International. J. Eng. Tech 3(1): 44-52, June 2006 A publication of “G-Science Implementation & Publication”

WEDGE INSTABILITY CALCULATION ALONG THE ROADWAY TUNNEL INSIDE MADHYAPARA HARDROCK MINE IN BANGLADESH M.S. ISLAM1*, Y.A. KHAN2, Q. CHOWDHURY2, and M. AHMED 2 ABSTRCT Wedge failure has been analyzed by means of the stereographic projection technique using plotted data supplied by Madhyapara Hard rock Mining Project, Dinajpur, Bangladesh and the project reports. The possible wedges that could be formed in the roadway tunnel had drowned. Wedges including the greatest wedge have measured by using Stereonet program and conventional method. From the calculated result, it is found that the greatest wedge has weight 23.45 tons on roof of the opening. It is also observed that most of the wedges are stable but should take remedial measure to protect other wedges from failure.

Key Words: Wedge, Tunnel, and kinematically.

INTRODUCTION There is no possibility to form a wedge in rock mass having one set of joints even two sets of joints of similar condition. A tunnel with three or more sets of intersected joints will make a wedge. If the size of a wedge is smaller than the radius or height of the tunnel only then it will fall down or slide kinematically and collapse the tunnel and widen the route. The failure is caused in jointed blocky rock mass. A block of rock may fall from the roof or the sidewall of the excavation with causing destruction. Roadway tunnel is situated below 270m below the ground surface. Reviewing the engineering geological characteristics of rock mass in and around mine tunnel wedges is calculated on roof and sidewall of the opening for possible rock fall. Wedge failure can be analyzed by means of the stereographic projection technique. Primarily rock mass along tunnel are categorized in three different types according to joint spacing (Category-I for spacing >2m, Category-II for spacing between 0.5 to 2.0m and Category-III for spacing <0.5m). Rock strength of different categories (105 MPa, 70MPa and 40 MPa for rock category-I, II and III respectively) is also measured. Regional and Geologic Setting The Madhyapara Hard rock Mine (MHM) is the first experience of hard rock mining and the second major mining project in Bangladesh. The Madhyapara Hard rock Mine (MHM) situated in Parbatipur Upazilla of Dinajpur districts in the northern part of Bangladesh and lies between the lattitude25032/44//N and 25037/34//N and the longitudes 88059/09//E and 89006/48//E (figure1). Madhyapara Hard rock Mine Project area is located in Rangpur Saddle. Rangpur Saddle is a possible connection between Indian Platform and Shillong massif and bounded by N-S trending faults (Figure2). Based on geophysical prospecting, in 1974-76, the Geological Survey of Bangladesh (GSB) located hard rock Archean Basement Complex comprises of Quartz-diorite, granodiorite, gneiss, amphibolites etc. The depth of basement complex at Madhyapara is about 150m. Interpretation of regional Bouger anomaly and magnetic anomaly maps gave a new idea of subsurface geological condition of the area. Interpretation of gravity data revealed that the structural set up of the basement rock is mainly fault controlled producing horst and Figure4. Gravity based structural interpretation of Madhyapara and adjoining area (Modified after Rahman,1994) graven. Graven and basin like structure is mainly reflected by gravity lows where gravity high in the Bouger anomaly maps generally due to the upliftment of the basement (figure3). Large negative anomalies in NW part of the Bangladesh is probably related to the Basement features (NAMNAM, 2001). Second derivative map of gravity supports the presence of its faults having varying throws and orientation in figure4. Fault F2-F2 and F1-F1 are the most significant and in the sense that they controlled the southern and eastern boundary of MHM are respectively, where asF7-F7, F10-F10, F11, F11and F3-F3 have given rise to the graven type of structure in western side of the study area near Phulbari area. 1 Department of Petroleum & Georesources Engineering, Shahjalal University of Science and Technology, Sylhet-3114, Bangladesh. 2 Department of Geology and Mining, Rajshahi University, Rajshahi-6205, Bangladesh. *Corresponding Author

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Figure: 1. Location map of Madhyapara Hardrock Mine (after NAMNAM, 1999)

Figure: 2. Tectonic map of Bangladesh and its adjoining area (Guha,1978)

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Figure: 3. Depth Contour map of Bedrock interface (NAMNAM, 2001)

Figure: 4. Gravity based structural interpretation of Madhyapara and adjoining area (Modified after Rahman,1994) 46

