Improved slope safety analysis by new Druker-Prager type criterion

Abstract

Based on Mohr-Coulomb (M-C) criterion, the parameters of Druker-Prager (D-P) criterion for geomaterial were determined under non-associated flow rule, and thus a new D-P type criterion was presented. Two assumptions were employed during the derivation: 1) principal strains by M-C model and D-P model are equal, and 2) the material is under plane strain condition. Based on the analysis of the surface on π plane, it is found that the proposed D-P type criterion is better than the D-P criterion with M-C circumscribed circle or M-C inscribed circle, and is applicable for stress Lode angle less than zero. By comparing the predicted results with the test data of sand under plane strain condition and other D-P criteria, the proposed criterion is verified and agrees well with the test data, which is further proved to be better than other D-P type criteria in certain range of Lode angle. The criterion was compiled into a finite difference package FLAC3D by user-subroutine, and was used to analyze the stability of a slope by strength reduction method. The predicted slope safety factor from the proposed criterion agrees well with that by Spencer method, and it is more accurate than that from classic D-P criteria.

Keywords

yield criterion / non-associated flow rule / dilatancy angle / plastic potential function

References

[1] KoiterW. T.. Stress-strain relations, uniqueness and variational theorems for elasto-plastic materials with a singular yield surface [J]. Quarterly of Applied Mathematics, 1953, 11(3): 350-354

[2] ChenW. F.Limit analysis and soil plasticity [M], 1975AmsterdamElsevier Scientific Press637-639

[3] LadeP. V., NelsonR. B.. Incrementalization procedure for elasto-plastic constitutive model with multiple, intersecting yield surfaces [J]. International Journal for Numerical and Analytical Methods in Geomechanics, 1984, 8(4): 311-323

[4] GudehusG.. A comprehensive constitutive equation for granular materials [J]. Soils and Foundations, 1996, 36(1): 1-12

[5] MatsuokaH., SakakibaraK. A.. A constitutive model for sands and clays evaluating principal stress rotation [J]. Soils and Foundation, 1987, 27(4): 73-88

[6] FakharianK., EvginE.. Elasto-plastic modeling of stress-path-dependent behavior of interface [J]. Int J Number Analyt Method Geomech, 2000, 24(2): 183-199

[7] DoveJ. E., JarrettB.. Behavior of dilative sand interface in a geotribology framework [J]. Journal of Geotech and Geoeviron Eng, 2002, 125(7): 545-555

[8] DejongJ. T., WestgateZ. J.. Role of overconsolidation on sand-geomembrane interface response and material damage evolution [J]. Geotxtilesand and Geomembranes, 2005, 23(6): 486-512

[9] SaidI., DegennaroV., FrankR.. Axisymmetric finite element analysis of pile loading test [J]. Computers and Geotechnics, 2009, 36(1/2): 6-19

[10] DrunkerD. C., PragerW.. Soil mechanics and plastic analysis in limit design [J]. Quarterly of Applied Mathematics, 1952, 10(2): 157-165

[11] WangF.-s., ChenC.-b., HwangJ. H., ChangP.-c., ChenW.-fang.. Models for evaluating the revolving cutter profile of circular-arc end mills [J]. Int J Adv Manuf Technol, 2006, 28(3/4): 228-235

[12] XuG.-c., ZhengY.-ren.. Study on application of yield criterions in geotechnical engineering [J]. Chinese journal of Geotechnical Engineering, 1990, 12(2): 93-99

[13] RamezaniS., NaghdabadiR., SohrabpourS.. An additive theory for finite elastic-plastic deformations of the micropolar continuous media [J]. Acta Mechanica, 2009, 206(1/2): 81-93

[14] ArslanH., StureS.. Finite element analysis of localization and micro-macro structure relation in granular materials [J]. Acta Mechanica, 2008, 197(3/4): 153-171

[15] LambrechtM., MieheC., Stuttgart, Germany. Two non-associated istotropic elastoplastic hardening models for frictional materials [J]. Acta Mechanica, 1999, 135(1/2): 73-90

[16] PallarésF. J., AgüeroA., IvorraS.. A comparison of different failure criteria in a numerical seismic assessment of an industrial brickwork chimney [J]. Materials and Structures, 2009, 42(2): 213-226

[17] GongX.-nan.Geotechnical computer analysis [M], 2000BeijingBuilding Industry Press222-226

[18] LiuY.-xue.. Study of several basic problems in constitutive theory of geomaterials [J]. Chinese Journal of Geotechnical Engineering, 2001, 23(1): 45-48

[19] YangX.-l., HuangFu.. Slope stability analysis considering joined influences of nonlinearity and dilation [J]. Journal of Central South University of Technology, 2009, 16(2): 292-296

[20] GanjianN., AskariF., FarzanehO.. Influences of non-associated flow rules on three-dimensional seismic stability of loaded slopes [J]. Journal of Central South University of Technology, 2010, 17(3): 603-611

[21] LavasanA. A., GhazaviM.. Influence of interference on failure mechanism of closely constructed circular footings on reinforced sand [C]. Proceedings of the 4th Aasia Regional Conference on Geosynthetics, 2008ShanghaiZhejiang University Press311-317

[22] ZhangL.-y., ShiW.-m., ZhengY.-ren.. The slope stability analysis by FEM under the plane strain condition [J]. Chinese Journal of Geotechnical Engineering, 2002, 24(4): 487-490

[23] ZhengY.-r., WangJ.-l., ZhuX.-kang.. Discussion on velocity of slip line theory for geotechnical materials [J]. Journal of Hydraulic Engineering, 2001, 32(6): 1-7

[24] LiG.-x., HuangY.-n., ZhangQ.-guan.. The principal stress of soil in the direction of plane strain [J]. Chinese Journal of Geotechnical Engineering, 2001, 23(3): 358-361

[25] KhalidA., HeathS. W.. A true triaxial apparatus for soil testing with mixed boundary conditions [J]. Geotechnical Testing Journal, 2005, 28(6): 534-543

[26] LadeP. V., DuncanJ. M.. Cubical triaxial tests on cohesionless soil [J]. Journal of the Soil Mechanics and Foundations Division, 1973, 99(SM10): 793-812

[27] LiG.-x., ZhangQ.-g., HuangY.-nan.. Study on transforming of principal stresses in constant stress ratio plane strain tests [J]. Rock and Soil Mechanics, 2006, 27(11): 1867-1872

[28] HuangM.-s., JiaC.-qin.. Strength reduction FEM in stability analysis of soil slopes subjected to transient unsaturated seepage [J]. Computers and Geotechnics, 2009, 36(1): 93-101