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.

Assessment of the spatial distribution of bedrock level (BL) as the lower boundary of soil layers is associated with many uncertainties. Increasing our knowledge about the spatial variability of BL through high resolution and more accurate predictive models is an important challenge for the design of safe and economical geostructures. In this paper, the efficiency and predictability of different artificial intelligence (AI)-based models in generating improved 3D spatial distributions of the BL for an area in Stockholm, Sweden, were explored. Multilayer percepterons, generalized feed-forward neural network (GFFN), radial based function, and support vector regression (SVR) were developed and compared to ordinary kriging geostatistical technique. Analysis of the improvement in progress using confusion matrixes showed that the GFFN and SVR provided closer results to realities. The ranking of performance accuracy using different statistical errors and precision/recall curves also demonstrated the superiority and robustness of the GFFN and SVR compared to the other models. The results indicated that in the absence of measured data the AI models are flexible and efficient tools in creating more accurate spatial 3D models. Analyses of confidence intervals and prediction intervals confirmed that the developed AI models can overcome the associated uncertainties and provide appropriate prediction at any point in the subsurface of the study area. 

Uncertainty quantification (UQ) is an important benchmark to assess the performance of artificial intelligence (AI) and particularly deep learning ensembled-based models. However, the ability for UQ using current AI-based methods is not only limited in terms of computational resources but it also requires changes to topology and optimization processes, as well as multiple performances to monitor model instabilities. From both geo-engineering and societal perspectives, a predictive groundwater table (GWT) model presents an important challenge, where a lack of UQ limits the validity of findings and may undermine science-based decisions. To overcome and address these limitations, a novel ensemble, an automated random deactivating connective weights approach (ARDCW), is presented and applied to retrieved geographical locations of GWT data from a geo-engineering project in Stockholm, Sweden. In this approach, the UQ was achieved via a combination of several derived ensembles from a fixed optimum topology subjected to randomly switched off weights, which allow predictability with one forward pass. The process was developed and programmed to provide trackable performance in a specific task and access to a wide variety of different internal characteristics and libraries. A comparison of performance with Monte Carlo dropout and quantile regression using computer vision and control task metrics showed significant progress in the ARDCW. This approach does not require changes in the optimization process and can be applied to already trained topologies in a way that outperforms other models. 

The correlation between Standard and Cone Penetration Tests (SPT and CPT) as two of the most used in-situ geotechnical tests is of practical interest in engineering designs. In this paper, new SPT-CPT correlations for southwest of Sweden are proposed and developed using an artificial neural networks (ANNs) approach. The influences of soil type, depth, cone tip resistance, sleeve friction, friction ratio and porewater pressure on obtained correlations has been taken into account in optimized ANN models to represent more comprehensive and accurate correlation functions. Moreover, the effect of particle mean grain size and fine content were investigated and discussed using graph analyses. The validation of ANN based correlations were tested using several statistical criteria and then compared to existing correlations in literature to quantify the uncertainty of the correlations. Using the sensitivity analyses, the most and least effective factors on CPT-SPT predictions were recognized and discussed. The results indicate the ability of ANN as an attractive alternative method regarding to conventional statistical analyses to develop CPT-SPT relations.

Although there are many proposed relations for different rock types to predict the uniaxial compressive strength (UCS) as a function of P-wave velocity (V-P) and point load index (Is), only a few of them are focused on marlstones. However, these studies have limitations in applicability since they are mainly based on local studies. In this paper, an attempt is therefore made to present updated relations for two previous proposed correlations for marlstones in Iran. The modification process is executed through multivariate regression analysis techniques using a provided comprehensive database for marlstones in Iran, including UCS, V-P and Is from publications and validated relevant sources comprising 119 datasets. The accuracy, appropriateness and applicability of the obtained modifications were tested by means of different statistical criteria and graph analyses. The conducted comparison between updated and previous proposed relations highlighted better applicability in the prediction of UCS using the updated correlations introduced in this study. However, the derived updated predictive models are dependent on rock types and test conditions, as they are in this study.

In the original version of this article, unfortunately a character of the Journal no in the reference 10 has been published incorrectly.

There is an increasing interest in creating high-resolution 3D subsurface geo-models using multisource retrieved data, i.e., borehole, geophysical techniques, geological maps, and rock properties, for emergency managements. However, dedicating meaningful, and thus interpretable 3D subsurface views from such integrated heterogeneous data requires developing a new methodology for convenient post-modeling analyses. To this end, in the current paper a hybrid ensemble-based automated deep learning approach for 3D modeling of subsurface geological bedrock using multisource data is proposed. The uncertainty then was quantified using a novel ensemble randomly automated deactivating process implanted on the jointed weight database. The applicability of the automated process in capturing the optimum topology is then validated by creating 3D subsurface geo-model using laser-scanned bedrock-level data from Sweden. In comparison with intelligent quantile regression and traditional geostatistical interpolation algorithms, the proposed hybrid approach showed higher accuracy for visualizing and post-analyzing the 3D subsurface model. Due to the use of integrated multi-source data, the approach presented here and the subsequently created 3D model can be a representative reconcile for geoengineering applications.

Rumslig fördelning av djup till berggrunden (DTB) är en viktig ochutmanande fråga i många geotekniska tillämpningar. På grund av att DTBassocieras med säkerhet och ekonomi i jord- och bergkonstruktionerkan generering av mer precisa modeller vara av avgörande betydelse.Med hjälp av resultat från Jb-sonderingar för ett infrastrukturprojekt iStockholm har vi skapat en optimerad visualiserad 3D -prediktiv DTBmodellvia en automatiserad artificiell intelligent datormetod (AI) ochjämfört den med den metod som ofta används, det geostatistiskaverktyget Ordinary Kriging (OK).

In the context of geo-infrastructures and specifically tunneling projects, analyzing the large-scale sensor-based measurement-while-drilling (MWD) data plays a pivotal role in assessing rock engineering conditions. However, handling the big MWD data due to multiform stacking is a time-consuming and challenging task. Extracting valuable insights and improving the accuracy of geoengineering interpretations from MWD data necessitates a combination of domain expertise and data science skills in an iterative process. To address these challenges and efficiently normalize and filter out noisy data, an automated processing approach integrating the stepwise technique, mode, and percentile gate bands for both single and peer group-based holes was developed. Subsequently, the mathematical concept of a novel normalizing index for classifying such big datasets was also presented. The visualized results from different geo-infrastructure datasets in Sweden indicated that outliers and noisy data can more efficiently be eliminated using single hole-based normalizing. Additionally, a relational unified PostgreSQL database was created to store and automatically transfer the processed and raw MWD as well as real time grouting data that offers a cost effective and efficient data extraction tool. The generated database is expected to facilitate in-depth investigations and enable application of the artificial intelligence (AI) techniques to predict rock quality conditions and design appropriate support systems based on MWD data.

