BEM-FORM Model for the Probabilistic Response of Circular Tunnels in Elastic Media (original) (raw)

Probabilistic Analysis of Circular Tunnels in Homogeneous Soil Using Response Surface Methodology

Journal of Geotechnical and Geoenvironmental Engineering, 2009

A probabilistic analysis of a shallow circular tunnel driven by a pressurized shield in a frictional and/or cohesive soil is presented. Both the ultimate limit state ͑ULS͒ and serviceability limit state ͑SLS͒ are considered in the analysis. Two deterministic models based on numerical simulations are used. The first one computes the tunnel collapse pressure and the second one calculates the maximal settlement due to the applied face pressure. The response surface methodology is utilized for the assessment of the Hasofer-Lind reliability index for both limit states. Only the soil shear strength parameters are considered as random variables while studying the ULS. However, for the SLS, both the shear strength parameters and Young's modulus of the soil are considered as random variables. For ULS, the assumption of uncorrelated variables was found conservative in comparison to the one of negatively correlated parameters. For both ULS and SLS, the assumption of nonnormal distribution for the random variables has almost no effect on the reliability index for the practical range of values of the applied pressure. Finally, it was found that the system reliability depends on both limit states. Notice however that the contribution of ULS to the system reliability was not significant. Thus, SLS can be used alone for the assessment of the tunnel reliability.

Probability of failure determination for tunnels in rock by using Monte Carlo simulation

Convergence-confinement method can be used to analyze rock support systems in interaction with rock mass in order to select the appropriate supports system for tunnels in rock. This method enables calculation of the charge applied to the support system and the factor of safety for the tunnel supports. The factor of safety calculated from traditional deterministic analysis methods cannot fully represent tunnel stability. There are many uncertainties in parameters used to calculate the factor of safety, and these uncertainties are not integrated in a deterministic analysis, but can be taken into account using a reliability analysis. Reliability analyses, used to calculate probability of failure for tunnel support system, is a complement of the factor of safety calculated by using deterministic analyses. In this paper, Monte Carlo Simulation is used to calculate probability of failure for tunnel support system.

A Two-Step Approach for Reliability Assessment of a Tunnel in Soft Soil

3 rd International Conference on Computational Methods in Tunnelling and Subsurface Engineering Ruhr University Bochum, 17-19 April 2013

We assess the reliability of a tunnel in Keuper marl with uncertain mechanical properties. The tunnel is constructed by the conventional tunneling method. The limit state function is expressed in terms of a two-dimensional finite element model of the tunnel. Plain strain finite elements are used to represent the soil and the yield surface is modeled with a hardening plasticity soil model. The three-dimensional arching effect is approximated by application of the stress reduction method. In a first step, the reliability analysis is performed by application of the first order reliability method (FORM) and the results are verified by importance sampling. The FORM provides information on the sensitivity of the reliability in terms of the uncertain variables. This information is used in a second step to account for the inherent spatial variability of the ground parameters with the largest influence through a random field modeling. The discretization of the random field leads to a large number of random variables. Therefore, we apply the subset simulation method, which is an adaptive Monte Carlo method known to be especially efficient for such high dimensional problems. The analysis is performed using a reliability tool that is integrated into the SOFiSTiK finite element software package.

Reliability Analysis for Tunnel Supports System by Using Finite Element Method

Reliability analysis is a method that can be used in almost any geotechnical engineering problem. Using this method requires the knowledge of parameter uncertainties, which can be expressed by their standard deviation value. By performing reliability analysis to tunnel supports design, can be obtained a range of safety factors and by using them, probability of failure can be calculated. Problem becomes more complex when this analysis is performed for numerical methods, such as Finite Element Method. This paper gives a solution to how reliability analysis can be performed to design tunnel supports, by using Point Estimate Method to calculate reliability index. As a case study, is chosen one of the energy tunnels at Fan Hydropower plant, in Rrëshen Albania. As results, values of factor of safety and probability of failure are calculated. Also some suggestions using reliability analysis with numerical methods are given.

Probabilistic Analysis and Design of Circular Tunnels against Face Stability

International Journal of Geomechanics, 2009

This paper presents a reliability-based approach for the three-dimensional analysis and design of the face stability of a shallow circular tunnel driven by a pressurized shield. Both the collapse and the blow-out failure modes of the ultimate limit state are studied. The deterministic models are based on the upper-bound method of the limit analysis theory. The collapse failure mode was found to give the most critical deterministic results against face stability and was adopted for the probabilistic analysis and design. The random variables used are the soil shear strength parameters. The Hasofer-Lind reliability index and the failure probability were determined. A sensitivity analysis was also performed. It was shown that ͑1͒ the assumption of negative correlation between the soil shear strength parameters gives a greater reliability of the tunnel face stability with respect to the one of uncorrelated variables; ͑2͒ FORM approximation gives accurate results of the failure probability; and ͑3͒ the failure probability is much more influenced by the coefficient of variation of the angle of internal friction than that of the cohesion. Finally, a reliability-based design is performed to determine the required tunnel pressure for a target collapse failure probability.

