Buried pipelines are tubular structures that cross large areas with different geological conditions. During an earthquake, imposed loads from soil deformations on pipelines may cause drastic damages. In this study two dimensional finite element models of pipelines and surrounding soils are usedfor simulation of seismic waves that propagate from the bedrock through thesoil. The models describe both longitudinal and transverse cross-sections ofpipelines and the soil-pipe interaction is described as a nonlinear behaviour.The effects of uniform ground with different burial depth and soil layer thickness, soil stiffness and non-uniform ground on the seismic response of reinforced concrete pipelines is studied. Two earthquakes, with high and low frequency contents, are employed for the dynamic analysis. The results show asignificant effect on the response due to non-uniform ground caused by inclined bedrock, especially for high frequency earthquake excitations.

Buried pipelines are tubular structures that cross large areas with different geological conditions. During an earthquake, imposed loads from soil deformations on concrete pipelines may cause severe damages. In this study, the use of two-dimensional finite element models of pipelines and surrounding soil for simulation of seismic waves that propagate from the bedrock through the soil are demonstrated. The models describe both longitudinal and transverse cross-sections of pipelines and the soil-pipe interaction is modelled as a nonlinear behaviour. The effects of uniform ground with different burial depths, soil layer thickness, soil stiffness and bedrock geometry on the seismic response of reinforced concrete pipelines is studied. Two earthquakes, with high and low frequency contents, are employed for the dynamic analysis. The results show that there is a much smaller risk of damage from high-frequency earthquakes, but that there is a significant effect on the response due to possible irregular ground with inclined bedrock.

Buried reinforced concrete pipelines are widelyused in e.g. water and wastewater systems. Failure of these infrastructures mayresult in drastic effects and recently they have been brought into focus asvital components in safety systems for nuclear power installations. The highlevel of safety has here lead to a demand for reliable earthquake risk analyses.In this paper, methods are compared and the use of seismic design loadsdemonstrated. FE analysis in 2D of soil-pipe interaction under seismic wavepropagation is performed. The performance of concrete pipes subjected toseismic waves with different frequency content is evaluated with respect todifferent soil condition but also water mass effect.

Concrete buttress dams could potentially be susceptible to high-frequency vibrations, especially in the cross-stream direction, due to their slender design. Previous studies have mainly focused on low-frequency vibrations in stream direction using a simplified foundation model with the massless method, which does not consider topographic amplifications. This paper therefore investigates the nonlinear behaviour of concrete buttress dams subjected to high-frequency excitations, considering cross-stream vibrations. For comparison, the effect of low-frequency excitations is also investigated. The influence of the irregular topography of the foundation surface on the amplification of seismic waves at the foundation surface and thus in the dam is considered by a rigorous method based on the domain-reduction method using the direct finite element method. The sensitivity of the calculated response of the dam to the free-field modelling approach is investigated by comparing the result with analyses using an analytical method based on one-dimensional wave propagation theory and a massless approach. Available deconvolution software is based on the one-dimensional shear wave propagation to transform the earthquake motion from the foundation surface to the corresponding input motion at depth. Here, a new deconvolution method for both shear and pressure wave propagation is developed based on an iterative time-domain procedure using a one-dimensional finite element column. The examples presented showed that topographic amplifications of high-frequency excitations have a significant impact on the response of this type of dam. Cross-stream vibrations reduced the safety of the dam due to the opening of the joints and the increasing stresses. The foundation modelling approach had a significant impact on the calculated response of the dam. The massless method produced unreliable results, especially for high-frequency excitations. The free-field modelling with the analytical method led to unreliable joint openings. It is therefore recommended to use an accurate approach for foundation modelling, especially in cases where nonlinearity is considered.

During blasting in tunnels and mines, the shotcrete-rock interaction is influenced by propagating stress waves. Shotcrete support in hard rock tunnels is here studied through numerical analysis and comparisons with previous numerical results, measurements and observations in situ. The stress response in the shotcrete closest to the rock when exposed to P-waves striking perpendicularly to the shotcrete-rock interface is simulated. The first model tested is an elastic stress wave model, which is onedimensional with the shotcrete assumed linearly elastic. The second is a structural dynamic model that consists of masses and spring elements. The third model is a finite element model implemented using the Abaqus/Explicit program. Two methods are used for the application of incident disturbing stress waves: as boundary conditions and as inertia loads. Results from these three types of models are compared and evaluated as a first step before a future extension to more detailed analyses using 3D models. 