Landslides as major geo-hazards in Sweden adversely impact on nearby environments and socio-economics. In this paper, a landslide susceptibility map using a proposed subdivision approach for a large area in southwest Sweden has been produced. The map has been generated by means of an artificial neural network (ANN) model developed using fourteen causative factors extracted from topographic and geomorphologic, geological, land use, hydrology and hydrogeology characteristics. The landslide inventory map includes 242 events identified from different validated resources and interpreted aerial photographs. The weights of the causative factors employed were analyzed and verified using accepted mathematical criteria, sensitivity analysis, previous studies, and actual landslides. The high accuracy achieved using the ANN model demonstrates a consistent criterion for future landslide susceptibility zonation. Comparisons with earlier susceptibility assessments in the area show the model to be a cost-effective and potentially vital tool for urban planners in developing cities and municipalities.

Applicering av överlast på kalkcementförstärkta jordar är ofta förekommande idag, forskning indikerar dock på att överlasten här, inte ger samma effekt som på oförstärkta jordar. Med grund i uppmätta värden i fält, visas i denna rapport, sättningsdifferenser mellan att använda överlast jämfört med att endast applicera brukslast. Resultat av analyserna visar på sättningsbeteende observerat i fält. Om erforderlig liggtid för brukslast finns, uppstår endast små sättningsdifferenser mellan att använda överlast eller inte.

Genom att utföra sensitivitetsanalys i FEM- programvaran PLAXIS studeras kryputvecklingen i den förstärkta jorden. Effekten av att applicera en överlast visas för krypsättningar över lång tid.

Inget resultat från de numeriska FEM- analyserna visade att märkbart gynnsam effekt uppstår på grund av överlastens applicering, med avseende på krypsättningar.

De numeriska analyserna utförs i 2 och 3 dimensioner för att belysa effekt av förenkling av ett lastfall som inte uppfyller krav för oförstärkta jordar i plant töjningstillstånd.

Utöver detta ges efter en litteraturstudie, förslag på hur vissa indataparametrar kan utvärderas från empiriska relationer. Indataparametrar som ligger till grund för analyserna är utvärderade från sonderingsresultat i kombination med värden från laborationsförsök och empiriska data.

Environmental sustainability is becoming more popular in the building industry. Sustainable thinking needs to be present during the whole construction process, from the idea phase to the final stages. The aim of this master thesis is to investigate how end-bearing concrete and steel pipes as well as composite concrete-filled steel tube piles can be designed with greater consideration to climate impact. The purpose of this study is primarily to encourage awareness during the material choice phase in early stages of project planning.

A Matlab code was programmed to perform a parametric study and analyze different parameters effect on pile bearing capacity. The structural bearing capacity of a number of different piles with various prerequisites were compiled in tables. The climate impact of the piles was expressed as global warming potential (GWP). In order to compare different pile types a functional unit was created as the ratio of the piles' bearing capacity and the corresponding climate impact. The ratio was calculated for all the piles and resulted in a number of figures with bearing capacity as a function of climate impact. These figures are supposed to be used as a basis to choose which pile type is most useful in a given situation. The usability of the results was verified with a calculation example. In the example, the figures were used to chose one pile out of several options as the most climate-efficient with the highest usage ratio.

Finally, a number of general conclusions could be drawn regarding pile types. When the corrosion is small (<2 mm), it can be ascertained that steel pipes are to prefer over composite pipes. With larger corrosion (>2 mm), it can be ascertained that composite piles are preferable, specifically in cases were the soil is looser. However, in firmer soil, with undrained shear strength between 10-25 kPa, composite concrete-filled steel pipes are the better option. The results show that the contribution of the concrete to the bearing capacity of the composity files is minimal compared to the contribution of the decreased inner corrosion. This implies that it is more important to have the pipes filled with to prevent inner corrosion, rather than use a strong material that contributes to the bearing capacity. With that said, composite piles are not sustainable and different filling materials can be examined to further investigate whether there is another material with smaller climate impact that makes for piles with larger ratio of bearing capacity to climate impact. The main conclusion of the master thesis is that there needs to be a standardised approach to calculating climate impact from foundation construction and it should be included in a building's life cycle analysis (LCA).

There are many old dams in Sweden and, since few dams are constructed today, the main task in risk assessment on the existing dams is often to reduce the risk of failure. RIDAS (Swedish Guidelines on Dam Safety) is used when designing new dams and assess the existing ones. The guidelines include stability requirements for different failure modes, e.g. overturning and sliding, which imply that the load effect from e.g. uplift and ice load need to be less than the resisting loads or moments. The ice load in RIDAS is given as a deter­ministic value depending on where in Sweden the dam is located. For many years, ice and ice load have been researched, but there is still a lack of knowledge regarding the magni­tude of the ice load and how it affects the probability of failure for dams. More knowledge about the actual ice load would result in a lower calculated probability of failure for the dam which could be used to design slender dams or avoid unnecessary reinforcement of existing dams.

Dam safety evaluation is often performed with deterministic methods based on safety factors. In recent years, the use of probabilistic methods in dam design has increased. The method has an advantage compared to deterministic methods in safety evaluations of existing dams, since probabilistic methods provide an answer to which parameters that have the greatest impact on the stability of the dam and take into account the variations in each parameter.

I this master thesis, a statistical distribution for the variation of the ice load’s annual maxi­mum value was calculated. This was used in the analysis of the probability of failure for solid gravity concrete dams and buttress concrete dams. The probability of failure was cal­culated for dams of different sizes for overturning and sliding failure modes, and also for three different load cases; without ice load, with a truncated ice load distribution and with an ice load distribution that has not been truncated. The probabilistic stability analysis was conducted in Comrel with ice load as one of the stochastic variables. It was found which sizes of the dams that have the largest impact from the ice load; also what effect extreme values on the ice load has on the failure probability of the dam.

