Introduccion

This document presents an example of the design of a hitched (or slab keyed into rock) type of plug.The approach presented follows the “Bulkhead & Dams for Underground Mines Design Guidelines” published by the Ontario Ministry of Labour, Occupational Health and Safety Branch (1995).

Hypothetical Case:A mine would like to build a hitched plug to close the access to the 130 haulage portal (Elev. 130 m) as part of the general closure plan for the mine. The plug will be required to retain water after mine closure and the static groundwater level is estimated to be at Elev. 465 m. For reference purposes,

Figure 1 shows a typical cross-section of a hitched plug.

Chemical analysis of the water indicated that it has a ph at approximately 7 and does not contain suspended solid. Any leakage water from the plug will not be used for domestic purposes.

The drift is 3.7 m wide and 3.4 m high at the planned plug location and the rock mass of granite has been classified as Fair quality through rock mass characterization.

The specifications for concrete and formwork presented in the course should be used.

BEARING CAPACITY OF ROCK

The Bulkhead Design Guidelines prepared by the Ontario Ministry of Labor (1995) includes estimation of bearing capacity of rock, which is reproduced here in Sections 2.1 and 2.2. These guidelines are used to assess the rock mass strength for incorporation into the plug design calculations of Section 4.0.

Homogéneos Rock

The bearing capacity of rock that is homogeneous is dependent upon the geometry of the rock surface that is undergoing loading, the unit weight of the rock, the cohesion of the rock and the internal angle of friction of the rock. Ordinarily, homogeneous rock has a compressive strength that is higher than that of concrete. Consequently, the bearing capacity of homogeneous rock in an anchor channel is not likely to be exceeded by the load transferred to it from a concrete bulkhead.

For uniform loading on an area of rock having a width W, the bearing capacity is given as:

Where: = the unit weight of the rock

c = the cohesion of the rock

And

Nand Nc are bearing capacity factorsNc = (Nq - 1) cot N= 1.5 (Nq - 1) tan Nq = e tantan2 (/4 + / 2)= the angle of friction of the rock

Cohesion and friction angle values for commonly encountered rock types are:

Discontinuous Rock

Rock in mining environments is seldom homogeneous and is usually characterized by blast induced fractures and geologic features such as joints, bedding planes or faults. Discontinuities ordinarily adversely influence the bearing capacity of the rock. Notwithstanding its compressive strength, the bearing capacity of a rock mass that is personified by discontinuities can be significantly lower than that of a homogeneous rock mass composed of the same rock type.In discontinuous rock the potential failure mechanism from bearing stress can be somewhat different from that resulting from excess bearing stress in homogeneous rock. The spacing, orientation and opening size of discontinuities in a rock mass will dictate how it responds to bearing pressures. In rock masses that are typified by discontinuities that are open, have a spacing that is less than the width over which the bearing load is applied and are oriented sub-parallel to the direction of the applied load, the load is essentially supported by unconfined columns of rock. The bearing capacity of such rock masses is approximately equal to the sum of the strengths of the individual rock columns, provided that each column has the same strength and rigidity.For bulkhead anchor channels that are excavated in jointed or fractured rock, it is crucial that the rock mass is carefully mapped to assess what influences, if any, the rock mass discontinuities will have on its bearing capacity. The

outcome of such mapping endeavors may reveal the necessity to adjust the bearing capacity as presented before for homogenous rock (Section 2.1).For explanation on rock mass characterization and the derivation of rock strength parameters, refer toAppendix B – Rock Mass Characterization of the Plug Design Guidelines.

DESIGN CONSIDERATIONS

The Bulkhead Design Guidelines prepared by the Ontario Ministry of Labour (1995) includes a section on plug design considerations, as presented in Sections 3.1 and 3.2. This outlines the basis for plug design requirements, design criteria followed, typical layout of a plug, and coefficients used for design.All are referenced to the design calculations of Section 4.0.

