Probabilistic methods for unified treatment of geotechnical and geological uncertainties in a geotechnical analysis

Abstract There are typically three types of models involved in a geotechnical analysis, i.e., the geologic model, the ground model, and the geotechnical model, each of which may be associated with uncertainty to a different extent. However, in a typical geotechnical analysis the geological uncertainty is seldom characterized and considered explicitly. In this paper, we discuss the probabilistic tools developed in the geotechnical profession for tasks such as uncertainty characterization, assessment of impact of uncertainties, uncertainty reduction, and evaluation of the value of uncertainty reduction. We postulate that the same tools may be used for a unified treatment of various types of uncertainties in a geotechnical analysis, which would necessitate the collaboration of the engineering geologists and the geotechnical engineers to comprehensively characterize these uncertainties consistently. To this end, the probabilistic tools or methods that are widely used in geotechnical engineering are examined to determine their applicability in the evaluation of geological uncertainties. Examples are provided to illustrate various concepts introduced in this paper.

[1]  W. Tang,et al.  SITE EXPLORATION STRATEGY FOR GEOLOGIC ANOMALY CHARACTERIZATION , 1993 .

[2]  Hongwei Huang,et al.  Characterising geotechnical model uncertainty by hybrid Markov Chain Monte Carlo simulation , 2012 .

[3]  Youssef M. A. Hashash,et al.  Simplified Model for Wall Deflection and Ground-Surface Settlement Caused by Braced Excavation in Clays , 2007 .

[4]  A.C.W.M. Vrouwenvelder,et al.  Value of information in retrofitting of flood defenses , 2015 .

[5]  Oswald Marinoni,et al.  Improving geological models using a combined ordinary–indicator kriging approach , 2003 .

[6]  Lei Wang,et al.  Reliability-based robust geotechnical design of spread foundations using multi-objective genetic algorithm , 2013 .

[7]  W. Tang,et al.  EFFICIENT RELIABILITY EVALUATION USING SPREADSHEET , 1997 .

[8]  Hongwei Huang,et al.  Efficient response surface method for practical geotechnical reliability analysis , 2015 .

[9]  L. Zhang,et al.  Bayesian Model Calibration Using Geotechnical Centrifuge Tests , 2009 .

[10]  Stephen Wu,et al.  Optimal Sampling Placement in a Gaussian Random Field Based on Value of Information , 2018, ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering.

[11]  Hongwei Huang,et al.  Bayesian Updating of Soil Parameters for Braced Excavations Using Field Observations , 2013 .

[12]  Jun Ma,et al.  Identification of representative slip surfaces for reliability analysis of soil slopes based on shear strength reduction , 2017 .

[13]  Wilson H. Tang,et al.  KRIGING NUMERICAL MODELS FOR GEOTECHNICAL RELIABILITY ANALYSIS , 2011 .

[14]  Yu Wang,et al.  Expanded reliability-based design of piles in spatially variable soil using efficient Monte Carlo simulations , 2013 .

[15]  Jianye Ching,et al.  Simplified procedure for estimation of liquefaction-induced settlement and site-specific probabilistic settlement exceedance curve using cone penetration test (CPT) , 2013 .

[16]  G. Fenton.  Random Field Modeling of CPT Data , 2000 .

[17]  Jie Zhang,et al.  Bayesian Methods for Geotechnical Applications—A Practical Guide , 2017 .

[18]  Bak Kong Low,et al.  Probabilistic evaluation of ground-support interaction for deep rock excavation using artificial neural network and uniform design , 2012 .

[19]  C. H. Juang,et al.  CPT-based liquefaction analysis, Part 2: Reliability for design , 2000 .

[20]  Kok-Kwang Phoon,et al.  Efficient Evaluation of Reliability for Slopes with Circular Slip Surfaces Using Importance Sampling , 2009 .

[21]  Zhongjie Zhang,et al.  Implementation of LRFD of Drilled Shafts in Louisiana , 2012 .

[22]  Junjie Li,et al.  System probabilistic stability analysis of soil slopes using Gaussian process regression with Latin hypercube sampling , 2015 .

