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Walsh, Kevin, Dizhur, Dmytro, Derakhshan, Hossein, Griffith, Michael, &Ingham, Jason(2015)Out-of-plane seismic assessment of clay brick masonry cavity walls con-sidering different boundary conditions.In Proceedings of the 12th North American Masonry Conference.The Masonry Society (TMS), United States of America, pp. 789-802.

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Published in the proceedings for 12th North American Masonry Conference, 17-20 May 2015, Denver, Colorado

OUT-OF-PLANE SEISMIC ASSESSMENT OF CLAY BRICK MASONRY

CAVITY WALLS CONSIDERING DIFFERENT BOUNDARY CONDITIONS

Kevin Walsh1,2, Dmytro Dizhur1, Hossein Derakhshan3, Michael Griffith3, and Jason Ingham1

Abstract

Extensive research has been performed previously on assessing the out-of-plane (OOP) seismic performance of unreinforced clay brick masonry (URM) walls and the retrofitting of URM load-bearing and infill walls having a solid wall thickness. However, comparatively little research has been performed pertaining to URM walls with cavities (i.e., continuous air gaps separating wythes of brick from one another), despite the prominence of cavity masonry construction in various parts of the world. Hence, research was pursued with an emphasis on efficiently retrofitting URM cavity walls to enable the formation of composite behavior when subjected to simulated seismic OOP loading. The research reported herein was based on an experimental testing approach wherein walls were loaded OOP using inflatable airbags. Ten tests total were performed on nine separate URM cavity wall panels located in two separate buildings. The intended outcomes of the research reported herein included determining the OOP behavior of cavity walls in one-way vertical flexure both when bordered and not bordered by rigid moment-resisting reinforced concrete frames; to quantify the improvement in drift levels of cavity walls prior to loss in strength and prior to collapse using a variety of cavity wall ties at different spacing; to establish an effective solid wall thickness for cavity walls with various retrofit tie conditions for use in existing OOP predictive models; and to estimate how the semi-composite action generated by the retrofitting of cavity walls with stiff cavity ties may be predicted.

Keywords: unreinforced masonry, earthquakes, out-of-plane, infill walls, cavity walls, masonry anchors, cavity wall ties

Introduction

The earthquake vulnerability of buildings constructed using conventional British architecture and unreinforced clay brick masonry (URM) construction prior to the introduction of modern earthquake loading standards is well-known in New Zealand [Brodie 1933; Davey 2010; Ingham 2011a,b]. A high proportion of such existing URM structures have not been retrofitted to resist design basis

1 Department of Civil and Environmental Engineering, University of Auckland, New Zealand, kq.walsh@gmail.com; ddiz001@aucklanduni.ac.nz; j.ingham@auckland.ac.nz 2 Property Department, Auckland Council, New Zealand, kq.walsh@gmail.com 3 School of Civil, Environmental and Mining Engineering, University of Adelaide, Australia, hossein.derakhshan@adelaide.edu.au; mcgrif@civeng.adelaide.edu.au

earthquake (DBE) forces. However, little experimental testing has been performed within New Zealand or elsewhere [Tasligedik 2011] on the behavior of URM walls with cavities (i.e., continuous air gaps separating wythes of brick from one another), despite the prominence of this construction type in the building population in the form of both load-bearing and infill walls [Walsh 2014a; Walsh 2014b]. An experimental program was undertaken in order to fill the knowledge gap that currently exists amongst New Zealand structural engineering practitioners regarding the out-of-plane (OOP) seismic behavior of URM cavity walls. URM cavity walls were physically tested in two different buildings utilizing an approach wherein lateral forces were applied using a system of airbags to simulate distributed OOP seismic forces. This approach was consistent with the testing procedures recommended by ASCE [2014] and previously utilized by Angel [1994] and Derakhshan [2013a]. The URM cavity walls were tested in vertically-spanning, one-way bending (herein referred to as “vertical flexure”) to facilitate comparison of the results with existing predictive models for estimating OOP behavior that assume vertical flexure only.

Testing Program

Preparation of Test Wall Panels and Test Setup

The test specimens consisted of nine wall panels in two separate New Zealand buildings located in Auckland (designated as “Auc”) and Hastings (designated as “Has”) as listed in Table 1. Both buildings were originally constructed primarily as one-story RC frames with URM infill walls. The test walls were isolated into vertically spanning panels that were restrained at the top and bottom only. Each wall panel had a base length of 1200 mm. In the Auckland building, the top row of bricks was removed from all three test walls in order to separate the tops of the walls from the RC beam above such that these walls, despite originally being infill walls, would behave as upper-story load-bearing walls. The original in situ wire “Warrington” cavity ties, comprised of 4 mm diameter (8 gauge) steel wire with a tensile yield strength of approximately 230 MPa, were left in place in all test walls in both buildings throughout testing. The in situ Warrington wire ties were placed in mortar joints and generally spaced at 900 mm horizontally and 320 mm vertically in a staggered arrangement in the walls in both buildings.

