Roof Support 1 Entry Design is a complex problem. 1. One can use a Roof Classification System 2. or one can use Beam Formulas Stand-Up Time (RMR): Maximum Unsupported Span (Q): According to the Q system, the maximum unsupported span (in m) can be obtained from the following equation: Beam Theory: 1. It is recommended to use the Simple Beam equation for Shallow overburden (< 300 ft) 2. And the Clamped Beam equation for Deep cover (> 300 ft). 3. In both cases, the Shear equation should also be evaluated to see if it produces a smaller width, which would then be used.

0.4Q ESR 2span Maximum

Simple Beam - For a simply supported roof beam of unit width, the Allowable Span, based on tensile failure, can be calculated as follows: It follows that given the span, thickness and uniform load, the Extreme Fiber Stress can be calculated as: Clamped Beam - For a clamped roof beam of unit width, the Allowable Span, based on tensile failure, can be calculated as follows: It follows that given the span, thickness and uniform load, the Extreme Fiber Stress can be calculated as:

3w

4 L

2at

beam of lengthunit per load uniformw

factor)safety / strength (tensile stress workingAllowableσ

thicknessBeamt

span Allowable L

a

2

2

e 4t

w3L σ

beam of lengthunit per load uniformw

thicknessBeamt

span Allowable L

stressfiber Extremeσe

w

σ2t L a

2

beam oflength unit per load uniformw

factor)safety strength / (tensile stress workingAllowableσ

thicknessBeamt

span Allowable L

a

2

2

e 2t

wL σ

beam oflength unit per load uniformw

thicknessBeamt

span Allowable L

stressfiber Extremeσe

Beam Shear - For either a simply supported or a clamped roof beam of unit width, the Allowable Span, based on shear failure, can be calculated as follows: Beam Theory – The proceeding beam equations require the use of the in situ tensile strength of the roof material. In many situations, the roof material is cracked or jointed and the in situ tensile strength may be much less than the laboratory value. It is generally considered an unreliable value.

3w

t τ4 L a

beam oflength unit per load uniformw

factor)safety strength /(shear stressshear Allowable

thicknessBeamt

span Allowable L

a

(Problem – Beam Span) The immediate roof in a new mining section of a limestone mine under shallow cover has been found to be free of any major defects. Its thickness is 4 ft, its modulus of rupture is 1200 psi, it shear strength is 2000 psi, and its specific gravity is 2.6. Utilizing a safety factor of 8, what is the maximum safe roof span in feet? First, we calculate the allowable span using the simple beam formula: To double check, we calculate the extreme fiber stress: Finally, we calculate the allowable span based on shear strength (not a limiting factor):

ft26.6

ftlb

62.4 * 2.6 *ft 4*3

ftin

144*/8inlb

1200*ft) (4*4

3w

4 L

3

2

2

22

2

at

psi 150in 144

ft*

ft

lb21,500

ft 4*4

ftlb

62.4*2.6*ft 4*ft 26.6*3

4t

w3L σ

2

2

2

2

3

2

2

2

e

ft 2,366

ftlb 62.4

*2.6*ft 4*3

ft144in

*in

lb 2000 *ft 4* 4

3w

t τ4 L

3

2

2

2

a

Coal Mine – Empirical Design: In addition, it is important to consider that although it is called Entry design, it may be more accurately called Intersection design. Typically, the largest spans in an underground coal mine are the diagonals at the intersections. Nominally, the intersection diagonal would be 41% (1/sin(45°)) wider than the entry; however, the pillar corners are known to slough, and frequently the pillar corners are cut to increase haulage mobility. Both of these activities increase the intersection span. In an analysis of roof falls at 37 coal mines where numerous intersections were measured, Molinda et al. (2000) found that the intersection spans averaged 4 to 6 ft wider than the nominal width in shallow (depth <400 ft) mines and 6 to 8 ft wider than the nominal span in deep (depth >400 ft) mines. In the same study, Molinda et al. (2000) found that 70% of all the roof falls occur in the intersections, although the intersections only total about 20% to 25% of the development entry lengths. They concluded that intersections are 8 to 10 times more likely to have a fall than an equivalent length of entry. Therefore, if the mine engineer can design a stable intersection span, then the entries in between the intersections should naturally be stable.

