THE USE OF YIELD LINE ANALYSIS AND PANEL TESTS FOR THE DESIGN OF SHOTCRETE

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25 Νοε 2013 (πριν από 3 χρόνια και 11 μήνες)

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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 Schema

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)

Contribution of TEST WORK

TEST 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
W
pe

8
pe
pe
W
m

8
pe
pe
W
m

8
pe
pe
W
m

8
pe
pe
W
m

8
pe
pe
W
m

where
:

W
pe

is

the

peak

load

(kN)

f
rom Yield Line


m
pe

=
W
pe
/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
Load (kN)
Deflection [mm]
A
B
C
D
6ut
Figure 8:

Example of EFNARC test results for steel fibre reinforced
shotcrete

(70 kg/m
3
)


LOAD
W
pe

Point support

Point support

Point support

Yield Line Pattern

RDP TEST RIG

from Yield Line


m
pe

=
W
pe
/5.54

ASTM RDP TEST WORK


Figure 9:

Example of ASTM C1550 RDP test results for steel fibre reinforced
shotcrete

(70 kg/m
3
)

0
10
20
30
40
50
60
70
0
5
10
15
20
25
30
35
40
45
Load (kN)
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 Observation

UNDERGROUND

OBSERVATION




Crack

formation




Crack monitoring




Crack measurement

YIELD LINE METHOD



Veracity

CHECK




Crack patterns




Rock Loading

Observation


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


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 Analysis

STRUCTURAL

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 Capacity


Panel tests


Moment Demand


Rock Loading


Dead weight


simple prism


Quasi Static


relationship with deformation


Rock Mass Assessment
-

Q


Dynamic


Energy absorption method


Contribution of Structural Analysis

YIELD LINE METHOD


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/m
2
)


Versatile


Closed
-
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 supported

Statically determinate

Continuous beams

Statically indeterminate

HINGE

LOAD

Unit Displacement =
δ

P (Load)

Lever Arm = L/2

Rotation = 2
θ

θ

P
δ

= 4m
θ

P
δ

= 2m
θ

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

m
d

=

wab
/
48

M
d

average

=

wab
/
36
.
5

Fan Mechanism


Fan Mechanism


Figure 3: Yield line pattern for the fan mechanism

m
d

=

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

m
d

=

wab
/
48

m
d

=

wc
2
/
144

Shotcrete

Design Schema

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)

Conclusions 1


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
fibre

density/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


Conclusions 2


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)


Yield Line methods used advantageously


Calculation of
Shotcrete

capacity (strength)


Calculation of
Shotcrete

demand (moment/load)

Thank You


from

William and Graham