Structural Engineering and Mechanics, Vol. 41, No. 1 (2012) 95-112

95

Experimental hysteretic behavior of in-plane loaded
reinforced grouted multi-ribbed aerated concrete blocks
masonry walls
Sheng-Cai Li*, Jian-Xi Dong and Li-Feng Li
School of Civil Engineering, Huaqiao University, Quanzhou, China(Received February 7, 2010, Revised August 3, 2011, Accepted December 13, 2011)
Abstract. In order to analyze the experimental hysteretic behavior of the in-plane loaded reinforced
grouted multi-ribbed aerated concrete blocks masonry walls (RGMACBMW), we have carried out thepseudo static testing on the six specimens of RGMACBMW. Based on the test results and shear failure
characteristics, the shear force hysteretic curves and displacement envelope curves of the models wereobtained and discussed. On the basis of the hysteretic curves a general skeleton curve of the shear force
and displacement was formed. The restoring model was adopted to analyze the seismic behavior andearthquake response of RGMACBMW. The deformation capacity of the specimens was discussed, and theformulas for calculating the lateral stiffness of the walls at different loading stages were proposed as well.
The average lateral displacement ductility factor of RGMACBMW calculated based on the test results was
3.16. This value illustrates that if the walls are appropriately designed, it can fully meet the seismic
requirement of the structures. The quadri-linear restoring models of the walls degradation by the test
results accurately reflect the hysteretic behaviors and skeleton curves of the masonry walls. The restoringmodel can be applied to the RGMACBMW structure in earthquake response analysis.
Keywords: RGMACBMW, pseudo static test, deformation behavior, stiffness, restoring model

1. Introduction
RGMACBMW is a new structural bearing member with perfect properties such as light weight,
high strength, low energy consumption and good seismic capacity (Li and Zeng 2005). This typeof wall is composed of insulation energy-saving blocks and an invisible multi-ribbed frame,
whose load-bearing capacity and seismic performance are different from common concrete
members. There has been much researched done on reinforced concrete masonry walls. The
flexural and shear strength behaviors of reinforced concrete masonry walls subject to bothmonotonic and cyclic lateral loads are examined based on experimental results obtained from 22
specimens of 6ft x 6ft masonry wall sections (Shing et al. 1990a, b). Thirty-six panels were
examined to investigate the in-plane behavior of grouted concrete masonry walls under welldefined bi-axial tension-compression loading conditions (Drysdale and Khattab 1995). To provide
data for the masonry wall panels, a bi-axial test frame was constructed capable of loading*Corresponding author, Professor, E-mail: lsc50605@hqu.edu.cn

96Sheng-Cai Li, Jian-Xi Dong and Li-Feng Li

masonry panels 80 cm high by 120 cm wide in tension and compression combination (Tikalsky etal. 1995). The tensile behavior of reinforced concrete and clay unit masonry members werestudied by conducting a series of 33 direct tension tests on instrumented specimens (Atkinson andHammons 1997). Ten single-story concrete masonry wall panels were tested at the University of
Auckland in order to examine the in-plane shear strength of concrete masonry walls constructedusing New Zealand masonry units utilizing pumice aggregate and assembled using common local
construction techniques and establish its design expression (Voon and Ingham 2006, 2007).
Through reversed cyclic lateral loading tests on six full-scale walls, the failure processes wereanalyzed. The effects of the amount and distribution of vertical reinforcement and the level ofaxial compressive stress on the inelastic behavior and ductility were investigated (Shedid et al.
2008, 2009). The different factors influencing the reliability of reinforced grouted concrete block
masonry in compression are studied, including model error, grouted block masonry strength, load
effect combinations, eccentricity, reinforcement ratio, live load type, structural safety class, liveto-dead load ratio and discretization of wall thickness, and a probabilistic model to calculate thestructural reliability of typical reinforced grouted concrete block masonry walls designed toChinese standards, loaded concentrically and eccentrically in compression is developed (Zhai and
Stewart 2010). In order to study the ductility and the lateral load carrying capacity of themasonry walls strengthened with CFRPs (Carbon Fiber Reinforced Polymer sheets), three pieces
of masonry walls subjected to cyclic loads with low frequency and vertical load of constant
amplitude have been tested. It is found that the critical loads the critical displacements, theultimate loads, the ultimate displacements and the ductile coefficients of the masonry walls
strengthened with CFRPs improve remarkably (6% similar to 57%). Therefore, the masonry
structures strengthened with CFRPs are of better ductility and of better lateral load carrying
capacity than the masonry structures without any strengthening measurements (Wei et al. 2007).
In this paper, six specimens were tested under cyclic horizontal loads to study the deformation
performance and the restoring model of the walls.

