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THE USE OF YIELD LINE ANALYSIS AND PANEL TESTS FOR THE DESIGN OF SHOTCRETEbyWC JOUGHIN* and GC HOWELL**SRK Consulting, Johannesburg* Principal Mining Engineer * Principal Geotechnical Civil Engineer

- Information available from Test Work
- Observation of crack formation
- Requirements of Analysis Methods
- Relationship between CAPACITY and DEMAND
- Yield Line method and how it is used
- Integration into the ShotcreteDesign Method
- Summary and Conclusions

TEST WORK

- Cube Tests
- Fibre Density
- EFNARC Panels
- RDP tests

- STRUCTURAL ANALYSIS
- Loads
- Moments
- Shear force
- Torsion

UNDERGROUND OBSERVATION

- Crack formation
- Crack monitoring
- Crack measurement

YIELD LINE METHOD

- Characteristic Strength
- Allowable Moment
- Moment CAPACITY

- Load/moment relationship
- Load DEMAND
- Moment DEMAND

- Veracity CHECK
- Crack patterns
- Rock Loading

SHOTCRETE DESIGN

- Factor of Safety (Capacity/Demand)
- Probability/Reliability (p(D – C) < 1.0)

TEST WORK

- Cube Tests
- Fibre Density
- EFNARC Panels
- RDP tests

YIELD LINE METHOD

- Characteristic Strength
- Allowable Moment
- Moment CAPACITY

EFNARC TEST WORK

where:

Wpe is the peak load (kN)

from Yield Line

mpe = Wpe/8

LOAD Wpe

Yield Line Pattern

EFNARC TEST RIG

Figure 8:Example of EFNARC test results for steel fibre reinforced shotcrete (70 kg/m3)

ASTM RDP TEST WORK

from Yield Line

mpe = Wpe/5.54

Point support

LOAD Wpe

Point support

Point support

Yield Line Pattern

RDP TEST RIG

ASTM RDP TEST WORK

Peak Load – Crack Formation

“Elastic” Energy Absorption

“Plastic” Energy Absorption

Figure 9:Example of ASTM C1550 RDP test results for steel fibre reinforced shotcrete (70 kg/m3)

- Moment Capacity development using Yield Line for a standard test panel
- Ratio of thickness of test panel to design thickness (on the wall) give the Design Moment Capacity
- Method allows a Characteristic Moment Capacity to be specified (cf Cube Strength)

UNDERGROUND OBSERVATION

- Crack formation
- Crack monitoring
- Crack measurement

YIELD LINE METHOD

- Veracity CHECK
- Crack patterns
- Rock Loading

- Cracking in shotcrete is due to different mechanisms
- Flexure or Bending (moment)
- Punching shear
- Adhesion loss
- Direct shear
- Axial force (tension)

- Sometimes difficult to categorize on the wall
- Long term monitoring required

- Look for patterns which resemble expected yield lines
- Take into account the in-plane axial (tensile) force component
- Locate areas of shear dislocation
- Ultimately
- Looking for yield line patterns

EXAMPLE

29 Mar ‘07

26 Apr ’07

11 May ‘07

08 Jun ‘07

15 Jun ‘07

23 Oct ‘07

20 Dec ’07

24 Jan ‘08

12 Feb ‘08

14 Mar ‘08

14 March 2008

- STRUCTURAL ANALYSIS
- Loads
- Moments
- Shear force
- Torsion

YIELD LINE METHOD

- Load/moment relationship
- Load DEMAND
- Moment DEMAND

- Develop relationship between
- DEMAND (load)
- CAPACITY (strength)

- Moment Capacity
- Panel tests

- Moment Demand
- Rock Loading
- Dead weight – simple prism
- Quasi Static – relationship with deformation
- Rock Mass Assessment - Q
- Dynamic – Energy absorption method

- Rock Loading

- Why YIELD LINE
- One of the PLASTIC suite of methods
- Based on Elastic Perfectly plastic behaviour
- Allows redistribution of stress
- Relatively simple analysis method
- Directly integrated with design
- Economical (less reinforcement/m2)
- Versatile
- Closed-form solution (cf FE, FD, BE numerical methods)

YIELD LINE METHOD

HINGE

LOAD

v

- External Work Done = Internal Work Done
- WD by Loads moving = WD by YL rotating

Simply supported

Statically determinate

Continuous beams

Statically indeterminate

Lever Arm = L/2

P (Load)

Pδ = 2mθ

Pδ = 4mθ

θ

Rotation = 2θ

Unit Displacement = δ

- Any arbitrary crack pattern gives a design moment less than the maximum for a given load
- Require MAXIMUM moment from all possible crack patterns

- Yield line moment for a given load w
- From SANS 0100 (Concrete Design Code)

md = wab/48

Md average = wab/36.5

Figure 2: Yield Line Pattern for a rectangular panel

- Fan Mechanism

md = P/12.56

Figure 3: Yield line pattern for the fan mechanism

Figure 4: Yield Line Pattern for a combined mechanism panel

Figure 4: Yield Line Pattern for a combined mechanism panel

- Triangular Mechanism
- Compare with Rectangular Mechanism
- 1/144 : 1/48 = 66% economy

md = wc2/144

md = wab/48

Figure 5: Yield Line Pattern for a triangular mechanism

TEST WORK

- Cube Tests
- Fibre Density
- EFNARC Panels
- RDP tests

- STRUCTURAL ANALYSIS
- Loads
- Moments
- Shear force
- Torsion

UNDERGROUND OBSERVATION

- Crack formation
- Crack monitoring
- Crack measurement

YIELD LINE METHOD

- Characteristic Strength
- Allowable Moment
- Moment CAPACITY

- Load/moment relationship
- Load DEMAND
- Moment DEMAND

- Veracity CHECK
- Crack patterns
- Rock Loading

SHOTCRETE DESIGN

- Factor of Safety (Capacity/Demand)
- Probability/Reliability (p(D – C) < 1.0)

- Shotcrete Moment Capacity
- Peak Moment Capacity reliably estimated for RDP Panels
- Steel fibre in particular

- Unreinforced panels give highly variable results
- Moment capacity reliably increases with fibredensity/mesh area
- Residual Moment capacities can be estimated using the same method (see following paper)
- Actual underground capacities are variable
- Dependant of local rock geometry and shotcrete application

- Peak Moment Capacity reliably estimated for RDP Panels

- Shotcrete Moment Demand
- Rock load influenced by the crack pattern
- Especially in irregular rock wall geometries

- Select crack pattern to give lowest moment of resistance
- Conventional Yield Line Design = 15% rule
- Shotcrete Yield Line Design = 50% rule (suggested)

- Rock load influenced by the crack pattern
- Yield Line methods used advantageously
- Calculation of Shotcrete capacity (strength)
- Calculation of Shotcretedemand (moment/load)

from

William and Graham