Application of GIS Technique in Three-Dimensional Slope Stability Analysis

COMPUTATIONAL MECHANICS ISCM2007, July 30-August 1, 2007, Beijing, China 2007 Tsinghua University Press & Springer Application of GIS Technique in Three-Dimensional Slope Stability Analysis Cheng Qiu 1, 2 *, Mowen Xie 1, Tetsuro Esaki 2 1 Civil and Environmental Engineering School, the University of Science and Technology Beijing, Beijing, 100083 China 2 Department of Civil and Structural Engineering, Kyushu University, Japan Email: qiucheng@ies.kyushu-u.ac.jp Abstract Currently, even though some computer programs are commercially available for three-dimensional (3D) slope stability analysis, practical application of the 3D method in engineering issues is still lacking. A suitable method that using a common data form for 3D analysis is urgently required. A Geographical Information System (GIS), as a computer-based system, allows easy data updating, modeling, nice result presentations, and complex spatial analysis. It is ideal and anticipant to embed the 3D models within GIS environment. In this paper, a new GIS raster-based 3D deterministic model is proposed to accomplish the combination of the column-based 3D method and the GIS raster data. Multiple column-based 3D methods can be applied in this model. After extracting all slope-related information from study area to create a set of corresponding raster data layers, the 3D safety factor can be efficiently calculated by analyzing the raster data within a column-based 3D model. A GIS-based system is developed to implement all processes. Comparison studies with other existing programs validate the correction of the proposed algorithm while the effect of the number of columns using in discretization of the slope on resultant safety factors is also discussed. Keywords: Slope stability analysis; column-based 3D method; GIS. INTRODUCTION In slope stability analysis, it is clear that a three-dimensional (3D) situation may become important in cases where the geometry of the slope and slip surface varies significantly in the lateral direction, the material properties are highly anisotropic, or the slope is locally loaded (Chang [7]). Even though many 3D methods of analysis have been proposed (Hovland [15]; Chen and Chameau [8]; Hungr, 1987; Gens et al. [13]; Lam and Fredlund [22]; Huang et al. [16]), practical application of 3D methods in engineering issues is still lacking. For assessing slope stability in a 3D degree, the data of topography, geology, and groundwater, which are calculated within 3D model, should distribute in three dimensions. The 3D data for geometric characteristics of study area, such as slope angle and dip direction, also needed to be derived from elevation information. These spatially-distributed data are generally derived by interpolating the discrete data such as contours and boring results. These tasks would be very tediously and can hardly be done accurately without an intelligent tool. The main difficulties in practical application of 3D methods can be summarized as (1) processing and managing a vast amount of complex information for natural topography and geology, and (2) creating 3D data for topography, strata, ground water and failure surface through limited investigations. Currently, there are several computer programs commercially available for 3D slope stability analysis: 3D-PCSTABL (Thomaz and Lovell [27]), CLARA (Hungr [18]), TSLOPE3 (Pyke [24]), etc. The applicability and limitation of these computer programs have been reported by Stark and Eid [25]. It is 703

seen that few progresses have been made by them for overcoming above-mentioned difficulties in practical application. In addition, each program uses a unique implementation method with a unique data form. This limitation hinders the general use of them. Therefore, a method that using a common data form for 3D analysis is urgently required. On the other hand, landslide hazard is considered a continuous, spatially aggregated variable. Natural slopes that have been stable for many years may suddenly fail because of changes in topography, seismicity, groundwater flows, and weathering. Hence, the renewal of the data would result in a different assessment for same site. With the fast development in geo-information science and earth observation, there are more and more tools available for quickly data acquisition. For example, high resolution remote sensing products can be used to derive DEMs (Digital Elevation Model) in any desired time period. This situation also requires a suitable tool with powerful capabilities for data processing and quick reestablishing of the hazard assessment to respond