John T. Christian

Bio: John T. Christian is an academic researcher from University of Massachusetts Lowell. The author has contributed to research in topics: Consolidation (soil) & Reliability (statistics). The author has an hindex of 23, co-authored 79 publications receiving 3704 citations. Previous affiliations of John T. Christian include Massachusetts Institute of Technology.

Reliability and statistics in geotechnical engineering

Abstract: Preface. Part I. 1 Introduction - uncertainty and risk in geotechnical engineering. 1.1 Offshore platforms. 1.2 Pit mine slopes. 1.3 Balancing risk and reliability in a geotechnical design. 1.4 Historical development of reliability methods in civil engineering. 1.5 Some terminological and philosophical issues. 1.6 The organization of this book. 1.7 A comment on notation and nomenclature. 2 Uncertainty. 2.1 Randomness, uncertainty, and the world. 2.2 Modeling uncertainties in risk and reliability analysis. 2.3 Probability. 3 Probability. 3.1 Histograms and frequency diagrams. 3.2 Summary statistics. 3.3 Probability theory. 3.4 Random variables. 3.5 Random process models. 3.6 Fitting mathematical pdf models to data. 3.7 Covariance among variables. 4 Inference. 4.1 Frequentist theory. 4.2 Bayesian theory. 4.3 Prior probabilities. 4.4 Inferences from sampling. 4.5 Regression analysis. 4.6 Hypothesis tests. 4.7 Choice among models. 5 Risk, decisions and judgment. 5.1 Risk. 5.2 Optimizing decisions. 5.3 Non-optimizing decisions. 5.4 Engineering judgment. Part II. 6 Site characterization. 6.1 Developments in site characterization. 6.2 Analytical approaches to site characterization. 6.3 Modeling site characterization activities. 6.4 Some pitfalls of intuitive data evaluation. 6.5 Organization of Part II. 7 Classification and mapping. 7.1 Mapping discrete variables. 7.2 Classification. 7.3 Discriminant analysis. 7.4 Mapping. 7.5 Carrying out a discriminant or logistic analysis. 8 Soil variability. 8.1 Soil properties. 8.2 Index tests and classification of soils. 8.3 Consolidation properties. 8.4 Permeability. 8.5 Strength properties. 8.6 Distributional properties. 8.7 Measurement error. 9 Spatial variability within homogeneous deposits. 9.1 Trends and variations about trends. 9.2 Residual variations. 9.3 Estimating autocorrelation and autocovariance. 9.4 Variograms and geostatistics. Appendix: algorithm for maximizing log-likelihood of autocovariance. 10 Random field theory. 10.1 Stationary processes. 10.2 Mathematical properties of autocovariance functions. 10.3 Multivariate (vector) random fields. 10.4 Gaussian random fields. 10.5 Functions of random fields. 11 Spatial sampling. 11.1 Concepts of sampling. 11.2 Common spatial sampling plans. 11.3 Interpolating random fields. 11.4 Sampling for autocorrelation. 12 Search theory. 12.1 Brief history of search theory. 12.2 Logic of a search process. 12.3 Single stage search. 12.4 Grid search. 12.5 Inferring target characteristics. 12.6 Optimal search. 12.7 Sequential search. Part III. 13 Reliability analysis and error propagation. 