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Computer Program AutoBlock for Analyzing the Stability of Foundations and Slopes in Rock based on a Digital Terrain Model P. Fritz, Institute for Geotechnical Engineering, Swiss Federal Institute of Technology, Zurich, Switzerland. St. Bergamin, RSE GmbH, Consulting Engineers, Oberengstringen, Switzerland.

Summary The CAD-based program AutoBlock enables engineers to analyze the stability of discrete blocks in a digital terrain model. These so called potential unstable blocks are endangered by sliding along known discontinuities or by separating from them. The digital terrain model is created from a digital terrain surface, which may be obtained from a digitized terrain map. Additionally, foundations or parts to be excavated may be superimposed. When determining the potential unstable blocks it must be taken into account that the digital terrain model is intersected by arbitrary sets of discontinuities, the geometry and strength properties of which have to be defined individually for each set. For each potential unstable block, which, based on kinematic considerations, may fail, the factor of safety against sliding is computed using the limit equilibrium method. AutoBlock is an add-on to the popular program "AutoCAD" and exploits its possibilities and its power (e.g. for 3D-visualizations). A specially implemented user interface with menus and dialog boxes enables one to use AutoBlock even without a detailed knowledge of AutoCAD. It provides all the tools necessary for representing and visualizing the results and facilitates a stability analysis with any number of potential unstable blocks. Thanks to these tools and by exploiting the services of AutoCAD, AutoBlock enables engineers to overview and handle the geometry of the discontinuities in the ground and to determine potential unstable blocks with a minimum of expense and a maximum of accuracy.

1 Introduction The stability analysis of a rock slope or a rock foundation usually has two goals. On the one hand, it must be determined which potential unstable blocks are kinematically admissible, and on the other, it is necessary to investigate the influence of the decisive parameters on the stability of such blocks. “Kinematically admissible” signifies that movement is possible based on kinematic considerations, without taking into account any forces. The first problem - the identification of kinematically admissible unstable blocks - is of the utmost importance in engineering practice. In a large area of investigation, which is crossed by many sets of discontinuities, there may be a large number of potential unstable blocks, whose recognition is difficult due to the often complicated topography. In addition, the three-dimensionality makes a (partially) manual investigation of characteristic values, like the size of the bounding surfaces or the volume of potential unstable blocks, extremely difficult. The second problem is to provide a mathematical treatment, which with regard to parametric analyses should be sufficiently simple but take into account the primary failure mechanisms (Fig. 1) in a coherent way. In practice, the limit equilibrium method has proved to be adequate ([1] and [2]), which also allows a uniform treatment [3]. AutoBlock attempts to solve both problems by means of a single tool. To the authors’ knowledge there is world-wide no other computer program with a similar aim. The following properties characterize the new program:

72th Annual Meeting of ICOLD, Seoul 2004

Computer Program AutoBlock for Analyzing the Stability of Foundations and Slopes in Rock

• The basis is a digitized terrain surface, which using auxiliary programs can be created to practically any accuracy from the contours of terrain maps and profile or grid measurements, etc.

• Several potential sets of discontinuities can be input in a simple way. • Slip on one or two planes according to Fig.1, cases a) or d) are handled, whereby further discontinuities

can be considered in the form of tension cracks. • Automatic determination of all kinematically admissible unstable blocks by a successive combination of

all given discontinuities and intersecting them with the terrain model previously constructed with AutoBlock.

• Important load quantities can be considered, such as self-weight, anchor forces, water pressure, etc. • Automatic determination of the failure mechanisms and the safety with respect to sliding for all

kinematically admissible potential unstable blocks. • Extensive visualization possibilities as a basis for the engineering interpretation of the results. AutoBlock is an add-on to AutoCAD of the firm Autodesk. This offers the advantages of a comfortable drawing infrastructure and the easy handling of this new tool by the many engineers who are already familiar with AutoCAD.

