Rock-soil slope stability analysis by two-phase random media and finite elements
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摘要
To investigate the strong random nature of the geometric interfaces between soil and rock, a rock-soil slope is considered as a two-phase random medium. A nonlinear translation of a Gaussian field is utilized to simulate the two-phase random media, such that the soil(or rock) volume fraction and the inclination of the soil layer can be examined. The finite element method with random media incorporated as the material properties is used to determine the factor of safety of the rock-soil slope. Monte-Carlo simulations are used to estimate the statistical characteristics of the factor of safety. The failure mode of the rock-soil slope is examined by observing the maximum principal plastic strain at incipient slope failure. It is found that the critical surface of a rock-soil slope is fairly irregular, and it significantly differs from that of a pure soil slope. The factor of safety is sensitive to the soil volume faction, but it is predictable. The average factor of safety could be well predicted by the weighted harmonic average between the strength of soil and rock; the prediction model is practical and simple. Parametric studies on the inclination of the soil layer demonstrate that the most instable scenario occurs when the slope angle is consistent with the inclination of the soil layer.
To investigate the strong random nature of the geometric interfaces between soil and rock, a rock-soil slope is considered as a two-phase random medium. A nonlinear translation of a Gaussian field is utilized to simulate the two-phase random media, such that the soil(or rock) volume fraction and the inclination of the soil layer can be examined. The finite element method with random media incorporated as the material properties is used to determine the factor of safety of the rock-soil slope. Monte-Carlo simulations are used to estimate the statistical characteristics of the factor of safety. The failure mode of the rock-soil slope is examined by observing the maximum principal plastic strain at incipient slope failure. It is found that the critical surface of a rock-soil slope is fairly irregular, and it significantly differs from that of a pure soil slope. The factor of safety is sensitive to the soil volume faction, but it is predictable. The average factor of safety could be well predicted by the weighted harmonic average between the strength of soil and rock; the prediction model is practical and simple. Parametric studies on the inclination of the soil layer demonstrate that the most instable scenario occurs when the slope angle is consistent with the inclination of the soil layer.
To investigate the strong random nature of the geometric interfaces between soil and rock, a rock-soil slope is considered as a two-phase random medium. A nonlinear translation of a Gaussian field is utilized to simulate the two-phase random media, such that the soil(or rock) volume fraction and the inclination of the soil layer can be examined. The finite element method with random media incorporated as the material properties is used to determine the factor of safety of the rock-soil slope. Monte-Carlo simulations are used to estimate the statistical characteristics of the factor of safety. The failure mode of the rock-soil slope is examined by observing the maximum principal plastic strain at incipient slope failure. It is found that the critical surface of a rock-soil slope is fairly irregular, and it significantly differs from that of a pure soil slope. The factor of safety is sensitive to the soil volume faction, but it is predictable. The average factor of safety could be well predicted by the weighted harmonic average between the strength of soil and rock; the prediction model is practical and simple. Parametric studies on the inclination of the soil layer demonstrate that the most instable scenario occurs when the slope angle is consistent with the inclination of the soil layer.
引文
Bocchini,P.,Deodatis,G.,2008.Critical review and latest developments of a class of simulation algorithms for strongly non-Gaussian random fields.Probabilistic Engineering Mechanics 23,394e407.
Feng,J.W.,Li,C.F.,Cen,S.,Owen,D.R.J.,2014.Statistical reconstruction of two-phase random media.Computers and Structures 137,78e92.
Goh,A.T.C.,Zhang,W.G.,2012.Reliability assessment of stability of underground rock caverns.International Journal of Rock Mechanics and Mining Sciences 55,157e163.
Griffiths,D.V.,Lane,P.A.,1999.Slope stability analysis by finite elements.Géotechnique 49(3),387e403.
Griffiths,D.V.,Paiboon,J.,Huang,J.,Fenton,G.A.,2012.Homogenization of geomaterials containing voids by random fields and finite elements.International Journal of Solids and Structures 49,2006e2014.
Li,D.Q.,Qi,X.H.,Phoon,K.K.,Zhang,L.M.,Zhou,C.B.,2014.Effect of spatially variable shear strength parameters with linearly increasing mean trend on reliability of infinite slopes.Structural Safety 49,45e55.
Li,D.Q.,Qi,X.H.,Cao,Z.J.,Tang,X.S.,Phoon,K.K.,Zhou,C.B.,2016.Evaluating slope stability uncertainty using coupled Markov chain.Computers and Geotechnics 73,72e82.
Li,D.Q.,Tang,X.S.,Phoon,K.K.,2015.Bootstrap method for characterizing the effect of uncertainty in shear strength parameters on slope reliability.Reliability Engineering and System Safety 140,99e106.
Liu,Y.,Lee,F.H.,Quek,S.T.,Chen,J.E.,Yi,J.T.,2015.Effect of spatial variation of strength and modulus on the lateral compression response of cement-admixed clay slab.Geotechnique 65(10),851e865.
