Master of Science theses supervised by staff of the Section Engineering Geology

1992. Reliability assessment of rock mass characteristics in GIS applications / by Luis Fernando Contreras Bohorquez. - Delft : ITC, 1992. - 120 p. ; 30 cm. - ITC MSc-thesis. ABSTRACT, supervisor: Hack, thesis availability: ITC Library

ABSTRACT

The engineering geological investigation of an area for mapping and classification purposes, or for the study of projects covering relatively extensive areas of land, includes the collection of geotechnical information at particular points, which is then interpreted in order to establish the conditions at unvisited locations. The use of this type of data for analysis with Geographic Information Systems (GIS) involves operations of map overlying where data maps containing information of various rock properties are combined to produce new maps with new types of information associated to geographical locations. The proper interpretation of the information contained in these maps, requires the differentiation between information corresponding to actual observations and information resulting from interpolation. Therefore a reliability assessment or evaluation of how well values at every location represent the expected conditions in the field, is required.

The purpose of the study is to identify and describe the available approaches of assessing the reliability of particular sets of information product of the process of estimation from data at observation points, and to discuss on the applicability and limitations of these techniques with geotechnical data, in particular with rock mass characteristics in GIS analysis applications. Some of the techniques described are illustrated with examples executed with a commercially available computer routine.

The result of the reliability analysis for a particular property ideally consists of a computer generated map, where a reliability coefficient takes a maximum value (say 1) at the points where the property was actually measured. Low values of the coefficient are associated with locations whose distance from the observation points and other attributes having an influence on the spatial variability of the property studied, indicate difficulties or lack of elements to properly carry out the estimation of the parameter.

Commonly the reliability assessment is achieved through the use of indices operating as uncertainty meters such as "errors of estimation" or "confidence intervals", resulting from the use of probabilistic techniques. In this case a low value of the index (usually zero at the observation points) is associated with high reliability and viceversa. The advantage of this type of indices is that they have more significance for they are measured in the same units as the property studied.

There are three major sources of uncertainty in engineering geology (Einstein and Baecher,  1982): (1) Spatial variability of geological formations, (2) errors introduced in measuring and estimating engineering properties, and (3) inaccuracies caused by modelling physical behaviour. The reliability of rock mass characteristics in relation to their use in GIS applications is related fundamentally to the first type of uncertainty, although the second type has also some influence.

Evaluation of the reliability of maps of rock mass characteristics generated from observations at discrete points is related to the quantification of the uncertainty of the estimates made from those observations. The possibility of evaluation of uncertainty depends on the method of interpolation considered. Broadly the available methods can be divided into two main groups: deterministic and stochastic. Deterministic methods (polygonal, triangulation, splines, moving averages) are not based on physical or geological models but on graphic or sometimes arbitrary criteria, therefore they are unable to provide measures of uncertainty of the estimates. Stochastic methods (trend surface, Fourier series, kriging) are based on models of random variables and therefore are intended to provide measures of uncertainty of the estimates.

Among the three most common stochastic methods of interpolation available, "kriging" is the one that offers most possibilities for use in engineering geology, in particular for the obtention of maps of rock mass characteristics required in analysis with GIS. It is a local method of interpolation which means that updating of information can be achieved with minimum disturbance of the interpretation in other areas. It is an exact interpolator which means that the estimated surface passes through the data points. It can be adapted to consider different types of data and conditions. This is also shown by the recent increase in the number of publications describing new variations of the basic procedure in order to deal with different situations.

Kriging is an estimation technique originally developed for mining applications, specifically for analysis of geochemical data in mineral exploration. The method considers the studied property as a regionalized variable whose variation is based on a random function model.It is assumed that the spatial variation of the phenomenon of interest can be expressed as the sum of three major components: (1) a structural component associated with a general trend, (2) a random, spatially correlated component, and (3) a random noise. The first step in a kriging analysis is the identification of the spatial correlation of the variable of interest through the construction of the semivariogram with the available data. The method of estimation is similar to a weighted moving average, but in this case the information contained in the semivariogram is used to calculate the set of weights that produce unbiased estimates with minimum error variances.