Auc-W1 was tested twice – initially with only the in situ ties (designated “Auc-W1A”) and secondly with proprietary 12 mm diameter mechanical cavity ties added (designated “Auc-W1B”). Walls Auc-W2 and Auc-W3 were retrofitted with proprietary 6 mm diameter adhesive ties and 8 mm diameter mechanical ties, respectively, prior to testing [see Figure 1(a)]. All retrofit cavity ties used in this testing program were spaced in two columns at approximately 600 mm horizontally on each test wall. Test wall Has-W5 was tested with only in situ ties, while all other test walls in the Hastings building were retrofitted using 12 mm diameter mechanical ties (the same ties as those used in Auc-W1B) but with varying vertical spacing. As with the walls tested in the Auckland building, the top row of bricks and mortar was removed in test walls Has-W3 and Has-W4 and replaced with a timber support. All other walls in the Hastings building were tested with the top of the walls left confined by the relatively rigid original RC beam above. The geometries and restraint conditions of the tested walls, as well as information pertaining to the retrofit cavity tie conditions, are summarized in Table 1. Note that the number of existing Warrington tie legs as listed in Table 1 represents twice the number of ties actually present in the wall panel because these tie legs are doubled back across the cavity in a “figure 8” or “butterfly” configuration [see Figure 1(b)]. The test height, htest , in Table 1 indicates the distance from the wall base to the bottom of the lateral support at the top on the loaded side of the wall.

Table 1. Geometry and cavity tie detailing of test walls.

Test ID Top edge restraint

Test height, htest (mm)

Full in situ height, h

(mm)

bwythes

(mm)* Cavity ties @ vertical spacing

Total # of tie

legs, n

Auc-W1A Propped 2700 3020 215 Existing wire ties only, 4 mm dia. 28

Auc-W1B Propped 2700 3020 215 Mechanical 12 mm dia. @ 320 mm 14

Auc-W2 Propped 2700 3020 215 Adhesive 6 mm dia. @ 320 mm 14

Auc-W3 Propped 2700 3020 215 Mechanical 8 mm dia. @ 320 mm 14

Has-W1 Rigid 3750 3950 225 Mechanical 12 mm dia. @ 338 mm 20

Has-W2 Rigid 3750 3950 225 Mechanical 12 mm dia. @ 611 mm 10

Has-W3 Propped 3570 3950 225 Mechanical 12 mm dia. @ 338 mm 20

Has-W4 Propped 3570 3950 225 Mechanical 12 mm dia. @ 611 mm 10

Has-W5 Rigid 3750 3950 225 Existing wire ties only, 4 mm dia. 34

Has-W6 Rigid 3750 3950 225 Mechanical 12 mm dia. @ 152 mm 26

*sum of the thickness of two brick wythes excluding the cavity [average cavity widths between brick wythes were 53 mm in the Auckland (Auc) walls and 65 mm in the Hastings (Has) walls]

(a) Retrofit cavity ties used in this study: mech. 12 mm, adhes. 6 mm, mech. 8 mm, respectively (bottom to top).

(b) In situ wire “Warrington” cavity tie, 4 mm diameter. (c) Schematic of OOP test bracing (left) and displacement

instrumentation (right) [h = test wall height, D = displacement gauge].

Figure 1. Test components for OOP loading of cavity walls.

All test walls rested on a reinforced concrete (RC) slab or grade beam. Test walls having the top row of bricks removed and replaced with a lateral restraint consisting of timber framing (referred to as “propped” herein) were assumed to have no arching action and be representative of walls in a typical load-bearing configuration with timber diaphragms, especially those URM load-bearing walls that extend into timber-framed roofs with little to no overburden load. Test walls wherein the masonry abutted a top edge restraint consisting of a rigid RC slab or beam framing (referred to as “rigid” herein) were assumed to be subjected to arching action during loading and be representative of walls in a typical infill configuration within a RC frame.

All test walls were loaded semi-cyclically at a quasi-static loading rate by gradually inflating one vinyl airbag located near the center of each wall. The airbag was positioned in a gap of 25-35 mm

between the test walls and a plywood-backed frame panel [see Figure 1(c)]. Further details of the test setup, instrumentation, and results processing are described in Walsh [2014c]. All test walls (with the exception of Auc-W1A) were able to be tested to complete collapse, and the instability drift was measured using photogrammetry.

Retrofit Cavity Tie Properties

Properties pertaining to the retrofit cavity tie types shown in Figure 1(a) are summarized in Table 2. The 12 mm diameter proprietary cavity tie used in wall Auc-W1B and all of the retrofitted Hastings walls was comprised of threaded, hardened high-carbon steel and was mechanically anchored by rotation setting, leaving an exposed hexagonal head on the outside surface of one of the URM wythes. The 6 mm diameter proprietary cavity tie used in wall Auc-W2 was comprised of threaded, galvanized carbon steel and was adhesively anchored inside a plastic sleeve using a two-component hybrid injection mortar. The proprietary cavity tie used in wall Auc-W3 was comprised of Austenitic stainless steel twisted into a helical shape, the outer edges of which spanned 8 mm in diameter. It was installed mechanically using a proprietary insertion tool attached to a hammer rotary drill. Once installed, the retrofit cavity ties used on walls Auc-W2 and Auc-W3 were entirely recessed below the outer surface of the URM cavity wall wythes.

