7th International Conference on Advances in Experimental Structural Engineering

Blind Prediction of a Three-Storey RC Frame Building with Masonry Infill Walls Alexander Kagermanov1, Paola Ceresa2 Scuola Universitaria di Studi Superiori, IUSS Pavia Piazza della Vittoria, 15, 27100, Pavia, Italy [email protected] 2 RED Risk Engineering + Design (formerly IUSS Pavia) Via Boezio, 10, 27100, Pavia, Italy [email protected] 1

Abstract. Results from the authors’ blind prediction of a recent shaking table test performed at the IZIIS´s Lab on a nearly full-scale RC frame building with masonry infills are presented. The specimen was subjected to ten unidirectional ground motions of increasing intensity, ranging from 0.05g to 1.2g. An overview of the experimental set up and testing procedure is presented. Details on the numerical model used for the blind prediction are provided. These include modeling of the RC members, infill panels (with and without openings), mass, damping and P-delta effects, among others. Finally, comparison is made between the experimental and predicted displacement time-histories, which were ranked second among ten international entries.

Keywords: blind prediction, infilled frame, reinforced concrete frame, nonlinear analysis.

295

DOI 10.7414/7aese.T2.109

Alexander Kagermanov, Paola Ceresa

1. INTRODUCTION The response of RC masonry infilled frames has been object of extensive analytical and experimental research due its complex behaviour and extended use in seismically prone regions. Blind predictions represent a unique opportunity to validate available methods and assess the state-of-the-art in nonlinear modelling techniques. In this context, a blind prediction contest was announced as part of the FRAMA2015 International Benchmark [Sigmund et al., 2015a], which consisted of dynamic testing of a threestorey reinforced concrete (RC) frame building with masonry infill walls. This international benckmark was part of the Croatian research project “Framed-Masonry Composites for Modelling and Standardization” (HrZZ Research Project No. I-2478-2014) and was supported by the Croatian Science Foundatin (HrZZ) and by the Faculty of Civil Engineering of the Josip Juraj Strossmayer University of Osijek. The participants of the FRAMA–2015 blind test contest were expected to submit, in a first phase, their numerical results based on the design data; then, in a second phase, their numerical results based on actual material and ground motion data recorded during the staking table test. In the present paper, second phase results submitted by the authors are discussed, which were ranked second among ten international entries.

2. THE FRAMA-2015 INTERNATIONAL BENCHMARK 2.1 PROPERTIES OF THE TEST STRUCTURE IN THE DESIGN PHASE The three-storey structure in Figure 1 was designed considering the constraints of the simulator earthquake environment of the Dynamic Testing Laboratory of the Institute of Earthquake Engineering and Engineering Seismology at Skopje, Macedonia. The test structure was constructed at 1:2.5 scale and was built as standard spatial RC frame structure, infilled with hollow clay masonry infill containg opening [Sigmund et al., 2015a]. A general overview of the test structure is given in Figure 2 ÷ Figure 4. The height of the building is 3600 mm above the shaking table. Floor slabs are 80 mm thick RC slabs monolithic with the girder. Rectangular cross-sections were designed for both columns and beams – 12cm ×16 cm – with the details shown in Figure 3. The main properties for the materials are summarised in Table 1. Hollow clay masonry units are cut from the standard units that are commonly used for non–load bearing masonry walls. From the standard units’ dimensions of 12 × 25 × 19 cm they are cut twice along the height and masonry unit for the model has dimensions 12 × 25 × 6 cm. The mortar joints are 10 mm thick and are constructed using a standard cement/lime/sand mortar in volume proportions of 1:1:5 and with target compressive strength of M5. The mortar joints are 10 mm thick and are fully mortared (for both horizontal and vertical joints). Furthmore, three sets of additional masses were placed on top of the slab at each floor (Figure 1). Each set contains four steel ingots with overall dimensions of 23.5 × 14 × 150 cm, with a weight of 4 kN each. The weights of the model are summarised in Table 2.

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Figure 1. Side views of the FRAMA-2015 model Table 1. Properties of the material

Material

Nominal Strength (MPa)

Young Modulus (MPa)

Concrete, C25/30 (at 28 days)

25

30500

Reinforcement, B500B

500

210000

Masonry unitis, M10

10

-

Mortarm, M5

5

-

Figure 2. General overview of the FRAMA-2015 test structure

Figure 3. Overview of the FRAMA-2015 model and typical cross-sections of columns and beams

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Table 2. Weights of the FRAMA model in the design phase [Sigmund et al., 2015a]

Weigth of model per element

Weigth (kN)

Weigth of the frame structure

74

Weigth of the masonry infill

33

Weigth of the foundation

47

Additional weights at the

1st

floor (12 ingots)

