SHAKE TABLE TESTING AND ANALYTICAL MODELING OF FULLY ... · 3 PhD, Martini, Mascarin and George Chair in Masonry Design, McMaster University, Civil Engineering Department, [email protected]

15th International Brick and Block Masonry Conference

Florianópolis – Brazil – 2012

SHAKE TABLE TESTING AND ANALYTICAL MODELING OF FULLY-GROUTED REINFORCED CONCRETE BLOCK MASONRY

SHEAR WALLS

Mojiri, Saeid1; Tait, Michael J.2; and El-Dakhakhni, Wael W.3 1MSc, Graduate student, McMaster University, Civil Engineering Department, [email protected]

2 PhD, Joe NG/JNE Consulting Chair in Design, Construction and Management in Infrastructure Renewal, McMaster University, Civil Engineering Department, [email protected]

3 PhD, Martini, Mascarin and George Chair in Masonry Design, McMaster University, Civil Engineering Department, [email protected]

Abstract This paper presents the details of a proposed shake table experimental program for investigation of seismic performance of reduced-scale fully-grouted reinforced concrete block shear walls. It describes the steps taken to date in terms of preparation of model wall specimens, test setup and selection of the model earthquake records. A preliminary analytical model is also proposed for estimation of seismic response of the walls and selected preliminary results including dynamic properties, lateral deformation, absorbed and dissipated energy, and ductility prediction based on nonlinear time history analysis utilizing the proposed analytical models are discussed. Keywords: Analytical models, Reinforced masonry, Seismic performance, Shake table testing, INTRODUCTION Current international seismic codes are essentially prescriptive which means they are based on a set of prescriptions for building design that should result in buildings attaining specific performance levels (e.g. life safety), during earthquakes. However, with the knowledge gained from large earthquakes events worldwide, it is safe to say that the exact performance of buildings under actual earthquakes is largely unknown. This is attributed to the inherent uncertainties in the level of ground shaking, material and structural behavior, which can vary significantly between structures designed to the same prescriptive code requirements to meet the same target performance levels. These uncertainties also lead to a non-uniform risk of failure for structures that are assumed to be identical, which is philosophically in contrast to the uniform seismic hazard approach adopted by the majority modern seismic codes. The uncertainties regarding the actual performance of structures designed based on prescriptive codes makes it very difficult to estimate the probable performance of these structures and thereby providing probabilistic estimation of economical losses and casualties in future earthquakes. The importance of these issues was further realized by the engineering research community after major seismic events like Northridge, California (1994) and Kobe, Japan (1995) when structures did achieve the life safety performance level but the economical



losses due to the damage to the contents in the structures as well as the downtime of the damaged structures was unacceptable to stakeholders. This situation has led to the development of performance based seismic design (PBSD) philosophy to be capable of providing design methodologies and criteria that will result in resilient performance, within certain confidence intervals, under different design earthquakes, and thereby providing uniform-risk designs. PBSD guidelines in the USA are still under development and its final goal, as outlined by Hamburger et al. (2008) and set in the ATC-58 (2011) document, is to provide design tools and probabilistic models to quantify the seismic performance of existing and new buildings in terms of economical losses and casualties that can be communicated to insurance companies and other stakeholders. Adoption of PBSD principles requires a conceptual change, in fact a paradigm shift, in the current seismic design philosophy, a more in-depth understanding of the actual seismic behavior of both structural components and systems from a performance-based point of view, and the development of analytical models to predict more accurately the seismic behavior of different structures in terms of the different structural performance indicators. A common type of construction in urban areas for low-rise buildings is masonry construction. In terms of the potential damage due to earthquake, there is a misconception that masonry structures, even when reinforced, do not have much ductility and are particularly vulnerable to seismic hazards. This situation has resulted from catastrophic failures of non-engineered unreinforced masonry buildings during recent earthquakes. Nevertheless, experimental research has shown that incorporation of reinforcement can greatly improve the seismic performance of well-designed masonry buildings in terms of displacement and ductility capacity, the energy dissipation capabilities, and the stability of the nonlinear response during seismic events. As a result, reinforced masonry (RM) construction can be shown to be a cost-effective alternative Seismic Force Resisting System (SFRS) compared to other construction systems (Paulay and Priestley, 1992, Drysdale and Hamid, 2005). Adoption of PBSD provisions in seismic codes requires a comprehensive in-depth understanding of the strength and displacement capacities of different structural components and systems, including RM. In fact, this understanding is even more critical in the case of RM construction due to its inherent complex non-homogenous behavior. In this regard, investigation of the seismic performance of masonry shear walls as isolated components can facilitate a better understanding of the seismic performance of the whole building (system). This understanding can be obtained by performing quasi-static and shake table lateral tests on masonry shear walls (FEMA461, 2007). Experimental research work employing similar test methods can be found in several documents (e.g. Seible et al., 1994 and Jo, 2010). Similar to other international codes, the current Canadian masonry design code (CSA-S304.1, 2004) has certain design prescriptions regarding reinforcement ratio, vertical and horizontal bar spacing, masonry strain limits, and aspect ratio for design of RM shear walls with limited and moderate ductility. However the use of these walls in areas of moderate and high seismicity is penalized by the National Building Code of Canada (NBCC 2010) because of their perceived limited ductility for such walls compared to other SFRS. This policy leads to increased seismic design demands of RM and makes their construction less economical compared to other types of SFRS (e.g. reinforced concrete).



