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Reliability analysis of deep excavations by RS and MCS methods: case study

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Abstract

In recent years, uncertainty inherent in geotechnical properties has caught great attention of researchers and engineers; thus, reliability analyses and non-deterministic methods have been applied widely. This paper presents the reliability analysis of a case study on deep excavation in a cemented coarse-grained alluvium adopting random set (RS) and Monte Carlo simulation (MCS) methods to tackle the inherent uncertainty associated with soil properties. The horizontal displacement of the excavated wall and safety factor of stability were adopted as a basis for assessing the system response. Pertinent codes were written by employing RS and generating random numbers of probability distribution functions in FLAC2D finite difference program. Introducing RS code into the numerical analysis process drastically reduced the computational effort required for this method. It was found that in cases of deep excavations with low target probability of failure, RS presents satisfactory performance and thus is preferable to MCS, while MCS can be employed as a beneficial tool for stability analysis and some special cases of deformation analysis in excavation problems. The results are presented and compared in terms of sampling procedure, as well as statistical moments, probability of occurrence and most likely values at every stage of construction.

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References

  1. Chowdhury SS, Deb K, Sengupta A (2013) Estimation of design parameters for braced excavation: numerical study. Int J Geomech. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000207

    Google Scholar 

  2. Chowdhury SS, Deb K, Sengupta A (2016) Effect of fines on behavior of braced excavation in sand: experimental and numerical study. Int J Geomech. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000487

    Google Scholar 

  3. Huang X, Schweiger HF, Huang H (2013) Influence of deep excavations on nearby existing tunnels. Int J Geomech. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000188

    Google Scholar 

  4. Nogueira CL, Azevedo RF, Zornberg JG (2009) Coupled analyses of excavations in saturated soil. Int J Geomech. https://doi.org/10.1061/(ASCE)1532-3641(2009)9:2(73)

    Google Scholar 

  5. Babu GLS, Singh VP (2009) Reliability analysis of soil nail walls. Georisk 3(1):44–54

    Google Scholar 

  6. Chowdhury SS (2017) Reliability analysis of excavation induced basal heave. Geotech Geol Eng 35(6):2705–2714

    Google Scholar 

  7. Christian JT, Baecher GB (1999) Point-estimate method as numerical quadrature. J Geotech Geoenviron. https://doi.org/10.1061/(ASCE)1090-0241(1999)125:9(779)

    Google Scholar 

  8. Duncan JM (2000) Factors of safety and reliability in geotechnical engineering. J Geotech Geoenviron. https://doi.org/10.1061/(ASCE)1090-0241(2000)126:4(307)

    Google Scholar 

  9. Hoeg K, Muruka RP (1974) Probabilistic analysis and design of a retaining wall. J Geotech Eng Div ASCE 100(3):349–365

    Google Scholar 

  10. Tobutt DC (1982) Monte Carlo simulation methods for slope stability. Comput Geotech 8(2):199–208

    Google Scholar 

  11. Alkasawneh W, Malkawi AH, Nusairat JH, Albataineh NA (2008) Comparative study of various commercially available programs in slope stability analysis. J Comput Geotech 35(3):428–435

    Google Scholar 

  12. Low BK, Gilbert RB, Wright SG (1998) Slope reliability analysis using generalized method of slices. J Geotech Geoenviron Eng 124(4):350–362

    Google Scholar 

  13. Mahdiyar A, Hasanipanah M, Armaghani DJ (2017) A monte carlo technique in safety assessment of slope under seismic condition. Eng Comput 33(4):807–817

    Google Scholar 

  14. Malkawi AIH, Hassan WF, Abdulla FA (2000) Uncertainty and reliability analysis applied to slope stability. J Struct Saf 22(2):161–187

    Google Scholar 

  15. Ramly HE, Morgenstern NR, Cruden DM (2002) Probabilistic slope stability analysis for practice. Can Geotech J 39:665–683

    Google Scholar 

  16. Peschl GM, Schweiger HF (2003) Reliability analysis in geotechnics with finite elements-comparison of probabilistic, stochastic and fuzzy set methods. In: Proceedings of the 3rd international symposium on imprecise probabilities and their applications (ISIPTA ‘03), Lugano, Switzerland, pp 437–451

  17. Schweiger HF, Thurner R, Pöttler R (2001) Reliability analysis in geotechnics with deterministic finite elements: theoretical concepts and practical application. Int J Geomech. https://doi.org/10.1061/(ASCE)1532-3641(2001)1:4(389)