Fig. 1 Possible sliding mechanisms [3]

The concept of AutoBlock is due to St. Bergamin and was developed within the framework of his dissertation [4]. The implementation is the work of Dr. P. Fritz, while the extensive tests were carried out by Messrs Abderhalden, Kolberg and Ferrari. The project was developed at the Institute of Geotechnical Engineering under the leadership of Prof. Dr. K. Kovári. AutoBlock is based on the paradigm of Object-Oriented Programming (OOP) and the programming language C++. OOP is characterized by abstract data types (so-called classes), inheritance and polymorphism [5]. Important classes in AutoBlock are, e.g., discontinuities, potential unstable blocks, but also the individual dialog boxes. The instance of a class is designated as an object. Objects are individual self-contained conceptional units, to which all planned functions (so called methods) can be applied at any time. The advantage, e.g., on the execution process of AutoBlock is that the sequence of the process has not to be prescribed. If an object does not already exist, it cannot be used; if it exists it can be used and in particular it can also be modified. Thus, e.g., results can only be viewed after the necessary calculations have been completed. This behavior is called "non-anticipation" and is supported by the OOP paradigm.

2 Structure of Program The arrangement of the main menu of AutoBlock reflects the sequence of a stability analysis. The most important items are:


Computer Program AutoBlock for Analyzing the Stability of Foundations and Slopes in Rockl

• Digital Terrain Model (DTM): The terrain surface to be investigated is approximated with the help of an auxiliary program by a net of triangles and quadrilaterals, which is imported in AutoBlock. AutoBlock extrudes this surface vertically downwards to depict a 3D body, onto which any foundation body can be superimposed (Fig. 2).

• Kinematics: Potential sets of discontinuities in the rock mass are defined by position, orientation and spacing. From all mutually dependent combinations of these discontinuities AutoBlock determines kinematically admissible potential unstable blocks. To limit their number, filters may be prescribed, e.g. upper and lower limit values for the volumes of unstable blocks, the areas of slip surfaces or the lengths of tracelines where the discontinuities outcrop. All calculated potential unstable blocks can be presented in tables and reproduced in the terrain model. For a large number of unstable blocks different options are available: they can be depicted, e.g., as tracelines on the terrain model or only as points (Fig. 3). In this way one obtains a visual idea, in which parts of the terrain model one can expect a large number of potential unstable blocks. Fig. 2 Digital terrain model with a

superimposed arch dam (both as 3D bodies) [4]

• Strength: Strength parameters for Mohr-Coulomb’s law are assigned to every set of discontinuities.

• Loads: Body forces (Fig. 4), concentrated forces and hydraulic forces can be specified, which act on the terrain model or in the discontinuities. For each potential unstable block AutoBlock determines the resultant of all loading quantities acting on it.

Fig. 3 Bottom outcrop point of

potential unstable blocks [4]

• Safety analysis: For each kinematically admissible potential unstable block the factor of safety against sliding is determined. If sliding is not possible, the reason is given (e.g. lift-off, prevention by other discontinuities, etc.). The safety factors and the properties of all potential unstable blocks can be displayed both in tabular form and also graphically in the terrain model. It is possible to display only the unstable blocks or only the rock mass with tracelines or points (Fig. 3), whereby individual unstable blocks can be clicked on to obtain additional information.

Fig. 4 Definition of body forces

In the following the individual items are described in more detail.

3 Digital Terrain Model AutoBlock is based on a terrain model, which must exist in a digitized form. For digitizing suitable auxiliary programs may be used, e.g. the AutoCAD add-on "Land Desktop“ from Autodesk (http://usa.autodesk.com/) or "Quicksurf" from Schreiber Instruments (http://www.schreiber.com/). Usually first the height contour lines of a map are digitized, over which by means of discretization using triangles and/or quadrilaterals a 3D-surface is placed (Fig. 5). This surface is named according to its elements "triangular" and "quadrilateral irregular network" (TIN and QIN) respectively. Often, one can also obtain directly a digitized part of a map from a governmental institution, e.g. in Switzerland from the



Federal Office for Land Topography (http:// www.swisstopo.ch/de/digital/dhm25.htm). It provides the so-called DHM25 contour model which is based on the Ordnance Survey Map 1:25'000 and exhibits in the matrix model a mesh width of 25 m, corresponding to a millimeter mesh superimposed on the Ordnance Survey Map. AutoBlock can import and process digitized surfaces, which stored in the following formats: • AutoCAD-compatible binary files with so-called

3D faces (surfaces formed by 3 or 4 corner points, which do not have to lie in a plane).