2. Test specimens and procedure
In this study, we have poured and constructed three groups of specimens of the multi-ribbed
concrete columns and beams. Each group consists of two specimens. The first specimen was
designed with C20 fine stone concrete and the other specimen was designed with M20 high strengthmortar. The specimens were composed of insulation energy-saving blocks and an invisible multiribbed frame. The block was an aerated concrete block mainly composed of industry waste such as
fly ash and furnace slag. The general view of blocks is shown in Fig. 1. There is a v-groove in eachside of the block except the front and the rear ends, which was used to pour the invisible reinforced
concrete columns (a prism with a 60-mm-long diagonal) and beams (the same size as the columns)
that eventually formed the invisible multi-ribbed frame. A large outer frame was formed around thesmall concrete frame (shown in Fig. 2) by increasing the diameter of reinforcing steel bars at theboth junctions of the wing sections, as well as the top or bottom beam of the main wall. The steel
reinforcing arrangements of the specimens are shown in Table 1; the material mechanical properties(National Standard of the People’s Republic of China 2002, 1998 and 2003) of the steel bar, theaerated concrete block and the concrete or mortar are shown in Tables 2~4 respectively.

Experimental hysteretic behavior of in-plane loaded reinforced grouted multi-ribbed aerated concrete blocks masonry walls

97

Fig. 1 Abridged general view of the blocks and their combination form

Fig. 2 Multi-ribbed frame wall

Table 1 Design of specimens
Specimens

Reinforced arrangement (HPB235)
Outer rib column

Inner rib column

Top/bottom rib beam

Inner rib beam

EW1-1 EW1-2

1φ8 (2.79%)

1φ6 (1.57%)

1φ8 (2.79%)

1φ6 (1.57%)

EW2-1 EW2-2

1φ10 (4.36%)

1φ8 (2.79%)

1φ8 (2.79%)

1φ6 (1.57%)

EW3-1 EW3-2

2φ8 (5.61%)

2φ6 (3.17%)

1φ10 (4.36%)

1φ8 (2.79%)

Note: The figures in parenthesis are reinforcement ratio.
Table 2 Steel bar (HPB235) material mechanical properties test results
Gauge

Diameter (mm) Yield strength (MPa) Ultimate strength (MPa) Elastic modulus (×105N/mm2)

φ6

6

248

331

2.1

φ8

8

276

310

2.1

φ10

10

289

306

2.1

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Sheng-Cai Li, Jian-Xi Dong and Li-Feng Li

Table 3 Aerated concrete block material mechanical properties test results
block material

Compressive strength(MPa)

Tensile strength(MPa)

Dry density(kN/m3)

Elastic modulus(N/mm2)aerated concrete block

1.67

0.17

6

1105

Table 4 Concrete or mortar material mechanical properties test results
Specimens
EW1-1
EW1-2
EW2-1
EW2-2
EW3-1
EW3-2

Members

Designed strength gradeof concrete or mortar

fcu, m (MPa)fcm (MPa)

multi-ribbed frame

C20

16.53

12.56

top beam

C20

37.74

28.68

multi-ribbed frame

M20

16.45

12.50

top beam

C20

22.80

17.33

multi-ribbed frame

C20

19.24

14.62

top beam

C20

36.18

27.50

multi-ribbed frame

M20

17.51

13.31

top beam

C20

22.74

17.28

multi-ribbed frame

C20

22.79

17.32

top beam

C20

30.09

22.87

multi-ribbed frame

M20

17.16

13.04

top beam

C20

21.97

16.70

Note: fcu, m is the mean value (the test value) of cubic compressive strength, fcm is the mean value of prism
compressive strength (because the test is carried out in the laboratory, modified factor is not considered, that is
fcm = 0.76 fcu, m)Fig. 3 Loading set-up

Experimental hysteretic behavior of in-plane loaded reinforced grouted multi-ribbed aerated concrete blocks masonry walls

99

Fig. 4 displacement loading process of specimens

The loading set-up is shown in Fig. 3. Considering the worst-case scenario for the stress state, thelow-cycle reversed lateral loading system was adopted on the basis of the comprehensive analysis of
the test objectives and the loading apparatus. The horizontal load was applied on the ends of thebeam by hydraulic actuator connected to the reaction frame. The procedure used displacementcontrol method. At first step we have used only one cycle for each incremental displacement before
the specimen yielded. After the appearance of the yield point, we increased the number of cycles
for each incremental displacement to two cycles until the specimen failed.
To simulate the mechanical behavior of a new building structure, an accurate finding on the actual
mechanical performance was not possible for the model walls specimen. In the actual loading
process of the test, based on establishing the initial loading criteria, the loading systems were
adjusted according to the trend change of the hysteretic curve of every wall. The practical loading
systems of every wall in this test are shown in Fig. 4.
Photos of the tested specimens are shown in Fig. 5.

