On Some Methods in Safety Evaluation in Geotechnics

Open access


The paper demonstrates how the reliability methods can be utilised in order to evaluate safety in geotechnics. Special attention is paid to the so-called reliability based design that can play a useful and complementary role to Eurocode 7. In the first part, a brief review of first- and second-order reliability methods is given. Next, two examples of reliability-based design are demonstrated. The first one is focussed on bearing capacity calculation and is dedicated to comparison with EC7 requirements. The second one analyses a rigid pile subjected to lateral load and is oriented towards working stress design method. In the second part, applications of random field to safety evaluations in geotechnics are addressed. After a short review of the theory a Random Finite Element algorithm to reliability based design of shallow strip foundation is given. Finally, two illustrative examples for cohesive and cohesionless soils are demonstrated.

[1] ASHRAF A.A., ABDALLAH S.B., Three-Dimensional Analysis of Seepage below and around Hydraulic Structures, J. Hydrologic Eng., 2009, 14(3), 243-247.

[2] ALONSO E., KRIZEK R.J., Stochastic formulation of soil properties, Proceedings of the 2nd International Conference on Applications of Statistics and Probability in Soil and Structural Engineering, Vol. II, Aachen, 1975, 9-32.

[3] BOWLES J.E., Foundation analysis and design, 5th ed. McGraw-Hill, 1996.

[4] BOX G.P., DRAPER N.R., Empirical model-building and response surface, J. Wiley & Sons, New York, 1996.

[5] BREITUNG K., Asymptotic approximation for multinormal integrals, J. Eng. Mech. ASCE., 1984, 110(3), 357-366.

[6] BRINCH HANSEN J., The ultimate resistance of rigid piles against transversal force, The Danish Geotechnical Institute, Bulletin, No. 12, Copenhagen, 1961.

[7] CAFARO F., CERUBINI C., COTECCHIA F., Use of the scale of fluctuation to describe the geotechnical variability of an Italian clay, Proceeding of the 8th International Conference on Applications of Statistics and Probability in Civil Engineering, eds. Melchers and Stewart, Rotterdam, 2000, 481-486.

[8] CHERUBINI C., Probabilistic approach to the design of anchored sheet pile walls, Computers and Geotechnics, 2000, 26(3-4), 309-330.

[9] CHERUBINI C., VESSIA G., PUŁA W., Statistical soil characterization of Italian sites for reliability analysis, Characterization and Engineering Properties of Natural Soil, eds. Tan W., Phoon K.K., Hight, Lerouell, Singapore, Taiwan, 2007, 2681-706.

[10] CHOK Y.H., JAKSA M.B., GRIFFITHS D.V., FENTON G.A., KAGGWA W.S., A parametric study on reliability of spatially random cohesive slopes, Australian Geomechanics, 2007, 42(2), 79-85.

[11] CORNELL C.A., A first-order reliability theory for structural design, Study No. 3, Structural Reliability and Codified Design, University of Waterloo, Ontario, 1969.

[12] CORNELL C.A., A probability-based Structural Code, ACI Journal, 1969, 66(12), 974-985.

[13] DER KIUREGHIAN A., KE J.-D., The stochastic finite element method in structural reliability, Probabilistic Engineering Mechanics, 1988, 3(2), 83-91.

[14] DITLEVSEN O., Principle of Normal Tail Approximation, Journal of the Engineering Mechanics Division, ASCE. 1981, 107(EM6), 1191-1208.

[15] DITLEVSEN O., MADSEN H.O., Structural Reliability Methods, John Wiley & Sons, Chichester, 1996.

[16] EN 1997-1:2004. Eurocode 7. Geotechnical Design, Part 1: General Rules. CEN, European Committee for Standardization, Brussels.

[17] EN 1990:2002. Eurocode: Basis of structural design. CEN, European Committee for Standardization, Brussels.

[18] FENTON G.A., VANMARCKE E., Simulation of random fields via local average subdivision, ASCE J. Geotech. Eng., 1990, 116(8), 1733-1749.