During blasting in tunnels and mines, the shotcrete-rock interaction is influenced by propagating stress waves. Shotcrete support in hard rock tunnels is here studied through numerical analysis and comparisons with previous numerical results, measurements and observations in situ. The stress response in the shotcrete closest to the rock when exposed to P-waves striking perpendicularly to the shotcrete-rock interface is simulated. The first model tested is an elastic stress wave model, which is onedimensional with the shotcrete assumed linearly elastic. The second is a structural dynamic model that consists of masses and spring elements. The third model is a finite element model implemented using the Abaqus/Explicit program. Two methods are used for the application of incident disturbing stress waves: as boundary conditions and as inertia loads. Results from these three types of models are compared and evaluated as a first step before a future extension to more detailed analyses using 3D models.

An experimental and theoretical study of the shear behaviour of steel-fibre-reinforced concrete is presented. Twenty-seven direct shear push-off tests were carried out on high-strength concrete, with and without steel fibre reinforcement. The test series contained uncracked and precracked specimens for the study of the slipping response and the shear stress that can be transferred across an open crack. The test variables were the fibre content and the reinforcement ratio. The test results were compared with information provided by the available codes and other, previous results. The test results indicated that incorporation of steel fibres and bars in concrete members subjected to shear leads to an improved mechanical behaviour before failure. Based on the presented experimental results, an equation governing the direct shear strength is proposed and verified against test results from other test series.

To study the behaviour of shotcrete under dynamic load, a non-destructive laboratory experiment was set up with P-wave propagation along a concrete bar, with properties similar to rock. Cement-based mortar with properties that resemble shotcrete was applied to 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. Finite-element modelling was used to verify the test results, which showed that the laboratory model with an impacting hammer could be used to initiate the same type of stress waves that result from blasting in good-quality rock. Previously recommended maximum allowed peak particle vibration velocities were verified.

During blasting in tunnels and mines, the interaction between shotcrete (sprayed concrete) and rock is influenced by propagating stress waves. Shotcrete support in hard rock tunnels is studied here through numerical analysis using three different modelling approaches. The stress response in the shotcrete closest to the rock when exposed to P-waves striking perpendicularly to the shotcrete–rock interface is simulated. 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 element beam elements interconnected with springs. The third is a one-dimensional elastic stress wave model. The models give comparable results, although the definition of the dynamic loads is different. The analysis results can be used to estimate whether the shotcrete will fail or not for a prescribed distance to detonating explosives inside the rock.

The effect on shotcrete from blasting operations during tunnelling is studied, with focus on young and hardening shotcrete. A finite element model specially adapted for analysis of the shotcrete behaviour is tested, it is able to describe stress wave propagation in two dimensions which is important for cases where shear stresses are dominant. The modelling results are compared with in situ measurements and observations, from construction blasting during tunnelling through hard rock. The comparison shows that the model gives realistic results and can be used to investigate the vulnerability of shotcrete, aiming at compiling recommendations and guidelines for practical use. The given recommendations emphasize that blasting should be avoided during the first 12 h after shotcreting and that distance and shotcrete thickness are important factors for how much additional time of waiting is possibly needed.

Numerical modelling in combination with in situ measurements, observations and laboratory testing will be important to future establishment of reliable guidelines for efficient civil and engineering work involving concrete casting close to e.g. blasting operations. Results from laboratory tests with impact loaded young concrete prisms are here evaluated using a 3D finite element model. Solid elements are used and a non-linear material model implemented, capable of describing cracking during stress wave propagation. The position of cracks and measured particle vibration velocities are calculated and compared with laboratory test results. The damaging effect of impact vibrations is evaluated using crack width and fracture energy as damage criteria. Alternative geometry for the test prisms, with a notched section, is analysed. This will give one wide crack at the centre of the prism instead of two or three cracks distributed over its length which will make future laboratory test more efficient and reliable. Recommended damage limits at concrete ages of 4, 6, 8 and 12 h are given, based on numerical calculations for concrete strength class C25 and C50.

An elastic finite element model is used tosimulate theinducedstress waves from blasting, propagating in rock towards shotcrete on a tunnel wall. Due to the inhomogeneous nature of the rock, the stress wavesattenuate onitsway from the point of explosiontowardsthe shotcrete on the rock surface. Material damping for the rock-mass is estimated from in-situ measurements. The vibration resistance of the shotcrete-rock support system depends on the material properties of the shotcrete. Age-dependent material properties are varied to investigate the behaviour of young shotcrete subjected to blast loading. Finally, finite element analysis results are presented and verified through comparison with other numerical models, measurements and observations.

Results from laboratory tests on statically loaded bolt-anchored, steel-fibre-reinforced shotcrete linings in interaction with rock are here evaluated using a 2D finite element model. Calculations are made to determine the state of stress in the rock-shotcrete interface near the rock joints. Plane-stress elements are used with a non-linear material model, capable of describing cracking and de-bonding during loading. The simulated crack position and force-displacement curves are compared with laboratory test results. Since most construction work in underground hard rock involves the use of explosives for excavation work, dynamic load cases are also analysed and compared to results from previous research on vibration resistance of shotcrete. 

