Continuous slip surface method for stability analysis of heterogeneous vertical trenches

Document Type : Article

Authors

1 Department of Civil Engineering, Faculty of Engineering, University of Guilan, P.O. 3756, Rasht, Guilan, Iran

2 Department of Civil Engineering, Faculty of Engineering, University of Guilan, P.O. 3756, Rasht, Guilan, Iran.

Abstract

Evaluating the reliability of trenches against sliding failure is complicated by the fact that most alluvial deposits are heterogeneous and spatially variable. This means that instead of perfectly circular or linear failure surfaces, trench failure tends to be more complex, following the weakest path or zones through the material, thereby, a new method named Continuous Slip-Surface (CSS) is adopted for calculating the critical excavation depth. CSS runs an algorithm to seek for continuous slip surface. The Finite Difference Method (FDM) coupled with random field theory and CSS method is well suited to slope stability calculations since it allows the failure surface to seek out the weakest path through the soil. For an unsupported vertical cut, it was shown that the critical excavation depth acquired from CSSM is indeed an upper bound solution. It was further shown both numerically and analytically through an idealized variation model that increasing the un-drained shear strength density fades the effect of shear strength variability. Correlation structure of the input variable was also shown to influence the results, although the behaviour was found different in low and high scales of fluctuation.

Keywords

Main Subjects


References
1. Chen, W.F., Limit Analysis and Soil Plasticity, Elsevier
Scienti c Publication (1975).
2. Zienkiewicz, O.C., Humpheson, C., and Lewis, R.W.
Associated and non-associated visco-plasticity and
plasticity in soil mechanics", Geotechnique, 25, pp.
671{689 (1975).
3. Naylor, D. Finite elements and slope stability", In
Numerical Methods in Geomechanics: Proceedings of
the NATO Advanced Study Institute, University of
Minho, Braga, Portugal, held at Vimeiro, Aug. 24{
Sept. 4, 92, pp. 229{244 (1982).
4. Matsui, T. and San, K. Finite element slope stability
analysis by shear strength reduction technique", Soils
and Foundations, 32(1), pp. 59{70 (1992).
5. Ugai, K. and Leshchinsky, D. Three-dimensional limit
equilibrium and nite element analyses: A comparison
of results", Soils and Foundations, 35, pp. 1{7 (1995).
6. Lane, P. and Griths, D. Finite element slope stability
analysis-Why are engineers still drawing circles",
In Proceeding of 6th International Symposium on Numerical
Models in Geomechanics, Balkema Publishers,
Rotterdam, The Netherlands, pp. 589{593 (1997).
7. Dawson, E., Roth, W., and Drescher, A. Slope stability
analysis by strength reduction", Geotechnique,
49(6), pp. 835{840 (1999).
8. Rachez, X., Billaux, D., and Hart, R. Slope stability
analysis with an integrated shear strength reduction
algorithm", In Proceeding of 5th European Conference
on Numerical Methods in Geotechnical Engineering,
pp. 731{736 (2002).
9. Ca la, M., Flisiakm J., and Tajdus, A. Slope stability
analysis with modi ed shear strength reduction
technique", In the 9th International Symposium on
Landslides: Evaluation and Stabilization, pp. 1085{
1089 (2004).
10. Drucker, D.C. and Prager, W. Soil mechanics and
plastic analysis or limit design", Quarterly of Applied
Mathematics, 10(2), pp. 157{165 (1952).
11. Davis, E., Theories of Plasticity and the Failure of Soil
Masses, Butterworth, London (1968).
12. Booker, J.R. Application of theories of plasticity to
cohesive frictional soils", Ph.D. Thesis, University of
Sydney (1969).
13. Atkinson, J.H., Foundations and Slopes: An Introduction
to Applications of Critical State Soil Mechanics,
McGraw-Hill, London (1981).
14. Michalowski, R.L. Limit analysis in stability calculations
of reinforced soil structures", Geotextiles and
Geomembranes, 16(6), pp. 311{331 (1998).
15. Song, E.X. Finite element analysis of safety factor
for soil structures", Chinese Journal of Geotechnical
Engineering, 19(2), pp. 1{7 (1997).
16. Lian, Z., Han, G., and Kong, X. Stability analysis
of excavation by strength reduction FEM", Chinese
Journal of Geotechnical Engineering, 23(4), pp. 407{
411 (2001).
17. Eberhardt, E. The role of advanced numerical methods
and geotechnical eld measurements in understanding
complex deep-seated rock slope failure mechanisms",
Canadian Geotechnical Journal, 45(4), pp.
484{510 (2008).
18. Sai, R., Shukla, S.K., Prasad, G., Vishnoi, R., and
Routela, T. Integrated approach for stabilization of
varunavat parvat landslide - case study", International
Conference on Case Histories in Geotechnical Engineering
(2008).
