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PREDICTED VERSUS EXPERIMENTAL OUT-OF-PLANE FORCE-DISPLACEMENT
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BEHAVIOUR OF UNREINFORCED MASONRY WALLS Walsh, Kevin1,2; Dizhur, Dmytro3; Giongo, Ivan4; Derakhshan, Hossein5; and Ingham, Jason3
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ABSTRACT
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Recognising that in situ conditions for URM walls rarely reflect the idealised conditions assumed in analytical
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predictive models, nineteen unreinforced masonry (URM) walls in six different buildings were physically tested in situ
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to establish their out-of-plane (OOP) force-displacement behaviour, and the measured results were compared to the
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forecasted results obtained from established predictive methods. The considered wall configurations represented a
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variety of geometries, boundary conditions, pre-test damage states, and material properties. The average ratio and
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associated coefficient of variation (CV) of predicted strengths to measured strengths were determined to be 0.84
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(CV 0.56) and 0.93 (CV 0.25) for the “unbounded” and “bounded” wall conditions, respectively, where the latter group
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represents walls used to infill frames. Use of the existing predictive methods resulted in over-prediction of the
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measured displacement parameters, which was likely due to most of the predictive methods being based on
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historical walls tests in one-way spanning conditions and without rigid bounding restraints capable of effectuating
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arching action in the wall, in contrast to many of the wall test conditions employed in the current study.
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KEYWORDS: unreinforced masonry (URM), earthquakes, out-of-plane, infill walls, airbag proof-testing, analytical
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methods
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1.1
INTRODUCTION Background
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Unreinforced masonry (URM) building construction is prominent in the form of loadbearing, partition, and infill walls.
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Significant out-of-plane (OOP) damage and collapse of URM walls often occurs during moderate and severe
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earthquake shaking, and such walls are often identified in structural engineering assessments as being amongst the
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elements most vulnerable to earthquakes (e.g., Moon et al. 2014). Predictive analytical models that apply to
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particular wall configurations and to various performance parameters have been developed over the past few
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decades (Sorrentino et al. 2017). However, the accuracy of such methods relative to in situ proof testing results has
1
Department of Civil & Environmental Engineering & Earth Sciences, University of Notre Dame, Indiana, United States,
[email protected]
2
Frost Engineering and Consulting, Mishawaka, Indiana, United States,
[email protected]
3
Department of Civil and Environmental Engineering, University of Auckland, New Zealand,
[email protected],
[email protected]
4
Department of Civil, Environmental and Mechanical Engineering, University of Trento, Italy,
[email protected]
5
School of Civil Engineering and Built Environment, Queensland University of Technology, Australia,
[email protected] 1
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not been widely reported. Furthermore, these predictive methods often involve the assumption of idealised boundary
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conditions and pre-existing damage states that may not exist in “real world” configurations. Hence, a study that
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compared the accuracy of widely used predictive methods and assumed input values to the results of experimental
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in situ tests was lacking and consequently was the subject of the investigation reported herein. The experimental
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results referenced are derived from the testing program carried out and previously reported in a companion article
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by Dizhur et al. (2018), including nineteen in situ URM walls wherein lateral forces were applied using airbags to
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simulate distributed OOP demands. The referenced test set of URM walls represented a variety of geometries,
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boundary conditions, pre-test damage states, and material properties, such that the compared predictive results
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reported herein may be especially useful for structural engineering practitioners.
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Practicing engineers have historically relied largely on strength-based assessments for direct comparison to
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computed force-based demands (e.g., accelerations in terms of gravity, g). Furthermore, other researchers have
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found especially weak correlation between the results of experimental data sets and the predictive displacement-
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based model that is incorporated within multiple internationally recognised standards such as ASCE 41 (2014) and
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FEMA 356 (2000) for URM walls. However, strength-based predictive methods often require knowledge of various
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material properties that are rarely available to the engineering practitioner and limit the amount of reserve capacity
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(i.e., equivalent ductility) that can be assumed by the engineer, whereas displacement-based predictive methods do
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not have these limitations. Given the benefits and drawbacks of both strength-based and displacement-based
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analytical models as they currently exist, it is incumbent to consider the entire force-displacement relationship of
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URM walls in OOP pushover conditions (see Figure 1).
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1.2
Established predictive models for force-displacement behaviour
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The predictive analytical methods considered herein (and the in situ wall conditions to which they are applied) are
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listed in Table 1 and can generally be categorised into “unbounded” and “bounded” wall conditions. In the case of
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unbounded URM walls (such as those generally found in buildings where URM is a loadbearing element or a
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continuous façade/parapet feature), practicing engineers may consider referencing the assessment methodology of
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the Australian Standard 3700 (AS 2011) for masonry design and related supplemental references (Lawrence and
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Marshall 2000; Lawrence and Page 2013). The method was later improved by Willis et al. (2004, 2006) to ensure
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more rational strength predictions although the improvement has not yet been incorporated into AS (2011). The AS
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(2011) design methods utilise a virtual work-based, one-way or two-way flexural analysis including weighted
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components of vertical flexure, horizontal flexure, and diagonal flexure where applicable, while accounting for
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different material properties and boundary conditions. Griffith and Vaculik (2007) validated the relative accuracy of
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the AS (2011) design method with experimental laboratory testing results, provided that return walls were assumed
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to provide only partial moment restraint such that the vertical edge restraint factor, Rf, equalled 0.5. Derakhshan et
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al. (2018) also determined that the AS (2011) method is accurate if mixed boundary conditions are assessed
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conservatively. Examples of these boundary conditions were out-of-plane restraint from partial-height door frames
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or top edge connections to flexible roof struts (in non-load-bearing walls) that were disregarded in assessment.
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Figure 1. Idealised force-displacement behaviour for one-way vertically spanning URM walls deformed OOP (based on notation used by Doherty et al. 2002; only positive displacement range shown) 61
Loadbearing URM walls often have timber diaphragms (AS 2011; NZSEE 2015) which have been experimentally
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shown to effectuate little to no compressive strut “arching” action in URM walls under OOP loading (ASCE 2014;
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Derakhshan et al. 2014a). In contrast, URM infill walls which are bounded by relatively rigid elements, such as RC
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frames, may form compressive strut “arching” mechanisms while deforming OOP, which generally increases the
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OOP strength of the URM walls as compared to unbounded wall conditions. Flanagan and Bennett (1999) compared
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the accuracy of the empirically-based Dawe and Seah (1989) predictive model for estimating the OOP strength of
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URM infill walls against the analytically derived predictive model proposed by Abrams et al. (1996) using a large
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experimental data set from seven different test programs including clay brick infills in concrete frames, clay tile infills
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in steel frames, clay brick infills in steel frames, and concrete masonry infills in steel frames. The experimental tests
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considered for the comparison included infill walls with height-to-thickness ratios ranging from 6.8 to 35.3. Flanagan
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and Bennett (1999) concluded that the Dawe and Seah (1989) model produced slightly more accurate predictions
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for the majority of a large experimental laboratory data set. Furthermore, the Dawe and Seah (1989) predictive model
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accounts for URM infill bounding restraints resulting in either one-way or two-way flexure. In comparison, the Abrams
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et al. (1996) predictive model only accounts for one-way flexure in the stronger of two directions, where applicable
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(Flanagan and Bennett 1999). However, Abrams et al. (1996) did uniquely provide OOP strength reduction factors
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to account for in-plane damage preceding OOP loading on URM infill walls. Hence, for the purposes of the analytical
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study reported herein, OOP strength for bounded walls was predicted using the revised Dawe and Seah (1989)
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model as proposed by Flanagan and Bennett (1999) and as recommended for use by the Masonry Standards Joint
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Committee (MSJC 2011). Strength reduction factors to account for in-plane damage recommended by Abrams et al.