Plug Design RequirementsThe design of the plug should account for the dimensions of the plug, the depth to which the plug will be hitched (keyed) into the rock, as well as the following components relevant to design:Factored LoadsFactored Shear LoadsFactored Moments (and reinforcement requirements)Bar Spacing & Slab ThicknessAnchorage into RockBearing on Concrete

3.2 Plug Design CriteriaThe Ontario guidelines consider:1. The bulkhead is designed in accordance with the CSA, CAN3-A23.3-M84, "Design ofConcrete Structures for Buildings", requiring that:Factored Resistance ³Effect of Factored Loads2. The Bulkhead is considered to be a two-way slab that is simply supported on four sides.3. Tectonic pressure is not considered4. Deep beam flexure "analysis" does not apply.5. The potential of hydraulic fracturing within the rock around the bulkhead has not been considered in the design of the Ontario guidelines.6. The bulkhead design has been designed to withstand static hydrostatic pressure with specific gravity equal to one.

3.3 Typical Plug LayoutThe following is the layout of a typical plug for illustration purposes:

Notes:1. Anchorage distance of h/2 is based on anchorage in sound rock with an allowable bearing pressure of 3800 kPa. If rock is fractured or allowable bearing is less than 3800 kPa, then appropriate adjustment to anchorage depth is required.2. Concrete cover = 75 mm ± 12 mm.3. For rectangular bulkheads, place reinforcement parallel to short dimension (la) on the outermost layer.4. For bulkheads that may be loaded from either side, place reinforcement, as indicated in tables, on both sides.5. Minimum bar spacing “s” = Bar dia. (db) + largest of:- 25 mm; or- db; or- 1.33 x max. size aggregate.

3.4 Coefficients and Notations Used in DesignThe following are notations used in the design calculations of Section 4.0:An Effective tension area of concrete surrounding the flexural tension.Reinforcement and having the same centroid as that.Reinforcement, divided by number of bars, mm2h.

As Area of tension reinforcement, square mmαD Load factor on dead load (Clause 9.2.3)*αL Load factor on live load (see Clause 9.2.3)*αQ Load factor on wind or earthquake load (see Clause 9.2.3)*αT Load factor in T-load (see Clause 9.2.3)*β Ratio of clear spans in long to short direction of two-way slabsβ1 Ratio of depth of rectangular compression block of depth of the neutral axis (see clause 10.2.7)*βc Ratio of the long side to short side of the concentrated load or reaction area

b With of compression face of member, mmbo Perimeter of critical section for slabs and footings, mmbw Web width, mmc Distance from extreme compression fibre to neutral axis, mmCad,Cbd Moment coefficients for positive dead load moments in short and long spans respectivelyCal, Cbl Moment coefficients for positive live load moments in short and long spans respectivelyD Dead load, ND Distance from extreme compression fibre to centroid of tension reinforcement, mmdb Nominal diameter of bar, wire or prestressing strand, mmdc Thickness of concrete cover measured from extreme tension fibre to the centre of the longitudinal bar or wire located closest to it, mmEs Modulus of elasticity of reinforcement, MPa (see clause 8.5.2 or 8.5.3)*єs Strain in reinforcingfs Calculated stress in reinforcement at specified loads, MPafy Specified yield strength of nonprestressed reinforcement, MPa

NOTE: For Clause numbers refer to CAN-A23.3-M84 Standardf’c Specified compressive strength of concrete, MPaf c Square root of specified compressive strength of concrete, MPag Gravitational acceleration, 9.81 m/s2

H Head of water in metresh Overall thickness of member, mmhs Overall depth of slab, mmL Live load NI Span length of one-way slab as defined in clauses 8.7.1 and 8.7.2;* clear projection of cantilever, mmIa Clear span of a two-way slab in short direction, mmIb Clear span of a two-way slab in long direction, mmMa Maximum moment in member at load stage at which deflection is computed, NmmMadPos, Positive dead load moments in short and and long spans respectively, N.mm/mMf Factored moment at section, N mmMr Factored moment resistance, calculated using the assumption in clauses 10.2 and 10.3,* and the resistance factors given in clause 9.3,* N mmm = 1a Ratio of short to long span of a two-way slab 1b

