Advanced reliability analysis of slopes in spatially variable soils using multivariate adaptive regression splines
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摘要
This study aims to extend the multivariate adaptive regression splines(MARS)-Monte Carlo simulation(MCS) method for reliability analysis of slopes in spatially variable soils. This approach is used to explore the influences of the multiscale spatial variability of soil properties on the probability of failure(P_f) of the slopes. In the proposed approach, the relationship between the factor of safety and the soil strength parameters characterized with spatial variability is approximated by the MARS, with the aid of Karhunen-Loeve expansion. MCS is subsequently performed on the established MARS model to evaluate Pf.Finally, a nominally homogeneous cohesive-frictional slope and a heterogeneous cohesive slope, which are both characterized with different spatial variabilities, are utilized to illustrate the proposed approach.Results showed that the proposed approach can estimate the P_f of the slopes efficiently in spatially variable soils with sufficient accuracy. Moreover, the approach is relatively robust to the influence of different statistics of soil properties, thereby making it an effective and practical tool for addressing slope reliability problems concerning time-consuming deterministic stability models with low levels of P_f.Furthermore, disregarding the multiscale spatial variability of soil properties can overestimate or underestimate the P_f. Although the difference is small in general, the multiscale spatial variability of the soil properties must still be considered in the reliability analysis of heterogeneous slopes, especially for those highly related to cost effective and accurate designs.
This study aims to extend the multivariate adaptive regression splines(MARS)-Monte Carlo simulation(MCS) method for reliability analysis of slopes in spatially variable soils. This approach is used to explore the influences of the multiscale spatial variability of soil properties on the probability of failure(P_f) of the slopes. In the proposed approach, the relationship between the factor of safety and the soil strength parameters characterized with spatial variability is approximated by the MARS, with the aid of Karhunen-Loeve expansion. MCS is subsequently performed on the established MARS model to evaluate Pf.Finally, a nominally homogeneous cohesive-frictional slope and a heterogeneous cohesive slope, which are both characterized with different spatial variabilities, are utilized to illustrate the proposed approach.Results showed that the proposed approach can estimate the P_f of the slopes efficiently in spatially variable soils with sufficient accuracy. Moreover, the approach is relatively robust to the influence of different statistics of soil properties, thereby making it an effective and practical tool for addressing slope reliability problems concerning time-consuming deterministic stability models with low levels of P_f.Furthermore, disregarding the multiscale spatial variability of soil properties can overestimate or underestimate the P_f. Although the difference is small in general, the multiscale spatial variability of the soil properties must still be considered in the reliability analysis of heterogeneous slopes, especially for those highly related to cost effective and accurate designs.
This study aims to extend the multivariate adaptive regression splines(MARS)-Monte Carlo simulation(MCS) method for reliability analysis of slopes in spatially variable soils. This approach is used to explore the influences of the multiscale spatial variability of soil properties on the probability of failure(P_f) of the slopes. In the proposed approach, the relationship between the factor of safety and the soil strength parameters characterized with spatial variability is approximated by the MARS, with the aid of Karhunen-Loeve expansion. MCS is subsequently performed on the established MARS model to evaluate Pf.Finally, a nominally homogeneous cohesive-frictional slope and a heterogeneous cohesive slope, which are both characterized with different spatial variabilities, are utilized to illustrate the proposed approach.Results showed that the proposed approach can estimate the P_f of the slopes efficiently in spatially variable soils with sufficient accuracy. Moreover, the approach is relatively robust to the influence of different statistics of soil properties, thereby making it an effective and practical tool for addressing slope reliability problems concerning time-consuming deterministic stability models with low levels of P_f.Furthermore, disregarding the multiscale spatial variability of soil properties can overestimate or underestimate the P_f. Although the difference is small in general, the multiscale spatial variability of the soil properties must still be considered in the reliability analysis of heterogeneous slopes, especially for those highly related to cost effective and accurate designs.
引文
Cheng, M.Y., Cao, M.T., 2014. Accurately predicting building energy performance using evolutionary multivariate adaptive regression splines. Applied Soft Computing 22,178-188.
Ching, J., Phoon, K.K., 2013. Effect of element sizes in random field finite element simulations of soil shear strength. Computers and Structures 126,120-134.
Ching, J., Wang, J.S., 2016. Application of the transitional Markov chain Monte Carlo algorithm to probabilistic site characterization. Engineering Geology 203,151-167.
