Key Block Analysis Method for Information Design and Construction Technology in Large Long Tunnels

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1 Ke Block Analsis Method for Information Design and Construction Technolog in Large Long Tunnels Jae-Yun HWANG Senior Research Fellow, Busan Metropolitan Council (00, Jungan-Daero, Yeonje-Gu, Busan Cit, 6-75, Korea) This paper is suggested a ke block analsis method for information design and construction technolog in large long tunnels. Then the application of the ke block analsis method for information design and construction technolog to the actual example of the large long tunnel with a ver-large cross section is described. The suggested method considers finite persistence of discontinuities. To illustrate the applicabilit of this analsis method for information design and construction technolog in large long tunnels, the analtical results are examined with those of the conventional analsis method. Ke Words :ke block analsis, information design and construction technolog, large long tunnel, discontinuit. INTRODUCTION The information design and construction technolog in tunnels has been becoming important recentl. Rock masses include various discontinuities such as joints, fractures, faults, bedding planes, cracks, cleavages, schistosities and fissures. In general, discontinuities can var from a few centimeters to man meters. The behavior of tunnels in hard rocks is, therefore, mainl controlled b various discontinuities (Ohnishi, 00; Hwang, 00). As for the assessment of the rock structure induced failures, the so-called block theor was suggested b Goodman and Shi (985). Excavations in discontinuous rock masses are frequentl affected b ke blocks, which are critical blocks of rock bounded b discontinuities and excavation surfaces. The block theor is a geometricall based on set of techniques that determine where dangerous blocks ma exist in a rock mass intersecting b variousl oriented discontinuities in D. The block theor is a quite useful method to determine the stabilit of rock blocks. However, the block theor is based on some assumptions which limit its usefulness. In the block theor, joint surfaces are assumed to extend entirel through the volume of interest; that is, no discontinuities will terminate within the region of a ke block (Ohnishi et al., 985). The block theor is based on the assumption of the infinite persistence of discontinuities, and does not consider the effects of finite discontinuit persistence, therefore cannot handle a complex concave shaped block (Fig. ). The rock block should be divided into convex sub-blocks. In practice, it is necessar to consider the persistence of finite discontinuities to attempt appling the block theor to successive excavations. This paper is suggested a new ke block analsis method for information design and construction technolog in large long tunnels. Then the application of the ke block analsis method for information design and construction technolog to the actual example of the large long tunnel with a ver-large cross section is described. The suggested method considers finite persistence of discontinuities. The new analsis method for information design and construction technolog in large long tunnels can handle concave and convex shaped blocks. To illustrate the applicabilit of this analsis method for information design and construction technolog in large long tunnels, the results are examined with those of the conventional analsis method

2 Fig. An example of concave shaped blocks in tunnel. Fig. Discontinuit disc model.. THREE-DIMENSIONAL DISCONUOUS ROCK MASS MODELING () Discontinuit disc model In order to build a three-dimensional model considering finite discontinuit persistence, the problem concerning geometric shape and spatial extent of discontinuities must be addressed. Several studies (Warburton, 980; Long and Billaux., 987; Pollard and Adin, 988; Priest, 99; Ohnishi et al., 994) have demonstrated that through the analsis of trace data and examination of discontinuit surfaces, discontinuities are likel to be roughl elliptical or circular. The fundamental feature of the discontinuit disc model is the assumption of circular discontinuit shapes (Ohnishi et al., 994; Mardia, 97; Pahl, 98; Dershowit, 984; Kulatilake et al., 99; Zhang and Einstein, 000) as shown in Fig.. The sie of circular discontinuities is defined completel b a single parameter, the discontinuit radius. Discontinuit radius ma be defined deterministicall, as a constant for all discontinuities, or stochasticall b a distribution of radii. The best and most widel adopted sampling strateg for determining discontinuit sie is based on the measurement of the lengths of the traces produced where the discontinuities intersect a planar face (Priest, 99). The probabilit distribution of discontinuit diameters ma be inferred from the distribution of the trace length, which can be measured through excavation surfaces or natural outcrops. However, the direct estimation of trace lengths is often influenced b varied biases, and the distribution inferred from trace length involves an integration that can onl be evaluated numericall, and this also becomes a barrier when building a statistical model with Monte Carlo simulation. In order to overcome these problems, the stochastic discontinuit sstem modeling process of this developed program first assumes that discontinuit diameter and trace length have the same distribution function, then determines the mean and standard deviation of discontinuit diameters through model calibration. Discontinuit location ma also be defined b a deterministic pattern or a stochastic process. The most frequentl used model to define the spatial location of stochastic discontinuities is the Poisson model. In the discontinuit sstem modeling process of this developed program, the spatial location of stochastic discontinuities was assumed to follow the Poisson model. () Region modeling for analsis The model region of this stud is a closed domain with a certain number of faces. The model region ma be of an shape closed b polgons. The excavation faces ma be convex or concave polgonal faces with or without interior holes. All excavation faces should form a closed domain of target rock mass for the analsis; if the do not form a closed domain, some fabricated faces, such as boundar faces, should be added. A curve face should be approximated b a number of polgonal faces.. IDENTIFICATION OF D LOOP In a discontinuit sstem, not all discontinuities are connected; some discontinuities do not intersect with