Research on RM shear walls that do not conform to the minimum prescriptive code provisions has shown significantly more ductility than what is currently specified in the NBCC (2010). Experimental tests on full- and reduced-scale RM shear walls has demonstrated their exceptional seismic performance in terms of strength, hysteretic energy dissipation, and ductility (Shedid et al., 2008, Shedid et al., 2010, Long 2006, and Wierzbicki, 2010). EXPERIMENTAL PROGRAM As a next step towards investigating the seismic performance of RM shear walls, it is planed to perform shake table tests on third-scale fully-grouted reinforced concrete block masonry shear walls. It is aimed to investigate the effect of aspect ratio, reinforcement ratio, axial load, wall length, and vertical reinforcement spacing on the seismic performance of the walls in terms of ductility, displacement capacity, residual drift, energy absorption and dissipation as well as stiffness degradation. The results of the study will draw a more realistic picture of the seismic response of RM shear walls. In addition, the data will be used to quantify relevant performance indicators for RM shear walls, generate fragility curves, and develop and calibrate simplified analytical structural models to predict the walls’ dynamic responses, which will eventually facilitate better understanding the seismic behavior of RM walls and establishment of necessary tools required for performance-based seismic design. This paper presents the steps taken to date towards the current research project in terms of construction of the model wall specimens and test setup and selection of the model earthquake records. Adopting a nonlinear time history analysis procedure utilizing the aforementioned analytical model resulted in preliminary predictions of the walls’ dynamic properties, lateral deformations, absorbed and dissipated energy levels, and ductility values. PROTOTYPE BUILDING The prototype buildings considered for the experimental program are single- and two-storey buildings with the same footprint. The plan of the prototype buildings consist of RM walls as the SFRS as well as two gravity load-designed columns to support a portion of the gravity loads which reduces the axial load on the RM walls. Figure 1 shows the plan of the prototype buildings. The numbers in the figure show the prototype shear walls considered for the experimental program. Based on approximate tributary areas, the axial load on the peripheral walls is 2% of the gross cross sectional ultimate axial resistance (0.02!!!!! ) and is 5% of the resistance of the gross section (0.05!!!!! ) for the central walls. SIMILITUDE REQUIREMENTS AND MODEL WALLS Due to the limitations in space and maximum payload of the shake table, reduced-scale models of prototype shear walls are considered for experimental testing. The scale factors obtained based on similitude considerations are presented in Table 1 where the length scale factor is defined as !! = !!"#$#$%!& !!"#$% and the modulus of elasticity scale factor is defined as !! = !!"#$#$%!& !!"#$%. The acceleration scale factor, !!, is unity. The true replica model in Table 1 satisfies all similitude requirements for inertial, gravitational, and restoring forces in a dynamic model as stated by Froude and Cauchy scaling requirements [Harris and Sabnis, 1999]. The prototype and model material characteristics are considered to be equivalent (!! = 1). To compensate for the difference in the mass density of the prototype and model material as required by similitude laws, extra mass is added to the model walls at the floor levels.



