Stratigraphic uncertainty characterization using generalized coupled Markov chain

Stratigraphic uncertainty widely exists in geotechnical structures. An efficient generalized coupled Markov chain (GCMC) model was proposed to simulate the stratigraphic uncertainty in the past. This model, however, cannot be directly applied to geotechnical problems because of the difficulty in directly estimating the horizontal transition probability matrices (HTPMs) of the GCMC from boreholes with large hole-to-hole distance. This paper, therefore, aims at addressing the above problem by using a maximum likelihood estimation (MLE) method and utilizing the MLE modified GCMC model to characterize stratigraphic uncertainty. In the framework of the GCMC, the validity of the proposed method is verified, and information entropy method is adopted to quantify the stratigraphic uncertainty. As an illustration, the proposed model is applied to a construction site in Hong Kong to characterize the stratigraphic uncertainty. A systematic comparison of coupled Markov chain (CMC) and GCMC model for stratigraphic uncertainty simulation was conducted. The influences of borehole layout scheme on transition probability matrices (TPMs) estimation and stratigraphic uncertainty simulation are explored. Results showed that the result of stratigraphic uncertainty simulation of the GCMC model is more reasonable than that of the CMC model. The borehole layout scheme is very important for estimating TPMs and significantly influences the stratigraphic uncertainty simulation. The information entropy map has the potential to become a useful guideline for the design of the borehole layout scheme in geotechnical engineering practice.

[1]  D. V. Griffiths,et al.  Quantitative risk assessment of landslide by limit analysis and random fields , 2013 .

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

[3]  Yung-ming Cheng,et al.  Incorporating stratigraphic boundary uncertainty into reliability analysis of slopes in spatially variable soils using one-dimensional conditional Markov chain model , 2020 .

[4]  Chuanrong Zhang,et al.  Two-dimensional Markov chain simulation of soil type spatial distribution , 2004 .

[5]  Iason Papaioannou,et al.  Bayesian updating of slope reliability in spatially variable soils with in-situ measurements , 2018 .

[6]  Yu Wang,et al.  Interpolation and stratification of multilayer soil property profile from sparse measurements using machine learning methods , 2020 .

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

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

[9]  T. Schweckendiek,et al.  Some observations on ISO2394:2015 Annex D (Reliability of Geotechnical Structures) , 2016 .

[10]  Gordon A. Fenton,et al.  Reliability-Based Deep Foundation Design , 2007 .

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

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

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

[14]  K. Phoon,et al.  An analytical method for quantifying the correlation among slope failure modes in spatially variable soils , 2017, Bulletin of Engineering Geology and the Environment.

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

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

[17]  Dian-Qing Li,et al.  Effect of spatial variability of shear strength parameters on critical slip surfaces of slopes , 2018 .

[18]  Jun Yang,et al.  Effect of soil variability on bearing capacity accounting for non-stationary characteristics of undrained shear strength , 2019, Computers and Geotechnics.

[19]  C. Juang,et al.  Probabilistic analysis and design of stabilizing piles in slope considering stratigraphic uncertainty , 2019, Engineering Geology.

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

[21]  Dian-Qing Li,et al.  Evaluating slope stability uncertainty using coupled Markov chain , 2016 .

[22]  Gordon A. Fenton,et al.  Probabilistic slope stability analysis by finite elements , 2004 .

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

[24]  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.

[25]  Chuanrong Zhang,et al.  A single-chain-based multidimensional Markov chain model for subsurface characterization , 2007, Environmental and Ecological Statistics.

[26]  Shui-Hua Jiang,et al.  Efficient probabilistic back analysis of spatially varying soil parameters for slope reliability assessment , 2020 .

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

[28]  Antonio G. Chessa,et al.  A Markov Chain Model for Subsurface Characterization: Theory and Applications , 2006 .

[29]  Rick Chalaturnyk,et al.  An overview of soil heterogeneity: quantification and implications on geotechnical field problems , 2003 .

[30]  F. Dekking,et al.  Reducing geological uncertainty by conditioning on boreholes: the coupled Markov chain approach , 2007 .

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

[32]  Dian-Qing Li,et al.  Reliability evaluation of slope considering geological uncertainty and inherent variability of soil parameters , 2017 .

[33]  C. Hsein Juang,et al.  Probabilistic methods for unified treatment of geotechnical and geological uncertainties in a geotechnical analysis , 2019, Engineering Geology.

[34]  Y. Cheng,et al.  Simplified framework for system reliability analysis of slopes in spatially variable soils , 2018 .

[35]  Dianqing Li,et al.  Probabilistic characterization of 2D soil profile by integrating CPT with MASW data , 2018 .

[36]  Li Min Zhang,et al.  Uncertainties in Geologic Profiles versus Variability in Pile Founding Depth , 2010 .