3 other discontinuities, and some discontinuities intersect with ver few discontinuities (Yu, 000). Before the rock block identification stage, unconnected discontinuities should be identified and eliminated. A discontinuit is referred to as connected onl when it plas a part in block. A connected discontinuit must feature the two following characteristics: (i) it is connected to at least discontinuities including excavation faces, (ii) within the planar disc of the considered discontinuit, the intersections between the considered discontinuit and other connected discontinuities or excavation faces must form at least one connected loop. Fig. shows some cases of connected and unconnected discontinuities. B checking ever discontinuit against the two characteristics mentioned above, all unconnected discontinuities can be identified and eliminated. It should be noted that this is an iteration procedure. Some discontinuities, which look connected, ma be identified to be unconnected after unconnected discontinuities are eliminated. (a) Connected. (b) Unconnected. Fig. Somes cases of connected and unconnected discontinuities. 4. IDENTIFICATION OF D LOOP A whole discontinuit does not form a surface of block. Therefore, after the elimination of unconnected discontinuities, intersections among discontinuities will be calculated, then the discontinuities which form a block will be identified. A face in a D closed region forms when other discontinuities cut the region. A D line loop should be established at the surfaces of the three-dimensional region. When this criterion is satisfied at all faces, one or more blocks are formed. (a) (b) (c) Fig.4 D loop

4 The algorithm of the D loop is demonstrated graphicall b an example in Fig. 4. One individual D loop ma be represented b its boundar nodes arranged in clockwise direction or counter-clockwise direction. The D loop ma also be represented b its boundar D loops arranged in clockwise direction or counter-clockwise direction. For example, a D loop on face P ma be represent b a closed D loop series L L L4 L5 L. Consequentl, a block is represented b a number of D loops; a D loop is represented b a number of D loops; a D loop is represented b the nodes on its boundaries; and a node is described b D coordinates. Naturall, all the above identification processes will be accomplished automaticall b computer. 5. FINALIZATION OF BLOCK SHAPE AND VOLUME The blocks will be identified b a simplex integration method. Simplex integration method is an accurate solution on n-dimensional domains with an shape. Simplex integration is based on the topolog (Shi, 00). 5. Different from the ordinar integration, the simplex integration has onl the simplex as the integral domain. The simplex also has positive and negative orientations. The positive and negative orientations are defined as positive and negative volumes respectivel. Fig.5 0,,, Dimensional simplex. The coordinates of the vertices V 0, V, V, V on an D simplex are supposed as (x 0, 0, 0 ), (x,, ), (x,, ) and (x,, ) respectivel. Therefore, the volume of the D simplex V 0 V V V is x0 0 0 x V! x () x The volume of simplex V V 0 V V is the negative volume of simplex V 0 V V V. The integration formulas on the domain of D simplex V 0 V V V with non-ero volume can be represented as follows (Shi, 00). Supposing (x 0, 0, 0 ), (x,, ), (x,, ) and (x,, ) are the coordinates of the vertices V 0, V, V and V respectivel. Set J () x x x x

5 6. EXAMPLE OF APPLICATION TO TUNNEL The actual tunnel is 900m long. Photo shows a photograph of cutting face of actual tunnel. The standard cross-section of the actual tunnel is ver large (00m ) and wide (8m) compared with ordinar tunnels. Photo Photograph of cutting face of the tunnel. The measurement from unrolled discontinuit trace map was performed. Fig. 6 shows the Schmidt net of discontinuities detected from unrolled trace map of the TBM pilot tunnel. Fig.6 Schmidt net of discontinuities detected from unrolled trace map