Table 1: Scale factors required for dynamic modeling

Scaled quantities Dimension True Replica model Scaled quantities Dimension True Replica

model

Force (F) Frequency (ω)

Acceleration (a) 1 Stress (σ) Gravitational acceleration (g) 1 Strain (ε) - 1

Velocity (V) Poisson ration (ν) - 1

Time (t) Modulus (E)

Length (L) Mass density (ρ)

Displacement (δ) Energy (E)

Figure 2 shows the elevation of the third-scale model walls with reinforcement details and their design parameters are given in Table 2. The design of model RM shear walls aimed at providing experimental data to investigate the effect of wall height, spacing of vertical reinforcement bars, axial stress, wall length, and vertical reinforcement ratio on the seismic performance of the walls.

Table 2: Design details of the prototype and the model walls

Wall P/M1 No. of Stories

Length (mm)

Asp. ratio

Vl. Reinf. !! (%)

2 !!3

(mm) Hor. Reinf. (First floor)

Axial stress

1 P 2 1,600 3.68 3#15 0.18 798 #10 @ 390 mm !.!"!!! M 598 3-d4* 0.2 266 W1.7 @ 130 mm

2 P 2 1,600 3.68 2#15 0.12 1596 #10 @ 390 mm !.!"!!! M 598 2-d4 0.13 532 W1.7 @ 130 mm

3 P 1 1,600 1.84 3#15 0.18 798 #10 @ 390 mm !.!"!!! M 598 3-d4 0.2 266 W1.7 @ 130 mm

4 P 2 2,600 2.54 3#15 0.12 1197 #10 @ 390 mm !.!"!!! M 865 3-d4 0.14 399 W1.7 @ 130 mm

5 P 2 1,600 3.68 2#25 0.29 1596 #10 @ 390 mm !.!"!!! M 598 2-d7** 0.24 532 W1.7 @ 130 mm

6 P 2 1,600 3.68 3#15 0.18 798 #10 @ 390 mm !.!"!!! M 598 3-d4 0.2 266 W1.7 @ 130 mm

1- Prototype or Model, 2- Longitudinal reinforcement ratio, 3- Longitudinal reinforcement spacing, *, * *d4: 26 mm2, d7: 45 mm2

F SESL2 T !1 SL

!1 2

LT !2 FL!2 SELT !2

LT !1 SL1 2

T SL!1 2 FL!2 SE

L SL FL!4T 2 SE SLL SL FL SESL

3

Figure 1: Plan of prototype buildings



Figure 3: Model walls under construction: a- Construction of the first half storey, b- Placement of vertical and horizontal reinforcement, c- The slab formwork

The walls are constructed using third-scale true replica of the standard 20 cm hollow concrete blocks, widely used in Canada and the USA. The maximum aggregate size used in the model mortar and grout is 1.25 mm and 2.5 mm respectively, which are the third-scale counterparts of what is used in common construction practice. Each wall is built on 200 mm deep reinforced concrete base, which will be used to anchor the wall on the shake table and act as the foundation. The floor slabs are also modeled by 80 mm thick reinforced concrete slabs that will be used to transfer the lateral inertial loads to the walls. The model walls are built by a professional mason in Applied Dynamics Laboratory (ADL) of McMaster University. Figure 3 shows one of the model walls during construction.

