Nearest Linear Failure Surface, a New Method to Determine the Reliability of Numerical Models in Geomechanics | |
| روش های تحلیلی و عددی در مهندسی معدن | |
| مقاله 4، دوره 14، شماره 41، دی 1403، صفحه 33-42 اصل مقاله (1.1 M) | |
| نوع مقاله: مقاله پژوهشی | |
| شناسه دیجیتال (DOI): 10.22034/anm.2024.18529.1643 | |
| نویسنده | |
| Yousef Mirzaeian Lardkeyvan* | |
| Dept. of Mining and Metallurgy Engineering, Yazd University, Yazd, Iran | |
| چکیده | |
| In geomechanical systems, reliability analysis aims to determine the failure probability according to the uncertainties existing in rock mass properties and support materials, as well as diagnosing the significance of each uncertainty. Although there are very diverse methods to determine the reliability of geomechanical models, the employment of precise methods for determining the reliability of a numerical model is practically impossible due to computational difficulties. The only general solution to solve the reliability problem is to use Monte Carlo simulation. However, for most systems, with engineering accuracy, thousands of realizations are required to use Monte Carlo simulation. Although this number of realizations for analytical functions can be performed very quickly, running this number of realizations for a numerical code is practically impossible. In the proposed Nearest Linear Failure Surface method (NLFS), with the least number of runs, the reliability of rock space and its failure probability is investigated during a short period of time and with appropriate accuracy. The idea of the NLFS method is inspired by finding the design point (β-point in the well-known First Order Reliability Method) assuming that the performance function is linear. In this research, a computer code has been developed to implement the NLFS method and by combining this code with FLAC 2D software, reliability of an underground road tunnel with uncertain cohesion, friction angle, and tensile strength of surrounding rock was determined. The results indicate the high efficiency of the proposed method in determining the reliability of numerical models in a very short time and with high accuracy. | |
| کلیدواژهها | |
| Reliability analysis؛ Numerical models؛ Nearest Linear Failure Surface؛ Geomechanical stability؛ First Order Reliability Method (FORM)؛ Monte-Carlo simulation | |
| عنوان مقاله [English] | |
| Nearest Linear Failure Surface, a New Method to Determine the Reliability of Numerical Models in Geomechanics | |
| نویسندگان [English] | |
| Yousef Mirzaeian Lardkeyvan | |
| Dept. of Mining and Metallurgy Engineering, Yazd University, Yazd, Iran | |
| چکیده [English] | |
| In geomechanical systems, reliability analysis aims to determine the failure probability according to the uncertainties existing in rock mass properties and support materials, as well as diagnosing the significance of each uncertainty. Although there are very diverse methods to determine the reliability of geomechanical models, the employment of precise methods for determining the reliability of a numerical model is practically impossible due to computational difficulties. The only general solution to solve the reliability problem is to use Monte Carlo simulation. However, for most systems, with engineering accuracy, thousands of realizations are required to use Monte Carlo simulation. Although this number of realizations for analytical functions can be performed very quickly, running this number of realizations for a numerical code is practically impossible. In the proposed Nearest Linear Failure Surface method (NLFS), with the least number of runs, the reliability of rock space and its failure probability is investigated during a short period of time and with appropriate accuracy. The idea of the NLFS method is inspired by finding the design point (β-point in the well-known First Order Reliability Method) assuming that the performance function is linear. In this research, a computer code has been developed to implement the NLFS method and by combining this code with FLAC 2D software, reliability of an underground road tunnel with uncertain cohesion, friction angle, and tensile strength of surrounding rock was determined. The results indicate the high efficiency of the proposed method in determining the reliability of numerical models in a very short time and with high accuracy. | |
| کلیدواژهها [English] | |
| Reliability analysis, Numerical models, Nearest Linear Failure Surface, Geomechanical stability, First Order Reliability Method (FORM), Monte-Carlo simulation | |
| مراجع | |
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[1] E. Hoek and A. Karakas, “Practical rock engineering,” Environmental and Engineering Geoscience, vol. 14, no. 1, pp. 55–58, 2008.
[2] Q. Lü and B. K. Low, “Probabilistic analysis of underground rock excavations using response surface method and SORM,” Computers and Geotechnics, vol. 38, no. 8, pp. 1008–1021, 2011.