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Sheng-Cai Li, Jian-Xi Dong and Li-Feng Li

Fig. 5 Photos of the tested specimens

3. Hysteretic characteristics and average skeleton curves
3.1 Hysteretic curves
3.4.1 Intercommunity of hysteretic curves of the model walls
From the hysteretic curves shown in Fig. 6, it’s evident that the model masonry walls deformation
is mainly elastic. Before initial cracking of the aerated concrete block, the shear force anddisplacement curves are basically linear. After the wall initially cracked while unloading thestiffness degenerative behavior of the model walls, the hysteretic loop’s area under the curve is verysmall. As we increased the load, the cracks became larger, and the hysteretic curves pinched to acertain extent, but it was not very severe as we unloaded it to zero. Meanwhile, the hysteretic
curves resemble a crescent moon shape, which means that no obvious shear deformation andslippage occurred. Then we continuously load the sample specimens to their ultimate load capacity
to reach the stiffness degenerative behavior of the model walls. The hysteretic loops plumped andpinched significantly near the origin of the coordinates, and the hysteretic curves show a reversed S
shape, because of the shear deformation and decline in hysteretic curves. In the loading cycle of thesame displacement point, the loads basically became inferior by 25% and the hysteretic loops
display the semi-steady condition. Henceforth, as the cyclic displacement increased step by step, theunloading flexural stiffness of the specimen became inferior rapidly, and the decline was extremely
serious as a result of the spalling damage of the aerated concrete block, which is all reflected in thehysteretic curve as its middle section pinched seriously approaching the displacement axis as aresult of the converse S shape.
3.1.2 The difference between the hysteretic curves
The initial flexural stiffness of the model wall EW1-2 was small in comparison to the others.
Before the ultimate load (the load at ultimate displacement), the flexural stiffness of the two model
walls EW3-1 and EW3-2 decreased quickly while the model wall EW1-1 exhibited much slower
decline. As for the loading condition of the same displacement prior to the ultimate load, the loadsof the specimens EW3-1 and EW3-2 deteriorated quickly while the load for the model wall EW1-1
deteriorated much slower. When the loading reached at 85% of the ultimate load, the hysteretic
loops of the four model walls EW1-1, EW1-2, EW2-2 and EW3-2 showed relatively a full oblique
shape (Fig. 6).

Experimental hysteretic behavior of in-plane loaded reinforced grouted multi-ribbed aerated concrete blocks masonry walls 101

Fig. 6 Hysteretic curves of model walls

Table 5 The main seismic properties of multi-ribbed frame walls
Specimens

Cracking
Pcr (kN) ∆cr (mm)Yield

Maximum

Ultimate

Py (kN)∆y (mm)Pm (kN)∆m (mm)Pu (kN)

Ductil-ity
factor∆u (mm)

EW1-1

83.0

1.12

165.7

3.06

203.7

5.56

173.2

59.77

3.19

EW1-2

125.0

1.80

172.5

2.30

207.8

5.32

174.6

8.62

3.75

EW2-1

90.1

1.18

180.0

2.54

207.7

4.89

——

——

——

EW2-2

122.5

1.59

213.4

3.13

253.9

6.03

214.5

59.15

2.92

EW3-1

96.8

1.26

196.1

2.76

221.4

5.60

187.9

57.17

2.60

EW3-2

133.2

1.77

222.1

3.26

272.0

7.79

230.8

10.92

3.35

3.1.3 Conclusion① As for the control specimens poured with the fine stone concrete in multi-ribbed beams andcolumns, the energy dissipation did not improve as the number of reinforcing steel bars increased.
But for the poured multi-ribbed beams and columns with high strength mortar, the energy
dissipation did improve as the number of reinforcing steel bars increased.
② Consequently, in the multi-ribbed beams and columns with the same displacement behavior
and loading condition, the greater number of reinforcing steel bars, the quicker degenerative
behavior of the load and flexural stiffness of the model walls.
3.2 Skeleton curves of shear force and displacement
The test characteristic values of the specimens under low-cycle reversed horizontal loads areshown in Table 5. The quadri-linear restoring model was applied to represent the skeleton curves ofthe models as the non-dimensional skeleton curves of the test under the same coordinates seemed to
be in good adherence to each other. The initial cracking point A, the yield point B, the maximum

