Modelling the flexural buckling failure of stratified rock slopes based on the multilayer beam model
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摘要
The buckling failure of stratified rock slopes intersected by a set of steep discontinuities that are approximately parallel to the slope surface is frequently encountered while constructing railways and roadways in mountainous areas. In this study, an analytical approach based on the energy equilibrium principle is presented to solve the flexural buckling stability of stratified rock slopes within the framework of multilayer beam theory. The generalized HoekBrown failure criterion is introduced to reflect the influences of slope size(scale effects) on the buckling stability. Subsequently, numerical and physical modellings from previous literatures are employed to validate the proposed approach. Furthermore, a practical case of Bawang Mountain landslide is also used for the comparative analysis. The study shows that the present analytical approach is capable to provide a more reasonable assessment for the buckling failure of stratified rock slopes, compared with several existing analytical approaches. Finally, a detailed parametric study is implemented, and the results indicate that the effects of rock strength, rock deformation modulus, geological strength index, layer thickness and disturbance degree of rock mass on the buckling failure of stratified rock slopes are more significant than that of rock type and slope angle.
The buckling failure of stratified rock slopes intersected by a set of steep discontinuities that are approximately parallel to the slope surface is frequently encountered while constructing railways and roadways in mountainous areas. In this study, an analytical approach based on the energy equilibrium principle is presented to solve the flexural buckling stability of stratified rock slopes within the framework of multilayer beam theory. The generalized HoekBrown failure criterion is introduced to reflect the influences of slope size(scale effects) on the buckling stability. Subsequently, numerical and physical modellings from previous literatures are employed to validate the proposed approach. Furthermore, a practical case of Bawang Mountain landslide is also used for the comparative analysis. The study shows that the present analytical approach is capable to provide a more reasonable assessment for the buckling failure of stratified rock slopes, compared with several existing analytical approaches. Finally, a detailed parametric study is implemented, and the results indicate that the effects of rock strength, rock deformation modulus, geological strength index, layer thickness and disturbance degree of rock mass on the buckling failure of stratified rock slopes are more significant than that of rock type and slope angle.
The buckling failure of stratified rock slopes intersected by a set of steep discontinuities that are approximately parallel to the slope surface is frequently encountered while constructing railways and roadways in mountainous areas. In this study, an analytical approach based on the energy equilibrium principle is presented to solve the flexural buckling stability of stratified rock slopes within the framework of multilayer beam theory. The generalized HoekBrown failure criterion is introduced to reflect the influences of slope size(scale effects) on the buckling stability. Subsequently, numerical and physical modellings from previous literatures are employed to validate the proposed approach. Furthermore, a practical case of Bawang Mountain landslide is also used for the comparative analysis. The study shows that the present analytical approach is capable to provide a more reasonable assessment for the buckling failure of stratified rock slopes, compared with several existing analytical approaches. Finally, a detailed parametric study is implemented, and the results indicate that the effects of rock strength, rock deformation modulus, geological strength index, layer thickness and disturbance degree of rock mass on the buckling failure of stratified rock slopes are more significant than that of rock type and slope angle.
引文
Adhikary DP,Mühlhaus HB,Dyskin AV(2001)A numerical study of flexural buckling of foliated rock slopes.International Journal for Numerical and Analytical Methods in Geomechanics 25(9):871-884.https://doi.org/10.1002/nag.157
Cavers DS(1981)Simple methods to analyze buckling of rock slopes.Rock Mechanics 14:87-104.https://doi.org/10.1007/BF01239857
Deere DU(1968)Geological considerations.In:Stagg KG&Zienkiewicz OC(eds)Rock mechanics in engineering practice.Wiley,New York.pp 1-20.
Garzon SER(2016)Analytical solution for assessing continuum buckling in sedimentary rock slopes based on the tangentmodulus theory.International Journal of Rock Mechanics and Mining Science 90:53-61.https://doi.org/10.1016/j.ijrmms.2016.10.002
Hoek E,Brown ET(1997)Practical estimates of rock mass strength.International Journal of Rock Mechanics and Mining Science 34(8):1165-1186.https://doi.org/10.1016/S1365-1609(97)80069-X
Hoek E,Carranza-Torres C,Corkum B(2002)Hoek-Brown failure criterion-2002 edition.In:Proceedings of NARMS-Tac 2002,Mining Innovation and Technology,University of Toronto,Toronto.pp 267-273.