to data renewal. A Geographical Information System (GIS), linked with remote sensing technology and telecommunications, have emerged as one of the most promising tools to support the landslide hazard assessment and management process. GIS as computer-based systems allow easy data updating, modeling evolution, nice and understandable result presentations, and, more important, complex spatial analysis. Recently, GIS techniques are increasingly used in landslide hazard analysis (Carrara et al. [4]; Kingsbury et al. [21]; van Westen [28]; Bonham-Carter [3]; Chung and Fabbri [9]; Terlien et al. [26]; Guzzetti et al. [14]; Dai et al. [11]; Xie et al., 2003; Chacon et al. [6]). Most of these studies adopted a statistical analysis method in which GIS is used just as a tool for database preparation and result presentation. When utilizing GIS to implement deterministic method of slope stability, two options exist: performing deterministic calculations inside or outside GIS. Performing calculations outside GIS needs to interface a third party solution, usually typified by static file transfer and disparate user interfaces. In this kind of approach, even though external existing models can be used directly without losing time in programming the model algorithms into GIS, unfortunately, it is always wrought with complication caused by data conversion between different hardware platforms, operating systems, database servers, and operational models, both in data input and result presentation. To overcome the difficulties in data conversion, deterministic calculations can be performed within GIS. However, so far, due to the use of complex algorithms and iteration procedures in deterministic model, and the inherent 2D structure of GIS data, only some simple models, such as infinite slope models that allow for calculating safety factor for each pixel of GIS raster data individually, have been applied inside GIS system (Carrara [5]; van Westen and Terlien [29]; Mankelow and Mupphy [23]; Dai and Lee [10]). The availability of the 3D method for analyzing practical slope issues is clear. It is therefore ideal and anticipant to embed 3D models within GIS environment through a suitable implementation approach. In this paper, a new GIS raster-based 3D deterministic model is proposed to embed the professional analysis model within GIS. All slope-related information is extracted from a study area to create a set of corresponding raster data layers. Then the GIS raster data is analyzed by a column-based 3D method to calculate the safety factor. A GIS-based system is developed to implement all processes. The comparison studies of the proposed method with other existing programs validate the correction of the proposed algorithm while the effect of the number of the columns using in discretization of the slope on resultant safety factors is also discussed. MECHANISM OF GIS RASTER-BASED 3D MODEL 1. Availability of GIS raster data model GIS raster data are composed of one or more equally spaced cells whose value usually records one property of a geographic phenomenon occurring over the patch of space it covers. In GIS, real-world features related to slope stability are normally modeled by raster data layers where each layer represents a certain type of information such as topography, stratum, or groundwater. The superposed structure of the strata can be therefore presented by overlay of the multiple raster layers. The overlay extends the 2D raster layers to a third dimension, which makes the application of 3D professional models possible. Each cell of raster layer at a local position can be imaged to a 3D column that consists of several layers. The elevations of the ground surface and all the boundary surfaces of strata 704

at the same x and y coordinates define the positions of the ground surface and the strata in the 3D column. As a result, the geometric characteristics of each grid-column within the sliding mass can be fully defined as shown in Fig. 1. Figure 1: The mechanism of GIS raster-based 3D model Coincidentally, most 3D deterministic methods for slope stability analysis use a column-based model in which the sliding mass is divided into a number of smaller soil columns. Combination of the grid-columns that derived from the overlay of GIS raster layers and the soil columns that derived from discretization of the sliding mass makes the application of 3D deterministic models possible. Based on the Mohr-Coulomb criterion, the safety factor of a slope failure mass is evaluated by comparison of the magnitude of available shear strength with the shear strength required just to maintain stability along a potential failure