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Sheng-Cai Li, Jian-Xi Dong and Li-Feng Li

Fig. 7 Skeleton curves of model walls

Fig. 8 The Park graphic analvsis methodload point C, and the ultimate load point D are the key points.
Likewise, the loads and displacements are: the cracking load Pcr, the cracking displacement ∆cr;
the yield load Py, the yield displacement ∆y; the maximum load Pm; the corresponding displacement∆m; the ultimate load Pu; the ultimate displacement ∆u. (Fig. 7).
3.3 Definition of the main characteristic points
The initial crack was defined as the point where the first group of obvious cracks formed on theskeleton curve. The value of this point could be determined by the corresponding test data at thefirst crack point where the curve is turning. At the point of maximum load, the deformation
increased rapidly while the load began to descend. Generally the ultimate load is defined as the
maximum load descended to about 85% and the relative deformation was the ultimate deformation.
In fact no clear yield point was obtained from the model walls. In order to discuss the deformation
appropriately, the supposed yield point must be rationally determined. The Park graphic analysis
method was used to analyze the skeleton curves of the model walls. With this method, the point I(0.6 Pm) was determined on the skeleton curve in Fig. 8. Then we connected the origin point O andExperimental hysteretic behavior of in-plane loaded reinforced grouted multi-ribbed aerated concrete blocks masonry walls 103

point I to draw the line OI and extended it to get the intersecting point A and draw the horizontal
line passed through point A to establish the ultimate load point G on the skeleton curve. The line
AB was drawn vertically to the abscissa, which intersected point B on the skeleton curve, anddesignated as the equivalent yield point. From Fig. 8 we can observe that the supposed yield load
was determined as 0.85 Pm, and the relative lateral displacement as ∆y.
3.4 Evaluation of the ductility capacity of RGMACBMWTaking the lateral displacement ∆y of the model walls at assumed yield point as its yielddisplacement, the average lateral displacement ductility factor of RGMACBMW calculated by test
results was 3.16. This value illustrates that the model walls were properly designed and they meetseismic requirements of the structures. In China and abroad the range of values in displacement
ductility factor of the structure is generally between 3 to 5, one can observe from Table 5 that themodel walls EW1-1, EW1-2 and EW3-2 have ductility factors larger than 3, which are satisfactory.
However, the model walls ductility seems to descend instead of escalation even with the increase of
the steel reinforcement bar members. Therefore, the failure mode of the model walls was mainly ashear force failure, and the rationally designed model walls could still be within the allowable
deformability. The “rationally design” here referred to a rational shearing-compression ratio andarrangement of the reinforcement of multi-ribbed beams and columns. So as to form rational failure
mechanism of wall, the wall fails in the following order: firstly, the cracking of blocks, secondly thecracking of the small inner multi-ribbed frame, thirdly cracking of the large outer frame, fourthly
reinforcement yielding of the small inner multi-ribbed beam, fifthly reinforcement yielding of thesmall inner multi-ribbed column, after that reinforcement yielding of the large outer frame beam,and then reinforcement yielding of the large outer frame column and concrete crushing.

4. Shear capacity formula
The blocks in the multi-ribbed frame members play a role of diagonal strut under the horizontal
shear force. Moreover, the interaction between the horizontal shear force of the blocks and themulti-ribbed frame structure exhibits the bending moment of the columns and beams to be verysmall, hence the columns and beams in the multi-ribbed frame structure are considered to be themain member bearing axial force.
The shear capacity of RGMACBMW in the nominal failure diagonal section is equated as thefollowing
V = Vc + Vck + Vq + Vqk + Vsh + Vsv(1)

Where V is the shear capacity of the walls; Vc is the shear capacity of the grout material on uncracked areas in nominal failure diagonal section; Vck is the shear capacity of the grout material on
cracked areas in nominal failure diagonal section; Vq is the shear capacity of aerated concrete blocks
on un-cracked areas in nominal failure diagonal section; Vqk is the shear capacity of aerated concrete
blocks on cracked areas in nominal failure diagonal section; Vsh is the shear capacity of multi-ribbed
beam reinforcement bars; Vsv is shear capacity of multi-ribbed column reinforcement bars (dowel
resistance of the longitudinal bars etc.).