Hoek E,Diederichs MS(2006)Empirical estimation of rock mass modulus.International Journal of Rock Mechanics and Mining Science 43(2):203-215.https://doi.org/10.1016/j.ijrmms.2005.06.005
Hoek E,Kaiser PK,Bawden WF(1995)Support of Underground Excavations in Hard Rock.A.A.Balkema,Rotterdam.
Hoek E,Marinos P,Benissi M(1998)Applicability of the geological strength index(GSI)classification for very weak and sheared rock masses.The case of the Athens Schist Formation.Bulletin of Engineering Geology and the Environment 57(2):151-160.https://doi.org/10.1007/s100640050031
Hoek E,Wood D,Shah S(1992)A modified Hoek-Brown failure criterion for jointed rock masses.In:Rock Characterization:ISRM Symposium,Eurock'92,Chester,UK.pp 209-214.
Li AH,Zhou DP,Feng J(2009)Failure modes of bedding rock cutting slope and design countermeasures.Chinese Journal Rock Mechanics and Engineering 28(S1):2915-2921.(In Chinese)
Li SS,Ren GM,Zuo SS(1995)Mechanical analysis of instability mechanism of consequent slope in bedded rockmass.Journal of Geological Hazards and Environment Preservation 6(2):24-29.(In Chinese)
Liao LP,Zhu YY,Yang ZQ,et al.(2016)Analysis on Rock Bedded Slope of Karakoram Highway,Pakistan.Chinese Journal of Underground Space and Engineering 12(1):243-249.(In Chinese)
Liu HY,Wang GH,Huang F(2016)Methods to analyze flexural buckling of the consequent slabbed rock slope under top loading.Mathematical Problems in Engineering 2016:1-8.https://doi.org/10.1155/2016/3402547
Lo CM,Feng ZY(2014)Deformation characteristics of slate slopes associated with morphology and creep.Engineering Geology 178:132-154.https://doi.org/10.1016/j.enggeo.2014.06.011
Lo CM,Weng MC(2017)Identification of deformation and failure characteristics in cataclinal slopes using physical modeling.Landslides 14:499-515.https://doi.org/10.1007/s10346-016-0735-1
Marinos P,Hoek E(2000)GSI:a geologically friendly tool for rock mass strength estimation.ISRM International Symposium,International Society for Rock Mechanics.
Marinos P,Hoek E(2001)Estimating the geotechnical properties of heterogeneous rock masses such as flysh.Bulletin of Engineering Geology and the Environment 60:85-92.https://doi.org/10.1007/s100640000090
Pant SR,Adhikary DP(1999)Implicit and explicit modelling of flexural buckling of foliated rock slopes.Rock Mechanics and Rock Engineering 32(2):157-164.https://doi.org/10.1007/s006030050029
Palmstr?m A,Singh R(2001)The deformation modulus of rock masses-comparisons between in situ tests and indirect estimates.Tunnelling and Underground Space Technology16(2):115-131.https://doi.org/10.1016/S0886-7798(01)00038-4
Pereira LC,Lana MS(2013)Stress-Strain Analysis of Buckling Failure in Phyllite Slopes.Geotechnical and Geological Engineering 31(1):297-314.https://doi.org/10.1007/s10706-012-9556-8
Qin S,Jiao JJ,Wang S(2001)A cusp catastrophe model of instability of slip-buckling slope.Rock Mechanics and Rock Engineering 34(2):119-134.https://doi.org/10.1007/s006030170018
Qi SW,Lan HX,Dong JY(2015)An analytical solution to slip buckling slope failure triggered by earthquake.Engineering Geology 194:4-11.https://doi.org/10.1016/j.enggeo.2014.06.004
Silva CHC,Lana MS(2014)Numerical modeling of buckling failure in a mine slope.Rem:Revista Escola de Minas 67(1):81-86.https://doi.org/10.1590/S0370-44672014000100012
Sun GZ(1988)Rock Mass Structure Mechanics.Science Press,Beijing.(In Chinese)
Tang MG,Ma X,Zhang TT,et al.(2016)Early recognition and mechanism of creep-buckling of bedding slope.Journal of Engineering Geology 03:442-40.(In Chinese)
Tommasi P,Verrucci L,Campedel P,et al.(2009)Buckling of high natural slopes:the case of Lavini di Marco(Trento-Italy).Engineering Geology 109(1):93-108.https://doi.org/10.1016/j.enggeo.2009.02.002
Weng MC,Chen TC,Tsai SJ(2017)Modeling scale effects on consequent slope deformation by centrifuge model tests and the discrete element method.Landslides 14(3):981-993.https://doi.org/10.1007/s10346-016-0774-7
Weng MC,Lo CM,Wu CH,et al.(2015)Gravitational deformation mechanisms of slate slopes revealed by model tests and discrete element analysis.Engineering Geology189:116-132.https://doi.org/10.1016/j.enggeo.2015.01.024
Wyllie DC,Mah C(2004)Rock Slope Engineering:Civil and Mining(4th Edition).Spon Press,London.
