the use of yield line analysis and panel tests for the design of shotcrete by wc joughin * and gc...

THE USE OF YIELD LINE ANALYSIS AND PANEL TESTS FOR

THE DESIGN OF SHOTCRETE by 

WC JOUGHIN* and GC HOWELL** SRK Consulting, Johannesburg

* Principal Mining Engineer * Principal Geotechnical Civil Engineer

Presentation Summary

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 Shotcrete Design Method Summary and Conclusions

Shotcrete Design SchemaTEST 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)

Contribution of TEST WORKTEST WORK

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

YIELD LINE METHOD

• Characteristic Strength• Allowable Moment• Moment CAPACITY

Yield Line Pattern

EFNARC TEST RIG

LOAD Wpe

8pe

peW

m

8pe

peW

m 8pe

peW

m 8pe

peW

m

8pe

peW

m where:Wpe is the peak load (kN)

from Yield Linempe = Wpe/8

EFNARC TEST WORK

EFNARC TEST WORK

0

20

40

60

80

100

120

140

0.0 5.0 10.0 15.0 20.0 25.0

Lo

ad

(kN

)

Deflection [mm]

A B C D

6ut

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

LOAD Wpe

Point support

Point supportPoint support

Yield Line PatternRDP TEST RIG

from Yield Linempe = Wpe/5.54

ASTM RDP TEST WORK

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

0

10

20

30

40

50

60

70

0 5 10 15 20 25 30 35 40 45

Lo

ad (k

N)

Deflection (mm)

A B C D

ASTM RDP TEST WORK

“Elastic” Energy Absorption“Plastic” Energy Absorption

Peak Load – Crack Formation

TEST WORK Summary

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)

Contribution of ObservationUNDERGROUND OBSERVATION

• Crack formation• Crack monitoring• Crack measurement

YIELD LINE METHOD

• Veracity CHECK• Crack patterns• Rock Loading

Observation

Cracking in shotcrete is due to different mechanismsFlexure or Bending (moment)Punching shearAdhesion lossDirect shearAxial force (tension)

Sometimes difficult to categorize on the wall Long term monitoring required

Observation 2 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

14 March 2008

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

EXAMPLE

Contribution of Structural AnalysisSTRUCTURAL

ANALYSIS• Loads• Moments• Shear force• Torsion

YIELD LINE METHOD

• Load/moment relationship• Load DEMAND• Moment DEMAND

Structural Analysis Develop relationship between

DEMAND (load)CAPACITY (strength)

Moment CapacityPanel tests

Moment DemandRock Loading

Dead weight – simple prismQuasi Static – relationship with deformationRock Mass Assessment - QDynamic – Energy absorption method

Contribution of Structural Analysis

YIELD LINE METHOD

Why YIELD LINEOne of the PLASTIC suite of methodsBased on Elastic Perfectly plastic behaviourAllows redistribution of stress

Relatively simple analysis methodDirectly integrated with designEconomical (less reinforcement/m2)VersatileClosed-form solution (cf FE, FD, BE numerical

methods)

Yield Line Basics

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

Simply supportedStatically determinate

vContinuous beamsStatically indeterminate

HINGE LOAD

Unit Displacement = δ

P (Load)

Lever Arm = L/2

Rotation = 2θ

θ Pδ = 4mθPδ = 2mθ

Upper Bound Theorem

Any arbitrary crack pattern gives a design moment less than the maximum for a given load

Require MAXIMUM moment from all possible crack patterns

Continuous Slab

Yield line moment for a given load w

From SANS 0100 (Concrete Design Code)

Figure 2: Yield Line Pattern for a rectangular panel

md = wab/48

Md average = wab/36.5

Fan Mechanism Fan Mechanism

Figure 3: Yield line pattern for the fan mechanism

md = P/12.56

Combined Mechanism

Figure 4: Yield Line Pattern for a combined mechanism panel

Figure 4: Yield Line Pattern for a combined mechanism panel

Triangular Mechanism Triangular Mechanism

Compare with Rectangular Mechanism

1/144 : 1/48 = 66% economy

Figure 5: Yield Line Pattern for a triangular mechanism

md = wab/48

md = wc2/144

Shotcrete Design SchemaTEST 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)

Conclusions 1 Shotcrete Moment Capacity

Peak Moment Capacity reliably estimated for RDP PanelsSteel fibre in particular

Unreinforced panels give highly variable resultsMoment capacity reliably increases with fibre density/mesh areaResidual 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

Conclusions 2 Shotcrete Moment Demand

Rock load influenced by the crack patternEspecially in irregular rock wall geometries

Select crack pattern to give lowest moment of resistanceConventional Yield Line Design = 15% ruleShotcrete Yield Line Design = 50% rule (suggested)

Yield Line methods used advantageouslyCalculation of Shotcrete capacity (strength)Calculation of Shotcrete demand (moment/load)

Thank You

fromWilliam and Graham