Cho, S.E., 2010. Probabilistic assessment of slope stability that considers the spatial variability of soil properties. Journal of Geotechnical and Geoenvironmental Engineering 136(7), 975-984.
Cho, S.E., 2012. Probabilistic analysis of seepage that considers the spatial variability of permeability for an embankment on soil foundation. Engineering Geology133-134, 30-39.
Dasaka, S.M., Zhang, L.M., 2012. Spatial variability of in situ weathered soil. Geotechnique 62(5), 375-384.
Fenton, G.A., Vanmarcke, E.H., 1990. Simulation of random fields via local average subdivision. Journal of Engineering Mechanics 116(8), 1733-1749.
Fenton, G.A., Griffiths, D.V., 2003. Bearing-capacity prediction of spatially random c-φsoils. Canadian Geotechnical Journal 40(1), 54-65.
Friedman, J.H., 1991. Multivariate adaptive regression splines. The Annals of Statistics 19(1), 1-67.
Griffiths, D.V., Fenton, G.A., 2004. Probabilistic slope stability analysis by finite elements. Journal of Geotechnical and Geoenvironmental Engineering 130(5),507-518.
Griffiths, D.V., Huang, J., Fenton, G.A., 2011. Probabilistic infinite slope analysis.Computers and Geotechnics 38(4), 577-584.
Hastie, T., Tibshirani, R., Friedman, J.H., 2009. The Elements of Statistical Learning:Data Mining, Inference and Prediction, second ed. Springer, California. 745 pp.
Huang, J., 2010. System reliability of slopes by RFEM. Soils and Foundations 50(3),343-353.
Huang, J., Lyamin, A.V., Griffiths, D.V., Krabbenhoft, K., Sloan, S.W., 2013. Quantitative risk assessment of landslide by limit analysis and random fields. Computers and Geotechnics 53, 60-67.
Huang, S.P., Quek, S.T., Phoon, K.K., 2001. Convergence study of the truncated Karhunen-Loeve expansion for simulation of stochastic processes. International Journal for Numerical Methods in Engineering 52(9), 1029-1043.
Ji, J., Liao, H.J., Low, B.K., 2012. Modeling 2-D spatial variation in slope reliability analysis using interpolated autocorrelations. Computers and Geotechnics 40,135-146.
Ji,J., Low, B.K., 2012. Stratified response surfaces for system probabilistic evaluation of slopes. Journal of Geotechnical and Geoenvironmental Engineering 138(11),1398-1406.
Ji,J., 2014. A simplified approach for modeling spatial variability of undrained shear strength in out-plane failure mode of earth embankment. Engineering Geology183, 315-323.
Ji, J., Zhang, C., Gao, Y., Kodikara, J., 2018. Effect of 2D spatial variability on slope reliability:a simplified FORM analysis. Geoscience Frontiers 9(6), 1631-1638.https://doi.org/10.1016/j.gsf.2017.08.004.
Ji,J.,Zhang, C., Gui, Y., Lu, Q., Kodikara,J., 2017. New observations on the application of LS-SVM in slope system reliability analysis. Journal of Computing in Civil Engineering 31(2), 06016002.
Jiang, S.H., 2014. A Non-intrusive Stochastic Method for Slope Reliability in Hydroelectricity Engineering. Ph.D thesis. Wuhan University, 224 pp.
Jiang, S.H., Li, D.Q., Zhang, L.M., Zhou, C.B., 2014. Slope reliability analysis considering spatially variable shear strength parameters using a non-intrusive stochastic finite element method. Engineering Geology 168,120-128.
Jiang, S.H., Li, D.Q., Cao, Z.J., Zhou, C.B., Phoon, K.K., 2015. Efficient system reliability analysis of slope stability in spatially variable soils using Monte Carlo simulation.Journal of Geotechnical and Geoenvironmental Engineering 141(2), 04014096.
Jiang, S.H., Huang, J.S., 2016. Efficient slope reliability analysis at low-probability levels in spatially variable soils. Computers and Geotechnics 75,18-27.
Kang, F., Han, S., Salgado, R., Li, J., 2015. System probabilistic stability analysis of soil slopes using Gaussian process regression with Latin hypercube sampling.Computers and Geotechnics 63,13-25.
