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In geotechnical engineering, and in the particular case of underground works, a great number of uncertainties arise due to the lack of knowledge of the involved formations and their variability. Geomechanical parameters are one of the main issues in the underground works design. In the initial stages, the available information about the rock masses characteristics is scarce. As the project advances to other stages more and more information from different sources becomes available and can be used for updating the geomechanical model. Bayesian methodologies use probability as the main tool to deal with uncertainty and manage to reduce it using new data via the Bayes theorem. In this work, a part of a developed Bayesian framework to the updating of the deformability modulus (E) in an underground structure is presented. Assuming E as a random variable, data from LFJ tests is used to obtain a posterior and less uncertain distribution of E. This approach led to good results and considerable uncertainty reduction and increased reliability. The developed Bayesian framework constitutes a rational and structured way of dealing with data with different sources and uncertainty levels.
2008
The collection of geomechanical information is a complex and dynamic process. As new information is available, the geotechnical model can be updated. However, this is not a straightforward process since the information sources may have different characteristics and reliability levels. This is a process based on judgment and experience. It lacks a systematic and mathematically valid process to deal with this problem and use new information to update the model parameters in order to reduce uncertainties. In this paper, it is intended to provide a contribution on this subject. A generic Bayesian framework for the updating of geomechanical parameters is presented. Emphasis is given to the theoretical aspects of uncertainty and to the Bayesian formulation. This framework is applied to the case of the deformability modulus updating in an underground structure. The prior distribution of the parameter was obtained through de application of analytical solutions based on the empirical classification systems. This distribution was then updated using the framework together with the results of a high quality in situ test. The Bayesian framework showed to be a mathematically valid way to deal with the problem of the geomechanical parameters updating and mostly in the uncertainty reduction related to the parameter real value.
International Journal of Rock Mechanics and Mining Sciences, 2009
A generic framework for the updating geomechanical parameters is presented. It is based on Bayesian probabilities, and considers several levels of uncertainty. It allows one to properly update the probability distribution function of a given parameter when new data are available. This framework is applied to the case of deformability modulus updating in a large underground structure. Two different approaches were tested in terms of initial knowledge about the parameter, namely no knowledge, and a prior distribution of the parameter based on geological/geotechnical data and application of analytical solutions based on the empirical classification systems. The updating was carried out using the framework together with the results of high quality in situ tests. The Bayesian framework was shown to be a mathematically valid way to deal with the problem of the geomechanical parameter updating and of uncertainty reduction related to the parameter's real value.
Journal of Rock Mechanics and Geotechnical Engineering, 2020
Deformation modulus of rock mass is one of the input parameters to most rock engineering designs and constructions. The field tests for determination of deformation modulus are cumbersome, expensive and time-consuming. This has prompted the development of various regression equations to estimate deformation modulus from results of rock mass classifications, with rock mass rating (RMR) being one of the frequently used classifications. The regression equations are of different types ranging from linear to nonlinear functions like power and exponential. Bayesian method has recently been developed to incorporate regression equations into a Bayesian framework to provide better estimates of geotechnical properties. The question of whether Bayesian method improves the estimation of geotechnical properties in all circumstances remains open. Therefore, a comparative study was conducted to assess the performances of regression and Bayesian methods when they are used to characterize deformation modulus from the same set of RMR data obtained from two project sites. The study also investigated the performance of different types of regression equations in estimation of the deformation modulus. Statistics, probability distributions and prediction indicators were used to assess the performances of regression and Bayesian methods and different types of regression equations. It was found that power and exponential types of regression equations provide a better estimate than linear regression equations. In addition, it was discovered that the ability of the Bayesian method to provide better estimates of deformation modulus than regression method depends on the quality and quantity of input data as well as the type of the regression equation.
Rock Mechanics and Rock Engineering, 2011
In tunnelling, a reliable geological model often allows providing an effective design and facing the construction phase without unpleasant surprises. A geological model can be considered reliable when it is a valid support to correctly foresee the rock mass behaviour, therefore preventing unexpected events during the excavation. The higher the model reliability, the lower the probability of unforeseen rock mass behaviour. Unfortunately, owing to different reasons, geological models are affected by uncertainties and a fully reliable knowledge of the rock mass is, in most cases, impossible. Therefore, estimating to which degree a geological model is reliable, becomes a primary requirement in order to save time and money and to adopt the appropriate construction strategy. The definition of the geological model reliability is often achieved by engineering geologists through an unstructured analytical process and variable criteria. This paper focusses on geological models for projects of linear underground structures and represents an effort to analyse and include in a conceptual framework the factors influencing such models. An empirical parametric procedure is then developed with the aim of obtaining an index called ''geological model rating (GMR)'', which can be used to provide a more standardised definition of a geological model reliability.