The results indicated that the probability of failure for dams lower than 15 m is more affected by the ice load, for both failure modes analyzed. The probability of failure is reduced for all dam types when eliminating extreme values of the ice load, particularly for dams lower than 15 m. In several cases, truncation of the ice load distribution is the differ­ence between an accepted and a non-accepted level of the probability of failure. It is also shown that reduced coefficient of variance for the ice load results in a decreased probability of failure. The conclusion is that solid gravity dams and buttress dams lower than 15 m, with a high consequence class, should be risk assessed with the ice load as a stochastic vari­able. The statistical distribution of the ice load is still uncertain and the distribution used in this report should not be used globally, rather in areas with a climate similar to northern Sweden. The reason for this is that the measurements that were used to derive the global distribution were mainly performed in areas with conditions similar to those in northern Sweden.

A recommendation for further research is to focus on determining statistical distributions for the ice load for southern, central and northern Sweden. An alternative is to use differ­ent ice load distributions for the different areas. Another alternative could be to use the same statistical distribution for southern, central and northern Sweden but with different values for where the ice load distribution is truncated, depending on the maximal ice thick­ness in each area. The recommendation is also to develop a reliable method for measuring the ice load. In addition, attempts should be made to determine whether extreme values on the ice load really exist or if they are effects of measurement errors.

Key words: concrete dams, ice load, probabilistic stability analysis, probability of failure

For piling works in sensitive soil, especially in inner city projects, it is essential to be aware of the available methods and to choose the most suitable method to minimize the risk of damaging existing buildings or endanger the workers at the construction site. Down-the-hole drilling of piles is a relatively safe method and can be separated into drilling with air powered hammers and water powered hammers. This study compares water powered drilling with air powered drilling and shows that the impact on the soil generated by air powered drilling is larger than that from water powered drilling.

A field study was carried out where 4 piles were drilled, two with air powered DTH drilling and two with water powered DTH drilling. The drilling was carried out in clay resting on an approximately 4 m layer of silt and friction soil. The total soil depth was about 12- 15 m. To analyze the soil influence, settlements were measured at ground level and in depth and pore pressure was measured in the middle of the clay layer. This study distinguished two major problems when drilling through this type of soil. The first is the risk of over-drilling in the friction layer. The second problem is the risk of increasing the pore pressure in the clay. Both these problems were experienced when using air powered drilling but for the water powered case only a small pore pressure increase and no over-drilling was observed. In conclusion, drilling with water has less influence on the soil in the sense that it gives a smaller effect on the pore water pressure and causes smaller settlements.

Despite advancements in computational resources, the discrete element method (DEM) still requires considerable computational time to solve detailed problems, especially when it comes to the large-scale models. In addition to the geometry scale of the problem, the particle shape has a dramatic effect on the computational cost of DEM. Therefore, many studies have been performed with simplified spherical particles or clumps. Particle scaling is an approach to increase the particle size to reduce the number of particles in the DEM. Although several particle scaling methods have been introduced, there are still some disagreements regarding their applicability to certain aspects of problems. In this study, the effect of particle scalping on the shear behavior of granular material is explored. Real granular particles were scanned and imported as polygonal particles in the direct shear test. The effect of particle size distribution, particle angularity, and the amount of scalping were investigated. The results show that particle scalping can simulate the correct shear behavior of the model with significant improvement in computational time. Also, the accuracy of the scalping method depends on the particle angularity and particle size range.

Modelling railway projects has a main challenge in the discrete element method (DEM). The granular material of the embankment consists of millions of fine angular particles which are difficult to model due to the long computational time. The long computational time also prevents the modeling of the higher number of loading cycles. As a result, researchers prefer to simulate the project in 2D to accelerate the simulation. While 2D simulations present a seemingly simple option for modeling railways, they tend to oversimplify the intricacies of particle interactions and the distribution of stress. Nonetheless, the extent to which these simplifications affect the authenticity of the simulations has remained ambiguous. In this study, the periodic cell replication method is used to build extensive long railway tracks significantly faster than conventional methods. Then, this DEM model is calibrated against the measurement results of a physical full-scale ballasted track. The model is then used to simulate several railway projects with different initial particle arrangements and model dimensions in both 2D and 3D. The results show that the 2D models are more dependant on the initial particle arrangement which shows different behavior for the same model. In addition, 2D simulations are incapable of reproducing the principal stress rotation in granular layers due to the moving load of the train wheel. As a result, 3D DEM simulations using the periodic cell replication method is suggested for studying the railway tracks.

Modelling railway embankments have two main challenges in the discrete ele-ment method (DEM). First, the granular material of the embankment consistof millions of fine angular particles which are difficult to model due to thelong computational time. As a result, researchers prefer to use spherical orscale-up particles as granular material. Also, it prevents the modeling of thehigher number of loading cycles. Second, the DEM is incapable of includingcontinuous rail beams due to its discrete nature. Therefore, most of the re-search is limited to ignoring the rail beam and other structural elements ofthe track. In this study, a DEM model is calibrated against the measure-ment results of a physical full-scale ballasted track. The model is then used toinvestigate the effect of including the rail beam for high-speed railways sub-jected to 2000 axle passages. The results show that although ignoring therail beam does not substantially affect the results for initial loading cycles,its influence is significant after a couple of hundred axle passages. The modelwithout a rail beam shows more principal stress rotation, more settlement,non-realistic vertical displacement of the sleepers, more particle rearrange-ment and more sleepers’ vibration. Therefore, it is necessary to include therail beam in the long-term analysis of the track to conclude realistic results.

The Discrete element method (DEM) is a methodology to investigatethe interactions among granular materials. It analyzes the behavior of par-ticulate environments by solving force-displacement equations that adhereto Newton’s second law of motion. Despite its usefulness, the DEM is notwithout limitations, and researchers are still facing certain challenges thatrestrict them from performing detailed analyses of granular materials. Thisstudy addresses two issues in DEM modeling of granular materials in rail-way embankments. Firstly, the long computational time required by theDEM for modeling fine angular particles in granular materials is addressedby exploring the effects of particle scaling on the shear behavior of granularmaterial. This study investigates the impact of particle size distribution,particle angularity, and the amount of scaling on the accuracy and compu-tational efficiency of DEM. Secondly, the limitations of DEM in includingthe continuous rail beam structure in the track are addressed by verifyinga DEM model against physical measurements of a full-scale ballasted trackand investigating the influence of including the rail beam structure on high-speed railway ballasted tracks. The results show that the use of particlescaling in the first study significantly improves the computational efficiencyof the DEM while maintaining accuracy, and this method is used in thesecond study to investigate the influence of the rail beam structure on thebehavior of railway tracks.