48

Additional weights at the

2nd

floor (12 ingots)

48

Additional weights at the roof

96

Total weight of the structure

346

The pre-test modelling (first phase) of the framed–masonry system was based on the data readily available to the structural designer. As a result, the participants had the opportunity to judge for themselves, the variations of the output that come from different numerical models used. The aim of this pre-test modelling was to test the constituent materials prior to construction of the physical models in order to provide data for numerical models calibration. These data were delivered to the competition participants on July 2015. 2.2 INPUT GROUND MOTIONS FOR THE DYNAMIC TESTS The test protocol included white–noise excitation, to identify the dynamic properties of the system, as well as historical earthquake record Herceg Novi, only N–S component recorded during the Montenegro 1979 earthquake. The dynamic tests were carried out on the shaking table in IZIIS’s Laboratory, whose main properties are summarised in Figure 5 [Sigmund et al., 2015e]. In all tests the model was fixed on the shaking table platform. Input motions were introduced to the shaking table in one direction, parallel with the longer side of the physical models. No vertical or rotational motions was introduced to the shaking table. The actual motion recorded on the shaking table platform and detailed photographic report were distributed to the contest participants. The ground motion record used for the dynamic test was recorded at the Herceg Novi station during the April 15th, 1979 Montenegro earthquake. The earthquake had a moment magnitude of 6.9 and a hypocentral depth of 12 km. To account for the fact that the structure is constructed at 1:2.5 scale, the record was scaled in time by reducing the duration by a factor 1/(√2.5). The record was base-line corrected and then scaled to match the different levels of peak ground acceleration (PGA) that were used as input signals for the dynamic test. Figure 6 [Sigmund et al., 2015a] shows the acceleration, velocity and displacement history for the combined record with a PGA of 0.1 g, 0.5 g and 1.0 g, while Figure 7 [Sigmund et al., 2015a] shows the acceleration spectra of the Montenegro record for a PGA of 0.5g. The design response spectra used for design in Eurocode 1998:2004 for Soil C, Type 1 and 5% damping is plotted in Figure 7 for 1:2.5 scaled structures with period shortened by a factor of 1/(√2.5). In the first phase the test structure was subjected to three tests with the nominal PGAs equal to 0.1, 0.5 and 1.0g. After each excitation, the test unit went through a period of free vibrations in order to establish the natural period of vibrations after each test run.

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Size 5.0 × 5.0 m Mass 330 kN Natural Frequency 48 Hz for maximum loading mass placed in the center of the table Material Pre-stressed Concrete Actuators Vertical: 4 × 222 kN Horizontal: 2 × 425 kN Maximum Model Mass 400 kN with a height of 6.0 m Maximum Acceleration Vertical: 0.50 g Horizontal: 0.70 g Maximum Displacement Vertical: ±0.050 m Horizontal: ±0.125 m Frequency Range 0 - 80Hz Maximum Overturning Moment 460 kNm Capacity of the Hydraulic System Static: 35 MPa Operating: 21 MPa Analog Control Servo Controlling Closed Loop System Figure 4. Technical and dynamic properties of the shaking table in IZIIS’s Laboratory [Sigmund et al., 2015e]

Figure 5. Target design input ground motion for the combined record with a PGA of 0.1 g, 0.5 g and 1.0 g

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Figure 6. Elastic response spectra with different viscous damping coefficients and EC8:2004 design response spectra compared with the input record with a PGA of 0.5 g

2.3 CONSTRUCTION OF THE TEST STRUCTURE The test structure was built from beginning of June till the end of July 2015 (Figure 8). The mock–up was cast in–situ in five distinct phases. First, the foundations were concreted and afterwards columns, beams and slabs at each floor in fazes two through four. Finally RC frames were filled with hollow clay masonry units. Concrete reinforcing steel, mortar and masonry samples were taken to characterize their mechanical behaviour [Sigmund et al., 2015g]. Two significant changes occurred in mock–up building and preparation for testing. Additional weight (steel ingots) at 3rd floor slab was reduced from originally 96 kN (Table 2) to 48 kN due to safety issues. Therefore, the total weight of the test structure is 298 kN. Second change with respect to the design phase was related to cutting of hollow clay masonry unit where are units cut from standard units that are commonly used for non–load bearing masonry walls. From the standard units’ dimensions of 12 × 25×19 cm they were twice cut along the height and masonry unit for the model had dimensions 12 × 25 × 6.5 cm. The compressive strength of concrete samples was determined using the procedure established on the EN 12390–3:2011 standard. The modulus of elasticity of concrete samples was determined using the procedure established on the EN 12390–13:2013 standard (Table 3). Table 3. Concrete properties – characteristic values

Compressive strength (MPa)

Modulus of elasticity (MPa)

1st storey

39.1

38839

2nd storey

42.8

38839

3rd storey

27.6

38839

Reinforcing steel bars of three different diameters were tested under tensile loading using the procedure established on the EN ISO 15630–1:2010 standard and the results obtained are summarised in Table 4.

