Variables Characteristics Effects on Static and Pseudo-Static Reliability-Based Design of Near Slope Shallow Foundations

Document Type : Research


1 M.Sc. in Earthquake Engineering, International Institute of Earthquake Engineering and seismology, Tehran, Iran.

2 Associate Professor, International Institute of Earthquake Engineering and seismology, Tehran, Iran.


Given the concept of reliability-based design (RBD) and the growing risk management trend in geotechnical engineering, proper understanding and quantification of uncertainties are very important. The complexity of methods and a large volume of calculations of probabilistic design methods are the most critical reasons for civil engineers not to be comfortable using these approaches. In this research, a practical probabilistic innovative approach is used to calculate the reliability index by applying the first-order reliability method (FORM). To analyze the bearing capacity of foundations, the Hansen method is used, and both static and seismic designs have been carried out. A scenario where the foundation is located above flat ground and another scenario where the foundation is located near the slope are both considered. Different angles of the slope are also considered. The reason for choosing two different angles for the slope is to examine the effect of slope increase on RBD. As we know, in the RBD of geotechnical structures, our knowledge of the statistical characteristics of variables is significant. That is why, in this paper, the effect of the parameters distribution type (normal or non-normal), the variables dependence, as well as the effect of coefficient of variation in the design results is evaluated. It is found that assuming normal distribution and independence of the variables yields conservative results. The coefficient of variation (COV) of variables is very influential on the results of RBD, and the effect of variation in the internal friction angle (φ) is more significant than variation in the other parameters.


