced concrete and simulate the experimental flexural response. Closed form equations for moment-curvature response of rectangular beams under four and three point loading in conjunction with crack localization rules are utilized. As a result, the stress distribution that considers a shifting neutral axis can be simulated which provides a more accurate representation of the residual strength of the fiber cement composites. The use of typical residual strength parameters by standards organizations ASTM, JCI and RILEM are examined to be incorrect in their linear elastic assumption of FRC behavior. Finite element models were implemented to study the effects and simulate the load defection response of fiber reinforced shotcrete round discrete panels (RDP's) tested in accordance with ASTM C-1550. The back-calculated material properties from the flexural tests were used as a basis for the FEM material models. Further development of FEM beams were also used to provide additional comparisons in residual strengths of early age samples. A correlation between the RDP and flexural beam test was generated based a relationship between normalized toughness with respect to the newly generated crack surfaces. A set of design equations are proposed using a residual strength correction factor generated by the model and produce the design moment based on specified concrete slab geometry. / Dissertation/Thesis / M.S. Civil and Environmental Engineering 2011

Concreto projetado é aquele pneumaticamente transportado e projetado a alta velocidade, sobre uma superficie, sendo auto-compactado. Assim, denota-se que suas propriedades são dependentes do processo de projeção utilizado. Desta forma, para se estudar o material, é importante ter-se o conhecimento do seu processo de produção (se por via seca ou úmida, equipamentos e mão-de-obra utilizados, etc.) e das propriedades especificas do concreto projetado (como a reflexão, o desplacamento e a liberação de poeira ou névoa) e as respectivas formas de controle. Foi executado o estudo experimental do concreto projetado via seca, onde foi possivel caracterizar algumas diferenças de comportamento em relação ao concreto convencional. Entre elas está o fato de que a maior compactação e resistência mecânica é obtida com o teor ótimo da mistura e não com a menor relação água/cimento. Constatou-se o fato da projeção do concreto no teto fornecer um material de melhor qualidade que aquele projetado na parede. Finalmente, para a obtenção de um material boa qualidade, é fundamental o controle rigoroso do teor de aditivo acelerador, a utilização de bicos afunilados, pressão de ar comprimido adequada, pré-umidificação com injeção de água sob pressão e seguir as recomendações para o controle da qualidade do processo de projeção como um todo. / Shotcrete is concrete pneumatically conveyed and projected at high speed onto a surface, compacting itself. Thus its properties depend on the shooting process. It is important to know the shooting process (wet ou dry-mix process, equipaments and working crew, etc.), the specific properties of shotcrete (rebound, sloughing and dust generation) and respective mean of controlo An experimental study was made using dry-mix shotcrete, where it was possible to point out some differences of the plain concrete analysis. One of these is the high compaction and stregth achieved with the optimum waterIdry materiaIs ratio and not the minimum water/cement ratio. Shotcrete, gunned in overhead, generates a better material compared to the vertical walls. Finally, to obtain a good quality material, it\'s very important to make a rigorous control of the accelerator admixture contento AIso, it is recommended to use a funnelshaped nozzle, adequate compressed air pressure, hidromix with high water pressure and to follow the recommendations on alI shotcreting process quality control.

Målet med projektet är att undersöka om det med matematiska modeller eller datorsimulationer går att förutsäga hur fibermängd mellan 20 kg/m³ och 60 kg/m³ i stålfiberarmerad sprutbetong med tjocklek mellan 5 cm och 15 cm påverkar attenuering av RFID signaler. Detta är intressant att undersöka eftersom RFID är en möjlig teknik att använda för mätning av betongtjocklek. Stålfibrernas påverkan på RFID signalen tillsammas med de möjligheter som finns att förutsäga densamma bestämmer i stor grad RFID-teknikens lämplighet att användas för mätning av betongtjocklek. I rapporten undersöks homogenisering med hjälp av Maxwell-Garnetts blandningsformel tillsammans med en analytisk metod som jämförs med en datorsimulation i CST Microwave studio. Utöver det utförs ytterligare en datorsimulation i CST där stålfiberarmerad betong modelleras som inhomogen bestående av stålfiber och betong. Mätdata från experiment som utförts på stålfiberarmerade betongblock presenteras och jämförs med de simulerade och beräknade fallen. Av de metoder som undersöks i projektet har ingen validerats. Beräkningarna för varje metod ger ofta olika resultat, varav inga är direkt jämförbara med den data som uppmätts experimentellt. Fibrernas påverkan på signalen verkar däremot vara signifikant och bidra med stora mätosäkerheter och förluster. Enligt den inhomgena simulationen är Maxwell-Garnetts blandningsmetod olämplig för syftet. Den tagg som testas verkar inte vara lämpad för detta användningsområde. Svårigheter med radiokommunikation genom betong identifieras och förslag ges på hur en tagg kan konstrueras för att fungera bättre i miljön.