surface. In a column-based 3D model, the available and the required shear strength can be approximately calculated by summating corresponding items of all soil columns. J I Fava( i, j) SF3 D = (1) F ( i, j) J I req where, SF 3 D =the 3D safety factor, F ava ( i, j), F req ( i, j) =the available and required shear strength function of the soil column ( i, j) within the sliding mass, respectively, and I, J =the number of rows and columns of the raster data within the sliding mass, respectively. The relevant items for calculating the available and required shear strength in the above equitation include elevation data of ground surface, slip surface, boundary of strata, groundwater level (if it exists), and topographical parameters such as gradient and aspect of the ground surface. Information for each item is stored in a raster layer. Because a single raster layer only represents a certain type of information, it is not effective to treat so many raster layers at the same time. In contrast, vector data that comprise three geometry data types point, line, and polygon, can describe many additional characteristics archived in an attribute table. Therefore, a point dataset is adopted here to manage the information of all raster layers. As shown in Fig. 2, the location of each point is set at the center of corresponding pixel of the rater data, and the fields of the attribute table relate to each raster layer respectively. The utilization of the point dataset greatly expedites and simplifies the computational process for the 3D safety factor. 2. Implementation of column-based 3D method using GIS raster data It is already known that the soil columns of a column-based 3D deterministic model can be accommodated by the overlay of the corresponding GIS raster layers. Consequently, all of the items in the equation for calculating the 3D safety 705

Figure 2: Point dataset for integrating multiple raster layers Figure 3: 3D view of one column and portion of slip surface for deriving geometric parameters factor may be acquired by analyzing raster data using GIS analysis functions. As shown in Fig. 3, the area of the slip surface of a soil column is calculated by 2 2 ( 1 sin θ sin θ ) 2 xz yz A = d (2) cosθ xz cosθ yz In which, θ xz and θ yz are derived by tanθ xz = tanθ sin( Asp) tanθ yz = tanθ cos( Asp) (3), In the above equations, θ and Asp can be automatically calculated by GIS spatial analysis functions from the elevation data of the slip surface. The apparent dip of the main inclination direction of the sliding mass can be calculated by following equation: tanθ = tanθ cos( Asp Asp) (4) where, A =the area of the slip surface of a soil column; d =the cell size of the raster data; θ xz =the apparent dip of x-axis; θ yz =the apparent dip of y-axis; θ =the slope angle of the slip surface of a soil column; θ =the apparent dip of the main inclination direction of the sliding mass; Asp =the inclination direction of the slip surface of a soil column; Asp =the main inclination direction of the slip surface of the sliding mass. Assuming that the intercolumn vertical shear forces are negligible, and the vertical force equilibrium of each column and the overall moment equilibrium of the column assembly are sufficient conditions to 706

determine all of the unknowns, the safety factor can be iteratively derived from the sum of moments around a common horizontal axis and the equilibrium equation of the vertical forces: 1 ( W U cosθ ) tanφ + c Acosθ SF D = ( W sinθ ) (5) 3 1 cosθ + SF tanφ sinθ J I J I 3D where, W =the weight of soil column; U =the pore pressure acting on the slip surface of soil column; φ =the effective friction angle; and c =the effective cohesion. This is the GIS form of the 3D algorithm proposed by Hungr [17], based on a generalization of the simplified Bishop s 2D method [2]. Using the same assumptions as the above-mentioned, it is also possible to iteratively derive the safety factor from the horizontal force equilibrium in the direction of motion. It is the GIS-based 3D equivalent of the Janbu s simplified method without a correction factor [20]. SF 3D = [ J I J I c A+ ( N U)tanφ ]cosθ N sinθ cos( Asp Asp) If the vertical sides of the soil columns are assumed to be frictionless (no slide forces on the vertical sides of the soil columns, or with their influence canceling out), as they are in Hovland s model [15], the 3D safety factor can be directly deduced from the horizontal force equilibrium in the direction of motion (Xie et al. [31]): [ c A + ( W cosθ U)tanφ J I W sinθ cosθ ]cosθ SF3 D = (7) J I It should be noted that, unlike other methods, the direction of y (or x) axis of the local coordinate system used in this model is not necessarily identical to the direction of sliding, which means the equations of various 3D methods that mentioned above can be applied in a unified 3D coordinate system. COMPUTATIONAL IMPLEMENTATION (6) Figure 4: Flowchart of computational procedures 707