Cracks in concrete structures such as a concrete dam can be exposed to water pressure, for example, uplift pressure. The water pressure can be significant and may result in cracks propagating through the structures and thus it may result in reduced service life. However, the knowledge of water pressure within the cracks is relatively limited and is often neglected or just roughly estimated. The influence of crack opening rate on the uplift pressure distribution in the crack and the pressure variation during opening or sudden crack closure are questions needed to investigate. As an attempt to answer those questions, a pilot study presented here describes the possibilities and limitations of the proposed experimental setup; and technology (penetrability meter and tomography) as an examination method for water pressure in propagation concrete cracks. The test specimens examined here are exclusively cylinders cast of concrete with or without an initial crack.

The penetrability meter can be used to apply water pressure and to visualize the crack opening, X-Ray computed tomography test, was performed. KTH Civil and Architectural Engineering department has organized the laboratory resources.

The examples reported in this work show that the technology and equipment have great potential for future work on crack propagation, however, sample design and preparation, as well as testing need further development.

This thesis forms the basis for a new documented experience of grouting design and work in the extension of the blue metro line in Stockholm. It includes documentation of the grouting design based on theoretical basis, stop criteria and fan geometries for favorable and unfavorable geological conditions. The work is concerned in evaluating the design stop criteria in different geological conditions to assess the efficiency of grouting process, and its compatibility to the maximum permissible leakage according to applications submitted to the land and environmental court in Stockholm.

The work was conducted in cooperation with TYPSA AB and SWECO; the joint venture who designed the grouting work.

This work was initiated by studying the design documents and reports, requirements, geological and hydrogeological prognosis documents. Six access tunnels were analyzed, with different work percentage based on the actual work achieved at the site at the time of conducting the study. Each access tunnel stretch was determined in terms of geological condition (rock quality), hydrogeological domain, and grouting class (IK1, IK2 or IK3). Evaluations and assessments were done for different aspects including evaluating the grout volume uptake per each grouting class, calculating the percentage of boreholes that stopped by time, volume or zero flow per grouting class, and comparing the measured leakage with prognosed leakage to check the efficiency of the design and implementation phases. RTGC (Real Time Grouting Control) method was also applied on some fans to check its validity in grout optimization, knowing that it is a relatively new method and not yet fully validated.

The results showed that geological mappings during the implementation phase were slightly different from the mappings done during the design phase, which is expected due to the high uncertainties in rock mass science. It was also shown that the design stop criteria in this project were promising, through which they have satisfied the requirements according to the application to the land and environmental court. Average grout uptake in typical injection classes were compatible with the results in City Line projects, where the average grout uptake in 2 L/m. However, results also showed that in weakness zones, the average grout uptake was different with high standard deviations. Knowing the fact that unfavorable geological conditions were classified based on different parameters, it is not possible to find one reference value for the grout uptake, but instead results can be used as references in similar geological conditions in main tunnels work and future projects. Some recommendations are made in this thesis on the design stop criteria in weakness zones, surface rock domains, and at fans injected at large water depth. These zones always form the basis for controversial discussions and thus, if documentation of grouting work is carried out and continued in this project, then more knowledge can be gained and transferred to other projects. As part of this thesis, RTGC was applied in favorable conditions where it showed very promising results, the matter that makes it possible to optimize the stop criteria and actual work by conducting trial grouting. However, in unfavorable geological conditions, the RTGC could not be applied because the dimensionality of the flow is 3D, while RTGC was developed for 1D and 1D flow. Therefore, and since it was proven to be as a promising tool, further studies are recommended to develop the method for 3D flow.

Swedish transport administration initiated this Master Thesis project and the aim was to compare regulations for the design of high-speed railways from three European countries: France, Germany and Spain. The reason why this is of interest for the Swedish transport administration is the design of the first Swedish high-speed railway, called Ostlänken. Therefore, a literature study of the regulations and other literature regarding high-speed railway has been carried out. A basic description of railway components, slab track and ballasted tracks is presented.

Ballasted embankments usually consist of a trackbed layer (ballast onto subballast), and the ultimate thickness of this layer is discussed, as there are a number of methods available to calculate the appropriate thickness, with a number of different design parameters. These design methods results in different trackbed thickness and choosing the “wrong” method might lead to an overestimation or underestimation of the trackbed layer. Constructing a ballastless railway line means that the ballast is replaced by another material, usually a slab made of reinforced concrete or asphalt, and the rail is cast onto this slab. Countries design their slab using different methods. Germany has constructed high-speed railway lines with a slab track solution, generally slabs with low flexible stiffness. France has until recently constructed their high-speed line ballasted but is now developing a new slab track technique, called NBT (New Ballastless Track) and Spain uses various methods.

It is difficult to compare the regulations, however, there are some factors that at least begin to explain the differences between the countries: the frost hazard, the inherent ground quality, purpose with the railway (mixed traffic, solely passenger traffic, etc.), design parameters (life, axle load, etc.). Furthermore, the settlement requirements, soil classification and bearing capacity are factors that varies from country to country, but the origin for this variation is harder to detect.

In recent decades, climate change has become a very pressing issue. The construction industry contributes significantly to greenhouse gas emissions and in Sweden, this sector accounts for over twenty percent of total CO2 emissions. Sustainable construction methods, such as using environmentally friendly materials and energy-efficient design, are essential to reducing the carbon footprint of construction projects. Geotechnics, which is an important component of the construction industry, plays a crucial role in this context for both the environmental impact and the monetary cost of the construction during its life cycle.In this thesis, two different geotechnical methods have been studied to limit settlement in clay during a fictitious road construction: Dry deep mixing with Cement Kiln Dust (CKD) and a combination of lime and cement as binder and excavation and refilling with light filling materials such as foam glass and expanded polystyrene (EPS). Their environmental impact and costs are evaluated using the Life Cycle Assessment (LCA) and Life Cycle Cost Analysis (LCCA) methods. The primary objective of this study is to emphasize the importance of LCA and LCCA in the evaluation of the environmental and economic consequences of construction projects and their integration into geotechnical methods and design to minimize the environmental footprint and reduce costs of such projects.In this specific case study, the summed results of LCA and LCCA show that Multicem, a mixture of CKD and Portland cement, can effectively reduce both climate impact and costs from production to construction. Lime/cement and EPS also offer favorable alternatives, while foam glass, despite having less climate impact than others, turns out to be the least desirable due to its higher material cost.