The problem with shotcrete on rock subjected to vibrations has previously been studied in place and through numerical modeling. Within the present project, an elastic finite element model is presented that consists of beam elements used to model the flexural stiffness and mass of the shotcrete lining and a section of rock. Spring elements are added for elastic coupling between shotcrete and rock. The loads on the model are acceleration-time series. Scaling laws for the magnitude of vibration velocities in rock as a function of distance and amount of explosives are used to study the damage to shotcrete at various. distances from the source of an explosion. Age-dependent shotcrete material properties are varied to investigate the vulnerability of young shotcrete exposed to explosion-induced vibrations. Recommended minimum shotcrete ages, based on the numerical results, are given for practical use.

Rock bolts of steel are the most frequently used components in systems for rock reinforcement. Special types are used as energy absorbing elements in systems exposed to dynamic loads and these must yield plastically under high loading velocities. A new type of energy absorbing rock bolt of soft steel has been suggested and tested. To investigate the strain rate effects on the yield stress and ultimate strength of the steel were bars dynamically loaded in a high speed testing machine. The observed tensile forces can be divided into one part from impact and another from quasi-static straining. The tests showed that there was a considerable strain rate effect on the yield stress of the steel. It is recommended that higher dynamic yield stresses are utilized in the dynamic design which has to incorporate the risk of high peak forces from impact loading.

Uncertainty about the vibration levels that can be tolerated near newly sprayed concrete (shotcrete) often leads to excessively conservative limit values being used in the construction of tunnels and structures in rock, with additional costs and planning uncertainties as a result. Previously, it has only been possible to give general recommendations for safe vibration levels. A project with the aim of producing a set of practical vibration limit levels for shotcrete work close to blasting in hard rock has therefore been carried out. These recommendations span situations that may arise during "normal" construction in hard rock, and contain guidelines for safe distances and waiting times for newly sprayed shotcrete exposed to vibrations. In the project, the focus is on wet-mixed shotcrete on hard rock, of the type found in Sweden and Scandinavia.

A large number of calculations have been carried out with a previously developed and relatively computationally effective numerical elastic stress wave propagation model. As input data, various combinations of the weight of explosives, distance, rock type, shotcrete type, shotcrete age and thickness are used. For each combination of input parameters, the stresses that arise at the bond interface between rock and shotcrete have been calculated. The results are saved in a database and can be illustrated graphically with a 3D surface, as a function of shotcrete age and distance to the explosive charge. This surface has then been compared with another, which represents the growth of bond strength between rock and shotcrete. The intersection curve between the two surfaces represents the limit for safe blasting, taking into account combinations of shortest distances and the youngest allowable shotcrete at time of blasting.

The report contains a larger number of graphs showing limit values for safe blasting, which will be of value as reference in design work, enable comparisons with data from the field, and thereby feedback of experience. Based on the recommended limit values, dimensioning in the design stage will be made so that the results will be undamaged and safer shotcrete with longer life. Reduced need for re-spraying and repair leads to a high economic sustainability for large infrastructure projects and environmental sustainability when material consumption is reduced. The safety of tunnels and underground constructions will also be increased.

A criterion for how close, in time and distance, to young shotcrete blasting can take place will be an important tool in planning for safe and economical tunnelling projects. As a first step, in situ tests with young, plain un-reinforced shotcrete have been conducted in a Swedish mine. Shotcrete panels were projected on tunnel walls and exposed to vibrations from explosive charges detonated inside the rock at shotcrete ages between I and 25 h. The shotcrete was tested to investigate growth of compressive strength and also to determine final compressive and adhesive strengths. The response of the rock was measured with accelerometers, giving signals that were later numerically integrated to particle vibration velocities. An average scaling relation of distance between explosive charges and the point of observation and weight of explosives was also derived. The recorded vibration levels showed that the shotcrete had withstood high particle velocity vibrations without being seriously damaged, even when the rock material was fragmented and ejected. Drumminess of shotcrete appeared, indicating that the major failure mechanism was sudden loss of adhesion at the shotcrete-rock interface. No differences in performance between shotcrete of different ages were observed. It was, thus, confirmed that young shotcrete without reinforcement can also survive high vibration levels without being seriously damaged.

The presented investigation combines in situ observations, measurements, testing and theoretical modelling. The in situ work was done to map and evaluate the shrinkage related cracking of shotcrete on short and long sections of soft, plastic drains. The occurrence of variation in shotcrete thickness and crack widths were of particular interest. The theoretical analysis focuses on the stresses that can occur due to uneven drying shrinkage in the two-layered shotcrete. The models used include variation in shotcrete thickness and in time of waiting between turns of spraying, with or without watering of the shotcrete. Watering will delay the shrinkage but has no effect on the strength development. Long times of waiting without watering before spraying a second layer will increase the tensile stresses in the shotcrete. It is recommended that the further work is directed towards establishing guidelines for the design of future drain constructions with shotcrete. Different methods for repair and strengthening of cracked shotcreted drains must be developed, tested and evaluated.

