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Geostatistics

An article outlining the issues that affect the use of geostatistics in geotechnical analysis. The profession needs to fully appreciate the power of the method, understand its concepts and tools, and make its use part of routine geotechnical analysis. software solutions used worldwide by geotechnical

Article prepared for RocNews Software tools for rock and Spring 2003 Geostatistics in : A fad or an empowering approach?

Geotechnical engineering is constantly evolving and its practitioners always on the lookout for tools, which improve design and help better cope with the large uncertainties and variations in soil and rock properties.

In recent years, several authors have the period from 1970 to 2003. It attempted to apply geostatistics found 64 such publications. We to the problems of geotechnical then sorted the outcome by year of engineering. Does this field hold publication and created a promise for geotechnical (Figure 1) of the resulting table. applications? Geotechnical engineering is constantly evolving and always seeking for tools, which improve design and help better cope with the large uncertainties and variations in soil and rock properties. In recent years, several authors have attempted to apply geostatistics to the problems of geotechnical engineering. Does this field hold promise for geotechnical applications?

To help track the evolution of the Figure 1 - A histogram plot of the of geotechnical interest of geotechnical engineers in publications on geostatistics over the last 33 years this science, we conducted a simple survey of geotechnical engineering papers that listed “geostatistics” in their titles, abstracts, descriptions or keywords. The search covered

2 The histogram indicates that up What is Geostatistics? until 1978, no paper existed that listed its focus as geostatistics and Geostatistics deals with spatial , geotechnical engineering. Over the i.e. data for which each value is rest of the period, interest seems associated with a location in . to peak and fall a few times, and In such analysis it is assumed that currently interest appears to be at there is some connection between another low. Is there going to be location and data value. From another peak or are we seeing the known values at sampled points, end of interest in geostatistics? Why geostatistical analysis can be used is geotechnical engineering losing to predict spatial distributions interest in geostatistics? Does it of properties over large areas or not offer the profession significant volumes. If the profession advantages? These are just a few of is unable to soon the questions that beg to be asked To determine geotechnical and harness the power from our simple analysis. geological conditions, such as the of geostatistics, stratigraphy of soil or rock layers application of the We believe that the profession is at a project site, are method might again at a crossroads with regards to drilled at some specified locations. be shelved. geostatistics. If the profession is Very often, and as expected, one able to fully appreciate the power finds that measurements from of the method and understand its boreholes near to each other tend concepts and tools, geotechnical to be more similar than those engineering will benefit from widely separated boreholes. tremendously. If the profession is This observation forms the basis unable to soon harness the power of the assumption in geostatistics of geostatistics, application of the that location has a relationship to method might again be shelved, measured properties. at least for a while. We believe that Rocscience can contribute in a way In what way does geostatistics that helps ensure successful use of differ from conventional ? geostatistics in routine geotechnical Statistics generally analyzes and analysis. interprets the uncertainty caused by limited . For example, a conventional statistical analysis of core samples from a site investigation program might show that measured values

3 of a material can be described by How can geostatistics a normal distribution. However, benefit geotechnical this distribution only describes the engineering? population of values gathered in the investigation; it does not offer To help appreciate what any information on which zones are geostatistics can do for geotechnical likely to have high cohesion values engineering, let us take a brief look and which areas low values. at the origins of the discipline and examine its successful application to Geostatistical analysis, on the a variety of fields. The method was other hand, interprets statistical originally conceived in the 1960’s distributions of data and also as a methodology for estimating examines spatial relationships. For recoverable reserves in mining the example given, it is capable of deposits. Today it is extensively revealing how cohesion values vary used in the mining and petroleum over distance, and of predicting industries, and in recent years has areas of high and low cohesion been successfully integrated into values. The discipline provides tools remote sensing and GIS. for capturing maximum information on a phenomenon from sparse, The problem in reserve estimation often biased, and often under- was that decisions on very costly sampled data. Ultimately it produces expenditure had to be made predictions of the probable based on very sparsely sampled distribution of properties in space. information. The ratio of the volume of samples recovered from We believe that the geotechnical exploration boreholes to the volume engineering profession should give of a deposit of interest was often strong consideration to adopting of the order of 1 x 10-9! Yet on this the techniques of geostatistics. Wide information recoverable reserves application of the discipline will lead had to be reliably estimated, and to more ready incorporation of the decisions made on investing large inherent uncertainty of soil and rock amounts of money into developing masses into numerical models and the deposit. the design process.