One of the main attractions of the method is the calculation of the estimation variance which can be interpreted as the error of estimation. When the assumptions are satisfied, these results are related to the uncertainty in the estimation of the unknown true value of the studied property at every location and therefore the construction of confidence intervals is meaningful. However if the assumptions are not fulfilled, the estimation variance still can be considered as an useful index related to the distribution of data points, where factors such as number, proximity and clustering of observations and the continuity of the phenomenon are taken into account.

The method has certain drawbacks such as its dependence on the assumptions of stationarity and normality of the variable studied, in order to have results that represent the real behaviour of phenomenon modelled. Another difficulty is related to the definition and interpretation of the semivariogram which is something that can be more difficult in engineering applications, for it depends heavily on the amount of available data. Various types of kriging procedures have been developed in order to confront this complications, however still one of the main inconveniences  is the identification of the difficulties for a particular data set so that the appropriate treatment can be implemented. Nevertheless, for most types of data the method is robust, meaning that if the assumptions are not satisfied, the estimates still are useful because not abnormal or strange values are obtained.

Rock mass characteristics used for mapping and classification purposes include: strength of the rock material (UCS, PLT, Brazilian, etc.), fracture state of the rock mass (spacing and persistence of discontinuities, RQD, SCR) and discontinuity characteristics mainly orientation and friction properties such as roughness, infill, joint wall condition, etc. Some aspects that should be considered when kriging rock mass characteristics are:

-               Definition of the domain for each property, which requires a previous knowledge of the geology of the area studied.

-               Requirement of previous treatment of data to remove noise and outliers.

-               Existence of anisotropy of the spatial variation.

-               Definition of the most adequate type of data to represent a particular rock property.

-               Possibility of incorporation of different sources of information.

When rock mass characteristics data are processed to produce maps used in GIS applications, or in general when the spatial variation of geotechnical properties is investigated using any interpolation technique, there are two main types of difficulties encountered: (1) the character of the variable is not always a simple scalar quantity, (2) the number of the available observation points (sample size in the statistical sense) is normally very small and not properly sampled.

Three techniques were described which corresponds to variations of the basic kriging method and that overcome some difficulties encountered when the spatial variation of geotechnical data is investigated.

The description of the techniques is illustrated with examples of application using the GEOSOFT mapping and processing computer system, where this was possible. The special algorithms or features required for the implementation of some of the techniques with the available griding routine, were highlighted.

The method of kriging vector quantities was originally described by La Pointe (1980). It allows the evaluation of the spatial variation of rock discontinuity orientations from observations. The method is illustrated with an example where the spatial variation of the bedding orientation is evaluated from a few field observations.The procedure can be applied using a conventional kriging routine developed for scalar quantities, although in this case the procedure is not efficient.

The method of kriging fuzzy data was originally described by Bardossy et al (1988). It allows the estimation of rock properties that have an imprecise character like those related to fracture state. In the method fuzzy numbers are used to represent geotechnical data, which because of its character, or because the available knowledge about it, can be considered a imprecise. The method can be used also for the incorporation of additional (imprecise) information into the analysis of any type of property, for the observations (hard data) can be considered as particular cases of fuzzy numbers. Fuzzy numbers have their own properties and their own definition of the mathematical operations, and the method is developed by incorporating these definitions into the basic kriging equations. In addition to the estimation variance which is a measure of the uncertainty of the data structure, the method produce a measurement of uncertainty related to the imprecision of data through the width of the fuzzy estimates. The method can not be executed with a conventional kriging routine.

Finally a brief description of a group of methods referred to as Bayesian types of kriging is presented. These methods allow the incorporation of additional (subjective) information (soft data) which is combined with the actual observations (hard data) to produce estimates.

The method described by Omre (1987) allows the combination of observations with an interpretation of the phenomena (qualified guess) over the whole area. This method might be very useful in engineering geological applications, where usually, from the geology of the area studied and from field observations, a subjective impression of the variation of certain rock properties can be obtained. It can not be executed with a conventional kriging routine.

The method presented as "The soft kriging approach" by Journel (1986) combines the observations (hard data) with additional information (soft data) in the form of intervals within which data are located and within which probability distributions can be assigned to these data. Additionally the method allows the nonparametric type of estimation, that is estimation independent of assumptions about the underlying distribution of the random function model. The method can be performed with a conventional kriging routine although in this case the handling of the data is rather cumbersome.

The incorporation of these methodologies into an interpolation routine is recommended as a first step for the reliability assessment of rock mass characteristics.