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Table 4. Steel properties

Es (GPa)

fy (MPa)

fmax (MPa)

fu (MPa)

y (%)

max (%)

u (%)

Ø 4 mm

204.25

753.50

780.40

500

0.555

1.122

2.780

Ø 6 mm

188.12

563.50

588.92

350

0.499

2.378

5.988

Ø 8 mm

198.62

590.50

620.75

400

0.498

2.846

7.786

Rebar

Figure 7. General view of the mock-up with and without infill walls (on the left) and distribution of the ingots at the 3rd floor (on the right) [Sigmund et al., 2015f]

The flexural and compressive strength of mortar samples was determined using the procedure established in the EN 1015–11:2008 standard (Table 5). Table 5. Mortar properties – characteristic values of strength

Flexural test fmt (MPa)

Compressive test fm (MPa)

1st storey

2.5

9.1

2nd

storey

3.1

10.4

3rd storey

4.3

12.2

Specification of hollow–clay masonry units (hollow–clay brick, HC–B) was determined using procedure established in the EN 771–1:2011 and the compressive strength EN 772–1:2011 standard. The characteristic values of the compressive strength are summarised in Table 7. The compressive strength of masonry wallet samples was determined using the procedure established on the EN 1052–1:2004 standard (Table 8). The referent diagonal tensile strength of masonry wallet samples was determined using the procedure established on the American ASTM E519/E519M–10 standard (Table 9). Table 6. Compressive strength of masonry units – characteristic values

Structural element

Dimensions (mm)

HC-B1

250 × 120 × 65

HC-B2

250 × 120× 65

HC-B3

250 × 120 × 65

HC-B4

120 × 65 × 250

HC-B5

120 × 65 × 250

HC-B6

120 × 65 × 250

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Compressive test fum (MPa) Vertical Dir.

14.59

Horizontal Dir.

3.43

Alexander Kagermanov, Paola Ceresa

Table 7. Compressive strength and diagonal tensile strength of masonry wallets – characteristic value

Structural element W1

Dimensions (mm)

fm (MPa)

510 × 120 × 550

W2

510 × 120 × 550

W3

510 × 120 × 550

1.5

Structural element

Dimensions (mm)

W4

640 × 120 × 640

W5

640 × 120 × 640

W6

640 × 120 × 640

ft,d (MPa)

0.05

3. NUMERICAL MODELING 3.1 GENERAL CONSIDERATIONS The structure is symmetric in the out-of-plane direction, having the same distribution of infills and openings for both frame planes (A and B in Figure 3), as well as the same mass distribution in plan. Moreover, the structure is subjected to unidirectional earthquake loading, thus under ideal testing and structural response conditions no torsional modes should occur. However, due to the heterogeneity in the response of masonry, mass and stiffness eccentricities are likely to occur affecting strength distribution in the inelastic range because of non-uniform infill damage. These effects can become important for weak frame–strong infill systems, where a significant portion of the base shear is carried by the infill panels. However, this did not seem to be the case of the present structure. Moreover, the diaphragm action of the slabs should preclude any type of out-of-phase motion between the two parallel frames. Based on the above considerations, the structure was idealized as a two-dimensional frame with beams and columns modeled with 1D elements. For masonry, typically two modeling approaches are possible: (i) a micro-modeling and (ii) a macro-modeling approach. The level of refinement and associated computational cost of the micro-modeling approach was deemed unnecessary. Moreover, this approach requires careful calibration of several constitutive model parameters, which can significantly influence numerical stability and accuracy. Hence, the macro-modeling approach with equivalent diagonal struts was adopted (Figure 8) [Kagermanov and Ceresa, 2017]. Analysis was performed using the program IDEEA2D [Kagermanov and Elnashai, 2012] for nonlinear static and dynamic analysis of reinforced concrete framed structures. The program uses inelastic displacement-based elements combined with a fiber-section discretization approach. Geometric and material nonlinearities are fully taken into account based on the co-rotational formulation and cyclic constitutive models. For reinforcing steel, the Menegotto-Pinto [1973] hysteretic rule is used, which assumes an elasto-plastic behavior prior to first unloading and the Bauschinger effect in subsequent cycles upon load reversal. For concrete, the Mander et al. [1988] model enhanced by Martinez-Rueda and Elnashai [1998] was used, which accounts for lateral confinement effects, plastic deformations, and strength and stiffness degradation of concrete in compression with the number of cycles. The method for solving the dynamic system of equations was the average acceleration Newmark method (γ=0.25, β=0.5) combined with the standard Newton-Raphson iterative scheme.

