Abstract
The design of high-rise buildings often necessitates ground excavation, where buildings are in close proximity to the construction, thus there is a potential for damage to these structures. This paper studies an efficient user-friendly framework for dealing with uncertainties in a deep excavation in layers of cemented coarse grained soil located in Tehran, Iran by non-deterministic Random Set (RS) method. In order to enhance the acceptability of the method among engineers, a pertinent code was written in FISH language of FLAC2D software which enables the designers to run all simulations simultaneously, without cumbersome procedure of changing input variables in every individual analysis. This could drastically decrease the computational effort and cost imposed to the project, which is of great importance especially to the owners. The results are presented in terms of probability of occurrence and most likely values of the horizontal displacement at top of the wall at every stage of construction. Moreover, a methodology for assessing the credibility of the uncertainty model is presented using a quality indicator. It was concluded that performing RS analysis before the beginning of every stage could cause great economical savings, while improving the safety of the project.
Similar content being viewed by others
References
Lacasse S, Nadim F. Uncertainties in characterizing soil properties. In: Shackelford C D, Nelson P P, Roth M J S, eds. Proceedings of Conference on Uncertainty in the Geologic Environment: From Theory to Practice (Uncertainty ‘96). American Society of Civil Engineers, 1996, 49–75
Griffiths D V, Fenton G A. Influence of soil strength spatial variability on the stability of an undrained clay slope by finite elements. Geo-Denver Conf. on Soil Stability, Denver, Colorado, United States, 2000, 184–193
Fenton G A, Griffiths D V. Bearing capacity of spatially random c–φ soils. In: Proceedings of the International Conference on Computer Methods and Advances in Geomechanics, Rotterdam, Balkema, 2001, 1411–1415
Ang A H S, Tang W H. Probability Concepts in Engineering Planning and Design: Volume I-Basic Principles. New York: Wiley & Sons, 1975
Harr M E. Reliability Based Design in Civil Engineering. New York: Dover publications, 1996
Haldar A, Mahadevan S. Probability, Reliability, and Statistical Methods in Engineering Design. New York: Wiley & Sons, 2000
Vu-Bac N, Lahmer T, Keitel H, Zhao J, Zhuang X, Rabczuk T. Stochastic predictions of bulk properties of amorphous polyethylene based on molecular dynamics simulations. Mechanics of Materials, 2014a, 68: 70–84
Vu-Bac N, Lahmer T, Zhang Y, Zhuang X, Rabczuk T. Stochastic predictions of interfacial characteristic of polymeric nanocomposites (PNCs). Composites. Part B, Engineering, 2014b, 59: 80–95
Vu-Bac N, Silani M, Lahmer T, Zhuang X, Rabczuk T. A unified framework for stochastic predictions of mechanical properties of polymeric nanocomposites. Computational Materials Science, 2015, 96: 520–535
Rackwitz R. Reviewing probabilistic soils modeling. Computers and Geotechnics, 2000, 26(3–4): 199–223
Phoon K, Kulhawy F H. Characterization of geotechnical variability. Canadian Geotechnical Journal, 1999, 36(4): 612–624
Duncan J M. Factors of safety and reliability in geotechnical engineering. Journal of Geotechnical and Geoenvironmental Engineering, 2000, 126(4): 307–316
Lee I K, White W, Ingles O G. Geotechnical Engineering. Boston: Pitman, 1983
Kulhway F H. On the evaluation of static soil properties. In: Proceedings of a Specialty ASCE Conference on Stability and Performance of Slopes and Embankments-II, Volume 1. Berkley, California, 1992, 95–115
Peschl G M, Schweiger H F. 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). Canada: Carleton Scientific, 2003, 437–451
Ben-Haim Y, Elishakoff I. Convex Models of Uncertainty in Applied Mechanics. Amsterdam: Elsevier, 1990
Oberguggenberger M, Fellin W. From probability to fuzzy sets: the struggle for meaning in geotechnical risk assessment. In: Proceedings of the International Conference on Probabilistics in Geotech-nics–Technical and Economical Risk Estimation, Essen: VGE, 2002, 29–38
Peschl G M. Reliability Analyses in Geotechnics with the Random Set Finite Element Method. Dissertation for PhD degree. Graz University of Technology, 2004
Dubois D, Prade H. Consonant approximation of belief functions. International Journal of Approximate Reasoning, 1990, 4(5–6): 419–449
Dubois D, Prade H. Random sets and fuzzy interval analysis. Fuzzy Sets and Systems, 1991, 42(1): 87–101
Walley P. Statistical Reasoning with Imprecise Probabilities. London: Chapman and Hall, 1991
Dempster A P. Upper and lower probabilities induced by a multivalued mapping. Annals of Mathematical Statistics, 1967, 38(2): 325–339