Laloy, E., Rogiers, B., Vrugt, J.A., Mallants, D., Jacques, D., 2013. Efficient posterior exploration of a high-dimensional groundwater model from two-stage Markov chain Monte Carlo simulation and polynomial chaos expansion. Water Resources Research 49(5), 2664-2682.
Li, D., Chen, Y., Lu, W., Zhou, C., 2011. Stochastic response surface method for reliability analysis of rock slopes involving correlated non-normal variables.Computers and Geotechnics 38(1), 58-68.
Li, D.Q., Jiang, S.H., Cao, Z.J., Zhou, W., Zhou, C.B., Zhang, L.M., 2015. A multiple response-surface method for slope reliability analysis considering spatial variability of soil properties. Engineering Geology 187, 60-72.
Li, D.Q., Xiao, T., Cao, Z.J., Zhou, C.B., Zhang, L.M., 2016a. Enhancement of random finite element method in reliability analysis and risk assessment of soil slopes using Subset Simulation. Landslides 13, 293-303.
Li, K.S., Lumb, P., 1987. Probabilistic design of slopes. Canadian Geotechnical Journal24(4), 520-535.
Li, X.Y., Zhang, L.M., Gao, L., Zhu, H., 2017. Simplified slope reliability analysis considering spatial soil variability. Engineering Geology 216, 90-97.
Liu, L.LI.,Cheng, Y.M., 2016. Efficient system reliability analysis of soil slopes using multivariate adaptive regression splines-based Monte Carlo simulation. Computers and Geotechnics 79, 41-54.
Liu, L.L., Cheng, Y.M. Jiang, S.H., Zhang, S.H., Wang, X.M., Wu, Z.H., 2017a. Effects of spatial autocorrelation structure of permeability on seepage through an embankment on a soil foundation. Computers and Geotechnics 87, 62-75.
Liu, L.L.,Cheng, Y.M.,Zhang, S.H.,2017b. Conditional random field reliability analysis of a cohesion-frictional slope. Computers and Geotechnics 82,173-186.
Low, B.K., 2007. Reliability analysis of rock slopes involving correlated nonnormals.International Journal of Rock Mechanics and Mining Sciences 44(6),922-935.
Low, B.K., 2014. FORM, SORM, and spatial modeling in geotechnical engineering.Structural Safety 49, 56-64.
Lu, Z.M., Zhang, D.X., 2007. Stochastic simulations for flow in nonstationary randomly heterogeneous porous media using a KL-based moment-equation approach. Multiscale Modeling&Simulation 6(1), 228-245.
Phoon, K.K., Kulhawy, F.H., 1999. Characterization of geotechnical variability. Canadian Geotechnical Journal 36, 612-624.
Phoon, K.K., Huang, S.P., Quek, S.T., 2002. Implementation of Karhunen-Loeve expansion for simulation using a wavelet-Galerkin scheme. Probabilistic Engineering Mechanics 17(3), 293-303.
Santoso, A.M., Phoon, K.K., Quek, S.T., 2011. Effects of soil spatial variability on rainfall-induced landslides. Computers and Structures 89, 893-900.
Silvestrini, R.T., Montgomery, D.C., Jones, B., 2013. Comparing computer experiments for the Gaussian process model using integrated prediction variance.Quality Engineering 25(2), 164-174.
Srivastava, A., Sivakumar Babu, G.L., Haldar, S., 2010. Influence of spatial variability of permeability property on steady state seepage flow and slope stability analysis. Engineering Geology 110, 93-101.
Sudret, B., Kiureghian, A.D., 2002. Comparison of finite element reliability methods.Probabilistic Engineering Mechanics 17(4), 337-348.
Wang, Y., Cao, Z.J., Au, S.K., 2011. Practical reliability analysis of slope stability by advanced Monte Carlo simulations in a spreadsheet. Canadian Geotechnical Journal 48,162-172.
Wang, Y., Cao, Z., Li, D., 2016. Bayesian perspective on geotechnical variability and site characterization. Engineering Geology 203,117-125.
Zhang, W.G., Goh, A.T.C., 2013. Multivariate adaptive regression splines for analysis of geotechnical engineering systems. Computers and Geotechnics 48, 82-95.
Ching, J., Phoon, K.K., 2013. Effect of element sizes in random field finite element simulations of soil shear strength. Computers and Structures 126,120-134.