Fig. 4 illustrates the computational procedures of the proposed model. All slope-related data is firstly translated into the form of GIS raster dataset, and be subsequently analyzed by GIS spatial analyst functions to obtain the necessary parameters for the slip surface and each column. These parameters are then assigned into the models to calculate the 3D safety factor. The proposed theory has been implemented into a GIS-based computer model programmed by Visual Basic language using Microsoft COM (Component Object Model) technology. COM is a protocol that can be used to build reusable software components that are interchangeable in distributed systems. Here, ArcObjects, the framework that forms the foundation of the ArcGIS TM applications (a GIS software developed by ESRI) with more than two thousands COM based components providing, has been used. The developed model was packaged as an extension working within ArcGIS TM for direct utilization of GIS functions of spatial data treatment. VERIFICATION The developed model has been tested to ensure that the method is properly implemented and the various features of the model are functioning properly. Two of the evaluation example problems are presented in this paper. 1. Example 1 The first example problem is a 3D, symmetrical, circular failure surface in a homogeneous, purely cohesive slope. The section view of the spherical slip surface and the material properties are illustrated in Fig. 5. The problem was studied by Baligh and Azzouz [1], using the closed-form solution; the 3D safety factor was calculated to be 1.402. Hungr et al. [19] used the CLARA model to compute the same problem and obtained the safety factor as 1.422. The problem was also solved by Lam & Fredlund [22], using the 3D-SLOPE model. The computed safety factor ranged from 1.386 to 1.402, corresponding to the number of columns using in discretization of the slope, ranged from 1,200 to 540. Huang et al. [16] studied the relationship between the safety factors and the column numbers distributed in a wider range than that was used by Lam & Fredlund [22]. The result showed an increase in the safety factors with the increase of the number of columns. Figure 5: Center section of circular 3D failure surface in cohesive slope Figure 6: Calculated values of safety factor versus number of columns using in discretization of the slope 708

Using three 3D methods provided by the proposed model, namely the 3D extension of Bishop method, the 3D extension of Janbu method, and the revised Hovland method, the resulting relationships between the calculated values of safety factor and the number of columns are shown in Fig. 6, with the results reported by Lam & Fredlund [22] and Huang [16] are also plotted. It is seen that the safety factors calculated by all methods demonstrated a consistent trend with Huang s result [16] when the numbers of columns were increased. Otherwise, the safety factors obtained by the revised Hovland s method showed a relatively slight change of 2.1%, compared to 5.4% by the 3D extension of Bishop s method and 10.6% by the 3D extension of Janbu s method. The difference between the methods may come from different assumptions on the intercolumn forces and different ways for derivation of the equations. 2. Example 2 The other example problem is a 3D composite slip surface in a homogeneous slope. Fig. 7 shows a section view of the example slope which is initially used by Fredlund and Krahn [12] for the 2D approach. Xing [32] firstly extended this example to a 3D study. The 3D safety factor was computed by Xing to be 1.553 for the composite slip surface without the water table and 1.441 with the water table. This problem was also studied by Hungr et al. [19] using CLARA; the resultant 3D safety factors were 1.62 without water table and 1.54 with water table. This failure surface was also used by Lam & Fredlund [22]; their results were 1.534 1.607 without the water table and 1.447 1.511 with the water table with the use of several different 3D approaches. The 3D safety factors obtained by Huang et al. [16] were 1.645 without the water table. Figure 7: 2D failure surface initially used by Fredlund and Krahn [12] Table 1: Calculated values of safety factor using three methods proposed in this study with different numbers of columns Models Number of columns 973 2674 24631 98537 157250 629823 3D