Determination of support pressure for tunnels and caverns using block theory
Introduction
In order to know the behavior or rock mass, in advance, all the theories are to be consulted. The analysis depends upon geology and rock material behavior of the specific site. Instability of excavations in rocks often initiates due to movement of unstable removable blocks, or key blocks. Block Theory proposed by Goodman and Shi (1985) can be used to analyze these unstable blocks for assessment of the stability of rock mass. Theses blocks can be identified by information of joint set orientations, the excavation shape and width of opening (Goodman, 1995). The authors present an algorithm for preliminary design of underground openings based on the concept of block theory. The main advantage of this algorithm is that it helps to fix up alignment of the opening with minimum reinforcement, in view of economy of supporting costs.
Section snippets
Objectives and assumptions
The main objective is to develop algorithm upon input information of three or more joint sets for determining the rock pressure and mechanical properties of rock. The proposed algorithm can be used prior to excavation to estimate the support pressure. As the excavation is progressed, the input parameters (geological) are reevaluated as face advances. Limitation of this technique is number of joint sets not less than three and width of the opening up to 25 m. Owing to limitations of the authors,
Input parameters
The proposed algorithm is based upon fourteen steps. Input parameters are geological information such as (i) joint sets’ nature (ii) alignment of the opening (iii) orientation of excavation plane (iv) width of the opening (v) water forces on joint planes (vi) friction angle, and (vii) cohesion of joint planes. All the wedges formed by 3, 4, 5, 6, …, n joints at a time can be analyzed by adopting all the combinations. The output parameters are (i) the weight and face areas of the wedge (ii) height of
Step1: Assumptions
Assume the wedge is formed by n-joint planes with excavation plane at roof/wall, (α1, β1), (α2, β2), …, (αn, βn) be the dip and dip direction of joint planes respectively, (αn+1, βn+1) be dip and direction of roof/wall, (αn+2, βn+2) be dip and dip direction of tunnel axis and Wb be the width of the opening. Unit vectors , , are considered along the along East, North and vertical directions (X, Y, Z) respectively as shown in Fig. 1.
Step2: Determination of unit outward normal vectors () to the joint and excavation planes () and tunnel axis ()
where
Case history
Tehri Hydro Power Complex has been constructed on the bank of river Bhagirathi in the Himalayan region, India for harnessing hydroelectric power of 2000 MW. The main part of the project comprises of a rock fill dam and underground powerhouse about 1 km downstream. A case history of Tehri Dam Power House (250 m × 50 m × 25 m) with orientation of N 52°W–S 52°E (true bearing = 308°) is presented. Rock mass quality index, Q-value varies between 0.64 and 9.12 (Qaverage = 4.88) in the rock cavern. Q-value of 4.88
Determination of rock pressure by empirical correlation
On the basis of available field values of rock quality designation (RQD), joint set number (Jn), joint roughness number (Jr), joint alteration number (Ja), joint water reduction factor (Jw) for Phyllite-II in which the powerhouse has been constructed, authors determined rock mass number (N-value) for this rock (Goel, 1994). Rock mass quality (Q) is expressed as following (Barton et al., 1974):where RQD is the rock quality designation, Jn is the join set number, J
Instrumentation
Construction-stage instrumentation was adopted to monitor the behavior of the surrounding rock masses. Load cells and closure studs were installed (Fig. 9). The purpose behind the instrumentation was to use the data subsequently for designing the support system of the powerhouse cavern. Table 4 depicts support pressure measured in the vicinity (Goel, 1994).
Conclusions
As it is clear from Table 2, Table 3 that the maximum and minimum rock pressures respectively estimated by block theory are 180 kPa and 80 kPa (Table 2), whereas these values are estimated to be 190 kPa and 55 kPa by Eq. (3) and 52 kPa and 126 kPa by Eq. (4) (Table 3) for the powerhouse (below 180–230 m). The support pressure observed in the field was in the range of 120–200 kPa. It indicates that the upper bound value of support pressure obtained from Eq. (3) (190 kPa) is close to upper bound value of
Acknowledgements
The authors are thankful to Indian National Committee of Rock Mechanics (INCRM), Ministry of Water Resources (Government of India) for giving financial grant for the study. Tehri Hydro Development Corporation (THDC), Uttarakhand (India) is acknowledged also for providing some geological information for the research work.
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