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(1996) were incorporated where appropriate.
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Doherty et al. (2002) recommended that experimental curvilinear URM pushover behaviour be idealised by a
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trilinear model with three different displacement parameters as illustrated in Figure 1. Δ1 represents the displacement
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for determining initial secant stiffness. Doherty et al. (2002) empirically derived ratios of Δ1/Δf from 0.06 to 0.20 for a
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range of degradation states (with the most severely damaged walls having the highest anticipated ratios of Δ1/Δf).
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By comparison, Derakhshan et al. (2013a) recommended that a ratio of Δ1/Δf equal to 0.04 be used for undamaged
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walls. The scope of the Derakhshan et al. (2013a) research included wall thicknesses up to 350 mm (i.e., multi-leaf 3
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walls with traditional brick sizes), and the tests in the Doherty et al. (2002) study were limited to either 50 mm or 110
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mm thickness (i.e., single-leaf walls with traditional brick sizes). Table 1. Summary of recommended predictive OOP performance models and associated applications Applicable performance metric
Top and bottom edge restraints
Side edge restraints
AS (2011)
Strength
Timber diaphragm or URM wall on contiguous levels*
URM return walls / piers
Flanagan and Bennett (1999) [referenced by MSCJ 2011]
Strength
RC slab or RC beam***
RC columns***
Predictive model
Abrams et al. (1996)
Doherty et al. (2002)
Doherty et al. (2002)
Derakhshan et al. (2014b) Flanagan and Bennett (1999) [modified from ASCE 2014 and FEMA 2000]
Strength reduction Δ1 = Displacement for determining initial stiffness (empirical) Δ2 = Displacement for determining secant stiffness (empirical, singleleaf) Δ2 = Displacement for determining secant stiffness (empirical, multileaf) Δ2 = Displacement for determining secant stiffness (infill walls)
RC slab or RC frame element*** (stronger of two arching directions – horizontal or vertical – assumed to govern) Diaphragm or URM wall on contiguous levels Diaphragm or URM wall on contiguous levels
Timber diaphragm or URM wall on contiguous levels*
RC slab or RC beam***
Free (unrestrained)**
Free (unrestrained)**
Free (unrestrained)**
n/a
Model assumptions and applications • one-way or two-way flexure • can accommodate edge restraints with varying flexural rigidity • an accommodate overburden loads • one-way or two-way flexure / arching (rigid elements – RC or steel – must be present on at least two opposing sides) • formation of compressive strut “arching” mechanisms • can accommodate bounding frame restraints with varying flexural rigidity • one-way flexure / arching only • utilised in the study reported herein for URM infill OOP strength reduction due to preceding in-plane damage • one-way vertical spanning only • empirically-derived • one-way vertical spanning only • empirically-derived • single-leaf walls
• one-way vertical spanning or cantilevered • simply supported restraints top and bottom • multi-leaf walls • one-way vertical spanning / arching only • Derived for use in infill walls with height-tothickness ratios ranging from 6.8 to 35.3
Δf = Static • one-way vertical spanning or cantilevered Timber diaphragm instability Free NZSEE (2015) or URM wall on displacement (unrestrained)** contiguous levels* (one-way) Δf = Static • two-way spanning (minimum translational Diaphragm or URM One or both Vaculik and instability support at bottom edge and at least one wall on contiguous sides laterally Griffith (2017) displacement vertical edge) levels restrained (two-way) *RC bond beams are also present at floor levels in many pre-WWII buildings with loadbearing URM walls and timber diaphragms in Australasia, but without vertical rigid elements (i.e., RC columns) to restrain the RC bond beams against vertical deflection, the RC bond beams are generally not assumed to effectuate compressive strut “arching” mechanisms in the URM walls under OOP loading. ** Recommended for best-practice use in the case of isolated piers between window/door openings or for long parapets (with no overburden loads), such that one-way vertical flexure (i.e., horizontal cracking rather than vertical or diagonal cracking) is likely to govern OOP collapse. ***URM infill walls may also be bounded by steel framing, but such an arrangement is far less common in Australasia.
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Due to its association with idealised initial stiffness, one may infer that Δ1 represents the predicted “yield” 4
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displacement by which an elastic analysis or identification of the initial period may be carried out, and for purposes
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of the current study, the association of Δ1 with the “yield” point was assumed for simplicity. However, Doherty et al.
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(2002) noted a lack of a definitive yield point in experimental results, and furthermore concluded that the instability
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collapse displacement Δf determined in dynamic, time-history analyses is relatively insensitive to the initial stiffness
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or the period determined from it. Thus, Doherty et al. (2002) did not explicitly define a definitive yield displacement
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parameter. The displacement Δ1 is also independent from displacement at initial crack-formation, which is related to
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mortar bond strength. Vaculik and Griffith (2017) did consider a predicted yield point for comparison to experimental
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results, and assumed it to be the average of the empirical Δ1 and Δ2 values, wherein 2 represents the second
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trilinear-defining parameter. For idealising the experimental results considered in the current study, the yield
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displacement was approximated by assuming an equivalent elasto-plastic system with reduced stiffness in which
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the initial slope of the idealised trilinear curve was set to intersect with the experimentally measured curve at the first
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point on the curve which represented a measured force equal to 75% of the maximum post-crack lateral force (Park
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1989). By comparison, Derakhshan et al. (2013a) defined 1 such that the initial slope of the idealised trilinear curve
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intersects the measured curvilinear response at 67% of the maximum post-crack lateral force, and recommended a
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formula to calculate 1 using the cracked moment of inertia.
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Δ2 in Figure 1 represents the displacement for determining the effective secant stiffness (which will hereafter be
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referred to simply as the secant stiffness) for use in nonlinear analysis as a substitute structure representation for a
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multi-degree-of-freedom system (Doherty et al. 2002). Other researchers (Griffith et al. 2003; Derakhshan et al.
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2014b) have recommended that the wall’s fundamental vibrational period assumed when estimating the wall’s
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maximum reliable dynamic displacement capacity be defined assuming the secant stiffness at the displacement Δ2.
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Hence, Δ2 and its corresponding force can be referred to as the “design” point on the force-displacement curve for
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many types of engineering analyses, especially in the design for the ultimate limit state (NZS 2004) or corresponding
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life safety (ASCE 2014) performance evaluation of existing walls.
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Doherty et al. (2002) identified that the secant stiffness for URM walls is different than for most other systems due
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to material strength variability and lack of definitive yield and/or softening points. Hence, Doherty et al. (2002) defined
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Δ2 as being the horizontal ordinate of the intersection point between the peak strength and the rigid bilinear idealised
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force-displacement curve (see Figure 1) and recommended empirically derived ratios of Δ2/Δf from 0.28 to 0.50 for
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a range of degradation states for single-leaf walls (with the most severely damaged walls having the highest
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anticipated ratios of Δ2/Δf). By comparison, Derakhshan et al. (2013a) tested multi-leaf (two-leaf and three-leaf) walls
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with and without overburden loads and recommended a formula for calculation of the ratio of Δ2/Δf, which typically
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produces smaller ratios than per Doherty et al. (2002) with an upper bound value of Δ2/Δf equal to 0.25. By further
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comparison, NTC (2008) recommends that Δ2/Δf be assumed equal to 0.40 in engineering assessments, unless
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limited by potentially unsafe conditions such as floor joist unseating.
