PROBABILISTIC AND STATISTICAL APPROACHES TO UNCERTAINTY ASSESSMENT IN LITHOTECHNOGENIC SYSTEMS

K. V. Kurguzova,#, I. K. Fomenkoa,##, and O. N. Sirotkinab,###


a Russian State Geological Prospecting University,
ul. Miklukho-Maklaya, 23, Moscow, 117997 Russia
b Lomonosov Moscow State University, Leninskie Gory, Moscow, 119991 Russia

#e-mail: kurgusov@yandex.ru,

##e-mail: ifolga@gmail.com,

###e-mail: onsirotkina@gmail.com

Uncertainty as a multidisciplinary scientific category has been an object of scrutiny for a long time. High level of uncertainty is a distinctive feature of geology among other sciences. The study, analysis and discussions of this category remain for the most part in rhetorical or philosophical fields; however, there is a direct require- ment to quantify this category in the engineering geology practice. Uncertainty is understood as an ambigu- ous property because of lacking information about engineering geological conditions. This definition arises a question, if the uncertainty relates to information, could it be fully considered quantitatively? There’s a fact that various random factors influence geological processes and soil (rocks) properties. In other words, geo- logical processes are not completely deterministic. Geological processes and soil properties pertain to time and spatial composition of deterministic and random multivariate fields. Uncertainty is an inherent feature of engineering geology and geotechnical engineering. But almost all engineering tasks are being solved with deterministic applications, without considering random factors quantitatively. Today the design methodolo- gy is based on a limit state design concept, which is considered as a semi-probabilistic procedure. It involves the application of various partial reliability factors to produce structures able to withstand against the occur- rence of ultimate and serviceability loadings (ULS and SLS). Apparently, this limit state design methodology is unable to provide the process of assembling the structure with defined level of reliability, for it doesn’t con- sider the random nature of site condition, engineering geology processes, soils variability, structural loads, etc. All these uncertainty factors and random nature of geological processes could be envisaged with an ap- plication of probability theory, statistics, as well as geostatistic. For quantitative uncertainty consideration it’s required to analyze various factors separately such as loads, variability of soil properties, uncertainty of math- ematical models, geology geometry (stratigraphy, geomorphology etc.). Various classifications of the geology uncertainty are shown in the article. In general, uncertainty, as a category, could be subdivided in two types: aleatoric (ontological) uncertainty that deals with a physical nature of processes; and epistemic (gnostic) un- certainty that pertains to lack of knowledge of physical processes. The quantitative consideration of uncer- tainty factors allows us to create the uncertainty model for the analyzed construction site (a random model). In geotechnical practice, failures do occur sometimes. Attributing them to a residual risk or a faulty execution of the project does not properly cover the range of causes. A closer scrutiny of the design, the engineering model, the data, the soil-structure interaction and the model assumptions are required. Usually, the uncer- tainties in initial and boundary conditions as well as material parameters are abundant. Deterministic meth- odology which is a basis for current norms and regulations is unable to analyze all the reasons that pertain to uncertainty, causing an engineer to leave the issue aside. Research and analysis of this complex category in the article reveals a high demand for thorough application of stochastic methods in geotechnics. Unfortunate- ly, it still does not have a broad usage in practice, due to various circumstances. Moreover, among geotech- nical engineers, who are used to deterministic calculations, there’s an opinion could be met that such cate- gory as uncertainty could hardly be assessed and estimated if at all. All these remind us of actuality of the subject.

Keywords: lithotechnical system, the uncertainty of LTS, probabilistic approach, geostatistics, stochastic geoengineering

DOI: 10.31857/S0869780920020071

REFERENCES

1. Bolotin, V.V. Primenenie metodov teorii veroyatnostei i teorii nadezhnosti v raschetakh sooruzhenii [Application of the methods of probability theory and reliability the- ory in the calculations of structures]. Moscow, Izd-vo literatura po stroitel’stvu, 1971, 255 p. (in Russian)

2. Bondarik, G.K. Obshchaya teoriya inzhenernoi (fizicheskoi) geologii [General theory of engineering (physical) geology]. Moscow, Nedra Publ., 1981, 256 p. (in Rus- sian)

3. Bondarik, G.K. Teoriya geologicheskogo polya [Geological field theory]. Moscow, VIMS Publ., 2002, 129 p. (in Russian)

4. Buslaeva, O.V., Korolev, V.A. Neopredelennosti v ekologo-geologicheskikh sistemakh i ikh sistematizatsiya [Indeterminacies in the environmental-geological systems and their systematization]. Inzhenernaya geologiya, 2013, no. 6, pp. 56–62. (in Russian)

5. Veksler, A.B., Ivashintsov, D.A., Stefanishin, D.V. Nadezhnost’, sotsial’naya i ekologicheskaya bezopasnost' gidrotekhnicheskikh ob’ektov: otsenka riska i prinyatie reshenii [Reliability, social and environmental safety of hydraulic facilities: risk assessment and decision-mak- ing]. St.Petersburg, OAO “VNIIG im. B.E. Vedeneeva” Publ., 2002, 591 p. (in Russian)

6. Vistelius, A.B. Osnovy matematicheskoi geologii [Funda- mentals of mathematical geology]. St.Petersburg, Nau- ka Publ., 1980, 389 p. (in Russian) 


7. Garagash, B.A. Nadezhnost’ sistem “Osnovanie-sooruzhenie” [Safety of the basis-engineering structure sys- tem], vol. 2, Moscow, ACB Publ., 2012, 471 p. (in Rus- sian) 