Bishop 1.686 1.704 1.720 1.723 1.723 1.724 3D Janbu 1.576 1.601 1.624 1.631 1.631 1.633 Revised Hovland 1.652 1.666 1.678 1.680 1.680 1.681 Without the water table considered, the safety factors were calculated by the proposed model, with different numbers of column were used, as tabulated in Table 1. The results of all methods gave a similar tendency to approach a steady value of the safety factor when the number of columns was increased. It can be seen that the revised Hovland s method gave a relative approximation of the safety factors by the 3D extension of Bishop s method (the average percentage difference was 2.35%), while the 3D extension of Janbu s method significantly underestimated the safety factors compared with the others (the average percentage difference was 5.68%). Table 2 summarizes the resultant safety factors of the composite slip surface with or without the water table calculated by various 3D methods. In comparison with other similar methods, the 3D methods implemented by the proposed model tended to approach a slightly bigger value of the safety factor. The average percentage difference between the results from the proposed model and 709

Table 2: Result of comparative study using the composite slip surface Methods Without watertable Cases With watertable Xing s 3D method 1.548 1.441 Huang s 3D method 1.645-3D Bishop method by Hungr 1.620 1.540 3D Bishop method by Lam & Fredlund 1.607 1.511 3D Bishop method by present study 1.720 1.630 3D Janbu method by Lam & Fredlund 1.558 1.481 3D Janbu method by present study 1.624 1.556 Revised Hovland method by present study 1.678 1.579 those from other methods was around 6%. The difference may be due to the use of a large number of columns, like the tendency that has already been shown in the first example program. Moreover, from both example problems, it found out that when the number of the columns is beyond 20000, the safety factor will show a tendency of becoming steady. CONCLUSIONS Nearly universal availability of computers and much improved understanding of the mechanics of slope stability analyses have brought about considerable change in the computation aspects of slope stability analysis. In contrast with most GIS-based studies that performing numerical analyses in a third party package while GIS only performs regional data preparation and presentation, this study embeds professional models within GIS by developing an enhanced GIS system for advanced application of GIS techniques in landslide hazard assessment. A GIS raster-based model for 3D slope stability analysis is presented. Multiple column-based 3D methods can be adopted in this model through translating various data forms into GIS raster data. Once GIS raster layers of slope stability related data are acquired, this approach is shown to have the ability to simplify the data-input procedure and the column discretization, and to expedite the safety factor computations. The use of GIS data form and GIS functions provides the convenience both in renewal of the data and in multiple cases study. The proposed GIS-based model was validated satisfactorily by two example problems. Safety factors that obtained by this model showed a little overestimation comparing other published 3D methods, due to the use of more columns. The number of columns using in discretization of the slope was found out to be at least 20000 for making the resultant 3D safety factor fixed. It is hoped that this study could broaden the horizon of the researchers as GIS provides an opened framework that allows users to build own model based on its spatial function system. It is possible to develop a suite of GIS tools which provide specific functions to many analysts, both within civil engineering and also in other disciplines which may rely on GIS. The ready availability of such functions would further position GIS as a tool for professional inquiry and analysis, rather than simply a sophisticated data display and query engine. REFERENCES 1. Baligh MM, Azzouz AS. End effects on the stability of cohesive slopes. ASCE Journal of the Geotechnical Engineering Division, 1975; 101(11): 1105-1117. 2. Bishop AW. The use of the slip circle in the stability analysis of slopes. Geotechnique, 1954; 5(1): 7-17. 3. Bonham-Carter GF. Geographic Information Systems for Geoscientists: Modeling with GIS. Pergamon, Ottawa, Canada, 1994. 710

