Determination of support pressure for tunnels and caverns using block theory

doi:10.1016/j.tust.2013.03.006

Tunnelling and Underground Space Technology

Volume 37, August 2013, Pages 55-61

https://doi.org/10.1016/j.tust.2013.03.006 Get rights and content

Highlights

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The algorithm used in the method can be easily adapted to the computer programme.
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The technique involves determination of geo-mechanical parameters for stability assessment.
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Alignment of the tunnel could easily be chosen to get the rock pressure to be minimum.

Abstract

The estimation of support requirements to stabilize underground structures is of prime importance for rational design of these structures. The characterizing parameters of rock mass may vary with depth. Determination of these parameters by drilled cores and Ground-Probing-Radar (GPR) is difficult and expensive due to anisotropy of rock mass. Laboratory testing is also expensive. Also the in situ conditions are difficult to simulate in the laboratory. The designer is thus resorting to empirical methods and analytical methods to determine these parameters. Often, the analytical techniques may mesmerize the designer to feel the problem and its solution on the screen of the computer. In this paper, an attempt has been made to develop algorithm based on Block Theory with geological information & mechanical properties of rock for determining the rock pressure. Limitations of this technique are number of joint sets not less than three and width of the opening up to 25 m. The algorithm determines all the wedges formed at a time by 3, 4, 5, 6, …, n joint planes with excavation plane responsible for manifestation of rock pressure at roof/wall. All the permutations and combinations for wedge formation can be considered in this respect. Rock pressure for design is determined for reinforcement of the underground openings. Spacing of rock bolts is found out as an additional feature. The alignment of the opening for optimal reinforcement can also be determined. Case history of Tehri Power House, India is taken up for analysis. The empirical correlations developed by Goel (1994) are used for comparative study. It was found that no appreciable rock pressure was developed at walls. Roof pressure is determined to be 140 kPa, which is almost same as observed. It is thus established that block theory may be applicable for design criterion up to depth of 500 m.

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), …, (α_n, β_n) be the dip and dip direction of joint planes respectively, (α_n₊₁, β_n₊₁) be dip and direction of roof/wall, (α_n+₂, β_n+₂) be dip and dip direction of tunnel axis and W_b be the width of the opening. Unit vectors $\bar{i}$ , $\bar{j}$ , $\bar{k}$ 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 ( ${\bar{a}}_{k}$ ) to the joint and excavation planes ( $\bar{f}$ ) and tunnel axis ( $\bar{g}$ )

${\bar{a}}_{k} = (a_{kx} \bar{i} + a_{ky} \bar{j} + a_{kz} \bar{k})$ where $α_{kx} = \sin α_{k} \cdot \sin β_{k}$ $α_{ky} = \sin α_{k} \cdot \cos β_{k}$ $α_{kz} = \cos α$

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 (Q_average = 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 (J_n), joint roughness number (J_r), joint alteration number (J_a), joint water reduction factor (J_w) 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): $Q -value = (RQD / J_{n}) \times (J_{r} / J_{a}) \times (J_{w} / SRF)$ where RQD is the rock quality designation, J_n 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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Goel, R.K., 1994. Correlations for Predicting Support Pressure and Closures in Tunnels. Ph.D. Thesis. Nagpur...

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