a b c

Figure 2: Elevation of the model specimens and reinforcement details



TEST SETUP AND INSTRUMENTATION The test platform consists of a 2.0 m by 2.15 m shake table with a Single-degree-of-freedom (SDOF) driven by an MTS actuator with stroke of 300 mm. Based on the configuration of the prototype building considered, the total model mass necessary to satisfy dynamic similitude requirements is 1000 kg for each floor. In order to keep the weight of the wall models within the table payload limits, a mass carrying system will be constructed adjacent to the shake table to support the required inertial mass (see Figure 4). Each mass will be connected through a loading beam to both sides of the floor slabs through pin connections. In this system each floor mass is placed on four linear bearings which facilitates the horizontal mass movement with a minimum amount of friction. This system also increases the performance of the table and the safety under collapse of the walls, reduces the out-of-plane deformations, and provides a simple and easy to setup system for transmitting the in-plane lateral loads to the walls. Separating the inertial model mass from the shake table is a technique that has been used by a other researchers (Carillo and Alcocer 2011). The axial load will be applied through post-tensioned tendons on the walls (see Figure 4). The tendons will be connected in series with a spring in order to control the axial load in the tendons during lateral movement of the walls. The total scale axial loads based on the configurations of the prototype building is approximately 10 kN for Walls 1, 2, 3, 4 and 5 and 30 kN for Wall 6. Both internal and external instrumentation will be used to record the response of the walls during dynamic testing. The internal instrumentation consists of strain gauges attached to the end vertical bars at different heights and will be used to measure the strain at different locations along the bars to determine the onset of yielding of the wall, extent of plasticity, and extent of strain penetration into the foundation. The external instrumentation consists of displacement potentiometers that will be mounted on the wall horizontally, vertically, and diagonally to measure the sliding, vertical, and diagonal shear displacements of the walls as well as the lateral displacements of the table. Such measurements will also be used to determine the wall curvature profiles, hysteretic behavior, extent of plasticity, and contribution of different displacement components (flexural, sliding, and shear) of the overall wall displacements. Accelerometers will also be mounted on the table and floor slabs to measure the acceleration hysteresis during the tests to determine the amount of lateral load and the acceleration amplification in the system. INPUT MOTION Based on the lateral load and displacement capacity of the shake table, the Loma Prieta 1989 earthquake record from PEER NGA strong motion database is selected as the dynamic load for the tests. The model record will be obtained using the scaling factors presented in Table 1. The dynamic properties of the model and prototype records are presented in Table 3. The dynamic test for each specimen will be repeated with increasing amplitudes of this record in terms of PGA until complete failure of the specimen is reached.

Table 3: Dynamic characteristics of input motion

Record Station Original record Scaled record

∆! (s)

PGA (g)

PGV (cm/s)

PGD (cm)

∆! (s)

PGA (g)

PGV (cm/s)

PGD (cm)

Loma Prieta Gilroy Array #2 40 0.37 32.91 7.15 22 0.37 19.02 2.39



Figure 4: Shake table test setup

PREDICTION OF STRENGTH OF WALLS The ultimate flexural strength and curvature (!!,!!) of the model walls obtained based on the provisions of CSA S304, and yield flexural strength and curvature (!! ,!!) of the model walls obtained at the unset of yielding of the vertical steel bars based on simple beam theory are presented in Table 4. The sliding shear (!!") and diagonal shear (!!") strength of the walls, obtained based on the equations proposed by CSA S304 for RM shear walls with moderate ductility, are also presented in Table 4. In computation of flexural and shear strength of the walls, the compressive strength of masonry, masonry Young’s modulus, ultimate masonry compressive strain, yield strength of the horizontal and vertical reinforcements, and Young’s modulus for steel are !′! = 18 !"# , !! = 14,380 !"# , !! = 0.00168 , !!! = 280 !"# , !!" =500 !"#, and !! = 200 !"#, respectively. These values represent the experimentally obtained properties of the wall construction materials. In this regard, the material strength reduction factors for masonry and steel (∅! and ∅!) are considered unity in the calculations of Table 4.

