TecMecRoc-L6_Example Hitched Plug

8/12/2019 TecMecRoc-L6_Example Hitched Plug

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EXAMPLE OF HITCHED PLUG DESIGN


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1.0 INTRODUCTION

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 Guidelinespublished 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.

Figure 1 General Layout 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.

2.0 BEARING CAPACITY OF ROCK

The Bulkhead Design Guidelines prepared by the Ontario Ministry of Labour (1995) includes

estimation of bearing capacity of rock, which is reproduced here in Sections 2.1 and 2.2. These


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guidelines are used to assess the rock mass strength for incorporation into the plug design

calculations of Section 4.0.

2.1 Homogenous 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:

Cb NcNWq += gg2

1

where: g= the unit weight of the rock

c = the cohesion of the rock

and

Ngand Ncare bearing capacity factors

Nc= (Nq - 1) cot f

Ng= 1.5 (Nq - 1) tan f

Nq = eptanf

tan2(p/4 + f/ 2)

f= the angle of friction of the rock

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

Rock Type Cohesion (c) (KPa) Friction Angle (f) (degrees)

Igneous Rock

- granite

- basalt

- porphyry

35000 - 55000 35 - 45

Metamorphic Rock

- quartzite

- gneiss

20000 - 40000 30 - 40


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- slateSedimentary Rock

- limestone

- dolomite

- sandstone

10000 - 30000 35 - 45

2.2 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 endeavours 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 to

Appendix B Rock Mass Characterization of the Plug Design Guidelines.

3.0 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.


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3.1 Plug Design Requirements

The 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 Loads

Factored Shear Loads

Factored Moments (and reinforcement requirements)

Bar Spacing & Slab Thickness

Anchorage into Rock

Bearing on Concrete

3.2 Plug Design Criteria

The 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 Effect of Factored Loads

2. The Bulkhead is considered to be a two-way slab that is simply supported on four sides.

3. Tectonic pressure is not considered

4. Deep beam flexure "analysis" does not apply.

5. The potential of hydraulic fracturing within the rock around the bulkhead has not beenconsidered in the design of the Ontario guidelines.

6. The bulkhead design has been designed to withstand static hydrostatic pressure withspecific gravity equal to one.


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3.3 Typical Plug Layout

The 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 outermostlayer.

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.


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3.4 Coefficients and Notations Used in Design

The following are notations used in the design calculations of Section 4.0:

A Effective tension area of concrete surrounding the flexural tensionreinforcement and having the same centroid as thatreinforcement, divided by number of bars, mm2h

As Area of tension reinforcement, square mm

D Load factor on dead load (Clause 9.2.3)*

L Load factor on live load (see Clause 9.2.3)*

Q Load factor on wind or earthquake load (see Clause 9.2.3)*

T Load factor in T-load (see Clause 9.2.3)*

Ratio of clear spans in long to short direction of two-way slabs1 Ratio of depth of rectangular compression block of depth of the neutral axis

(see clause 10.2.7)*

c Ratio of the long side to short side of the concentrated load or reaction area

b With of compression face of member, mm

bo Perimeter of critical section for slabs and footings, mm

bw Web width, mm

c Distance from extreme compression fibre to neutral axis, mm

Cad,Cbd Moment coefficients for positive dead load moments in short and long spansrespectively

Cal,Cbl Moment coefficients for positive live load moments in short and long spans

respectively

D Dead load, N

d Distance from extreme compression fibre to centroid of tension reinforcement,mm

db Nominal diameter of bar, wire or prestressing strand, mm

dc Thickness of concrete cover measured from extreme tension fibre to the centreof the longitudinal bar or wire located closest to it, mm

Es Modulus of elasticity of reinforcement, MPa (see clause 8.5.2 or 8.5.3)*

!s Strain in reinforcing

fs Calculated stress in reinforcement at specified loads, MPa

fy Specified yield strength of nonprestressed reinforcement, MPa


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* NOTE: For Clause numbers refer to CAN-A23.3-M84 Standardfc Specified compressive strength of concrete, MPa

cf Square root of specified compressive strength of concrete, MPa

g Gravitational acceleration, 9.81 m/s2

H Head of water in metres

h Overall thickness of member, mm

hs Overall depth of slab, mm

L Live load N

I Span length of one-way slab as defined in clauses 8.7.1 and 8.7.2;* clearprojection of cantilever, mm

Ia Clear span of a two-way slab in short direction, mm

Ib Clear span of a two-way slab in long direction, mm

Ma Maximum moment in member at load stage at which deflection is computed, Nmm

MadPos, Positive dead load moments in short and and long spans respectively, N.mm/m

Mf Factored moment at section, N mm

Mr Factored moment resistance, calculated using the assumption in clauses 10.2and 10.3,* and the resistance factors given in clause 9.3,* N mm

m = 1a1b

Ratio of short to long span of a two-way slab

" Ratio of nonprestressed tension reinforcement = As/bd

Q Live load due to wind or earthquake, whichever produces the moreunfavourable effect

s Spacing between layers of reinforcement, mm

T Cumulative effects of temperature, creep, shrinkage and differential settlement