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Finally, Δf in Figure 1 represents the instability displacement under quasi-static loading (hereafter referred to as the
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static instability displacement). For simply-supported, one-way vertically spanning URM walls without overburden
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loads nor rigid restraints causing arching action to develop, it has been shown that the static instability displacement
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is expected to be equal to the wall thickness (Ewing et al. 1984; Doherty et al. 2002; Sorrentino et al. 2008;
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Derakhshan et al. 2013b; Penner and Elwood 2016). However, the static instability displacement is expected to be 5
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smaller for one-way vertically spanning walls with applied overburden loads. Also, the instability displacement value
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can be significantly larger than the wall thickness for two-way spanning walls (Vaculik and Griffith 2017). In any given
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overburden load or spanning condition, note that utilising the full static displacement capacity for a practitioner
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engineering assessment is non-conservative as much of the wall’s displacement capacity is associated with
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“negative stiffness” (i.e., displacement increases with reducing lateral force; see Figure 1). Numerical dynamic time-
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history analyses (Derakhshan et al. 2014b) have shown that one-way vertically spanning URM wall displacements
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beyond 0.5Δf and 0.25Δf for simply-supported and cantilevered walls, respectively, are rarely reversible and generally
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lead to wall collapse. Furthermore, displacement capacity is extremely sensitive to resonance occurring between
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the wall rocking and the ground (or floor) motion, such that dynamic URM wall displacement capacity may vary
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significantly depending on the ground-motion record and building characteristics being considered in analysis
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(Wilhelm 2007; Derakhshan et al. 2014b).
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Displacement-based models recommended for use in determining the three different displacement parameters (Δ1 ,
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Δ2 , and Δf ) for various wall boundary conditions are also listed in Table 1. Various alternative methods for predicting
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the OOP behaviour of URM walls have been documented elsewhere (Ferreira et al. 2015). For determining the
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secant stiffness at displacement parameter Δ2, a predictive model developed explicitly for infill walls is presented in
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assessment standards FEMA 356 (2000) and ASCE 41 (2014), with modifications proposed by Flanagan and
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Bennett (1999). Currently, there is no research basis known to the authors for distinguishing between “unbounded”
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and “bounded” URM wall types for estimating OOP displacement parameters Δ1 and Δf . However, in previously
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reported research on retrofitted URM cavity walls tested in one-way vertically spanning conditions, Walsh et al.
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(2015) concluded that “bounded” walls with arching action were likely to have lower fundamental vibrational periods
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than “unbounded” walls. Furthermore, “bounded” walls were determined to have much more significant strength
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capacity as compared to “unbounded” wall types, controlling for geometry and material characteristics.
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While not considered in the study reported herein, multiple alternative predictive models exist for predicting the
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strength and displacement performance of walls under OOP loads as well as in combined in-plane and OOP
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interaction (e.g., Komaraneni et al. 2011; Ferreira et al. 2015; Mosalam and Günay 2015; Furtado et al. 2016;
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Libratore et al. 2016; Shing et al. 2016; Asteris et al. 2017; Pasca et al. 2017). Numerical finite element (FE) and
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discrete element (DE) models for OOP wall performance are considered further by Galvez et al. (2018).
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A total of nineteen tests on masonry walls were performed in six different buildings (see Table 2) utilising an approach
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wherein lateral forces were applied using a system of airbags to simulate distributed OOP forces. Test walls were
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located within six different buildings in New Zealand: the Weir House (WH) estate in Wellington (constructed 1932),
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the Oriental Bay (WO) apartments in Wellington (early 1900s), the Wellington Railway Station (WR, 1937), an
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automotive garage (AG) in the Auckland CBD (1958), a retail building (AO) located in Orakei, Auckland (1938), and
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a mixed-used building on Kingston Street (AK) located in the Auckland CBD (1927). The experimental approach
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was consistent with the testing procedures recommended by the American Society of Civil Engineers (ASCE 2014)
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and previously utilised by Abrams et al. (1996) and Derakhshan et al. (2013a, 2014a). The experimental test setup,
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wall conditions, experimental observations, and data processing are described in more detail in the companion article
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(Dizhur et al. 2018).
IN SITU TEST WALL CONDITIONS
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The test samples represented a variety of geometries, boundary conditions, pre-test damage states, and material
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properties. Geometries and pre-test damage states are summarised in Table 2. Note that walls with test
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identifications (IDs) ending with a letter (e.g., A, B, or C) are walls that were tested multiple times with different levels
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of simulated damage or changes in boundary conditions. As noted in Table 2, test walls WO1B, WO1C, and AG2
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were prepared with simulated damage by saw cutting 50 mm deep “cracks” into the wall’s compression side (i.e.,
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the side of the wall being directly laterally loaded) prior to testing. Test wall AO1 was saw cut 50 mm deep through
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the bottom masonry course to simulate the effects of the smooth lead damp-proof course on the exterior leaves of
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the perimeter walls. Most of the test walls in the WR building (WR1, WR2B, WR3, WR4, WR6) were tested
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unrestrained on the sides (vertical edges) by utilising either saw cuts or tall door openings to conservatively simulate
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one-way vertical flexure for purposes of analysis elsewhere in the building. Plaster was retained on both sides of test
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walls in the WH and WO buildings, and on various other walls in this testing programme, but otherwise ignored in
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the analytical portion of the current study. It was assumed that the marginal contribution to OOP strength by the
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plaster would be approximately equally offset by its marginal self-weight as well as its rapid deterioration under cyclic
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loading as observed in previous experimental studies (Derakhshan et al. 2013a). More recent experimental studies
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incorporating and considering the effects of plaster on OOP wall performance can be found elsewhere (Derakhshan
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et al. 2018). For purposes of estimating the self-weight of the test walls in the current study, only the brick thicknesses
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listed in Table 2 were considered. Note that all URM test walls in current study consisted of only a single brick leaf.
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2.1
Material Properties
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Brick, mortar, and masonry prism samples were extracted from the test walls and tested in accordance with the
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relevant ASTM standards. Please refer to the companion article (Dizhur et al. 2018) for the complete list of standards.
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The gross cross-section of bricks was assumed for determining all material strengths. A summary of the material
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test results is included in Table 3 where all strength values are in units of MPa, unless noted otherwise. When it was
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not possible to test for certain material strengths, empirical equations were used to estimate the predicted mean
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values, as described by Dizhur et al. (2018). For comparison with the values in Table 1, nearly half of a group of
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tested samples from 98 pre-1950 buildings in New Zealand had brick compressive strengths (𝑓𝑏′ ) ranging between
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10 – 20 MPa with a median value near 17 MPa, and mortar compressive strengths (𝑓𝑗′ ) ranging between 0.5 –
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2.0 MPa (i.e., the range of “soft” mortar with low cohesion) with a median value near 1.8 MPa (Almesfer et al. 2014).
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Hence, the bricks and masonry were generally stronger in the test buildings considered in this study than is typical
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in more historic URM buildings in New Zealand.