Table 2. Summary of retrofit cavity tie locations and properties.

Test wall(s) Tie

type

Nominal tie material yield

strength (MPa)

Tie diameter /

length (mm)

# samples

Most commonly observed

failure mode

Mean capacity (kN) / coefficient of variation

Auc-W1B, all retrofitted Has walls

Mech. 400 - 500 12 / 230 6 brick conical

breakout 15.2 / 0.46

Auc-W2 Adhes. 400 6 / 230 3 tie steel yield 8.7 / 0.07

Auc-W3 Mech. 316 8 / 220 4 pull-out 1.9 / 0.24

The retrofit cavity tie types were tested in direct tension following their installation into URM walls at the Auckland building. These pull-out tests involved the use of a steel V-shaped reaction brace (with a clear span between supports so as to allow conical break-out of the masonry), hand-actuated pump, and digital load cell. The results from these pull-out tests are summarized in Table 2. Note that the 12 mm diameter mechanical cavity tie type was determined to have the highest isolated pull-out strength, presumably due to its relatively large diameter.

Masonry Material Properties

Undamaged brick and mortar samples were extracted from the test walls in the two buildings. A summary of the various material tests, relevant standards, and results is included in Table 3. Where appropriate samples for particular tests were not available, values were determined from empirically-based formulae [Almesfer 2014; Lumantarna 2014]. Note that the relative strengths of the bricks and mortar in the Hastings building are unusual, as compared to historical URM construction typically encountered in New Zealand which is generally expected to be comprised of brick that is relatively stronger than its associated mortar [Almesfer 2014; Lumantarna 2014]. Note

also that the masonry prism compressive strength, 𝑓𝑚′ , is the most influential material property for

determining the out-of-plane capacity of URM infill walls with arching action Angel [1994], although it is substantially less influential on the ultimate performance of load-bearing walls without arching action.

Table 3. Summary of measured and calculated masonry material characteristics.

Material characteristic Associated standards and references for testing and

processing results

Number of samples / mean / sample standard deviation

(MPa unless noted otherwise)

Auckland building Hastings building

Mortar compression strength, 𝑓𝑗

′ Valek [2005], ASTM C1314-11a [ASTM

2011a] and Lumantarna [2014] 5 / 13.9 / 1.2 8 / 27.9 / 7.2

Brick compression strength, 𝑓𝑏

′ ASTM C67-11 [ASTM 2011b] 5 / 35.5 / 2.9 8 / 11.2 / 1.9

Masonry prism bond rupture strength, 𝑓𝑓𝑏

′ ASTM C1072-11 [ASTM 2011c] 0.42* 4 / 0.28 / 0.10

Masonry prism

compression strength, 𝑓𝑚′

ASTM C1314-11a [ASTM 2011a] 2 / 9.4 / 2.8 3 / 8.2 / 1.6

Stacked masonry prism density, ρm (kg/m3)

ASTM C1314-11a [ASTM 2011a] 3 / 1720 / 51.7 3 / 1659 / 15.9

* Determined by empirically-based formulae [Almesfer 2014; Lumantarna 2014]

One-way Vertical Flexure without Arching Action

Predictive Model

Based on experimental testing [Derakhshan 2013a] and previous model iterations [Derakhshan 2013b], Derakhshan [2014] proposed an assessment procedure for determining the OOP response of simply-supported URM load-bearings walls in vertical flexure based largely on the consideration of a semi-rigid rocking wall mechanism developing post-cracking. Buildings in Australasia with load-bearing URM walls typically have timber diaphragms [Walsh 2014a] which have been experimentally shown to provide little to no arching action to URM walls [ASCE 2014]. Assuming one-way vertical flexure and that the floor/roof diaphragm is sufficiently stiff to prevent higher mode effects, the laterally loaded wall is expected to respond to OOP forces in a simply supported condition as defined by the following equations:

𝐹0 = (𝑊 + 𝑂)𝑏𝑤

ℎ1+

𝑊2+𝑂

ℎ1ℎ2𝑏𝑤ℎ −

2𝑂𝑒𝑤

ℎ2 [1]

∆𝑖𝑛𝑠 = (𝑊2+𝑂)(ℎ+ℎ2)𝑏𝑤+𝑊1ℎ2𝑏𝑤−2𝑒𝑤𝑂ℎ1

2𝑂ℎ+2𝑐𝑊2(ℎ2+ℎ)+𝑊1ℎ2 [2]

where F0 is the maximum lateral resistance (N) of the cracked wall assuming uniformly distributed

lateral force and rigid-body motion, and Δins is the displacement (m) associated with the point of

“static” instability when the wall is subjected to a quasi-static “pushover” test such as the airbag tests described herein. Note that utilizing full static displacement capacity, Δins , for an engineering

assessment is non-conservative as most of the wall’s displacement capacity (i.e., displacement >