• AutoCAD-compatible binary files with closed so-called polylines (connected line segments) each with 3 or 4 corner points.

• Text files with data types 45 and 58 according to the regulations for electronic payment for construction work (REB) 22.013 of the German Federal Department of Civil Engineering and Regional Planning (BBR) (see http://www.edo-software.de/produkte/reb/da.htm).

To determine potential unstable blocks the terrain model is intersected by discontinuity planes. The prerequisite for this is the conversion of the surface into a so-called Solid Model. A solid model defines the geometry of a closed subset of the 3D space, guaranteeing completeness, integrity and the required accuracy [6]. To describe the solid, AutoBlock uses the representation as a “Boundary Model”, which is supported since Version 13 of AutoCAD. A boundary model is described by its boundaries, which in turn are described by simple curves, especially polylines. Other possibilities of representation would be “Construction Models” (used by AutoCAD up to Version 12) and “Decomposition Models” [5]. The advantage of boundary models is, among other things, that they support the creation of simple geometrical constructions, e.g. Boolean operations.

Fig. 5 Digitized terrain surface consisting of shaded 3D faces with a foundation body (dam) before creation of the digital terrain model of Fig. 2 [4]

AutoBlock constructs a solid of the region under investigation by extruding the terrain surface vertically downwards (Fig. 2). Additionally it is possible to insert foundation bodies and to simulate the necessary excavation for their construction. Such foundation bodies have to be preliminarily created as solids (e.g. the arch dam in Fig. 5), imported to AutoBlock and committed with respect to their state (planned, excavated or constructed). The digital terrain model created in this way forms the starting point for all further investigations. On the basis of existing discontinuities, from it potential unstable blocks are determined whose stability has to be checked.

Fig. 6 Definition of a discontinuity

4 Kinematics Instabilities of rock slopes or foundations take place primarily along existing discontinuities (disturbances, joints or bedding planes, etc.), which are characterized by their position (location and orientation) and their properties. The position of discontinuities is decisive for the shape and size of "kinematically admissible" unstable blocks. As briefly mentioned above, “kinematically admissible” means that a displacement is possible just based on kinematic considerations (i.e. without considering forces). This requires that each failure surface either outcrops at the terrain surface or is limited by other failure surfaces. On the other hand, the properties of the discontinuities are decisive for the failure mechanism (sliding, heave, etc.) and the value of the factor of safety (see section 6: Calculation of the Factor of Safety).



A single discontinuity is defined by an arbitrary reference point in it ("Point of Reference") as well as its orientation ("Dip Direction" and "Dip", Fig. 6). A set of discontinuities is specified by a single discontinuity, which is translated in the direction of the normal to the surface (Fig. 7). The most important parameters for this are the discontinuity spacing and the variation range ("Position From To"). In Fig. 7 some more parameters may be detected: e.g., the minimum length of tracelines where discontinuities outcrop may be specified, since a surface which only outcrops over a very small stretch is unlikely to be relevant. Conversely, very large tracelines can be excluded, since local failure is usually more likely than global failure. In the same way the area of the bounding surfaces or the volume of the unstable blocks can also be limited.