[3] Mollon, G., Dias, D., & Soubra, A. H. (2009). Probabilistic analysis of circular tunnels in homogeneous soil using response surface methodology. Journal of geotechnical and geoenvironmental engineering, 135(9), 1314-1325.
[4] G. Mollon, D. Dias, and A. H. Soubra, “Probabilistic analysis of the face stability of circular tunnels,” in Contemporary Topics in In Situ Testing, Analysis, and Reliability of Foundations (GSP 186), 2009, pp. 348–355.
[5] H.-Z. Li and B. K. Low, “Reliability analysis of circular tunnel under hydrostatic stress field,” Computers and Geotechnics, vol. 37, no. 1, pp. 50–58, Mar. 2010.
[6] Y. Mirzaeian, K. Shahriar, and M. Sharifzadeh, “Tunnel Probabilistic Structural Analysis Using the FORM,” Journal of Geological Research, vol. 2015, p. 9, 2015.
[7] F. Hasheminasab, R. Bagherpour, A. Baghbanan, and M. Monjezi, “First-Order-Second-Moment Analysis of Reliability in Predicting the Rate of Penetration (in persian),” Analytical and numerical methods in mining engineering, vol. 7, no. 14, pp. 13–21, 2018.
[8] A. N. Gharahasanloo, R. Khalokakaie, M. Ataei, and M. Mokhberdoran, “Mining Spare Parts Provision by Reliability Analysis, Case Study: Sungun Copper Mine (in persian),” Analytical and numerical methods in mining engineering, vol. 8, no. 15, pp. 25–38, 2018.
[9] W. Liu, E. J. Chen, E. Yao, Y. Wang, and Y. Chen, “Reliability analysis of face stability for tunnel excavation in a dependent system,” Reliability Engineering and System Safety, vol. 206, p. 107306, Feb. 2021.
[10] Z. Zhang, J. Ji, X. Guo, and S. H. Goh, “Inverse reliability analysis and design for tunnel face stability considering soil spatial variability,” Journal of Rock Mechanics and Geotechnical Engineering, vol. 16, no. 5, pp. 1552–1564, 2024.
[11] K. You, Y. Park, and J. S. Lee, “Risk analysis for determination of a tunnel support pattern,” Tunnelling and Underground Space Technology, vol. 20, no. 5, pp. 479–486, 2005.
[12] T. D. Wiles, “Reliability of numerical modelling predictions,” International Journal of Rock Mechanics and Mining Sciences, vol. 43, no. 3, pp. 454–472, 2006.
[13] D. V Griffiths, G. A. Fenton, and C. B. Lemons, “Probabilistic analysis of underground pillar stability,” International Journal for Numerical and Analytical Methods in Geomechanics, vol. 26, no. 8, pp. 775–791, 2002.
[14] D. Youssef Abdel Massih and A. Soubra, “Reliability-Based Analysis of Strip Footings Using Response Surface Methodology,” International Journal of Geomechanics, vol. 8, no. 2, pp. 134–143, 2008.
[15] A. M. Hasofer and N. C. Lind, “An exact and invariant first order reliability format,” Journal of Engineering Mechanics Division, vol. 100, no. 1, pp. 111–121, 1974.
[16] R. Rackwitz, “Reliability analysis-a review and some perspectives,” Structural Safety, vol. 23, no. 4, pp. 365–395, 2001.
[17] M. L. Shooman, Probabilistic Reliability: An Engineering Approach. McGraw-Hill (New York) , 1968.
[18] Phoon, K. K. (Ed.). (2008). Reliability-based design in geotechnical engineering: computations and applications. CRC Press.
[19] C. B. Do, “The multivariate Gaussian distribution.” Section Notes, Lecture on Machine Learning, CS, 229, 2008.
[20] Rubinstein, R. Y., & Kroese, D. P. (2016). Simulation and the Monte Carlo method. John Wiley & Sons.
[21] R. H. Byrd, M. E. Hribar, and J. Nocedal, “An Interior Point Algorithm for Large-Scale Nonlinear Programming,” SIAM Journal on Optimization, vol. 9, no. 4, pp. 877–900, 1999.
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