0.25Δins) is associated with “negative stiffness” (i.e., displacement increases with reducing lateral

force). Numerical dynamic analyses [Derakhshan 2013b] have shown that wall displacements beyond 0.5Δins and 0.25Δins for simply-supported and cantilever walls, respectively, are rarely

reversible and generally lead to wall collapse. Furthermore, displacement capacity is extremely sensitive to resonance occurring between the wall rocking and the ground motion. As a result, capacity reduction factors should be utilized in seismic assessments [Walsh 2014a; Derakhshan 2014]. The variables hi , mi , and Wi are, respectively, the wall height (m), mass (kg) and weight (N), with index i referring to the individual wall segments [e.g., variables h1 and h2 represent the height (m) of the individual wall segments below and above, respectively, the primary horizontal crack]. O and ew are, respectively, the applied overburden (N) and its eccentricity (m). Parameter c is related

to the location of the center of mass of the top segment. Parameter bw is the solid wall thickness (m) measured across the mortar joints, determined as follows:

𝑏𝑤 = 𝑏𝑤,𝑛𝑜𝑚 − 2𝑝 [3]

where bw,nom is the nominal solid wall thickness (m), and 𝑝 is the average inset depth (m) of mortar pointing (or loss of degraded mortar material) on each side of the wall. For simply-supported walls without arching action (as is the case assumed for the model), Derakhshan [2013b] recommend that the crack height be assumed to occur such that h1 = 0.67(h1 + h2). The OOP drift below the crack to cause instability (ϴins) can be determined as follows:

𝛳𝑖𝑛𝑠 =𝛥𝑖𝑛𝑠

ℎ1 [4]

Test Results and Considered Influences on Effective Cavity Wall Thickness

The experimentally measured force and displacement capacities for the six cavity walls tested in vertical flexure with propped top supports are summarized in Table 4. The experimental results were compared to the expected results from the procedure proposed by Derakhshan [2014] by altering the values assumed for the effective solid wall thickness measured across the mortar joints until the error between force and displacement ratios of model and experimental values was balanced. In the case of Auc-W1B, the derived effective solid wall thickness was limited to the total out-to-out wall thickness including the cavity. This effective solid wall thicknesses, bw,eff,exp , replaces bw in [1] and [2] as well as the wall thickness assumed to calculate weights W1 and W2 in the Derakhshan [2014] method. Note that the ratios bw,eff,exp / bwythes shown in Table 4 are much higher for all test walls than the effective wall thickness recommended for OOP assessment by BS 5628 [BS 2005] which is only two-thirds of the sum of the two wythe thicknesses of the wall excluding the cavity (i.e., 2/3 bwythes). For the test walls listed in Table 4, the average crack height was h1 =

0.70(h1 + h2) which is nearly equal to but slightly higher than the crack height recommended by Derakhshan [2014]. The values derived from the Derakhshan [2014] model for bw,eff,exp were correlated with multiple factors expected to influence the effective semi-composite section behavior of a URM cavity wall with ties represented by the following generic relationship:

𝑏𝑤,𝑒𝑓𝑓 = 𝐾 𝑘𝑐𝑜𝑚𝑝𝑤 𝑘𝑡𝑒𝑛𝑠

𝑥 𝑘𝑠ℎ𝑒𝑎𝑟𝑦

𝑏𝑔𝑎𝑝𝑧

𝑏𝑤𝑦𝑡ℎ𝑒𝑠

[5]

where K, w, x, y, and z are empirically-based constants to be determined, bgap is the cavity gap width (m), bwythes is the sum of the two wythe thicknesses of the wall excluding the cavity (m), and

𝑘𝑐𝑜𝑚𝑝 =

𝑛 𝑃𝑐𝑜𝑚𝑝

𝑊 [6]

𝑘𝑡𝑒𝑛𝑠 =

𝑛 𝑃𝑡𝑒𝑛𝑠

𝑊 [7]

𝑘𝑠ℎ𝑒𝑎𝑟 =

𝑛 𝑃𝑠ℎ𝑒𝑎𝑟

𝑊 [8]

where n is the number of the most rigid type of cavity ties in the wall, Pcomp , Ptens , Pshear represent individual tie capacity (kN) governed by the limit states for compression, tension, and shear, respectively, and W is the wall weight (kN) determined from the wall panel length, height, actual wythe thicknesses and masonry prism density, ρm. The values for k represent elastic strength ratios, but they were used in this study as proxies for cavity tie stiffness and the associated local deformations occurring within the cavity ties and within the masonry to which the ties were anchored.

Table 4. Summary of test results for walls tested without arching action and comparison to expected results.

Test

ID

Cavit

y t

ie c

on

dit

ion

(typ

e, d

ia., v

ert

.

sp

acin

g)

Experimental test results Derakhshan [2014]

model

Expe

rim

enta

lly

dete

rmin

ed

effe

ctive

so

lid w

all

thic

kn

ess,

bw

,eff

,exp

Model results /

experimental results

Max e

ffective

post-

cra

ck

forc

e,

Fo, e

xp

(kN

)

Insta

bili

ty

dis

pla

cem

ent,

Δin

s,ex

p (m

m)

Insta

bili

ty d

rift

,

ϴin

s,ex

p (m

m)

Max p

ost-

cra

ck

loa

d,

Fo (kN

)

Insta

bili

ty

dis

pla

cem

ent,

Δin

s (m

m)

Insta

bili

ty d

rift

,

ϴin

s (%

)

