Probabilistic Analysis of Pressurized Tunnels against Face Stability Using Collocation-Based Stochastic Response Surface Method

Mollon, Guilhem; Dias, Daniel; Soubra, Abdul‐Hamid

doi:10.1061/(asce)gt.1943-5606.0000443

Cited by 106 publications

(69 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…CSRSM involves the propagation of the uncertainties of the input parameters through a computational model to arrive at a random output (Isukapalli et al 1998, Huang et al 2009, Li et al 2011, Mollon et al 2011, Houmadi et al 2012, Mao et al 2012. Thus, this method allows one to determine the PDF of the system response by taking into account the uncertainties of the input parameters via their PDFs.…”

Section: Review Of the Csrsmmentioning

confidence: 99%

“…It should be remembered here that in CSRSM, the PCE coefficients are determined by using the values of the system response calculated at several collocation points. Although the roots of the one-dimensional Hermite polynomials are generally used for the determination of the collocation points (Isukapalli et al 1998, Huang et al 2009, Li et al 2011, Mollon et al 2011, this technique is not mandatory. In this article, the combination between SS approach and CSRSM is carried out by using the realisations calculated by SS approach as collocation points to construct the PCE in CSRSM.…”

Section: Extension Of the Ss Approachmentioning

confidence: 99%

“…In the present study, the PCE-based Sobol indices are used (e.g. Sudret 2008, Mollon et al 2011. It should be emphasised here that the computation of the PCEbased Sobol indices does not require any additional call of the deterministic model.…”

Section: Extension Of the Ss Approachmentioning

confidence: 99%

“…Sudret 2008, Mollon et al 2011. The computation of the Sobol indices is important since it provides the contribution of each random variable to the variability of the system response.…”

mentioning

confidence: 99%

“…The multivariate Hermite polynomials are given in Mollon et al (2011), among others. The size P of the PCE is given by:…”

mentioning

confidence: 99%

See 4 more Smart Citations

Extension of subset simulation approach for uncertainty propagation and global sensitivity analysis

Ahmed

Soubra

2012

Georisk: Assessment and Management of Risk for Engineered Syste

Self Cite

View full text Add to dashboard Cite

The subset simulation (SS) method is a probabilistic approach which is devoted to efficiently calculating a small failure probability. Contrary to Monte Carlo Simulation (MCS) methodology which is very time-expensive when evaluating a small failure probability, the SS method has the advantage of assessing the small failure probability in a much shorter time. However, this approach does not provide any information about the probability density function (PDF) of the system response. In addition, it does not provide any information about the contribution of each input uncertain parameter in the variability of this response. Finally, the SS approach cannot be used to calculate the partial safety factors which are generally obtained from a reliability analysis. To overcome these shortcomings, the SS approach is combined herein with the Collocation-based Stochastic Response Surface Method (CSRSM) to compute these outputs. This combination is carried out by using the different values of the system response obtained by the SS approach for the determination of the unknown coefficients of the polynomial chaos expansion in CSRSM. An example problem that involves the computation of the ultimate bearing capacity of a strip footing is presented to demonstrate the efficiency of the proposed procedure. The validation of the present method is performed by comparison with MCS methodology applied on the original deterministic model. Finally, a probabilistic parametric study is presented and discussed.

show abstract

Section: Review Of the Csrsmmentioning

confidence: 99%

Section: Extension Of the Ss Approachmentioning

confidence: 99%

Section: Extension Of the Ss Approachmentioning

confidence: 99%

“…Sudret 2008, Mollon et al 2011. The computation of the Sobol indices is important since it provides the contribution of each random variable to the variability of the system response.…”

mentioning

confidence: 99%

“…The multivariate Hermite polynomials are given in Mollon et al (2011), among others. The size P of the PCE is given by:…”

mentioning

confidence: 99%

See 3 more Smart Citations

Extension of subset simulation approach for uncertainty propagation and global sensitivity analysis

Ahmed

Soubra

2012

Georisk: Assessment and Management of Risk for Engineered Syste

Self Cite

View full text Add to dashboard Cite

show abstract

Bearing capacity of strip footings on spatially random soils using sparse polynomial chaos expansion

Al-Bittar

Soubra

2012

Num Anal Meth Geomechanics

Self Cite

View full text Add to dashboard Cite

. Bearing capacity of strip footings on spatially random soils using sparse polynomial chaos expansion. International Journal for Numerical and Analytical Methods in Geomechanics, Wiley, 2013Wiley, , 37 (13), pp.2039Wiley, -2060Wiley, . 10.1002Wiley, /nag.2120 Bearing capacity of strip footings on spatially random soils using sparse polynomial chaos expansion A probabilistic model is presented to compute the probability density function (PDF) of the ultimate bearing capacity of a strip footing resting on a spatially varying soil. The soil cohesion and friction angle were considered as two anisotropic cross-correlated non-Gaussian random fields. The deterministic model was based on numerical simulations. An efficient uncertainty propagation methodology that makes use of a non-intrusive approach to build up a sparse polynomial chaos expansion for the system response was employed. The probabilistic numerical results were presented in the case of a weightless soil. Sobol indices have shown that the variability of the ultimate bearing capacity is mainly due to the soil cohesion. An increase in the coefficient of variation of a soil parameter (c or ') increases its Sobol index, this increase being more significant for the friction angle. The negative correlation between the soil shear strength parameters decreases the response variability. The variability of the ultimate bearing capacity increases with the increase in the coefficients of variation of the random fields, the increase being more significant for the cohesion parameter. The decrease in the autocorrelation distances may lead to a smaller variability of the ultimate bearing capacity. Finally, the probabilistic mean value of the ultimate bearing capacity presents a minimum. This minimum is obtained in the isotropic case when the autocorrelation distance is nearly equal to the footing breadth. However, for the anisotropic case, this minimum is obtained at a given value of the ratio between the horizontal and vertical autocorrelation distances.

show abstract

Pseudo‐static analysis of tunnel face stability using the generalized Hoek–Brown strength criterion

Saada

Maghous

Garnier

2013

Num Anal Meth Geomechanics

View full text Add to dashboard Cite

International audienceThe stability of a tunnel face driven by a pressurized shield is investigated in the light of a limit analysis kinematic approach formulated in the context of the modified Hoek-Brown strength criterion. The analysis focuses on evaluating the destabilizing effects induced by seismic loading. The pseudo-static approach is adopted to account for the effects of inertial forces developed in the rock mass by the passage of seismic waves. Taking advantage of the ability to compute analytically, the expressions of the support functions for the modified Hoek-Brown strength criterion, rigorous limit analysis solutions can be derived semi-analytically for the tunnel face stability. Particular emphasis is given to the description of the Horn failure mechanism and associated lower bound estimates of the limit face supporting pressure. The approach is then applied to investigate the influence of some relevant strength and loading parameters in the tunnel face stability. © 2013 John Wiley and Sons, Ltd

show abstract

Probabilistic Analysis of Pressurized Tunnels against Face Stability Using Collocation-Based Stochastic Response Surface Method

Cited by 106 publications

References 18 publications

Extension of subset simulation approach for uncertainty propagation and global sensitivity analysis

Extension of subset simulation approach for uncertainty propagation and global sensitivity analysis

Bearing capacity of strip footings on spatially random soils using sparse polynomial chaos expansion

Pseudo‐static analysis of tunnel face stability using the generalized Hoek–Brown strength criterion

Contact Info

Product

Resources

About