Energy absorbing rock bolts are used as part of rock support systems in underground constructions that are exposed to e.g., rock bursts and detonating explosives. A rock bolt capable of absorbing kinetic energy from these loads must be able to yield with the ground movements and also deform plastically over large distances, at high displacement rates. A new type of energy absorbing rock bolt has been developed and tested in laboratory. The bolt is without a casing and consists of a steel bar that has an inner ribbed-like anchorage section and an outer nut that transfers the load from the rock via a circular disc. When subjected to a dynamic load, the lengthening of the steel bar leads to a decrease in diameter whereby the adhesive bond between bar and grout is lost and the outer end of the bolt is free to yield. The rock bolt is given a very good protection from corrosion when fully grouted in cement. In a laboratory, rock bolts in concrete cylinders were subjected to free fall tests to achieve a loading velocity of 10 m/s. The tests demonstrated that the distribution of plastic strain along the length of a grouted rock bolt is not constant when dynamically loaded. The sections where plastic yielding was allowed were not fully utilized in any of the cases, opposite to that in previous static tests which show almost constant elongation of the bolts. The tests also verified that the load-carrying components of the bolt, the nut and the anchorage, are reliable when dynamically loaded. Elastic and plastic waves will start to propagate through the rock bolt as it is suddenly loaded, resulting in permanent deformation along a section of the bolt. This yield process is demonstrated through a combined graphical and numerical method.

Limited knowledge on safe vibration levels near newly sprayed concrete (shotcrete) often leads to over-conservative limits in underground construction and tunnelling, with additional costs and planning uncertainties as a consequence. Work on compiling a database of practical vibration levels for shotcrete work close to blasting in hard rock have been initiated and will provide guidelines for safe distances and waiting times for newly sprayed wet-mix shotcrete. A large number of calculations are carried out with a previously developed and relatively computationally effective numerical elastic stress wave propagation model, which will result in a systematically compiled database. These guidelines, giving relationships between the amount of explosives, distance, rock type, shotcrete type, age and thickness, will be of great value as reference for design work and facilitate comparisons with in situ data. It will be possible to adopt the design to ensure undamaged and safer shotcrete constructions with longer service life.

Shotcrete is sprayed concrete applied pneumatically on, for example, a rock surface to prevent fallout of rock blocks and thereby securing the arch-shape of a tunnel profile. A finite element model, especially adapted to the dynamic analysis of shotcrete on rock that is subjected to vibrations from blasting, has been developed and tested. The model consists of spring and beam elements that are used to simulate the behaviour of an elastic concrete area, bound to a rock surface through adhesion. This facilitates the calculation of a two-dimensional displacement field, using mode superposition and Duhamel integral. The loads applied on the model are accelerations that give rise to inertia forces on the system. The accelerations are calculated from given weights of explosives, geometrical conditions and rock properties. The presented numerical examples demonstrate the response of shotcrete to vibrations, based on material data from an extensive literature survey. A series of calculations are compiled to give recommendations for how close to shotcrete blasting in rock can be allowed.

Shotcrete sprayed on rock is vulnerable to stress waves from large-scale blasting in tunnels and mines. Shotcrete support in a Swedish underground mine is studied through numerical analysis and comparisons with previous results, measurements and observations in situ. A previously developed finite-element model that consists of beam and spring elements is used to calculate the response of shotcrete to vibrations from production blasts in the mine. The modelling approach is similar to that of a building during an earthquake, with accelerations measured in situ used as loads. The analysis shows that the calculated bond stresses exceed the strength in the interface between shotcrete and rock close to the blasts. The results show that it is possible to optimise the scheme of the blasting so that shotcrete is protected from damaging vibrations. Also recommended, for practical use, are minimum distances to large amounts of explosives given. This set of recommendations is a supplement to previously given guidelines valid for small amounts of explosives at short distances from shotcrete on rock.

Tunnels and underground openings in hard rock are often constructed with arch-shaped ceilings and complicated 3D geometries arise at intersections with cross tunnels and other openings. This is further complicated due to the often irregular shape of the rock surface and the uneven shotcrete thickness, making it difficult to analyse the interaction between rock and support systems. A study of the interaction in 3D between an irregular, rough rock surface and supporting rock bolts and shotcrete has begun, through finite element modelling using non-linear material models and formulations capable of describing large deformations. Various cases that may cause failure are to be studied, such as falling blocks or heavily jointed rock, bolt failure and drumminess between rock and shotcrete. An important conclusion from the preliminary results is that rock bolts should be placed at points where the shotcreted surface is locally convex, i.e. at peaks.