ASCE Geo-Institute Geotechnical Special Publication 229 - Foundation Engineering in the Face of Uncertainty: Honoring Fred H. Kulhawy, pp. 254-270. Geo-Congress 2013, 2013
The geotechnical risk of a tunnel is strongly dependent on ground properties and on the construction techniques and rate of advance. In urban environment, design is often determined by serviceability limit states of adjacent structures and, to a lesser extent, of the tunnel itself. The observational method (OM) is an effective risk management tool in geotechnical engineering and particularly in tunnel construction. It helps on deciding in the presence of uncertainty in ground conditions. A fundamental prerequisite for its application is that only epistemic uncertainties are present, so that uncertainty reduction of the relevant parameters may be achieved by monitoring. Deterministic models are often used, limiting the versatility and significance of the OM. In this paper conceptual considerations about the implications of ground uncertainty with due account of spatial correlation are presented. A combined computational framework for random finite difference models based on MATLAB and FLAC and is introduced. A case study of a tunnel in stiff clayey ground is presented to evaluate the relative importance of the magnitude, type of variability and spatial correlation of both deformability and shear resistance parameters. A simulated application of the OM is presented with a comparative analysis of the decisions in an OM approach.
Uncertainty is a fact of life in geotechnical and geoenvironmental engineering practice. Nature in its complexity offers soil profiles often very different from those assumed in analysis and design; loads and environmental conditions likewise defy accurate prediction; and limited sampling, measurement errors and shortcomings of analysis procedures further complicate the engineer's task. Probabilistic methods, complementing conventional analyses, provide the means for quantifying and communicating degrees of uncertainty, evaluating data acquisition strategies, and assessing hazard mitigation measures. The methods range from probabilistic site characterization, which involves quantifying the variability and heterogeneity of stratigraphy and material properties, to risk-based decision analysis, which provides a framework for identifying the kinds and degrees of risk involved in a project, and the consequences should "failure" occur, and evaluating the effectiveness of alternative actions (in site exploration, design, construction, or monitoring) aimed at controlling or reducing risks. These lecture notes for the Workshop on Probabilistic Methods in Geotechnical Engineering present basic concepts of probabilistic modeling, along with many examples of how they can be used to deal with uncertainties inherent in site characterization and geotechnical performance prediction, safety assessment and monitoring. The notes progress through increasingly complex methodology, starting with the basics of event and fault trees, through single and multiple random variables, to fundamentals of random fields and geostatistics. Among the applications considered: rock slope maintenance, clay barrier containment, proof testing of piles, and predicting differential settlement.
Acta Polytechnica, 2008
The behaviour of a geomechanical model and its final results are strongly affected by the input parameters. As the inherent variability of rock mass is difficult to model, engineers are frequently forced to face the question “Which input values should be used for analyses?” The correct answer to such a question requires a probabilistic approach, considering the uncertainty of site investigations and variation in the ground. This paper describes the statistical analysis of input parameters for FEM calculations of traffic tunnels in the city of Prague. At the beginning of the paper, the inaccuracy in the geotechnical modelling is discussed. In the following part the Fuzzy techniques are summarized, including information about an application of the Fuzzy arithmetic on the shotcrete parameters. The next part of the paper is focused on the stochastic simulation – Monte Carlo Simulation is briefly described, Latin Hypercubes method is described more in details. At the end several practica...
Common questions asked during the process of mine design are "how much geotechnical information is required for an acceptable design" and "how to measure its confidence". These are key aspects associated not only with the determination of parameters but more generally with the definition of the geotechnical model for design.
2014
The creation of underground mine excavation disturbs the original state of the rock mass surrounding the excavation which often leads to instability of the excavation. This poses a threat to the safety of personnel and equipment in and around such excavations. Therefore the stability of underground mine excavations has always been a major concern to geotechnical engineers. The stability of the excavations depends on physical and mechanical properties of the rock masses as well as the in situ stress condition. For stability analyses, these parameters are determined either by in situ investigations or laboratory tests. Because of the inherent uncertainties associated with natural materials such as rock masses, the precise values of the properties are never known. The sources of these uncertainties could be inherent variability caused by random process (aleatory uncertainty) or it could be a knowledge-based uncertainty (epistemic uncertainty) such as measurement error or model transfor...
2004
° Viale Marconi. 5, I 24044 Dalmine (BG), ITALY, Tel. +39-035-2052339; Fax. +39-035-562779 Il Dipartimento ottempera agli obblighi previsti dall'art. 1 del DLL 31.8.1945, n. 660 e successive modificazioni. ... Series Economics and Management (EM): Stefano Paleari, Andrea ...
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ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering
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Tunnelling and Underground Space Technology, 2013
Journal of Materials in Civil Engineering, 2007
International Journal for Numerical and Analytical Methods in Geomechanics, 1996
Natural Hazards and Earth System Science, 2008