INTERPRETATION OF IN-PLANE RESPONSE AND · PDF fileINTERPRETATION OF IN-PLANE RESPONSE AND DEFINITION OF DAMAGE LEVELS FOR MASONRY INFILLED RC FRAMES Hak, ... strut tw has been assumed

15th International Brick and Block Masonry Conference

Florianópolis – Brazil – 2012

INTERPRETATION OF IN-PLANE RESPONSE AND DEFINITION OF DAMAGE LEVELS FOR MASONRY INFILLED RC FRAMES

Hak, Sanja1; Morandi, Paolo2 ; Magenes, Guido3 1 PhD student, Rose School, Pavia, [email protected]

2 PhD, Post-Doctoral Research Fellow, Università degli Studi di Pavia and EUCENTRE, [email protected]

3 PhD, Associate Professor, Università degli Studi di Pavia and EUCENTRE, [email protected]

Since a wide range of material types and building techniques is commonly being adopted for the construction of masonry infills in Europe and worldwide, involving significant sources of uncertainties, a unified approach for the definition of accurate performance criteria is difficult to be achieved. Thus, experimental studies present one of the fundamental sources for the evaluation of strength, stiffness and deformation properties for masonry infills. In the present work a method for the interpretation of experimental results representing the cyclic in-plane response of single-bay, single-storey masonry infilled RC frames is proposed, aimed to allow the comparison of different infill typologies and facilitate the calibration of infill models for numerical applications. Based on a numerical simulation of the in-plane response of the infilled frames, representing the masonry infill as a compressive diagonal strut pinned at its ends to the intersection of beam and column centrelines, the approach is applied to some in-plane experimental tests on infilled RC frames carried out in the past. Based on the comparison of experimental and numerical results for infilled and bare frames, a calibration of the numerical model can be performed with particular attention to the evaluation of the strain properties characterizing the nonlinear behaviour of the strut. Having in mind the importance of in-plane damage limitations for masonry infills, performance levels for infilled RC frames can be defined as a function of increasing masonry infill damage in terms of values of strains in the equivalent strut and related inter-storey frame drifts.

Keywords: Masonry infills, RC frames, in-plane seismic response, experimental results, damage limit states INTRODUCTION The in-plane behaviour of masonry infilled RC frames has been a topic of interest in many experimental investigations, addressing a wide range of important issues. Experimental studies focused on the behaviour of masonry infilled RC frames are frequently carried out by means of cyclic static tests on single-storey single-bay frame subassemblies, e.g. by Combescure et al. (1996), Mehrabi et al. (1996), Crisafulli (1997), Calvi & Bolognini (2001). Such testing technique may be the preferred solution in particular when the performance of the masonry infill itself is of primary interest rather than its influence on the structural system. In the case of extensive numerical studies, despite the fact that other more refined modelling techniques are available, a simple pin-ended single-strut model is often being adopted to