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Figure 8. Frame model for global analysis (axis units in meters).

3.2 MATERIALS The material properties for concrete and steel are summarized in Table 8. Those parameters not directly available from the test data were estimated from available equations or as suggested in the literature. For instance, the confinement factor for the columns was estimated as 1.3 based on the cross-section geometry and reinforcement layout [Mander et al., 1988]. For the beams, the effect of transverse confinement was neglected. Although the compressive strength of concrete varied between storeys (see Table 3), an intermediate value between the 1st and 2nd storey of 40MPa was assumed for simplicity. Table 8. Material properties considering the material models in Figure 10.

Steel

Concrete

Young Modulus Es(MPa)

200000

Tangent Modulus Ec(MPa)

38839

Yield Strength fy (MPa)

(see Table 4)

Compressive Strength fc(MPa)

40

Strain hardening b

0.005

Peak strain εo

0.002

Ultimate strain εu

(see Table 4)

Tensile strength fct (MPa)

3

Baushinger Parameters R0, a1, a2

20, 18.5, 0.15

Confinement factor k

1.3

Figure 9. Material models for concrete (left) and steel (right).

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For masonry, the material properties available from the test data (Table 5 ÷ Table 7) were used to define the equivalent diagonal struts, as explained in the corresponding section. 3.3 BEAMS, COLUMNS AND JOINTS As mentioned before, explicit modeling of slabs was neglected, assuming they present sufficient in-plane stiffness thus precluding any torsional modes of the structure. However, their contribution to the yield moment of the beams is not negligible. This was taken into account by means of an effective flange width of the T-beams, which was assumed to be the beam width plus 7% of the clear span of the beam on either side of the web [Fardis, 1994]. The cross sections of the beams and columns were discretized into 10 layers (Figure 10). Reinforcement was defined following the actual position and amount of steel, as described in the construction drawings, indicated as single dots in Figure 10.

Figure 10. Column and beam cross-section (axes units in meters).

Beams and columns were defined following the centerline of the members, with flexural fiber-based frame elements. The members were well reinforced in shear, hence no attempt was made to model flexure-shear interaction. Detailed modelling of the joint regions was neglected. Beams and columns were directly extended into the joint region, thus providing some joint flexibility in order to take into account possible rebar slippage. Since displacement-based elements are used in the numerical model, several elements have to be used in the plastic hinge regions for sufficient accuracy. In the present case, each member was discretized into five elements: 2×160mm long elements in the end regions, and a remaining central element (Figure 11). Ground-floor column elements were extended into the beam foundation until the centreline intersection, to account for strain penetration effects, and fixed at the base since the actual specimen was also “rigidly” anchored to the shaking table.

Figure 11. Member and cross-section discretization for beams and columns.

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3.4 MASONRY STRUTS Masonry was modelled with equivalent diagonal struts (compression only) with a bilinear hysteretic curve based on [Decanini et al., 2004] (Figure 12), which is summarized herein. The following parameters are needed to define the hysteretic curve: the width of the equivalent strut, ω, the lateral stiffness at complete cracking stage, Km, the lateral strength, H, and a reduction factor, ρ, which accounts for the presence of openings.

Figure 12. Definition of equivalent masonry struts.

The width of the strut, ω, is defined as a function of the relative stiffness parameter λh proposed by [Stafford-Smith, 1966] and two constants, K1 and K2, calibrated from experimental tests [Decanini et al., 2004]:  K1  K  d 2   h 

(1)

 

where d is the length of the equivalent strut, and the parameter λh is defined as [Stafford-Smith, 1966]: h  4

E m e sen(2 ) h 4 Ec Ihm

(2)

where Em is the elastic equivalent modulus of the masonry panel at complete cracking stage, Ec the elastic modulus of concrete, θ is the strut inclination, e is the thickness of the masonry panel, h the storey height, hm the height of the masonry panel and I the moment of inertia of the columns. The constants K1 and K2 are given in Table 11 as a function λh [Decanini et al., 2004]. Table 9. Parameters for masonry

K1

K2

λh≤3.14

1.3

-0.178

3.14<λh≤7.85

0.707

0.01

λh>7.85

0.47

0.04

The lateral stiffness of the equivalent strut at complete cracking stage is given as: Km 

Em e  cos 2  d

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(3)

Alexander Kagermanov, Paola Ceresa

The lateral strength of the panel is given as a function of the equivalent compressive stress σbr, which depends on the mode of failure of the infill panel: (i) diagonal tension, (ii) sliding shear along horizontal bed joints, (iii) panel crushing in the frame corners, and (iv) diagonal compression. The corresponding values of σbr are summarized below: Diagonal tension:  br (1) 

0.6 mo  0.3 o K1

h

(4)