[23]  Amir Hossein Alavi,et al.  Machine learning in geosciences and remote sensing , 2016 .

[24]  A. Keith Turner,et al.  Challenges and trends for geological modelling and visualisation , 2006 .

[25]  Kok-Kwang Phoon,et al.  Probability distribution for mobilised shear strengths of spatially variable soils under uniform stress states , 2013 .

[26]  Dian-Qing Li,et al.  A generalized surrogate response aided-subset simulation approach for efficient geotechnical reliability-based design , 2016 .

[27]  Yu Wang,et al.  Bayesian Approach for Probabilistic Site Characterization Using Cone Penetration Tests , 2013 .

[28]  Siu-Kui Au,et al.  Three-dimensional slope reliability and risk assessment using auxiliary random finite element method , 2016 .

[29]  Dian-Qing Li,et al.  CPT-Based probabilistic characterization of three-dimensional spatial variability using MLE , 2018 .

[30]  Lulu Zhang,et al.  Unsaturated soil slope characterization with Karhunen–Loève and polynomial chaos via Bayesian approach , 2018, Engineering with Computers.

[31]  Wilson H. Tang.  Probabilistic Evaluation of Penetration Resistances , 1979 .

[32]  D. V. Griffiths,et al.  Risk Assessment in Geotechnical Engineering , 2008 .

[33]  Li Min Zhang,et al.  Probabilistic model calibration for soil slope under rainfall: effects of measurement duration and frequency in field monitoring , 2014 .

[34]  Peng Zeng,et al.  An approximation to the reliability of series geotechnical systems using a linearization approach , 2014 .

[35]  Daniel Straub,et al.  Reliability updating with equality information , 2011, 1203.5405.

[36]  Eungyu Park,et al.  A multidimensional, generalized coupled Markov chain model for surface and subsurface characterization , 2010 .

[37]  Yu WangY. Wang,et al.  Practical reliability analysis of slope stability by advanced Monte Carlo simulations in a spreadsheet , 2011 .

[38]  K. Phoon,et al.  Characterization of Geotechnical Variability , 1999 .

[39]  Eulogio Pardo-Igúzquiza,et al.  AMLE3D: a computer program for the inference of spatial covariance parameters by approximate maximum likelihood estimation , 1997 .

[40]  G. Baecher.  Reliability and Statistics in Geotechnical Engineering , 2003 .

[41]  Yu Wang,et al.  Reliability-based design of spread foundations by Monte Carlo simulations , 2011 .

[42]  John Knill,et al.  Core values: the first Hans-Cloos lecture , 2002 .

[43]  Robert Y. Liang,et al.  Quantifying stratigraphic uncertainties by stochastic simulation techniques based on Markov random field , 2016 .

[44]  Sez Atamturktur,et al.  Efficient robust geotechnical design of drilled shafts in clay using a spreadsheet , 2015 .

[45]  Gordon A. Fenton,et al.  Estimation for Stochastic Soil Models , 1999 .

[46]  Kok-Kwang Phoon,et al.  Fully Probabilistic Framework for Evaluating Excavation-Induced Damage Potential of Adjacent Buildings , 2011 .

[47]  Shadi Najjar,et al.  Importance of Lower-Bound Capacities in the Design of Deep Foundations , 2009 .

[48]  D. V. Griffiths,et al.  Reliability-based geotechnical design in 2014 Canadian Highway Bridge Design Code , 2016 .

[49]  K. Phoon,et al.  Observations on Geotechnical Reliability-Based Design Development in North America , 2013 .

[50]  Wilson Tang.  Bayesian method; a natural tool for processing geotechnical information , 2008 .

[51]  Bak Kong Low,et al.  Insights from Reliability-Based Design to Complement Load and Resistance Factor Design Approach , 2017 .

[53]  Bak Kong Low.  Reliability-based design: Practical procedures, geotechnical examples, and insights , 2018 .

[54]  Yu Wang,et al.  Bayesian model comparison and selection of spatial correlation functions for soil parameters , 2014 .