4. Carrara A, Cardinali M, Detti R, Guzzetti F, Pasqui V, Reichenbach P. GIS techniques and statistical models in evaluating landslide hazard. Earth Surface Processes and Landforms, 1991; 16: 427-445. 5. Carrara A, Cardinali M, Guzzetti F, Reichenbach P. GIS technology in mapping landslide hazard. In: Geographical Information Systems in Assessing Natural Hazards, Kluwer Academic Publisher, Dordrecht, The Netherlands, 1995, pp.135-175. 6. Chacon J, Irigaray C, Fernandez T, El Hamdouni R. Engineering geology maps: landslide and geographical information systems. Bulletin of Engineering Geology and the Environment, 2006; 65(4): 341-411. 7. Chang M. A 3D slope stability analysis method assuming parallel lines of intersection and sifferential straining of block contacts. Canadian Geotechnical Journal, 2002; 39: 799-811. 8. Chen RH, Chameau JL. Three-dimensional limit equilibrium analysis of slopes. Geotechnique, 1983; 32(1): 31-40. 9. Chung CF, Fabbri AG. Multivariate regression analysis for landslide hazard zonatin. In: Carrara A, Guzzetti F eds. Geographical Information Systems in Assessing Natural Hazards. Kluwer Academic Publisher, Dordrecht, The Netherlands, 1995, pp.107-142. 10. Dai FC, Lee CF. Terrain-based mapping of landslide susceptibility using a geographical information system: a case study. Canadian Geotechnical Journal, 2001; 38: 911-923. 11. Dai FC, Lee CF, Ngai YY. Landslide risk assessment and management: an overview. Engineering Geology, 2002; 64: 65-87. 12. Fredlund DG, Krahn J. Comparison of slope stability methods of analysis. Canadian Geotechnical Journal, 1977; 14: 429-439. 13. Gens A, Hutchison JN, Gavounidis S. Three dimensional analysis of slices in cohesive soils. Geotechnique, 1988; 38: 1-23. 14. Guzzetti F, Carrara A, Cardinali M, Reichenbach P. Landslide hazard evaluation: a review of current techniques and their application in a multi-scale study, Central Italy. Geomorphology, 1999; 31: 181-216. 15. Hovland HJ. Three-dimensional slope stability analysis method. Journal of the Geotechnical Engineering, Division Proceedings of the ASCE, 1977; 103(9): 971-986. 16. Huang C, Tsai C, Chen Y. Generalized method for three-dimensional slope stability analysis. Journal of Geotechnical and Geoenvironmental Engineering, 2002; 128(10): 836-848. 17. HungrO. An extension of Bishop s simplified method of slope stability analysis to three dimensions. Geotechnique, 1987; 37(1): 113-117. 18. Hungr O. CLARA: Slope Stability Analysis in Two or Three Dimensions. O. Hungr Geotechnical Research, Inc., Vancouver, B.C., Canada, 1988. 19. Hungr O, Salgado FM, Byrne PM. Evaluation of a three-dimensional method of slope stability analysis. Canadian Geotechnical Journal, 1989; 26: 679-686. 20. Janbu N, Bjerrum L, Kjaernsli B. Soil Mechanics Applied to Some Engineering Problems. Norwegian Geotechnical Institute, Publication 16, 1956. 21. Kingsbury PA, Hastie WJ, Harrington AJ. Regional landslide hazard assessment using a geographical information system. Proceedings of the Sixth International Symposium Landslides, Christchurch, New Zealand, 1992; 2: 995-999. 22. Lam L, Fredlund DG. A general limit equilibrium model for three-dimensional slope stability analysis. Canadian Geotechnical Journal, 1993; 30: 905-919. 23. Mankelow MJ, Mupphy W. Using GIS in probabilistic assessment of earthquake triggered landslide hazard. Journal of Earthquake Engineering, 1998; 2(4): 593-623. 24. Pyke R. TSLOPE3: Users Guide. Taga Engineering Systems and Software, Lafeyette, Calif., USA, 1991. 711

25. Stark TD, Eid HT. Performance of three-dimensional slope stability methods in practice. Journal of Geotechnical and Geoenvironmental Engineering, 1998; 124(11): 1049-1060. 26. Terlien MTJ, van Asch TWJ, van Westen CJ. Deterministic modeling in GIS- based landslide hazard assessment. In: Geographical Information Systems in Assessing Natural Hazards, Kluwer, London, UK, 1995, pp. 57-77. 27. Thomaz JE, Lovell CW. Three dimensional slope stability analysis with random generation of surfaces. Proc. 5th Int. Symp. on Landslides, 1988; 1: 777-781. 28. Van Westen CJ. Application of Geographical Information System to Landslide Hazard Zonation. ITC Publication No.15, ITC, Enschede, The Netherlands, 1993. 29. Van Westen CJ, Terlien MTJ. Deterministic landslide hazard analysis in GIS: a case study from Manizales (Colombia). Earth Surface Process Landforms, 1996; 21: 853-868. 30. Xie M., Esaki T, Zhou G, Mitani Y. GIS-based 3D critical slope stability analysis and landslide hazard assessment. Journal of Geotechnical and Geoenvironmental Engineering, ASCE, 2003; 129(12): 1109-1118. 31. Xie M, Esaki T, Zhou G. Three-dimensional stability evaluation of landslides and a sliding process simulation using a new geographic information systems component. Natural Hazards, 2004; 43: 503-512. 32. Xing Z. Three-dimensional stability analysis of concave slopes in plan view. Journal of Geotechnical Engineering, 1988; 114(6): 658-671. 712