Although the financial costs of the average geotechnical project may not be as high as those of exploration projects, geotechnical engineering has similar concerns. In almost every geotechnical project,

4 the volume of samples obtained for Among its many potential benefits characterizing soil or rock masses to geotechnical engineering, constitutes only a minute fraction of geostatistical analysis offers the the volume of material that impacts following: design and behaviour of proposed w Powerful analytical tools structures. Just like the attributes for forming relatively simple, measured in resource exploration, yet accurate, models of the engineering properties of soil inhomogeneous material based and rock masses are heterogeneous, on limited sample data with properties varying from location to location. In addition, w Approaches for optimizing the financial resources committed sampling locations so that to geotechnical field investigations they maximize the amount of Given the potential often represent a significant portion information at minimized cost improvements of total project costs. to design and w Techniques for estimating the successes of Regularly, either for the sake of engineering properties at geostatistics in simplicity or for lack of information, different locations with minimum resource estimation, geotechnical engineers assume that estimation error. geotechnical properties are the same throughout engineering should a material domain. However, they We shall briefly examine some of embrace the know that the use of averaged these potential benefits. discipline. parameter values can lead to Optimization of Site conclusions that significantly differ Investigation Locations from true behaviour, and recognize that accurate knowledge of the In our opinion, the most immediate spatial distribution of soil and rock benefits of applying geostatistics to mass properties promotes safe geotechnical engineering lie in the and economic design. Given the optimization of site investigation potential improvements to design sampling locations. A most and the successes of geostatistics challenging task in site investigation in resource estimation, we believe is to design a minimal cost sampling that geotechnical engineering program that best captures should seriously consider the information on underground discipline. Geostatistics will facilitate conditions. The site investigator accurate interpretation of ground is often required to answer conditions based on the sparse the question, “If more ground input information characteristic of investigation is to be done, will the geotechnical engineering. additional information acquired justify the extra cost or delay?”

5 Geostatistics provides spatial Simulation and Numerical modelling tools that can Modelling help answer these questions. Geostatistical simulation can help Geostatistical analysis can create geotechnical engineers assess maps that show the magnitude uncertainty and risks in design. and distribution of the values It produces many, equally likely, of a parameter over an area or digital spatial representations of volume. These digital maps provide a parameter that are consistent estimates, which most accurately with values at sampled locations estimate the spatial distributions of and with in situ variability. The sampled properties. differences between alternative models provide a measure of spatial Contour plots of the standard uncertainty. The spatially distributed deviations of predicted values at realizations of a variable can be non-sampled locations are a very input into numerical models and useful outcome of geostatistical used to evaluate risks. analysis. These contours show areas of higher uncertainty (higher Geostatistical simulation has been standard deviations). Sampling from used to study the of these locations can substantially fractured rock masses. In these improve the accuracy of predictions. studies, different three-dimensional networks are generated, The tools of geostatistics enable the and then analyzed for flow patterns. spatial variability of properties to be Simulation can also be applied to visualized. They also allow different stress analysis problems. In finite hypotheses and assumptions on element analysis, for example, variability to be readily tested. each element in a model can be This makes it possible to establish assigned its own deformation and the most likely structure of spatial strength properties. It is possible variability and determine from a to assign different properties to variety of interpretations the ones different elements in a manner most consistent with the available that realistically reflects the true data. conditions and heterogeneity of a soil or rock mass using geostatistics. Studies have shown that the results of such analyses can differ substantially from those obtained from analyses that employ averaged values.

6 Successful application of used to determine the boundary geostatistics to Channel between the Chalk Marl and the Project Gault , based on data available before . Contours of Among the many factors that made the standard deviations of predicted the success of the Channel Tunnel depths of this boundary were project possible, geostatistics was also generated. As a result of the deemed to have played a significant geostatistical analysis, engineers role. It enabled the careful were able to improve the originally assessment of geological risks and proposed alignment of the tunnel. was used to optimize the alignment The contours of the tunnel. helped engineers to realize that improved precision was required at Engineers were Figure 2 shows a typical geological certain tunnel sections, as a result able to improve the cross-section of the seabed through of which they were able to design originally proposed which the tunnel was excavated. a complementary geophysical alignment of One of the most important criteria survey of the seafloor. As more data the tunnel using in optimizing the alignment was to became available from surveys and geostatistical ensure that the tunnel was bored ongoing construction, geostatistics analysis. within the Chalk Marl, avoiding enabled the tunnel engineers to the Gault Clay material. , readily improve the spatial model of a geostatistical technique, was the Chalk Marl–Gault Clay interface.

