FORMATION OF THE NUMERICAL MODEL AND INTERACTION MATRIX FOR CARBONATE ROCK MASS AROUND HYDROTECHNICAL TUNNEL

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1 Author FORMATION OF THE NUMERICAL MODEL AND INTERACTION MATRIX FOR CARBONATE ROCK MASS AROUND HYDROTECHNICAL TUNNEL Azra Špago, phd, a graduate civil engineer, the Faculty of Civil Engineering, University Džemal Bijedić Mostar Milorad Jovanovski, phd, a gradute geologist, the Faculty of Civil Engineering, "Ss. Cyril and Methodius" University, Skiopje Suad Špago, phd, a graduate civil engineer, the Faculty of Civil Engineering, University Džemal Bijedić Mostar ABSTRACT Analysis conducted in this paper has two aims. First objective was to show numerical models can be used as a useful tool for designers. With the software package Examine2D, the state of induced stress around the hydrotechnical tunnel in carbonate rock complexes has been modeled and the results were compared to the site investigation results conducted aruound the same tunnel(hydrotehnical tunnel Fatnica, Bileća-accumulation in the hydropower system on Trebišnjica, Bosnia and Herzegovina). Numerical model can be used in this way to offer a picture of rock masiff stress behavior. This is particularly useful in the initial stages of design since coslty and extensive site investigation can be avoided. Second objective was to form the interaction matrix between carbonate rock complexes as geological medium and engineering activity by variation of properties and condition parameters of carbonate complex, radius of hydrotechnical tunnel as construction parameter, i.e. engineerng activity as well as variation of stress states with software package Examine2D in order to examine the rock mass reaction, its stress-strain behaviour and in accordance with the obtained information define the best technical solution of a given task. 1

2 1. INTRODUCTION Application of numerical models in mechanics is common in recent time, for solving stress-strain behavior around the underground openings or under the foundation of large surface structures. Analysis conducted in this paper has two aims. First objective was to show numerical models can be used as a useful tool for designers. With the software package Examine2D, the state of induced stress around the hydrotechnical tunnel in carbonate rock complexes has been modeled and the results were compared to the site investigation results conducted aruound the same tunnel. Numerical model can be used in this way to offer a picture of rock masiff stress behavior. This is particularly useful in the initial stages of design since coslty and extensive site investigation can be avoided. Second objective was to form the interaction matrix between carbonate rock complexes as geological medium and engineering activity by variation of properties and condition parameters of carbonate complex, radius of hydrotechnical tunnel as construction parameter, i.e. engineerng activity as well as variation of stress states with software package Examine2D in order to examine the rock mass reaction, its stress-strain behaviour and in accordance with the obtained information define the best technical solution of a given task. Results of such analysis may not be the only ones that need to be relied on when making practical decisions, but should serve to clarify issues which cause doubt and uncertainty of designer. Assumptions about homogeneity, isotropy and linear elasticity of the material this software package is based on, make designers take results of such analysis with caution and it also means that the decision-making during the design must use the experience, knowledge, and engineering evaluation. However, when these models are formed on the basis of reliable input parameters and when mathematical formula that realistically reflect the behavior of rock mass in real conditions are used, they can be very useful in the design process in optimizing the geometry of the excavation, the preliminary costs for supporting and ensuring the excavation, achieving the required strength factors, or the simulation of extensive and costly site testing in the initial stages of design. 2. APPLICATED FIELD TESTING METHODS OF STRESS STATE AROUND HYDROTECNICAL TUNNEL IN CARBONATE ROCK MASSIFS Starting from the accepted assumption that the propagation velocities of elastic waves are the function of stress in rock massif the experiment was condiced by Langof ([3], [4]) in order to determine the correlative relation between in situ and induced stress states and wave propagation velocity and therefore to find the in situ stress value by the combination of static and dynamic method. Tests were conducted for hydrotehnical tunnel Fatnica, Bileća-accumulation in the hydropower system on Trebišnjica, Bosnia and Herzegovina (Geotechnical Department of Civil Engineering Faculty in Sarajevo). Tunnel diameter is D = 7.10 m is found in the compact banked limestones and dolomites at a depth of 50 m. This study used a combined static Tincelin-Mayer method for determining the induced stress with two mutually perpendicular hydraulic flat jacks and geophysical methods of ventilation between the two pairs of parallel and mutually perpendicular drill holes at a distance of 0,80 m deepth of 6,0 m. This static method obtains a induced stress in two directions ( s V i s H) while the method of ventilation between the drill holes the wave propagation velocities i.e. in situ in two directions (vertical and horizontal) before creating the cut in the deeper zones (v p V and v p H) and after creating the cut (v s V and v s H), during the action load on the hydraulic flat jacks (Picture 1 (a) and (b)). 2