Uplift water pressure is one of the dominating forces with signicant impact acting on a dam. It is usually measured with piezometers installed along the dam. However, the value of the pressure along the dam is often hard to measure due to the limited number of piezometers available (Bernstone et al., 2009). Furthermore, uplift pressure can oscillate substantially in a single hole both with time and also spatially under the dam due to the combination of rock mass characteristics in the foundation, loads and temperature variations.There is still a lack of information regarding the magnitude and variation of the uplift pressure. The aim of this thesis is to investigate the spatial variation of the uplift pressure based on uplift pressure measurements taken from Storfinnforsen and Ramsele dams. The aim is also to investigate how the uplift pressure depends on the rock mass conditions. The two dams Storfinnforsen and Ramsele provides a unique opportunity due to the signicant amount of piezometers, 270 in total, installed along the rock foundation for the new monitoring programme at the monoliths of both dams.Based on the measured uplift pressure, a probabilistic distribution has been assigned to the uplift pressure. In addition, a possible correlation between the rock mass quality and the uplift pressure as well as the joint aperture and the uplift pressure was analysed.

The Eurocode for Geotechnical Design, EN-1997-1:2004, informally known as Eurocode 7 or EC7, was fully implemented within the European Union in 2010. This Eurocode is intended to apply to all geotechnical engineering design, including rock engineering. In recognition that all codes must continue to evolve in order to remain applicable, and the long time that such evolution takes, work is already underway under the auspices of the European Committee for Standardisation, CEN, to identify how the code should develop for future revisions. This paper presents a summary of the maintenance procedures for Eurocodes in general and the specific maintenance work currently being undertaken on EC7 in respect of rock engineering design. It also highlights potential future development of EC7, and the need for enthusiastic involvement by the European rock engineering community to direct these developments. 

Anisotropy is a very common condition in rock mass; it can be due to different factors and directly affects the failure mechanisms affecting the rock mass. For example, metamorphic rocks that are foliated, sedimentary rocks that are stratified or volcanic formations with alternating layers. Despite the existence of several studies related to anisotropy those specifically addressing the tensile strength of anisotropic rocks are quite limited. The present study is focused on the determination of the deformability, compressive and tensile strength of anisotropic rocks. It must be highlighted that the mechanical behavior of the anisotropic rock mass is dependent on the angle between the inclination of planes of weakness (e.g. foliation) and the direction of the load. Assuming a vertical load, the two extremes of tensile strength are 0°(horizontal) and 90° (vertical). A series of laboratory tests has been done in anisotropic sandstone (lithic arkose), from Burgos (Spain), including uniaxial compressive strength tests, direct tensile strength tests, and diametric compression (Brazilian tests). The tests were carried out with strain gauges that allowed estimating the elastic modulus. To determine the anisotropic direction, ultrasonic pulse wave velocity tests were also performed. The variation of strength and deformability as a function of anisotropy is analyzed, as well as the variation of elastic behavior in tensile and compressive.

Rock grouting is a commonly used process for sealing rocks in tunnels to reduce water ingress. In order to achieve sufficient sealing level the grout must effectively penetrate into rock fractures while the limiting factor is filtration of cement based grout. Many devices and measuring methods have been developed to study filtration and to measure the penetrability. The filter pump and the penetrability meter are two of the most commonly used instruments for measuring filtration tendency in the field and in the lab, while short slot is used mainly in the lab. The results obtained from these devices have relatively different estimations of the penetrability partly due to the weaknesses in measuring methods and test procedures. Furthermore, there are no clear criteria to find out which of the results are closer to the reality or how much the results differ among these instruments. The aim of this study is comparing, and evaluating the results of these devices in relatively similar conditions while using more accurate methods of weight-time and pressure-time compared to the less reliable total volume method. The filter pump and the penetrability meter were modified In order to fulfill the requirement of testing in similar conditions and to improve their accuracy and versatility.

The results show that increasing the pressure improves the penetrability significantly. The modification of the filter pump results in reducing many uncertainties related to the testing procedure. Probably the modified filter pump has higher accuracy in measuring the penetrability compared to regular filter pump. The short slot has the highest accuracy in estimating penetrability of cement based grout especially at higher pressures, furthermore, the short slot provides a more flexible way to measure penetrability with different pressures in the range of 1-15 bars.

Site investigations are often performed prior to the design of pile foundations with the aim to collect data regarding soil properties including boulder content. The obtained data is typically limited due to non-homogeneous characteristic of the soil. The geological conditions of the Mälardalen region are characterized by glacial and post glacial clay overlaying on the layer of moraine containing boulders on a bedrock. Thus, pile refusal in results of encountering boulders is a common issue during pile driving in this region. The current methods to assess the pile refusal risk are mostly qualitative and relies on the expertise gained from experience.This thesis aims to develop a numerical model to quantify the boulder content in a soil strata with a confidence interval based on the site investigation results. Furthermore, this study estimates the probability and the consequences of hitting boulders while installing piles.The model simulations show that an increase in the boulder content raises the probability of hitting a boulder, but it is not proportional to the diameter of piles. It means that even in low rate of boulder content with small piles there is a high probability to hit a boulder. Results from simulations using simplified quantitative method show that slender piles have substantial consequences in case they encounter boulders. Thus, these piles are more prone to pile refusal or breakage. It is suggested that in projects where small piles are preferred due to the superstructure design, enough tests be performed to have an estimate of boulder content with tighter interval and more precise design. On the other hand, in projects with low pile counts, it is recommended to have a conservative design with large diameter piles instead of performing numerous in-situ tests. This is because the price for piling becomes relatively low compared to site investigations’ cost.

The strength variability of soils improved by lime-cement columns is very high, and assessment of the reliability is associated with high uncertainty. Previous research on natural soils has shown that variability has a major impact on the reliability of geotechnical systems. However, concerning ground improvement with lime-cement columns, the effect of the uncertainties associated with improved strength properties on the reliability is unknown. This paper addresses the integration of reliability-based design in the design of embankments founded on soil improved by lime-cement columns by an analysis of a project conducted in Sweden. The uncertainties associated with estimating the strength property based on results from cone penetration tests and their effect on the assessed system reliability are addressed and discussed. The use of variance reduction with respect to the spatial variability of the shear strength of the columns was found to have a major influence on the assessed system reliability. Furthermore, it was found that the transformation uncertainty from measurements based on cone penetration tests has a significant impact on the assessed system reliability. System reliability cannot be improved significantly simply by performing a large number of tests.