Yang ZL(2003)Research on mode amplitude for side slope with stratified rock mass.Rock and Soil Mechanics 24(5):764-770.(In Chinese)
Yang ZL(2010)Instability behavior for side slope with bedding rock mass.Chinese Journal of Geotechnical Engineering32(12):1881-1891.(In Chinese)
Zhang LM,Lv SR,Zhang JH,et al.(2014)Instability analysis of bedding rock slope based on the statistical constitutive damage model.Geotechnical Investigation&Surveying 9:7-29.(In Chinese)
Zhang YB,Chen GQ,Zheng L,et al.(2013)Effects of near-fault seismic loadings on run-out of large-scale landslide:A case study.Engineering Geology 166:216-236.https://doi.org/10.1016/j.enggeo.2013.08.002
Zhang YB,Zhang J,Chen GQ,et al.(2015)Effects of vertical seismic force on initiation of the Daguangbao landslide induced by the 2008 Wenchuan earthquake.Soil Dynamics and Earthquake Engineering 73:91-102.https://doi.org/10.1016/j.soildyn.2014.06.036
Cavers DS(1981)Simple methods to analyze buckling of rock slopes.Rock Mechanics 14:87-104.https://doi.org/10.1007/BF01239857
Deere DU(1968)Geological considerations.In:Stagg KG&Zienkiewicz OC(eds)Rock mechanics in engineering practice.Wiley,New York.pp 1-20.
Garzon SER(2016)Analytical solution for assessing continuum buckling in sedimentary rock slopes based on the tangentmodulus theory.International Journal of Rock Mechanics and Mining Science 90:53-61.https://doi.org/10.1016/j.ijrmms.2016.10.002
Hoek E,Brown ET(1997)Practical estimates of rock mass strength.International Journal of Rock Mechanics and Mining Science 34(8):1165-1186.https://doi.org/10.1016/S1365-1609(97)80069-X
Hoek E,Carranza-Torres C,Corkum B(2002)Hoek-Brown failure criterion-2002 edition.In:Proceedings of NARMS-Tac 2002,Mining Innovation and Technology,University of Toronto,Toronto.pp 267-273.
Hoek E,Diederichs MS(2006)Empirical estimation of rock mass modulus.International Journal of Rock Mechanics and Mining Science 43(2):203-215.https://doi.org/10.1016/j.ijrmms.2005.06.005
Hoek E,Kaiser PK,Bawden WF(1995)Support of Underground Excavations in Hard Rock.A.A.Balkema,Rotterdam.
Hoek E,Marinos P,Benissi M(1998)Applicability of the geological strength index(GSI)classification for very weak and sheared rock masses.The case of the Athens Schist Formation.Bulletin of Engineering Geology and the Environment 57(2):151-160.https://doi.org/10.1007/s100640050031
Hoek E,Wood D,Shah S(1992)A modified Hoek-Brown failure criterion for jointed rock masses.In:Rock Characterization:ISRM Symposium,Eurock'92,Chester,UK.pp 209-214.
Li AH,Zhou DP,Feng J(2009)Failure modes of bedding rock cutting slope and design countermeasures.Chinese Journal Rock Mechanics and Engineering 28(S1):2915-2921.(In Chinese)
Li SS,Ren GM,Zuo SS(1995)Mechanical analysis of instability mechanism of consequent slope in bedded rockmass.Journal of Geological Hazards and Environment Preservation 6(2):24-29.(In Chinese)
Liao LP,Zhu YY,Yang ZQ,et al.(2016)Analysis on Rock Bedded Slope of Karakoram Highway,Pakistan.Chinese Journal of Underground Space and Engineering 12(1):243-249.(In Chinese)
Liu HY,Wang GH,Huang F(2016)Methods to analyze flexural buckling of the consequent slabbed rock slope under top loading.Mathematical Problems in Engineering 2016:1-8.https://doi.org/10.1155/2016/3402547
Lo CM,Feng ZY(2014)Deformation characteristics of slate slopes associated with morphology and creep.Engineering Geology 178:132-154.https://doi.org/10.1016/j.enggeo.2014.06.011
Lo CM,Weng MC(2017)Identification of deformation and failure characteristics in cataclinal slopes using physical modeling.Landslides 14:499-515.https://doi.org/10.1007/s10346-016-0735-1
Marinos P,Hoek E(2000)GSI:a geologically friendly tool for rock mass strength estimation.ISRM International Symposium,International Society for Rock Mechanics.