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Knowledge of the masonry dimensions in test walls was required in order to compare the measured results to the
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predictive results of the AS (2011) method. The average measured brick height, brick length, and mortar joint
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thickness in each relevant building were as follows (all dimensions in mm): 160, 300, and 15 for the Wellington Weir
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House (WH); 76, 230, and 18 for the Wellington Oriental Bay apartment building (WO); 78, 223, and 13.5 for the
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Wellington Railway Station (WR); 72, 224, and 11 for the Auckland Garage (AG); and 76, 225.5, and 13.5 for the
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Auckland Orakei retail building (AO). All masonry walls tested were constructed in running bond pattern with half
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brick length overlaps. Where needed for predictive calculations, the “equivalent” bed joint shear friction coefficient
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was assumed to be 1.04 to account for residual moment capacity in horizontal bending along a square bed joint
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(Vaculik and Griffith 2017). 7
Table 2. Summary of test wall geometries, boundary conditions, and preparations Test ID
Top edge restraint
Side (vertical) edge restraints
Bottom edge restraint
Features and preparations
WH1
4100
3600
95
RC slab with contiguous URM wall above
700x500 mm RC column and URM return wall
WH2
3850
2730
95
Gypsum board (free)
RC column and URM return wall
RC slab
Plaster 15–20 mm thick each side, existing minor cracks
WH3
3480
2730
95
Gypsum board (free)
RC shear wall and timber wardrobe
RC slab
Plaster 15–20 mm thick each side, existing minor cracks
WO1A
3900
2740
110
Timber (lateral only)
URM return walls both sides
URM / RC
Plaster 15–20 mm thick each side
WO1B
3900
2740
110
Timber (lateral only)
URM return walls both sides
URM / RC
Plaster 15–20 mm thick each side, horizontal 50 mm deep cut at 1600 mm above floor height
WO1C
3900
2740
110
Timber (lateral only)
URM return walls both sides
URM / RC
Plaster 15–20 mm thick each side, horizontal and vertical 50 mm deep cut at 1600 mm above floor height and at the horizontal midway mark
WO2
2600
2740
110
Timber (overburden)
URM return wall and short door opening
URM / RC
Plaster 15–20 mm thick each side, loadbearing wall (overburden load)
WR1
2180
4280
108
127 mm RC slab
Free (unrestr.) both sides
RC slab on grade
Side edges saw cut free
WR2A
2662
4342
108
127 mm RC slab
URM return wall and URM pier
RC slab on grade
WR2A tested in its existing condition prior to saw cutting edges and retesting as WR2B
WR2B
1915
4342
108
127 mm RC slab
Free (unrestr.) both sides
RC slab on grade
Side edges of WR2B saw cut free after testing WR2A
WR3
3385
2700
108
127 mm RC slab
Free (unrestr.) both sides
127 mm RC slab
Side edges saw cut free (one side was saw cut above existing door opening)
WR4
1900
2450
108
127 mm RC slab
Free (unrestr.) and tall door opening
127 mm RC slab
WR5
2580
2980
108
Timber (lateral only)
URM return wall and short door opening
RC slab
One side edge saw cut free and other side edge had nearly full height door opening
WR6
1305
2400
108
Timber (lateral only)
Free (unrestr.) both sides
RC slab
305x265mm concrete-encased steel columns both sides, contiguous infill on one side
RC slab on grade
Brick masonry veneer (as part of cavity infill wall) removed prior to testing Brick masonry veneer (as part of cavity infill wall) removed prior to testing, simulated in-plane cracking with 50 mm deep cut in X-shape
RC slab with contiguous Plaster 15–20 mm thick each side URM wall below
AG1
4400
3400
112.5
280x150mm RC beam
AG2
4400
3400
112.5
280x150mm RC beam
305x265mm concrete-encased steel columns both sides, contiguous infill one side
RC slab on grade
AO1
3380
2655
109
300x375mm RC beam
350x350mm RC column (interior) with contiguous infill and 300x300mm RC column (exterior)
Timber
AK1
3350
2750
75
RC beam
RC column
RC beam
75
300x475mm RC beam
Free (unrestr.) both sides
300x475mm RC beam
AK2
205
Full in Brick Length situ thickness (mm) height* (mm) (mm)
1450
2750
Side edges saw cut free
Original cavity steel wire ties Vertically cut through the 75 mm brick and removed original cavity steel wire ties
8
206
Bounding frame concrete compressive strength, 𝑓𝑐′
Masonry prism density, 𝜌𝑚 (kg/m3)
Brick rupture strength (modulus ′ of rupture), 𝑓𝑚𝑟
Masonry prism bond rupture ′ strength, 𝑓𝑓𝑏
Masonry prism compression strength, 𝑓𝑚′
Mortar compression strength, 𝑓𝑗′
Brick compression strength, 𝑓𝑏′
Parameter
Test wall(s)
Table 3. Summary of measured and estimated masonry material characteristics (all strength values in MPa unless noted otherwise)
Mean 12.5 26.7 13.8 0.80 1.5 1650 CV 0.50 0.26 Est. Est. Est. Est. (hollow) # 4 3 28 Mean 25.6 12.6 18.7 0.38 3.1 1807 WO1 CV 0.28 0.29 WO2 Est. Est. Est. Est. # 7 18 Mean 24.6 9.9 16.9 0.30 3.0 1780 WR1 CV 0.15 0.30 Est. Est. Est. Est. # 4 6 Mean 42.0 11.2 26.2 0.34 5.0 1878 WR2 CV 0.09 0.23 Est. Est. Est. Est. # 4 6 Mean 33.0 7.9 19.5 0.24 4.0 1806 WR3 CV 26 WR4 Avg. Avg. Avg. Avg. Avg. Avg. # Mean 37.4 8.0 21.6 0.24 4.5 1829 WR5 CV 0.12 0.31 Est. Est. Est. Est. # 3 6 Mean 28.5 7.8 17.5 0.23 3.4 1783 WR6 CV 0.25 0.26 Est. Est. Est. Est. # 3 5 Mean 35.5 13.9 9.4 0.42 3.6 1720 AG1 CV 0.08 0.09 0.30 0.23 0.03 42 AG2 Est. # 5 5 2 4 3 Mean 27.6 8.4 17.5 0.25 3.3 1783 AO1 CV 0.29 0.41 34 Est. Est. Est. Est. # 4 6 Mean 8.0 1.2 3.8 0.04 1.0 1628 AK1 CV 0.27 0.22 28 AK2 Est. Est. Est. Est. # 7 13 Notes: mean = average of measured values; CV = coefficient of variation defined as the sample standard deviation divided by the mean; # = number of test samples; Est. = estimated (predicted mean) value by empirical equation; Avg. = average of corresponding WR5 and WR6 values; all values for 𝑓𝑐′ were estimated per the accompanying text WH1 WH2 WH3
207 208
Knowledge of the RC bounding element dimensions (See Table 2) as well as expected concrete compression
209
strength was required in order to compare the measured results to the predictive results of the Flanagan and Bennett
210
(1999) method. The expected concrete compression strength for each relevant building was determined as follows:
211
26 MPa for the Wellington Railway Station (WR) per Peng and McKenzie (2013); 42 MPa for the Auckland Victoria
212
Street automotive garage (AG) estimated as the specified strength for contemporary concrete of 21 MPa (TNZ 2004)
213
multiplied by 2.0 to account for age and overstrength (NZSEE 2006); 34 MPa for the Auckland Orakei retail building
214
(AO) estimated as the specified strength for contemporary concrete of 17 MPa (TNZ 2004) multiplied by 2.0 to
215
account for age and overstrength (NZSEE 2006); and 28 MPa for both the Wellington Weir House (WH) and the
216
Auckland Kingston Street (AK) building, estimated as the specified strength for contemporary concrete of 14 MPa
217
(TNZ 2004) multiplied by 2.0 to account for age and overstrength (NZSEE 2006). The elastic modulus of concrete, 9
218
𝐸 (MPa), was estimated as a function of the compressive strength of concrete, 𝑓′𝑐𝑜 (MPa), assuming 𝐸 = 3320√𝑓′𝑐𝑜 +
219
6900 in accordance with NZS (2006).