13.1 Loads, resistances and reliability. 13.2 Results for different distributions of the performance function. 13.3 Steps and approximations in reliability analysis. 13.4 Error propagation - statistical moments of the performance function. 13.5 Solution techniques for practical cases. 13.6 A simple conceptual model of practical significance. 14 First order second moment (FOSM) methods. 14.1 The James Bay dikes. 14.2 Uncertainty in geotechnical parameters. 14.3 FOSM calculations. 14.4 Extrapolations and consequences. 14.5 Conclusions from the James Bay study. 14.6 Final comments. 15 Point estimate methods. 15.1 Mathematical background. 15.2 Rosenblueth's cases and notation. 15.3 Numerical results for simple cases. 15.4 Relation to orthogonal polynomial quadrature. 15.5 Relation with 'Gauss points' in the finite element method. 15.6 Limitations of orthogonal polynomial quadrature. 15.7 Accuracy, or when to use the point-estimate method. 15.8 The problem of the number of computation points. 15.9 Final comments and conclusions. 16 The Hasofer-Lind approach (FORM). 16.1 Justification for improvement - vertical cut in cohesive soil. 16.2 The Hasofer-Lind formulation. 16.3 Linear or non-linear failure criteria and uncorrelated variables. 16.4 Higher order reliability. 16.5 Correlated variables. 16.6 Non-normal variables. 17 Monte Carlo simulation methods. 17.1 Basic considerations. 17.2 Computer programming considerations. 17.3 Simulation of random processes. 17.4 Variance reduction methods. 17.5 Summary. 18 Load and resistance factor design. 18.1 Limit state design and code development. 18.2 Load and resistance factor design. 18.3 Foundation design based on LRFD. 18.4 Concluding remarks. 19 Stochastic finite elements. 19.1 Elementary finite element issues. 19.2 Correlated properties. 19.3 Explicit formulation. 19.4 Monte Carlo study of differential settlement. 19.5 Summary and conclusions. Part IV. 20 Event tree analysis. 20.1 Systems failure. 20.2 Influence diagrams. 20.3 Constructing event trees. 20.4 Branch probabilities. 20.5 Levee example revisited. 21 Expert opinion. 21.1 Expert opinion in geotechnical practice. 21.2 How do people estimate subjective probabilities? 21.3 How well do people estimate subjective probabilities? 21.4 Can people learn to be well-calibrated? 21.5 Protocol for assessing subjective probabilities. 21.6 Conducting a process to elicit quantified judgment. 21.7 Practical suggestions and techniques. 21.8 Summary. 22 System reliability assessment. 22.1 Concepts of system reliability. 22.2 Dependencies among component failures. 22.3 Event tree representations. 22.4 Fault tree representations. 22.5 Simulation approach to system reliability. 22.6 Combined approaches. 22.7 Summary. Appendix A: A primer on probability theory. A.1 Notation and axioms. A.2 Elementary results. A.3 Total probability and Bayes' theorem. A.4 Discrete distributions. A.5 Continuous distributions. A.6 Multiple variables. A.7 Functions of random variables. References. Index.

