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Science in China Series E: Technological Sciences © 2007

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3D integrated modeling approach to geo-engineering objects of hydraulic and hydroelectric projects ZHONG DengHua†, LI MingChao & LIU Jie Department of Hydraulic and Hydroelectric Engineering, School of Civil Engineering, Tianjin University, Tianjin 300072, China

Aiming at 3D modeling and analyzing problems of hydraulic and hydroelectric engineering geology, a complete scheme of solution is presented. The first basis was NURBS-TIN-BRep hybrid data structure. Then, according to the classified thought of the object-oriented technique, the different 3D models of geological and engineering objects were realized based on the data structure, including terrain class, strata class, fault class, and limit class; and the modeling mechanism was alternative. Finally, the 3D integrated model was established by Boolean operations between 3D geological objects and engineering objects. On the basis of the 3D model, a series of applied analysis techniques of hydraulic and hydroelectric engineering geology were illustrated. They include the visual modeling of rock-mass quality classification, the arbitrary slicing analysis of the 3D model, the geological analysis of the dam, and underground engineering. They provide powerful theoretical principles and technical measures for analyzing the geological problems encountered in hydraulic and hydroelectric engineering under complex geological conditions. 3D integrated model, engineering geology, geological analysis, hydraulic and hydroelectric project

Hydraulic and hydroelectric projects are thriving in China for reasons of economic sustainable development and the strategy for developing western regions. Most of the projects are located in high mountains and gorges, and there are complex geological structures and huge amounts of geological information to deal with. Thus, great difficulties are generated for engineering exploration, design, and construction[1]. However, it is hard for the traditional static 2D management and analysis mode of numerous geological data to satisfy the spatial analysis demands of geological engineers and designers. As the basis of digitization and visualization for the design and construction of hydraulic and hydroelectric projects, the relevant 3D geo-engineering modeling and analysis is a challenging and desiderative key problem. Received January 11, 2006; accepted January 23, 2007 doi: 10.1007/s11431-007-0042-0 † Corresponding author (email: [email protected]) Supported by the National Natural Science Foundation of China (Grant Nos. 50479048 and 50539120) and the National Science Fund for Distinguished Young Scholars of China (Grant No. 50525927)

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Sci China Ser E-Tech Sci | June 2007 | vol. 50 | no. 3 | 329-342

The problem is a hot and difficult topic in many fields, such as mathematics geology, mining geology, petroleum geology, hydrogeology, engineering geology, and computer science[2]. Houlding[2] presented the conception of 3D geoscience modeling in the early stages, and elaborated some fundamental technologies and methods, for example, the building of a spatial geological database, generating and fixing triangulation networks, and linking geological boundaries. Aiming at the particularity and complexity of geological bodies, Mallet[3] brought forward a discrete smooth interpolation modeling method, which became the kernel technology of GOCAD and gained support from many geophysics and petroleum companies[4]. De Kemp[5] applied 3D Bézier tools to construct visual models of complex geological structures, and Sprague et al.[6] used an advanced Bézier-NURBS hybrid structure to fit 3D geological surfaces. Courrioux et al.[7] realized an automatic volume reconstruction method using Voronoi diagrams for geological objects. Chai et al.[8] developed a set of 3D visualization systems of rock mass structures of the Xiluodu hydropower station, which could build 3D geological models and offer several simple slicing analysis. Wu and Xu put forward a geological modeling method with multi-source data integration[9], and established the architecture of 3D geological modeling for mining applications[10]. These achievements have contributed to the growth of 3D geological modeling theories and methods. In general, overseas studies on geological modeling were carried out earlier, and numerous commercial software packages are available, such as GOCAD, Earthvision, Gemcom, and Surpac. These tools have proved to be very successful in petroleum and mining applications. However, they are not designed specifically for application in the field of hydropower engineering geology, and are limited by great performance requirements and high cost. There are some similar research efforts, and many studies have been based on 3D geological modeling of hydropower engineering in China. But there are a few gaps in practical applications, for the conflict between the data storage capacity and the accuracy of the model, and the problem of simple analysis functions. So it is desirable to develop 3D geo-engineering modeling and analysis theories and technical methods for hydraulic and hydroelectric projects. Therefore, with reference to actual hydropower engineering projects, a complete methodological scheme is presented to realize 3D geo-engineering modeling and analysis of hydraulic and hydroelectric projects. It is integrated with advanced theories and techniques from hydraulic and hydroelectric engineering science, engineering geology, mathematical geology, and computer science; and it can solve three major problems in the following areas: (i) 3D data structure suitable for hydraulic and hydroelectric geo-engineering information. The 3D geological model derived from common data structures was limited by large data storage quantity, and it was hard to satisfy the needs of practical applications. It is necessary for the appropriate data structures to solve the conflict among complex geological structures, large amounts of information, and high analysis requirements. (ii) 3D geological modeling method integrating with multi-source data. The approach should construct 3D models of all kinds of geological structures systematically using complicated geological data; and the accuracy of the models should meet actual demands. (iii) Analysis and applications based on the 3D geo-engineering model. The purpose of the research is that the built model can be applied to engineering exploration, design, and construction of hydraulic and hydroelectric projects effectively and offer many useful services. This paper will trace and discuss the three problems in depth. 330

