Joints are the main features encountered in rock and sliding of rock blocks on joints is classified as the principal source of instability in underground excavations. In this regard, joints’ peak shear strength is the controlling parameter. However, given the difficulty in estimating it, shear tests are often performed. These are often quite expensive and also time consuming and, therefore, it would be valuable if shear tests could be artificially performed using numerical models. The objective of this study is to prove the possibility to perform virtual numerical shear tests in a PCF2D environment that resemble the laboratory ones. A numerical model of a granite rock joint has been created by means of a calibration process. Both the intact rock microparameters and the smooth joint scale have been calibrated against macroparameters derived from shear tests performed in laboratory. A new parameter, the length ratio, is introduced which takes into account the effective length of the smooth joint compared to the theoretical one. The normal and shear stiffnesses, the cohesion and the tensile force ought to be scaled against the length ratio. Four simple regular joint profiles have been tested in the PFC2D environment. The analysis shows good results both from a qualitative and from a quantitative point of view. The difference in peak shear strength with respect to the one computed with Patton´s formula is in the order of 1% which indicates a good accuracy of the model. In addition, four profiles of one real rough mated joint have been tested. From the scanned surface data, a two-dimensional profile has been extracted with four different resolutions. In this case, however, interlocking of particles along the smooth joint occurs, giving rise to an unrealistic distribution of normal and shear forces. A possible explanation to the problem is discussed based on recent developments in the study of numerical shear tests with PFC2D.

The stability of rock masses is influenced by the occurrence of rock joints. Therefore, the shear strength of rock joints must be considered in dimensioning of underground constructions. One way to predict the shear strength is through usage of failure criteria, which are validated from results of direct shear tests under controlled laboratory conditions. Consequently, the quality of the results from the tests are crucial to the accuracy with which the criteria will be able to predict the shear strength. Since rock joints are unique by nature usage of replicas (man-made copies of rock joints) is of importance in parameter studies. The overall objective of this work is to facilitate the development of improved criteria for predictions of the shear strength of rock joints. To support this objective, two sources of uncertainty have been investigated, namely the geometry of replicas and the influence of the normal stiffness of test systems. Two quality assurance parameters for evaluation of geometrical differences between replicas and rock joints based on scanning data have been derived. The first parameter describes the morphological deviations. The second parameter describes the deviations in orientation with respect to the shear plane. The effective normal stiffness approach, which compensates for the influence of the normal stiffness of the test system in direct shear testing, has been developed, validated, and applied. With help of the quality assurance parameters it is demonstrated that it is possible to reproduce replicas within narrow tolerances. Application of the effective normal stiffness approach basically eliminates the normal load error. In all, the results support generation of improved quality of test data and consequently, the development of shear strength criteria with improved accuracy will also be facilitated. / <p>Academic Dissertation which, with due permission of the KTH Royal Institute of  Technology, is submitted for public defence for the Degree of Licentiate of Engineering on Wednesday the 9th June 2021, at 9:00 a.m. in M108, Brinellvägen 23, Stockholm.</p><p><strong>Paper A</strong>: Larsson J, Flansbjer M, Portal N W, Johnson E, Johansson F, and Mas Ivars D. (2020) Geometrical Quality Assurance of Rock Joint Replicas in Shear Tests – Introductory Analysis. Paper presented at the ISRM International Symposium - EUROCK 2020, physical event not held. https://onepetro.org/ISRMEUROCK/proceedings-abstract/EUROCK20/All-EUROCK20/ISRM-EUROCK-2020-101/451187  In Diva: http://urn.kb.se/resolve?urn=urn:nbn:se:ri:diva-51987 </p><p><strong>Paper B:</strong> Larsson J, Johansson F, Mas Ivars D, Johnson E, Flansbjer M and Portal N W. (2021) Rock joint replicas in direct shear testing – Part 1: Extraction of geometrical quality assurance parameters. To be submitted to Rock Mechanics and Rock Engineering  In DiVA: http://urn.kb.se/resolve?urn=urn:nbn:se:ri:diva-53111 </p><p><strong>Paper C:</strong> Larsson J and Flansbjer M. (2020) An Approach to Compensate for the Influence of the System Normal Stiffness in CNS Direct Shear Tests. Rock Mechancis and Rock Engineering 53, 2185–2199 https://doi.org/10.1007/s00603-020-02051-0  In DiVA: http://urn.kb.se/resolve?urn=urn:nbn:se:ri:diva-44085  </p><p><strong>Paper D:</strong> Larsson J. (2021) Experimental investigation of the system normal stiffness of a 5 MN direct shear test setup and the compensation of it in CNS direct shear tests. Submitted to ISRM International Symposium - EUROCK 2021  In DiVA: http://urn.kb.se/resolve?urn=urn:nbn:se:ri:diva-53112 </p>