3 Author (a) (b) Picture 1. Velocity diagram along the horizontal (a) and vertical (b) hydraulic flat jack in limestone, where the average velocity: (1) before cut formation, and (2) during the load = s V i s H. Correlation is estabilished between iduced stress in two directions ( s V i s H) and in situ stress in two directions ( p V i p H) throught the relation of in situ (v p V i v p H) and induced (v s V i v s H) velocities i.e.: p p s v V V V 1,3MPa (1) v s V p p s v H H H 2,0MPa (2) v s H Picture 2 Lines of stress distribution and characteristic zones: (1) released, (2) increased and (3) in situ stress, obtained by static-geophysical methods in the limestone dolomite massif. From the obtained in situ stress results according to expressions (1) and (2) the coffeicient of P P lateral pressure is obtained K = 1,54 ( H / V 2,0/1,3 1, 54) for particular case of the tunnel in compact limestones and dolomites. Along with the use of data from the static dynamic model and theoretical relations for the stress distribution according to the theory of elasticity, distribution of radial r and tangential t stress with zones around the tunnel is obtained (Picture 2). 3

4 3. NUMERICAL MODEL OF STRESS-STRAIN BEHAVIOUR AROUND HYDROTECHNICAL TUNNEL IN CARBONATE ROCK MASSIVE FORMED WITH AID OF SOFTWARE PACKAGE EXAMINE 2D Based on the example shown above and, and by the appplication of the principle of conceptual interaction matrix [2], example of interaction matrix is given with main tree components: elasticity modulus which depends on geological environment characteristics, tunnel diameter as a construction component i.e. engineering activity and stress state as interaction between rock massif and structure. Modulus of elasticity Ex i Ey (MPa) 1 1 The value of the elasticity modulus affects the distribution of induced stress states 1 2 The value of the elasticity modulus affects the possible tunnel openings to be build without supporting system or it affects the choice of the support 1 3 The value of the induced stress affects the deformability Stress state High stress level affects possible failures around the excavatio Size of the excavation affects the radius of plasticisation zone and the depth of the relived stresses zone 3 1 The size of the excavation affects the way of forming the induced stress state Diameter of tunnel Picture 3 Matrix of interactions with three elements in the diagonal for the case of hydrotechnical tunnel in compact limestone and dolomite, [1]. Further text provides series of analysis using software package Examine2D, [5] COMPARISON RESULTS OF FIELD INVESTIGESTION AND RESULTS OBTAINED WITH SOFTWARE PACKAGE EXAMINE 2D Picture 4 and 5 show diagrams of radial and tangential stress in the sides of hydrotechnical tunnel of diameter D = 7,1 m, depth d = 50 m in compact limestones and dolomites formed with Examine 2D software package for the coefficient of later pressure 1,54. From radial and tangential stress diagram it can be see that numerical analysis and site test values overlap and the zone of in situ stress appers to be present at the distance of approximately 8 m from the edge of excavation i.e. undesturebed elastic zone where radial stress starts to asimptoticialy approach the value of horizontal stress H = 2,0 MPa and tangential stress approaches values of vertical 4

5 Author stress V = 1,3 MPa. Since the calculations are made on the basis of elasticity theory, tangential stress diagram does not strat at zero, i.e. coordinate begining which and the case according to the theory of plasticity where fact that after the excavations stress desintegration occurs and as a consequence of this zone of released stress or disturbed zone is formed between the excavation contour and plastic zone - zone of increased stress is considered. This zone usually cannot take over the stress and tangential stress values are reduced to zero. Picture 4 Diagram of radial stress on side of ( = 0 ) hydrotechnical tunnel (diameter D = 7.10), at a depth of 50 m in the compact banked limestones and dolomites for the lateral pressure coefficient of 1.54, obtained with the software package Examine2D, [1]. Picture 5 Diagram of tangential stress on side of ( = 0 ) hydrotechnical tunnel (diameter D = 7.10), at a depth of 50 m in the compact banked limestones and dolomites for the lateral pressure coefficient of 1,54, obtained with the software package Examine2D, [1] ANALYSIS OF INFLUENCE IN THE MATRIX OF INTERACTION Forming the matrix of interaction as show in Picture 3 between carbonate rock complex as geological medium and engineering activity and therefore the assesment of rock mass reaction i.e its stress-strain behaviour is conducted in three steps: Step I First of all the variation of Young modulus as rock massif parameter is done for following values: (I) option: E x = MPa, E y = MPa, GSI = 30, ci = 50 MPa; (II) option: E x = MPa, E y = MPa, GSI = 50, ci = 75 MPa; (III) option: E x = MPa, E y = MPa, GSI = 80, ci = 100 MPa, in order to asses the influence of this geological environment parameter on rock massif stress behavior and possible tunnel excavation with or without supporting i.e. its infuence on technical procedure which will be applied during excavations. It was done with hydrotechnical tunnel diameter D = 7,10 m, in situ stress state p V = 1,3 MPa, p H = 2,0 MPa i.e. lateral coefficient pressure K = 1,54. 5