ZHONG DengHua et al. Sci China Ser E-Tech Sci | June 2007 | vol. 50 | no. 3 | 329-342

1 Hybrid data structure for hydraulic and hydroelectric geo-engineering model 1.1

NURBS-TIN-BRep hybrid data structure

The data structure of engineering geology is the basis of 3D geological modeling. Because of the complex geological structures, the large amounts of information, and the high analysis requirements in hydraulic and hydroelectric engineering regions, an appropriate 3D data structure is very important. At present, the data structures representing 3D entities include surface representation and voxel representation. The former has the advantage of presenting the boundaries, visualization, and geometric transformation of spatial objects, while the latter is dominant in displaying the internal information of spatial objects. Hydraulic and hydroelectric engineering is not concerned about the internal microcosmic attributes of geological bodies, but the effect of geological conditions on the design and construction and volume visualization techniques are immature and in progress. Therefore, we propose a new hybrid data structure with three surface representations for 3D hydraulic and hydroelectric geo-engineering models, which is composed of the Non-Uniform Rational B-Spline (NURBS) structure, the Triangulated Irregular Network (TIN) model, and the Boundary Representation (BRep) structure. The NURBS technique is the only expression standard in STEP (ISO, 1991) for free-form curves and surfaces and gives the uniform mathematical expression for all graphics[11]. For the irregular configuration of complex geological bodies, it has the advantages of small memory space, efficient computer processing, convenient database management, dimensional uniqueness, and geometric invariability[12]. Moreover, the TIN model has high accuracy but large memory capacity, so is regarded as a medium transitional format of the 3D digital terrain models using NURBS tools. The BRep structure defines solids by boundary surfaces, and provides an efficient volume description mode for geological objects[13]. In the BRep structure, the boundary surface can be any type of closed and orientable free-form surface, and topological relations of NURBS surfaces are organized in the study. The hybrid data structure is illustrated in Figure 1, and we design seven basic geometric elements, including points, curves, NURBS curves, NURBS surfaces, triangles, Mesh and BRep solid. It can not only represent geometric shapes and topological relationships of geological objects effectively, but must also combine the geometric objects with the relative information of geological attributes conveniently. The corresponding model has the advantages of high accuracy, small data quantity, and efficient Boolean operation. Therefore, the hybrid data structure can satisfy the demands of 3D geo-engineering modeling and analysis. 1.2

3D entity mathematical model of geological structures

Traditional geological elements usually are the defined minimum cell sets for dividing one whole geological body[9]. Generally, a 3D model based on these kinds of geological elements can meet the accuracy requirements, but occupies too large processing space or time. It will lower the geological analysis speed not to respond to user operations for plentiful data of hydraulic and hydroelectric engineering. Accordingly, based on the hybrid data structure and objective geological rules, we put forward the general entity mathematical model of geological structures, in which each kind of geological structure is regarded as a whole geological element. NURBS surfaces of geological structures are reconstructed by discrete points and curves of each layer, while geological bodies consist of different structural surfaces[14]. Then, the 3D entity mathematical model in the complete geological region Ω can be defined as follows: ZHONG DengHua et al. Sci China Ser E-Tech Sci | June 2007 | vol. 50 | no. 3 | 329-342