6 The prediction of ke blocks using the suggested ke block analsis method in actual tunnel was performed. The ke blocks were predicted and prevented before the main tunnel excavation. To illustrate the validit and applicabilit of the suggested sstem, the analtical results are compared and examined with results b conventional analsis method. The ke block analsis b the method stated earlier was based on the assumption of infinite persistent discontinuities, and considering the effects of discontinuit persistence was not possible using it. However, the ke block analsis of this stud considered finite discontinuit persistence. The discontinuit information was acquired from the investigation of the advancing drift with TBM. Discontinuities were generated within the modeled region as shown in Fig. 7. Fig.7 Discontinuities generated within the modeled region. In this suggested method, the radii of discontinuit discs were determined to be 0m and 45m. Table shows the number of ke blocks in STA The distance between each STA is 00m. Two ke blocks were predicted in STA The number of ke blocks in suggested method was exactl the same as that in the conventional method as shown in Table. The ke block No. of this suggested method is compared with that of the conventional method as shown in Fig. 8. Viewpoints in each ke block are slightl different. However, the upper case ke block No. of this stud shows a good match with that of the conventional method. Table Predicted ke blocks

7 (a) Conventional method. (b) The suggested method in this stud. Fig.8 Ke block No.. 7. CONCLUSIONS This paper is suggested a new ke block analsis method for information design and construction technolog in large long tunnels. Then the application of the ke block analsis method for information design and construction technolog to the actual example of the large long tunnel with a ver-large cross section is described. Three-dimensional rock block identification with consideration of the persistence of discontinuities is performed b using discontinuit disc model. The new analsis method for information design and construction technolog in large long tunnels can handle concave and convex shaped blocks. The ke block analsis method considering discontinuit persistence for information design and construction technolog consists of the following major steps: Discontinuit measurement from unrolled trace map, D discontinuous rock mass modeling, Identification of D loop, Identification of D loop, Finaliation of block shape and volume, Removabilit and stabilit analsis of rock blocks. In order to illustrate the applicabilit of this developed analsis method for information design and construction technolog in large long tunnels, the results are examined and compared with those of the conventional method. The ke block analsis b the suggested method in this stud shows a good match with that b the conventional method. ACKNOWLEDGMENT: The author is grateful to Prof. Yuo Ohnishi, Vice-President of Koto Universit, for his help and encouragement in this stud. REFERENCES ) Dershowit, W. S. (984), Rock Joint Sstems, Ph.D. Dissertation, Massachusetts Institute of Technolog, Cambridge, USA. ) Goodman, R. E. and Shi, G. H. (985), Block Theor and Its Application to Rock Engineering, Prentice-Hall. ) Hwang, J.-Y. (00), Stabilit Evaluation of Rock Blocks in Tunnels for Observational Method, Ph.D. Dissertation, Koto Universit, Koto, Japan, pp ) Kulatilake, P. H. S., Wathugala, D. N. M. and Stephansson, O. (99), "Joint Network Modeling with a Validation Exercise in Stripa Mine, Sweden", International Journal of Rock Mech. Min. Sci. & Geomech. Abstr., Vol 0: 5, pp ) Long, J. C. S. and Billaux, D. M. (987), "From field data to fracture network modeling: an example incorporating spatial structure", Water Resources Research, Vol., No. 7, pp ) Mardia, K. V. (97), Statistics of Directional Data, Academic Press Inc., London. 7) Ohnishi, Y. (00), "Numerical Methods and Tunneling", Proc. of the Fourth International Summer Smp., JSCE, Koto, Japan, pp. -. 8) Ohnishi, Y., Nagano, K. and Fujikawa, T. (985), "Evaluation of Stabilit of Excavated Jointed Rock Mass b Block Theor", Journal Geotechnical Engineering, JSCE, No. 64 / -4, pp ) Ohnishi, Y., Nakagawa, S. and Tanaka, M. (994), "Methods of Estimation for Geometric Distributions of Rock Joints", Journal

8 Geotechnical Engineering, JSCE, No. 499 / -8, pp ) Pahl, P. J. (98), "Estimating the mean length of discontinuit traces", International Journal of Rock Mech. Min. Sci. & Geomech. Abstr., Vol. 8, pp. -8. ) Pollard, D. and Adin, A. (988), Progress in Understanding Jointing over the Past Centur, Geol. Soc. of America Bulletin, Vol. 00, pp ) Priest, S. D. (99), Discontinuit Analsis for Rock Engineering, Chapman & Hall. ) Shi, G. H. (00), "Three Dimensional Discontinuous Deformational Analses", Proc. Fourth International Conf. on Analsis of Discontinuous Deformation, Edited b Nenad Bicanic, pp.-. 4) Warburton, P. M. (980), A sterological interpretation of joint trance data, International Journal of Rock Mech. Min. Sci. & Geomech. Abstr., Vol. 7, pp ) Yu, Q. (000), Analses for Fluid Flow and Solute Transport in Discrete Fracture Network, Ph.D. Dissertation, Koto Univ., Koto, Japan. 6) Zhang, L. and Einstein, H. H. (000), "Estimating the intensit of rock discontinuities", International Journal of Rock Mech. Min. Sci., Vol 7, Issue 5, pp