Fo /

Fo,e

xp

Δin

s /

Δin

s,ex

p

ϴin

s /

ϴin

s,ex

p

bw

,eff

,exp

/ b

wyt

hes

Auc-W1A in situ 2.9 - - 2.9 217 10.8% 217 1.00 - - 1.01

Auc-W1B mech. 12

@ 320 4.2 293 15.5% 4.4 268 13.5% 268* 1.04 0.91 0.86 1.25

Auc-W2 adhes. 6 @ 320

2.9 235 11.9% 3.0 224 11.1% 224 1.05 0.95 0.93 1.04

Auc-W3 mech. 8 @ 320

3.2 246 14.2% 3.3 234 11.6% 234 1.04 0.95 0.82 1.09

Has-W3 mech. 12

@ 338 5.7 258 10.3% 4.9 290 11.0% 290 0.87 1.12 1.07 1.29

Has-W4 mech. 12

@ 611 5.4 249 9.9% 4.7 282 10.7% 282 0.86 1.13 1.08 1.25

*total out-to-out thickness of the wall including cavity

The compression strength, Pcomp , of an individual tie is governed by the smaller of the flexural buckling, flexural-torsional buckling, and torsional buckling capacities of the tie itself, as well as the bearing capacity and bed-joint shear capacity of the brick to which the tie is anchored. However, assuming the considered tie is circular in cross-section and the cavity width is relatively small (e.g., < 70 mm), flexural-torsional buckling and torsional buckling capacity of the tie are unlikely to govern. The flexural buckling capacity of a single cavity tie (kN) is estimated as follows (adapted from the American Institute of Steel Construction [AISC 2005]):

𝑃𝑐𝑜𝑚𝑝,𝑓𝑙𝑒𝑥 = [0.658

𝐹𝑦

𝐹𝑒

]𝐹𝑦 if 𝐹𝑒 ≥ 0.44𝐹𝑦 [9]

𝑃𝑐𝑜𝑚𝑝,𝑓𝑙𝑒𝑥 = 0.877𝐹𝑒 if 𝐹𝑒 < 0.44𝐹𝑦 [10]

where Fy is the yield strength of the tie material (MPa), and Fe is the elastic critical buckling stress (MPa) determined as follows:

𝐹𝑒 =𝜋2 𝑑𝑡𝑖𝑒

2

𝐸

16𝑏𝑔𝑎𝑝2

[11]

where dtie is the diameter of a single tie (m), E is the elastic modulus of the cavity tie material (MPa), and bgap is the clear width of the cavity gap between wythes (m). The bearing capacity of the cavity tie on the brick (kN) is estimated as follows (adapted from the American Concrete Institute [ACI 2011]):

𝑃𝑐𝑜𝑚𝑝,𝑏𝑒𝑎𝑟 = 191 √𝑓′𝑏

(𝑏𝑤,1 − ℎ𝑒𝑓) [12]

where f’b is the brick compressive strength (MPa), bw,1 is the width of a single brick parallel to the cavity tie (m), and hef is the effective embedment length of the tie in the brick (m). Note that f’b was chosen for the material strength in [12] because cavity ties are generally placed in bricks rather than in mortar joints, and even when cavity ties are placed in mortar joints, the “failure cone”

associated with compressive bearing or tensile pull-out of the tie from the masonry is likely to encompass bricks. The bed-joint shear capacity of a single brick with no overburden load being pushed OOP by a cavity tie (kN) is estimated conservatively as follows (adapted from Almesfer [2014]):

𝑃𝑐𝑜𝑚𝑝,𝑏𝑗 =1

17857 𝑓′

𝑗

𝑙𝑤,1 𝑏𝑤,1 [13]

where f’j is the mortar compressive strength (MPa), bw,1 is the width of a single brick parallel to the cavity tie (m), and lw,1 is the length of a single brick perpendicular to the cavity tie (m). By computing [6] and [9] – [13] for each test wall listed in Table 4, a relationship between kcomp and the effective wall thickness bw,eff,exp was determined.

The tensile strength, Ptens , of an individual tie is governed by the smaller of the steel yielding capacity of the tie itself, tensile breakout and pull-out strengths of the cavity tie within the masonry, and the bed-joint shear capacity of the brick to which the tie is anchored. The equations presented below for the first three limit states were found to predict the average tensile strengths listed in Table 2 either accurately or conservatively. For purposes of this analysis, the representative cavity tie is assumed to be adequately far enough from the edge of a wall panel so as to not be limited by “side-face” blowout. The tensile yielding capacity of a single cavity tie (kN) is estimated as follows:

𝑃𝑡𝑒𝑛𝑠,𝑦𝑖𝑒𝑙𝑑 = 250𝜋 𝐹𝑦𝑑𝑡𝑖𝑒2

[14]

where Fy is the yield strength of the tie material (MPa) and dtie is the diameter of a single tie (m). Cavity tie tensile breakout strength (kN) is estimated as follows (adapted from ACI [2011]):