The stability of rock masses is influenced by the occurrence of rock joints. Therefore, the shear strength of rock joints must be considered in dimensioning of underground constructions. One way to predict the shear strength is through usage of failure criteria, which are validated from results of direct shear tests under controlled laboratory conditions. Consequently, the quality of the results from the tests are crucial to the accuracy with which the criteria will be able to predict the shear strength. Since rock joints are unique by nature usage of replicas (man-made copies of rock joints) is of importance in parameter studies. The overall objective of this work is to facilitate the development of improved criteria for predictions of the shear strength of rock joints. To support this objective, two sources of uncertainty have been investigated, namely the geometry of replicas and the influence of the normal stiffness of test systems. Two quality assurance parameters for evaluation of geometrical differences between replicas and rock joints based on scanning data have been derived. The first parameter describes the morphological deviations. The second parameter describes the deviations in orientation with respect to the shear plane. The effective normal stiffness approach, which compensates for the influence of the normal stiffness of the test system indirect shear testing, has been developed, validated, and applied. With help of the quality assurance parameters it is demonstrated that it is possible to reproduce replicas within narrow tolerances. Application of the effective normal stiffness approach basically eliminates the normal load error. In all, the results support generation of improved quality of test data and consequently, the development of shear strength criteria with improved accuracy will also be facilitated. / Bergmassors stabilitet påverkas av bergssprickor. Bergssprickors skjuvhållfasthet behöver därför beaktas vid fastställandet av vilka laster berganläggningar skall dimensioneras mot. Skjuvhållfastheten predikteras bland annat med hjälp av brottkriterier, vilka valideras med hjälp av resultaten från skjuvtester i kontrollerad laboratoriemiljö. Kvaliteten på resultaten från testerna är därför av avgörande betydelse för med vilken noggrannhet kriterierna kommer att kunna prediktera skjuvhållfastheten. Det övergripande målet med detta arbete är att underlätta utvecklingen av förbättrade kriterier för prediktioner av bergssprickors skjuvhållfasthet. Som ett bidrag till att uppnå detta mål har två osäkerhetsfaktorer undersökts, nämligen geometrin av replikor (kopior) av bergssprickor och inverkan av testsystems normalstyvhet. Två kvalitetssäkringsparametrar för utvärdering av de geometriska skillnaderna mellan replikor och bergprov baserade på skanningdata har tagits fram. Den första parametern beskriver de morfologiska avvikelserna. Den andra parametern beskriver avvikelserna i orientering med avseende på skjuvplanet. Ett tillvägagångssätt med en effektiv systemnormalstyvhet, vilken kompenserar för inverkan av testsystemets normalstyvhet, har utvecklats, validerats och tillämpats. Med hjälp av kvalitetssäkringsparametrarna påvisas att det ar möjligt att reproducera replikor inom snäva toleranser. Genom tillämpning av tillvägagångssättet med en effektiv normalstyvhet kan felet i normallast i princip elimineras. Sammantaget stödjer resultaten framtagning av testdata med förbättrad kvalitet och därigenom underlättas även utvecklingen av skjuvhållfasthetskriterier med förbättrad noggrannhet. / <p>QC 210518</p>

When the point under consideration is not near to the source of vibration, the strains developed in the rock mass due to the passage of waves are usually of small magnitude, and within the elastic range. However, the rock mass may be subjected to a wide range of strain levels depending on the source of vibration and the wave frequency, even within the elastic limit. The present study is based on the two general conditions existing at field, long wave length propagation of waves and intermediate wavelength propagation of waves. When the wavelength of propagating wave is much longer than the joint spacing, it is referred to as long wavelength condition and is associated with propagation of low frequency waves across closely spaced joints. When wavelength of propagating wave is nearly equal to joint spacing, it is known