[55]  Junjie Li,et al.  Artificial Bee Colony Algorithm Optimized Support Vector Regression for System Reliability Analysis of Slopes , 2016, J. Comput. Civ. Eng..

[56]  Yu Wang,et al.  Direct simulation of random field samples from sparsely measured geotechnical data with consideration of uncertainty in interpretation , 2018, Canadian Geotechnical Journal.

[57]  R. Rackwitz,et al.  Reviewing probabilistic soils modelling , 2000 .

[58]  Robert Y. Liang,et al.  A method for slope stability analysis considering subsurface stratigraphic uncertainty , 2018, Landslides.

[59]  K. Phoon,et al.  Complexity of Limit Equilibrium Based Slope Reliability Problems , 2010 .

[60]  H. H. Einstein,et al.  Probabilistic and Statistical Methods in Engineering Geology I. Problem Statement and Introduction to Solution , 1982 .

[61]  Erik H. Vanmarcke,et al.  Random Fields: Analysis and Synthesis. , 1985 .

[62]  Michael A. Hicks,et al.  Reduction of slope stability uncertainty based on hydraulic measurement via inverse analysis , 2016 .

[63]  Sondipon Adhikari,et al.  System reliability analysis of soil slopes with general slip surfaces using multivariate adaptive regression splines , 2017 .

[64]  T. Schweckendiek,et al.  Reliability updating and decision analysis for head monitoring of levees , 2013 .

[65]  Bruno Sudret,et al.  Meta-models for structural reliability and uncertainty quantification , 2012, 1203.2062.

[66]  Lei Wang,et al.  Probabilistic Inverse Analysis of Excavation-Induced Wall and Ground Responses for Assessing Damage Potential of Adjacent Buildings , 2014, Geotechnical and Geological Engineering.

[67]  Pijush Samui,et al.  Spatial Variability of Rock Depth in Bangalore Using Geostatistical, Neural Network and Support Vector Machine Models , 2008 .

[68]  P. G. Fookes,et al.  Geology for Engineers: the Geological Model, Prediction and Performance , 1997, Quarterly Journal of Engineering Geology.

[69]  János Fodor,et al.  Traditional and New Ways to Handle Uncertainty in Geology , 2001 .

[70]  James R. Martin,et al.  Model selection in geological and geotechnical engineering in the face of uncertainty - Does a complex model always outperform a simple model? , 2018, Engineering Geology.

[71]  Yu Wang,et al.  Bayesian approach for probabilistic characterization of sand friction angles , 2010 .

[72]  Youssef M A Hashash,et al.  Simplified Model for Evaluating Damage Potential of Buildings Adjacent to a Braced Excavation , 2009 .

[73]  Wenping Gong,et al.  Subdomain sampling methods - efficient algorithm for estimating failure probability , 2017 .

[74]  Wilson H. Tang.  A Bayesian Evaluation of Information for Foundation Engineering Design , 2017 .

[75]  Lei Wang,et al.  Robust Geotechnical Design of Drilled Shafts in Sand: New Design Perspective , 2013 .

[76]  I. Papaioannou,et al.  Reliability updating in geotechnical engineering including spatial variability of soil , 2012 .

[77]  K. Phoon,et al.  Characterisation of model uncertainties for laterally loaded rigid drilled shafts , 2005 .

[78]  Gordon A. Fenton,et al.  Influence of spatial variability on slope reliability using 2-D random fields. , 2009 .

[79]  Aurèle Parriaux,et al.  Geological uncertainties associated with 3-D subsurface models , 2006, Comput. Geosci..

[80]  Adrian E. Raftery,et al.  Bayesian model averaging: a tutorial (with comments by M. Clyde, David Draper and E. I. George, and a rejoinder by the authors , 1999 .

[81]  W. Tang,et al.  Efficient Spreadsheet Algorithm for First-Order Reliability Method , 2007 .

[82]  Jianye Ching,et al.  New Sampling Method and Procedures for Estimating Failure Probability , 2016 .