𝑃𝑡𝑒𝑛𝑠,𝑏𝑟𝑒𝑎𝑘 = 191 √𝑓′𝑏

ℎ𝑒𝑓 [15]

where f’b is the brick compressive strength (MPa), and hef is the effective embedment length of the tie in the brick (m). Cavity tie tensile pull-out represents the thread grip failure and bond failure of mechanical and adhesive ties, respectively. The “grip” or “bond” stress capacity of the tie embedded within the brick or mortar joint varies greatly amongst tie and brick types and sizes. Based on the observations noted in Table 2, the pull-out limit state was assumed to potentially limit the tensile capacity of cavity ties in only test walls Auc-W1A (in situ) and Auc-W3 (mechanical, 8 mm diameter). For these two walls, cavity tie pull-out (kN) was estimated as follows (adapted from ACI [2011]):

𝑃𝑡𝑒𝑛𝑠,𝑝𝑢𝑙𝑙 = 1800𝜋 𝑑𝑡𝑖𝑒2 ℎ𝑒𝑓

[16]

where dtie is the diameter of a single tie (m), and hef is the effective embedment length of the tie in the brick or mortar joint (m). The constant 1800 is a product of constants representing unit conversion, masonry mechanical properties, and characteristic bond stress between the cavity tie and masonry. Its accuracy is likely limited to the cavity ties and test wall materials considered in this program. The bed-joint shear capacity of a single brick with no overburden load being pulled OOP by a cavity tie, Ptens,bj , (kN) is estimated conservatively using [13]. By computing [7] and [13] – [16] for each test wall listed in Table 4, a relationship between ktens and the effective wall thickness

bw,eff,exp was determined.

The shear strength, Pshear , of an individual tie is governed by the smaller of the steel shear yielding and shear buckling capacity of the tie itself, as well as the shear breakout and pry-out strengths of the cavity tie within the masonry. However, assuming that the considered tie is circular and solid in cross-section and that the cavity width is relatively small (e.g., < 70 mm), shear buckling is unlikely to govern. As assumed for tensile capacity, the representative cavity tie is assumed to be located

adequately far enough from the edge of a wall panel so as to not be limited by “side-face” blowout. The shear yielding capacity of a single cavity tie (kN) is estimated as follows (adapted from AISC [2005]):

𝑃𝑠ℎ𝑒𝑎𝑟,𝑦𝑖𝑒𝑙𝑑 = 75𝜋 𝐹𝑦 𝑑𝑡𝑖𝑒2

[17]

where dtie is the diameter of a single tie (m), and Fy is the yield strength of the tie material (MPa). Shear breakout of the tie within the masonry (kN) is estimated as follows (adapted from ACI [2011]):

𝑃𝑠ℎ𝑒𝑎𝑟,𝑏𝑟𝑒𝑎𝑘 = 65 √𝑓′𝑏

𝑏𝑤,1

1.5

[18]

where f’b is the brick compressive strength (MPa) and bw,1 is the width of a single brick parallel to the cavity tie (m). Shear pry-out capacity of the tie within the masonry, Pshear,pry , (kN) is estimated using [15]. By computing [8], [15], [17], and [18] for each test wall listed in Table 4, a relationship between kshear and the effective wall thickness bw,eff,exp was determined. kshear was estimated to have the relatively strongest correlation with bw,eff,exp , which was consistent with test observations wherein all cavity ties (especially the relatively smaller ties) visibly deformed by shear mechanisms more so than by tensile or compressive mechanisms. ktens was estimated to have a relatively moderate correlation with bw,eff,exp , which was consistent with test observations for these walls wherein, at high lateral displacements, the outer wythe was observed to be effectively hanging from the inner, loaded wythe rather than supporting its own weight. kcomp was estimated to have such a relatively weak correlation with bw,eff,exp that it was ignored as a component of the combined equation based on [5]. Hence, bw,eff (m) for cavity walls in one-way vertical flexure without arching action may be predicted as follows:

𝑏𝑤,𝑒𝑓𝑓 = 5.58 𝑘𝑡𝑒𝑛𝑠 0.01

𝑘𝑠ℎ𝑒𝑎𝑟0.08

𝑏𝑔𝑎𝑝0.6

𝑏𝑤𝑦𝑡ℎ𝑒𝑠 [19]

where bwythes is the sum of the two wythe thicknesses of the wall not including the cavity (m). Note that equation [19] for bw,eff inherently accounts for the inset depth of the mortar joints in the test walls, which were considered typical (i.e., < 5 mm each side). A graphical comparison of effective wall thicknesses as determined from experimental testing and as predicted from [19] is included in Figure 2. The correlation R2 between the two arrays shown in Figure 2 is 0.97.

Figure 2. Correlation between experimentally-determined effective wall thickness,

bw,eff,exp , and predicted effective wall thickness, bw,eff , for cavity walls tested in one-way vertical flexure without arching action for use in the Derakhshan [2014] model.