Liu,Y.,Hu,J.,Wei,H.,Saw,A.L.,2017a.A direct simulation algorithm for a class of beta random fields in modelling material properties.Computer Methods in Applied Mechanics and Engineering 326,642e655.
Liu,Y.,Lee,F.H.,Quek,S.T.,Beer,M.,2014.Modified linear estimation method for generating multi-dimensional multi-variate Gaussian field in modelling material properties.Probabilistic Engineering Mechanics 38,42e53.
Liu,Y.,Quek,S.T.,Lee,F.H.,2016.Translation random field with marginal beta distribution in modeling material properties.Structural Safety 61,57e66.
Liu,Y.,Shields,M.D.,2017.A direct simulation method and lower-bound estimation for a class of gamma random fields with applications in modelling material properties.Probabilistic Engineering Mechanics 47,16e25.
Liu,Y.,Zhang,W.,Zhang,L.,Zhu,Z.R.,Hu,J.,Wei,H.,2018.Probabilistic stability analyses of undrained slopes by 3D random fields and finite element methods.Geoscience Frontiers 9(6),1657e1664.
Ni,S.H.,Lu,P.C.,Juang,C.H.,1996.A fuzzy neural network approach to evaluation of slope failure potential.Computer-Aided Civil and Infrastructure Engineering 11,59e66.
Qi,X.H.,Li,D.Q.,2018.Effect of spatial variability of shear strength parameters on critical slip surfaces of slope.Engineering Geology 239,41e49.
Qi,X.H.,Li,D.Q.,Phoon,K.K.,Cao,Z.J.,Tang,X.S.,2016.Simulation of geologic uncertainty using coupled Markov chain.Engineering Geology 207,129e140.
Shields,M.D.,Bocchini,P.,Deodatis,G.,2016.Discussion of Feng et al.(2014).“Statistical reconstruction of two-phase random media”.Computers and Structures 163,83e85.
Shields,M.D.,Deodatis,G.,2013.Estimation of evolutionary spectra for simulation of non-stationary and non-Gaussian stochastic processes.Computers and Structures 126,149e163.
Tang,X.S.,Li,D.Q.,Rong,G.,Phoon,K.K.,Zhou,C.B.,2013.Impact of copula selection on geotechnical reliability under incomplete probability information.Computers and Geotechnics 49,264e278.
Tang,X.S.,Li,D.Q.,Zhou,C.B.,Phoon,K.K.,2015.Copula-based approaches for evaluating slope reliability under incomplete probability information.Structural Safety 52,90e99.
Tang,Y.,Xu,J.,2016.Shield tunneling in rock-soil interface composite formations.Geotechnical and Geological Engineering.https://doi.org/10.1007/S10706-016-9994-9.
Taylor,D.W.,1937.Stability of earth slopes.Journal of Boston Society of Civil Engineers 24(3),197e246.
Toth,A.,Gong,Q.,Zhao,J.,2013.Case studies of TBM tunneling performance in rocksoil interface mixed ground.Tunnelling and Underground Space Technology 38,140e150.
West,L.J.,Hencher,S.R.,1991.Assessing the Stability of Slopes in Heterogeneous Soils.Proceedings of the 6th International Symposium on Landslides.Christchurch,New Zealand,pp.591e595.
Xiao,T.,Li,D.Q.,Cao,Z.J.,Zhang,L.M.,2018.CPT-based probabilistic characterization of three-dimensional spatial variability using MLE.Journal of Geotechnical and Geoenvironmental Engineering 144(5),04018023.
Zhang,J.,Qu,H.,Liao,Y.,Ma,Y.,2012.Seismic damage of earth structures of road engineering in the 2008 Wenchuan earthquake.Environmental Earth Sciences65,987e993.
Zhang,W.G.,Goh,A.T.C.,2012.Reliability assessment on ultimate and serviceability limit states and determination of critical factor of safety for underground rock caverns.Tunnelling and Underground Space Technology 32,221e230.
Feng,J.W.,Li,C.F.,Cen,S.,Owen,D.R.J.,2014.Statistical reconstruction of two-phase random media.Computers and Structures 137,78e92.
Goh,A.T.C.,Zhang,W.G.,2012.Reliability assessment of stability of underground rock caverns.International Journal of Rock Mechanics and Mining Sciences 55,157e163.
Griffiths,D.V.,Lane,P.A.,1999.Slope stability analysis by finite elements.Géotechnique 49(3),387e403.
Griffiths,D.V.,Paiboon,J.,Huang,J.,Fenton,G.A.,2012.Homogenization of geomaterials containing voids by random fields and finite elements.International Journal of Solids and Structures 49,2006e2014.