Fig. 7 Limitations for kinematically admissible unstable blocks Then AutoBlock determines all potential unstable blocks in the digital terrain model, which are kinematically admissible and comply with the selection criteria given in Fig. 7. This is accomplished, in that all possible combinations of all locations of the different families of discontinuities are investigated. If, e.g., there are two sets, for each discontinuity of the first set the second is varied within the prescribed region with the specified spacing, and the intersection with the terrain model is determined. Then for each intersected body it is checked if it is kinematically admissible. With respect to the computation time this is the most demanding part of AutoBlock. By means of careful programming together with a combination of fast self-written code and general routines of AutoCAD, however, the computational time is kept within reasonable limits. The question now arises, how it is possible to identify the critical blocks from a large number of potential kinematically admissible unstable blocks? A conceivable approach could be to let AutoBlock determine the factors of safety and to consider the block with the lowest factor as the critical one. However we do not recommend this approach. Instead we are in favor of a prudent investigation by means of an engineering approximation and discussion. For this purpose AutoBlock provides extensive visualization and representation possibilities. A simple test example is shown in Fig. 8: In this terrain model the ground is displayed, without the two potential unstable blocks (which correspond to the "peaks"), from different perspectives. The user may also view individual (or all) potential unstable blocks and with the click of the mouse on individual surfaces, sides or corners, request geometric information. For the representation of a large number of unstable blocks it may be recommendable to limit the display to tracelines or even to individual points, e.g. the lowest outcropping point of each unstable block (Fig. 9 or 3). Zones with a high concentration of points would indicate potential critical rock zones, which can then be investigated in greater detail.



Fig. 8 Terrain model without two unstable blocks, which correspond to the peaks

(isometric and plan views) The determination and visualization of potential unstable blocks are perhaps the most important contributions of AutoBlock in the analysis of rock slopes and foundations. They form the basis for extensive rock mechanics discussions, which sometimes even make the calculation of actual factors of safety unnecessary. One gains insights into the failure mechanism and results, which would be hardly possible without such a program.

5 Loads The forces acting on each kinematically admissible potential unstable block can be divided up into body forces (Fig. 4), concentrated forces Iand distributed forces. Body forces include self-weight and seismic loading (the latter as statically-equivalent loads). Concentrated forces can also be defined as force couples in space to simulate anchors. The input of the forces is usually defined with reference to the terrain model, with the exception of the water pressure, which acts in the slip surfaces and tension cracks of the individual unstable blocks. Before calculating the factors of safety the individuaunstable blocks. The self-weight of an unstable blowith the unit weight. If a free anchor passes throughthe anchor both lie outside (or inside) it, then thetherefore not considered in the analysis. With thinvestigated, without having to repeat the time-counstable blocks. Finally, for each potential unstab

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Fig. 9 Display possibilities for kinematically

admissible unstable blocks

l forces are automatically assigned to the corresponding ck, for example, is determined from its volume, multiplied an unstable block, but the starting and the end points of anchor has no influence on the unstable block and is is procedure as many load cases as desired can be nsuming determination of the kinematically admissible le block AutoBlock determines the total resultant of all

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forces acting on it. All calculated forces together with their assignments to the unstable blocks can be displayed and visually inspected.

6 Calculation of the Factor of Safety When investigating the safety with respect to sliding the direction of motion of the assumed rigid unstable block has to be known. This depends on the orientation of its bounding discontinuities and on the direction of the resultant force acting on it. Four cases can be distinguished:

1) Movement along one discontinuity in the direction of the component of the resultant force parallel to the discontinuity.

2) Movement along two discontinuities in the direction of the component of the resultant force parallel to the line of intersection.

3) Heave (includes toppling, since only equilibrium with respect to force components, but no to moments is formulated).