In underground construction and tunnelling, the strive for a more time-efficient construction process naturally focuses on the possibilities of reducing the times of waiting between stages of construction. The ability to project shotcrete (sprayed concrete) on a rock surface at an early stage after blasting is vital to the safety during construction and function of e.g. a tunnel. A complication arises when the need for further blasting affects the hardening of newly applied shotcrete. If concrete, cast or sprayed, is exposed to vibrations at an early age while still in the process of hardening, damage that threatens the function of the hard concrete may occur. There is little, or no, established knowledge on the subject and there are no guidelines for practical use. It is concluded from previous investigations that shotcrete can withstand high particle velocity vibrations without being seriously damaged. Shotcrete without reinforcement can survive vibration levels as high as 0.5−1 m/s while sections with loss of bond and ejected rock will occur for vibration velocities higher than 1 m/s. The performance of young and hardened shotcrete exposed to high magnitudes of vibration is here investigated to identify safe distances and shotcrete ages for underground and tunnelling construction, using numerical analyses and comparison with measurements and observations. The work focuses on finding correlations between numerical results, measurement results and observations obtained during tunnelling. The outcome will be guidelines for practical use. The project involves development of sophisticated dynamic finite element models for which the collected information and data will be used as input, accomplished by using the finite ele­ment program Abaqus. The models were evaluated and refined through comparisons between calculated and measured data. First, existing simple engineering models were compared and evaluated through calculations and comparisons with existing data. The first model tested is a structural dynamic model that consists of masses and spring elements. The second is a model built up with finite beam elements interconnected with springs. The third is a one-dimensional elastic stress wave model. The stress response in the shotcrete closest to the rock when exposed to P-waves striking perpendicularly to the shotcrete-rock interface was simulated. Results from a non-destructive laboratory experiment were also used to provide test data for the models. The experiment studied P-wave propagation along a concrete bar, with proper­ties similar to rock. Cement based mortar with properties that resembles shotcrete was applied on one end of the bar with a hammer impacting the other. The shape of the stress waves travelling towards the shotcrete was registered using accelerometers positioned along the bar. Due to the inhomogeneous nature of the rock, the stress waves from the blasting attenuate on the way from the point of explosion towards the shotcrete on the rock surface. Material damping for the rock mass is therefore accounted for, estimated from previous in-situ measurements. The vibration resistance of the shotcrete-rock support system depends on the material properties of the shotcrete and here were age-dependent properties varied to investigate the behaviour of young shotcrete subjected to blast loading. The numerical simulations require insertion of realistic material data for shotcrete and rock, such as density and modulus of elasticity. The calculated results were in good correspondence with observations and measurements in-situ, and with the previous numerical modelling results. Compared to the engineering models, using a sophisticated finite element program facilitate modelling of more complex geometries and also provide more detailed results. It was demonstrated that wave propagation through rock towards shotcrete can be modelled using two dimensional elastic finite elements in a dynamic analysis. The models must include the properties of the rock and the accuracy of the material parameters used will greatly affect the results. It will be possible to describe the propagation of the waves through the rock mass, from the centre of the explosion to the reflection at the shotcrete-rock interface. It is acceptable to use elastic material formulations until the material strengths are exceeded, i.e. until the strains are outside the elastic range, which thus indicates material failure. The higher complexity of this type of model, compared to the engineering models, will make it possible to model more sophisticated geometries. Examples of preliminary recommendations for practical use are given and it is demonstrated how the developed models and suggested analytical technique can be used to obtain further detailed limit values. / Inom