ρ Ratio of nonprestressed tension reinforcement = As/bdQ Live load due to wind or earthquake, whichever produces the more unfavorable effects Spacing between layers of reinforcement, mmT Cumulative effects of temperature, creep, shrinkage and differential settlementVc Factored shear resistance provided by tensile stresses in the concrete, NVf Factored shear force at section, NVr Factored shear resistance, NVs Factored shear resistance provided by shear reinforcement, NWdf Factored dead load per unit area, kPaWf Factored load per unit area,, kPaWlf Factored live load per unit area, kPa (kN/m2)

For Clause numbers refer to CAN-A23.3-M84 Standard

z Quantity limiting distribution of flexural reinforcement kN/mm (see clause 10.6)*γ Importance factor (see Clause 9.2.6)**Factor to account for low density of concrete (see clause 11.2.3) גγc Density of concrete, kg/m3φc Resistance factor for concrete (see Clause 9.3.2)*φs Resistance factor for reinforcing bars (see Clause 9.3.3)*ψ Load combination factor (see Clause 9.2.4)*

* Note: For Clause numbers refer to CAN-A23.3-M84 Standard

Table E-2 of the Ontario Ministry of Labour Guidelines (1995) is provided for reference purposes which presents the coefficients for live and dead load positive moments. These coefficients will be utilized in Section 4.0.

4.0 DESIGN CALCULATIONSThe following section provides details related to the calculation of factored loads, and the ultimate requirements for plug design, using the hypothetical case presented in Section 1.0. These calculations are based on the Bulkhead Design Guidelines from the Ontario Ministry of Labour (1995).Refer to Section 3.4 for an itemized list of notations used in the following calculations.

4.1 Initial ConditionsThe following presents initial conditions related to data input such as geometries, material strengths, etc.Opening (long side x short side), la x lb = 3400 mm x 3700 mmHead of Water, H = 335 m (Elev. 465 m – Elev. 130 m)Concrete Compressive Strength, f’c = 30 MPaReinforcing Yield Strength, fy = 400 MPaLive load due to hydrostatic pressure, (w):w = H x rw x g = 3287 kN/m2

Where, g = 9.81 m/s2

rw = 1000 kg/m3, (density of water)

4.2 Design CoefficientsThe following are design coefficients related to the bulkhead geometrical requirements, and design layout:

Moment coefficient, Cal (See Table E-2 – Case 1) = 0.0431Moment coefficient, Cbl (See Table E-2 – Case 1) = 0.0305

4.3 Total Factored Load, WfThe total factored load (Wf) incorporates the various loads acting on the bulkhead including; dead loads, live loads, wind and earthquake loads, and temperature loads. A factor is applied to the loads to weight the loads accordingly.Total Factored Load (Wf):

Wf = aDD + gc(aLL + aQQ +aTT) (CSA 9.2.2)Where, D = Dead loadL = Live loadQ = Wind, EarthquakeT = TempLoad Factors (a):aD = 1.25, aL = 1.50, aQ = 1.50, aT = 1.25 (CSA 9.2.3)Load Combination Factor (c):c = 1.0 one of L, Q, Tc = 0.7 two of L, Q, Tc = 0.6 three of L, Q, TSince only a live load is considered in this design, c = 1.0 is considered.Importance Factor (g):g = 1.0 (CSA 9.2.6)

For vertical bulkheads (load acting horizontally across bulkhead), such as in the hypothetical case analyzed, D = 0.00. For horizontal bulkheads (e.g., built in vertical shafts, the load would be acting vertically across bulkhead), the dead load should be estimated based on the plug volume and density of the concrete. For this example, D = 0.Wf = 0 + 1.50 x 3287 kN/m2