    Google Scholar 

  18. Schweiger HF, Peschl GM (2005) Reliability analysis in geotechnics with the random set finite element method. Comput Geotech 32(6):422–435

    Google Scholar 

  19. Schweiger HF, Peschl GM, Pöttler R (2007) Application of the random set finite element method for analysing tunnel excavation. Georisk Assess Manag Risk Eng Syst Geohazards 1(1):43–56

    Google Scholar 

  20. Tonon F, Bernardini A, Mammino A (2000) Determination of parameters range in rock engineering by means of random set theory. Reliab Eng Syst Saf 70(3):241–261

    Google Scholar 

  21. Tonon F, Bernardini A, Mammino A (2000) Reliability analysis of rock mass response by means of random set theory. Reliab Eng Syst Saf 70(3):263–282

    Google Scholar 

  22. Harr ME (1996) Reliability based design in civil engineering. Dover Publications, New York

    Google Scholar 

  23. Kulhway FH (1992) On the evaluation of static soil properties. In: Proceedings of a specialty ASCE conference on stability and performance of slopes and embankments-II, vol 1, Berkley, California, United States, pp 95–115

  24. Lee IK, White W, Ingles OG (1983) Geotechnical engineering. Pitman Publishing Ltd., Boston

    Google Scholar 

  25. Phoon K, Kulhawy FH (1999) Characterization of geotechnical variability. Can Geotech J 36(4):612–624

    Google Scholar 

  26. Rackwitz R (2000) Reviewing probabilistic soils modeling. Comput Geotech 26(3–4):199–223

    Google Scholar 

  27. Dubois D, Prade H (1991) Random sets and fuzzy interval analysis. Fuzzy Set Syst 42(1):87–101

    Google Scholar 

  28. Goodman IR, Nguyen HT (1985) Uncertainty models for knowledge-based systems; a unified approach to the measurement of uncertainty. North Holland Publications, Amsterdam

    Google Scholar 

  29. Kendall DG (1974) Foundations of a theory of random sets. In: Harding EF, Kendall DG (eds) Stochastic geometry. Wiley, New York

    Google Scholar 

  30. Matheron G (1975) Random sets and integral geometry. Wiley, New York

    Google Scholar 

  31. Peschl GM (2004) Reliability analyses in geotechnics with the random set finite element method. Dissertation, Graz University of Technology

  32. Tonon F, Mammino A, Bernardini A (1996) A random set approach to the uncertainties in rock engineering and tunnel lining design. In: Proceedings of ISRM international symposium on prediction and performance in rock mechanics and rock engineering (EUROCK ‘96), Torino, Italy, pp 861–868

  33. Rieben EH (1966) Geological observation on alluvial deposits in Northern Iran. Geol. Surv. and Min. Expl. of Iran: rep. no. 9

  34. Duncan JM, Byrne PM, Wong KS, Marby P (1980) Strength, stress-strain and bulk modulus parameters for finite element analysis of stresses and movements in soil mass: rep. no. UCB/GT/80-01, College of Engineering, Office of Research Services, University of California

  35. Seed RB, Duncan JM (1984) SSCOMP: a finite element analysis program for evaluation of soil structure interaction and compaction effects: report no. UCB/GT/84-02, Department of Civil Engineering, University of California, Berkeley

  36. Briaud JL, Lim Y (1999) Tieback walls in sand: numerical simulations and design implications. J Geotech Geoenviron. https://doi.org/10.1061/(ASCE)1090-0241(1999)125:2(101)

    Google Scholar 

  37. Ou CY, Chiou DC, Wu TS (1996) Three-dimensional finite element analysis of deep excavations. J Geotech Eng. https://doi.org/10.1061/(ASCE)0733-9410(1996)122:5(337)

    Google Scholar 

  38. Briaud JL, Lim Y (1997) Soil nailed wall under piled bridge abutment: simulation and guidelines. J Geotech Geoenviron Eng 23(11):1043–1050

    Google Scholar 

  39. Dunlop P, Duncan JM (1970) Development of failure around excavated slopes. J Soil Mech Found Div ASCE 96(2):471–493

    Google Scholar 

  40. Lim Y, Briaud JL (1996) Three dimensional nonlinear finite element analysis of tieback walls and of soil nailed walls under piled bridge abutment. Representatives to the Federal Highway Administration and the Texas Department of Transportation, Department of Civil Engineering, Texas A&M University, College Station, Tex