6 From the chart in Picture 6 (a) and (b) one can see how the change in elasticity modulus affects distribution of induced radial and tangencijal stress, where by the induced stress increase with the decrease of the module i.e. increase of deformability of rock massif. This change will influence the possible tunnel openings which can be constructed without support or with a choice of support. This can be seen on the Picture 7 (a), (b) i (c) which shows strength factor diagrams and failure trajecotry of tunnel side ( = 0 ) up to the 10 m depth around the considered hydrotechnical tunnel for different options of elasticity modulus. Strength factor is a quantitative measure of relationship between strength of rock massif and induced stress, which allows user to define failure criteria for rock massif. If it is less than 1, then the failure in the rock massif under given stress will occur. Figure shows that the failure zone is higher as rock massif has smaller module, and (I) option should be eliminated due to the large failure zone, (II) option will require adequate support to be provided, and in (III) option the tunnel can be executed without support. (a) (b) Picture 6 Distribution of radial (a) and tangentijal (b) stress in a hydrotechnical tunnel sides ( = 0 ), diameter D = 7.10, at a depth of 50 m, the coefficient of lateral pressure of 1.54 and different values of modulus of elasticity obtained with the software package Examine2D, [1]. Step II (a) (b) (c) Picture 7 Diagrams of strength factors and failure trajectories in the sides hydrotechnical tunnel ( = 0 ), diameter D = 7.10, at a depth of 50 m, the coefficient of lateral pressure of 1.54, and the option (I) (a), option (II) (b) and option (III) (c) the values of elasticity modulus were obtained with a software package Examine2D, [1]. In the second step hydrotechnical tunnel diameter change was performed for the following values: (I) option D = 5,0 m; (II) option D = 7,1 m; (III) option D = 10,0 m, 6

7 Author where the modulus of elasticity was E x = MPa, E y = MPa, the value of GSI = 50, uniaxial compressive strength ci = 75 MPa, in situ stress conditions p V = 1.3 MPa, p H = 2.0 MPa, i.e., coefficient of lateral pressure K = (a) (b) Picture 8 Distribution of radial (a) and tangentijal (b) stress in a hydrotechnical tunnel sides ( = 0 ), for the elastic modulus E x = MPa, E y = MPa, GSI = 50, uniaxial compressive strength ci = 75 MPa, coefficient lateral pressure coefficient of 1.54 and different values of the tunnel diameter D obtained with software package Examine2D, [1]. The aim was to consider the impact of the excavation size on the way of forming the induced stress and deformability of rock massif through plastification zone radius and the depth of the released stress zone. The Picture 8 (a) and (b) shows that with increasing diameter of the tunnel leads to the decrease of radial and the increase in tangential stress and increase of the radius of the plastification zone and depth of the released stress zone. Step III In the third step, the induced stress conditions around the tunnel (Picture 9 (a) and (b)) over the three options of in situ stress conditions, i.e. lateral pressure coefficient K: option K = 0,0, option K = 1,5, option K = 2,0, for the Young elacticity modulus E x = MPa, E y = MPa, value GSI = 50, uniaxial compressive strength ci = 75 MPa and hydrotechnical tunnel diameter D = 7,10 m. (a) (b) Picture 9. Distribution of radial (a) and tangetial (b) stress in the sides of hydrotechnical tunnel ( = 0 ), for Young module E x = MPa, E y = MPa, value of GSI = 50, uniaxial compressive strength ci = 75 MPa, the tunnel diameter D = 7.1 m, and different values of the lateral pressure coefficient, obtained with a software package Examine2D, [1]. 7

8 Picture 10 Displacements in the sides of hydrotechnical tunnel ( = 0 ), the elastic modulus E x = MPa, E y = MPa, value of GSI = 50, uniaxial compressive strength ci = 75 MPa, tunnel diameter D = 7.1 m and different values of the coefficient of lateral pressure obtained with a software package Examine2D, [1]. The impact of changes of induced stress on rock massif deformability and possible failure in excavations is analised. The picture 9 (a) and (b) shows the growth of radial and tangential stress with increase in lateral pressure coefficient K which leads to increased displacements, The picture 10., i.e. deformation, and consequently to increase in failures during tunnel excavations. 4. CONCLUSION Analyzed variations clearly indicate complexity of the model formation and large number of possible influences between the parameters in the matrix, but at the same time it also points out the great benefits of such approaches because from the potential impacts we can obtain knowledge on the expected behavior of a complex system of rock-structure. It is a great skill of researchers to choose the most important parameters for analysis, to set a good concept and to make a realistic analysis. 5. RESOURCES [1] ŠPAGO, A., Doctoral thesis: Methodology of geotechnical modelling of carbonate rock complexis, the Faculty of Civil Engineering, "Ss. Cyril and Methodius" University, Skopje. [2] HUDSON, J. A., Rock Properties. Comprehensive Rock Engineering. [3] LANGOF, Z., Određivanje prirodnih napona u nekim slučajevima degradiranih sedimentnih struktura, IV jugoslavenski simpozij o mehanici stena i podzemnih radova, Kosovska Mitrovica, Zvečani, str [4] LANGOF, Z., BIJELJANIN, Lj., Sekundarna naponska stanja i deformacije oko podzemnog otvora u jednom krečnjačkom masivu. 6 simpozijum Jugoslovenskog društva za mehaniko hribin in podzemna dela, 1, Titovo Velenje, str [5] 8