220
2.2
Experimental Test Setup and Instrumentation
221
The predictive content presented herein considers experimental results reported in a companion paper (Dizhur et
222
al. 2018), but a brief extract from that reported study is included here for convenience. During the experimental
223
portion of the research program, loading was applied to all test walls by using an air compressor to gradually inflate
224
1–3 (depending on the wall length) vinyl airbags that were positioned in a gap of 25–35 mm between the test wall
225
panel and a plywood backing panel. The loaded area from each airbag was approximately 1150 mm by 2050 mm.
226
The plywood backing panel consisted of an assemblage of plywood sheets and timber frames [see Figure 2(a)]. The
227
applied force from the airbags was transferred from the plywood backing panel to the braced reaction frame using 6
228
to 8 s-shaped load cells which provided the primary source of horizontal stability to the plywood-backed frame panel
229
[see Figure 2(a)]. The total lateral load, V, at any given time was calculated as the summation of the force recorded
230
by all load cells. The instrumentation used to measure the OOP displacement of each test wall was generally placed
231
on an isolated frame located on the opposite side of the test wall to the loading frame [see Figure 2(b)].
232
(a) Schematic of OOP test reaction frame (left of wall cross-section) and displacement instrumentation (right of wall cross-section) [h = test wall height, D = displacement gauge] (not to scale)
(b) Displacement instrumentation placed on framing opposite side of wall from reaction frame
Figure 2. Test setup for OOP loading of wall panels
233
3
MEASURED WALL OOP FORCE-DISPLACEMENT BEHAVIOUR
234
All test walls were laterally loaded semi-cyclically at a quasi-static loading rate. The maximum lateral-force value
235
(expressed as an acceleration with respect to gravity, g) for each wall was determined by dividing the maximum total
236
test lateral force, V, by the weight of the test wall (see Figure 3). For tests in which the maximum total test lateral 10
237
force, V, represented the limiting capacity of the testing equipment, only the peak force is noted in Figure 3. In many
238
of the test buildings in which the test walls were required to remain in place after testing, testing was concluded after
239
the peak strength of the test walls had been reasonably assumed to have been reached. In such cases, idealised
240
curves were added to the measured force-displacement curves shown in Figure 3. The idealised curves shown in
241
Figure 3 connect the origin, the idealised yield drift determined by assuming an equivalent elasto-plastic system with
242
reduced stiffness (Park 1989), and the post-crack peak strength “design point”. Wall AG2 was able to be tested to
243
complete collapse, and the instability drift was measured using photogrammetry. The relatively high lateral force
244
measurements at low drifts shown in Figure 3(p) represent situations where the test wall may have uncut small
245
portions of masonry at a boundary interface prior to that portion cracking. The values for OOP drift measured with
246
respect to the initial base position are shown in Figure 3 as the ratio (%) of the OOP displacement at mid-height to
247
the vertical distance between the wall base and the mid-height displacement gauge (i.e., approximately half the wall
248
height). Additional observations from the wall tests are addressed in the companion article (Dizhur et al. 2018).
249 0.00%
50 2.0
40 1.5 30 1.0
20
V / (test wall weight) (g)
2.5
V (kN)
V / (test wall weight) (g)
60
0.20% 50
3.0
70
3.0
OOP drift from initial base (%) 0.05% 0.10% 0.15%
0.18%, 46.2 kN
0.14%
2.5
45 40 35
2.0
30 25
1.5
20
1.0
V (kN)
OOP drift from initial base (%) 0.01% 0.02% 0.03%
0.00%
15 10
0.5
5
0.5
10
0.0
0 0.0
0.1
0.2 0.3 0.4 0.5 OOP displacement at midheight (mm)
0.6
0
0.0
0.7
0.5 Measured
(a) WH1
1.0 1.5 2.0 2.5 OOP displacement at midheight (mm) Idealisation
3.0
Secant stiffness
(b) WH2
OOP drift from initial base (%) 0.05% 0.10% 0.15%
0.00%
0.0
0.20% 50
3.0
0.18%, 46.8 kN
45 40
2.5
35 30
2.0
25
1.5
20
V (kN)
V / (test wall weight) (g)
0.14%
15
1.0
10
0.5
5
0.0
0
0.0
0.5
Measured
1.0 1.5 2.0 2.5 OOP displacement at midheight (mm) Idealisation
(c) WH3
3.0
Secant stiffness
(d) WO1A
11
(e) WO1B
(f) WO1C
(g) WO2
(h) WR1
(i) WR2A
(j) WR2B
12
(k) WR3
(l) WR4
(m) WR5
(n) WR6
(o) AG1
(p) AG2
13
(p) AG2 (showing instability displacement)
1.8
0.20%
0.29%, 19.9 kN 20
1.3
15
1.0 10
0.8 0.5
5
0.3
V (kN)
1.5
V / (test wall weight) (g)
25
2.0
V / (test wall weight) (g)
0.00% 2.3
0.30%
0.02%
OOP drift from initial base (%) 0.04% 0.06% 0.08% 0.05%
2.0
0.10% 12
0.08%, 10.2 kN 10
1.8 8
1.5 1.3
6
1.0 4
0.8
0.5
2
0.3
0.0
0 0.0
1.0 2.0 3.0 4.0 OOP displacement at midheight (mm) Measured
Idealisation
5.0
Secant stiffness
V (kN)
OOP drift from initial base (%) 0.10% 0.20%
0.00%
(q) AO1
0.0
0 0.0 Measured
0.5 1.0 OOP displacement at midheight (mm) Idealisation
(r) AK1
1.5
Secant stiffness
(s) AK2
Figure 3. Force-displacement responses for test walls COMPARISON OF PREDICTED AND MEASURED WALL BEAHVIOUR
250
4
251
4.1
Predicted versus measured strength
252
A summary of ratios of predicted and measured performance and assumptions made as part of the predictive
253
modelling inputs are charted in Figure 4 and listed in Table 4. Note that most of the test walls were assessed as
254
being either unbounded [i.e., having no arching action per AS (2011)] or being bounded [i.e., having arching action
255
per Flanagan and Bennett (1999)] and compared explicitly to the appropriate predictive model. However, three test
256
walls (WH1, WR2A, and AO1) were reasonably deemed as appropriate to be assessed with either predictive model
257
due to having potentially rigid bounding elements in one flexural direction but not in the other. For walls assessed for
258
strength using the AS (2011) model, all but one wall were assumed to experience two-way flexure during OOP
259
deformation. The exception was test wall WR6 which was assessed using AS (2011) criteria assuming only one-
260
way vertical flexure. As noted in Table 4, design length, Ld , and design height, Hd , values were assumed either
261
equal to full or half of the in situ wall dimensions depending on the presence of boundary restraints in the respective
262
directions. Side (vertical) edge rotational restraints factors, Rf1 and Rf2 , were assumed equal to 0.0, 0.5, or 1.0 for 14
restraints consisting of timber, URM (Grifith and Vaculik 2007), and RC elements respectively. Experimental Equiv. Force-Based Capacity (kN)
263
80 WH1
70
AO1 WR5
AO1
60 WO1C
50
WR3
WR4 WR1
30 AK2
AG2 WO1A WR2B
10 WR6
WR2A
WO1B
WO2
20
AG1
WH2 WR2A
WH3
40
WH1
Strength Over-predicted
0 0
10
20 30 40 50 60 70 Predicted Force-Based Capacity (kN) AS 3700 / Think Brick Flanagan & Bennett / Dawe & Seah Mean ratio 0.84 (CV 0.56) Mean ratio 0.93 (CV 0.25)
80
Figure 4. Comparison of predicted and experimentally measured wall strength 264
For walls assessed for strength using the Flanagan and Bennett (1999) model, the relative stiffness factors for the
265
bounding elements, α and β, were determined in accordance with the recommendations of MSJC (2011) whereby
266
the average values used in the model, αavg and βavg, as noted in Table 4 were determined by averaging the respective
267
factors for the elements on opposite edges from each other. RC slabs on grade were assumed to provide the
268
maximum stiffness value permissible in the model of 50.0. Bounding elements separating contiguous URM infill
269
panels were also assumed to provide the maximum stiffness value permissible in the model of 50.0 (e.g., the column
270
separating test walls AG1 and AG2). Elements unlikely to provide enough relative stiffness to effectuate significant
271
arching action (e.g., timber framing) were assigned relative stiffness factors of 0.0. Other elements (e.g., RC slabs
272
and beams) were assigned relative stiffness factors proportional to their flexural rigidities (EI). Where top or bottom
273
bounding elements were RC slabs, the moment of interia, I , was calculated assuming an effective flange width of
274
16 times the thickness of the slab per the recommendation of NZS (2006). RC sections were assumed to be
275
uncracked. Strength reduction due to simulated in-plane damage was assumed in accordance with the
276
recommendations of Abrams et al. (1996). The reduction factors utilised as shown in Table 4 for walls WO1B, WO1C,
277
and AG2 were chosen blindly per engineering judgment prior to carrying out the predictive analysis. Even though
278
the strength reduction factors proposed by Abrams et al. (1996) were based on tests of masonry infill panels with
279
arching action and, hence, most appropriately applied to test wall AG2, assumed strength reduction factors were
280
applied to the predicted OOP strengths of test walls WO1B and WO1C due to a lack of existing, relevant research
281
for pre-damaged URM walls without arching action.