= 4931 kN/m2

4.4 Factored Shear Resistance, VcThe following series of equations consider the bulkheads resistance to shear failure.Factored shear resistance (Vc):Vc = (1 + 2 / bc) 0.2 l fc (f’c)0.5 bo d Formula (1) (CSA 11.10.2.2)

But not greater than, Vc = 0.4 l fc (f’c)0.5 bo d Formula (2) (CSA 11.10.1.3)

Where, bo = perimeter of critical sectiond = effective depth, mmbo = 2 (la + lb – 2d)= 2 (3400+3700-2d)= 14200 – 4d (mm)

Importance factor (l ):l = 1.0 (CSA g.2.6)Resistance factor (fc):fc = 0.60 (CAN g.3.2)

Design coefficient (bc):bc = 1.088 (Section 4.2)Strength of concrete (f’c):(f’c)0.5 = (30)0.5 = 5.477where f’c is expressed in MPaEvaluating Formula (1):Vc = (1 + 2 / bc) 0.2 l fc (f’c)0.5 bo d,= (1+2 / 1.088) 0.2 x 1.0 x 0.60 x 5.477 x bo d= 1.8654 bo dFormula (1) cannot be greater than Formula (2).

4.5 Evaluating Formula (2):Vc = 0.4 l fc (f’c)0.5 bo d= 0.4 x 1.0 x 0.6 x 5.477 bo d= 1.3145 bo dWhich is less than Vc in Formula (1)Therefore, use Vc in Formula (2) & substitute (14200 – 4d) for bo:Vc = 1.3145 (14200 – 4d) d= 18665.9 d – 5.258 d2 (N)= 18.6659 d - 0.005258 d2 (kN) Formula (3)

4.6 Factored Shear Loads, VfThe following equations consider the applied shear loads on the bulkhead:Factored shear load (Vf) :Vf = Wf (la – d) (lb – d)= 4931 (3.400 – 0.001 d) (3.700 – 0.001 d) (kN)= 4931 (12.58 – 0.0034 d – 0.0037 d + 0.000001 d2) (kN)= 0.004931 d2 – 35.0101 d + 62031.98 (kN)Where, Wf = total factored load = 4931 (kN) (Section 4.3)

4.7 Factored Thickness of Bulkhead, dThe following equations consider the factored thickness of the bulkhead based on the factored shear resistance and factored shear load.

Let:Factored Shear Resistance (Vc) = Factored Shear Load (Vf)18.6588 d - 0.005256 d2 = 0.004931 d2 – 35.0101 d + 62031.980.010187 d2 – 53.6689 d + 62031.98 = 0Solving quadratic equation for d:ad2 + bd + c = 0d = (-b 6 (b2 – 4ac)0.5) / (2a)= (53.6689 6 (2880.350827 – 2527.679121)0.5) / 0.020374= (53.6689 6 18.77955554) / 0.020374= 1713 mmUse d = 1800 mm

4.8 Factored Moment (Short Side), MfThe following equation considers the moment acting along the short side of the bulkhead. Factored moment, short side, (Mf):Mf = Mal + Mad (CSA E2.8)Where, live load positive moment, (Mal):Mal = Cal Wlf la2

= 0.0431 x 4931 x (3.40)2

= 2457 kN.m per metre widthAnd, dead load positive moment, (Mad):Mad = Cad wdf la2

= 0Therefore, Mf = 2457 kN.m per metre width

4.9 Reinforcement Steel Area for Preliminary Calculations (Short Side)

The following formulae consider the reinforcement steel area which is required for preliminary calculations regarding the bulkhead reinforcing steel requirements. These formulae refer to the CPCA Concrete Design Handbook 2.9. Steel area, (As):