Reliability analysis of tunnel final lining

Tunnel final linings are usually designed according to the methods and safety levels required by the Eurocodes. These codes are mainly applicable in conventional structures, where variability of the permanent loads is mainly due to the uncertainty of unit weights. On the contrary, the loads on the final lining of tunnels result from the interaction of the surrounding rock mass with the temporary support and the final lining. Therefore, they are subjected to much larger uncertainty as the geotechnical properties of the rock mass and the calculation model of the structural interaction both involve appreciable uncertainty. This paper investigates the variation of final lining loads using Monte Carlo simulation for the variability of the rock mass geotechnical parameters. The analyses show that the coefficient of variation of the loads is 20% - 50%, appreciably larger than the usually assumed typical value of 10% corresponding to the self weight and other permanent loads. As a result, reinforced concrete tunnel lining sections designed according to the partial factors of the Eurocodes have appreciably larger probability of failure than conventional reinforced concrete structures. The paper finally calculates the required modification of the partial factors for tunnel linings to achieve different reliability levels (e.g. the same reliability level with the conventional structures).

Reliability analysis of unreinforced tunnel final lining

The permanent loads of final lining mainly come from the surrounding geomaterial. These loads have large variation, due to the uncertainties of the geotechnical conditions, the calculation methods and the complex interaction of geomaterial - temporary support - final lining. Yet, in structural design, final lining is analyzed using the same partial factors with “conventional” structures, the permanent loads of which have smaller variation. This paper uses the Point Estimation Method combined with 3D numerical analyses to study the variation of tunnel loads due to the inherent uncertainties of geotechnical parameters and calculation methods for a specific combination of “average geotechnical parameters”. The results show that the variation of the geotechnical conditions alters not only the values, but also the distribution of the loads and the coefficient of variation of the tunnel loads (Vp) lies in the lower part of the range proposed in [5]. However, the numerical analyses tend to underestimate the load variation, due to the paradoxical behaviour observed in case of rigid support and small excavation step [3]. In the second part of the paper, reliability analyses are carried out for unreinforced concrete sections showing that the critical parameters for the achieved reliability level of the design are the value of Vp, the correlation between the axial force and bending moments and the average load eccentricity.

Probabilistic analysis of the face stability of circular tunnels

2009

This paper presents a reliability-based approach for the threedimensional analysis of the face stability of a shallow circular tunnel driven by a pressurized shield. Only the collapse failure mode of the ultimate limit state is studied. The deterministic model is based on the upper-bound method of the limit analysis theory. The random variables used are the soil shear strength parameters. The Hasofer-Lind reliability index and the failure probability were determined. A sensitivity analysis was also performed. It was shown that (i) the assumption of negative correlation between the soil shear strength parameters gives a greater reliability of the tunnel face against collapse, with respect to the hypothesis of uncorrelated variables, (ii) the failure probability is much more influenced by the coefficient of variation of the angle of internal friction than that of the cohesion and (iii) when no correlation between shear strength parameters is considered, a more spread out CDF of the tunnel pressure was obtained in comparison to the case of correlated shear strength parameters.

Probabilistic Analysis of Tunnel Liners

Advances in Computational Methods for Simulation

The use of probabilistic methods to analyse reliabiliy of structures is being applied to a variety of engineering problems due to the possibility of establishing the failure probability on rational grounds. In this paper we present the application ofclassical reliability theory to analyse the safety of underground tunnels.

UNCERTAINTY MODELLING AND LIMIT STATE RELIABILITY OF TUNNEL SUPPORTS UNDER SEISMIC EFFECTS

IJRET.ORG, 2012

Underground openings and excavations are increasingly being used for civilian and strategic purposes all over the world. Recent earthquakes and resulting damage have brought into focus and raised the awareness for aseismic design and construction. In addition, underground tunnels, particularly, have distinct seismic behavior due to their complete enclosure in soil or rock and their significant length. Therefore, seismic response of tunnel support systems warrant closer attention. The geological settings in which they are placed are often difficult to describe due to limited site investigation data and vast spatial variability. Therefore, the parameters which govern the design are many and their variabilities cannot be ignored. A solution to this issue is reliability based analysis and design. These real conditions of variability can only be addressed through a reliability based design. The problem addressed here is one of reliability-based analysis of the support system of an underground tunnel in soil. Issues like the description of the interaction between the tunnel lining and the surrounding medium, the type of limit state that would be appropriate, the nonavailability of a closed form performance function and the advantages of response surface method [RSM] are looked into. Both static and seismic environment with random variability in the material properties are studied here. Support seismic response is studied in terms of thrust, moment and shear forces in the lining. Interactive analysis using finite element method [FEM], combined with RSM and Hasofer-Lind reliability concept to assess the performance of the tunnel support, has proven useful under real field situations.