282
The average ratio and associated coefficient of variation (CV) of predicted strengths to measured strengths were
283
determined to be 0.84 (CV 0.56) and 0.93 (CV 0.25) for the AS (2011) and Flanagan and Bennett (1999) methods,
284
respectively. Note that all cases of predicted strength ratios higher than 1.0 listed in Table 4 were associated with
285
test walls that may not have been loaded to their peak force capacities. Test walls WR5 and WR6 had notably low
286
predicted strength ratios of 0.24 and 0.25, respectively. In the case of test wall WR5, neglecting the contribution from 15
287
the spandrel above the door opening to side (vertical) edge rotational restraint may have contributed to the significant
288
underestimation of OOP strength. Note however, that the contribution from the spandrel above the door opening
289
was also neglected in predicting the OOP strength of test wall WO2. In the case of test wall WR6, the vertical saw
290
cut preparations were executed in such a fashion that a relatively deep spandrel remained above the portion of the
291
wall tested in one-way vertical flexure. This spandrel may have applied a greater rotational restraint condition and/or
292
overburden load to the wall during OOP deformation than was assumed, thus increasing the test wall’s OOP strength
293
and reducing the accuracy of the one-way flexural model applied to it per AS (2011). If the ratios for test walls WR5
294
and WR6 were neglected, the average ratio and associated CV of predicted to measured strengths listed in Table 4
295
would become 0.97 (CV 0.42) for the AS (2011) method.
296
As shown at the end of Table 4, predicted capacity reduction factors of 0.55 and 0.70 would ensure 100% of the
297
test wall specimens considered herein were underpredicted for strength capacity using the AS (2011) and Flanagan
298
and Bennett (1999) methods, respectively, notwithstanding that some test walls were not able to be experimentally
299
tested to their ultimate capacities. By comparison, both AS (2011) and MSJC (2011) specify the use of a capacity
300
reduction factor of 0.60 for flexure in unreinforced masonry. Note that AS (2011) and MSJC (2011) reduction factors
301
are used in conjunction with other factors of safety inherent to new design practice (e.g., specified lower-bound
302
material strength) that were not considered in the predicted capacities of existing walls as reported herein.
303
4.2
Predicted versus measured displacements
304
Experimental and predicted values for displacement at yield, displacement at the “design point” for secant stiffness,
305
and static instability displacement were compared, and the relative values are depicted in Table 5. Using the Doherty
306
et al. (2002) empirical average values, the average ratio of predicted to measured yield was 2.65 with a high
307
coefficient of variation (CV) of 0.96. This apparent overprediction may be due to some of the walls tested in the
308
current study not actually being tested to peak strength (note the few force-displacement curves in Figure 3 without
309
measured softening) or due to some of the walls tested in the current study being much stiffer relative to the Doherty
310
et al. (2002) test walls due to two-way spanning conditions as well as arching action from the rigid bounding elements
311
– neither of which was explicitly considered by Doherty et al (2002). Furthermore, the apparent over-prediction is
312
largely controlled by three test specimens – WO1C, AO1, and AK2 – all of which experienced two-way spanning
313
action, arching action in at least one direction, or both actions). If these three outlier data points are removed from
314
the data set, the average of the ratios of predicted to measured yield would be reduced to 1.39 (CV 0.68). Regardless,
315
the empirical average values for parameter Δ1 as published by Doherty et al. (2002) differ notably from those
316
obtained in the current study from the experimental measurement idealisation of the “yield” point based on an
317
equivalent elasto-plastic system with reduced stiffness (Park 1989).
