Probabilistic Analysis of Circular Tunnels in Homogeneous Soil Using Response Surface Methodology (original) (raw)

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.

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.

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.

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.

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.

The stability of shallow circular tunnels in soil considering variations in cohesion with depth

Tunnelling and Underground Space Technology, 2015

This paper presents an upper bound investigation of the three dimensional stability of a tunnel face in a deposit of soil whose strength varies with depth. The upper bound theorem of limit analysis incorporating the linear variation of the soil cohesion with depth was used to calculate the pressure at the tunnel face of a closed face excavation. For an open face excavation, the factor of safety against the tunnel face instability was calculated using the strength reduction technique and the upper bound theorem. The results, in terms of the minimum required face pressure, were then compared with other solutions available from the literature for verification, and the numerical results in the form of dimensionless design charts are also presented. In addition, a comparative study between the simplified approaches adopting a singular soil cohesion parameter representing the whole layer instead of considering its actual variation with depth is presented. It was concluded that adopting the mean soil cohesion that does not vary with depth would lead to a conservative design, that is, a higher minimum face pressure being required during construction and a lower factor of safety against face instability. However, adopting the local cohesion obtained from the tunnel face may result in underestimating the required face pressure and may lead to an unsafe design.

Stability of a circular tunnel in cohesive-frictional soil subjected to surcharge loading

Computers and Geotechnics, 2011

The stability of circular tunnels in cohesive-frictional soils subjected to surcharge loading has been investigated theoretically and numerically assuming plane strain conditions. Despite the importance of this problem, previous research on the subject is very limited. At present, no generally accepted design or analysis method is available to evaluate the stability of tunnels/openings in cohesive-frictional soils. In this study, continuous loading is applied to the ground surface, and both smooth and rough interface conditions are modelled. For a series of tunnel diameter-to-depth ratios and material properties, rigorous lower-and upper-bound solutions for the ultimate surcharge loading are obtained by applying finite element limit analysis techniques. For practical use, the results are presented in the form of dimensionless stability charts with the actual tunnel stability numbers being closely bracketed from above and below. As an additional check on the solutions, upper-bound rigid-block mechanisms have been developed and the predicted collapse loads from these are compared with those from finite element limit analysis. Finally, an expression that approximates the ultimate surcharge load has been devised which is convenient for use by practising engineers.

Site Specific Seismic Performance of Circular Tunnels in Dry Sand

Lecture Notes in Civil Engineering, 2019

Past earthquakes revealed that underground tunnel structures are exposed to seismic risk and their seismic vulnerability is mainly function of the tunnel structure technology, the soil-tunnel interaction developing during the seismic shaking and the intensity of the seismic event. Each of these factors plays an important role in terms of the probability of damage and loss of functionality due to the tunnel deformations induced by increments in internal forces. Currently, the fragility curves are among the most widespread methods for the rapid assessment of structural performance at different hazard levels, giving the probability of reaching a defined damage level with respect to a given level of seismic motion. In the present work, a recently developed approach to evaluate the seismic risk has been applied to circular tunnels, whereby the main focus is the expression of the failure annual rate through the convolution of the fragility of the system under investigation and the seismic...

BEM-FORM Model for the Probabilistic Response of Circular Tunnels in Elastic Media

KSCE Journal of Civil Engineering, 2020

Problems involving cavities or excavations are widely addressed in geomechanics, in both analytical and numerical approaches. The boundary element method (BEM) is well-known as an interesting choice for half plane problems, providing accurate results at a low computational cost. This work deals with the probabilistic analysis of circular tunnels embedded in elastic media, coupling a BEM formulation to a structural reliability model. The gravitational loading and material parameters are treated as random variables, whose statistical description is taken from the literature. The loadings considered include the vertical overburden stress and the lateral earth pressure. Regarding the reliability evaluation, first order reliability method (FORM) and Monte Carlo simulation technique are employed, being compared in terms of accuracy. Regarding the BEM model, the Multiple Reciprocity Method (MRM) is used in the evaluation of domain integrals, and the subregion technique is employed for the analysis of the tunnel lining. Some analyses are presented, in order to validate the coupled BEM-FORM model and apply it to the estimation of failure probability, evaluating the influence of the random variables taken into account in the probabilistic response. Structural reliability Boundary element method Half-plane problem Multiple reciprocity method FORM