represent the masonry infill response, especially when the overall displacement behaviour is of primary interest rather than possible local effects. However, in order to ensure an appropriately realistic behaviour of the strut model, particular attention has to be devoted to the definition of the corresponding strut properties. This fact is additionally pronounced in the case when the main interest is not only focused on the structural frame response, but on the assessment of the masonry infill behaviour and the corresponding distribution of damage. A masonry infill strut model is commonly defined by an axial stress-strain (or force-displacement) hysteretic rule in the case of cyclic loading or the corresponding envelope in the case of monotonic loading, as well as assigned strength and stiffness properties, which are closely related to the evaluation of the equivalent strut width. Since a wide range of infill typologies is commonly being used and many sources of uncertainties related to material properties and construction techniques are playing an important role, the definition of a unique performance criterion is not a straightforward task. Focusing in first place on the response of masonry infills themselves, the objective of this study is to propose a general method for the interpretation of experimental results obtained from in-plane cyclic tests on infilled single-storey single-bay RC frames, in order to allow a consistent comparison of infill properties in terms of strength, stiffness and deformation capacity for various masonry typologies and to enable the simple implementation of available test data for numerical applications. In particular, the calibration of a simple single-strut infill model, which may subsequently be used for extensive nonlinear analyses, is envisaged, based on the comparison of experimental and numerical results for infilled and bare frames, with particular attention to the evaluation of strain values characterizing the nonlinear behaviour of the strut. Subsequently, corresponding damage limit states of single masonry infill panels based on increasing levels of damage are defined. In this work the method has been applied to three different types of masonry infills based on existing results from an experimental program carried out by Calvi & Bolognini (2001). INTERPRETATION OF IN-PLANE TEST RESULTS The loading for cyclic static in-plane experiments on single-storey, single-bay masonry infilled RC frame specimens is commonly introduced by means of a displacement-controlled loading history, during which nd levels of increasing top horizontal displacement are imposed, and commonly nc reverse cycles (nc=3 is a common choice) are performed for each target displacement. Experimental results describing the response of the test specimen to the induced loading are commonly displayed in terms of force-displacement curves for the entire displacement history, that is, for all loading cycles and all intensity levels. Due to the initial degradation of the specimen, the response at different loading cycles may significantly differ from cycle to cycle, in particular at higher levels of imposed displacement, and commonly stabilizes around the third cycle at a given target displacement. Therefore, the interpretation of such test results and the comparison of infill properties for different typologies based on overall maximum response envelopes in some cases may be misleading. Moreover, the determination of adequate force-displacement envelopes for numerical applications in general, and for the calibration of simple equivalent diagonal strut models in particular, is not a straightforward task when, for example, the structural response obtained from experimental investigations results in non-symmetric force-displacement curves or significant strength degradation occurs during reverse cyclic loading. The discrepancy between experimental findings and the need for simplicity in numerical applications may be tackled through a



simplified interpretation of experimental results based on an averaged force-displacement curve obtained from force-displacement curves determined for each loading cycle separately. In particular, in the case of masonry infilled RC frames an overall average capacity curve should be determined for both bare and infilled frames from available experimental data, as illustrated for a typical set of test results in Figure 1, Figure 2 and summarised as follows:

1. The experimentally obtained force-displacement response of the specimen should be displayed separately for each reverse cycle i = 1 ... nc, including all j = 1 ... nd displacement levels.

2. One force displacement curve Fi (dj), i = 1 ... nc, should be found for each cycle enveloping the response at all j = 1 ... nd displacements levels.

3. One average force displacement curve F (dj) should be found from the nc envelope curves for each cycle, such that its force amplitude, at any displacement dj, corresponds to the average of the force amplitudes from the envelopes for each cycle Fi (dj), i = 1 ... nc, at the same displacement dj; see Equation 1:

• ( ) ( ).F1F1∑=

=cn

iji

cj d

nd (1)

Clearly, the average values of force F (dj) have to be determined at displacements dj, available in all envelope curves corresponding to the single cycles Fi (dj), i = 1 ... nc.

4. One final average force displacement curve Fm (dj) should be found as the average of the positive and negative branches of the average force displacement curve F (dj), such that its force amplitude, at any displacement dj, corresponds to the average of the absolute values of force amplitudes F+(dj) and F-(dj), at the same displacement dj; see Equation 2:

• ( ) ( ) ( )[ ]{ }.FF21F jjjm dabsdd −+ += (2)

Figure 1: Typical bare frame response test results (nc= 3, nd= 4)



Figure 2: Typical infilled frame response test results (nc= 3, nd= 4)

An initial estimation of the corresponding average contribution of the masonry infill to the overall capacity can be determined subtracting the average force displacement curve of the bare frame from that of the infilled frame, as illustrated in Figure 3(a) and Figure 3(b), representing a starting point for the definition of strength and deformation properties of the equivalent diagonal strut through the calibration on a numerical model.