4) No movement, e.g. due to prevention by existing discontinuities. In the first two cases other discontinuities may be involved, from which the potential unstable blocks move away (so-called tension cracks). In the third case the unstable block moves away from all discontinuity surfaces. Knowing the type and direction of movement, in the bounding discontinuities the normal reactions and the existing resultant shear force can be determined [7]. After calculating the maximum shear resistance using the Mohr-Coulomb failure criterion one obtains the factor of safety as the ratio of the maximum shear resistance to the existing shear force, as usual in structural mechanics. The definition of the factor of safety still often met within similar stability investigations, namely the ratio of the "resisting" to "driving" forces leads – as shown in [8] – to ambiguous results and is therefore not employed. AutoBlock determines the factor of safety for each kinematically admissible unstable block; if sliding is not possible, the reason is given (e.g. "heave" or "prevention by other discontinuities"). Since here too a large number of potential unstable blocks can occur, again different filter and visualization possibilities can be selected. For instance, one can display just those unstable blocks, whose factor of safety or sliding direction lie within a certain range. In addition, individual blocks can be clicked on, whereupon the corresponding information (type and direction of movement, factor of safety, reactions, etc.) appear in text form or graphically. As an alternative the terrain surface with the tracelines of the potential unstable blocks can be shown, whereby the factors of safety are plotted as vectors (Fig. 10): from the direction of the vectors the sliding directions of the associated blocks may be seen, their lengths representing the values of the factor of safety.

Fig. 10 Visualization of the factor of safety of potential unstable blocks



7 Final Remarks Thanks to automation and specially developed visualization means, especially for the kinematics and the calculated factors of safety, AutoBlock offers a powerful tool to engineering practice. Fundamental significance attaches to the automation: its advantage is not only in the smaller manual effort involved, but above all in guaranteeing that the critical potential unstable blocks and the critical areas within the region of investigation are really identified. It is impossible to describe all the features of AutoBlock here. Thus, for instance, it offers the option of exporting selected data and importing them into other programs (e.g. Excel), where they can be analyzed and represented at will. In addition, each view created in AutoBlock can be separately saved and further used. For a detailed description the reader is referred to the program manual or to AutoBlock’s help file (see http:// www.igt.ethz.ch/?product=5). Despite the extensive possibilities outlined above, application of AutoBlock by practicing engineers revealed the need for further extensions. For example, these include • Terrains with overhanging areas. Presently, overhanging areas can only be simulated by the introduction

of excavations. • Activation of an arbitrary number of sets of discontinuities. At the moment this is limited to four. • Extended visualization possibilities (e.g. "exploding" potential unstable blocks). • Introduction of arbitrary line loads and distributed loads as well as of water pressures, which can be

obtained from flow nets. • Extension of the admissible sliding mechanisms to the cases b), e) and c), f), respectively, of Fig. 1.

Literature [1] Londe, P. (1965): Une méthode d'analyse à trois dimensions de la stabilité d'une rive rocheuse.

Annales des Ponts et Chaussées, Paris, pp. 37-60. [2] Hoek, E., Londe, P. (1974): Surface Workings in Rock. Proceedings of the 3rd Congress of the Int.

Soc. Rock Mechanics, vol.1. [3] Kovari, K., Fritz, P. (1984): Recent Developments in the Analysis and Monitoring of Rock Slopes. IVth

Int. Symp. on Landslides, Toronto [http://www.igt.ethz.ch/?publ=19]. [4] Bergamin, St. (2004): Die Stabilität der Felsfundamente von Staumauern. Dissertation, Institut für

Geotechnik, ETH Zürich. [5] Fritz, P., Zheng, X. (1998): A Finite Element Framework for Geotechnical Applications based on

Object-Oriented Programming. Report, Institute for Geotechnics, ETH Zürich [http://www.igt. ethz.ch/?publ=145].

[6] Mäntylä, M. (1988): An introduction to solid modeling. Computer Science Press, Rockville, U.S.A. [7] Kovari, K., Fritz P. (1993): Re-Evaluation of the Stability of Large Concrete Structures on Rock.

Comprehensive Rock Engineering, v.4, pp. 671-694; J.A. Hudson. Pergamon Press; Oxford [http://www.igt.ethz.ch/?publ=24].

[8] Kovari, K., Fritz, P. (1976): Ein Beitrag zum Problem der Standsicherheit von Felsböschungen. 2. Nati-onale Tagung über Felsmechanik; Aachen [http://www.igt.ethz.ch/?publ=4].


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