Marinos P,Hoek E(2001)Estimating the geotechnical properties of heterogeneous rock masses such as flysh.Bulletin of Engineering Geology and the Environment 60:85-92.https://doi.org/10.1007/s100640000090
Pant SR,Adhikary DP(1999)Implicit and explicit modelling of flexural buckling of foliated rock slopes.Rock Mechanics and Rock Engineering 32(2):157-164.https://doi.org/10.1007/s006030050029
Palmstr?m A,Singh R(2001)The deformation modulus of rock masses-comparisons between in situ tests and indirect estimates.Tunnelling and Underground Space Technology16(2):115-131.https://doi.org/10.1016/S0886-7798(01)00038-4
Pereira LC,Lana MS(2013)Stress-Strain Analysis of Buckling Failure in Phyllite Slopes.Geotechnical and Geological Engineering 31(1):297-314.https://doi.org/10.1007/s10706-012-9556-8
Qin S,Jiao JJ,Wang S(2001)A cusp catastrophe model of instability of slip-buckling slope.Rock Mechanics and Rock Engineering 34(2):119-134.https://doi.org/10.1007/s006030170018
Qi SW,Lan HX,Dong JY(2015)An analytical solution to slip buckling slope failure triggered by earthquake.Engineering Geology 194:4-11.https://doi.org/10.1016/j.enggeo.2014.06.004
Silva CHC,Lana MS(2014)Numerical modeling of buckling failure in a mine slope.Rem:Revista Escola de Minas 67(1):81-86.https://doi.org/10.1590/S0370-44672014000100012
Sun GZ(1988)Rock Mass Structure Mechanics.Science Press,Beijing.(In Chinese)
Tang MG,Ma X,Zhang TT,et al.(2016)Early recognition and mechanism of creep-buckling of bedding slope.Journal of Engineering Geology 03:442-40.(In Chinese)
Tommasi P,Verrucci L,Campedel P,et al.(2009)Buckling of high natural slopes:the case of Lavini di Marco(Trento-Italy).Engineering Geology 109(1):93-108.https://doi.org/10.1016/j.enggeo.2009.02.002
Weng MC,Chen TC,Tsai SJ(2017)Modeling scale effects on consequent slope deformation by centrifuge model tests and the discrete element method.Landslides 14(3):981-993.https://doi.org/10.1007/s10346-016-0774-7
Weng MC,Lo CM,Wu CH,et al.(2015)Gravitational deformation mechanisms of slate slopes revealed by model tests and discrete element analysis.Engineering Geology189:116-132.https://doi.org/10.1016/j.enggeo.2015.01.024
Wyllie DC,Mah C(2004)Rock Slope Engineering:Civil and Mining(4th Edition).Spon Press,London.
Yang ZL(2003)Research on mode amplitude for side slope with stratified rock mass.Rock and Soil Mechanics 24(5):764-770.(In Chinese)
Yang ZL(2010)Instability behavior for side slope with bedding rock mass.Chinese Journal of Geotechnical Engineering32(12):1881-1891.(In Chinese)
Zhang LM,Lv SR,Zhang JH,et al.(2014)Instability analysis of bedding rock slope based on the statistical constitutive damage model.Geotechnical Investigation&Surveying 9:7-29.(In Chinese)
Zhang YB,Chen GQ,Zheng L,et al.(2013)Effects of near-fault seismic loadings on run-out of large-scale landslide:A case study.Engineering Geology 166:216-236.https://doi.org/10.1016/j.enggeo.2013.08.002
Zhang YB,Zhang J,Chen GQ,et al.(2015)Effects of vertical seismic force on initiation of the Daguangbao landslide induced by the 2008 Wenchuan earthquake.Soil Dynamics and Earthquake Engineering 73:91-102.https://doi.org/10.1016/j.soildyn.2014.06.036
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