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Uncertainty and likelihood of geological and geotechnical property models of the sub-surface - hazard and risk analyses

Uncertainty model

In engineering geology or geotechnical work common practice is (or should be) to make an estimation of the error (or likelihood) of properties in the subsurface and the influence of these errors on the engineering application to be built in or on the sub-surface. The later is also denoted as a hazard and risk analyses for an engineering structure due to uncertainty in geotechnical properties in the sub-surface. Different methodologies, such as "geotechnical base-line methods", probability studies, Monte Carlo simulations, exist to be able to give a certain amount of quantification of possible errors made in the design of an engineering structure due to uncertainty in sub-surface properties. However, two very important main points are only very rudimentary or not addressed in these analysis. To understand this it is necessary to go back to the basics of engineering geology or geotechnical engineering.

 Fig 1. Example of 3D-GIS visualization of proposed tunnel alignment in a solid volume model of distribution of CPT cone resistance values, with boreholes showing geotechnical units and two cut-planes to show the distribution of CPT values (Heinenoord Tunnel, Netherlands; after Ozmutlu, 2002)

It is normal to make a three-dimensional model of the geotechnical property distribution of the sub-surface (fig.1). Such a model consists of a boundary model that gives the boundaries between the different defined geotechnical units (note 1) and a property model for the distribution of geotechnical properties in the geotechnical units. In principle the model has to be three dimensional and be able to represent changes in time of geotechnical properties (e.g. the model should be four-dimensional with time as fourth dimension).

Statistical routines exist, in extenso, to calculate the temporal-spatial distribution of properties in a unit. Also the likelihood of the distribution, or better the error made by estimating a property at a certain location in space, is well defined if appropriate statistical routines are used. But inherit to the likelihood of properties is the correctness of the boundaries the geotechnical units. This correctness depends on 1) the geology and 2) the variation in properties allowed for each geotechnical unit.

Geology interpretation

The interpretation of the geology is normally done by a geologist, engineering geologist, or a geotechnical engineer. In the interpretation the geologist or engineer makes use of a priori existing knowledge of the geological environments which he or she thinks to be present. The quality of this information which is essential in the interpretation, can, in general, not be quantified at present. If the engineer is good there will be a good model, or a poor model will result if the geologist is not so good. How "good" or how "poor" nobody can quantify.

Establishment of geotechnical units

The establishment of geotechnical units, as well the boundaries as the allowed variation of properties within each unit, depends on engineering judgment. Generally, it will be based on a balance between improved detail against higher costs (see also below note1).

It is clear that no decent analyses of hazard and risk can be made if these two interpretation errors cannot be quantified. Any analysis up-to-date describe wonderfully all sorts of uncertainties in measurable properties, but is totally lacking the main parameters resulting from the interpretation. Lets make that clear with an example.

Example: marine or fluvial

In the western part of the Netherlands sedimentary layers have mostly a marine or a fluvial origin. Assume that a foundation has to be made on a sand body in the sub-surface. Some boreholes (or in the Netherlands Dutch Cone Penetration tests, CPT's) have been made and show in all a sand layer to exist roughly at the required depth. Now the interpretation starts. If the sand layer is of marine origin it can reasonably safe be assumed that the layer is continuous, however, if the sand layer is of fluvial origin it is in contrary likely to be a lens with a limited lateral extension, and may or may not be continuous between two boreholes or CPT's. An engineer who knows in which formation the sand layer is situated (e.g. of marine or fluvial origin) will likely make  a correct interpretation, while, his colleague who does not know or who makes the wrong assumption, produces a completely wrong interpretation with all consequences for the foundation and the building resting on it.

Research at ITC

The problem of quantification of interpretation errors and unknown likelihood of geological models and geotechnical units has been subject of research already for many years in ITC's Section of Engineering Geology. The research question originated with the use of two- and three-dimensional GIS for sub-surface interpretation. It was not long after the first use of GIS that the question came "what is the reliability of all these wonderful computer generated models". Nobody could give an answer except with "it looks good, so it is probably good", which is clearly unsatisfactory! Therefore years ago research has started to try to develop methodologies to solve this type of problems.

Ongoing research:

Likelihood of geological and geotechnical models of the sub-surface (work title). PhD research. Researcher: Sicai Zhu, Supervisors: Hack, Turner & Hale

Homogeneity of units by Lidar (work title), Researchers: Slob & Hack

Published research output:

Articles: See Publications

PhD research theses:

1997. Predicting subsurface conditions for geotechnical modelling / by B. Orlic. - Delft : ITC, 1997. - 192 p. ; 25 cm. - PhD thesis Technical University Delft ; Summaries in Dutch and English. - ISBN 90-6164-140-3. (ITC Publication ; 55) (ITC Dissertation ; 46). ABSTRACT, supervisor: Hack, thesis availability: ITC Library