Figure 3: (a) Average capacity curves for bare and infilled frame (b) Average force

contribution of the masonry infill INFILL MODEL CALIBRATION AND DEFINITION OF DAMAGE LIMITS For the needs of this study, the numerical calibration based on experimental results has been implemented for a nonlinear structural model adopting the concentrated plasticity approach for RC structural elements and the simple equivalent diagonal strut model representing the masonry infill (Figure 4(a)). A more detailed discussion on the modelling strategy followed can be found in Morandi et al. (2010). An analogous procedure may however be applied in



the case of various modelling assumptions related to the representation of structural and non-structural elements. In particular, for the representation of the stress-strain relationship of the equivalent masonry strut several constitutive models are available. Examples can be found in the early findings by Klingner & Bertero (1976), or in the further developments by Crisafulli (1997) or, more recently, by Rodrigues et al. (2010). A general simplification of the strut behaviour for nonlinear static analyses is suggested by Fardis (2006). Herein, the axial strain-stress envelope proposed by Crisafulli (1997), as shown in Figure 4(b), has been used to model the capacity of the equivalent strut for the case of monotonic loading, representing suitably the experimentally obtained average infill contribution (see Figure 3(b)). Alternative constitutive laws, as summarised in Figure 4(b) or others, may however be implemented. Independently of the model that is being adopted, two important parameters can be associated to the extent of masonry infill damage, namely the axial strain (or displacement) corresponding to maximum axial stress (or force), with reference to the onset of slight damage, and the ultimate strain (or displacement), associated to the achievement of severe damage. The strength and stiffness properties of the masonry strut have been determined evaluating the ratio bw/dw, where bw is the equivalent strut width and dw is the diagonal length of the infill, based on the model proposed by Bertoldi et al. (1993), while the thickness of the strut tw has been assumed equal to the thickness of the infill. The elastic modulus of masonry Ewθ assigned to the inclined direction of the strut has been evaluated based on a common model for orthotropic elastic materials subjected to bi-axial tensile stresses.

Figure 4: (a) Single strut masonry infill model; (b) Stress-strain envelope after Crisafulli (1997), Klingner & Bertero (1976), Fardis (2006), Rodrigues et al.(2010)

The parameters required to define the stress-strain relationship that need to be determined through calibration are the peak axial stress fm’ and the corresponding strain εm’, as well as the ultimate strain εu. Above all when the calibrated model is to be used for numerical analyses in which the assessment of achieved damage in non-structural masonry elements is of primary interest, the strain parameters are of particular importance, since they can be directly related to the masonry infill deformation capacity. The axial strain ε = ∆ld/ld in a compressed diagonal strut of initial length ld for a single-bay single-storey frame structure can be expressed as a function of the inter-storey drift δ = dr/h, where dr is the inter-storey horizontal displacement, and the ratio of frame centreline span vs. frame height L/h, through a simple geometrical expression, given in Equation 3:



• .1

11,

2

2

⎟⎠⎞

⎜⎝⎛+

⎟⎠

⎞⎜⎝

⎛ −+−=⎟

⎠

⎞⎜⎝

⎛=

hL

hd

hL

hL

hd

f

r

rε (3)

Accordingly, as a first approximation the strain at maximum stress εm’ and the ultimate strain εu can be assumed equal to strain values corresponding, respectively, to the experimentally obtained displacement dm,exp’ at which the maximum horizontal force in the masonry infill Fw,h,exp is achieved, and the displacement du,exp upon which the masonry infill contribution vanishes (see Figure 3(b)). Similarly, an initial peak axial stress of the strut may be evaluated from the experimentally obtained average peak force in the masonry infill Fw,h,exp, as given by Equation 4, where θ represents the inclination of the strut:

• , ,exp' .cosθ

w hm

w w

Ff

t b= (4)

Following these initial assumptions a numerical model of both test specimens, the bare and the infilled frame, can be established in order to carry out a sequence of nonlinear static pushover analyses. Comparing the numerically obtained force-displacement curves to the previously determined average experimental response, provided a good agreement has been achieved for the bare frame model, a calibration of the initially assumed strength (fm’) and strain (εm’, εu) parameters assigned to the equivalent strut can be carried out on the infilled frame, performing a series of analyses adjusting the strut properties until an adequate match of experimental and numerical capacity curves is obtained. Based on the strain values and the corresponding inter-storey drifts of a single-storey single-bay infilled frame structure obtained from calibration, performance levels for a single masonry panel can be defined as a function of the strain in the equivalent strut or the corresponding inter-storey drift of the frame as summarised in Table 1, representing increasing levels of infill damage. Such classification of damage limits on a single masonry infill panels may be used for the definition of performance limit states for entire infilled RC frame buildings as discussed in Morandi et al. (2010). It is however essential to emphasise that the calibration of a numerical model and the corresponding definition of limit states always has to be carried out considering the actual propagation of damage during the experiment. Table 1: Performance levels for a single masonry infill Limit State Reference Strain Drift Description