Table 4: Predicted strength and mechanical properties of the model walls

Wall 1 2 3 4 5 6 My (kN.m) 11 9.6 11 16.4 14.6 15.8

Mu(kN.m) 13.5 10.1 13.5 20.1 15.1 18.7

!y (mm!1 "10!6 ) 5.412 5.299 5.412 3.551 5.460 5.758

!u(mm!1 "10!5 ) 3.784 5.402 3.784 3.784 4.253 2.491

Vrs (kN ) 34.3 25.2 34.3 34.3 38.5 48.3 Vrd (kN ) 11.7 11.7 11.7 16.4 11.7 14.2

Ko(kN.mm2 !109 ) 2.037 1.818 2.037 4.613 2.669 2.740

r 0.0381 0.0048 0.0381 0.0233 0.0058 0.0547 lp(mm) 190 190 190 210 250 190



PREDICTION OF WALL DYNAMIC RESPONSE In order to model the dynamic behavior of the model walls, two dimensional beam-column elements are used where the nonlinear behavior of the walls is lumped at the plastic hinge zone represented by plastic hinge length of the wall (Paulay and Priestley 1992). The values of plastic hinge length are obtained based on the relationship proposed by Paulay and Priestley (1992) for RM shear walls. The elastic properties of the walls are based on their cracked sections. For nonlinear behavior of the plastic hinge a bi-linear elastic-plastic moment-curvature model represented by an initial stiffness (!!) obtained from stiffness of the cracked section of the wall and a post yield stiffness (!"!) is considered. The values of !!, !!, and ! obtained for the model walls are presented is Table 4. The mass of the wall is considered as distributed along its height and the floor masses are modeled as lumped at floor heights. A Rayleigh damping model with 7% damping ratio at the first two modes of the structure suitable for masonry buildings is also assumed (Drysdale and Hamid, 2005). The dynamic responses of the model walls are obtained through nonlinear time history analysis using the Ruaumoko code (Carr, 2004). The input motion considered is the scaled Loma Prieta record (see Table 3) amplified to a PGA of 0.48g (130%). Table 5 shows the computed dynamic response of the model walls.

Table 5: Dynamic response of the model walls to 130 % Loma Prieta earthquake

Wall 1 2 3 4 5 6 !!"#,!"! (%) 0.83 1.32 0.18 0.68 0.83 0.78 !!"#,!"# (%) 0.49 0.73 0.18 0.38 0.47 0.47 ∆!"# (!!) 18.30 29.10 1.90 14.90 18.20 17.20 ∆!"#,!" (!!) 18.10 20.30 19.30 11.30 23.20 23.90 ∆!"# (!!) 0.20 11.60 0.00 1.80 6.50 3.70

!!,!"# (!".!) 12.70 10.00 9.70 18.60 14.80 18.50 !!,!"# (!") 8.10 6.70 8.80 11.70 9.40 10.90 !!,!",!"# (!") 12.60 13.10 8.80 19.50 22.40 22.40 !!"#$ (!") 19.40 18.80 8.80 24.00 32.10 32.10

! 1.50 2.00 1.00 1.70 2.30 2.10 !! 5.20 10.30 0.00 6.70 4.20 4.20

! (!"#) 0.29 0.30 0.09 0.19 0.25 0.25 !!"!#$ (!") 0.47 0.41 0.03 0.49 0.55 0.57 !!"#$ !!"! 0.48 0.49 0.00 0.56 0.42 0.37 !! !!"! 0.52 0.51 1.00 0.44 0.58 0.63



DISCUSSION OF THE RESULTS Based on the dynamic response of the walls presented in Table 5 the following observations can be made: - The amount of nonlinear deformations of the walls can be compared based on the values of

maximum curvature ductility (!!), maximum residual drift (∆!"#), and ratio of the hysteretic energy dissipated in the wall to the total input energy (!!!"# !!"!).

- The amount of energy dissipated through nonlinear deformations (!!!"#) is close to the amount of energy dissipated through inherent damping of the walls (!!), which proves the effectiveness of hysteretic energy dissipation in walls with nonlinear behavior.

- The values of response modification factors (R) obtained from the ratio of maximum elastic base shear (!!,!",!"#) and actual (inelastic) maximum base shear attracted by the walls (!!,!"#) shows that in most cases the values of response modification factors obtained from analytical models are more than the values prescribed by NBCC (2010) for conventional RM shear walls (R = 1.5). In addition, the values in the table are obtained for the situation when most of the walls have not reached significant inelastic deformations or ultimate failure. Higher values can be expected upon initiation of wall failures.

- The variability of the response modification factor values for the analyzed walls challenges the current code approach in terms of assigning a single value for every SFRS.

- The amount of maximum nonlinear displacement of the walls (∆!"#) are close to the amount of maximum displacement of the walls considering only elastic behavior for the walls (∆!"#,!"), thus supporting the validity of equal-displacement approach used in the NBCC for the computation of response modification factors.

- The values of base shear obtained from response spectrum analysis assuming Single-Degree-of-Freedom (SDOF) wall response (!!"#$) based on the fundamental periods of the walls (!), compared to the maximum base shear of the walls considering only the elastic wall behavior (!!,!",!"#) shows that the SDOF idealization for the two-story walls is conservative.

