Yusuke Honjo

Application of Akaike information criterion statistics to geotechnical inverse analysis: the extended Bayesian method

Abstract A new type of indirect inverse analysis procedure is proposed to overcome the difficulties the geotechnical inverse analyses are encountering such as unstability and nonuniqueness of the solutions as well as multicollinearity. Also, the problem of model identification is emphasized. These difficulties are eased by combining the objective information (i.e. the observation data) with the subjective information (i.e. the prior information) in an appropriate way by the so-termed extended Bayesian method. The method is based on the new view on the Bayesian model proposed by Akaike based on the Akaike Information Criterion Statistics. The criterion is also employed in the model identification in this study. A rather detailed description of Akaikes proposal on the Bayesian model is presented. A case study on an embankment on soft clay is presented to illustrate the effectiveness of the new method.

General and local estimation of local average and their application in geotechnical parameter estimations

Two kinds of estimation variance functions for estimating a local average (LA) of a stationary (homogeneous) random field (RF) are derived. One is local estimation (LE) and the other is general estimation (GE) of LA. The former is for estimating LA at the observation location, and the latter is for obtaining LA at any arbitrary location within the RF. The geotechnical implications of these two estimations are that LE is for estimating LA of geotechnical parameters at the spot where the investigations are made, whereas GE is for estimating LA at any arbitrary location within the same layer. The behavior of the two estimation variance functions differs greatly, controlled by the number of observations (i.e. sample size) and the normalized layer thickness (layer thickness divided by autocorrelation distance of RF). Based on the derived estimation variance functions, methods for determining reliable characteristic values of geotechnical parameters and necessary sample size are proposed. The methods are based on the same framework as that of the traditional statistical theory, i.e. confidence interval of estimated parameters. However, the assumption of independently and identically distributed (i.i.d.) samples in the traditional statistical theory is replaced by the assumption of correlated samples from a stationary RF. The results obtained from the proposed methods for LE and GE differ from each other as well as from the traditional results, which has significant implications for geotechnical parameter estimation in geotechnical engineering practice.

Why Consider Reliability Analysis for Geotechnical Limit State Design

There is a need to draw a clear distinction between accepting reliability analysis as a necessary theoretical basis for geotechnical design and downstream calibration of simplified multiple- factor design formats, with emphasis on the former. Reliability analysis provides a consistent method for propagation of uncertainties and a unifying framework for risk assessment across disciplines (structural and geotechnical design) and national boundaries. Simplified reliability-based design (RBD) equations are probably required for routine design at present, but their limitations have no bearing on the generality of reliability theory. If reliability analysis is accepted as the basis for developing multiple-factor formats, then it is necessary to define the characteristic values in an unambiguous way with reference to the probability distribution function. The key consideration is that the engineer should not be allowed to introduce additional conservatism into the design by using some lower bound value, when the RBD equations are calibrated using, say, mean parameters. The implementation of reliability-based LRFD equations, along with potential advantages and pitfalls, is discussed using a specific example. If the goal of LRFD is to maintain uniform reliability, the example shows that a single resistance factor is not adequate. In practice, it is probably sufficient to partition the parameter space (spanning typical ranges of deterministic and statistical parameters) into smaller domains and calibrate a single resistance factor for each domain. Deviations from the target reliability index can be controlled to an acceptable level by adjusting the sizes of the domains.

Matching objective and subjective information in groundwater inverse analysis by Akaike's Bayesian information criterion

In order to overcome the illposedness of groundwater inverse analysis it is inevitable to introduce prior information of some form and thus Bayesian statistics. One of the essential problems in Bayesian inverse formulation is the optimum matching between the objective information (i.e., the observation) and the subjective information (i.e., the prior information). In this study, Akaikes Bayesian Information Criterion (ABIC) is introduced to overcome this problem. ABIC is also effective in the model identification problem, and this aspect is also emphasized. The effectiveness of the method is illustrated by analyses on an actual aquifer system. Both steady and transient state analyses are carried out. The paper also provides the background of ABIC in some detail.

Reliability analysis of shallow foundations in reference to design codes development

Abstract In this study, FORM analysis is carried out for shallow foundation of a typical building in order to evaluate relative magnitude of uncertainties involved in the force and the resistance sides. The distinguished feature of this study is to take into account the uncertainty of the earthquake force as much as possible. Tthis is because, the seismic design dominates major part of structural design in Japan, and without referring to this problem, no useful information of practical value is gained. The results of the FORM analysis exhibited the reliability index values between 2.0 to 3.5, which is considered to be in a reasonable range. Since the 50 year maximum earthquake force is considered in the reliability calculation, calculated reliability index values are for the period of 50 years. The sensitivity factor obtained in a case more realistic ground variability is taken into account exhibited values not very different from those obtained in the upper structures.