16
Strength (Flanagan and Bennett 1999)
Ratio of predicted to experimental forcebased capacity
Strength (AS 2011)
Experimental equivalent force-based capacity (g)
Experimental equivalent force-based capacity (kN)
Test ID
Table 4. Comparison of predicted and experimentally measured wall strength
Assumptions used in the predictive model
AS (2011): hu = 160 mm; lu = 300 mm; tj = 15 mm; Ld = 2050 mm; Hd = 1800 mm; Rf1 = 1.0 (RC column); Rf2 = 0.5 (URM return wall) Flanagan and Bennett (1999): αleft = 50 (RC column); αright = 0 (assumed URM return wall would not effectuate arching action on its own, but in conjunction with RC column on other side, would effectuate some arching action, in contrast to timber); αavg = 25.0 βtop = βbottom = βavg = 50 (RC slab above and below with contiguous infill)
WH1
72.7
3.20
0.82
0.84
WH2
46.2
2.86
0.75
-
hu = 160 mm; lu = 300 mm; tj = 15 mm; Ld = 1925 mm; Hd = 2730 mm; Rf1 = 1.0 (RC column); Rf2 = 0.5 (URM return wall)
WH3 WO1A
46.8 23.6
3.20 1.13
0.69 1.81
-
hu = 160 mm; lu = 300 mm; tj = 15 mm; Ld = 1740 mm; Hd = 2730 mm; Rf1 = 1.0 (RC column); Rf2 = 0.0 (timber wardrobe)
WO1B
39.7
1.91
0.92
-
WO1C
47.8
2.30
0.67
-
WO2
22.9
1.65
0.84
-
WR1
24.5
1.39
-
0.97
αleft = αright = αavg = 0.0 (saw cut free edges) βtop = 36.3 (RC slab with effective width = 16 × thickness per NZS 2006); βbottom = 50.0 (RC slab on grade); βavg = 43.2 AS (2011): hu = 78 mm; lu = 223 mm; tj = 13.5 mm; Ld = 1331 mm; Hd = 2171 mm; Rf1 = Rf2 = 0.50 (URM return wall or pier) Flanagan and Bennett (1999): αleft = αright = αavg = 0.0 (URM return wall and UMR pier) βtop = 32.9 (RC slab with effective width = 16 × thickness per NZS (2006); βbottom = 50.0 (RC slab on grade); βavg = 41.4
hu = 76 mm; lu = 230 mm; tj = 18 mm; Ld = 1950 mm; Hd = 1370 mm; Rf1 = Rf2 = 0.50 (URM return walls) hu = 76 mm; lu = 230 mm; tj = 18 mm; Ld = 1950 mm; Hd = 1370 mm; Rf1 = Rf2 = 0.50 (URM return walls) Strength reduction factor to account for in-plane damage, R1 = 0.85 (Abrams et al. [11]) hu = 76 mm; lu = 230 mm; tj = 18 mm; Ld = 1950 mm; Hd = 1370 mm; Rf1 = Rf2 = 0.50 (URM return walls) Strength reduction factor to account for in-plane damage, R1 = 0.75 (Abrams et al. [11]) hu = 76 mm; lu = 230 mm; tj = 18 mm; Ld = 2600 mm; Hd = 1370 mm; Rf1 = 0.5 (URM return wall); Rf2 = n/a (door opening)
WR2A
41.6
1.81
1.52
0.91
WR2B
20.7
1.25
-
1.41
WR3
43.6
2.17
-
1.04
αleft = αright = αavg = 0.0 (saw cut free edges) βtop = 38.7 (RC slab with effective width = 16 × thickness per NZS (2006); βbottom = 50.0 (RC slab on grade); βavg = 44.4 αleft = αright = αavg = 0.0 (saw cut free edges) βtop = βbottom = βavg = 29.1 (RC slab with effective width = 16 × thickness per NZS (2006)
WR4
38.6
3.43
-
0.88
αleft = αright = αavg = 0.0 (saw cut free edges) βtop = βbottom = βavg = 38.9 (RC slab with effective width = 16 × thickness per NZS (2006)
17
Table 4. Comparison of predicted and experimentally measured wall strength
Test ID
Experimental equivalent force-based capacity (kN)
Experimental equivalent force-based capacity (g)
Strength (AS 2011)
Strength (Flanagan and Bennett 1999)
Ratio of predicted to experimental forcebased capacity
WR5
65.1
4.37
0.24
-
WR6
7.0
0.96
0.25
-
AG1
61.3
2.16
-
1.00
αleft = 32.8 (column against door opening); αright = 50.0 (column against contiguous infill); αavg = 41.4 βtop = 18.4 (shallow RC beam); βbottom = 50.0 (RC slab on grade); βavg = 34.2
AG2
38.4
1.35
-
0.96
αleft = 50.0 (column against contiguous infill); αright = 32.8 (column against door opening); αavg = 41.4 βtop = 18.4 (shallow RC beam); βbottom = 50.0 (RC slab on grade); βavg = 34.2 Strength reduction factor to account for in-plane damage, R1 = 0.60 (Abrams et al. 1996)
0.70
AS (2011): hu = 76 mm; lu = 225.5 mm; tj = 13.5 mm; Ld = 1690 mm; Hd = 1328 mm; Rf1 = Rf2 = 1.0 (RC columns) Flanagan and Bennett (1999): αleft = 50 (larger interior column with contiguous infill on the opposite side); αright = 39.8 (smaller exterior column); αavg = 44.9; βavg = 0.0 (assumed suspended timber floor not stiff enough to effectuate arching action)
0.72
Assumptions used in the predictive model
hu = 78 mm; lu = 223 mm; tj = 13.5 mm; Ld = 2580 mm; Hd = 1490 mm; Rf1 = 0.5 (URM return wall); Rf2 = n/a (door opening) Only one-way vertical flexure considered (AS 2011; Lawrence and Page 2013)
AO1
63.9
3.74
AK1
19.9
1.81
This wall is not considered in this analysis because it was tested with in situ cavity ties that are outside the scope of the considered predictive methods.
AK2
10.2
2.68
-
0.55
αleft = αright = αavg = 0.0 (saw cut free edges) βtop = βbottom = βavg = 50.0 (deep RC beam)
Avg.
0.84
0.93
-
Underprediction rate using predicted capacity reduction factor of 1.0
82%
70%
-
Underprediction rate using predicted capacity reduction factor of 0.75
82%
90%
-
Underprediction rate using predicted capacity reduction factor of 0.65
91%
100%
-
Underprediction rate using predicted capacity reduction factor of 0.55
100%
100%
-
318 18
319
“Design points” associated with the secant stiffness were predicted using both the Doherty et al. (2002) empirical
320
average values and the modified version of the standards’ (FEMA 2000; ASCE 2014) analytical equation per
321
Flanagan and Bennett (1999), with the latter pertaining explicitly to infill walls and limited to a height-to-thickness (h/t)
322
ratio of 30. Both predictive methods resulted in high overpredictions of the “design point” displacement relative to the
323
experimental values, with average ratios of predicted to measured results being 7.31 and 20.93, respectively (see
324
Table 5). In particular, use of the standards’ equation, even with the modification, overpredicted the displacement
325
values severely in the current study, although this observation is consistent with the conclusions reached by
326
Flanagan and Bennett (1999). Notably, both predictive methods were based largely on tests in vertical one-way
327
spanning conditions. In contrast, the walls tested in the current study were configured in mostly two-way spanning
328
conditions, and thus were measured as being comparatively stiff. However, test walls that were able to loaded to
329
more severe damage levels due to intended removal following testing (e.g., AG1 and AG2) were measured as having
330
drifts at peak strength more consistent with the predictive model and with other researchers’ experimental data.
331
Ductility, as considered here, is the ability of a component to reach its peak strength and continue deforming under
332
demands without weakening. While URM walls are not traditionally considered as having true ductility behaviour due
333
to their brittle materials, they can be considered as having equivalent ductility capacity due to OOP rocking for
334
purposes of identifying quantitatively performance limit states, or for use in linear (i.e., strength-based) assessment
335
procedures. Note that the average measured equivalent ductility of the tested wall specimens in this study would be
336
the ratio of the displacement at the design point to the displacement at yield, or 0.96% / 0.39% = 2.5. By comparison,
337
the average equivalent ductility capacity of the test walls using the predicted values per Doherty et al. (2002) would
338
be 3.9, although this value would be smaller if more walls were considered to be damaged prior to deforming OOP.
339
By further comparison, a provision in the upcoming version of ASCE 41 (2017) identifies an equivalent m-factor of
340
1.5 for URM wall OOP behaviour for use in linear static and linear dynamic procedures (LSP and LDP, respectively).
341
By further comparison, NTC (2008) recommends a behaviour factor of 2.0 for application in linear procedures based
342
on kinematic analysis. Identification of test walls in the study reported herein with especially low drifts at measured
343
peak strengths (e.g., WR1, WR2B, WR4, and AO1 as shown in Figure 2) validates for purposes of proof testing that
344
such walls were unlikely to have been loaded to their peak strengths, or at the very least, that some amount of
345
equivalent ductility capacity existed beyond the measured peak strengths.
346
Only one wall in the current study was able to be tested to collapse (AG2). Note that the ratio of predicted to
347
measured static instability displacement was an accurate 1.05 (albeit, this being only one data point). Notably and
348
in contrast to the other displacement-based predictive methods considered herein, the model used to predict the
349
OOP static instability displacement of this test wall (Vaculik and Griffith 2017) accounted for the two-way spanning
350
conditions that were present in the tested wall.