As = (Mf x 106) / (0.90 fs fy d) (CSA 9.3.3)Where, Mf = 2457 kN.m per metre widthd = 1800 mmFor fs = 0.85, fy = 400 MPaTherefore, As = (2457 x 106) / (306 x 1800)= 4461 mm2 / mConsider two steel layers of 30M at 200 mm:As = 2 [(30/2)2] / 0.200= 7068 mm2 / mRatio of non-prestressed tension reinforcement, (r):r = As / (b d)Where b = 1000 mm unit widthr = 7068 / (1000 x 1800),= 0.003927

4.10 Factored Moment Resistance (Short Side), MrThe following formulae consider the factored moment resistance acting across the short side of the bulkhead. Refer to CPCA Concrete Design Handbook 2.7 and CSA Appendix B3.

Factored moment resistance, (Mr):Mr = r fs fy [1 – (r fs fy) / (1.7 fc f’c)] bd2

= 0.003927 x 0.85 x 400 [1 – (0.003927 x 0.85 x 400) / (1.7 x 0.60 x 30)] 1000 x 18002

= 4137 kN.mSince Mr $ Mf , OK.

4.11 Ratio of Tension Reinforcement (Short Side), rThe following formulae consider the ratio of tension reinforcement of the bulkhead. Three criteria are to be met:Preliminary:r= 0.003927 (Section 4.8)1. Temp. & shrinkage reinforcing.rmin = 0.0020,Since rrmin, OK2. Max. Allowable steel ratio rmax

(to ensure ductile failure)rmax = (c / s) [(0.85 x f’c x 1 x 600) / fy (600 + fy)]Where, f’c = 30, 1 = 0.85rmax = (0.60 / 0.85) [(0.85 x 30 x 0.85 x 600) / 400 (600 + 400)]= 0.02295,Since rrmax, OK3. Minimum Reinforcing for Flexurermin = 1.4 / fy or 1.33 x rreq’d for flexure (CSA 10.5)= 1.4 / 400 = 0.0035,Since rrmin, OKTherefore initial reinforcing steel area estimation (Section 4.8) of two layers of 30 M at 200

4.13 Reinforcement Steel Area for Preliminary Calculations (Long Side)The following formulae are the second iteration for considering the reinforcement steel area which is required for preliminary calculations. The bulkhead reinforcing steel requirements for moments acting along the long side of the bulkhead are considered. These formulae refer to the CPCA ConcreteDesign Handbook 2.9.Steel area, (As):As = (Mf x 106) / (0.90 fs fy d) (CSA 9.3.3)Where, Mf = 2059 kN.m per metre width (long side)d = 1800 mmFor fs = 0.85, fy = 400 MPaTherefore, As = (2059x 106) / (306 x 1800)= 3738 mm2 / m

Consider two steel layers of 30M at 250 mm:As = 2 [(30/2)2] / 0.250= 5655 mm2 / mRatio of non-prestressed tension reinforcement, (r):r = As / (b d)Where b = 1000 mm unit widthr = 5655 / (1000 x 1800),= 0.00314mm are satisfactory. (As = 7068 mm2 / m)4.12 12. Factored Moment (Long Side), MfFactored moment, long side, (Mf):Mf = Mbl + Mbd (CSA E2.8)Where Mbd = 0 (dead load, D = 0)Mbl = Cbl Wlf lb2

= 0.0305 x 4931 x (3.70)2

= 2059 kN.m per metre widthMf = 2059 kN.m per metre width

4.14 Factored Moment Resistance (Long Side), MrThe following formula considers the factored moment resistance acting across the long side of the bulkhead. Refer to CPCA Concrete Design Handbook 2.7 and CSA Appendix B3.Factored moment resistance, (Mr):Mr = r fs fy [1 – (r fs fy) / (1.7 fc f’c)] bd2

= 0.002618 x 0.85 x 400 [1 – (0.002618 x 0.85 x 400) / (1.7 x 0.60 x 30)] 1000 x 18002

= 2800 kN.mSince Mr $ Mf, OK.