Shafer G. A Mathematical Theory of Evidence. Princeton: Princeton University Press, 1976
Tonon F, Bernardini A, Mammino A. Determination of parameters range in rock engineering by means of Random Ret Theory. Reliability Engineering & System Safety, 2000, 70(3): 241–261
Dong W, Shah H C. Vertex method for computing functions of fuzzy variables. Fuzzy Sets and Systems, 1987, 24(1): 65–78
Cornell C A. First-order uncertainty analysis of soils deformation and stability. In: Proceedings of the International Conference on Applications of Statistics and Probability (ICASP1), 1971, 129–144
Alonso E E, Krizek R J. Stochastic formulation of soil profiles. In: Proceedings of the International Conference on Applications of Statistics and Probability (ICASP2). Aachen, Germany, 1975, 9–32
Lumb P. 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, 1975, 397–421
Vanmarcke E H. Probabilistic modeling of soil profiles. Journal of the Geotechnical Engineering Division, ASCE, 1977, 103: 1227–1246
Vanmarcke E H. Random Fields–Analysis and Synthesis. Cambridge, MA: MIT-Press, 1983
Itasca. FLAC2D (Fast Lagrangian Analysis of Continua) version 7.0 user’s manual. Minneapolis, MN, USA: Itasca Consulting Group, 2011
Christian J T, Ladd C C, Baecher G B. Reliability applied to slope stability analysis. Journal of Geotechnical Engineering 1994, 120 (12): 2180–2207
Rieben E H. Geological observation on alluvial deposits in northern Iran. Geological Organization of Iran, Report 9, 1966 (in French)
Duncan J M, Byrne P M, Wong K S, Marby P. Strength, stress-strain and bulk modulus parameters for finite element analysis of stresses and movements in soil mass. Rep. No. UCB/GT/80-01, University of California, Berkeley, California, 1980
Seed R B, Duncan J M. SSCOMP: a finite element analysis program for evaluation of soil structure interaction and compaction effects. Report No. UCB/GT/84-02, University of California, Berkeley, California, 1984
Briaud J L, Lim Y. Tieback walls in sand: numerical simulations and design implications. Journal of Geotechnical and Geoenvironmental Engineering, 1999, 125(2): 101–110
Lim Y, Briaud J L. Three dimensional nonlinear finite element analysis of tieback walls and of soil nailed walls under piled bridge abutment. Report to the Federal Highway Administration and the Texas Department of Transportation, Department of Civil Engineering, Texas A&M University, College Station, Texas, 1996
Dunlop P, Duncan J M. Development of failure around excavated slopes. Journal of the Soil Mechanics and Foundations Division, ASCE, 1970, 96: 471–493
Finno R J, Blackburn J T, Roboski J F. Three dimensional effects for supported excavations in clay. Journal of Geotechnical and Geoenvironmental Engineering, 2007, 133(1): 30–36
U.S. EPA. TRIM FaTE Technical Support Document Volume I: Description of Module. EPA/43/D-99/002A, Office of Air Quality Planning and Standards, 1999
Vu-Bac N, Rafiee R, Zhuang X, Lahmer T, Rabczuk T. Uncertainty quantification for multiscale modeling of polymer nanocomposites with correlated parameters. Composites. Part B, Engineering, 2015, 68: 446–464
Vu-Bac N, Lahmer T, Zhuang X, Nguyen-Thoi T, Rabczuk T. A software framework for probabilistic sensitivity analysis for computationally expensive models. Advances in Engineering Software, 2016, 100: 19–31
Baecher G B. Geotechnical Error Analysis. Special Summer Course 1.60s. Cambridge: Massachusetts Institute of Technology, 1985
Kulhawy F H, Birgisson B, Grigoriu M D. Reliability based foundation design for transmission line structures: transformation models for in situ tests. Electric Power Research Institute, Palo Alto, California: Report EL-5507(4), 1992
Li K S, White W. Reliability index of slopes. In: Proceedings of 5th International Conference on Application of Statistics and Probability in Soil and Structural Engineering, 1987, (2): 755–762
Federal Highway Administration (FHWA). Soil nail walls reference manual. U.S. Department of Transportation Federal Highway Administration, 2015
US Army Corps of Engineers (USACE). Introduction to probability and reliability methods for use in geotechnical engineering. Engineering Technical Letter No. 1110–2-547, 1997
Long M. Database for retaining wall and ground movements due to deep excavations. Journal of Geotechnical and Geoenvironmental Engineering, 2001, 127(3): 203–224
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Sekhavatian, A., Choobbasti, A.J. Application of random set method in a deep excavation: based on a case study in Tehran cemented alluvium. Front. Struct. Civ. Eng. 13, 66–80 (2019). https://doi.org/10.1007/s11709-018-0461-y
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11709-018-0461-y