[19] FENTON G.A, GRIFFITHS D.V., Bearing capacity prediction of spatially random c-φ soils, Canadian Geotechnical Journal, 2003, 40(1), 54-65.

[20] FENTON G.A., GRIFFITHS D.V., CAVERS W., Resistance factors for settlement design, Canadian Geotechnical Journal, 2005, 42(5), 1422-1436.

[21] FENTON G.A., GRIFFITHS D.V., ZHANG X.Y., Load and resistance factor design of shallow foundations against bearing failure, Canadian Geotechnical Journal, 2008, 45(11), 1556-1571.

[22] FENTON G.A., GRIFFITHS D.V., Risk assessment in geotechnical engineering, John Wiley & Sons, New York, 2008.

[23] FISZ M. Probability theory and mathematical statistics, Wiley, New York, 1960.

[24] GHANEM R., SPANOS P., Stochastic Finite Elements: A Spectral Approach, Springer-Verlag, New York, 1991.

[25] GRIFFITHS D.V., FENTON G.A., Seepage beneath water retaining structures founded on spatially random soil, Geotechnique, 1993, 43(6), 577-587.

[26] GRIFFITHS D.V., FENTON G.A., Probabilistic analysis of exit gradients due to steady seepage, Journal of Geotechnical and Geoenvironmental Engineering, 1998, 124(9), 789-797.

[27] GRIFFITHS D.V., FENTON G.A., Bearing capacity of spatially random soil: The undrained clay Prandtl problem revisited, Geotechnique, 2001, 54(4), 351-359.

[28] GRIFFITHS D.V., FENTON G.A., TVETEN D.E., Probabilistic earth pressure analysis by the Random Finite Element Method, Proc. of the 11th International Conference on Computer Methods and Advances in Geomechanics (IACMAG 05), G. Barla and M. Barla (eds.), Turin, 2005, 4, 235-249.

[29] GRIFFITHS D.V., FENTON G.A., ZIEMANN H.R., The influence of strength variability in the analysis of slope failure risk, Proc. of the Second Japan-U.S. Workshop on Testing, Modeling and Simulation, Kyoto, P.V. Lade and T. Nakai (eds.), 2005, also in: Geotechnical Special Publication, 2006, 156, 113-123.

[30] GRIFFITHS D.V., FENTON G.A., ZIEMANN H.R., Reliability of passive earth pressure, Georisk: Assessment and Manag. of Risk for Engineered Systems and Geohazards, 2008, 2(2), 113-121.

[31] GRIFFITHS D.V., FENTON G.A., Probabilistic settlement analysis by stochastic and random finite element methods, Journal of Geotechnical and Geoenvironmental Engineering, 2009, 135(11), 1629-1637.

[32] HASOFER A.M., LIND N.C., An Exact and Invariant First- Order Reliability Format, Journal of Engineering Mechanics Division, ASCE, 1974, 100(EM1), 111-121.

[33] HISADA T., NAKAGIRI S., Stochastic finite element developed for structural safety and reliability, Proc. of the 4th International Conference on Structural Safety and Reliability ICOSSAR-3, 1981, 395-408.

[34] HOHENBICHLER M., GOLLWITZER S., KRUSE W., RACKWITZ R., New light on first and second-order reliability methods, Structural Safety, 1987, 4, 267-284.

[35] HOHENBICHLER M., RACKWITZ R., Improvement of the secondorder reliability estimates by importance sampling, Journal Eng. Mech., ASCE, 1988, 114(12), 2195-2199.

[36] KUO Y.L., JAKSA M.B., KAGGWA W.S., FENTON G.A., GRIFFITHS D.V., GOLDSWORTHY J.S., Probabilistic analysis of multi-layered soil effects on shallow foundation settlement, Proc. of 9th Australia New Zealand Conference on Geomechanics, G. Farquhar et al. (eds.), University of Auckland, 2004, 2, 541-547.