From their analysis of the roof falls rates at the study mines, Molinda et al. (2000) determined that a mine with a given CMRR would avoid high roof fall rates (>3 falls per 10,000 ft of entry development) if the sum of the diagonals of the intersection span (Is), in feet, was kept below

(EQ 3.51)

If the CMRR > 65, then it should be set equal to 65 in Equation 3.51. Therefore, if the CMRR is 45 at a 600-ft-deep mine, then the maximum intersection span should be

(EQ 3.52)

And given that the actual span averages 7 ft wider than nominal (Molinda et al. 2000), the entry width (we) should be less than

(EQ 3.53)

CMRR*0.66 31Is

ft 60.7

45 * 0.66 31

CMRR*0.66 31Is

ft19.0

45sin*2760.7we

Roof Bolting General types of roof bolts: 1. Point-Anchor 2. Resin Grouted / Cement Grouted 3. Friction Bolts a. Split-Sets b. Swellex 4. Cable Bolts

Figure. Mechanical-Anchor Bolt.

Figure. Resin-Assisted, Mechanical-Anchor Bolt.

Figure. Fully Grouted Bolt.

Figure. Tensioned Rebar Bolt

Figure. Combination Bolt.

Figure. Cable Bolts.

Roof Bolt Parameters: 1. Length 2. Diameter a. (No. 5 bar = 5/8 in dia.) 3. Strength / Grade a. (grade 40 = 40,000 psi yield) 4. Anchorage Type a. Expansion shell b. Resin c. Combination Support Principles - Roof bolting supports the roof using three general principals 1. Suspension 2. Beam Building 3. Reinforcement

Roof Suspension - For designing bolts for suspending the roof, the rock weight supported by each bolt is calculated and compared to the allowable resistance of the bolt.

Figure. Schematic of uniformly spaced, suspension design. Rock Weight - For Uniform Spacing of the roof bolts, the Rock Weight supported by each bolt can be calculated as:

w b

l b

w b

/2w b

l b/2

CoalPillar

CoalPillar

w b /2w b

hr

l b

Plan View

Cross Section View

TributaryArea

w b

w b

bbrr l*w*h*ρ P

entry theoflength thealong Spacingl

entry theof width theacross Spacingw

loadrock ofHeight h

rock theofDensity ρ

boltper loadRock P

b

b

r

r

Rock Height - The Rock Load Height can be determined from Geology, Observation, or from the Rock Mass Classification as: Bolt Strength - The Allowable Load for each bolt is the yield strength times the area divided by the safety factor. (Problem - Sample Test Question #20) A mine has the following two types of un-tensioned, resin-grouted rock bolts available. Roof rock at the mine weighs 160 lb/ft3. What is the most economical bolting pattern and bolt to support a rock column 6 ft thick if the maximum allowable load on the bolts is 80% of yield? 1. #6 Rebar, grade 40 2. #6 Rebar, grade 60 The rock weight for 6 ft height with a 4’ x 4’ or 5’ x 5’ pattern is: The Bolt Strength of the two bolts types are: Neither bolting pattern is strong enough at the 5 ft spacing and only the grade 60 bolt is strong enough at the 4 ft spacing.

