GRINDING AIDS Reducing the clinker factor in masonry cements
Reducing uncertainty in the assessment of the masonry...
Transcript of Reducing uncertainty in the assessment of the masonry...
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Reducing uncertainty in the assessment of
the masonry buildings by moving from
empirical to analytical drift capacity
models
Katrin Beyer, EPFL
http://eesd.epfl.ch/
The 42nd Risk, Hazard & Uncertainty Workshop, Hydra, Greece
June 2016
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Collaborators
• Bastian Wilding, Dr. Sarah Petry, Marco Tondelli, Dr. Panos Mergos
Grants
• FP7-Programme for access to TREES laboratory of EUCENTRE
• Swiss National Science Foundation
• Federal Office for the Environment in Switzerland (OFEV)
• In-kind contributions by Morandi Frères SA
Acknowledgments
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Drift capacity of unreinforced masonry walls
State of practice (e.g. Eurocode 8)
Empirical model
• Shear failure: du=0.4%
• Flexural failure: du=0.8% H0/L
H0=Shear span
L= Wall length
State of the art
Empirical models with further parameters
• Axial stress ratio
• Parameter describing moment profile H0/H
Shear failure Flexural failure
ROCKI
NG:
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State-of-the-art: Unreinforced masonry walls
• Determining the displacement capacity
from quasi-static cyclic tests
V
D
• Assemble data bases + fit empirical
models
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State-of-the-art: Unreinforced masonry walls
Empirical model (EC8)
Walls failing in flexure Walls failing in shear
Masonry typology:
Clay brick masonry with
normal cement mortar
• Poor prediction of mean response
• Very large scatter
Prediction of drift capacity with empirical model d=D/H
1.8±1.1 1.7±1.0
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Drift capacity of masonry walls
• Biased towards unrepresentative small test units
• General problem of structural engineering: Large tests required
number of tests will always be limited
Limits for empirical models
Drift capacity
reduces with the
size of the test
unit.
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Change the scale at which we measure and predict
Global response
Local response
PUP3: g at Vmax
V D
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Analytical model of masonry walls: Critical Diagonal Crack Model
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0 0
50
100
150
200
PUP1 Model
Test pos. env.
0.1 0.2 0.3 0.4 0.5 0 0.5 1 1.5 2 2.5 0
0.2
0.4
0.6
0.8
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u f l /u Model
u s h
/u Model
u f l /u Test
u s h
/u Test
Drift δ [%]
Sh
ea
r fo
rce V
[kN
]
Horiz. displ. u [mm]
Dis
pla
ce
ment co
mp
one
nts
[-]
PUP1
Validation of analytical model
against experimental results on the
global and local level
Analytical model of masonry walls: Critical Diagonal Crack Model
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Empirical model (EC8)
Analytical model
Walls failing in flexure Walls failing in shear
Performance of empirical vs analytical model
Drift capacity of
masonry walls
Research results
Proof of concept that developing such analytical models for predicting the
drift capacity of unreinforced masonry walls is feasible.
Better because they connect local to global deformation measures
1.8±1.1 1.7±1.0 0.7±0.3 0.9±0.4
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Analytical model of masonry walls: Critical Diagonal Crack Model
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Suite of cycles with increasing amplitudes
• Variables:
• Number of cycles per drift amplitude (often n=2 or n=3)
• Increase of amplitudes Dd
n=3 Dd
Loading history
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Does the choice of the loading history influence the obtained drift
capacities?
Systematic study on cumulative damage effects on URM walls missing
Pairs of monotonic and cyclic tests:
Ganz & Thürlimann (1984)
• W1 (monotonic) & W6 (cyclic)
• W2 (monotonic) & W7 (cyclic)
Magenes & Calvi (1992)
• MI1m (monotonic) & MI1 (cyclic)
Loading history
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• Force capacity is not affected by cumulative damage demand
• Displacement capacity from monotonic tests is twice as large as from
cyclic tests.
Displacement capacity depends on the demand.
Does the choice of the loading history influence the obtained drift
capacities?
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• Flexural failure: Unaffected by number of cycles
• Shear and hybrid failures: Displacement capacity reduces with increasing number of cycles that are applied
Displacement history that is applied in cyclic tests matters.