 K2

Sliding shear along horizontal bed joints:  br ( 2) 

(1.2 sin   0.45 cos  )u  0.3 o K1

(5)

 K2 h

Crushing in the frame corners:  br (3) 

1.12 sin  cos  mo K 1 (h) 0.12  K 2 (h) 0.88

(6)

Diagonal compression:  br ( 4) 

1.16 mo tan  K1  K 2  h

(7)

where σmo is the vertical compression strength of the panels, τmo is the shear strength from the diagonal compression test, u is the sliding resistance of the joints from the triple test, and σo is the vertical stress due to working loads. The above expressions were used to evaluate the strength of the infill panel based on the mean values for σmo and τmo obtained from material tests prior to the shaking-table test. The sliding resistance was not directly available, hence it was estimated based on the Mohr-Coulomb criterion as: u   o   o

(8)

where τo is the cohesive stress and μ the friction coefficient. Typical ranges for τo and μ are 0.1< τo <1.5 MPa and 0.3< μ <1.2 [Kwon and Kim, 2010]. The working loads σo are negligible since the construction of the infills took place after the placement of the steel ingots on the bare frame structure. Hence, the friction contribution to shear sliding is neglected. For the cohesive stress the following is adopted τo =0.04 σmo MPa [Paulay and Priestley, 1992; Kwon and Kim, 2010]. Table 10. Adopted masonry strength values

Stress

(MPa)

σmo

1.5

τmo

0.05

U

0.06

σo

0

The dominant failure mode was diagonal tension, mainly due to the low value of τmo. Table 11 summarizes the equivalent properties of the masonry struts for the panels without consideration of openings, where K, F and dres have the same meaning as Km, H and δres in Figure 13 but in the axial direction of the strut. This

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causes tensile and compressive forces in the leeward and windward columns, respectively, which in turn affects their moment capacity, captured through the fiber-section approach. Table 11. Masonry strut values

Panel(cm2)

K(kN/m)

F(kN)

dres(mm)

112×104 (1st bay)

59529

5.5

3.15

67960

9.2

4.65

232×104

(2nd

bay)

3.5 MASONRY OPENINGS Upon literature review, a significant variation was found in terms of strength and stiffness reduction factors accounting for the effect of openings in the infill panel [Anil and Antin, 2007; Imai, 1989; Mondal and Jain, 2008; Decanini, 2004]. These reduction coefficients depend on several parameters such as type of frame (steel or reinforced concrete), type of masonry (brick, lightweight concrete, confined masonry, etc…), whether the opening is reinforced, partially reinforced or non-reinforced, and the scale of the experiment, among others. Due to these complexities and the assumption that the influence of openings would be limited to the undamaged stage of the panels, the presence of openings was neglected in the final numerical model. 3.6 GRAVITY LOADS, MASS, P-DELTA AND DAMPING Masses due to the infills, steel ingots and the slab (the portion that was not part of the beam flange) were distributed based on the tributary areas and lumped at the beam column joints. Since only one of the two parallel frames is modeled, only half of the total mass is considered. Thus, the total lumped mass at the first, second and third storey was 2, 6 and 4 tons, respectively. Masses due to the self-weight of beams and columns (25kN/m3) were distributed along the elements using the consistent mass matrix. A modal damping model, with a 5% damping ratio in each mode, was used. This type of damping model minimizes spurios damping moments in the plastic hinge regions [Chopra and McKenna, 2016]. Gravity loads were defined at the beam-column joints in order to consider axial load effects on the flexural response of the columns, as well as P-delta. 3.7 PRELIMINARY RESPONSE ASSESSMENT The following figures include some of the numerical results corresponding to: (i) horizontal top displacement, (ii) maximum Inter-storey-DRift (IDR) and displacement profile at maximum top displacement, and (iii) hysteretic curves for masonry struts. The structure was subjected to increasing levels of PGA, from 0.05g to 1.2g. At PGA=0.05g, the maximum displacement was 0.2mm, which is barely recognizable in Figure 13. The displacement increased almost linearly with the PGA. At a PGA of 1.2g, the maximum horizontal displacement was about 40mm, with a displacement profile close to linear. The maximum IDR reached 1.5% at the 2nd storey, while for the 1st and top storeys it was about 1%.

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Figure 13. Horizontal top displacement, maximum IDR and maximum displacement profile.

The response of two selected masonry struts are shown below. These correspond to the first storey, left and right bay, respectively. It can be observed that full collapse was reached by the end of the analysis, with zero residual capacity. The same situation also happened with the panels at the 2nd and 3rd storeys. This suggests that the frame behaviour was close to the bare-frame response when approching collapse.

Figure 14. Hysteretic curves for some masonry struts.