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Figure 1 Hybrid data structure of 3D geological modeling. n ⎧ ⎪ M Ω = ∪ Mci , i =1 ⎪ ⎪ ⎛ mi ⎞ ⎪ = ∪ ∪ Mc S S ⎜⎜ ∪ Slik ⎟⎟ , i = 1, 2, n, ⎨ i i1 i2 ⎪ ⎝ k =1 ⎠ ⎪ S = s ( P ), i = 1, 2, n; j = 1, 2, ij ⎪ ij ⎪⎩ Slik = s '({vik }),(vik ∈ ∂Si1 ∪ ∂Si 2 ), i = 1, 2,

(1)

n; k = 1, 2,

mi ,

where MΩ is the whole BRep geological model in Ω; n is the total number of geological bodies; Mci denotes a geological body, which consists of two dominant structural surfaces of Si1, Si2, and some peripheral surfaces Slik connecting Si1 and Si2, k=1, 2,…mi; Si1 and Si2 are the NURBS surfaces fitted by their point sets Pi1, Pi2; Slik is the NURBS surfaces generated by the vertex set {vik} from the boundaries of Si1 and Si2; ∂Sij is the set of all bounding vertexes of Sij, j = 1, 2; and mi is the number of boundary surfaces in the i element. Figure 2 describes a simple solid geological model. According to the spatial subdivision principle, any object with complex geometric shape can be subdivided into finite simple elements. Then, the reconstructed geological model by eq. (1) can represent the spatial geometric configurations of complex geological bodies wholly, rapidly and objectively.

Figure 2 A simple geological entity model.

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2 Classified modeling of geo-engineering objects in hydraulic and hydroelectric projects 2.1

Classification of engineering and geological objects

In hydraulic and hydroelectric engineering, investigated geological objects include plenty of irregular terrains, strata, overburdens, folds, faults, intrusive masses, dip offsets belts, joints, and deep fissures. Abundant geological information is often too disordered to gain a clear comprehension. On the basis of the classified thought of the object-oriented technique, the geological objects are generalized to several big classes with similar geometric shapes and attribute characters, and the corresponding hierarchical structure can be established; and it will improve 3D geological modeling greatly. The classification structure of engineering and geological objects is shown in Figure 3.

Figure 3

2.2

Classification structure of engineering and geological objects.

Classified modeling methodology

2.2.1 NURBS modeling of 3D digital terrain. Terrain is the most visible feature of geological structures. 3D Digital Terrain Models (DTM) converge all logic operations during the 3D geological body modeling process. Balancing the lower data storage requirements, and maintaining accuracy and efficiency in graphic manipulation, has always been a challenge for 3D geological modeling. Conventionally, 3D DTMs have been created using either regular GRID or TIN techniques. However, the precision of the GRID model is relatively low, while the data required by a TIN model is relatively large. Neither of these models meets the requirements of geological modeling, so the NURBS technique is used to build the 3D DTM. Because the original contours usually cannot describe the cliffs and gullies accurately and are discontinuous, it is difficult to generate the NURBS-DTM directly. While a TIN model can present these complex special shapes perfectly, therefore, integration of the NURBS technique and the TIN data model is an alternative solution for this challenge. This new integrated algorithm is described as follows: (i) Set up initial contours. If the contours are too sparse or dense, new contours are added by interpolation or redundant contours are reduced. (ii) Define the TIN model. Based on the adjusted contours, a 3D DTM can be defined in TIN ZHONG DengHua et al. Sci China Ser E-Tech Sci | June 2007 | vol. 50 | no. 3 | 329-342