[83]  Kok-Kwang Phoon,et al.  Constructing Site-Specific Multivariate Probability Distribution Model Using Bayesian Machine Learning , 2019, Journal of Engineering Mechanics.

[84]  Wilson H. Tang,et al.  REDUCING UNCERTAINTY OF PREDICTION FROM EMPIRICAL CORRELATIONS , 2004 .

[85]  Zhe Luo,et al.  Probabilistic back analysis of slope failure – A case study in Taiwan , 2013 .

[86]  Robert V. Whitman,et al.  EVALUATING CALCULATED RISK IN GEOTECHNICAL ENGINEERING , 1984 .

[87]  M.K. Lo,et al.  Bayesian updating of subsurface spatial variability for improved prediction of braced excavation response , 2019, Canadian Geotechnical Journal.

[88]  G. L. Sivakumar Babu,et al.  Reliability Analysis of Unsaturated Soil Slopes , 2005 .

[89]  Steven L. Kramer,et al.  Geotechnical Characterization and Random Field Modeling of Desiccated Clay , 2012 .

[90]  Kok-Kwang Phoon,et al.  Identification of statistically homogeneous soil layers using modified Bartlett statistics , 2003 .

[91]  Kok-Kwang Phoon,et al.  Role of reliability calculations in geotechnical design , 2017 .

[92]  Fumie Yokota,et al.  Value of Information Analysis in Environmental Health Risk Management Decisions: Past, Present, and Future , 2004, Risk analysis : an official publication of the Society for Risk Analysis.

[93]  Jeffrey R. Keaton,et al.  Selection of Geotechnical Parameters Using the Statistics of Small Samples , 2014 .

[94]  Shadi Najjar,et al.  Rational Decision Framework for Designing Pile-Load Test Programs , 2017 .

[95]  Wilson H. Tang,et al.  Probability Concepts in Engineering: Emphasis on Applications to Civil and Environmental Engineering , 2006 .

[96]  Andrew Brownlow.  Evaluation and Uncertainty Quantification of VS30 Models Using a Bayesian Framework for Better Prediction of Seismic Site Conditions , 2017 .

[97]  K. Phoon,et al.  Bayesian identification of random field model using indirect test data , 2016 .

[98]  Wan-Huan Zhou,et al.  An efficient probabilistic back-analysis method for braced excavations using wall deflection data at multiple points , 2017 .

[99]  Jie Zhang,et al.  Bayesian Framework for Characterizing Geotechnical Model Uncertainty , 2009 .

[100]  M. Jaksa.  The influence of spatial variability on the geotechnical design properties of a stiff, overconsolidated clay. , 1995 .

[101]  Jie Zhang,et al.  Slope Reliability Analysis Considering Site-Specific Performance Information , 2011 .

[102]  Weidong Li,et al.  Markov Chain Random Fields for Estimation of Categorical Variables , 2007 .

[103]  S. Parry,et al.  Engineering geological models: an introduction: IAEG commission 25 , 2014, Bulletin of Engineering Geology and the Environment.

[104]  C. Hsein Juang,et al.  Characterization of the uncertainty of the Robertson and Wride model for liquefaction potential evaluation , 2004 .

[105]  Dian-Qing Li,et al.  Probabilistic Stratification Modeling in Geotechnical Site Characterization , 2017 .

[106]  C. H. Juang,et al.  Reliability-based code revision for design of pile foundations: Practice in Shanghai, China , 2015 .

[107]  Jie Zhang,et al.  Geotechnical reliability analysis with limited data: Consideration of model selection uncertainty , 2014 .

[108]  Kok-Kwang Phoon,et al.  Risk and Reliability in Geotechnical Engineering , 2018 .

[109]  Kok-Kwang Phoon,et al.  Model uncertainty of cylindrical shear method for calculating the uplift capacity of helical anchors in clay , 2016 .

[110]  John Burland.  Nash lecture; The teaching of soil mechanics; a personal view , 1989 .

[111]  Sung Eun Cho,et al.  Probabilistic stability analyses of slopes using the ANN-based response surface , 2009 .

