SOME DEVELOPMENTS ON PERFORMANCE-BASED SEISMIC DESIGN OF MASONRY STRUCTURES

SOME DEVELOPMENTS ON PERFORMANCE-BASED SEISMIC DESIGN OF MASONRY STRUCTURES

Sergio M. AlcocerJuan G AriasLeonardo E Flores

Institute of Engineering, UNAM, Mexico

Sergio M. AlcocerJuan G AriasLeonardo E Flores

Institute of Engineering, UNAM, Mexico

Masonry construction in Mexico 1

Because of the large housing deficit in Mexico (4.3 M houses), over 70% of the construction industry is focused on housing development and rehabilitation

Over 50% of housing projects are built with masonry

Historically, one-third of the total losses infringed by earthquakes has concentrated in housing

Because of the large housing deficit in Mexico (4.3 M houses), over 70% of the construction industry is focused on housing development and rehabilitation

Over 50% of housing projects are built with masonry

Historically, one-third of the total losses infringed by earthquakes has concentrated in housing

Masonry construction in Mexico 2

Confined masonry, confined with tie-columns and bond-beams, is the prevalent masonry system in the country (and in Latin America)

Excellent performance when properly confined: amount and detailing

Improvements in design practice, based on sound principles and models, will have a significant economical impact because housing prototypes are largely replicated

All savings of families are invested in their houses; therefore, a house is the most cherished family asset

Confined masonry, confined with tie-columns and bond-beams, is the prevalent masonry system in the country (and in Latin America)

Excellent performance when properly confined: amount and detailing

Improvements in design practice, based on sound principles and models, will have a significant economical impact because housing prototypes are largely replicated

All savings of families are invested in their houses; therefore, a house is the most cherished family asset

Confined masonry requirements

tie-colwall

H

Bond beam in parapets

Distancebetweentie-columns

slab

Tie-columnsIn parapets

Confining elementsaround openings

Dis

tanc

e be

twee

nbo

nd b

eam

s ≤

3 m

Tie-columns at wall intersections

≤4 m1.5H

wall

wall

Tie-columns

brick

slabbeam

brick

Beam bond

Hysteresis curves of confined masonry wallsHysteresis curves of confined masonry walls

V*V*RDFRDF

VVRDFRDF

00

-100-100

-200-200

200200

100100

Drift angle, mm/mmDrift angle, mm/mm-0.02-0.02 -0.01-0.01 00 0.010.01 0.020.02

0.60.6

0.40.4

0.20.2

00

-0.2-0.2

-0.4-0.4

-0.6-0.6

Late

ral l

oad,

kN

Late

ral l

oad,

kN

00

-100-100

-200-200

200200

100100

Drift angle, mm/mmDrift angle, mm/mm

Shea

rstr

ess,

MPa

Shea

rstr

ess,

MPa

0.60.6

0.40.4

0.20.2

00

-0.2-0.2

-0.4-0.4

-0.6-0.6 Shea

rstr

ess,

MPa

Shea

rstr

ess,

MPa

M1 (M-3/8-Z6)M1 (M-3/8-Z6)

M3 (M-5/32-E20)M3 (M-5/32-E20)

M2 (M-0-E6)M2 (M-0-E6)

M4 (M-1/4-E6)M4 (M-1/4-E6)

1 kg/cm² = 0.0981 MPa1 kg/cm² = 0.0981 MPa

-0.02-0.02 -0.01-0.01 00 0.010.01 0.020.02

Late

ral l

oad,

kN

Late

ral l

oad,

kN

Masonry shear strength

Masonry contribution to shear strength

VmR = FR (0.5 vm* AT + 0.3 P) ≤ 1.5 FR vm* AT

Contribution of horizontal reinforcement to shear strength

VsR = FR η ph fyh AT

Masonry contribution to shear strength

VmR = FR (0.5 vm* AT + 0.3 P) ≤ 1.5 FR vm* AT

Contribution of horizontal reinforcement to shear strength

VsR = FR η ph fyh AT

Allowable inelastic lateral drift angle

γinelastic = Q γ reduced load

0.006 infill walls0.0035 load bearing confined masonry walls,

solid units and horizontal reinforcement or wire mesh

0.0025 confined masonry walls: solid units or hollow units with horizontal reinforcement or wire mesh

0.0020 internally reinforced masonry0.0015 unreinforced, unconfined masonry

γinelastic = Q γ reduced load

0.006 infill walls0.0035 load bearing confined masonry walls,

solid units and horizontal reinforcement or wire mesh

0.0025 confined masonry walls: solid units or hollow units with horizontal reinforcement or wire mesh

0.0020 internally reinforced masonry0.0015 unreinforced, unconfined masonry

Final damage state

Model proposed• Shear plastic hinge at ground story• Basic design parameter is drift angle