Vc Factored shear resistance provided by tensile stresses in the concrete, N

Vf Factored shear force at section, N

Vr Factored shear resistance, N

Vs Factored shear resistance provided by shear reinforcement, N

Wdf Factored dead load per unit area, kPa

Wf Factored load per unit area,, kPa

Wlf Factored live load per unit area, kPa (kN/m2)

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


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z Quantity limiting distribution of flexural reinforcement kN/mm (see clause 10.6)*

# Importance factor (see Clause 9.2.6)*

Factor to account for low density of concrete (see clause 11.2.3)*

#c Density of concrete, kg/m3

$c Resistance factor for concrete (see Clause 9.3.2)*

$s Resistance factor for reinforcing bars (see Clause 9.3.3)*

% 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.


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4.0 DESIGN CALCULATIONS

The 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. Thesecalculations 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 Conditions

The following presents initial conditions related to data input such as geometries, material strengths,

etc.

Opening (long side x short side), lax lb = 3400 mm x 3700 mm

Head of Water, H = 335 m (Elev. 465 m Elev. 130 m)

Concrete Compressive Strength, fc = 30 MPa

Reinforcing Yield Strength, fy = 400 MPa

Live load due to hydrostatic pressure, (w):

w = H x rwx g = 3287 kN/m2

Where, g = 9.81 m/s2

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

4.2 Design Coefficients

The following are design coefficients related to the bulkhead geometrical requirements, and design

layout:

088.13400

3700

_

_====

a

bc

l

l

sideshort

sidelongb

919.03700

3400

_

_====

b

a

l

l

sidelong

sideshortm


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

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

4.3 Total Factored Load, Wf

The total factored load (W f) 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 load

L = Live load

Q = Wind, Earthquake

T = Temp

Load 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, T

c= 0.7 two of L, Q, T

c= 0.6 three of L, Q, T

Since only a live load is considered in this design, c= 1.0 is considered.

Importance Factor (g):

g= 1.0 (CSA 9.2.6)

Therefore, the total factored load (W f) is resolved to:

Wf = Wdf + Wlf

= 1.25D +1.50L

For vertical bulkheads (load acting horizontally across bulkhead), such as in the hypotheticalcase analyzed, D = 0.00. For horizontal bulkheads (e.g., built in vertical shafts, the load


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would be acting vertically across bulkhead), the dead load should be estimated based on theplug volume and density of the concrete. For this example, D = 0.

\Wf = 0 + 1.50 x 3287 kN/m2

= 4931 kN/m2


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4.4 Factored Shear Resistance, Vc

The following series of equations consider the bulkheads resistance to shear failure.

Factored shear resistance (Vc):

Vc= (1 + 2 / bc) 0.2 lfc(fc)0.5bod Formula (1) (CSA 11.10.2.2)

But not greater than,

Vc= 0.4 lfc(fc)0.5bod Formula (2) (CSA 11.10.1.3)

Where, bo= perimeter of critical section

d = effective depth, mm

bo= 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 (fc):

(fc)0.5= (30)0.5= 5.477

where fcis expressed in MPa

Evaluating Formula (1):

Vc= (1 + 2 / bc) 0.2 lfc(fc)0.5bod,

= (1+2 / 1.088) 0.2 x 1.0 x 0.60 x 5.477 x bod= 1.8654 bod

Formula (1) cannot be greater than Formula (2).


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4.5 Evaluating Formula (2):

Vc = 0.4 lfc(fc)0.5bod

= 0.4 x 1.0 x 0.6 x 5.477 bod= 1.3145 bod

Which is less than Vcin Formula (1)

Therefore, use Vcin 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, Vf

The 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, d

The 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 = 0

Solving quadratic equation for d:

ad2+ bd + c = 0

d = (-b 6(b2 4ac)0.5) / (2a)

= (53.6689 6(2880.350827 2527.679121)0.5) / 0.020374

= (53.6689 618.77955554) / 0.020374

= 1713 mm

Use d = 1800 mm


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4.8 Factored Moment (Short Side), Mf

The 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 = CalWlfla2

= 0.0431 x 4931 x (3.40)2= 2457 kN.m per metre width

And, dead load positive moment, (Mad):Mad = Cadwdfla

2= 0

Therefore, 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= (Mfx 106) / (0.90 fsfyd) (CSA 9.3.3)

Where, Mf= 2457 kN.m per metre width

d = 1800 mmFor fs= 0.85, fy = 400 MPa

Therefore, As= (2457 x 106) / (306 x 1800)

= 4461 mm2/ m

Consider two steel layers of 30M at 200mm:

As= 2 [p(30/2)2] / 0.200

= 7068 mm2 / m

Ratio of non-prestressed tension reinforcement, (r):

r = As/ (b d)

Where b = 1000 mm unit width\r = 7068 / (1000 x 1800),

= 0.003927


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4.10 Factored Moment Resistance (Short Side), Mr

The 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 = rfsfy[1 (rfsfy) / (1.7 fcfc)] 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 1800 2= 4137 kN.m

Since Mr $Mf, OK.