[112]  Dian-Qing Li,et al.  Response surface methods for slope reliability analysis: Review and comparison , 2016 .

[113]  Jeffrey R. Keaton,et al.  Engineering Geology: Fundamental Input or Random Variable? , 2013 .

[114]  J. M. Duncan,et al.  Factors of Safety and Reliability in Geotechnical Engineering , 2000 .

[115]  Kok-Kwang Phoon,et al.  R-LRFD: Load and resistance factor design considering robustness , 2016 .

[116]  Xiaojun Li,et al.  Coal seam surface modeling and updating with multi-source data integration using Bayesian Geostatistics , 2013 .

[117]  K. Phoon,et al.  Statistical characterization of random field parameters using frequentist and Bayesian approaches , 2016 .

[118]  Evert Hoek,et al.  Putting numbers to geology—an engineer's viewpoint , 1999, Quarterly Journal of Engineering Geology.

[119]  Gregory B. Baecher,et al.  Estimating Autocovariance of In‐Situ Soil Properties , 1993 .

[120]  Sunny Ye Fang,et al.  First-Order Reliability Method for Probabilistic Liquefaction Triggering Analysis using CPT , 2006 .

[121]  Dian-Qing Li,et al.  Simulation of geologic uncertainty using coupled Markov chain , 2016 .

[122]  Wilson H. Tang,et al.  Efficient system reliability analysis illustrated for a retaining wall and a soil slope , 2011 .

[123]  Bak Kong Low,et al.  System Reliability Assessment for a Rock Tunnel with Multiple Failure Modes , 2013, Rock Mechanics and Rock Engineering.

[124]  Kok-Kwang Phoon,et al.  On characterizing spatially variable soil Young’s modulus using spatial average , 2017 .

[125]  Michel Dekking,et al.  A Markov Chain Model for Subsurface Characterization: Theory and Applications , 2001 .

[126]  C. Juang,et al.  Probabilistic analysis of tunnel longitudinal performance based upon conditional random field simulation of soil properties , 2018 .

[127]  Wilson H. Tang.  Updating anomaly statistics—single anomaly case , 1986 .

[128]  James R. Martin,et al.  Calibration of empirical models considering model fidelity and model robustness — Focusing on predictions of liquefaction-induced settlements , 2016 .

[129]  Wilson H. Tang,et al.  Optimal ground-water detection monitoring system design under uncertainty , 1999 .

[130]  Robert Y. Liang,et al.  A hidden Markov random field model based approach for probabilistic site characterization using multiple cone penetration test data , 2018 .

[131]  K. Phoon,et al.  Effective Young’s modulus of a spatially variable soil mass under a footing , 2018, Structural Safety.

[132]  Lei Wang,et al.  Robust design in geotechnical engineering – an update , 2014 .

[133]  Kok-Kwang Phoon,et al.  Characterization of Model Uncertainty for Cantilever Deflections in Undrained Clay , 2015 .

[134]  C. Hsein Juang,et al.  Bayesian updating of KJHH model for prediction of maximum ground settlement in braced excavations using centrifuge data , 2012 .

[135]  Kenneth Gavin,et al.  System reliability of slopes using multimodal optimisation , 2016 .

[136]  Geoffrey E. Hinton,et al.  Deep Learning , 2015, Nature.

[137]  Yu Wang,et al.  Simulation of cross-correlated random field samples from sparse measurements using Bayesian compressive sensing , 2018, Mechanical Systems and Signal Processing.

[138]  Tien H. Wu,et al.  Prediction and mapping of landslide hazard , 2000 .

[139]  M. Hicks,et al.  Effect of sampling plan and trend removal on residual uncertainty , 2018 .

[140]  Jianye Ching,et al.  Cone penetration test (CPT)-based stratigraphic profiling using the wavelet transform modulus maxima method , 2015 .

[141]  John T. Christian,et al.  Geotechnical Engineering Reliability: How Well Do We Know What We Are Doing? , 2004 .

[142]  O. Ditlevsen.  Narrow Reliability Bounds for Structural Systems , 1979 .