Stability assessment of highway embankments is a common practice in geotechnical engineering. Rational estimation of soil properties is essential for reliable and safe design. However, previous research has shown that high degree of uncertainty is associated with engineering properties and the behavior of the ground improvement with lime-cement columns. Current design methods for stability of lime-cement column are deterministic and the uncertainties are not treated rationally. A reliable design requires rational treatment of uncertainties. This paper addresses the need for application of partial factor design for safety and reliability assessment of lime-cement columns. The study was carried out on an example highway embankment of 6 m height. Resistance and load parameters were considered random variables. The sensitivity factors for the random variables were evaluated from the first order reliability method (FORM). Partial factors were evaluated for the random variables according to the approximate location of the design values. It was shown that the design by partial factor method fulfills both safety and reliability requirements.

Ground improvement by deep mixing (DM) is a generic term used for a number of methods in which a binding agent, often lime and/or cement, is mechanically mixed with the soil to increase its engineering properties. The inherent variability with respect to the engineering properties of the improved soil is high due to the variations in geology and the complex mixing process. High variability introduces uncertainty in estimating improved soil properties and the performance of the structure.

Current design methodology deals with soil properties deterministically and the uncertainties involved are incorporated in a single value represented by a total factor of safety (FS). The chosen FS is highly dependent on the engineer’s judgment and past experience, in which both of these factors vary between different geotechnical designers. Therefore, current design methodology used in practice for DM does not deal with uncertainties in a rational way. In order to design a geotechnical system with the desired level of confidence, the uncertainties involved must be integrated in the DM design. This can be achieved by using reliability-based design (RBD) methods.

The research work in this thesis is presented as a collection of three papers. In the first paper, a comprehensive statistical analysis of cone penetration test (CPT) data is described. The objective was to make a contribution to empirical knowledge by evaluating the strength variability of lime-cement columns within the group of tested columns. In the second paper, the effect of the spatial variability and statistical uncertainty with regard to the embankment’s reliability was investigated within the framework of RBD. The study in the third paper investigated the strength variability in lime-cement columns based on two test methods, namely CPT and column penetration test (KPS). In this study, the effect of different test methods on the evaluation of the design value was addressed.

The main conclusions from this study can be summarized as follows. First, the probability distribution function (PDF) for the undrained shear strength of lime-cement columns can be modeled in RBD as normal or log-normal distributions. However, the use of log-normal distribution is recommended for RBD analyses. Second, the evaluated scales of fluctuation indicate ranges of 2 to 4 m and 0.2 to 0.8 m in the horizontal and the vertical directions respectively. This means that in order to fulfill the requirements of independent/uncorrelated samples for assessment of the design value, the spacing between samples must exceed the horizontal scale of fluctuation. It is therefore proposed that the spacing between individual samples should be at least 4 meters. Third, the design values evaluated using CPT and KPS were approximately the same. However, the inherent variability evaluated differs due to the larger volume tested with the KPS probe than with the CPT probe. However, this difference was not significant between the two tests. Fourthly, due to the limitation in the deterministic design in terms of dealing with uncertainties, it is recommended that RBD design should be used in parallel with the deterministic design of lime-cement column.

Spatial variability with respect to the strength in lime-cement columns is an unavoidable source of uncertainty that should be considered in design. Current design method for the assessment of embankment stability, based on the deterministic factor of safety, cannot address the effect of spatial variability. Reliability-based design methodology is a powerful tool that can be used to integrate the variability into the analysis. In this paper, the spatial variability with respect to the undrained shear strength in the soil and in the columns was evaluated based on CPT test. The first order second moment (FOSM) reliability method was applied to address the impact of the spatial variability of the strength in the soil and in the columns on the reliability of an embankment founded on improved soil by lime-cement columns. The paper also presents a technique to evaluate the variance reduction factor over the failure surface. The results propose that the undrained shear strength in the soil and in the columns can be modelled following normal or lognormal distribution. The analysed example show that the reliability increased significantly when the spatial variability was considered

Natural and improved soils have relatively high inherent property variability that should be taken into consideration in design. Investigations of the spatial variability in lime-cement columns are important since they provide a rational quantification of the variability parameters needed for a reliability-based design analysis of geotechnical systems. Statistical analyses are used to evaluate the spatial variability parameters, i.e. the mean, the variance, and the scale of fluctuation, which is the distance within which soil properties reveal strong correlation. This paper presents a field test, in which 30 CPT soundings were performed and analyzed statistically in order to address the spatial variability in a group of lime-cement columns, with respect to the cone tip resistance. The objective of this paper is to describe the statistical analyses and to make a contribution to the empirical knowledge about strength variability in a volume of lime-cement columns. Stationarity has been assessed, and the scale of fluctuation has been evaluated in the vertical and horizontal directions. Random field theory was used based on the sample autocorrelation function ACF. The scale of fluctuation was found to be within the range of 0.2-0.7 m and 2-3 m in the vertical and horizontal direction, respectively. A simple design consideration shows that the variance reduction factor has a major influence on the determination of the design value.

This master thesis presents results from a laboratory study on a clay from Enköping which was stabilized with lime and clay. Isotropic consolidated undrained compressive tests were performed on samples and compared to unconfined compressive testing.

The two methods have shown no difference in the evaluation of undrained shear strength. However the modulus of elasticity was shown to be much higher for the triaxial tests. For the unconfined compressive tests the relation between the undrained shear strength and secant modulus was within the range of 44-146. The equivalent for the triaxial tests was in the interval of 112-333. However no pattern was extinguishable between the two tests as this relation has varied between 1,0 to 3,5.

A lower and higher back pressure was used during the triaxial testing. However, both back pressures have succeeded in saturating the sample. Results show that the back pressure has little effect on the results, as long as the sample has been fully saturated.

In addition to this extension tests were performed on samples as well. The tests performed were isotropic consolidated undrained. However two different shearing methods were used. The first test was strain rate dependant while the second test was stress rate dependant. In the first test the vertical stress decreased while the radial stresses were kept constant, while in the other test the radial stresses increased while the vertical stress were kept constant.

The undrained shear strength was compared to lime/cement column penetration tests in field. Results showed that tests in field show a much higher undrained shear strength than laboratory testing.