3.8 BLIND PREDICTION A total of ten international entries were submitted to the contest, mostly from European universities but also from oversees and industry. The participants were asked to provide the horizontal displacement time histories at each storey. The participants were classified based on the error between estimated displacements and measured displacements. The first equation for calculating errors is given by the sum of the root mean square errors (RMS) as [Sigmund et al., 2015g]: errorRMS 

1 N

N

 i 1

( DxInum,i  DxI exp,i )2 

1 N

N



( DxIInum,i  DxII exp,i )2 

i 1

1 N

N

( D

xIIInum,i

 DxIII exp,i )2

(9)

i 1

where N is the number of sampling points, and DxI, DxII and DxIII are the horizontal displacements at levels I, II and III. It was noted that errorRMS can provide unrealistic results when the response is close to or equal to zero. To avoid this problem, there is an additional term that takes into account the area under the response curve, relative to the experimental response, as shown in the following equation [Sigmund et al., 2015g]:

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t

t



( DxI exp,i dt  errorE 

0



t



0 t

t





( DxI exp,i dt  DxInum,i dt) 0

t



( DxII exp,i dt 

DxInum,i dt)2

0

0



t



0 t

t





( DxII exp,i dt  DxIInum,i dt) 0

0

t



( DxIII exp,i dt 

DxIInum,i dt)2

0

D

xIIInum,i

dt )2

(10)

0 t

t





( DxIII exp,i dt  DxIIInum,i dt) 0

0

In order to take into account the differences in the response amplitudes and the associated area under the response curves, overall error was expressed as: (11)

errorE  RMS  errorRMS  errorE

The indicator errorE−RMS showed the best agreement with a visual comparison of the dynamic response, hence it was used for the ranking of participants [Sigmund et al., 2015g].

80 70 60 50 40 30 20 10 0

Numerical Experimental

error E

Top displacement (mm)

The next figures show the maximum horizontal top displacements and the estimates of the three error measures mentioned before. Generally speaking, it can be said that the best agreement was at intermediate PGA levels, between 0.2g-0.8g. The error measure “errorE” always increases since it squares the difference between displacements, which become larger with increasing intensity. Hence it does not quantify the relative improvement in accuracy, nor even among the different storeys. “errorRMS” shows a better performance since the difference between displacements is normalized by the area under the displacement time-history.

0

0.2

0.4

0.6

PGA(g)

0.8

1

9 8 7 6 5 4 3 2 1 0

1st storey 2nd storey 3rd storey

0

1.2

0.2

0.4

0.6

0.8

1

1.2

PGA(g)

10 9 8 7 6 5 4 3 2 1 0

12

1st storey 2nd storey 3rd storey

1st storey 2nd storey 3rd storey

10

errorE-RMS

errorRMS

Figure 15. Comparison of maximum top displacements and the error measure “errorE”.

8 6 4 2

0

0.2

0.4

0.6

0.8

1

0

1.2

0

PGA(g)

0.2

0.4

0.6

0.8

1

1.2

PGA(g)

Figure 16. Comparison of error measures “errorRMS” and “errorE-RMS”.

In the figures below the horizontal displacement time-histories at each storey are reported. Only results for PGA=0.05g, 0.6g and 1.2g are presented because of space limitations, and because they are sufficiently representative of the overall accuracy of the prediction.

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The agreement at 0.05g is very low, with the experimental displacements being significantly underestimated. The reason for this could be minor pre-cracking of the structure, possibly due to shrinkage or loading during transportation. In any case, note that displacements at this PGA level were very low, less than 0.2mm. It is also known that fiber-models use an initial un-cracked stiffness, hence a possible improvement could be to impose low-amplitude cycles prior to the analysis in order to simulate pre-cracking. As mentioned before, the best agreement with the experimental data was at intermediate PGA levels. Results for PGA=0.6g (Figure 18) show very good agreement in terms of frequency content, peak response and its time occurrence. The predicted peak displacement at the 1st storey was about 6mm vs. 13mm in the experiment, at the 2nd level 16mm vs. 15mm, and at the 3rd level 22mm vs. 18mm, respectively. For all ground motions the best agreement was at the 2nd and 3rd storeys, whereas 1st storey displacements were underestimated. Finally, results at PGA=1.2g are reported in Figure 19. Significant damage to the infills and RC members occurred at this level. The maximum top displacement reached 70mm, and important period elongation was observed. The prediction at this stage was not as accurate, with important underestimation of the experimental displacements, especially at the 1st storey. In the experiment, a soft-storey mechanism was triggered at the ground level, with a maximum IDR of about 3%. However, in the analysis the displacement profile was approximately linear, and the maximum IDR occurred at the 2nd storey with 1.5% (Figure 13).

Figure 17. Relative displacements at PGA=0.05g.