Operational Point A '32

mA εεε =≤ ⎟⎠⎞

⎜⎝⎛=≤

hLf AA ,

32 εδδ

Damage Limitation Point B 'mBA εεεε =≤< ⎟

⎠⎞

⎜⎝⎛=≤<

hLf BBA ,εδδδ

Life Safety Point C uCB εεεε =≤< ⎟⎠⎞

⎜⎝⎛=≤<

hLf CCB ,εδδδ



APPLICATION TO DIFFERENT MASONRY INFILL TYPOLOGIES The proposed method has been applied to three different types of masonry infill tested by Calvi & Bolognini (2001). The experimental study consisted of a series of static cyclic tests on full-scale single-story, single-bay frame specimens with a height of 2.875 m and a span of 4.50 m, on traditional weak unreinforced masonry infills (Figure 5(a)) and lightly reinforced masonry infills representing improved solutions; specifically, one typology with reinforcement consisting of 2φ6 rebars in the bed joints every two courses at 50 cm, having a reinforcement area vs. vertical spacing ratio of As,in/sin = 0.113 mm2/mm (Figure 5(b)) and one with reinforcement consisting of meshes in the plaster on both sides of the infill connected with steel plates in the bed joints every two courses at 50 cm, having a reinforcement area vs. vertical spacing ration of As,ext/sext = 0.126 mm2/mm (Figure 5(c)).

Figure 5: (a) Unreinforced infill; (b) Reinforced infill - rebars in the bed joint;

(c) Reinforced infill - mesh in the plaster For both the bare and the infilled frames, test results taken into consideration herein, include nd = 3 increasing displacement levels imposed during nc = 3 reverse cycles, with exception of the specimen with mesh reinforcement in the plaster for which the last displacement level j = 3 is available only for cycle i = 1 and the missing points on the envelope curves for cycle i = 2 and i = 3 have been approximated based on the corresponding strength degradation for displacement levels j = 1 and j = 2. The evaluation of the average capacity curve for the bare frame specimen is illustrated in Figure 6.

Figure 6: Bare frame response test results (nc= 3, nd= 3)



The evaluation of the average capacity curves for the frame specimen with unreinforced, and both reinforced infill typologies is illustrated in Figure 7, Figure 8 and Figure 9. The related comparison of average experimental (Exp.) and numerical (Num.) capacity curves for bare and infilled frames for all considered infill types is shown in Figure 10. In the case of unreinforced infill (Figure 10(a)) and infill reinforced with rebars (Figure 10(b)), a good matching with the experimental results could be obtained and the adopted infill model based on the Crisafulli constitutive law has been found to represent adequately the infill action. For infills with mesh reinforcement (Figure 10(c)), the calibrated numerical model could capture the experimental results with lower accuracy at higher deformation demands, due to the residual resistance of the reinforced infill. The final strut properties evaluated through calibration are summarised in Table 2. The actual damage reported during the tests corresponds well to the performance levels defined by means of drift values evaluated through calibration.