The geological disposal of nuclear waste, in underground openings and the long-term performance of these openings demand a detailed understanding of fundamental rock mechanics. A full scale field experiment: Äspö Pillar Stability Experiment was conducted at a depth of 450 m in sparsely fractured granitic rock to examine the rock mass response between two deposition holes. An oval shaped tunnel was excavated parallel to the σ3 direction to provide access to the experiment and also provide elevated stress magnitudes in the floor. In the tunnel floor two 1.75-m diameter 6-m deep boreholes were excavated so that a 1-m thick pillar was created between them. In one of the holes a confinement pressure of 700 kPa was applied and in the other displacement transducers were installed. The pillar volume was monitored by an Acoustic Emission System. Spatially distributed thermocouples were used to monitor the temperature development as the pillar was heated by electrical heaters. The excavation-induced stress together with the thermal-induced stress was sufficient to cause the wall of the open borehole to yield. The temperature-induced stress was increased slowly to enable detailed studies of the rock mass yielding process. Once the rock mass loading response was observed, the rock mass was unloaded using a de-stress slotting technique.

This thesis focuses on the in-situ study of the rock mass response to coupled mechanical thermal loading and thermal-mechanical unloading. The experiment, its design, monitoring and observations are thoroughly described. An estimate of the yielding strength of the rock mass is presented and compared with laboratory test and results from other rock mass conditions reported elsewhere in the open literature. General conclusions about the effect of the confining pressure and the observations from the unloading of the pillar are also presented.

Important findings are that the yielding strength of the rock mass has been successfully determined, low confinement pressures significantly affects the onset of yielding, the primary mode of fracture initiation and propagation is extensional, no significant time dependency of the yielding process was observed. The unloading studies also indicated that what appeared to be shear bands likely was a propagating zone of extensile failure that weakened the rock so that displacements in the shear direction could occur.

A 1-m-thick pillar was subject to coupled excavation- and thermal-induced stresses to induce brittle rock mass yielding. The yielding strength of the heterogeneous and fractured rock mass consisting of Aspo diorite was evaluated at eighteen discrete locations using data from the displacement, acoustic emission, and thermal monitoring systems. The average rock mass yielding strength was determined to be 0.59 of the uniaxial compressive strength. The onset of dilation in uniaxial laboratory tests, determined from strain gauge data, was found to occur at approximately 0.45 of the uniaxial compressive strength. It was shown that that the onset of acoustic emission events in situ also occurred when the tangential stress exceeded 0.43 of the uniaxial compressive strength. For sites with absence of in situ data it is recommended that this lower-bound value determined from laboratory data may be used for assessing the in situ rock mass yielding strength. Visual observation and displacement monitoring showed that extent of rock mass yielding is sensitive to small changes in the tangential stress magnitudes. It was determined using three-dimensional modelling that changes in the tangential stress magnitude of approximately 1 MPa was sufficient to cause yielding of the pillar to propagate in what appeared to be intact rock. Observations suggest that without this small stress change yielding of the rock mass would not occur. In other words, there appeared to be a well defined boundary, and if the stresses reached this boundary yielding was observed. However, if stresses were only slightly below this boundary yielding or time-dependant processes were not observed over the monitoring period used in the experiment.

Byggbranschen kantas idag av förseningar och fördyringar av projekt där flera studier har undersökt vad problematiken grundar sig i. Tidigare studier pekar mot att det beror på bland annat otydliga förfrågningsunderlag, bristfällig riskhantering och tolkningsproblem. När det kommer till marken och geotekniken kantas de av stora osäkerheter där riskhanteringen och riskidentifiering blir ännu viktigare då variationen i marken måste beaktas. Rapport för geotekniska bedömningsgrunder (eng. Geotechnical Baseline Report) är ett kontraktsdokument som ursprungligen utvecklats i USA vars syfte är att skapa en bas för prissättningen av risker och fördela riskägandet av oförutsedda markförhållanden mellan parterna. Meningen är att bedömningsgrunderna ska ge en gemensam syn på vilka förhållanden anbudsgivaren ska beakta och även hjälpa till med regleringen under projektets gång. Detta examensarbete har undersökt hur bedömningsgrunderna skulle kunnat tillämpas på den svenska marknaden och hur de hade kunnat avhjälpa de problem tidigare studier har identifierat. Detta har gjorts genom att titta på hur de geotekniska bedömningsgrunderna skulle kunna utformas genom exemplet föroreningar för bostads- och lokalprojekt. Examensarbetet börjar med en litteraturstudie och övergår sedan i en fallstudie som ger ett exempel på hur föroreningar hade kunnat hanteras i kontrakt med de geotekniska bedömningsgrunderna i totalentreprenader inom bostads- och lokalprojekt. Slutsatsen är att de geotekniska bedömningsgrunderna är tillämpbara på grundläggning inom hus- och lokalprojekt för att hantera föroreningar. Det skulle kunna hjälpa branschen att få tydligare förfrågningsunderlag, gemensam syn på förhållandena och snabbare samt tydligare reglering under projekten.

Foundation work can cause damage to adjacent buildings and infrastructure. Drilling is performed in sensitive areas in urban projects and where the ground conditions are difficult. It is important to be aware of the installation effects from drilling. Pneumatic drilling is commonly used in production but hydraulic drilling is advised in sensitive areas. Hydraulic drilling is believed to cause less disturbance in the ground, although there are no available field studies regarding the installation effects induced by water driven drilling.By measuring the pore water pressure and the settlements during the installation of a RD-pile wall the magnitude and extent of the installation effects induced by water powered DTH drilling is investigated in fill material and esker material. The results indicate settlements close to the installed piles in both materials, larger in the esker material. The pore pressure shows both increases and decreases in the esker material, the decreases implies the Venturi effect is present in water driven drilling. The pore water pressure changes are larger at the measurement point furthest away from drilling in the fill material but the settlements are the smallest there. The largest increases of the pore pressure are seen when the hammer flushes water out into the formation and not during drilling.

This master thesis is a study of risk assessment tools and other risk management

documentation created by consultants and contractors in the US and Sweden for

underground construction projects. Risk management as part of managing

underground projects is common practice in both countries for underground

construction projects. Depending on location and other parameters other types of risks

than the geological ones need to be considered, for example of the settings of the

project is an urban environment or if it is situated in a less densely populated area.

Normally underground project also involves large investments and therefore

managing cost is important. Risk management is a way of managing cost and other

areas that may be of concern.

The main goals of this thesis are to:

Identify a theoretical general approach to risk management and specifically risk

assessments based on a literature study

Identify similarities between risk management practices in the two countries

Identify differences between risk management practices in the two countries

Identify how risk management practices differ in the two countries from the

theoretical approach established from the literature study

Apart from the study of theoretical literature 12 projects in total were studied; 5

Swedish projects and 7 projects from the USA. The conclusions of this thesis are

generally not statistically significant nor do they indicate trends; they are purely

observation on the specific documentation studied.