4.15 Ratio of Tension Reinforcement (Long Side), rThe following formulae consider the ratio of tension reinforcement of the bulkhead. Three criteria are to be met:Preliminary:r= 0.00314 (Section 4.12)1. Temp. & shrinkage reinforcing.rmin = 0.0020,Since rrmin, OK2. Max. Allowable steel ratio rmax

(To ensure ductile failure)rmax = (c / s) [(0.85 x f’c x 1 x 600) / fy (600 + fy)]Where, f’c = 30, 1 = 0.85rmax = (0.60 / 0.85) [(0.85 x 30 x 0.85 x 600) / 400 (600 + 400)]= 0.02295Since rrmax, OK3. Minimum Reinforcing for Flexurermin = 1.4 / fy or 1.33 x rreq’d for flexure (CSA 10.5)= 1.33x As/ (b x d)= 1.33 x 3738/ (1000 x 1800)= 0.0028Since rrmin, OKTherefore initial reinforcing steel area estimation (Section 4.8) of two layers of 30 M at 250 mm are satisfactory. (As = 5655 mm2 /m)

4.16 Bar Layer Spacing and Slab ThicknessThe following formulae consider the spacing of reinforcement steel bar layers, as well as the thickness of the bulkhead concrete slab.

Bar Layer Spacing, (s):s = db + 1.33 x 35 mm (max. aggregate size)Where, db = diameter of the reinforcing bar (30 mm)s = 30 mm + 46.55 mm= 76.55 mm, use 80 mmSlab Thickness, (h):h = d + s / 2 + dc + db / 2

Where, d = 1800 mm (effective depth)dc = 75 mm (concrete cover to bar)h = 1800 + 80 / 2 + 75 + 30 / 2= 1930 mm

4.17 Anchorage in RockThe following formulae consider the anchorage depth of the bulkhead into the rock based on the bulkhead geometry and allowable bearing capacity of the rock.

Total bulkhead area, (A):A = A2 – A1

Where, A2 = outside area of bulkhead (including anchorage in rock)A1 = inside area of bulkhead (not including anchorage in rock)A = (la + h) (lb + h) – (la x lb)= lalb + lbh + lah + h2 – lalb= (h2 + lbh + lah)Where, h / 2 = Anchorage in RockHydrostatic Pressure = 3287 kN / m2

Allowable Bearing Pressure = 3800 kN / m2

3287 A1 = 3800 AA1 / A = 3800 / 3287 = 1.156

Where, la = 3.40 mlb = 3.70 m(3.4 x 3.7) / (h2 + 3.7h + 3.4h) = 1.15612.58 = 1.156 h2 + 8.2076 hh2 + 7.1 h – 10.8824 = 0Solving quadratic equation:ah2 + bh + c = 0h = (-b 6 (b2 – 4ac)0.5) / (2a)= (-7.1 6 (50.41 + 43.5296)0.5) / 2= (-7.1 6 9.6922) / 2= 1.30 mTherefore, anchorage required = h/2 = 1.30 / 2 = 0.65 mFor additional factor of safety:Anchorage required = h / 2, let h = d, 1800 / 2 = 900 mm = 0.90 m

4.18 Bearing on ConcreteThe following formulae consider the allowable bearing pressure of the concrete slab compared to the bearing pressure of the live load.At support:Pressure = 3800 kN / m2 x 1.5 (live load factor)= 5700 kN / m2

= 5.70 MPaOn Face = 3287 kN / m2 x 1.5= 4931 kN / m2

= 4.93 MPaAllowable Bearing Pressure on Concrete:= 0.85 c f’c (CSA 10.15.1.1)= 0.85 x 0.60 x 30= 15.3 MPaSince Allowable Bearing Pressure on Concrete>Pressure on Face (due to live load), OK

Bulkhead Design ExampleFigure D2– Results of the bulkhead design calculations for an opening 3400mm x 3700mm.