Ching, J., Wang, J.S., 2016. Application of the transitional Markov chain Monte Carlo algorithm to probabilistic site characterization. Engineering Geology 203,151-167.
Cho, S.E., 2010. Probabilistic assessment of slope stability that considers the spatial variability of soil properties. Journal of Geotechnical and Geoenvironmental Engineering 136(7), 975-984.
Cho, S.E., 2012. Probabilistic analysis of seepage that considers the spatial variability of permeability for an embankment on soil foundation. Engineering Geology133-134, 30-39.
Dasaka, S.M., Zhang, L.M., 2012. Spatial variability of in situ weathered soil. Geotechnique 62(5), 375-384.
Fenton, G.A., Vanmarcke, E.H., 1990. Simulation of random fields via local average subdivision. Journal of Engineering Mechanics 116(8), 1733-1749.
Fenton, G.A., Griffiths, D.V., 2003. Bearing-capacity prediction of spatially random c-φsoils. Canadian Geotechnical Journal 40(1), 54-65.
Friedman, J.H., 1991. Multivariate adaptive regression splines. The Annals of Statistics 19(1), 1-67.
Griffiths, D.V., Fenton, G.A., 2004. Probabilistic slope stability analysis by finite elements. Journal of Geotechnical and Geoenvironmental Engineering 130(5),507-518.
Griffiths, D.V., Huang, J., Fenton, G.A., 2011. Probabilistic infinite slope analysis.Computers and Geotechnics 38(4), 577-584.
Hastie, T., Tibshirani, R., Friedman, J.H., 2009. The Elements of Statistical Learning:Data Mining, Inference and Prediction, second ed. Springer, California. 745 pp.
Huang, J., 2010. System reliability of slopes by RFEM. Soils and Foundations 50(3),343-353.
Huang, J., Lyamin, A.V., Griffiths, D.V., Krabbenhoft, K., Sloan, S.W., 2013. Quantitative risk assessment of landslide by limit analysis and random fields. Computers and Geotechnics 53, 60-67.
Huang, S.P., Quek, S.T., Phoon, K.K., 2001. Convergence study of the truncated Karhunen-Loeve expansion for simulation of stochastic processes. International Journal for Numerical Methods in Engineering 52(9), 1029-1043.
Ji, J., Liao, H.J., Low, B.K., 2012. Modeling 2-D spatial variation in slope reliability analysis using interpolated autocorrelations. Computers and Geotechnics 40,135-146.
Ji,J., Low, B.K., 2012. Stratified response surfaces for system probabilistic evaluation of slopes. Journal of Geotechnical and Geoenvironmental Engineering 138(11),1398-1406.
Ji,J., 2014. A simplified approach for modeling spatial variability of undrained shear strength in out-plane failure mode of earth embankment. Engineering Geology183, 315-323.
Ji, J., Zhang, C., Gao, Y., Kodikara, J., 2018. Effect of 2D spatial variability on slope reliability:a simplified FORM analysis. Geoscience Frontiers 9(6), 1631-1638.https://doi.org/10.1016/j.gsf.2017.08.004.
Ji,J.,Zhang, C., Gui, Y., Lu, Q., Kodikara,J., 2017. New observations on the application of LS-SVM in slope system reliability analysis. Journal of Computing in Civil Engineering 31(2), 06016002.
Jiang, S.H., 2014. A Non-intrusive Stochastic Method for Slope Reliability in Hydroelectricity Engineering. Ph.D thesis. Wuhan University, 224 pp.
Jiang, S.H., Li, D.Q., Zhang, L.M., Zhou, C.B., 2014. Slope reliability analysis considering spatially variable shear strength parameters using a non-intrusive stochastic finite element method. Engineering Geology 168,120-128.
Jiang, S.H., Li, D.Q., Cao, Z.J., Zhou, C.B., Phoon, K.K., 2015. Efficient system reliability analysis of slope stability in spatially variable soils using Monte Carlo simulation.Journal of Geotechnical and Geoenvironmental Engineering 141(2), 04014096.
Jiang, S.H., Huang, J.S., 2016. Efficient slope reliability analysis at low-probability levels in spatially variable soils. Computers and Geotechnics 75,18-27.
