Tunnel static behavior assessed by a probabilistic approach to the back-analysis

Problem statement: The steps of the validation procedure of the project of a tunnel are briefly illustrated in this study, starting from the geological and structural surveys on the excavation walls and the measurement of the physical and mechanical parameters during the excavation works. Unfortunately, however, the knowledge of the rock mass, which is fundamental to the project, is usually approximate before the study is started. This knowledge improves considerably once construction of the tunnel is started, when it is possible to have direct access to the rock and analyze its behavior in relation to the excavation and support works. Approach: The measurement of displacements and stresses in the rock mass and in the support structures represents a different methodology for the evaluation of the Geotechnical characteristics of a rock mass and therefore also of the support work conditions. To correctly interpret the measurements it is necessary to make use of a more complex procedure, called back-analysis, that, starting from an estimation of the unknown parameters of the rock mass obtained through a preliminary characterization, integrated and modified by sampling of the rock mass during the construction stage and by the performed stress and displacement measurements, is able to define the unknown parameters of the rock mass. Results and Conclusion: Back-analysis in engineering in the rock field occurs, however, in an uncertainty context, which complicates the problem. The preliminary estimation of the Geotechnical characteristics of the rock mass has in fact a degree of reliability that is a function of the intensity of the preliminary investigations. The performed measurements present a certain precision in relation to the various typologies of error that can occur. The final result of the back-analysis therefore also consists in the definition of the Geotechnical parameters of the rock mass that are considered to be of influence in the problem under examination, with a certain reliability and precision that is obviously greater than that relative to the initial estimation of the same parameters. The purpose of this study is to present a global approach to back-analysis in a probabilistic context that is aimed to obtain a reliable calibration of the parameters of the rock mass that are necessary to study the behavior of the support structure

A probabilistic approach to evaluate the risk due to a fire in unidirectional road tunnels ventilated by jet fans

The risk produced by a fire is one of the most important aspects to be analysed for the safety of a road tunnel. In one-way ventilated tunnels with jet-fans it may happen that during a fire the fumes move in the opposite direction to that of the fresh air entering the tunnel. This phenomenon (back-layering) can involve people fleeing towards the mouth of the mountain with dramatic consequences. Since many parameters that characterize the phenomenon are known only with a certain approximation, it is necessary to adopt a probabilistic approach. In this work this approach is illustrated, applying it to a road tunnel in Northern Italy. The probability that the fumes of the fire can reach people fleeing has been plotted as a function of the total number of jet-fans in the tunnel, so that the definition of the ventilation system can be carried out in the design phase in relation to safety during the emergency phase

A simplified mathematical approach for the evaluation of the stabilizing forces applied by a passive cemented bolt to a sliding rock block

Passive bolting is used to stabilise unstable rock blocks in surface and underground structures due to the various advantages it offers. Despite its use, the design phase still presents aspects of considerable complexity because the fact that the load of the bolt and therefore, its static action depends on its interaction with the block and the stable rock. In the present work, a mathematical model was developed which is capable of directly calculating the stabilisation forces as a function of the characteristic parameters of the bolt and of its interaction with the rock. This discussion is based on a simplified hypothesis of bolt behaviour, which provides negligible errors, and on the observation that the critical point is positioned at the intersection of the bolt with one of the lateral surfaces that separate it from the portion of stable rock. The formulation of the stabilisation forces obtained made it possible to evaluate the static contribution of each single bolt to the stability of the rock block, by varying the diameter of the steel bar and then designing the bolting operation to achieve acceptable stability conditions for the rock block. The application of stabilising equations to a real case, for which the results of load tests on bolt tests were available, allowed us to outline steps to be taken in the bolt design process

A probabilistic approach for the evaluation of the stabilizing forces of fully grouted bolts

The essential task of the ground reinforcement techniques is to keep the rock as stable as possible. In particular passive rock bolt should resist the rock movements along its entire length and through the resulting reaction forces, to improve the load-bearing capacity of the rock. Among different calculation techniques, the calculations based on Block Reinforcement Procedure (BRP) was used in this paper, also adopting some simplified equations available in the scientific literature. However, parameters influencing the interaction are difficult to evaluate. Therefore, the problem of the reliable definition of the parameters that most influence the behavior of the bolts and the evaluation of the stabilizing forces of the potentially unstable block of rock remains. A new probabilistic approach is presented in this article, able to appropriately manage the uncertainties present on the fundamental parameters of the bolt-rock interaction and on the mechanical characteristics of the sliding surface of the block. Through the use of a Monte Carlo procedure, in fact, it was possible to obtain different samples of the safety factors of the rock block, one for each diameter of the steel bars used for its stabilization. Finally, the probabilistic management of the safety factor samples allowed the correct design of the steel bars, by evaluating the probability that the safety factor of the block with regard to potential slipping has a value lower than a pre-established limit. The probabilistic approach developed was applied to a real problem of stabilization of a potentially unstable rock block due to planar sliding, present on a municipal road in North Italy

On topological defect formation in the process of symmetry breaking phase transitions

By resorting to some results in quantum field theories with spontaneous breakdown of symmetry we show that an explanation based on microscopic dynamics can be given of the fact that topological defect formation is observed during the process of non-equilibrium phase transitions characterized by a non-zero order parameter. We show that the Nambu-Goldstone particle acquires an effective non-zero mass due to the boundary (finite volume) effects and this is related with the size of the defect. We also relate such volume effect with temperature effect.Comment: 12 pages, no figure

Convergence and frequency-domain analysis of a discrete first-order model reference adaptive controller