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Sheng-Cai Li, Jian-Xi Dong and Li-Feng Li

To evaluate the shear capacity of the walls, the following formula is obtained
1 [ 0.09 ( f A + f A ) + 0.12f A + 0.06f A ] + [ 0.42f A + 0.28f A + 1.05f A ]V = --------------ca ca
q q
cz cz
cl cl
ya sa
yz sz
yl sl
λ – 0.5(2)
Where λ is the height-width ratio of the walls (λ = H / L) and is called the shear span ratio of thesection, it ranges between 1.5 and 2.2; Aca, Aq, Acz, and Acl are the sectional areas of the large outer
frame column, the aerated concrete blocks (not including those sections of the flanges only thehorizontal cross-section of the blocks), the small inner multi-ribbed column (not including thosesections of the flanges) and the small inner multi-ribbed beam (not including those sections of theflanges) respectively; fca, fq, fcz, and fcl are the design compressive strength values of grout materialof the large outer frame column, the aerated concrete blocks, the grout material of small innermulti-ribbed column and the small inner multi-ribbed beam respectively; fya, fyz and fyl are the design
tensile strength values of steel reinforcement bars in the large outer frame column, the small innermulti-ribbed column and the small inner multi-ribbed beam respectively; Asa, Asz, and Asl are thesectional areas of steel reinforcement bars in the large outer frame column, the small inner multiribbed column and the small inner multi-ribbed beam respectively.

5. Stiffness calculations of all stress stages and restoring force model
5.1 Average stiffness K1 before cracking
Through the observation of the skeleton curves of RGMACBMW in Fig. 7, the model walls werebasically in elastic condition before any cracking. Therefore, the model wall with the adjoining wall
could be simplified as I-shape section beam and the average flexural stiffness can be obtained byelastic theory.
As shown in Fig. 9, the displacement δ was called lateral flexibility when a unit force was applied
to the top end of the model wall, the lateral stiffness is the reciprocal of the lateral flexibility:
K = 1 / δ.
Assuming that the model wall is a cantilever structural member, and the total deformation of themodel wall was composed of the flexural deformation δb and the shearing deformation δs under thehorizontal unit force. So the elastic lateral stiffness of the homogeneous model wall is calculated as
Eq. (3)
1
1
K = --------------- = --------------------------3
δb + δs
HµH⎛ --------- + --------⎞⎝ 3EI GA⎠

(3)

Where H represents the height of wall; A is the area of the wall cross section (I-shape section); µ is
the shearing stress coefficient of the model wall for I-shape section µ = A ⁄ A′ , where A′ is the areaof the web section; I represents the moment of inertia for the I-shape section; E is the elastic
modulus; and G represents the shearing modulus.
The reinforced grouted multi-ribbed aerated concrete blocks masonry structure was composed ofenergy-saving blocks and an invisible multi-ribbed frame. The elastic moduli of two parts wereExperimental hysteretic behavior of in-plane loaded reinforced grouted multi-ribbed aerated concrete blocks masonry walls 105

Fig. 9 Flexural deformation and shearing deformation of model wall under a unit force

Table 6 Calculated results of the lateral stiffness
Specimens

K1 (kN/mm)

K0 (kN/mm)

K1/K0

EW1-1

74.11

88.70

0.84

EW1-2

69.44

88.67

0.78

EW2-1

76.36

89.36

0.85

EW2-2

77.04

88.94

0.87

EW3-1

76.83

90.04

0.85

EW3-2

75.25

88.87

0.85

Note: K1 is the experimental initial stiffness, and K0 is the analytical initial stiffness

different to a large extent, so the elastic lateral flexural stiffness of the homogeneous model wall
could not be calculated directly (Zhao et al. 1999). The composite material method (Wang 2003)
was applied to calculate and figure out the elastic constants of the model wall. Hence the elastic
lateral flexural stiffness could be calculated by the preceding formula in Eq. (3). The calculated
results are shown in Table 6.
Through the test of the whole bearing wall member composed of energy-saving blocks and aninvisible multi-ribbed frame, the deformation capacity and the common behavior of all its
components have been maintained until the blocks failed. In macroscopic view, the wall was anelastic composite panel with energy-saving blocks being the main body and concrete rib beams,
columns and outer frame as reinforcing fiber. A simplified model of the wall panel is shown in Fig.
10. Based on the equivalent principle the concrete volume ratio of the wall remained unchanged,
this was contributed by the concrete rib beams, columns and outer frame having a large quantity offine aggregates homogeneously and uniformly distributed through out the matrix which is composedof energy-saving blocks. Therefore, the wall was considered as an orthotropic fiber-reinforced
elastic composite panel.
Theoretically based on the stiffness calculation for an orthotropic fiber-reinforced composite
material we can calculate the stiffness characteristics of the wall. Since the mechanical property ofthe orthotropic materials is very complicated; a more simplified method of calculation was
ascertained for isotropic materials. This simplified method considers the average elastic modulus