[143]  J. Wellmann,et al.  Uncertainties have a meaning: Information entropy as a quality measure for 3-D geological models , 2012 .

[144]  Kok-Kwang Phoon,et al.  Random field characterisation of stress-normalised cone penetration testing parameters , 2005 .

[145]  Yusuke Honjo,et al.  Inverse analysis of an embankment on soft clay by extended Bayesian method , 1994 .

[146]  Bruno Sudret,et al.  Application of Conditional Random Fields and Sparse Polynomial Chaos Expansions to Geotechnical Problems , 2015 .

[148]  Y. Zhou,et al.  Laboratory characterization of rainfall-induced loess slope failure , 2017 .

[149]  Masahiro Shirato,et al.  DETERMINATION OF PARTIAL FACTORS FOR A VERTICALLY LOADED PILE BASED ON RELIABILITY ANALYSIS , 2002 .

[150]  Yan-Gang Zhao,et al.  Closure of "Estimating Joint Failure Probability of Series Structural Systems" , 2007 .

[151]  Lei Wang,et al.  Robust design of rock slopes with multiple failure modes: modeling uncertainty of estimated parameter statistics with fuzzy number , 2014, Environmental Earth Sciences.

[152]  J. Zhang,et al.  Study of time-dependent reliability of old man-made slopes considering model uncertainty , 2009 .

[153]  Giovanni B. Crosta,et al.  Distributed modelling of shallow landslides triggered by intense rainfall , 2003 .

[154]  Dian-Qing Li,et al.  Slope safety evaluation by integrating multi-source monitoring information , 2014 .

[155]  C. Juang,et al.  A new framework for probabilistic analysis of the performance of a supported excavation in clay considering spatial variability , 2017 .

[156]  Wilson H. Tang,et al.  Updating Anomaly Statistics—Multiple Anomaly Pieces , 1988 .

[157]  Siu-Kui Au,et al.  System reliability analysis of slope stability using generalized Subset Simulation , 2017 .

[158]  S. Lacasse,et al.  Uncertainties in characterising soil properties , 1996 .

[159]  G. L. Sivakumar Babu,et al.  A Bayesian framework for updating model parameters while considering spatial variability , 2017 .

[160]  C. Hsein Juang,et al.  Response surface-based robust geotechnical design of supported excavation – spreadsheet-based solution , 2017 .

[161]  Li Min Zhang,et al.  Characterizing geotechnical anisotropic spatial variations using random field theory , 2013 .

[162]  Paul W. Mayne,et al.  Stratigraphic delineation by three-dimensional clustering of piezocone data , 2007 .

[163]  W. H. Tang,et al.  Model Uncertainty in Offshore Geotechnical Reliability , 1995 .

[164]  Helmut Bock,et al.  Common ground in engineering geology, soil mechanics and rock mechanics: past, present and future , 2006 .

[165]  C. H. Juang,et al.  Maximum likelihood principle and its application in soil liquefaction assessment , 2018, Risk and Reliability in Geotechnical Engineering.

[166]  Jesús Carrera,et al.  Application of Multiple Point Geostatistics to Non-stationary Images , 2008 .

[167]  Zi-Jun Cao,et al.  Bayesian identification of soil strata in London Clay , 2014 .

[168]  John Quiggin,et al.  The value of information and the value of awareness , 2016 .

[169]  C. Hsein Juang,et al.  Reliability Analysis and Updating of Excavation-Induced Ground Settlement for Building Serviceability Assessment , 2008 .

[170]  Xueyou Li,et al.  Using Conditioned Random Field to Characterize the Variability of Geologic Profiles , 2016 .

[171]  S. M. Dasaka,et al.  Spatial variability of in situ weathered soil , 2012 .

[172]  F. Horowitz,et al.  Towards incorporating uncertainty of structural data in 3D geological inversion , 2010 .

[173]  Stefano Marelli,et al.  UQLab: a framework for uncertainty quantification in MATLAB , 2014 .

[174]  J. M. Duncan,et al.  The accuracy of equilibrium methods of slope stability analysis , 1980 .