Efficient Probabilistic Approach to Analyze Tunnel Support with Uncertain Probability Distribution Function of Input Parameters
Publication: International Journal of Geomechanics
Volume 24, Issue 12
Abstract
Due to the inherent random variations in the engineering properties of soils and rocks, considering probabilistic analysis rather than the deterministic one is a safer option for the design of geotechnical structures. However, the probabilistic methodologies often rely on prior knowledge of probability density function (PDF) of the considered random variables (RVs). In this study, a new formulation called the fourth-moment pseudo-normal transformation (FMNT) is employed to perform the probabilistic analysis of a tunnel support system. FMNT requires only the first four statistical moments of the random variables instead of complete information about their PDF to calculate the failure probability (Pf). Further, it is an efficient technique that is demonstrated by performing analytical as well as numerical probabilistic analysis of circular and noncircular tunnels using FLAC 3D. FMNT is used in two different ways to highlight its flexibility: (1) with the first-order reliability method (FORM) called FORM-based FMNT; and (2) with point estimated method (PEM) called PEM-based FMNT. The results of the latter align adequately with the results of Monte Carlo simulation (MCS) and the analysis requires only 21 and 26 simulations for four and five random variables, respectively, instead of 100,000 simulations required by the MCS. The compatibility of this framework in actual field settings is demonstrated through an exercise using the nonnormal random variables.
Practical Applications
Soil and rocks possess inherent variability. This makes it hard for engineers and scientists to predict exactly how they will behave under different situations. Therefore, they use probabilistic methods that deal with this uncertainty. One common method is called Monte Carlo simulation (MCS). It is good at handling uncertainties and giving accurate results and that is why it is commonly used as a benchmark method for comparisons. But to use it, we need to know some information about the input parameters such as their distribution. This information is generally not available when dealing with field data. To solve this, we need a method that gives us results comparable to MCS but is also efficient enough to use in the field. This study presents a new probabilistic technique named fourth-moment pseudo-normal transformation (FMNT) to do this job. It is useful and easy for assessing the safety of geotechnical structures that are demonstrated by conducting a probabilistic analysis of tunnels in the present study. This method will help the field engineers plan and deal with uncertainties in a better way.
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Data Availability Statement
Some or all data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.
1.
MATLAB code for determining the tunnel convergence using CCM method.
2.
MATLAB code to perform probabilistic analysis using the FMNT method.
Acknowledgments
This research has been supported by a Mission Mode Project of CSIR-Central Building Research Institute (CSIR-CBRI), Roorkee, India named “Geotechnical Novel Solutions for Underground Infrastructures” (MLP-062002).
Notation
The following symbols are used in this paper:
- a0
- radius of tunnel;
- c
- cohesion of rock mass;
- joint PDF;
- fZ(z)
- PDF of performance function;
- GMass
- shear modulus of the rock mass;
- performance function;
- G1(X)
- first performance function;
- G2(X)
- second performance function;
- Pf
- failure probability;
- pi
- internal support pressure;
- critical internal support pressure;
- Rpl
- plastic radius;
- ur
- radial deformation;
- Xs
- standardized RV;
- σ0
- far-field stresses; and
- ϕ
- angle of internal friction.
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Published In
International Journal of Geomechanics
Volume 24 • Issue 12 • December 2024
Copyright
© 2024 American Society of Civil Engineers.
History
Received: Nov 9, 2023
Accepted: May 22, 2024
Published online: Sep 20, 2024
Published in print: Dec 1, 2024
Discussion open until: Feb 20, 2025
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