- Comparison of the maximum roof and inter-storey drift ratios (!!"#,!"!, !!"#,!"#) for different walls confirms the higher lateral deformation capacity of slender walls.

CONCLUDING REMARKS There is an urgent need for a fundamental understanding of the seismic performance of RM wall SFRS in order to facilitate the development of relevant PBSD provisions. The proposed shake table experimental program in this paper can help understand the dynamic response and capacity of RM shear walls during real earthquakes. The seismic response of the proposed model walls was investigated using a simplified analytical model. The future research work consists of model calibration based on the shake table experimental data and verification of model accuracy by comparing the experimental and analytical results. ACKNOWLEDGMENT The financial support to this project has been provided by the McMaster University Centre for Effective Design of Structures (CEDS) funded through the Ontario Research and Development Challenge Fund (ORDCF) as well as the Natural Sciences and Engineering Research Council (NSERC) of Canada. Provision of mason time by Ontario Masonry Contractors Association (OMCA) and Canada Masonry Design Centre is appreciated. The provision of the scaled blocks through a grant from the Canadian Concrete Masonry Producers Association (CCMPA) is gratefully acknowledged.



REFERENCES Applied Technology Council (ATC). (2011). “Seismic performance assessment of buildings volume 1 - methodology.” ATC-58-1 75% Draft, ATC, Redwood City, California. Carillo, J., Alcocer, S. “Improved external device for a mass-carrying sliding system for shaking table testing”, Journal of Earthquake Engineering and Structural Dynamics, 40, 2011, pp 393-411 Carr, A.J. Ruaumoko, Volume 1: Theory manual. Christchurch, New Zealand, September, 2004. CSA Standrard (S3014.1-04). Design of masonry structures. Canadian Standards Association, Mississuaga, December 2004. Drysdale, R.G., Hamid, A.A. Masonry Structures: Behaviour and Design. Canada Masonry Design Centre, 2005. FEMA-461 (2007) “Interim testing protocols for determining the seismic performance characteristics of structural and nonstructural components” ATC, 201 Redwood Shores Parkway, Suite 240 Redwood City, California 94065 Hamburger, R., Rojahn, C., Moehle, J., Bachman, R., Comartin, C., Whitakker, A. “ATC-58 Project: Development of next-generation performance-based earthquake engineering design criteria for buildings”, 13th WCEE, Vancouver, B.C., Canada, 2004. Harris, H.G., Sabnis, G.M. Structural modeling and experimental techniques, Second edition, CRC Press, 1999. Jo, S. Seismic behavior and design of low-rise reinforced concrete Masonry with clay masonry veneer. PhD thesis, University of Texas at Austin, May 2010. Long, L. Behaviour of half-scale reinforced concrete masonry shear walls. Master thesis, Civil Engineering Department of McMaster University, Hamilton, Canada, 2006. National Building Code of Canada (NBCC). Institute for Research In Construction (IRC), 2010. Paulay, T., and Priestley, M.J.N. “Seismic Design of Reinforced Concrete and Masonry Buildings”. Wiley, 1992. Seible, F., Priestley, M.J.N., Kingsley, G.R., Kürkchübasche, A.G. ”Seismic response of full-scale five-storey reinforced-masonry building”. Journal of Structural Engineering (ASCE), 120, 3, March 1994. Shedid, M.T., Drysdale, R.G., El-Dakhakhni, W.W., ”Behaviour of fully grouted reinforced concrete masonry shear walls failing in flexure: experimental results” Journal of Structural Engineering, 134, 11, November, 2008. Shedid, M.T., El-Dakhakhni, W.W. Drysdale, R.G. ”Alternate strategies to enhance the seismic performance of reinforced concrete-block shear wall systems”. Journal of Structural Engineering, 136, 6, June, 2010. Wierzbicki, J.C., Behaviour of a reduced-scale fully grouted concrete block shear walls. Master thesis, Civil Engineering Department of McMaster University, Hamilton, Canada, 2010.

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SHAKE TABLE TESTING AND ANALYTICAL MODELING OF FULLY ... · 3 PhD, Martini, Mascarin and George Chair in Masonry Design, McMaster University, Civil Engineering Department, [email protected]