Loading history: Influence of number of cycles on du
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• Many protocols have been proposed:
• One specific for URM structures: SPD protocol (Porter 1987),
result of US-Japan workshop
• One that is most frequently used: SAC protocol (ATC 1992)
Loading proctocols for quasi-static cyclic tests
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• All existing loading protocols derived for regions of high seismicity
• When applied to structural elements for regions of moderate
seismicity: Test units subjected to too many cycles
Sion Basel
Distance [km]
Ma
gn
itu
de
Distance [km]
Mag
nit
ud
e
Existing protocols
De-aggregation Results for Switzerland for T=2475 yrs (2/50)
Sion (agd=0.15g for T=475 yrs) Basel (agd=0.12g for T=475 yrs)
Sion Basel
Loading proctocols for quasi-static cyclic tests
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New loading protocols: Moderate vs. High Seismicity
2 4 6 8 10 12 14-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
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Number of cycles
Norm
aliz
ed c
ycle
am
plit
ude
f(t)=0.50-0.55exp(t2.4
)
f(t)=-0.50+0.55exp(t2.4
)
T=0.2s
2 4 6 8 10-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
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Number of cycles
No
rma
lize
d c
ycle
am
plit
ud
e
f(t)=-0.50+0.55exp(t2,2
)
f(t)=0.50-0.55exp(t2,2
)
T=0.3s
Mo
dera
te
seis
mic
ity
Hig
h
seis
mic
ity
5 10 15 20 25-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Number of cycles
No
rma
lize
d c
ycle
am
plit
ud
e
5 10 15 20-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
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Number of cycles
Norm
aliz
ed c
ycle
am
plit
ude
ntot=14
α=2.4
ntot=10
α=2.2
ntot=24
α=2.8
ntot=20
α=1.9
Loading proctocols for quasi-static cyclic tests
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Summary & Outlook
Summary
• Analytical drift capacity models seem feasible (for all limit
states)
• As long as we do not have a model that captures cumulative
damage effects on masonry performance, we should test with
realistic testing protocols.
Future research
• Effect of cyclic degradation / cumulative damage
• Effect of strain rates
• Failure criteria for other masonry typologies (thin bed mortar,
stone masonry, …)
eyy
eyy
gxy
gxy
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Change the scale at which we measure and predict
Coupling of shear and flexural deformations
Axial strain profiles
Shear strains
concentrate in
the compression
strut
Linear strain
profile in
compression
zone is a
reasonable
assumption
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Criteria for onset of crushing:
Confinement effect at the base of the wall
Onset of crushing in 2nd joint
Strength of masonry fu
determinant in 2nd joint
Strength of brick fcB
in base joint
Change the scale at which we measure and predict
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Shear critical walls: Critical Diagonal Crack Model
Assumptions:
- Deformations in diagonal crack can be lumped in a single diagonal crack
(“Critical Diagonal Crack” = CDC)
- Geometry of CDC:
- Geometry of wall
- Geometry of bricks V
N
M
Critical diagonal crack
Analytical model of URM walls: CDC Model
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Onset of formation of CDC: Modified Mann – Müller criterion
- Stress demand: Plane section analysis
Compute position along the CDC where the vertical bed joint stresses
due to N, M, T are for the first time zero
Location where diagonal crack starts to form
τxy
σN
σT
L
H0
H-H0
H
N
M(x=H)
V
x
y
τxy
(y,x=Hcrit )
σN
σT
lB
hB
σM
σM
H crit
τxy
τxy
σN
σT
L
H0
H-H0
H
N
M(x=H)
V
x
y
τxy
(y,x=Hcrit )
σN
σT
lB
hB
σM
σM
H crit
τxy
Analytical model of URM walls: CDC Model
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Analytical model of URM walls: CDC Model
Peak strength: Mohr-Coulomb criterion based on local stresses
- Stress demand:
- Axial stresses: Plane section analysis
- Shear stresses: Parabolic stress distribution, shear only carried by area in
compression
- Peak strength reached when
- Mohr-Coulomb criterion is exceeded
- Compressive strength is exceeded (confinement effect considered)
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Analytical model of URM walls: CDC Model
Stiffness of wall
• Only area in compression contributes to the stiffness
• The diagonal crack divides the wall section into two sections
(composite beam)
• Limited shear stress transfer between the sections allowed
y
τxy
(y)σxx
(y)
y
L1 L2
L
y y
Lc Lc
L1 L2
L
σxx
(y) τxy
(y)
L
H
x
L2(x)L1(x)
y
Uncracked
section
Flexural
decompression
Shear cracking
g-factor approach
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Analytical model of URM walls: CDC Model
Residual strength: Zero stress transfer in CDC
- Stress demand: - Axial stresses: Plane section analysis
- Shear stresses: Parabolic stress distribution, shear only carried by area in compression
- Residual strength reached when - Tensile strength of top and bottom brick exceeded (Turnsek-Cacovic)
- Compressive strength is exceeded (confinement effect considered)