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Blind Prediction of a Three-Storey RC Frame Building with Masonry Infill Walls

Figure 18. Relative displacements at PGA=0.6g.

Several causes can be attributed to the above mentioned discrepancies, mostly related to the inability of the numerical model to fully capture the inelastic response. For instance, neglecting the presence of infill openings and the simplified single-strut representation might have affected the response in the plastichinge regions of the RC members. Also loss of mass due out of plane projection of masonry, which was about 30% of the total building mass, and torsional modes due to strength/mass eccentricity and diaphragm damage, could have contributed. These should be verified once additional experimental data on damage distribution becomes available. Damping is another source of uncertainty. From visually comparing the displacement decay, it seems that excessive damping was present in the numerical response. A value of 5% viscous damping seems to be excessive considering that hysteretic damping was explicitly modelled in the nonlinear response of RC members and masonry struts. Table 12 summarizes the final ranking of the blind-prediction. The presented results were ranked 2nd among ten international entries.

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Figure 19. Relative displacements at PGA=1.2g Table 12. Blind-prediction ranking.

Rank

Team Name

Team Country

errorE-RMS

1st

Pol. Inst. Of Leira and Univ. of Porto

Portugal

102.79

2nd

UME School Pavia

Italy

110.65

3rd

IUSS Pavia, EUCENTRE

Italy

140.71

4th

University of Minho

Portugal

181.48

5th

Bauhaus-Universität Weimar

Germany

226.11

6th

262.31

Istanbul Technical University

Turkey

7th

RWTH Aachen Universität

Germany

288.26

8th

Nihon University

Japan

376.75

9th

Seismosoft, SRL

Italy

836.45

10th

John A. Blume, Stanford University

USA

3549686

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Blind Prediction of a Three-Storey RC Frame Building with Masonry Infill Walls

4. CONCLUSIONS Results from the presented blind-prediction indicate relatively good agreement with the experimental data, at least in terms of global response parameters, using a simple two-dimensional model with beam-column elements and equivalent diagonal struts. The best agreement was obtained at intermediate ground motion intensity levels, between 0.2g-0.8g, and at the top storey. Several modelling aspects could be improved for better accuracy, such as more refined models for masonry infills, modelling of panel openings (which were not taken into account) and damping. Further investigation should address the comparison with the observed failure modes, the progression of damage during the sequence of ground shaking and floor accelerations and base shear, among others. At the present time, part of the experimental data is being post-processed, and therefore was not available to the authors during the preparation of the manuscript.

REFERENCES Anil Ö and Altin S (2007), “An Experimental Study on Reinforced Concrete Partially Infilled Frames”, Engineering Structures, Vol. 29, No. 3, pp. 449-460. Chopra, A. K., McKenna, F., [2016] “Modeling viscous damping in nonlinear response history analysis of buildings for earthquake excitation” Earthquake Engng. Struct. Dyn. Vol. 45, No. 193-211. Decanini, L., Liberatore, L., Mollaioli, F. [2004] “Strength and stiffness reduction factors for infilled frames with openings” Earthq. Eng. Eng. Vib. Vol. 13, No. 3, pp. 437-454 Decanini, L., Mollaioli, F., Mura, A., Saragoni, R. [2004] “Seismic performance of masonry infilled RC frames” 13th World Conference on Earthquake Engineering, Vancouver, Canada Fardis, M.N. [1994] "Analysis and design of reinforced concrete buildings according to Eurocode 2 and 8”, Configuration 3, 5 and 6, Reports on Prenormative Research in Support of Eurocode8. Imai H (1989), “Seismic Behavior of Reinforced Masonry Walls with Small Opening”, Proceedings of 5° Jornadas Chilenas de Sismología e Ingeniería Antisísmica, 2, Santiago, Chile, Kagermanov, A, Elnashai, A.S. [2012] “IDEEA3D: inelastic dynamic analysis for earthquake engineering applications”. https://sites.google.com/site/ideeanalysis/. Kagermanov, A, Ceresa, P. [2017] “Modelling Flexure-Shear Failures in Masonry-Infilled RC frames with Inelastic Fiber-based Frame Elements” Proceedings of COMPDYN 2017 and 6th ECCOMAS Thematic Conference of Compuational Methods in Structural Dynamics and Earthquake Engineering, Rodhes I, June 15-17, Greece. Kwon, O., Kim, E. [2010] “Case study: Analytical investigation on the failure of a two-story RC building damaged during the 2007 Pisco-Chincha earthquake” Engineering Structures, Volume 32, Issue 7. Mander, J. B., Priestley, M. J. N., Park, R. [1988] “Theoretical stress–strain model for confined concrete”. J Struct Eng Vol. 114, No. 8, pp. 1804-1826 Martinez-Rueda, J. E., Elnashai, A. S. [1997] "Confined concrete model under cyclic load”, Materials and Stmctures Vol. 30, No. 197, pp. 139-147.