A Simple Method to Assess the Effects of Soil Spatial Variability on the Performance of a Shallow Foundation

ABSTRACT: The performance of a geotechnical structure is controlled not by the properties of soil at a point but by the average over a certain line, area or volume, as pointed out by Vanmarcke (1977) who proposed the variance function. This paper develops his idea, and attempts to specify the size of the local averaging of soil parameters to evaluate the resulting variability in performance of a geotechnical structure. In other words, the mean and variance of a local average of a geotechnical parameter for an appropriate volume are used to evaluate the effects of soil spatial variability on the performance of a geotechnical structure. The size seems to be highly dependent on the type of geotechnical problem under consideration. This paper examines the deformation and stability of a shallow foundation to specify the averaging volume size. The results suggest that the concept can be extended to many other geotechnical reliability analyses.

Settlement prediction by spatial-temporal random process using Asaoka's method

A methodology was presented for observation-based settlement prediction with consideration of the spatial correlation structure of soil. The spatial correlation is introduced among the settlement model parameters and the settlements at various points are spatially correlated through these geotechnical parameters, which naturally describe the phenomenon. The method is based on Bayesian estimation by considering both prior information, including spatial correlation and observed settlement, to search for the best estimates of the parameters at any arbitrary points on the ground. Within the Bayesian framework, the optimised selection of auto-correlation distance by Akaikes Bayesian Information Criterion (ABIC) is also proposed. The application of the proposed approach in consolidation settlement prediction using Asaokas method is presented in this paper. Several case studies were carried out using simulated settlement data to investigate the performance the proposed approach. It is concluded that the accuracy of the settlement prediction can be improved by taking into account the spatial correlation structure and the proposed approach gives the rational prediction of the settlement at any location at any time with quantified uncertainty.

Pumping-rate control for contaminated groundwater with VOCs by using fuzzy inference model

In this paper, a new method is proposed for the remediation of contaminated groundwater. The method is based on fuzzy inference and risk evaluation. The effectiveness of the presented method is assessed in numerical simulations. The main results of the study are as follows: 1) A pump-and-treat control algorithm was proposed by using the fuzzy inference and the human health risk calculation model, 2) It was found that applying the proposed algorithm was likely to reduce the pumped quantity, and 3) It was found that the proposed model can be used to notify residents of the human health risk; the model is based on the ASTM RBCA model for residents. A new fuzzy control system for contaminated groundwater can be used as a useful model for characterising the effects of contaminants on human health and providing helpful information on the human risk assessment of the contaminated groundwater site.

Continuous River Levee Safety Assessment based on a Reliability Analysis

A design scheme is proposed to evaluate the safety of continuous linear structure i.e. river levee. The scheme is developed to establish a procedure to continuously evaluate the stability failure of embankment during flood runoff by seepage, and to identify locations for reinforcement of river levee. A 20km stretch of a fairly large river running through one of the major cities in Japan is chosen for a case study. First all the information available for this river levee for the both side of river have been collected and complied. The data include river levee configurations for every 200m, all the soil investigation results done in the past and the results of levee safety inspection by MLIT. The strength parameters of the embankment and the foundation are obtained from about 50 triaxial test results (CUbar). The permeability coefficient is estimated from about 300 grain size distribution and 15 permeability test results. The configurations of the levee sections are analyzed, and the ranges of various dimensions, such as slope inclinations, crown width, height of retaining wall at edge of slope etc., are obtained. Based on these information, detailed seepage and stability analyses for the possible dimensions of levee sections and material properties are carried out to get the response function (RS) for the safety assessment. Based on this information, the response surface (RS) for the river levee is developed. In developing RS, the experimental design technique is applied for efficiency. MCS is applied to evaluate the failure probability of the levee based on the parameters obtained from the all the analyses explained above for every 200m interval along the levee because all the configuration dimensions of the levee is available at these sections. Results of MCS are presented along the levee, which immediately shows less safe sections.

Reliability Analysis of Long River Dike Against Liquefaction Failure

The authors proposed a reliability analysis method for long continuous structures considering investigation sites to counter liquefaction failure. This method is characterized by continuously calculating the failure probability caused by liquefaction at an arbitrary point and quantifying the uncertainty concerning the investigation site. The purpose of this study is to verify its effectiveness based on application to an actual river dike that suffered liquefaction failure due to the 2011 Earthquake off the Pacific coast of Tohoku.