Performance criteria

LimitLimit StateState CriterionCriterion Residual Residual crack crack widthwidth, ,

mmmm

DriftDrift angleangle, %, %

ServiceabilityOnset of masonry inclined cracking (cracking

strength)0,1 0,15

RepairabilityInclined cracking fully formed over masonry

wall; hairline cracking into tie-columns; onset of masonry crushing

2 0,25

SafetyStrength of wall; wall cracking penetrates

into tie-column ends; yielding of tie-column reinforcement due to shearing; onset of tie-

column crushing

5 0,40

0

0.5

1

1.5

2

0 0.005 0.01 0.015

Drift angle, mm/mm

V / V

cr

Rehabilitation criteria

VV

DcrDcr DMDM D80D80

Reh

abili

tatio

nR

ehab

ilita

tion Epoxy resin

Epoxy mortarCement mortarJacketingBar insertionReplacement (brick / concrete)

Epoxy resinEpoxy mortarCement mortarJacketingBar insertionReplacement (brick / concrete)

Crack width, mmCrack width, mm0.10.1 22 55 1515

DD

InjectionInjection

Stiffness law – degrading behavior1

/ (St

iff/ I

nitS

tiff.)

80 30

Unloading branch

0 0.005 0.01 0.01

Loading branch

0 0.005 0.01 0.015

7025

60

0

10

20

30

40

50

0

5

10

15

20

5

a = 1 x 10 9b = 1000

a (γmax) 4 + b γmax + 1

a = 1 x 10 8b = 600

a (γmax) 4 + b γmax + 1

Maximum drift ratio (γmax)Maximum drift ratio (γmax)

0

0

W-W

Shea

rStr

ess,

MPa

Drift Ratio, mm/mm Drift Ratio, mm/mm

0.6

1.2

-0.6

-1.20 0.005 0.01 0.015-0.005-0.01-0.015

-0.02 -0.01 0 0.01 0.02

W/o horizontal reinforcement

-0.4

0.4

0.8

-0.8M-¼-E6

Experimental Calculated0 0.005 0.01 0.015-0.005-0.01-0.015

W-W

Experimental Calculated M-¼-E6-0.02 -0.01 0 0.01 0.02

Shea

rStr

ess,

MPa

With horizontal reinforcement

Shaking table tests to assess seismicperformance

3,52

3,52

A

C

B

2 3 4 5

0,922,00

2,000,92

2,46 2,12 2,46

7,16

7,16

0,97 1,00

0,92

1,68

Response spectra of records applied

T (s)

0.001

0.01

0.1

1

10

100

1000

0.01 0.1 1 10

Dis

plac

emen

t(cm

)

1

10

100

1000

10000

0.01 0.1 1 10

Diana 7.6Diana 7.8Diana 8.0Diana 8.3Manz 8.1

Acc

eler

atio

n(c

m/s

2 )

T 3T 1• A M7.6 earthquake record was used as a Green function to simulate records of higher magnitude (and intensity) and longer duration

T 3T 1

-150 0

-100 0

-50 0

0

50 0

100 0

150 0

0 5 10 15 2 0 25 30 3 5 40 4 5 50

-0.30

-0.25

-0.20

-0.15

-0.10

-0.05

0.00

0.05

0.10

0.15

0.20

0.000 5.000 10.000 15.000 20.000 25.000 30.000 35.000 40.000 45.000 50.000

Time, s

Dis

plac

emen

tatg

roun

dst

ory,

cm

MeasuredLARZ

-25,000.00

-20,000.00

-15,000.00

-10,000.00

-5,000.00

0.00

5,000.00

10,000.00

15,000.00

20,000.00

25,000.00

30,000.00

0.000 5.000 10.000 15.000 20.000 25.000 30.000 35.000 40.000 45.000 50.00

Time, s

Bas

e sh

ear,

kg

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0.0 0.5 1.0 1.5 2.0 2.5

Drift angle at first story, %

Kp

/ Ko Static testing

Static testingDynamic testing

Improvements under development

plastic hinge

expansion

Shear

Shear

Wall with horizontal reinforcement

Concluding remarks

• A simplified model to predict the nonlinear response of masonry structures was developed from static cyclic tests

• A performance evaluation series of tests on a shaking table is underway

• Calculated response departs from measured response

• Improvements on nonlinear modeling of complex confined masonry structures are needed

• Simulation needs to capture the effect of confinement and perpendicular walls

• A simplified model to predict the nonlinear response of masonry structures was developed from static cyclic tests

• A performance evaluation series of tests on a shaking table is underway

• Calculated response departs from measured response

• Improvements on nonlinear modeling of complex confined masonry structures are needed

• Simulation needs to capture the effect of confinement and perpendicular walls