One-way Vertical Flexure with Arching Action

Has-W3

Has-W4

Auc-W1A

Auc-W1B

Auc-W2 Auc-W3

210

230

250

270

290

310

210 230 250 270 290 310

Predicted

bw

,eff

(m

m)

Experimental bw,eff ,exp (mm)

Predictive Model

Various methods for predicting the OOP behaviour of vertically-spanning solid URM infill walls have been considered previously based on applications of energy dissipation, finite elements, yield lines, failure lines, compressive struts, spring-struts, and rigid bodies as summarized by Liberatore [2014]. The current method recommended by NZSEE [2006] for determining the OOP load capacity of masonry infill walls with arching action is a compressive strut method proposed by Angel [1994]. Assuming that the wall being considered is undamaged from any preceding in-plane demands, the proposed equation by Angel [1994] for estimating the uniformly distributed OOP load capacity (kPa) is simplified as follows:

𝑤 =0.308𝑓′

𝑚

(ℎ

𝑏𝑤)

𝑒−0.0985(

ℎ

𝑏𝑤)𝑅2

[20]

where f’m is the masonry prism compressive strength (kPa), h is the total wall height (m), bw is the solid wall thickness (m), e is the mathematical constant approximately equal to 2.718, and R2 is a stiffness reduction factor for the bending frame members determined as follows:

𝑅2 = 0.35 + 2.45(10)−5𝐸𝐼 ≤ 1.0 [21]

where EI is the flexural rigidity (kN-m2) of the weakest frame element on the non-continuous side of the infill panel. If the panel being considered resides within a frame that is surrounded by infill panels in all directions, then R2 = 1.0. In the case of the cavity infill walls tested in this program, the surrounding frame was determined to be rigid enough that R2 = 1.0. In walls restrained top and bottom by rigid supports, the applied overburden load on the wall from arching action is likely to be far larger than gravity loads from self-weight. As a result, the primary horizontal crack for walls tested in one-way vertical flexure with arching action is expected to occur at approximately half of the total wall height rather than at two-thirds of the total wall height as is typical for walls without arching action.

Test Results and Considered Influences on Effective Cavity Wall Thickness

The experimentally measured force and displacement capacities for the four cavity walls tested in one-way vertical flexure with arching action are summarized in Table 5. The experimental results were compared to the expected results for force-based capacity based on the procedure proposed by Angel [1994], by altering the values assumed for the wall thickness measured across the mortar joints until the model and experimental values for force capacity were approximately equivalent (to the extent that rounding off to the nearest mm would allow). For the test walls listed in Table 5, the average crack height was h1 = 0.51(h1 + h2) which is nearly equal to but slightly higher than the crack height assumed in the model by Angel [1994].

Table 5. Summary of test results for walls tested with arching action and comparison to expected results for force-based capacity.

Test

ID

Cavit

y t

ie c

on

dit

ion

(typ

e, d

ia., v

ert

.

sp

acin

g)

Experimental test results

Angel

[1994]

model

Experi

men

tally

dete

rmin

ed e

ffective

solid

wa

ll th

ickness,

bw

,eff

,exp

Model results /

experimental

results

Max effective*

post-crack

force, Fo,exp

(kN)

Instability

displ.,

Δins,exp

(mm)

Instability

drift,

ϴins,exp

(mm)

Max post-

crack

force, Fo

(kN) Fo /

Fo,e

xp

bw

,eff

,exp

/ b

wyt

hes

Has-W1 mech. 12 @

338 22.7 264 13.9% 22.5 134 0.99 0.60

Has-W2 mech. 12 @

611 16.4 291 16.3% 16.2 124 0.99 0.55

Has-W5 in situ 13.9 103 4.6% 14.1 120 1.01 0.53

Has-W6 mech. 12 @

152 29.0 210 12.5% 29.1 143 1.00 0.64

The trendline shown in Figure 3 was developed using the same method as for vertically spanning walls without arching action (i.e, [5] – [18]). kcomp and kshear were estimated to have the relatively strongest correlations with bw,eff,exp . ktens was estimated to have such a relatively weak correlation with bw,eff,exp such that it was ignored as a component of the combined equation based on [5]. No difference in cavity gap width existed amongst the considered walls with arching action. Furthermore, walls with arching action are relatively less sensitive to geometric instability OOP due to the prominence of the arching force. Hence, bgap was set equal to zero. As a result, bw,eff (m) for cavity walls in one-way vertical flexure with arching action may be predicted as follows:

𝑏𝑤,𝑒𝑓𝑓 = 0.445 𝑘𝑐𝑜𝑚𝑝 0.11

𝑘𝑠ℎ𝑒𝑎𝑟 0.02

𝑏𝑤𝑦𝑡ℎ𝑒𝑠 [22]

where bwythes is the sum of the two wythe thicknesses of the wall not including the cavity (m). As before, note that equation [22] for bw,eff inherently accounts for the inset depth of the mortar joints in the test walls, which were considered typical (i.e., < 5 mm each side). A graphical comparison of effective wall thicknesses as determined from experimental testing and as predicted from [22] is included in Figure 3. The correlation R2 between the two arrays shown in Figure 5 is 0.97. However, note that the proposed empirical relationship was based on only four test walls, all with the same geometry as well as masonry material strengths. Furthermore, arching action in these walls enhanced the OOP stiffness of both wythes which, combined with quasi-static lateral loading being applied to only one wythe, resulted in greater compressive forces being transferred across the cavity ties than in the case of the walls tested without arching action. Hence, the authors expect that [22] would likely be amended to indicate a greater relative sensitivity of the effective thickness, bw,eff , to the cavity tie shear strength ratio, kshear , than is currently indicated in [22] were additional test walls with different geometries and masonry material strengths considered, and were these tests repeated with dynamic loading applied to both wythes simultaneously.