19
351 Table 5. Comparison of predicted and experimentally measured wall displacements Measured drifts1
Ratio of predicted to
Predicted drifts1
Static instabilityD (%)
Yield
Design pointB
Design pointC
Static instability
-
-
2.98
10.81
-
-
WH3
0.14% 0.18%
-
0.42% 1.95%
-
-
2.98
10.69
-
-
WO1C 0.23% 0.35%
-
1.04% 3.21%
-
-
4.54
9.13
-
-
Design pointB (%)
0.42% 1.95%
YieldA (%)
-
Design point** (%)
0.14% 0.18%
Yield* (%)
WH2
Test ID
Design pointC (%)
Static instability *** (%)
experimental
Assumptions and other notes
Moderate damage per Doherty et al. (2002) WR1
0.29% 0.71%
-
0.30% 1.41%
-
-
1.04
1.98
-
-
WR2B 0.43% 0.59%
-
0.30% 1.39%
-
-
0.69
2.34
-
-
WR4
0.34% 0.45%
-
0.42% 1.95%
8.1%
-
1.23
4.30
17.83
-
WR5
0.49% 0.78%
-
0.43% 2.03%
-
-
0.89
2.62
-
-
WR6
0.39% 1.29%
-
0.43% 2.03%
-
-
1.12
1.58
-
-
AG1
0.93% 3.03%
-
0.40% 1.85%
9.3%
-
0.43
0.61
3.08
-
AG2
1.19% 3.79% 12.6% 1.32% 3.31%
9.3%
13.2%
1.11
0.87
2.46
1.05
Severe damage per Doherty et al. (2002) AO1
0.06% 0.10%
-
0.49% 2.30%
5.9%
-
8.21
23.32
60.34
-
AK2
0.05% 0.08%
-
0.33% 1.53%
-
-
6.55
19.50
-
-
Avg.
0.39% 0.96%
-
0.53% 2.08%
8.18%
-
2.65
7.31
20.93
-
-
-
0.96
1.04
1.30
-
CV
-
-
-
-
-
Notes: All drifts in this table represent the ratio of lateral displacement to the wall’s vertical height below the location of primary horizontal cracking (assumed, and generally observed during testing, to have occurred at half the wall’s total height). * Intended to correspond with the idealised Δ1 parameter, based on an equivalent elasto-plastic system with reduced stiffness (Park 1989). ** Intended to correspond with the idealised Δ2 parameter, representing the displacement at peak force for determining the effective secant stiffness for use in nonlinear analysis (Doherty et al. 2002). In contrast, Derakhshan et al. (2014b) recommended that secant stiffness be determined at the point of 75% of the rigid-body action threshold force. *** Intended to correspond with the idealised Δf parameter for static wall instability. Measured using photogrammetry. A Based on empirical averages for Δ1 per Doherty et al. (2002) for undamaged/new wall conditions unless otherwise noted in the table. Note that Doherty et al. (2002) did not explicitly define Δ1 as the definitive yield displacement parameter. In contrast, Vaculik and Griffith (2017) considered the predicted yield point to be the average of Δ1 and Δ2. B Based on empirical averages for Δ2 per Doherty et al. (2002) for undamaged/new wall conditions unless otherwise noted in the table. C Based on the equation modified by Flanagan and Bennett (1999) from ASCE (2014) and FEMA (2000). Walls in this table without predicted values in this column were either not considered infill walls, or were infill walls with h/t ratios exceeding 30. D Based on the analytical equation proposed by Vaculik and Griffith (2017). 1
352
20
353
5
SUMMARY AND RECOMMENDATIONS
354
A total of 19 URM walls located in six buildings in New Zealand were tested for out-of-plane (OOP) behaviour, and
355
the measured behaviour was compared to established predictive methods considering range of wall geometries,
356
boundary conditions, pre-test damage states, and material properties. Hence, a study that compares the accuracy
357
of widely used displacement-based predictive methods and assumed input values to the results of experimental in
358
situ tests was the subject of the investigation reported herein. The referenced experimental test setup, test wall and
359
building conditions, experimental observations, and data processing are described in more detail in the companion
360
article (Dizhur et al. 2018).
361
On average, both primary predictive strength models produced relatively accurate results using the assumed inputs
362
as noted in Table 4 (for various boundary restraint conditions and pre-damage states). The variance of the results
363
was notably high for the AS (2011) predictive model, which may be the result of the AS (2011) model accommodating
364
a larger range of configurations and boundary condition types compared to the Flanagan and Bennett (1999) method.
365
The predictive strength models produced similar results for two of the three walls (WH1 and AO1) assessed using
366
both “unbounded” and “bounded” predictive models. In contrast, wall WR2A was predicted to have varying
367
performances using the two strength models, perhaps due to its comparably unique boundary conditions. The mean
368
ratio of predicted to experimental strength capacity using the Flanagan and Bennett (1999) method of 0.93
369
contradicts the conclusion drawn by Flanagan and Bennett that the Dawe and Seah (1989) method systematically
370
overpredicts the capacity of walls by a factor of 1.09, and for which Flanagan and Bennett proportionally adjusted
371
the coefficient of the Dawe and Seah predictive equation. For the walls considered in the current study, predicted
372
strength capacity reduction factors of 0.55 and 0.70 would ensure 100% of the test wall specimens considered herein
373
were underpredicted for strength capacity using the AS (2011) and Flanagan and Bennett (1999) methods,
374
respectively. Note, however, that Flanagan and Bennett (1999) referenced laboratory tests as opposed to the in situ
375
experimental tests considered herein. Amongst other factors and as noted previously, plaster was retained on both
376
sides of test walls in the WH and WO buildings, and on various other walls in this testing programme.
377
Displacement-based predictive methods for determining the OOP capacity of URM walls suffer from many of the
378
limitations present in the use of strength-based methods. The predictive results were compared to previously
379
reported experimental results of twelve of the experimental tests on existing URM walls performed in situ (see Table
380
5). In general, use of the existing predictive displacement-based methods results in the over-prediction of the
381
measured displacement parameters, which is likely due to most of the predictive methods being based on historical
382
wall tests in one-way spanning conditions and without rigid restraints capable of effectuating arching action in the
383
wall, in contrast to the wall test conditions in the current study. This apparent overprediction may also be due to some
384
of the test walls not actually being tested to peak strength. Hence, the authors strongly recommend that further
385
experimental tests on URM walls be carried out in two-way spanning conditions with and without rigid boundary
386
elements, and where possible, that testing conditions allow for pushing walls to complete collapse in such a fashion
387
that can be accurately measured.
21
ACKNOWLEDGEMENTS
388
6
389
A portion of the experimental testing was funded by the Building Research Association of New Zealand (BRANZ)
390
through grant LR0441 and the Natural Hazards Research Management Platform (NHRP) through grant C05X0907.
391
The authors are also grateful for the in-kind donations provided by the owners of the tested buildings, including
392
KiwiRail and Mansons TCLM Ltd. Technical advisory for both testing and analysis of the Wellington Railway Station
393
walls was provided by Holmes Consulting Group. Students and staff who participated in the various field and
394
laboratory testing efforts include Anthony Adams, Mark Byrami, Marta Giaretton, Mark Liew, Jeff Melster, Alexandre
395
Perrin, Laura Putri, Jerome Quenneville, Ross Reichardt, and Gye Simkin.
396
7
397
Abrams, D., Angel, R., and Uzarski, J. (1996). “Out-of-plane strength of unreinforced masonry infill panels.” Earthquake
398 399
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