1. Christian J, Ladd C, Baecher G (1994) Reliability Applied to Slope Stability Analysis. Journal of Geotechnical [DOI:10.1061/(ASCE)0733-9410(1994)120:12(2180)]
2. Onisiphorou C (2010) Reliability-based assessment of rock slope stability. In:ISRM International Symposium-EUROCK. Lausanne, Switzerland, 563-566
3. Baecher G B, Christian J T (2003) Reliability and statistics in geotechnical engineering. John Wiley, London
4. Engineering 120:2180-2207. [DOI:10.1061/(asce)0733-9410(1994)120:12(2180)]
5. Phoon K K (ed) (2014). Reliability-based design in geotechnical engineering: computations and applications. CRC Press. [DOI:10.1201/9781482265811]
6. Hicks M A (ed) (2007) Risk and variability in geotechnical engineering. Thomas Telford, London. [DOI:10.1680/ravige.34860]
7. Fenton G A, Griffiths V D (2008) Risk assessment in geotechnical engineering. John Wiley & Sons, New York [DOI:10.1002/9780470284704]
8. Hicks M A, Onisiphorou C (2005) Stochastic evaluation of static liquefaction in a predominantly dilative sand fill. Geotechnique 55(1):123-133 [DOI:10.1680/geot.]
9. Chenari, R. J., Roshandeh, S. P., & Payan, M. (2019). Stochastic analysis of foundation immediate settlement on heterogeneous spatially random soil considering mechanical anisotropy. SN Applied Sciences, 1(7), 660. [DOI:10.1007/s42452-019-0684-0]
10. Low B K (2005) Reliability-Based Design Applied to Retaining Walls. Geotechnique 55(1):63-75 [DOI:10.1680/geot.2005.55.1.63]
11. Abdel Massih D Y, Soubra A H, Low B K (2008) Reliability-based analysis and design of strip foundation against bearing capacity failure. Journal of Geotechnical and Geoenvironmental Engineering, ASCE 134 (7):917-928 [DOI:10.1061/(ASCE)1090-0241(2008)134:7(917)]
12. Zhalehjoo, N., Chenari, R. J., & Pouya, K. R. (2012). Evaluation of bearing capacity of shallow foundations using random field theory in comparison to classic methods. In GeoCongress 2012: State of the Art and Practice in Geotechnical Engineering 2971-2980. [DOI:10.1061/9780784412121.304]
13. Jamshidi Chenari, R., & Mahigir, A. (2014). The effect of spatial variability and anisotropy of soils on bearing capacity of shallow foundations. Civil Engineering Infrastructures Journal, 47(2):199-213
14. Rezaie Soufi, G., Jamshidi Chenari, R., & Karimpour Fard, M. (2019). Influence of random heterogeneity of the friction angle on bearing capacity factor Nγ. Georisk: Assessment and Management of Risk for Engineered Systems and Geohazards, 1-21. [DOI:10.1080/17499518.2019.1566554]
15. Jamshidi Chenari, R., & Alaie, R. (2015). Effects of anisotropy in correlation structure on the stability of an undrained clay slope. Georisk: Assessment and Management of Risk for Engineered Systems and Geohazards, 9(2):109-123 [DOI:10.1080/17499518.2015.1037844]
16. Mohseni, S., Payan, M., & Chenari, R. J. (2018). Soil-structure interaction analysis in natural heterogeneous deposits using random field theory. Innovative Infrastructure Solutions, 3(1), 62. [DOI:10.1007/s41062-018-0168-x]
17. Liu H, Low B K (2018) Reliability-based design of tunnelling problems and insights for Eurocode 7. Computers and Geotechnics 97:42-51 . [DOI:10.1016/j.compgeo.2017.12.005]
18. Low B K (1996) Practical probabilistic approach using spreadsheet. ASCE Geotech Spec Pub 58:1284-1302
19. Hasofer A M, Lind N C (1974) Exact and invariant second-moment code format. Journal of Engineering Mechanics 100:111-121
20. Low B K, Tang W H (2004) Reliability analysis using object-oriented constrained optimization. Structural Safety 26(1):69-89 [DOI:10.1016/S0167-4730(03)00023-7]
21. Ditlevsen O (1981) Uncertainty modeling with applications to multidimensional civil engineering systems. McGraw-Hill, New York
22. Low B K (1997) Reliability analysis of reinforced embankments on soft ground. Canadian Geotechnical Journal 34(5):672-685 [DOI:10.1139/t97-032]
23. Ang H S, Tang W H (1984) Probability concepts in engineering planning and design. John Wiley, New York
24. Melchers R E (1999) Structural reliability analysis and prediction, 2nd edn. John Wiley, New York
25. Soubra, A.-H. _1999_. "Upper-bound solutions for bearing capacity of foundations." J. Geotech. Geoenviron. Eng., 125_1_, 59-68. [DOI:10.1061/(ASCE)1090-0241(1999)125:1(59)]
26. EN 1997−1:2004. Eurocode 7, Geotechnical design. European Committee for Standardization (CEN), Brussels
27. Phoon, Kok-Kwang, and Fred H. Kulhawy. "Characterization of geotechnical variability." Canadian geotechnical journal 36, no. 4 (1999): 612-624. [DOI:10.1139/t99-038]
28. Cherubini, C. "Reliability evaluation of shallow foundation bearing capacity on c'φ'soils." Canadian Geotechnical Journal 37, no. 1 (2000): 264-269. [DOI:10.1139/cgj-37-1-264]
29. Harr, Milton E. "Reliability-based design in civil engineering. 1987."
30. Wolff, Thomas Francis. Analysis and design of embankment dam slopes: a probabilistic approach. University Microfilms, 1985.
31. Yucemen, Mehmet Semih, Wen Hu Tang, and AH-S. Ang. A probabilistic study of safety and design of earth slopes. University of Illinois Engineering Experiment Station. College of Engineering. University of Illinois at Urbana-Champaign., 1973.
32. Lumb, Peter. "Safety factors and the probability distribution of soil strength." Canadian Geotechnical Journal 7, no. 3 (1970): 225-242. [DOI:10.1139/t70-032]
33. Fenton, Gordon A., and D. V. Griffiths. "Bearing-capacity prediction of spatially random c φ soils." Canadian geotechnical journal 40, no. 1 (2003): 54-65. [DOI:10.1139/t02-086]
34. Mahadevan, Sankaran. Probability, reliability, and statistical methods in engineering design. Wiley, 2000.
35. Rackwitz, Rüdiger, and Bernd Flessler. "Structural reliability under combined random load sequences." Computers & Structures 9, no. 5 (1978): 489-494. [DOI:10.1016/0045-7949(78)90046-9]