as intermediate wavelength condition and is associated with propagation of high frequency waves. Long wave length propagation of waves has been studied by conducting laboratory experiments using Resonant Column Apparatus on developed plaster gypsum samples. The influence of joint types, joint spacing and joint orientation on wave propagation has been analyzed at three confining stresses under various strain levels. The wave velocities and damping ratios at various strain levels have been obtained and presented. Shear wave velocities are more dependent on confining stress than compression wave velocities across frictional joints whereas, compression wave velocities are more dependent on confining stress than shear wave velocities across filled joints. Wave velocities are at minimum and wave damping is at maximum across horizontal joints whereas wave velocities are at maximum and wave damping is at minimum across vertical joints. Shear wave velocity and shear wave damping are more dependent on joint orientations than compression wave velocity and compression wave damping. As Resonant Column Apparatus has some limitations in testing stiff samples, a validated numerical model has been developed using Discrete Element Method (DEM) that can provide resonant frequencies under torsional and flexural vibrations. It has been found from numerical simulations, that reduction of normal and shear stiffness of joint with increasing strain levels leads to wave velocity reduction in jointed rock mass. Intermediate wave length propagation of waves has been studied by conducting tests using Bender/ extender elements and the numerical simulations developed using 3DEC (Three Dimensional Distinct Element Code).Parametric study on energy transmission, wave velocities and wave amplitudes of shear and compression waves, has been carried out using the validated numerical model. The propagation of waves across multiple parallel joints was simulated and the phenomenon of multiple reflections of waves between joints could be observed. The transformations of obliquely incident waves on the joint have been successfully modeled by separating the transmitted transformed P and S waves. The frequency dependent behavior of jointed rocks has been studied by developing a numerical model and by applying a wide range of wave frequencies. It has been found that low frequency shear waves may involve slips of rock blocks depending on the strength of rock joint, leading to less transmission of energy; while low frequency compression waves are well transmitted across the joints. High frequency shear and compression waves experience multiple reflections and absorptions at joints.

In Sweden, the rock mass is commonly used for construction of tunnels and caverns. The rockmass is also used as a foundation for large structures such as bridge abutments and dams. Forthese structures, the understanding of the rock mechanical properties play a key role for reachingan acceptable safety level and minimizing cost. One of the properties that has a high uncertaintyis the shear strength of rock joints. These rock joints constitute the weakest link in the rock massand often govern it´s strength. The uncertainty lies in the amount of factors that affect the shearstrength such as the degree of weathering, the matedness, the roughness of the surface and thescale. Various authors have tried to develop a failure criterion that can predict the peak shearstrength of rock joints and takes into account the influence of the various factors.The aim of this thesis is to evaluate the ability of the newly developed Casagrande et al.criterion to determine the peak shear strength for perfectly mated and natural rock joints withdifferent degrees of matedness. All samples analyzed in this thesis have been scanned andcustomized to run in the programmed version of the Casagrande et al. criterion. This iterativeprocess will stop as the application reach the apparent dip angle where the total shearing force issmaller than the total sliding force. This angle combined with the basic friction angle gives thepeak friction angle for calculations of the peak shear strength.The result show that the Casagrande et al. criterion can predict the peak shear strength forperfectly mated joint. However, for the natural rock joint, as the degree of matedness decreases,the accuracy of the prediction of the peak shear strength decreases. The conclusion of this studyis that the Casagrande’s criterion cannot determine the peak shear strength of natural rock jointsand that further development of the Casagrande et al. criterion is needed taking this parameterinto account. / Sverige är berg ett vanligt material för byggande av tunnlar och bergrum. För dessakonstruktioner spelar bergegenskaperna en nyckelroll för att nå en acceptabel säkerhetsnivåoch minimera kostnaden. En av de egenskaper som har stor osäkerhet är skjuvhållfastheten förbergsprickor. Osäkerheten ligger i de många faktorer