8. Dmitriev, V.V., Yarg, L.A. Metody I kachestv olaboratornogo izucheniya gruntov [Methods and quality of labora- tory study of soils]. Moscow, KDU Publ., 2008, 542 p. (in Russian) 


9. Zemtsov, V.M., Zemtsova, I.V. Elementy teorii veroyatnostei i matematicheskoi statistiki [Elements of probabil- ity theory and mathematical statistics]. Moscow, ACB Publ., 2013, 538 p. (in Russian) 


10. Kaufman, B.D., Shul’man, S.G. Dinamika sistem sooruzhenie – osnovanie pri nepolnoi iskhodnoi informatsii (uchet sluchainykh i neopredelennykh faktorov) [Dynamics of construction-base systems with incomplete initial information (accounting for random and uncer- tain factors)]. St.Petersburg, OAO “VNIIG im. B.E. Vedeneeva” Publ., 2016, 418 p. (in Russian) 


11. Kurguzov, K.V., Fomenko, I.K. Sravnitel’naya otsenka metodov rascheta svai na gorizontal’nuyu nagruzku [Comparison of calculating methods for laterally loaded piles]. Vestnik MGSU, 2019, vol. 14, no. 10, pp. 1280–1291. 
DOI: 10.22227/1997-0935.2019.10.1280-1291 


12. Kurguzov, K.V., Fomenko, I.K., Sirotkina O.N. Otsenka nesushchei sposobnosti svai. Metody rascheta i problematika. [Calculation of driven pile bearing capacity. Analytical methods and issues]. Izvestiya Tomskogo politekhnicheskogo universiteta. Inzhiniring georesursov, 2019, vol. 330, no. 10, pp. 7–25. 
DOI: 10.18799/24131830/2019/10/2294 


13. Moiseev, N.N. Matematicheskie zadachi sistemnogo analiza [Mathematical problems of system analysis]. Moscow, Nauka Publ., 1981, 487 p. (in Russian) 


14. Pshenichkin, A.P. Osnovy veroyatnostno-statisticheskoi teorii vzaimodeistviya sooruzhenii s neodnorodnymi gruntovymi osnovaniyami [Bases of probabilistic-statistical theory of interaction of structures with inhomogeneous soil bases]. Volgograd, VoLGASU Publ., 2006, 207 p. (in Russian) 


15. Rzhanitsyn, A.R. Teoriya rascheta stroitel’nykh kon- struktsii na nadezhnost' [The theory of calculation of building structures on reliability]. Moscow, Stroiizdat, 1978, 239 p. (in Russian) 


16. Stefanishin, D.V., Malizderskii, R.N. [Probabilistic as- sessment of the stability of the shore abutments of the arch dam Nam Chien (Vietnam) under uncertainty]. Sbornik dokladov 3 nauchno-tekhnicheskoi konferentsii 
“Gidroenergetika. Novye razrabotki i tekhnologii” [Proceedings of 3rd scientific and technical conference “Hydropower. New developments and technologies”]. St.Petersburg, OAO “VNIIG im. B.E.Vedeneeva” Publ., 2008, pp. 229–237. (in Russian)

17. Pendin, V.V. Kompleksnyi kolichestvennyi analiz infor- matsii v inzhenernoi geologii [Complex quantitative analysis of information in engineering geology]. Moscow, KDU Publ., 2009, 349 p. (in Russian)

18. Analyzing uncertainty in civil engineering. Fellin, W., Lessmann, H., Oberguggenberger, M., Vieider, R., Eds., New York, Springer, 2005. 244 p. DOI: 10.1007/b138177

19. Dithinde, M. et al. Characterization of model uncertainty in the static pile design formula. Journal of geo- technical and geoenvironmental engineering. 2010, vol. 137, issue 1, pp. 70–85. doi.org/10.1061/(ASCE)GT.1943-5606.0000401

20. Fenton, G.A., Griffith, D.V. Risk assessment in geotechnical egnineering. New Jersey: WILEY, 2008, 480 p. DOI:10.1002/9780 47028470 4

21. Galbraith, A.P. et al. Uncertainty in pile resistance from static load tests database. Geotechnical Engineer- ing, 2014, vol. 167, issue 5, pp. 431–446. doi.org/10.1680/geng.12.00132

22. Lee, I.K. et al. Geotechnical engineering. Boston, Pitman, 1982, 432 p.

23. McMahon, B.K. Geotechnical Design in the face of uncertainty. Australian Geomechanics. 1985, no. 10, pp. 7–19.

24. National cooperative highway research program (NCHRP). Load and Resistance Factor Design (LRFD) for Deep Foundations, Report 507. Washington, Transportation Research Board, 2004, 77 p.

25. Probabilistic methods for structural design. Guedes Soares, C., Ed., Lisbon, Springer science, 1997, 408 p. doi.org/10.1007/978-94-011-5614-1

26. Russelli, C., Vermeer, P.A. Probabilistic methods applied to geotechnical engineering. 2nd International Workshop of Young Doctors in Geomechanics (WHYDOC), Champs-sur-Marne, Paris, 2005, pp. 361–366.

27. Trevor, L.L. How Eurocode 7 addresses uncertainty, risk and decision making in geotechnical design. Second International Conference on Vulnerability and Risk Analysis and Management (ICVRAM) and the Sixth International Symposium on Uncertainty, Mod- eling, and Analysis (ISUMA), Liverpool, ASCE Press, 2014, vol. 4, pp. 2419–2428. doi.org/10.1061/9780784413609.243

28. Whitman, R.V. Evaluating calculated risk in geotechnical engineering. Geotechnical engineering ASCE. 1984, col. 110, no. 2, pp. 145–188. doi.org/10.1061/(ASCE)0733-9410(1984)110:2(143)