METHOLOGY There are many fissures marked by NAMNAM in Roadway tunnel are Plotted in the design map. Considering the plotted data, several wedges in roof and sidewall of the opening are identified. By using stereo net program and other conventional methods were used to determine the greatest wedge in roof and sidewall. The possible wedge shape, weight of the wedge and stability calculations is elaborately suchReview of Literature and Collection of data Geological, hydrogeological and engineering data were collected from the boreholes and underground Roadway levels (production level, sub-level and ventilation) from different agencies and departments like GSB, NAMNAM etc. The different previous research work and different technical papers and analyses records were consulted for the present research work. The strength of a rock mass is often estimated by back calculation, where examples of failure have been carefully documented. In brittle rock masses failure around the tunnels occurs in the form of spalling or fracturing. Laboratory Works and Field Investigation Geo-engineering data like fault, fracture, fissure etc. are collected from mine. Mechanical properties of rock materials (like uniaxial compressive strength) are tested in the Road and Highway laboratory of Rajshahi University of Engineering and Technology. Samples are collected from different locations of underground Madhyapara Hard rock Mining Project and tested. Samples cutting and polishing are performed in the department of Geology and Mining, University of Rajshahi laboratory. Field investigations: Several investigations were carried out in and around the mine area are performed. Sequence of Study1. Collection of rock samples from different location along the Roadway level of Madhyapara Mine. 2. Two different types of sample are prepared for testing of Uniaxial Compressive strength. Block shape and cylindrical samples were created in the departmental Laboratory. 3. Samples were tested in the laboratory. 4. Wedge calculation-There is many fissures are plotted in Roadway tunnel marked by NAMNAM in the design map. Considering the plotted data, several wedges in roof and sidewall of the opening are identified. To determine the greatest wedge in roof and sidewall, stereonet program and other conventional methods were used. The possible wedge shape, weight of the wedge and stability were measured. Wedge Calculation Roofwall Failure The very simple kinematics check is useful for evaluating the potential for roof fall during preliminary studies of structural geology data, which has been collected, for the design in underground excavation. The stereographic method also used for detail evaluation of the shape and the volume of potential unstable wedges.

(a)

(b)

Figure5. (a) Projection of joints on stereonet. (b) Geometry of wedge.

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Three planes are represented by their great circles, marked by A, B and C in figure5 (a). The strike lines of the planes are marked by a, b, c and the traces of the vertical planes through the center of the net and the great circle intersections are marked by ab, ac and bc. The directions of the strike lines correspond to the traces of the planes A, B and C on the horizontal roof of the tunnel. These strike lines can be combined to give the maximum size of the triangular figures, which can accommodate within the tunnel roof span. The volume of the wedge is given by 1/3 x h x A, Where A is the base area and h is the wedge as determined from the plane view are define in figure 5(b). The joint intersects to form a wedge in the roof of an underground excavation but the vertical lines through the apex of the wedge does not fall within the base of the wedge, failure can only occur by sliding on one of the joint surfaces, or along one of the line of intersection. The volume and weight of different wedge on roof those could form in underground roadway tunnel are shown in figure5 (b). Wedge calculation on roof Surface area = ½ x base of triangle x height of triangle ___ ___ Sr = ½ x A x hA Volume of wedge = 1/3 x Surface area x height of wedge ------Vr = 1/3 x Sr x hw Therefore, weight of wedge Wr = Volume of wedge x volumetric weight of rock Wr = Vr x γ --- ---

_

(1) (2 )

- ---

(3)

Side wall failure In the sidewall of an excavation in jointed rock, failure of wedge can occur at same time as in the roof except that free-fall. Most of the sidewall failures involve sliding in a plane, or along the line of intersection of two planes. The failed wedges of the side wall are presented below: The traces a, b, and c of the joints in the sidewall of the tunnel are found by determining the apparent dips α, β, and ξ of the planes in a vertical plane parallel to the tunnel axis. The angle ψabt is given by

ψ abt =

tanψ ab cosθ ab

___

___ __

(4)

Where θ ab is the angle between the tunnel axis and the projection of the lines of intersection ab on the horizontal plane ψbc and ψab is the true dip of the line of intersection ab.

(b) Figure6. (a) Projection of joints on stereonet (b) Geometry of wedge The angles ψbc and ψab are found in the same way. The height h, of the wedge is found by the determining the angles ψabt/ , ψbct/ , and ψact/ ,which represent the dips of the lines of intersection in a vertical plane at right angle to the tunnel axis. The angle ψabt/ is given by ---(5) tanψ

tanψ abt ′ =

ab

sin θ ab

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The volume and finally weight of different wedge on roof those could form in underground roadway tunnel are shown in figure6. Wedge calculation for sidewall Surface area = ½.

× Base of triangle × height of triangle

Ss = ½ x A x hA Volume of wedge = 1/3 × Surface area ×height of wedge Vs = 1/3 x Ss x hw Weight of wedge = Volume of wedge x volumetric weight of rock Ws = Vs x γ

---------

----- ------ - (4) -----

---

-- (5) -

(7)

Table1. Wedge calculation (height, volume and weight) Section 1

Rock category I

2

II

3

III

4

I

5

II

Surface area (m2) 9.825 5.13 3.72 2.64 6.748 2.40 3.575 9.12 3.90 4.70

Height (m) 0.7 0.3 0.70 0.4 1.6 3.0 0.3 1.5 0.65 1.5

Position of wedge Roof Sidewall Roof Sidewall Roof Sidewall Roof Sidewall Roof Sidewall