Reliability Applied to Slope Stability Analysis

Abstract: Formally probabilistic methods for the analysis of slope stability have had relatively little impact on practice. Many engineers are not familiar with probabilistic concepts, and it has been difficult to incorporate concepts of reliability into practice. Also, there is confusion over what reliability and probability of failure mean. The most effective applications of probabilistic methods are those involving relative probabilities of failure or illuminating the effects of uncertainties in the parameters. Attempts to determine the absolute probability of failure are much less successful. The paper describes how probabilistic descriptions of soil parameters can be derived from field and laboratory data and applied in stability analysis. The first-order, second-moment approach is explored and applied to the design of embankment dams. The example illustrates the relative contributions of uncertainties about different parameters to the reliability of the embankment. Reliability analysis is especially useful in establishing design values of factors of safety representing consistent risks for different types of failure.

Geotechnical Engineering Reliability: How Well Do We Know What We Are Doing?

Abstract: Uncertainty and risk are central features of geotechnical and geological engineering. Engineers can deal with uncertainty by ignoring it, by being conservative, by using the observational method, or by quantifying it. In recent years, reliability analysis and probabilistic methods have found wide application in geotechnical engineering and related fields. The tools are well known, including methods of reliability analysis and decision trees. Analytical models for deterministic geotechnical applications are also widely available, even if their underlying reliability is sometimes suspect. The major issues involve input and output. In order to develop appropriate input, the engineer must understand the nature of uncertainty and probability. Most geotechnical uncertainty reflects lack of knowledge, and probability based on the engineer’s degree of belief comes closest to the profession’s practical approach. Bayesian approaches are especially powerful because they provide probabilities on the state of nature rather than on the observations. The first point in developing a model from geotechnical data is that the distinction between the trend or systematic error and the spatial error is a modeling choice, not a property of nature. Second, properties estimated from small samples may be seriously in error, whether they are used probabilistically or deterministically. Third, experts generally estimate mean trends well but tend to underestimate uncertainty and to be overconfident in their estimates. In this context, engineering judgment should be based on a demonstrable chain of reasoning and not on speculation. One difficulty in interpreting results is that most people, including engineers, have difficulty establishing an allowable probability of failure or dealing with low values of probability. The \IF-N\N plot is one useful vehicle for comparing calculated probabilities with observed frequencies of failure of comparable facilities. In any comparison it must be noted that a calculated probability is a lower bound because it must fail to incorporate the factors that are ignored in the analysis. It is useful to compare probabilities of failure for alternative designs, and the reliability methods reveal the contributions of different components to the uncertainty in the probability of failure. Probability is not a property of the world but a state of mind; geotechnical uncertainty is primarily epistemic, Bayesian, and belief based. The current challenges to the profession are to make use of probabilistic methods in practice and to sharpen our investigations and analyses so that each additional data point provides maximal information.

Risk Assessment in Construction Schedules

Abstract: Construction projects are initiated in complex and dynamic environments resulting in circumstances of high uncertainty and risk, which are compounded by demanding time constraints. This paper describes a systematic way to consider and quantify uncertainty in construction schedules. The system incorporates knowledge and experience acquired from many experts, project-specific information, decision analysis techniques, and a mathematical model to estimate the amount of risk in a construction schedule at the initiation of a project. The model provides the means for sensitivity analyses for different outcomes wherein the effect of critical and significant risk factors can be evaluated. The paper focuses on lessons learned from past projects and describes a risk assessment process involving typical inputs and expected outputs. The paper also briefly reviews the information technology of HyperCard and Excel, which were used to develop the system.

Consolidation at constant rate of strain

Abstract: IN RESPONSE TO QUESTIONS RAISED BY THE AUTHORS' ORIGINAL PAPER, ENTITLED "CONSOLIDATION AT CONSTANT RATE OF STRAIN," THE FOLLOWING OBSERVATIONS ARE MADE: 1. THE HYDRAULIC GRADIENT MUST INDEED BE CONSTANT AT THE DRAINAGE SURFACE TO ATTAIN A CONSTANT RATE OF STRAIN WITH LINEAR MATERIAL PROPERTIES. THIS DOES NOT MEAN THAT THE GRADIENT MUST BE CONSTANT THROUGHOUT THE SAMPLE. IN THE ACTUAL SOLUTION, THE GRADIENT VARIES LINEARLY FROM THE SURFACE OF THE SAMPLE TO THE IMPERVIOUS BOTTOM, LEADING TO A PARABOLIC VARIATION OF THE EXCESS PORE PRESSURE FOR THE LINEAR MATERIAL. 2. THE PORE PRESSURE AT THE BASE MUST REMAIN CONSTANT FOR A LINEAR MATERIAL. FOR THE NONLINEAR MATERIAL, IT WILL NOT REMAIN CONSTANT. IN PRACTICE, NORMALLY CONSOLIDATED SAMPLES WILL HAVE GRADUALLY INCREASING PORE PRESSURES WITH TIME AT THE BASE. THIS IS PRECISELY WHAT IS PREDICTED BY THE NONLINEAR THEORY. 3. THE FORM OF THE STRESS/STRAIN RELATION HAS TO BE INDEPENDENT OF TIME OR STRAIN RATE. THE PROPOSED CONSTANT RATE OF STRAIN CONSOLIDATION TEST PROVIDES A STRAIGHTFORWARD MEANS OF OBTAINING VALUES OF VOID RATIO VERSUS EFFECTIVE STRESS FOR PREDETERMINED STRAIN RATES. THESE COULD, THEN, BE USED IN VISCOELASTIC ANALYSES. IN CONCLUSION, IT IS EMPHASIZED THAT ALTHOUGH THE SOLUTIONS PRESENTED START AT TIME ZERO, THEY SHOULD BE USED IN AN INCREMENTAL MANNER ONCE A STEADY STATE HAS BEEN REACHED; THE DATA IN THE ORIGINAL PAPER WERE HANDLED IN PRECISELY THIS MANNER.

