抗剪强度参数统计特征的精确估计方法（英文）
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摘要
强度参数的精度对岩土工程的成本和安全都至关重要。首先,本文对比了三种现有的强度参数统计特征计算方法的精度。在工程实践中,线性回归中的均值方差经常被误用为强度参数的方差,这会导致很大的误差。本文提出了一种改进的线性回归方法,它能够精确估计强度参数的均值和方差。改进的线性回归方法被用于小浪底心墙坝的抗剪强度数据分析,结果表明:改进线性回归方法能够提供最精确的强度参数估计;将无量纲的公式用于线性回归效果要好于有量纲的公式。本文提出的方法不仅能够用于三轴强度数据的分析,还可以应用于直剪数据分析以及成层土体的不排水强度分析。
The cost and safety of geotechnical engineering are highly depending on the accuracy of soil shear strength parameters. There are three methods often used to estimate soil shear strength parameters, i.e., moment method, 3-sigma rule and linear regression method. In this study, the accuracy of these three methods is compared. Traditional linear regression method(LRM) can only offer the mean of shear strength parameters. Some engineers misuse the standard error of shear strength indexes as the standard deviations. Such misuse may highly underestimate the uncertainty and induce high risk to the geotechnical design. A modified LRM is proposed to determine both the mean and variance of shear strength parameters. The moment method, three-sigma rule and LRM are used to analyze the tri-axial test data in Xiaolangdi Hydraulic Project and three numerical shear strength tests. The results demonstrate that: 1) The modified LRM can offer the most accurate estimation to shear strength parameters; 2) A dimensionless formula is much preferred in LRM rather than a dimensional formula. The stress ratio formula is much better than stress relation in the shear strength parameter analysis. The proposed method is applicable to shear strength parameter analysis for tri-axial test data, direct shear test and the un-drained shear strength test of stratified clay.
The cost and safety of geotechnical engineering are highly depending on the accuracy of soil shear strength parameters. There are three methods often used to estimate soil shear strength parameters, i.e., moment method, 3-sigma rule and linear regression method. In this study, the accuracy of these three methods is compared. Traditional linear regression method(LRM) can only offer the mean of shear strength parameters. Some engineers misuse the standard error of shear strength indexes as the standard deviations. Such misuse may highly underestimate the uncertainty and induce high risk to the geotechnical design. A modified LRM is proposed to determine both the mean and variance of shear strength parameters. The moment method, three-sigma rule and LRM are used to analyze the tri-axial test data in Xiaolangdi Hydraulic Project and three numerical shear strength tests. The results demonstrate that: 1) The modified LRM can offer the most accurate estimation to shear strength parameters; 2) A dimensionless formula is much preferred in LRM rather than a dimensional formula. The stress ratio formula is much better than stress relation in the shear strength parameter analysis. The proposed method is applicable to shear strength parameter analysis for tri-axial test data, direct shear test and the un-drained shear strength test of stratified clay.
引文
[1] PHOON K K. Role of reliability calculations in geotechnical design[J]. Georisk, 2017, 11(1):4-21.
[2] PHOON K K, RETIEF J V, CHING J, DITHINDE M,SCHWECKEN-DIEK T, WANG Y, ZHANG L M. Some observations on IS02394:2015 Annex D(reliability of geotechnical structures)[J]. Structural Safety, 2016, 62:24-33. DOI:10.1016/j.strusafe.2016.05.003.
[3] ZHANG J, WANG H, HUANG H W, CHEN L H. System reliability analysis of soil slopes stabilized with piles[J].Engineering Geology, 2017, 229(7):45-52. DOI:doi.org/10.1016/j.enggeo.2017.09.009.
[4] KHALKHALI A, SARMADI M, YOUSEFI S.Reliability-based robust multi-objective optimization of a5-DOF vehicle vibration model subjected to random road profiles[J]. Journal of Central South University, 2017, 24(1):104-113.
[5] CAO Z, WANG Y. Bayesian model comparison and characterization of undrained shear strength[J]. Journal of Geotechnical and Geoenvironmental Engineering, 2014,140(6):04014018. DOI:10.1061/(ASCE)GT. 1943-5606.0001108.
[6] LI D Q, ZHANG L, TANG X S, ZHOU W, LI J H, ZHOU C B, PHOON K K. Bivariate distribution of shear strength parameters using copulas and its impact on geotechnical system reliability[J]. Computers and Geotechnics, 2015, 68:184-195. DOI:10.1016/j.compgeo.2015.04.002.