er w*100

RMR-100h

entry ofWidth w

Rating MassRock RMR

loadrock ofHeight h

e

r

SF

4d π*σ S

2y

b

FactorSafety SF

bolt ofDiameter d

bolt ofstrength Yield σ

strengthbolt AllowableS

y

b

lbs 15,360

4*4*6*160

l*w*h*ρ P bbrr

lbs 24,000

5*5*6*160

l*w*h*ρ P bbrr

lbs 14,137

40.75* π*0.80*40,000

SF

4d π*σ S

2

2y

b

lbs 21,205

40.75* π*0.80*60,000

SF

4d π*σ S

2

2y

b

Figure. Complex suspension design. Example – (Complex Suspension Design) - The immediate roof consists of 3.5 ft of weak shale overlain by a competent sandstone, all with a density of 158 lb/ft3. The entry is 16 ft wide and the row spacing down the entry is 5 ft. The outside bolts are: 5.5 ft long, #5 rebar, grade 60, fully-grouted bolts and they are installed 3 ft from the rib of the entry. The center bolt in this example is assumed to be an 8 ft long, 0.6 in dia. (30 ton) cable bolt.

CoalPillar

CoalPillar

Plan View

Cross Section View

2.5

8.05.5

5.03.0

5.0

5.03.0

3.5

1.51.5

2.5 2.5

5.0

5.0

5.0

4.0

2.5 1.51.52.5

TributaryArea

TributaryArea

Rock Load - the width of the tributary area for the outside bolt would be calculated as the sum of half of the distance to the center bolt (2.5 ft) and half the distance to the rib (1.5 ft), for a total of 4 ft (see Figure). The width of the tributary area for the center cable bolt would then be 5 ft, and the length of the tributary area for both types of bolts is equal to the row spacing of 5 ft. With this bolting plan, the width of the support area for the entire bolt row is then 13 ft and the length of the support area for the entire row is 5 ft. The Rock Load for the 3.5 ft height, 13 ft width and 5 ft spacing is then: The Strength of the rebar bolt is then: The combined bolt capacity is then: And the safety factor is:

lbs 35,945

ft 5 *ft 13*ft 3.5*lbs/ft 158

l*w*h*ρ P3

bbrr

lbs 18,400

/4in 0.625*3.14159*psi 60,000

4d π*σ S2

2yb

lbs 96,800

lbs 60,000lbs 18,400*2 Sr

70.2lbs 35,945

lbs 96,800

P

S SF b

Wedge Support:

1. Rock bolting can be used to support a sliding block or a block susceptible to falling under gravity.

2. Assumes that the blocks are discreetly defined. 3. A limit equilibrium analysis can be used to determine bolting support 4. Commercial software facilitate this type of analysis

Beam Building: RMR Bolt Design for tunnels:

RMR Bolt Design for coal:

Q Bolt Design for Hard Rock:

The Q value is related to tunnel support requirements by defining the equivalent dimensions of the excavation. This equivalent dimension, which is a function of both the size and the purpose of the excavation, is obtained by dividing the span, diameter, or the wall height of the excavation by a quantity called the excavation support ratio (ESR). Thus,

ESR

(meters)height or diameter, span, Excavation dimension Equivalent

The ESR is related to the use for which the excavation is intended and the degree of safety demanded, as shown below.

Excavation category ESR No. of cases A. Temporary mine openings 3-5 2 B. Vertical shafts: Circular section 2.5 - rectangular/square section 2.0 - C. Permanent mine openings, water tunnels for 1.6 83 hydropower (excluding high-pressure penstocks), pilot tunnels, drifts, and headings for large excavations D. Storage rooms, water treatment plants, minor 1.3 25 highway and railroad tunnels, surge chambers, access tunnels. E. Power stations, major highway or railroad 1.0 73 tunnels, civil defense chambers, portals, inter- sections F. Underground nuclear power stations, 0.8 2 railroad stations, factories The relationship between the index Q and the equivalent dimension of an excavation determines the appropriate support measures. Barton et al. (1974) provide 38 support categories which give estimates of permanent support. For temporary support determination, either Q is increased to 5Q or ESR is increased to 1.5 ESR. For selection of the support measures using the Q-system, the reader should consult the original paper by Barton et al. (1974) or the book by Hoek and Brown (1980). The maximum unsupported span can be obtained as follows: Maximum span (unsupported) = 2(ESR)Q0.4 (6.7)

Q – Bolt Length: