The partial factor method is the most common approach to verify structural safety in Eurocode 7. Given the ongoing discussion on the European level to include also underground excavations in rock in the scope of the Eurocodes, there is a clear need to investigate the applicability of partial factors to the design of rock tunnels. However, implementing fixed partial factors, in accordance with the suggestion in the current Eurocode 7, may not be appropriate to account for the large uncertainties and variable conditions prevalent in rock engineering. This paper studies the critical characteristics and underlying assumptions of different reliability-based partial factor formats. The suitability of the analyzed partial factor formats to evaluate safety is analysed and discussed with reference to a design example of a rock-shotcrete interaction system for support against block failure in an underground opening. The results show that reliability-based partial factor methods outperform the traditional partial safety format suggested in the Eurocode in terms of accuracy and consistency.

The effective shear strength is a critical parameter for evaluating ultimate and serviceability limit states of geotechnical structures. To conduct a fully probabilistic assessment or to determine characteristic values according to the second generation of Eurocodes, it is essential to quantify the uncertainty of ground properties due to inherent variability, measurement error, transformation, and statistical uncertainty. However, unlike other ground properties, shear strength parameters are not directly measured, even in laboratory settings. Instead, they are derived from the relationship between shear and normal stresses, making uncertainty analysis nontrivial. This study applies two regression approaches and the extended multivariate approach (EMA) to estimate the effective friction angle for non-cohesive soils. Firstly, an ordinary least squares (OLS) and a Bayesian linear regression (BLR) approach are utilized to quantify the uncertainties inherent in data from direct shear and tri-axial tests from an offshore wind project. Secondly, the EMA is utilized to integrate cone penetration tests (CPT) and shear test data via Bayesian inference. The results are discussed based on characteristic values according to Eurocode 7 (EN 1997-1:2024) highlighting the importance of accurately and precisely estimating mean and uncertainty.

Budget overrun and schedule delay of infrastructure projects result in mismanagement of huge amounts of resources. Studies show that accounting for uncertainties in time and cost estimation of such projects can help the decision-makers in better understanding the involved risks. Several probabilistic models have been developed during the last two decades to facilitate such estimations. A common aspect of all these models is the subjective assessment of unit activities’ duration, which affects the accuracy of the estimated time and cost significantly. Despite this, the mechanism governing the variability of unit activities’ duration has seldom been studied. Thus, this paper focuses on addressing this gap by using a unique set of data from a tunnel project. The variability in unit activities’ duration (construction performance variability) is governed by three main components: typical performance variability, minor machinery delays, and minor performance delays. Using these components, a novel method for modeling construction performance variability in probabilistic time estimation of tunneling projects is proposed. The application of the proposed method is demonstrated through a case example with a discussion on its important aspects, advantages, and limitations. The findings of this paper offer a resource to improve the accuracy of time estimation for tunneling projects.

Budget overrun and schedule delay of infrastructure projects result in the mismanagement of huge amounts of resources. Studies show that accounting for uncertainties in time and cost estimation of such projects can help the decision-makers in better understanding the involved risks. Several probabilistic models have been developed during the last two decades to facilitate such estimations. A common aspect of all these models is the subjective assessment of unit activities' duration, which affects the accuracy of the estimated time and cost significantly. Despite this, the mechanism governing the variability of unit activities' duration has seldom been studied. Thus this paper focuses on addressing this gap by using a unique set of data from a tunnel project. The variability in unit activities' duration (construction performance variability) is governed by three main components: typical performance variability, minor machinery delays and minor performance delays. Using these components, a novel method for modelling construction performance variability in probabilistic time estimation of tunnelling projects is proposed. The application of the proposed method is demonstrated through a case example with a discussion on its important aspects, advantages and limitations. The findings of this paper offer a resource to improve the accuracy of time estimation for tunnelling projects.

Time and cost estimation of tunnelingprojects is usually performed in a deterministic manner.However, because the deterministic approach isnot capable of dealing with uncertainty, probabilisticmethods have been developed over the years to betteraccount for this problem. Three models of this typeare the Decision Aids for Tunneling (DAT) and twomodels developed at KTH Royal Institute of Technologyand the Czech Technical University in Prague.To conduct a probabilistic time and cost estimation,it is important to understand and account for not onlythe uncertain factors that affect the project time andcost but also the involved parties’ different interestsand contractual responsibilities. This paper developsa risk model for the specific purpose of time andcost estimation of tunneling projects. In light of thismodel, the practical application of the three probabilisticmodels is discussed from a risk-aware decisionmaker’sperspective. The acquired insights can behelpful in increasing the experts’ risk-awareness inmodeling time and cost of tunneling projects.

Considering that a large part of Sweden is covered by glacial till, which is classified as an unsorted sediment formed by glaciers that can contain fragments of rock known as boulders, driving piles constitutes a substantial economic risk. Piles driven into glacial till may encounter boulders and undergo structural damages leading to premature refusal and to the loss of piles. Even though geotechnical investigations as of today form a solid basis for the design of pile foundations, the unpredictable presence of boulders and their hard resistance to breakage, makes it challenging to penetrate boulders by standard investigation methods. Currently, the only available source of information used by the Swedish construction industry to confirm the existence of boulders is a dynamic penetration test known as soil–rock sounding. Relying on the results from only one testing method may for most projects underestimate the existence of boulders and their potential impact to piles, leading to an unsuitable design of the entire piling system. This paper discusses the benefit in using the input from soil–rock soundings for quantifying the probability of boulder encounters in glacial till based on Poisson point process.

To optimally design a geotechnical engineering structure, an iterative decision-making process is required due to the prevailing uncertainty of the ground conditions. At present, these decisions are taken based on simple deterministic rules and models. This paper proposes a risk-based decision-theoretic framework to the optimal planning for geotechnical construction. This framework combines geotechnical probabilistic models, cost analysis using Monte Carlo simulation and the observational method. The framework is illustrated on the design of the surcharge for an embankment on soft soil, whereby the optimal preloading sequence of added surcharge is adapted to the observed settlement. The approach balances the cost of surcharge material against financial penalties related to project delays and insufficient overconsolidation, which causes damage due to residual settlement. The result is a preloading strategy that optimally accounts for information obtained from settlement measurements under uncertain ground conditions. The findings highlight the potential of using risk-based decision planning in geotechnical engineering, in particular in combination with the observational method. For the investigated case-study, we observe a reduction in the expected cost in the order of 25%.

Transport infrastructure projects frequently encounter challenges such as schedule delays and cost overruns, leading to substantial misallocation of public or private resources. These issues are often exacerbated by uncertainties in time and cost estimation outcomes. To address this, various models have been developed in recent years to enable probabilistic estimation for tunneling projects, considering uncertainties. However, the impact of uncertainties on the critical path and its implications on time and cost estimations have not been discussed explicitly and in detail for network underground structures encompassing multiple construction paths. In this study, we update the KTH time and cost estimation model using the Markov Chain Monte Carlo (MCMC) method. This updated model enables simultaneous round-by-round construction simulation across all paths in network underground structures. Consequently, it accommodates uncertainty in the critical path and its influence on time estimation outcomes. Additionally, the updated model introduces an innovative technique to model geological uncertainties along tunnel routes, thereby contributing to the field's diversity. Practical application of the updated model is showcased using the Uri Hearace tunnel as an illustrative example. The paper also delves into the practical implications of the findings from a decision-maker's standpoint, as well as discussing the model's limitations.

EN 1990 defines structural reliability as the ability of a structure to fulfil the specified requirements during the service life for which it has been designed; the notion covers safety, serviceability and durability. According to this definition reliability is the concern of all parts of the whole suite of Eurocodes. In a more narrow sense of the word, reliability refers to the way uncertainties are dealt with in design and assessment by the use of partial factors or more advanced probabilistic methods. This document deals primarily with this more narrow definition, it describes both the probabilistic and semi-probabilistic approach and gives special attention to their underlying relationship.Chapter 2 should be considered as a general introduction to this report and introduces relevant basic notions such as uncertainty, probability, risk, member and system failure, time dependency, effects of deterioration and inspection, etc. In chapter 3 the focus is on the basic reliability requirements in EN 1990 related to the persistent as well as the accidental and seismic design situations. Some special attention is given to the new materials: glass, fibre reinforced polymers and membrane structures included in the second generation of the Eurocodes.In chapter 4 attention is given to the special problems that may arise in assessment of existing structures. Important is the treatment of several types of observations (inspections, monitoring, proof loads etc), the various decision options (further inspection, repair, demolishment) and of course typical reliability issues (updating, reduced targets). The explicit risk and full probability methods described in Chapter 5 are intended to support these approaches where allowed and meaningful. It also gives background for code calibrations.Annex A gives an overview of probabilistic models for actions, material properties and model uncertainties. It may be considered as a reflection of the present state of knowledge in the various Eurocode subcommittees, working groups and horizontal groups. Annex B shows a number of example applications related to various parts of the theory.

The transition to a fossil-free energy matrix may require large quantities of hydrogen gas, which could be stored efficiently in an underground lined rock cavern (LRC). Since the consequences of failure can be catastrophic, the LRC design needs to have a small probability of failure. However, the current design practice for LRCs is deterministic, which limits the possibility to stringently address geotechnical uncertainties in the design. In this paper, a reliability-based design tool is presented for LRCs. The adaptive directional importance sampling (ADIS) method, which requires a relatively small number of samples, is used with a 3D finite element (FE) model to evaluate small probabilities of failure. An illustrative example based on the LRC in Skallen, southwestern Sweden, demonstrates the implementation and applicability of the developed design tool. The considered uncertainties are related to the geological conditions and the steel lining. The results show that the reliability of this LRC design meets the expected safety requirements. Considering different geological conditions with correlations, at least “good” quality rock mass is needed for the LRC design. An additional sensitivity analysis is performed to study the potential influence of corrosion and hydrogen embrittlement on the reduction of the LRC design reliability.