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Menegotto, M., Pinto, P. E. [1973] “Method of analysis of cyclically loaded reinforced concrete plane frames including changes in geometry and non-elastic behavior of elements under combined normal force and bending.” IABSE symposium, resistance and ultimate deformability of structures acted on by welldefined repeated loads, IABSE, Zurich, Switzerland Mondal, G., and Jain, S. K. (2008), “Lateral Stiffness of Masonry Infilled Reinforced Concrete (RC) Frames with Central Openings”, Earthquake Spectra, Vol. 24, No. 3, pp. 701-723 Paulay, T., Pristley, M. J. N. [1992] Seismic design of reinforced concrete and masonry buildings, Wiley, New York, pp. 744. Sigmund, V., Guljas, I., Markulak, D., Varevac, D., Brana, P., Bosnjak-Klecina, M., Zovkic, J., Penava, D., Matosevic, D., Kalman-Sipos, T., Grubisic, M., Gazic, G., Galic, M., Kraus, I., Kozoman, E., Dzakic, D., [2015a] “FRAmed–MAsonry — FRAMA–2015 Design Report — version 1.0”, HrZZ Research Project IP–11–2013– 3013, Faculty of Civil Enginering, University of Osijek, Croatia. Sigmund, V., Guljas, I., Markulak, D., Varevac, D., Brana, P., Bosnjak-Klecina, M., Zovkic, J., Penava, D., Matosevic, D., Kalman-Sipos, T., Grubisic, M., Gazic, G., Galic, M., Kraus, I., Kozoman, E., Dzakic, D., [2015b] “FRAmed–MAsonry — FRAMA–2015— Construction Drawings”, HrZZ Research Project IP–11–2013– 3013, Faculty of Civil Enginering, University of Osijek, Croatia. Sigmund, V., Guljas, I., Markulak, D., Varevac, D., Brana, P., Bosnjak-Klecina, M., Zovkic, J., Penava, D., Matosevic, D., Kalman-Sipos, T., Grubisic, M., Gazic, G., Galic, M., Kraus, I., Kozoman, E., Dzakic, D., [2015c] “FRAmed–MAsonry — FRAMA–2015— Reinforcement Drawings”, HrZZ Research Project IP–11–2013– 3013, Faculty of Civil Enginering, University of Osijek, Croatia. Sigmund, V., Guljas, I., Markulak, D., Varevac, D., Brana, P., Bosnjak-Klecina, M., Zovkic, J., Penava, D., Matosevic, D., Kalman-Sipos, T., Grubisic, M., Gazic, G., Galic, M., Kraus, I., Kozoman, E., Dzakic, D., [2015d] “FRAmed–MAsonry — FRAMA–2015— Ingot Drawings”, HrZZ Research Project IP–11–2013–3013, Faculty of Civil Enginering, University of Osijek, Croatia. Sigmund, V., Guljas, I., Markulak, D., Varevac, D., Brana, P., Bosnjak-Klecina, M., Zovkic, J., Penava, D., Matosevic, D., Kalman-Sipos, T., Grubisic, M., Gazic, G., Galic, M., Kraus, I., Kozoman, E., Dzakic, D., [2015e] “FRAmed–MAsonry — FRAMA–2015— Shaking table properties”, HrZZ Research Project IP–11–2013– 3013, Faculty of Civil Enginering, University of Osijek, Croatia. Sigmund, V., Guljas, I., Markulak, D., Varevac, D., Brana, P., Bosnjak-Klecina, M., Zovkic, J., Penava, D., Matosevic, D., Kalman-Sipos, T., Grubisic, M., Gazic, G., Galic, M., Kraus, I., Kozoman, E., Dzakic, D., [2015f] “FRAmed–MAsonry — FRAMA–2015— Material Data and Construction Report Test”, HrZZ Research Project IP–11–2013–3013, Faculty of Civil Enginering, University of Osijek, Croatia. Sigmund, V., Guljas, I., Markulak, D., Varevac, D., Brana, P., Bosnjak-Klecina, M., Zovkic, J., Penava, D., Matosevic, D., Kalman-Sipos, T., Grubisic, M., Gazic, G., Galic, M., Kraus, I., Kozoman, E., Dzakic, D., [2015g] “FRAmed–MAsonry — FRAMA–2015 Final Report — Rankings & Winner Announcement”, HrZZ Research Project IP–11–2013–3013, Faculty of Civil Enginering, University of Osijek, Croatia. Stafford-Smith, B. [1966] “Behavior of square infilled frames” J. Struct. Div., Vol. 92, No. 1, pp. 381-403.

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