Figure 2 - Geological cross-section through the seafloor of the Channel Tunnel (taken from Reference [2]).

7 With the help of geostatistical Many of the existing geostatistics analysis, engineers of the Channel software tools are not formulated in Tunnel were able to maintain risks ways that can be readily integrated of penetrating the Gault Clay at into geotechnical analysis. This acceptable levels and to achieve makes geotechnical engineers their objectives of avoiding the unwilling to make the time and Gault Clay formation. Penetration of effort commitments required to the Gault Clay occurred only twice learn to use the method. and in areas that had been already predicted from the geostatistical model. At the end of the project What can Rocscience when engineers compared actual do to facilitate locations of the Chalk Marl-Gault routine geotechnical Clay boundary to the predictions geostatistical analysis? from the geostatistical model, they found the two to be in For the geotechnical profession to good agreement. If there were fully exploit the advantages and any doubters to the usefulness power of geostatistics, it requires of geostatistics to geotechnical appropriately adapted tools, engineering, this project should and needs to develop a tradition have helped put their fears to rest. of applying the discipline. A natural starting point for bringing geostatistics into mainstream The reluctance of geotechnical engineering practice geotechnical engineers seems to be through application to in adopting geostatistics site investigations.

We have not fully analyzed the Given Rocscience’s success reasons why geostatistics has not in developing geotechnical become a routine application in engineering software, the company geotechnical engineering. However, can play a vital role in helping the we believe that one of the biggest profession to adopt geostatistics. reasons could be widespread The company can create easy- unfamiliarity with the concepts of to-use geostatistical software geostatistics. As , the theoretical tools specifically developed complexity and the effort required for the geotechnical . to perform a geostatistical study Organized intuitively, such tools could be factors. will greatly minimize the time and effort required to understand

8 the principles of geostatistics, for geotechnical engineers will allow and significantly reduce the effort them to realistically incorporate required to apply them. inherent spatial variability into numerical models. Geostatistical analysis tools, appropriately implemented in the Given the levels of financial and company’s suite of user-friendly other resources devoted to field applications, will facilitate powerful investigations and , and interactive visualization of the and which already capture the spatial distributions of geotechnical inherent spatial variability of soil parameters. It will aid in the and rock masses, geotechnical correct interpretation of data. engineering will be well served by Such software will also enable and adopting geostatistics. Rocscience is encourage exploration of alternative prepared to play a role. assumptions and interpretations in the analysis of ground conditions. NB: If you have any comments, questions Through export of the spatial or ideas on geostatistics and its usefulness to geotechnical engineering, you may distribution of geotechnical email your thoughts to: properties, geostatistical software [email protected]

References

1. Isaaks, E.H. and Srivastava, R.M. An Introduction to Applied Geostatistics, Oxford University Press, Toronto. 1989. Description: This book provides an excellent introduction to Geostatistics, and does not overwhelm the reader with mathematical theory. It also explains geostatistical concepts through practical application to a sample . 2. Chiles, J-P. and Delfiner, P. Geostatistics: Modeling Spatial Uncertainty, John Wiley & Sons, Toronto. 1999. Description: This meticulously written book is one of the most definitive references currently available on geostatistics. However, it is not an introductory text. It covers a wide of techniques and theories, and into considerable depth. 3. Geostatistics for Environmental and Geotechnical Applications, ASTM STP 1283, eds. S. Rouhani, R.M. Srivastava, A.J. Desbarats, M.V. Cromer, and A.I. Johnson. 1996. Description: This Special Technical Publication of the ASTM contains an excellent collection of papers that provide an overview of geostatistics and describe applications to environmental and geotechnical engineering. 4. La Pointe, P.R. “Analysis of the spatial variation in rock mass properties through geostatistics,” in Proceedings of the 21st Symposium on : A State 0f the Art, University of Missouri, Rolla, May 28 – 30, 1980, pp. 570-580. Description: This is a well-written paper that describes the specific application of geostatistics to rock engineering. 9