undermarks- och tunnelbyggande leder strävan efter en mer tidseffektiv byggprocess till fokus på möjligheten att reducera väntetiderna mellan byggetapper. Möjligheten att projicera sprutbetong på bergytor i ett tidigt skede efter sprängning är avgörande för säkerheten under konstruktionen av t.ex. en tunnel. En komplikation uppstår när behovet av ytterligare sprängning kan påverka härdningen av nysprutad betong. Om betong, gjuten eller sprutad, utsätts för vibrationer i ett tidigt skede under härdningsprocessen kan skador som hotar funktionen hos den hårdnade betongen uppstå. Kunskapen i ämnet är knapphändig, eller obefintlig, och det finns inga etablerade riktlinjer för praktisk användning. Slutsatsen från tidigare undersökningar visar att sprutbetong kan tåla höga vibrationer (partikelhastigheter) utan att allvarliga skador uppstår. Oarmerad sprutbetong kan vara oskadd efter att ha utsatts för så höga vibrationsnivåer som 0,5–1 m/s medan partier med förlorad vidhäftning till berget kan uppträda vid vibrationshastigheter högre än 1 m/s. Funktionen hos ung och hårdnande sprutbetong som utsätts för höga vibrationsnivåer undersöks här för att identifiera säkra avstånd och sprutbetongåldrar för undermarks- och tunnelbyggande, med hjälp av numeriska analyser och jämförelser med mätningar och observationer. Arbetet fokuserar på att finna samband mellan numeriska resultat, mätresultat och observationer från tunnelbyggande. Det slutliga resultatet kommer att vara riktlinjer för praktisk användning. Projektet omfattar utveckling av sofistikerade dynamiska finita elementmodeller för vilka insamlad information och data kommer att användas som indata för det finita elementprogrammet Abaqus. Modellerna utvärderades och förfinats genom jämförelser mellan beräknade och uppmätta resultat. Först jämfördes befintliga enkla mekaniska, ingenjörsmässiga modeller vilka utvärderades genom beräkningar och jämförelser med befintliga data. Den första modellen är en strukturdynamisk modell bestående av massor och fjäderelement. Den andra är en modell uppbyggd av finita balkelementet sammankopplade med fjädrar. Den tredje är en endimensionell elastisk spänningsvågsmodell. Spänningstillståndet i sprutbetongen närmast berget, utsatt för vinkelrätt inkommande P-vågor simulerades. Resultat från icke-förstörande laborationsprovningar användes också som testdata för modellerna. Experimentellt studerades P-vågsutbredning i en betongbalk med egenskaper likvärdiga med berg. Cementbruk med egenskaper liknande sprutbetong applicerades på balkens ena ände medan en hammare användes i den andra. Formen hos den genererade spänningsvågen som propagerade mot sprutbetongänden registrerades med accelerometrar utplacerade längs balken. På grund av bergets inhomogena karaktär kommer spänningsvågorna från sprängningen att dämpas ut på vägen från detonationspunkten till sprutbetongen på bergytan. Materialdämpningen hos bergmassan måste därför beaktas och kan uppskattas utifrån resultat från fältmätningar. Vibrationståligheten hos förstärkningssystem av sprutbetong och berg beror av materialegenskaperna hos sprutbetongen och i den här studien varierades de åldersberoende egenskaperna för att undersöka beteendet hos nysprutad och hårdnande sprutbetong utsatt för sprängbelastning. De numeriska simuleringarna kräver realistiska materialdata för sprutbetong och berg, som t.ex. densitet och elasticitetsmodul. De beräknade resultaten var i god överensstämmelse med observationer och mätningar i fält plats, och med de tidigare numeriska resultaten. Jämfört med de mekaniska modellerna kan ett sofistikerat finit elementprogram underlätta modellering av mer komplexa geometrier och också ge mer detaljerade resultat. Det visades att vågutbredning genom berg och fram emot sprutbetong kan beskrivas med tvådimensionella elastiska finita element i en dynamisk analys. Modellerna måste beskriva bergets egenskaper och noggrannheten i dessa parametrar kommer att ha stor inverkan på resultaten. Det kommer att vara möjligt att beskriva vågutbredningen genom bergmassan, från detonationspunkten till reflektionen vid bergytan, det vill säga gränssnittet mellan sprutbetong och berg. Det är acceptabelt att använda elastiska materialformuleringar tills materialet elasticitetsgräns överskrids tills töjningar utanför det elastiska området nås, vilket därmed indikerar materialbrott. Den högre komplexiteten hos den här typen av modell, jämfört med de mekaniska modellerna, kommer att göra det möjligt att analysera mer komplexa tunnelgeometrier. Exempel på preliminära rekommendationer för praktiskt bruk ges och det visas hur de utvecklade modellerna och den föreslagna analysmetodiken kan användas för att fastställa ytterligare detaljerade gränsvärden. / QC 20120427

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