Kang, F., Han, S., Salgado, R., Li, J., 2015. System probabilistic stability analysis of soil slopes using Gaussian process regression with Latin hypercube sampling.Computers and Geotechnics 63,13-25.
Laloy, E., Rogiers, B., Vrugt, J.A., Mallants, D., Jacques, D., 2013. Efficient posterior exploration of a high-dimensional groundwater model from two-stage Markov chain Monte Carlo simulation and polynomial chaos expansion. Water Resources Research 49(5), 2664-2682.
Li, D., Chen, Y., Lu, W., Zhou, C., 2011. Stochastic response surface method for reliability analysis of rock slopes involving correlated non-normal variables.Computers and Geotechnics 38(1), 58-68.
Li, D.Q., Jiang, S.H., Cao, Z.J., Zhou, W., Zhou, C.B., Zhang, L.M., 2015. A multiple response-surface method for slope reliability analysis considering spatial variability of soil properties. Engineering Geology 187, 60-72.
Li, D.Q., Xiao, T., Cao, Z.J., Zhou, C.B., Zhang, L.M., 2016a. Enhancement of random finite element method in reliability analysis and risk assessment of soil slopes using Subset Simulation. Landslides 13, 293-303.
Li, K.S., Lumb, P., 1987. Probabilistic design of slopes. Canadian Geotechnical Journal24(4), 520-535.
Li, X.Y., Zhang, L.M., Gao, L., Zhu, H., 2017. Simplified slope reliability analysis considering spatial soil variability. Engineering Geology 216, 90-97.
Liu, L.LI.,Cheng, Y.M., 2016. Efficient system reliability analysis of soil slopes using multivariate adaptive regression splines-based Monte Carlo simulation. Computers and Geotechnics 79, 41-54.
Liu, L.L., Cheng, Y.M. Jiang, S.H., Zhang, S.H., Wang, X.M., Wu, Z.H., 2017a. Effects of spatial autocorrelation structure of permeability on seepage through an embankment on a soil foundation. Computers and Geotechnics 87, 62-75.
Liu, L.L.,Cheng, Y.M.,Zhang, S.H.,2017b. Conditional random field reliability analysis of a cohesion-frictional slope. Computers and Geotechnics 82,173-186.
Low, B.K., 2007. Reliability analysis of rock slopes involving correlated nonnormals.International Journal of Rock Mechanics and Mining Sciences 44(6),922-935.
Low, B.K., 2014. FORM, SORM, and spatial modeling in geotechnical engineering.Structural Safety 49, 56-64.
Lu, Z.M., Zhang, D.X., 2007. Stochastic simulations for flow in nonstationary randomly heterogeneous porous media using a KL-based moment-equation approach. Multiscale Modeling&Simulation 6(1), 228-245.
Phoon, K.K., Kulhawy, F.H., 1999. Characterization of geotechnical variability. Canadian Geotechnical Journal 36, 612-624.
Phoon, K.K., Huang, S.P., Quek, S.T., 2002. Implementation of Karhunen-Loeve expansion for simulation using a wavelet-Galerkin scheme. Probabilistic Engineering Mechanics 17(3), 293-303.
Santoso, A.M., Phoon, K.K., Quek, S.T., 2011. Effects of soil spatial variability on rainfall-induced landslides. Computers and Structures 89, 893-900.
Silvestrini, R.T., Montgomery, D.C., Jones, B., 2013. Comparing computer experiments for the Gaussian process model using integrated prediction variance.Quality Engineering 25(2), 164-174.
Srivastava, A., Sivakumar Babu, G.L., Haldar, S., 2010. Influence of spatial variability of permeability property on steady state seepage flow and slope stability analysis. Engineering Geology 110, 93-101.
Sudret, B., Kiureghian, A.D., 2002. Comparison of finite element reliability methods.Probabilistic Engineering Mechanics 17(4), 337-348.
Wang, Y., Cao, Z.J., Au, S.K., 2011. Practical reliability analysis of slope stability by advanced Monte Carlo simulations in a spreadsheet. Canadian Geotechnical Journal 48,162-172.
Wang, Y., Cao, Z., Li, D., 2016. Bayesian perspective on geotechnical variability and site characterization. Engineering Geology 203,117-125.
Zhang, W.G., Goh, A.T.C., 2013. Multivariate adaptive regression splines for analysis of geotechnical engineering systems. Computers and Geotechnics 48, 82-95.
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