When comparing application in Sweden vs. application in the USA; main conclusions

are:

It is recognized that practices within risk management are generally the same in

the two countries as established when studying theoretical literature on the

subject. However categorization of risk parameters is normally less detailed in

both countries’ project specific documentation than found in theoretical

literature.

The US risk management as a rule includes a numerical simulation to determine

contingency levels for cost and schedule high ranked risks but the simulations

were not done in the Swedish project specific documents. However it must be

remembered that the US-projects studied were provided from one soul provider

and is not in any way significant for this country but for the particular provider

studied.

Evaluating the risk registers of the projects studied there seem to be more

concern for damages to third party in the US as compared to in Sweden. Also

right-of-way, insurance and financial issues are of higher concern in the US

projects studied as compared to the Swedish projects studied.

The projects in Sweden put a slightly higher emphasis on space availability for

construction than in the US projects.

For more detailed findings; please read on!

In this paper column penetration tests for lime-cement columns in deep soil mixing are reviewed. In principle, column penetration tests and reversed column penetration tests are considered. Improved test techniques are presented and discussed based on tests from two test sites in Sweden. The investigations indicate that the reversed column penetration test is the most suitable method for the primary quality test with reference to the uniformity and continuity of the columns. The probe should, however, be installed by the lime-cement column machine short after the manufacturing of the column to avoid disturbances in the mixing process and to enable a random test selection.

Block stability analysis around a large excavation is analyzed with both Probabilistic Kinematics Limit Equilibrium (PKLE) and Discrete Fracture Network-Distinct Element Method (DFNDEM) approaches. Different combination of geometric parameters of fracture sets are selected in PKLE method and a series of numerical DEM modeling are performed on generated and validated DFN models in DFN-DEM approach to measure volume of potential unstable blocks and also minimum required support patterns. The mean volume of unstable blocks for PKLE with limited joint length assumption is fairly close to DFN models and they are far from mean value of PKLE when the joint length is extended infinitely. The minimum required support pattern for PKLE is smaller than DEM models which means that the PKLE design tool is underestimated compared with DFN-DEM method which benefits more realistic conceptual model and facilitates more sophisticate simulation tool.

This thesis presents a discussion of design tools for analysing block stability around a tunnel. First, it was determined that joint length and field stress have a significant influence on estimating block stability. The results of calculations using methods based on kinematic limit equilibrium (KLE) were compared with the results of filtered DFN-DEM, which are closer to reality. The comparison shows that none of the KLE approaches– conventional, limited joint length, limited joint length with stress and probabilistic KLE – could provide results similar to DFN-DEM. This is due to KLE’s unrealistic assumptions in estimating either volume or clamping forces.

A simple mechanism for estimating clamping forces such as continuum mechanics or the solution proposed by Crawford-Bray leads to an overestimation of clamping forces, and thus unsafe design. The results of such approaches were compared to those of DEM, and it was determined that these simple mechanisms ignore a key stage of relaxation of clamping forces due to joint existence. The amount of relaxation is a function of many parameters, such as stiffness of the joint and surrounding rock, the joint friction angle and the block half-apical angle.

Based on a conceptual model, the key stage was considered in a new analytical solution for symmetric blocks, and the amount of joint relaxation was quantified. The results of the new analytical solution compared to those of DEM and the model uncertainty of the new solution were quantified.

Further numerical investigations based on local and regional stress models were performed to study initial clamping forces. Numerical analyses reveal that local stresses, which are a product of regional stress and joint stiffness, govern block stability. Models with a block assembly show that the clamping forces in a block assembly are equal to the clamping forces in a regional stress model. Therefore, considering a single block in massive rock results in lower clamping forces and thus safer design compared to a block assembly in the same condition of in-situ stress and properties.

Furthermore, a sensitivity analysis was conducted to determine which is  the most important parameter by assessing sensitivity factors and studying the applicability of the partial coefficient method for designing block stability.

It was determined that the governing parameter is the dispersion of the half-apical angle. For a dip angle with a high dispersion, partial factors become very large and the design value for clamping forces is close to zero. This suggests that in cases with a high dispersion of the half-apical angle, the clamping forces could be ignored in a stability analysis, unlike in cases with a lower dispersion. The costs of gathering more information about the joint dip angle could be compared to the costs of overdesign. The use of partial factors is uncertain, at least without dividing the problem into sub-classes. The application of partial factors is possible in some circumstances but not always, and a FORM analysis is preferable.

Block failure is one of the most common failure modes in tunnels. Design tools have some simplifications and, therefore, they also have some model uncertainties. The purpose of this licentiate thesis is to assess the model uncertainty for different design tools in order to estimate block stability.

Different approaches of kinematic limit equilibrium (KLE) including conventional KLE, limited joint length, limited joint length and stress field consideration and probabilistic KLE were compared to that of DFN-DEM. In this approach, the results of the calibrated DFN-DEM with field mapping were considered to be of true value. The results show that the conventional KLE is overdesign due to it’s over simplification. By considering fracture length and stress field, the volume of predicted unstable blocks is reduced. The probabilistic approach of KLE by considering finite joint length and stress field predicts the volume of unstable blocks to be lower than DFN-DEM approach. Therefore there is a great model uncertainty of our standard design tools for block stability analysis.

The assumption made in this study is that the results from DEM were considered to have a true value; the results from analytical solution based on joint relaxation process were compared to those of DEM in a different condition of depth, K0, apical and friction angle, Kn and Ks value, and ratio of Kn/Ks. The comparison shows that for shallow depth with K0 less than 1, analytical solution leads to an overestimation of block stability. The analytical solution predicts that the block is stable, while the analyses from numerical solution show the block is unstable. The analyses show that by increasing K0, accuracy of analytical solution also increases. Moreover, for the cases with close value of friction angle to semi-apical angle, the use of analytical solution is not recommended. As the ratio of Kn/Ks increases, the accuracy of analytical solution decreases. Increasing the angle ratio (ratio between semi-apical angle to friction angle) is one source of increasing uncertainty in the model. The analytical solution is very uncertain in cases with a low value of K0, and a high value of stiffness ratio and angle ratio. On the other hand, the analytical solution is more certain in conditions with a high value of K0 and a low value of stiffness ratio and angle ratio. According to current information (K0, angle ratio, stiffness ratio), one can determine the value of model uncertainty by using the diagrams presented in Chapter 6 of the thesis. The analyses show that by having more information about the key parameters, the model uncertainty could be identified more precisely. However, having more information means spending more money, and this increase in cost must be compared to the cost of failure or delay in the project or overdesign.