M.Sc. research theses

Theses fully directed towards uncertainty and likelihood

2001. Variability analysis of rock mass properties using in-situ block size distribution / by Abera Abebo Hamore - Delft : ITC, 2001. - 109 p. ; 30 cm. - ITC-MSc thesis. ABSTRACT, supervisor(s): Slob, thesis availability: ITC Library

2000. Uncertainty in 3D subsurface geometry modeling Comparison of expert versus alpha-complex modeling / by S. Staffhorst, MS Thesis, Delft University of Technology, Delft (2000). ABSTRACT, supervisor(s): Hack & Turner (Technical University Delft), thesis availability: Technical University Delft

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(s): Hack, thesis availability: ITC Library

Theses related partial to certainty and likelihood:

2000. Comparative settlement analysis by using 3D-GIS and 2D-FEM approaches / by N.B. Yenigul, Delft : ITC, 2000. - 117 p. ; 30 cm. - ITC MSc-thesis. ABSTRACT, supervisor(s): Ozmutlu & Zigterman, thesis availability: ITC Library

1998. The development of an Expert System for TBM application in soft soil / by A.M.van Noort. ABSTRACT, supervisor(s): Hack, M.T.J.H. Smits (Fugro Engineers, Leidschendam, The Netherlands), & C.N.Bremmer (NITG, Delft, The Netherlands).  thesis availability: Technical University Delft

1997. A decission support system for shield tunneling; for For bored tunnel projects in soft soils in the Netherlands. / by ing. R.P. van der Putten. ABSTRACT, supervisor(s): Hack & M.T.J.H. Smits (Fugro Engineers, Leidschendam, The Netherlands).  thesis availability: Technical University Delft

1996. GIS application in foundation coast zonation for an area in Sliedrecht The Netherlands Vol. II. appendix. / door Senaka Welideniya. - Delft : ITC, 1996. - 125 p. ; 30 cm. - ITC MSc-thesis. ABSTRACT, supervisor(s): Hack, thesis availability: ITC Library

1995. 3D - GIS Modelling for geotechnical purposes: Sliedrecht, Netherlands /by Panya Somboon-anek.  - Delft : ITC, 1995. - ?? p. ; 30 cm. - ITC MSc-thesis. ABSTRACT, supervisor(s): B. Orlic (NITG, Delft, The Netherlands) & Rengers, thesis availability: ITC Library

1990. The application of ILWIS in the estimation of safety of mine pillars / by B. Orlic. - Delft : ITC, 1990. - 80 p. ; 30 cm. - ITC MSc-thesis. ABSTRACT, supervisor(s): Bekendam (Technical University Delft). thesis availability: ITC Library

### Note: Geotechnical units

 Fig. 1 . Mass components (after Hack, 1998)

Theoretically, a proper description or geotechnical calculation to determine the behavior of a soil or rock mass and engineering structure in or on the soil or rock mass should include all properties in the mass including all spatial variations of the properties. This would be unrealistic and is not possible without disassembling the mass. Therefore, a standard procedure is to divide a mass into homogeneous geotechnical units. A geotechnical unit is, in theory, a part of the mass in which the mechanical properties of the soil or intact rock material are uniform and the mechanical properties of the discontinuities (including anisotropy of properties) within each set of discontinuities are the same. The anisotropy of properties in a geotechnical unit should be also uniform. This additional condition is not always specified in the literature; however, in engineering it is an obvious requirement because of the large influence of anisotropic features (e.g. discontinuities, etc.) on engineering.

Fig. 1 shows a schematic visualization of a ground mass and its division in geotechnical units. In practice, homogeneity is seldom found and material and discontinuity properties vary within a selected range of values within the unit. The allowable variation of the properties within one geotechnical unit depends on: 1) the degree of variability of the properties within a mass, and 2) the context in which the geotechnical unit is used.

A ground mass containing a large variation of properties over a small distance necessarily results in geotechnical units containing larger variations in properties. This is because it is impossible to establish with sufficient accuracy all boundaries between the various areas with different properties within the mass. The smaller the allowed variability of the properties in a geotechnical unit the more accurate the geotechnical calculations can be. Smaller variability of the properties of the geotechnical units involves, however, collecting more data and is thus more costly. The higher accuracy obtained for a calculation based on more data has, therefore, to be balanced against the economic and environmental value of the engineering structure to be built and the possible risks for the engineering structure, environment, or human life. The variations allowed within a geotechnical unit for the foundation of a highly sensitive engineering structure (for example, a nuclear power station) will be smaller than for a geotechnical unit in a calculation for the foundation of a standard house.

 Fig. 2. . Different geotechnical units present in a single slope. Greenish and bluish gray layers consist of calcareous shale and brownish, pinkish off-white layers consist of dolomite and limestone.

No standard rules are available for the division of a mass into geotechnical units and this transformation depends on experience and ‘engineering judgment’. However, features such as changes in lithology, faults, shear zones, etc., are often the boundaries of a geotechnical unit. In Fig. 2 a slope is shown in which different geotechnical units are present. The influence of the different geotechnical units on the form of the slope is clearly visible through the changes in slope surface steepness.