[7] ZHANG L M, TANG W H, ZHANG L L. ZHENG J G.Reducing uncertainty of prediction from empirical correlations[J]. Journal of Geotechnical and Geoenvironmental Engineering, 2004, 130(5):526-534. DOI:10.1061/(ASCE)1090-0241(2004)130:5(526).
[8] ZHANG L L, ZHANG L M, TANG W H. Uncertainties of field pullout resistance of soil nails[J]. Journal of Geotechnical and Geoenvironmental Engineering, 2009,135(7):966-972. DOI:10.1061/(ASCE)GT. 1943-5606.0000014.
[9] ZHANG L L,ZHANG J,ZHANG L M, TANG W H. Back analysis of slope failure with Markov chain Monte Carlo simulation[J]. Computers and Geotechnics, 2010, 37(7):905-912. DOI:doi.org/10.1016/j.compgeo.2010.07.009.
[10] AL-NAQSHABANDY M S, LARSSON S. Effect of uncertainties of improved soil shear strength on the reliability of embankments[J]. Journal of Geotechnical and Geoenvironmental Engineering, 2013, 139(4):619-632. DOI:10.1061/(ASCE)GT. 1943-5606.0000798.
[11] ORR T L L. Defining and selecting characteristic values of geotechnical parameters for designs to Eurocode 7[J].Georisk:Assessment and Management of Risk for Engineered Systems and Geohazards, 2017, 11(1):103-115.
[12] NG I T, YUEN K V, DONG L. Estimation of undrained shear strength in moderately OC clays based on field vane test data[J]. Acta Geotechnica, 2017, 12(1):145-156. DOI:10.1007/s11440-016-0433-0.
[13] ZHANG S, DU H, HARBOR J. The effect of confining pressure and water content on compressive strength and deformation of ice-rich silty sand[J]. Permafrost and Periglacial Processes, 2017, 28(1):298-305. DOI:doi.org/10.1002/ppp.1906
[14] DUNCAN J M. Factors of safety and reliability in geotechnical engineering[J]. Journal of Geotechnical and Geoenvironmental Engineering, 2000, 126(4):307-316. DOI:10.1061/(ASCE)1090-0241(2000)126:4(307).
[15] FOYE K C, SALGADO R, SCOTT B. Assessment of variable uncertainties for reliability-based design of foundations[J]. Journal of Geotechnical and Geoenvironmental Engineering, 2006, 132(9):1197-1207. DOI:10.1061/(ASCE)1090-0241(2006)132:9(1197).
[16] GAO Y, WANG Y H, SU C P. Mechanisms of aging-induced modulus changes in sand under isotropic and anisotropic loading[J]. Journal of Geotechnical and Geoenvironmental Engineering, 2006, 139(3):470-482. DOI:10.1061/(ASCE)GT. 1943-5606.0000772.
[17] XIE Q. Report of digging and sampling experiment of cut-off wall of main dam of Xiaolangdi and comprehensive analysis of site detection results[R]. 2001.(in Chinese)
[18] WEISBERG S. Applied linear regression[M]. New Jersey:John Wiley&Sons, Inc., Hoboken, 2005.
[19] LINDLEY D V. Regression lines and the linear functional relationship[J]. Supplement to the Journal of the Royal Statistical Society, 1947, 9(2):218-244.
[20] PARADINE C G, RIVETT B H. Statistics for technologists[M]. London:English Universities Press Ltd. 1953.
[21] FISHER R A, YATES F. Statistical tables, for biological agricultural and medical research,[M]. 6th Edition. London:Oliver&Boyd, 1963.
[22] YAN X, SU X G. Linear regression analysis-Theory and Computing[M]. Singapore:World Scientific Publishing Co.Pte. Ltd. 2009.
[23] LUMB P. The marine soils of Hong Kong and Macau[C]//Proceedings of the International Symposium on Soft Clay.Bangkok, Thailand, 1977:45-58.
[24] DNV/Norsk. Hydro technical report No. 2006-1437.guidance notes statistical representation of soil data[R].2006.
[25] MARK D M, CHURCH M. On the misuse of regression in earth science[J]. Mathematical Geology, 1977, 9(1):63-75.