Volume of wedge (m3) 2.29 2.22 0.875 0.352 3.57 2.40 0.358 4.61 0.845 2.41

Weight of wedge (tons) 6.42 6.216 3.50 1.00 10.01 6.72 1.001 12.91 2.366 6.748

Greatest wedge calculation Strike and dip of joints are considered in stereonet and determine the concentration of joints by contouring method. On the basis of concentration, it was found four sets of joint of greater concentration (more than 5 sets) points on stereonet (figure7). Among these we select 3 points and have the following strikes and dips:

Figure7. Contouring of joint in underground Roadway level

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Table2. Strike and dip angle for determination of the greatest wedge Strike 332 285 145

Dip 750 700 650

Using the data (table2) in stereo-program and we can calculate the volume of wedge of roof and sidewall by the above method. Table3. Height, volume and weight of greatest wedge Position of wedge

Weight of wedge

Roof Sidewall

8.424 tons 1.63 tons

Stability analysis of wedges Stability analysis of wedges is the major criterion after considering the stress around the opening. It has been assumed that the kinematically unstable wedges and blocks are acting upon by gravitation and is measured by the following equation (9). In case of block with height hb and the weight w is acted upon by an average normal stress σn (Fig.1.9). .The condition of limiting equilibrium for the block can be written as: - - - - - - - - - - - (8) w. sin ξ

σn =

2h b tan φ

Where φ is the angle of friction of the discontinuity surfaces. When the average normal stresses σn, calculated from the stress distribution around the opening and the weight of the block, is less than the right hand side of the equation, the block will be unstable and reinforcement is required in order to restore its stability.

Figure8. Shows the configuration of wedge in tunnel Factor of Safety Factor of safety is the ratio between the maximum insitu stress around the opening and normal stresses on the boundary due to wedge formation (equation 9). ---

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- - - - (9)

Consequently normal stress and factor of safety (F.S) of other section are calculated and given in table3. Table.3 Factor of safety of different wedges in roadway tunnel of MHM.

Section Section-1 Section-2 Section-3 Section-4 Section-5

Greatest wedge

Category of rock category-I category-II category-III category-I category-II If category-I If categoryII If categoryIII

Normal stress(σn) on roof (due to wedge) 3.46MPa 3.43MPa 4.98MPa 1.26MPa 2.48MPa 2.51MPa

Normal stress(σn) on sidewall (due to wedge) 7.81MPa 1.71MPa 3.34MPa 3.25MPa 3.066MPa 0.9 MPa

4.41MPa 3.13MPa

Factor of safety

Maximum in situ stress (average)

For roof

9.058MPa 9.058MPa 9.058MPa 9.058MPa 9.058MPa 9.058MPa

2.62 2.64 1.81 7.19 4.5 3.60

For sidewall 1.16 5.29 2.71 2.78 2.96 10.06

1.59 MPa

9.058MPa

2.05

5.69

1.85 MPa

9.058MPa

2.89

4.89

Figure: 9. Shows the different wedge locations along the roadway tunnel

Wedge stability result on factor of safety It is found from the given table-1.3 that the factor of safety (F.S) is mainly more than 2 and that is why most of the wedges are stable with few exception (Section-1 whose F.S is 1.16).

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DISCUSSION Wedge formation in underground is another cause for failure or collapse of tunnel. These wedges are kinematically falling down within tunnel. The shape, size and volume of wedge have been calculated by using Stereonet program and conventional methods (Hoek and Bray 1989). It is found that the greatest wedges with volume of 8.424m3 and 1.63m3 are identified on roof and sidewall of the opening respectively. From the stability analysis in this research it is observed that most of the wedges are stable. In regards to the regional setting and in graven structure it has some risk for free tunnel rather than any support. Though it is seems that there is little possibility to free fall or sliding of rock mass but wedges could create mass destruction of any tectonic movement will occur around the mine area. Moreover, this type of study is further needed for the complete understanding of stress condition and related failure inside the tunnel. Studies on installment of supports in category-III to protect wedge failure are strongly suggested.

REFERENCES Guha, D.K., 1978. Tectonic Framework and oil and gas prospect of Bangladesh. Proc., of 4th Annual Conference, Bangladesh Geological Society, Dhaka. p65-78. Hoek E and J. Bray, 1989. Rock Slope Engineering, 3rd Edition, The Institution of mining and metallurgy, London, p358 NAMNAM, 1999. Geological reports of boreholes drilling of Madhyapara Hard rock Mining Project (Revision). Unpublished report of MHM p141. NAMNAM, 2001.Geological survey data of underground Roadway of Madhyapara Hard Rock Mining Project. p1-16 Rahman, M.A., I. Mia, and B.R. Blank, 1984. Gravity and Magnetic investigation in Badargonj- Nowabgonj-Hilli and adjoining areas, Rangpur and Dinajpur Districts Bangladesh. Records of Geological Survey of Bangladesh (unpublished).

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