SUMMARY We study the convergence properties of a direct model reference adaptive control system by applying techniques from numerical analysis. In particular, a first-order discrete system coupled to a minimal control synthesis algorithm discretized by the one-step one-stage zero-order-hold sampling is studied. This results in a strongly non-linear dynamic system owing to the adaptive mechanism where stability at steady state, i.e. at the operating point, equates to successful control. This paper focuses on the convergence analysis of the overall dynamical system for understanding accuracy, stability and performance at steadystate. The local stability of the steady state solution is considered by linearizing the system in the neighbourhood of an operating point when the input is a step function. This analysis allows us to specify two gain space domains which define the region of local stability. Moreover, both the accuracy and the frequency-domain analyses give insight into the range of adaptive control weightings that results in optimal performance of the minimal control synthesis algorithm and also highlights a possible approach to a priori selection of the time step and adaptive weighting values. The effectiveness of the proposed analysis is further demonstrated by simulations and experiments on a first-order plant. Copyright # 2006 John Wiley & Sons, Ltd

The Buoyancy of the Tunnel Segmental Lining in the Surrounding Filling Material and its Effects on the Concrete Stress State

Segmental lining is subject to significant upward buoyancy forces when a grouting material (slurry), initially fluid, is adopted to fill the gap between its external profile and the wall of a tunnel excavated with a TBM machine. The analysis of the effects of these forces is important in order to correctly dimension the segmental lining and avoid damage to the lining and subsequent costly maintenance and restoration actions. Given the complexity of the behavior of a segmental lining consisting of segmental rings and circular joints that alternate in the longitudinal direction of the tunnel, a specific numerical model has been implemented, adopting the Finite Element Method (FEM). This model is able to obtain the development of the vertical displacements of the segmental lining starting from the TBM tail, together with the bending moments and the shear forces induced inside it. The developed model is able to assess the risks of breaking and damaging the concrete and steel bolts that are used to connect the segmental rings at the circular joints; therefore, it represents a useful design tool for being able to correctly dimension the segmental lining also in relation to the risks produced by the appearance of considerable buoyancy forces around it, due to the presence of the initially fluid filling material. The proposed numerical model was applied to a real case (Ningbo metro tunnel) and allowed to obtain satisfactory results from the comparison of the calculated displacements with in situ measurements. Some sensitivity analyzes developed on the studied case have made it possible to detect which are the influencing parameters that have the greatest impact on the behavior of segmental lining in the presence of the studied buoyancy forces

The important role of stiffnesses values of circular joints on the stress state developed in the tunnel segmental lining

Under the application of the fluctuating Tunnel Boring Machine (TBM) jack thrust and the non-uniformly distributed total pressure of the slurry around the lining, the bending and the shear deformation occur on the segmental lining along the longitudinal direction, which cause a stress concentration and increase the damage risk of the segmental tunnel lining. The analysis of the circular joint stiffness is a critical step during the evaluation of the stress state of the segmental lining so as to decrease the associated risk of damage. In order to investigate the lining rings and the circular joint separately, an integrated numerical model which is composed of segment elements and joint elements was developed. Furthermore, stiffness equations for describing in the detail the circular joint behaviour of the tunnel segmental lining are derived. The new stiffness equation of the circular joint is also used to analyse the segment lining behaviour based on a well-known indoor test result by the scientific literature, and satisfactory results were obtained. A simplified estimation of the bending stiffness of the circular joint based on the Boltzmann equation is then suggested in order to obtain quickly its calculation. Finally, based on a specific numerical model, the calculated joint stiffnesses are adopted to analyse the vertical displacement of a real case (The Ningbo metro tunnel in China). Through a developed sensitivity analysis, some useful suggestions are proposed to reduce the damage risk of the segmental lining

Reliability analysis of deep pressurized tunnels excavated in the rock mass with rheological behavior

Design of pressurized tunnels in rock masses which have a time -dependent behavior is a challenging task. On the one hand, time -dependent behavior not only imposes extra pressure to the tunnel lining but also leads the rock mass hydraulic conductivity to vary continuously; this aspect can exert another adding pressure to the lining. On the other hand, the uncertainty of the rock mass properties, which can differ from one point to another one, is another source of instability. Furthermore, the excavation method, i.e., poor blasting, which creates a weaker damaged zone around the tunnel, intensifies the complexity of the problem. This paper presents a probabilistic approach to investigate the influencing factors on the behavior of underwater tunnels. The behavior of the original and damaged rock masses is considered as visco-elastoplastic (using the CVISC model) in order to be able to consider its rheological character. Four parameters including Geological Strength Index (GSI), rock mass permeability, thickness of the damaged zone, and Kelvin shear modulus, which showed the most influencing effects in a developed sensitive analysis, were chosen as random variables. The Monte Carlo Method (MCM) was used to generate random values for these variables, adopting the normal distribution. Then, the response surface methodology (RSM) was used to intelligently lessen the number of generated values, and then to prepare datasets with the inclusion of all variables. The calculations were carried out for each provided dataset by a tridimensional numerical model (FLAC3D code) to obtain the tunnel wall displacement and the lining pressure, over time, as the results of the calculation. The RSM is again employed to obtain the relationships between inputs and output values and finally to have the probability function of the outputs. The results show that a right-skewed Gamma distribution governs the outputs: i.e. the distribution mass is concentrated on the left side of the probability distribution. Furthermore, when the water pressure is enhanced, the skewness of the probability distribution for the tunnel wall convergence and the lining pressure increases and decreases, respectively. Finally, it was possible to detect how the designing of pressurized tunnels using a deterministic approach, which adopts a unique value for the input parameters, may be misleading when the internal water pressures are high