Figure 7: Infilled frame response test results (nc= 3, nd= 3) – Unreinforced infill

Figure 8: Infilled frame response test results (nc= 3, nd= 3) – Rebars in the bed joint

Figure 9: Infilled frame response test results (nc= 3, nd= 3) – Mesh in the plaster



Figure 10: (a) Unreinforced infill, (b) Reinforced infill - rebars in the bed joint;

(c) Reinforced infill - mesh in the plaster; (d) Bare frame Table 2: Calibrated strength and displacement properties of the equivalent strut model

Infill fm ' [MPa] εm' εu Fw,h

[kN] δm ' [%]

δu [%]

Fw,h vs. d and δ [kN] [mm] [%]

Unreinforced 1150 0.0013 0.0045 108.7 0.287 0.993

Rebars in the bed joints 1400 0.0016 0.0045 132.4 0.353 0.993

Mesh in the plaster 1550 0.0022 0.0100 146.6 0.494 2.205

CONCLUSIONS A procedure for the interpretation of experimental results from cyclic static in-plane tests on single-story single-bay masonry infilled RC frames and the calibration of simple equivalent strut models has been proposed in this work and applied to three masonry infill typologies. The obtained results allow a simple comparison of strength and deformation properties of the considered types of infills, the application of the calibrated models for extensive numerical analyses and the numerical assessment of the infill damage based on the defined performance levels as a function of achieved strain or drift amplitudes.



In the case of improved infill solutions a strength increase of about 22% and 35% has been obtained for reinforced masonry infills with rebars and mesh reinforcement respectively, in comparison to the unreinforced typology. Furthermore, it can be noted that the relation of infill strength values for the reinforced infill typologies (Fw,h,ext/Fw,h,int = 1.11) is about equal to the quotient of corresponding reinforcement ratios ((As,ext/sext)/ (As,int/sint) = 1.12). Importantly, a significant improvement of the deformation capacity of the infills can be observed due to the presence of light reinforcement; in terms of drift at maximum strut force for infills reinforced with rebars in the bed joints an increase of 23% has been found, while due to the presence of mesh reinforcement this increase reaches 72%. The ultimate drift that can be sustained by the infill before failure is not influenced by the presence of rebars in the bed joints; it is however largely increased by the presence of mesh reinforcement in the plaster. The calibrated infill models are currently being used in a parametric nonlinear dynamic simulation of the seismic response of multi-storey infilled RC frame structures. REFERENCES Bertoldi, S.H., Decanini, L.D. and Gavarini, C.“Telai tamponati soggetti ad azione sismica, un modello semplificato: confronto sperimentale e numerico” (in Italian), Atti del VI convegno nazionale ANIDIS, 1993, Perugia, Italy. Calvi, G.M., Bolognini D.“Seismic response of RC frames infilled with weakly reinforced masonry panels”, Journal of Earthquake Engineering, 2001, Vol. 5, No. 2, pp 153–185. Combescure, D., Pires, F., Cerqueira, P., Pegon, P. “Test on masonry infilled RC frames and its numerical interpretation”, Proceedings of 11th World Conference on Earthquake Engineering, 1996, Acapulco, Mexico. Crisafulli, F.J. Seismic behaviour of reinforced concrete Structures with masonry infills, PhD Thesis, 1997, Department of Civil Engineering, University of Canterbury, New Zealand. Fardis, M.N. “Seismic design issues for masonry-infilled RC frames”, Proceedings of 1st European Conference on Earthquake Engineering and Seismology, 2006, Geneva, Switzerland Klingner, R.E., Bertero, V.V. Infilled frames in earthquake-resistant construction, Report No. EERC 76-32, 1976, University of California, Berkeley, USA. Mehrabi, A.B., Shing, P.B., Schuller, M.P., Noland, J.L. “Experimental evaluation of masonry-infilled RC frames”, Journal of Structural Engineering, 1996, Vol. 122, No. 3, pp 228-23. Morandi, P., Hak, S., Magenes, G., “Comportamento sismico delle tamponature in laterizio in telai in c.a.: definizione dei livelli prestazionali e calibrazione di un modello numerico” (in Italian), Atti del XIV convegno nazionale ANIDIS, 2011, Bari, Italy. Rodrigues, H., Varum, H. and Costa, A. “Simplified macro-model for infill masonry panels“, Journal of Earthquake Engineering, 2010, Vol. 14, No. 3, 390–416.

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INTERPRETATION OF IN-PLANE RESPONSE AND · PDF fileINTERPRETATION OF IN-PLANE RESPONSE AND DEFINITION OF DAMAGE LEVELS FOR MASONRY INFILLED RC FRAMES Hak, ... strut tw has been assumed