Li,D.Q.,Qi,X.H.,Phoon,K.K.,Zhang,L.M.,Zhou,C.B.,2014.Effect of spatially variable shear strength parameters with linearly increasing mean trend on reliability of infinite slopes.Structural Safety 49,45e55.
Li,D.Q.,Qi,X.H.,Cao,Z.J.,Tang,X.S.,Phoon,K.K.,Zhou,C.B.,2016.Evaluating slope stability uncertainty using coupled Markov chain.Computers and Geotechnics 73,72e82.
Li,D.Q.,Tang,X.S.,Phoon,K.K.,2015.Bootstrap method for characterizing the effect of uncertainty in shear strength parameters on slope reliability.Reliability Engineering and System Safety 140,99e106.
Liu,Y.,Lee,F.H.,Quek,S.T.,Chen,J.E.,Yi,J.T.,2015.Effect of spatial variation of strength and modulus on the lateral compression response of cement-admixed clay slab.Geotechnique 65(10),851e865.
Liu,Y.,Hu,J.,Wei,H.,Saw,A.L.,2017a.A direct simulation algorithm for a class of beta random fields in modelling material properties.Computer Methods in Applied Mechanics and Engineering 326,642e655.
Liu,Y.,Lee,F.H.,Quek,S.T.,Beer,M.,2014.Modified linear estimation method for generating multi-dimensional multi-variate Gaussian field in modelling material properties.Probabilistic Engineering Mechanics 38,42e53.
Liu,Y.,Quek,S.T.,Lee,F.H.,2016.Translation random field with marginal beta distribution in modeling material properties.Structural Safety 61,57e66.
Liu,Y.,Shields,M.D.,2017.A direct simulation method and lower-bound estimation for a class of gamma random fields with applications in modelling material properties.Probabilistic Engineering Mechanics 47,16e25.
Liu,Y.,Zhang,W.,Zhang,L.,Zhu,Z.R.,Hu,J.,Wei,H.,2018.Probabilistic stability analyses of undrained slopes by 3D random fields and finite element methods.Geoscience Frontiers 9(6),1657e1664.
Ni,S.H.,Lu,P.C.,Juang,C.H.,1996.A fuzzy neural network approach to evaluation of slope failure potential.Computer-Aided Civil and Infrastructure Engineering 11,59e66.
Qi,X.H.,Li,D.Q.,2018.Effect of spatial variability of shear strength parameters on critical slip surfaces of slope.Engineering Geology 239,41e49.
Qi,X.H.,Li,D.Q.,Phoon,K.K.,Cao,Z.J.,Tang,X.S.,2016.Simulation of geologic uncertainty using coupled Markov chain.Engineering Geology 207,129e140.
Shields,M.D.,Bocchini,P.,Deodatis,G.,2016.Discussion of Feng et al.(2014).“Statistical reconstruction of two-phase random media”.Computers and Structures 163,83e85.
Shields,M.D.,Deodatis,G.,2013.Estimation of evolutionary spectra for simulation of non-stationary and non-Gaussian stochastic processes.Computers and Structures 126,149e163.
Tang,X.S.,Li,D.Q.,Rong,G.,Phoon,K.K.,Zhou,C.B.,2013.Impact of copula selection on geotechnical reliability under incomplete probability information.Computers and Geotechnics 49,264e278.
Tang,X.S.,Li,D.Q.,Zhou,C.B.,Phoon,K.K.,2015.Copula-based approaches for evaluating slope reliability under incomplete probability information.Structural Safety 52,90e99.
Tang,Y.,Xu,J.,2016.Shield tunneling in rock-soil interface composite formations.Geotechnical and Geological Engineering.https://doi.org/10.1007/S10706-016-9994-9.
Taylor,D.W.,1937.Stability of earth slopes.Journal of Boston Society of Civil Engineers 24(3),197e246.
Toth,A.,Gong,Q.,Zhao,J.,2013.Case studies of TBM tunneling performance in rocksoil interface mixed ground.Tunnelling and Underground Space Technology 38,140e150.
West,L.J.,Hencher,S.R.,1991.Assessing the Stability of Slopes in Heterogeneous Soils.Proceedings of the 6th International Symposium on Landslides.Christchurch,New Zealand,pp.591e595.
Xiao,T.,Li,D.Q.,Cao,Z.J.,Zhang,L.M.,2018.CPT-based probabilistic characterization of three-dimensional spatial variability using MLE.Journal of Geotechnical and Geoenvironmental Engineering 144(5),04018023.
Zhang,J.,Qu,H.,Liao,Y.,Ma,Y.,2012.Seismic damage of earth structures of road engineering in the 2008 Wenchuan earthquake.Environmental Earth Sciences65,987e993.
Zhang,W.G.,Goh,A.T.C.,2012.Reliability assessment on ultimate and serviceability limit states and determination of critical factor of safety for underground rock caverns.Tunnelling and Underground Space Technology 32,221e230.
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