[37] LIU P.L., DER KIUREGHIAN A., Optimization algorithms for structural reliability, Structural Safety, 1991, 9, 161-177.

[38] LOW B.K., TANG W.H., Reliability analysis using objectoriented constrained optimization, Structural Safety, 2004, 26(1), 69-89.

[39] LOW B.K., TANG W.H., Efficient spreadsheet algorithm for first-order reliability method, Journal Eng. Mech, ASCE, 2007, 133(12), 1378-1387.

[40] LOW B.K., PHOON K.K., Reliability based design and its complementary role to Eurocode 7 design approach, Computers and Geotechnics, 2015, 65, 30-44.

[41] LUMB P., The variability of natural soils, Canadian Geotechnical Journal, 1966, 3(2), 74-97.

[42] NUTTALL J.D., HICKS M.A., LLORET CABOT M., Stochastic approach to slope stability analysis with in-situ data, Industrial safety and life cycle engineering, 2013, 527-538.

[43] PIECZYŃSKA J., Random finite element method in analysis of a bearing capacity of a shallow foundation, PhD Thesis, Wrocław University of Technology, 2012, (in Polish).

[44] PIECZYŃSKA-KOZŁOWSKA J.M., PUŁA W., GRIFFITHS D.V., FENTON G.A., Influence of embedment, self-weight and anisotropy on bearing capacity reliability using the random finite element method, Computers and Geotechnics, 2015, 67, 229-238.

[45] PN-EN 1997-1:2008/Ap2. Polish annex to PN-EN 1997-1:2008.

[46] PUŁA W., Applications of Structural Reliability Theory to safety evaluation of Foundations, Wrocław University of Technology Press, 2004, (in Polish).

[47] PUŁA W., Reliability of laterally loaded rigid piles, [in:] Probabilistic methods in geotechnical engineering, CISM Courses and Lectures, Springer, 2007, No. 491, 169-183.

[48] PUŁA W., RÓŻAŃSKI A., Reliability of rigid piles subjected to lateral loads, ACME, 2012, 12, 205-218.

[49] PUŁA W., ZASKÓRSKI Ł., Estimation of the probability distribution of the bearing capacity of cohesionless soil using the random finite element method, Structure and Infrastructure Engineering, 2014, 11 (5), 707-720.

[50] RACKWITZ R., FIESSLER B., Structural reliability under combined random loads sequences, Computers and Structures, 1978, 9, 489-494.

[51] RACKWITZ R., Reviewing probabilistic soils modeling, Computers and Geotechnics, 2000, 26(3-4), 309-330.

[52] ROSENBLATT M., Remarks on a multivariate transformation, Annals of Mathematical Statistics, 1952, 23, 470-472.

[53] THAO N.T.P., Geotechnical analysis of a chosen region of the Wrocław city by statistical method, Wrocław University of Technology, Wrocław, 1984, (in Polish).

[54] TOMLINSON M.J., Foundation design and construction, 7th ed., Prentice Hall, 2001.

[55] TVEDT L., Two second-order approximations to the failure probability, Det Norske Veritas, RDIV/20-004-83, 1983.

[56] VANMARCKE E.H., Probabilistic Modeling of Soil Profiles, Journal of the Geotechnical Engineering Division, ASCE, 1977, 103(GT11), 1227-1246.

[57] VANMARCKE E.H., Reliability of earth slopes, J. Geotech. Eng. Div., 1977, 103(GT11), 1247-1265.

[58] VANMARCKE E.H., Random Fields - Analysis and Synthesis. MIT Press, 1983.

Studia Geotechnica et Mechanica

The Journal of Wrocław University of Science and Technology and AGH University of Science and Technology

Journal Information

CiteScore 2017: 0.14

SCImago Journal Rank (SJR) 2017: 0.131
Source Normalized Impact per Paper (SNIP) 2017: 0.448

Cited By


All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 219 215 19
PDF Downloads 101 101 15