som påverkar skjuvhållfastheten, såsomgraden av vittring, passning, ytans råhet och skala. Olika författare har försökt att anpassa ettbrottkriterium för bergsprickor som tar hänsyn till faktorernas inflytande och som kan användastill att uppskatta den maximala skjuvhållfastheten.Syftet med detta examensarbete är att utvärdera förmågan hos det nyligen utveckladebrottkriteriet av Casagrande et al. att bestämma den maximala skjuvhållfastheten för perfektpassade sprickor och naturliga sprickor med olika grad av passning. Alla prover i detta arbetehar skannats in och anpassats för att köras i den programmerade algoritmen som beräknar denmaximala skjuvhållfastheten enligt kriteriet av Casagrande et al.. Kriteriet använder sig av eniterativ process som pågår tills algoritmen når den vinkel där den totala skjuvkraften är mindreän den totala glidkraften. Denna vinkel kombinerad med sprickans basfriktionsvinkeln ger denmaximala friktionsvinkeln för beräkning av skjuvhållfastheten.Resultaten visar att Casagrande et al. kan förutspå den maximala skjuvhållfastheten förperfekt passade sprickor. När passningsgraden minskar för naturliga bergsprickor minskar kriterietsförmåga att prediktera den maximala skjuvhållfastheten. Slutsatsen från detta arbete äratt kriteriet av Casagrande et al. kan prediktera skjuvhållfastheten för perfekt passade sprickormen saknar förmågan att beakta inverkan från passning, vilket leder till att skjuvhållfasthetenöverskattas om kriteriet användas på naturliga sprickor som inte är perfekt passade. Fortsattforskning krävs för att vidareutveckla kriteriet så att graden av passning kan beaktas.

Résumé: L’objectif de cette thèse est d’interpréter la dégradation des aspérités des joints rocheux sous différentes conditions de chargement. Pour cela, la variation des aspérités durant les différentes étapes du cisaillement d’un joint rocheux est observée. Selon le concept appelé “tiny windows”, une nouvelle méthodologie de caractérisation des épontes des joints a été développée. La méthodologie est basée sur les coordonnées tridimensionnelles de la surface des joints et elles sont mesurées après chaque essai. Après la reconstruction du modèle géométrique de la surface du joint, les zones en contact sont identifiées à travers la comparaison des hauteurs des “tiny windows” superposées. Ainsi, la distribution des zones de la surface en contact, endommagées et sans contact ont été identifiées. La méthode d’analyse d’image a été utilisée pour vérifier les résultats de la méthodologie proposée. Les résultats indiquent que cette méthode est appropriée pour déterminer la taille et la distribution des surfaces du joint en contact et endommagées à différentes étapes du cisaillement. Un ensemble de 38 répliques ont été préparées en coulant du mortier sans retrait sur une surface de fracture obtenue à partir d’un bloc de granite. Différentes conditions de chargement, incluant des chargements statiques et cycliques ont été appliquées afin d’étudier la dégradation des aspérités à différentes étapes du procédé de cisaillement. Les propriétés géométriques des “tiny windows” en contact en phase pré-pic, pic, post-pic et résiduelle ont été analysées en fonction de leurs angles et de leurs auteurs. Il a été remarqué que les facettes des aspérités faisant face à la direction de cisaillement jouent un rôle majeur dans le cisaillement. Aussi, il a été observé que les aspérités présentent différentes contributions dans le cisaillement. Les aspérités les plus aigües (“tiny windows” les plus inclinées) sont abîmées et les aspérités les plus plates glissent les unes sur les autres. Les aspérités d’angles intermédiaires sont définies comme “angle seuil endommagé” et “angle seuil en contact”. En augmentant la charge normale, les angles seuils diminuent d’une part et, d’autre part, le nombre de zones endommagées et en contact augmentent. Pour un petit nombre de cycles (avec faible amplitude et fréquence), indépendamment de l’amplitude, une contraction apparaît ; par conséquent, la surface en contact et les paramètres de résistance au cisaillement augmentent légèrement. Pour un grand nombre de cycles, la dégradation est observée à l’échelle des aspérités de second ordre, d’où une baisse des paramètres de résistance au cisaillement. Il a été aussi observée que les “tiny windows” avec différentes inclinaisons contribuent au processus de cisaillement, en plus des “tiny windows” les plus inclinées (aspérités plus aigües). Les résultats de la méthode proposée montrent que la différenciation entre les zones en contact et celles endommagées s’avère utile pour une meilleure compréhension du mécanisme de cisaillement des joints rocheux. / Abstract: The objective of the current research is to interpret the asperity degradation of rock joints under different loading conditions. For this aim, the changes of asperities during different stages of shearing in the three-dimensional joint surface are tracked. According to a