Soil Behaviour and Critical State Soil Mechanics

Abstract: Soils can rarely be described as ideally elastic or perfectly plastic and yet simple elastic and plastic models form the basis for the most traditional geotechnical engineering calculations. With the advent of cheap powerful computers the possibility of performing analyses based on more realistic models has become widely available. One of the aims of this book is to describe the basic ingredients of a family of simple elastic-plastic models of soil behaviour and to demonstrate how such models can be used in numerical analyses. Such numerical analyses are often regarded as mysterious black boxes but a proper appreciation of their worth requires an understanding of the numerical models on which they are based. Though the models on which this book concentrates are simple, understanding of these will indicate the ways in which more sophisticated models will perform.

Landslide hazard assessment: summary review and new perspectives

Abstract: This paper deals with several aspects of the assessment of hazard and risk of landsliding. In recent years the interest in this topic has increased greatly and there are many technical papers dealing with this subject in the literature. This article presents a summary review and a classification of the main approaches that have been developed world-wide. The first step is the subdivision between qualitative and quantitative methods. The first group is mainly based on the site-specific experience of experts with the susceptibility/hazard determined directly in the field or by combining different index maps. The approaches of the second group are formally more rigorous. It is possible to distinguish between statistical analyses (bivariate or multivariate) and deterministic methods that involve the analysis of specific sites or slopes based on geo-engineering models. Such analyses can be deterministic or probabilistic. Among the quantitative methods discussed is the Neural Networks approach which has only recently been applied to engineering geology problems. Finally several considerations concerning the concept of acceptable risk and risk management are presented.

Fundamentals of Poroelasticity

Abstract: Publisher Summary This chapter focuses on fundamentals of poroelasticity. The presence of a freely moving fluid in a porous rock modifies its mechanical response. Two mechanisms play a key role in the interaction between the interstitial fluid and the porous rock: (i) an increase of pore pressure induces a dilation of the rock; and (ii) compression of the rock causes a rise of pore pressure, if the fluid is prevented from escaping the pore network. These coupled mechanisms bestow an apparent time-dependent character to the mechanical properties of the rock. If excess pore pressure, induced by compression of the rock, is allowed to dissipate through diffusive fluid mass transport, further deformation of the rock progressively takes place. The rock is more compliant under drained conditions than undrained ones. The chapter discusses the formulation and analysis of coupled deformation–diffusion processes, within the framework of the Biot theory of poroelasticity. The Biot model of a fluid-filled porous material is constructed on the conceptual model of a coherent solid skeleton and a freely moving pore fluid.

Factors of safety and reliability in geotechnical engineering

Abstract: Simple reliability analyses, involving neither complex theory nor unfamiliar terms, can be used in routine geotechnical engineering practice. These simple reliability analyses require little effort beyond that involved in conventional geotechnical analyses. They provide a means of evaluating the combined effects of uncertainties in the parameters involved in the calculations, and they offer a useful supplement to conventional analyses. The additional parameters needed for the reliability analyses—standard deviations of the parameters—can be evaluated using the same amount of data and types of correlations that are widely used in geotechnical engineering practice. Example applications to stability and settlement problems illustrate the simplicity and practical usefulness of the method.