[26] MANN C J. Misuses of linear regression in earth sciences[M]//Use and Abuse of Statistical Methods in the Earth Sciences. New York:Oxford University Press, 1987, 1:74-106.
[27] KENDALL M G, STUART A. The advanced theory of statistics, vol. 2[M]. New York:Hafner, 1965.
[28] CHEN Li-hong, CHEN Zu-yu, LI Guang-xin. A modified linear regression method to estimate shear strength parameters[J]. Rock and Soil Mechanics, 2007, 28(7):1421-1426.(in Chinese)
[29] LUMB P. Safety factors and the probability distribution of soil strength[J]. Canadian geotechnical Journal, 1970, 7(3):225-242.
[30] CHEN L H, CHEN Z Y. Effect of nonlinear strength of rockfill on slope stability of high earth-rock dam[J]. Rock and Soil Mechanics, 2007, 9(28):1807-1810.(in Chinese)
[31] KULHAWY F H. On the evaluation of soil properties[J].ASCE Geotechnical Special Publication, 1992, 31:95-115.
[32] PHOON K K, KULHAWY F H. Characterization of geotechnical variability[J]. Canadian Geotechnical Journal,1999, 36:612-624. DOI:10.1139/t99-038.
[33] CHING J Y, CHEN J R, YEH J Y, PHOON K K. Updating uncertainties in friction angles of clean sands[J]. Journal of Geotechnical and Geoenvironmental Engineering, 2012,138(2):217-229. DOI:10.1061/(ASCE)GT. 1943-5606.0000573.
[2] PHOON K K, RETIEF J V, CHING J, DITHINDE M,SCHWECKEN-DIEK T, WANG Y, ZHANG L M. Some observations on IS02394:2015 Annex D(reliability of geotechnical structures)[J]. Structural Safety, 2016, 62:24-33. DOI:10.1016/j.strusafe.2016.05.003.
[3] ZHANG J, WANG H, HUANG H W, CHEN L H. System reliability analysis of soil slopes stabilized with piles[J].Engineering Geology, 2017, 229(7):45-52. DOI:doi.org/10.1016/j.enggeo.2017.09.009.
[4] KHALKHALI A, SARMADI M, YOUSEFI S.Reliability-based robust multi-objective optimization of a5-DOF vehicle vibration model subjected to random road profiles[J]. Journal of Central South University, 2017, 24(1):104-113.
[5] CAO Z, WANG Y. Bayesian model comparison and characterization of undrained shear strength[J]. Journal of Geotechnical and Geoenvironmental Engineering, 2014,140(6):04014018. DOI:10.1061/(ASCE)GT. 1943-5606.0001108.
[6] LI D Q, ZHANG L, TANG X S, ZHOU W, LI J H, ZHOU C B, PHOON K K. Bivariate distribution of shear strength parameters using copulas and its impact on geotechnical system reliability[J]. Computers and Geotechnics, 2015, 68:184-195. DOI:10.1016/j.compgeo.2015.04.002.
[7] ZHANG L M, TANG W H, ZHANG L L. ZHENG J G.Reducing uncertainty of prediction from empirical correlations[J]. Journal of Geotechnical and Geoenvironmental Engineering, 2004, 130(5):526-534. DOI:10.1061/(ASCE)1090-0241(2004)130:5(526).
[8] ZHANG L L, ZHANG L M, TANG W H. Uncertainties of field pullout resistance of soil nails[J]. Journal of Geotechnical and Geoenvironmental Engineering, 2009,135(7):966-972. DOI:10.1061/(ASCE)GT. 1943-5606.0000014.
[9] ZHANG L L,ZHANG J,ZHANG L M, TANG W H. Back analysis of slope failure with Markov chain Monte Carlo simulation[J]. Computers and Geotechnics, 2010, 37(7):905-912. DOI:doi.org/10.1016/j.compgeo.2010.07.009.
[10] AL-NAQSHABANDY M S, LARSSON S. Effect of uncertainties of improved soil shear strength on the reliability of embankments[J]. Journal of Geotechnical and Geoenvironmental Engineering, 2013, 139(4):619-632. DOI:10.1061/(ASCE)GT. 1943-5606.0000798.
[11] ORR T L L. Defining and selecting characteristic values of geotechnical parameters for designs to Eurocode 7[J].Georisk:Assessment and Management of Risk for Engineered Systems and Geohazards, 2017, 11(1):103-115.