concept named ‘tiny window’, a new methodology for the characterization of the joint surfaces was developed. The methodology is based on the three-dimensional coordinates of the joints surface that are captured before and after each test. After the reconstruction of geometric models of joint surface, in-contact areas were identified according to the height comparison of the face to face tiny windows. Therefore, the distribution and size of just in-contact areas, in-contact damaged areas and not in-contact areas are identified. Image analysis method was used to verify the results of the proposed method. The results indicated that the proposed method is suitable for determining the size and distribution of the contact and damaged areas at any shearing stage. A total of 38 replicas were prepared by pouring non-shrinking cement mortar on a fresh joint surface of a split granite block. Various loading conditions include monotonic and cyclic loading were applied to study the asperities degradation at different stages of shearing. The geometric properties of the in-contact tiny windows in the pre-peak, peak, post-peak softening and residual shearing stages were investigated based on their angle and height. It was found that those asperities facing the shear direction have the primary role in shearing. It is remarkable that different part of these asperities has their own special cooperation in shearing. The steepest parts (steeper tiny windows) are wore and the flatter parts (flatter tiny windows) are slid. The borderlines between these tiny windows defined as “damaged threshold angle” and “in-contact threshold angle”. By increasing normal load, both the amounts of threshold angles are decreased and contact and damaged areas increased. During low numbers of cycles (with low amplitude and frequency), independent of the type of cycle, contraction occurs and consequently the contact area and the shear strength parameters slightly increased. During larger number of cycles, degradation occurred on the second order asperities, therefore the shear strength parameters slowly decreased. It was also observed that tiny windows with different heights participate in the shearing process, not just the highest ones. The results of the proposed method indicated that considering differences between just in-contact areas and damaged areas provide useful insights into understanding the shear mechanism of rock joints.

The shear behaviour of rough rock joints was investigated by both laboratory testing and numerical simulation. The most powerful servo-controlled direct shear box apparatus in the world with normal forces up to 1000 kN, shear loading up to 800 kN and frequencies up to 40 Hz under full load was used to investigate the shear strength of schistose rock blocks with dimensions of up to 350 x 200 x 160 mm in length, width and height, respectively. The experiments were performed to study the behaviour of rough rock joints under constant normal load, constant normal stiffness and dynamic boundary conditions. The joint surface of rock specimen was scanned 3-dimensional at the initial stage before shearing by new 3D optical-scanning equipment. The 3D-scanner data were used to estimate the joint roughness coefficient (JRC) and to reconstruct rough surface of rock discontinuities in numerical models. Three dimensional numerical models were developed using FLAC3D to study the macro and micromechanical shear behaviour of the joints. Numerical simulation results were compared to experimental results. Three dimensional characteristic of the joint surface including micro-slope angle, aperture, contact area and normal stress distribution were determined and analyzed.

The shear behaviour of rough rock joints was investigated by both laboratory testing and numerical simulation. The most powerful servo-controlled direct shear box apparatus in the world with normal forces up to 1000 kN, shear loading up to 800 kN and frequencies up to 40 Hz under full load was used to investigate the shear strength of schistose rock blocks with dimensions of up to 350 x 200 x 160 mm in length, width and height, respectively. The experiments were performed to study the behaviour of rough rock joints under constant normal load, constant normal stiffness and dynamic boundary conditions. The joint surface of rock specimen was scanned 3-dimensional at the initial stage before shearing by new 3D optical-scanning equipment. The 3D-scanner data were used to estimate the joint roughness coefficient (JRC) and to reconstruct rough surface of rock discontinuities in numerical models. Three dimensional numerical models were developed using FLAC3D to study the macro and micromechanical shear behaviour of the joints. Numerical simulation results were compared to experimental results. Three dimensional characteristic of the joint surface including micro-slope angle, aperture, contact area and normal stress distribution were determined and analyzed.