Figure 3. Correlation between experimentally-determined effective wall thickness, bw,eff,exp ,

and predicted effective wall thickness, bw,eff , for cavity walls tested in one-way vertical flexure with arching action for use in the Angel [1994] model.

Recommendations for Assessment

The results in Table 4 and Table 5 indicate that existing OOP assessment methods may be viable for assessing cavity walls in vertical flexure provided that the effective solid wall thickness is determined firstly. However, note that the effective solid wall thicknesses listed in Table 4 and Table 5 are only directly applicable to the considered models (e.g., Derakhshan [2014] and Angel [1994], respectively), hence the dichotomy in effective solid wall thicknesses for the in situ walls being 1.01bwythes (Auc-W1A in Table 4) and 0.53bwythes (Has-W5 in Table 5), respectively, due to the absence or presence of arching action and the corresponding analytical model. Recognizing the inherent uncertainty in many of the input values used in these assessment models, these values for effective wall thickness can be simplified to 1.0bwythes and 0.5bwythes , respectively. Considering that the separate brick wythes were equally thick in any given wall, Has-W5 was measured as having a nearly equivalent OOP strength as to what would be predicted by applying the Angel [1994] model to a single wythe. Hence, in the case of Auc-W5 with in situ ties under quasi-static loading, OOP strength was dominated by arching action on a single masonry wythe.

URM cavity walls with arching action are more sensitive to the assumed effective wall thickness based on the parameters in the considered models. Walls with arching action have an expected OOP force capacity per the Angel [1994] model that is related to the slenderness ratio to a power of 4, whereas walls without arching action (and without any overburden load) have an expected OOP force capacity that is related to the slenderness ratio to a power of only 2 per the Derakhshan [2014] model (see Figure 4 wherein hypothetical walls were assumed to have the same properties as Has-W1, but the effective thickness, bw,eff , was incrementally adjusted). The estimated OOP force capacities of walls with partially rigid restraints can presumably be determined by utilizing the Angel [1994] model and determining an adjustment factor, R2 , for frame stiffness that is less than 1.0, although further testing of this variable is desirable.

While the walls considered in the test program detailed herein were not subjected to overburden loads, typical cavity walls on the critical top stories of load-bearing URM buildings with timber-framed roofs (as is common in New Zealand) are likely to have little overburden load. Nonetheless, the proposed predictive equations should only be used to assess walls that are similar in geometry and material properties to the walls tested in this program. Lower-bound material characteristics should be considered for consulting purposes as was done by Walsh [2014a] for typical URM walls in Auckland, New Zealand. Note that the proposed provisional equations [19] and [22] for

Has-W1

Has-W2

Has-W5

Has-W6

110

120

130

140

150

110 120 130 140 150Predicted

bw

,eff

(m

m)

Experimental bw,eff,exp (mm)

determining the effective wall thickness are intended to predict expected OOP wall performance based on a relatively small sample size of test walls, and the empirically-based, simplified approach did not explicitly consider the spacing and location of individual ties in wall panel zones of especially high flexural stresses (i.e., near the crack height of the walls) or shear flow stresses (i.e., near the boundaries at the top and bottom of the walls). Furthermore, vertical wall strips are assumed to deform through mechanisms that are sensitive to dynamic inputs, whereas the testing performed in this study utilized quasi-static loading.

Figure 4. Sensitivity of two considered OOP wall capacity models to changes in

slenderness ratio.

Summary of Conclusions

The study reported herein sought to address the paucity of information available on the OOP response of URM cavity wall construction, addressing both as-built and retrofitted wall conditions. Significant results that can be drawn from this research program are as follows:

Existing OOP assessment methods are viable for assessing cavity walls in vertical flexure provided that the effective solid wall thickness is estimated firstly. However, the estimated effective solid wall thickness is only directly applicable to the analytical model being considered (see Table 4 and Table 5);

Rigid restraint from the surrounding frame causing arching action can greatly increase the OOP capacity of vertically-spanning infill walls, which may be more sensitive to changes in composite behavior achieved by cavity tie retrofitting than non-arching walls (see Figure 4); and

Cavity tie retrofits with adequate spacing, and adequate compressive and shear stiffness,

can substantially improve the OOP capacity of URM cavity walls, and provisional,

empirically-based relationships were proposed in an attempt to predict the OOP

performance of URM cavity walls with various cavity tie conditions (see [19] and [22]).

Acknowledgements The authors would like to express their sincere gratitude for the funding provided by the Building Research Association of New Zealand (BRANZ) through grant LR0441. The authors are also grateful for the in-kind donations provided by Mansons TCLM Ltd. (owners of the Auckland building) and the owners of the Hastings building. Technical advisory for both testing and analysis was provided by EQ STRUC Group and Strata Group. Students and staff who participated in the various field and laboratory testing efforts include Anthony Adams, Mark Byrami, Samuel Corney, Marta Giaretton, Miroslav Ignacak, Mark Liew, Jeff Melster, Jerome Quenneville, Ross Reichardt, Daniel Ripley, and Guojue Wang.

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