4.11 Ratio of Tension Reinforcement (Short Side),

The 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 r>rmin, OK

2. Max. allowable steel ratio rmax(to ensure ductile failure)

rmax= (fc/ fs) [(0.85 x fcx b1x 600) / fy(600 + fy)]

Where, fc= 30, b1= 0.85

rmax = (0.60 / 0.85) [(0.85 x 30 x 0.85 x 600) / 400 (600 + 400)]= 0.02295,

Since rrmin, OK

Therefore initial reinforcing steel area estimation (Section 4.8) of two layers of 30 M at 200mm are satisfactory. (As= 7068 mm

2/ m)


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4.12 12. Factored Moment (Long Side), Mf

Factored moment, long side, (Mf):

Mf= Mbl+ Mbd (CSA E2.8)

Where Mbd= 0 (dead load, D = 0)Mbl= CblWlflb

2= 0.0305 x 4931 x (3.70)2

= 2059 kN.m per metre width

\Mf= 2059 kN.m per metre width

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 Concrete

Design Handbook 2.9.

Steel area, (As):

As= (Mfx 106) / (0.90 fsfyd) (CSA 9.3.3)

Where, Mf= 2059 kN.m per metre width (long side)d = 1800 mmFor fs= 0.85, fy = 400 MPa

Therefore, As= (2059x 106) / (306 x 1800)

= 3738 mm2/ m

Consider two steel layers of 30M at 250mm:

As= 2 [p(30/2)2] / 0.250

= 5655 mm2 / m

Ratio of non-prestressed tension reinforcement, (r):r = As/ (b d)

Where b = 1000 mm unit width\r = 5655 / (1000 x 1800),

= 0.00314

4.14 Factored Moment Resistance (Long Side), Mr

The 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.


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Factored moment resistance, (Mr):

Mr= rfsfy[1 (rfsfy) / (1.7 fcfc)] 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 1800 2

= 2800 kN.m

Since Mr $Mf, OK.

4.15 Ratio of Tension Reinforcement (Long Side),

The 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 r>rmin, OK

2. Max. allowable steel ratio rmax(to ensure ductile failure)

rmax = (fc / fs) [(0.85 x fc x b1 x 600) / fy (600 + fy)]

Where, fc= 30, b1= 0.85

rmax = (0.60 / 0.85) [(0.85 x 30 x 0.85 x 600) / 400 (600 + 400)]

= 0.02295

Since rrmin, OK

Therefore 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 Thickness

The following formulae consider the spacing of reinforcement steel bar layers, as well as the thickness

of the bulkhead concrete slab.


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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 mm

Slab 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 Rock

The 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) (lax lb)= lalb+ lbh + lah + h

2 lalb= (h2+ lbh + lah)

Where, h / 2 = Anchorage in Rock

Hydrostatic Pressure = 3287 kN / m2

Allowable Bearing Pressure = 3800 kN / m2

\3287 A1= 3800 A

A1/ A = 3800 / 3287 = 1.156

A1A2 l

lb

h/2


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lalb/ (h2+ lbh + lah) = 1.156


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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 = 0

Solving 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 69.6922) / 2

= 1.30 m

Therefore, anchorage required = h/2 = 1.30 / 2 = 0.65 m

For additional factor of safety:

Anchorage required = h / 2, let h = d, 1800 / 2 = 900 mm = 0.90 m

4.18 Bearing on Concrete

The 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 / m2x 1.5 (live load factor)= 5700 kN / m2= 5.70 MPa

On Face = 3287 kN / m2x 1.5= 4931 kN / m2= 4.93 MPa

Allowable Bearing Pressure on Concrete:

= 0.85 fcfc (CSA 10.15.1.1)= 0.85 x 0.60 x 30= 15.3 MPa

Since Allowable Bearing Pressure on Concrete>Pressure on Face (due to live load), OK


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Bulkhead Design Example

Figure D2 Results of the bulkhead design calculations for an opening 3400 mm x 3700

mm.


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5.0 REFERENCES

Ontario Ministry of Labour, 1995, Bulkheads & Dams For Underground Mines Design

Guidelines, Occupational Health & Safety Branch, Sudbury, Ontario.

CAN3-A23.3-M84. Design of Concrete Structures for Buildings. Canadian Standards

Association.

CAN3-A23.1-M77.Concrete Materials and Methods of Concrete Construction, Canadian

Standards Association.

CPCA 1989, Concrete Design Handbook First Edition, Canadian Portland Cement

Association, Ottawa.

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TecMecRoc-L6_Example Hitched Plug