19. Zheng, Y., Tang, X., Zhao, S., Deng, C., and Lei,
W. Strength reduction and step-loading nite element
approaches in geotechnical engineering", Journal of
Rock Mechanics and Geotechnical Engineering, 1(1),
pp. 21{30 (2009).
20. Huang, M. and Cang, Q.J. Strength reduction FEM
in stability analysis of soil slopes subjected to transient
unsaturated seepage", Computers and Geotechnics,
36(1), pp. 93{101 (2009).
R. Jamshidi Chenari et al./Scientia Iranica, Transactions A: Civil Engineering 27 (2020) 2657{2668 2667
21. Wei, W. and Cheng, Y. Soil nailed slope by strength
reduction and limit equilibrium methods", Computers
and Geotechnics, 37(5), pp. 602{618 (2010).
22. Eser, M., Aydemir, C., and Ekiz, I. E ects of soil
structure interaction on strength reduction factors",
Procedia Engineering, 14, pp. 1696{1704 (2011).
23. FLAC 5.0 Reference Manual, Minneapolis, Itasca Consulting
Inc (2007).
24. Bowles, L.E., Foundation Analysis and Design,
McGraw-Hill (1996).
25. Chen, W.F. and Liew, J.R., The Civil Engineering
Handbook, 2th Editions, Crc Press (2002).
26. Jamshidi Chenari, R. and Zamanzadeh, M. Uncertainty
assessment of critical excavation depth of vertical
unsupported cuts in undrained clay using random
eld theorem", Scientia Iranica, 23(3), pp. 864{875
(2016).
27. Lacasse, S. and Nadim, F. Uncertainties in characterising
soil properties", In Uncertainty in the Geologic
Environment from Theory to Practice, ASCE Conference,
pp. 49{75 (1997).
28. Garzon, L.X., Caicedo, B., Sanchez-Silva, M., and
Phoon, K.K. Physical modelling of soil uncertainty",
International Journal of Physical Modelling in
Geotechnics, 15(1), pp. 19{34 (2015).
29. Vanmarcke, E.H. Probabilistic modeling of soil pro-
les", Journal of the Geotechnical Engineering Division,
103(11), pp. 1227{1246 (1977).
30. Phoon, K.K. and Kulhawy, F.H. Characterization
of geotechnical variability", Canadian Geotechnical
Journal, 36(4), pp. 612{624 (1999).
31. Babu, G.S. and Mukesh, M. E ect of soil variability
on reliability of soil slopes", Geotechnique, 54(5), pp.
335{337 (2004).
32. Cho, S.E. E ect of spatial variability of soil properties
on slope stability", Engineering Geology, 92, pp. 97{
109 (2007).
33. Haldar, S. and Babu, G.S. E ect of soil spatial
variability on the response of laterally loaded pile in
undrained clay", Computers and Geotechnics, 35(4),
pp. 537{547 (2008).
34. Griths, D., Huang, J., and Fenton, G.A. In
uence of
spatial variability on slope reliability using 2-D random
elds", Journal of Geotechnical and Geoenvironmental
Engineering, 135(10), pp. 1367{1378 (2009).
35. Cho, S.E. Probabilistic assessment of slope stability
that considers the spatial variability of soil properties",
Journal of Geotechnical and Geoenvironmental Engineering,
136(7), pp. 975{984 (2009).
36. Kasama, K. and Zen, K. E ects of spatial variability
of soil property on slope stability", First International
Symposium on Uncertainty Modeling and Analysis and
Management (ICVRAM 2011); and Fifth International
Symposium on Uncertainty Modeling and Anaylsis
(ISUMA), April 11{13, Hyattsville, Maryland,
United States (2011).
37. Jamshidi Chenari, R., Zhalehjoo, N., and Karimian,
A. Estimation on bearing capacity of shallow foundations
in heterogeneous deposits using analytical and
numerical methods", Scientia Iranica, 21(3), pp. 505{
515 (2014).
38. Jiang, S.H., Li, D.Q., Zhang, L.M., and Zhou, C.B.
Slope reliability analysis considering spatially variable
shear strength parameters using a non-intrusive
stochastic nite element method", Engineering geology,
168, pp. 120{128 (2014).
39. Eslami Kenarsari, E., Jamshidi Chenari, R., and Eslami,
A. Characterization of the correlation structure
of residual CPT pro les in sand deposits", International
Journal of Civil Engineering, 11(1), pp. 29{37
(2013).
40. Lee, I.K., White, W., and Ingles, O.G., Geotechnical
Engineering, Pitmans Books Limited (1983).
41. Harr, M.E., Reliability Based Design in Civil Engineering,
McGraw Hill, New York (1987).
42. Seyedein, M.S., Jamshidi Chenari, R., and Eslami, A.,
Investigation on probability density function for cone
penetration test data", In Proceeding of International
Conference on Geomechanics and Engineering, pp. 26{
29 (2012).
43. Duncan, J.M. Factors of safety and reliability in
geotechnical engineering", Journal of Geotechnical and
Geoenvironmental Engineering, 126(4), pp. 307{316
(2000).
44. Fenton, G.A. and Griths, D. Statistics of block
conductivity through a simple bounded stochastic
medium", Water Resources Research, 29(6), pp. 1825{
1830 (1993).
45. El-Kadi, A.I. and Williams, S.A. Generating twodimensional
elds of auto-correlated, normally distributed
parameters by the matrix decomposition technique",
Ground Water, 38(4), pp. 530{532 (2000).