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format using the Delaunay triangulation algorithm in GIS. And the long and narrow triangles should be deleted to get the TIN model with higher precision. (iii) Data conversion. Convert the generated TIN model from a GIS environment to a polygon mesh in the developed NURBS disposal system, ensuring the integrality of triangles. (iv) Compute control points. Extract adequate contour curves of continuous and uniform distribution from the mesh in u or v directions by a given interval, and control points can then be back-calculated based on these curves. (v) Fit the NURBS terrain surface. After collecting the control information, the terrain surface is fitted and generated newly using the designed function FitSurface (U-spans, V-spans, Stiffness), where the parameters represent grid number in u, v directions and surface stiffness, respectively. (vi) Generate the NURBS terrain skeleton. The NURBS surface is cut out by the defined range to gain the simplified terrain model. Moreover, the whole topographic skeleton model can be easily derived through Boolean operations. The method is convenient and has the advantages of fast processing speed and great practicability, for all complex graphics and mathematical operations are encapsulated into the bottom layer. The case study showed that the size of the NURBS-DTM model based on the TIN model decreases considerably by one order of magnitude, while the accuracy of the model is within the first-level standard of the China Bureau of Surveying and Cartography[14]. The NURBS-DTM model offers a feasible foundation for 3D geological modeling. 2.2.2 Geological modeling of strata class. The strata class objects include strata, overburden layers and interlayer dip offset belts. The geometric modeling method of the class objects will be carried on for strata bodies. For a single continuous stratal surface, the realization of NURBS structure is given by eq. (1). Each body is enclosed by six boundary surfaces including top and bottom, front and back, left and right. In fact, a stratal body is formed by Boolean operations among NURBS surfaces of top, bottom, and the topographic skeleton body. For several bedded strata, their contact relations consist of conformable contact, accordant unconformity contact, and angular unconformity contact; and from the viewpoint of the spatial geometric, there are four different connections between adjacent strata (Figure 4): inclusion, overlay, intersection, and multilayer intersections. It is difficult to match together these immediate surfaces if we use different data from adjacent strata. A simple method of trimming-overlap is provided here to sew stratal surfaces of adjacent strata. Taking the immediate surfaces of strata T1 and T2 in Figure 4 as an example, this method is simple (Figure 5): (i) Build the upper surfaces S1 and S2 of T1 and T2 according to their initial geological data (Figure 5(a)); (ii) Compute the intersecting lines l1 and l2 between S1 and S2 (Figure 5(b)); (iii) Trim S2 using l1 and l2 to obtain the surface S3, which is the joint surface between T1 and T2 (Figure 5(c)). Then, the surface S3 is regarded as the bottom of T1, which can match the stratum T2 perfectly. The strata models with other adjacent connections can be accomplished using a similar method. For folded strata, monodrome surfaces are the same as the above, while multi-value surfaces are emphasized. A complex geological surface from an overturned fold contains multiple z values for the same point (x, y). It cannot be interpolated and fitted by the acquired discrete data, so we propose a typical profile curves method based on NURBS tools to model multi-z surfaces. This 334


Figure 4

Sketch map of strata spatial connection.

Figure 5

Sewing surfaces of two adjacent strata.

algorithm includes four steps: (i) Collect data from drill-holes and cross-sections (Figure 6(a)), and analyze the geological and geometric features of the fold; (ii) To retain useful information, new typical profile curves can be interpolated with drill-hole data and fold elements such as nodal points and turning points (Figure 6(b)); (iii) Adding relevant boundary constraints, the collection of all curves is fitted to the smooth folded surface using the NURBS surface tool from network of curves (Figure 6(c)); (iv) Another boundary will be generated by the same way, and then the fold model is constructed by the BRep structure (Figure 6(d)).

Figure 6 Geometric modeling of an overturned fold. (a) Data collection; (b) typical profile curves; (c) NURBS folded surface; (d) fold solid.

2.2.3 Geological modeling of fault class. The fault class objects include faults, intrusive masses, deep fissures, and intrastratal dip offset belts. Fault disposal is a research area that presents difficulties in 3D geological modeling, and up to now there have been no perfect software tools or easy-to-handle solutions[9]. The main problems of fault modeling include multi-results of path curves between joint sections, and deficient information of extrapolating 3D fault deformation. In the complex geological region of hydraulic and hydroelectric projects, many crossed faults form very intricate fault networks. Therefore, we should not only construct a single fault body accurately, but also deal with the critical issue of two or more intersected faults. To model two crossed faults, two restrictions must be introduced as follows: (i) Boundary constraint (OnTsurf constraint). The hangingwall and footwall blocks, namely two parts of the broken fault, should be terminated at the breaking fault. That is to say, their borderline, the result of breaking movement, must be on the surface of the breaking fault body. (ii) Vector Link constraint (VecLink constraint). The displacement vector λ of broken fault can ZHONG DengHua et al. Sci China Ser E-Tech Sci | June 2007 | vol. 50 | no. 3 | 329-342

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be set by the change of relative position which is linked with the movement of the hangingwall and footwall blocks. Aiming at two different cases shown in Figure 7, respective methods should be adopted for modeling: (i) Direct breaking method. This applies to the case of the minor displacement of the broken fault (|λ|