[12] NG I T, YUEN K V, DONG L. Estimation of undrained shear strength in moderately OC clays based on field vane test data[J]. Acta Geotechnica, 2017, 12(1):145-156. DOI:10.1007/s11440-016-0433-0.
[13] ZHANG S, DU H, HARBOR J. The effect of confining pressure and water content on compressive strength and deformation of ice-rich silty sand[J]. Permafrost and Periglacial Processes, 2017, 28(1):298-305. DOI:doi.org/10.1002/ppp.1906
[14] DUNCAN J M. Factors of safety and reliability in geotechnical engineering[J]. Journal of Geotechnical and Geoenvironmental Engineering, 2000, 126(4):307-316. DOI:10.1061/(ASCE)1090-0241(2000)126:4(307).
[15] FOYE K C, SALGADO R, SCOTT B. Assessment of variable uncertainties for reliability-based design of foundations[J]. Journal of Geotechnical and Geoenvironmental Engineering, 2006, 132(9):1197-1207. DOI:10.1061/(ASCE)1090-0241(2006)132:9(1197).
[16] GAO Y, WANG Y H, SU C P. Mechanisms of aging-induced modulus changes in sand under isotropic and anisotropic loading[J]. Journal of Geotechnical and Geoenvironmental Engineering, 2006, 139(3):470-482. DOI:10.1061/(ASCE)GT. 1943-5606.0000772.
[17] XIE Q. Report of digging and sampling experiment of cut-off wall of main dam of Xiaolangdi and comprehensive analysis of site detection results[R]. 2001.(in Chinese)
[18] WEISBERG S. Applied linear regression[M]. New Jersey:John Wiley&Sons, Inc., Hoboken, 2005.
[19] LINDLEY D V. Regression lines and the linear functional relationship[J]. Supplement to the Journal of the Royal Statistical Society, 1947, 9(2):218-244.
[20] PARADINE C G, RIVETT B H. Statistics for technologists[M]. London:English Universities Press Ltd. 1953.
[21] FISHER R A, YATES F. Statistical tables, for biological agricultural and medical research,[M]. 6th Edition. London:Oliver&Boyd, 1963.
[22] YAN X, SU X G. Linear regression analysis-Theory and Computing[M]. Singapore:World Scientific Publishing Co.Pte. Ltd. 2009.
[23] LUMB P. The marine soils of Hong Kong and Macau[C]//Proceedings of the International Symposium on Soft Clay.Bangkok, Thailand, 1977:45-58.
[24] DNV/Norsk. Hydro technical report No. 2006-1437.guidance notes statistical representation of soil data[R].2006.
[25] MARK D M, CHURCH M. On the misuse of regression in earth science[J]. Mathematical Geology, 1977, 9(1):63-75.
[26] MANN C J. Misuses of linear regression in earth sciences[M]//Use and Abuse of Statistical Methods in the Earth Sciences. New York:Oxford University Press, 1987, 1:74-106.
[27] KENDALL M G, STUART A. The advanced theory of statistics, vol. 2[M]. New York:Hafner, 1965.
[28] CHEN Li-hong, CHEN Zu-yu, LI Guang-xin. A modified linear regression method to estimate shear strength parameters[J]. Rock and Soil Mechanics, 2007, 28(7):1421-1426.(in Chinese)
[29] LUMB P. Safety factors and the probability distribution of soil strength[J]. Canadian geotechnical Journal, 1970, 7(3):225-242.
[30] CHEN L H, CHEN Z Y. Effect of nonlinear strength of rockfill on slope stability of high earth-rock dam[J]. Rock and Soil Mechanics, 2007, 9(28):1807-1810.(in Chinese)
[31] KULHAWY F H. On the evaluation of soil properties[J].ASCE Geotechnical Special Publication, 1992, 31:95-115.
[32] PHOON K K, KULHAWY F H. Characterization of geotechnical variability[J]. Canadian Geotechnical Journal,1999, 36:612-624. DOI:10.1139/t99-038.
[33] CHING J Y, CHEN J R, YEH J Y, PHOON K K. Updating uncertainties in friction angles of clean sands[J]. Journal of Geotechnical and Geoenvironmental Engineering, 2012,138(2):217-229. DOI:10.1061/(ASCE)GT. 1943-5606.0000573.
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