  41. Finno RJ, Blackburn JT, Roboski JF (2007) Three dimensional effects for supported excavations in clay. J Geotech Geoenviron. https://doi.org/10.1061/(ASCE)1090-0241(2007)133:1(30)

    Google Scholar 

  42. Alonso EE, Krizek RJ (1975) Stochastic formulation of soil profiles. In: Proceedings, international conference on applications of statistics and probability (ICASP2), Aachen, Germany, pp 9–32

  43. Cornell CA (1971) First-order uncertainty analysis of soils deformation and stability. In: Proceedings of the 1st international conference on applications of statistics and probability to soil and structural engineering (ICASP1), Hong Kong, China, pp 129–144

  44. Lumb P (1975) Spatial variability of soil properties. In: Proceedings of the 2nd international conference on the application of statistics and probability to soil and structural engineering (ICASP), Aachen, Germany, pp 397–422

  45. Vanmarcke EH (1977) Probabilistic modeling of soil profiles. J Geotech Eng Div (ASCE) 103(11):1227–1246

    Google Scholar 

  46. Vanmarcke EH (1983) Random fields: analysis and synthesis. MIT-Press, Cambridge

    Google Scholar 

  47. Griffiths DV, Fenton GA (2000) Influence of soil strength spatial variability on the stability of an undrained clay slope by finite elements. In: Geo-Denver 2000 conference on soil stability, Denver, Colorado, United States, pp 184–193

  48. Duncan JM, Chang CY (1970) Nonlinear analysis of stress and strain in soils. J Soil Mech Found Div (ASCE) 96(5):1629–1653

    Google Scholar 

  49. Janbu N (1963) Soil compressibility as determined by oedometer and triaxial tests. In: European conference on soil mechanics and foundation engineering (ECSMFE), Wiesbaden, Germany, vol 1, pp 19–25

  50. Li KS, White W (1987) Reliability index of slopes. In: Proceedings of 5th international conference on application of statistics and probability in soil and structural engineering, vol 2, Vancouver, Canada, pp 755–762

  51. U.S. EPA: TRIM (1999) Total risk integrated methodology, TRIM FATE technical support document volume I: description of module, EPA/43/D-99/002A, Office of Air Quality Planning and Standards

  52. FHWA (2015) Soil nail walls reference manual. U.S. Department of Transportation Federal Highway Administration, Washington

    Google Scholar 

  53. US Army Corps of Engineers (1997) Introduction to probability and reliability methods for use in geotechnical engineering: engineering technical letter no. 1110-2-547, US Army Publications, United States of America

  54. Broding WC, Diederich FW, Parker PS (1964) Structural optimization and design based on a reliability design criterion. J Spacecr 1(1):56–61

    Google Scholar 

  55. Carter JP, Desai CS, Potts DM, Schweiger HF, Sloan SW (2000) Computing and computer modeling in geotechnical engineering. In: Proceedings of geoengineering 2000, Melbourne, Australia, vol 1, pp 1157–1252

  56. Pukelsheim F (1994) The three sigma rule. Am Stat 48(2):88–91

    Google Scholar 

  57. Geoslope (2007) Stability modelling with SLOPE/W 2007 version: an engineering methodology. GEO-SLOPE International Ltd, Calgary

    Google Scholar 

  58. TASCA (2011) User’s manual FLAC2D: fast lagrangian analysis of continua: version 7.0. Itasca Consulting Group, Minneapolis

    Google Scholar 

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Authors and Affiliations

  1. Department of Civil Engineering, Babol Noshirvani University of Technology, Babol, Iran

    Arash Sekhavatian & Asskar Janalizadeh Choobbasti

Authors
  1. Arash Sekhavatian
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  2. Asskar Janalizadeh Choobbasti
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Correspondence to Asskar Janalizadeh Choobbasti.

Appendix

Appendix


Def standardnormal_rand

mean_ = 0

std_ = 1

standardnormal_rand = mean_ + grand*std_

end


Def logrand

standardnormal_rand

r = location + (standardnormal_rand)*scale

logrand = exp(r)

end


Def normalrand

mean_ = mean_

std_ = std_

normalrand = mean_ + grand*std_

end

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Sekhavatian, A., Janalizadeh Choobbasti, A. Reliability analysis of deep excavations by RS and MCS methods: case study. Innov. Infrastruct. Solut. 3, 60 (2018). https://doi.org/10.1007/s41062-018-0166-z

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