106

Sheng-Cai Li, Jian-Xi Dong and Li-Feng Li

Fig. 10 A simplified material model of the wallvalue of the two directional orthotropic fiber-reinforced elastic composite panel models; and theshear modulus of the orthotropic fiber-reinforced elastic composite panel model.
The flexural stiffness before cracking of every specimen was calculated by Eq. (3). The calculated
results were 15% higher than the experimental results in average. This was contributed due to thecontinuous development of the hairline cracks of RGMACBMW prior to the formation of any
visible cracks. Therefore, Eq. (3) must be modified as: K1 = 0.85K .
5.2 The stiffness of the model walls after cracking
The model walls exhibit a nonlinear performance after the initial crack. There has been a change
in the force transferring mechanism. At this point, the model walls restrained by the exterior frame
formed a resisting lateral force system which consisted by the oblique-compression bar and thetension reinforcement. Since the stress calculation for this experiment is very complicated, andsolving the deformation of the model walls theoretically becomes very difficult. Therefore, thestatistical method was applied to solve the stiffness of the model walls.
Through observation from the skeleton curves in Fig. 7, the following four main characteristic
points (the initial crack point, the yield point, the maximum point and the ultimate point), the lateraldisplacement and loading coordinates were obtained respectively: (1.45, 108.43), (2.84, 191.63),(5.87, 227.75) and (9.13, 196.20). Presumably the stiffness after cracking is K2 = α2 K1 , thestiffness after yielding is K3 = α3 K1 and the stiffness after the maximum loading is K4 = α4 K1 , thefollowing results were calculated from the geometric relation in Fig. 5 that α2 = 0.80, α3 = 0.16,
α4 = −0.13.
5.3 Determination of load and displacement of every feature points
The shear capacity, maximum load Pm was calculated according to formula (2).
The initial cracking load of the specimens which were manufactured using C20 concrete wascalculated using the following formula (4)Pcr = 0.43Pm(4)

The initial cracking load of the specimens which were manufactured using M20 mortar wasExperimental hysteretic behavior of in-plane loaded reinforced grouted multi-ribbed aerated concrete blocks masonry walls 107

Fig. 11 The restoring model of model

calculated using the following formula (5)Pcr = 0.52Pm(5)The yield load and ultimate load was calculated according to formula (6)Py = Pu = 0.85Pm(6)The cracking displacement was calculated according to formula (7)∆cr = Pcr ⁄ K1

(7)

The yield displacement was calculated according to formula (8)∆y = ( Py – Pcr ) ⁄ K2 + ∆cr(8)

The displacement of maximum load was calculated according to formula (9)∆m = ( Pm – Py ) ⁄ K3 + ∆y

(9)

The ultimate displacement was calculated according to formula (10)∆u = ( Pu – Pm ) ⁄ K4 + ∆m

(10)

5.4 The restoring model of specimens
For the specimens a gradual failure process was designed and the test procedure was used to108

Sheng-Cai Li, Jian-Xi Dong and Li-Feng Li

demonstrate the design principle of energy–dissipation. Combining the skeleton curves and theflexural stiffness degeneration of the model walls, considering the practical rules to define themaximum point on the curve when the load is applied in the opposite direction, the degrading
quadrilinear restoring force model (see in Fig. 11) was chosen in the paper as shown below(Tomazevic et al. 1996, Tomazevic and Lutman 1996). In Tomazevic and Lutman’s restoring force
model, the skeleton curve is a simple symmetric, tri-linear hysteresis envelope, determined by threepairs of values of lateral load and displacement, which define the cracking point, maximum
resistance, and ultimate limit state of the behavior of a wall respectively. The shortcoming of theTomazevic and Lutman’s restoring force model was that there is no yield point; hence we havechosen to overcome this shortcoming and determine the degrading quadrilinear restoring force
model in this paper. By comparing the results in this paper with the models developed by
Tomazevic and Lutman, the hysteretic behavior of the two experiments are quite similar except theyield point.
5.4.1 The loading stiffness
The transformation rule on the loading stiffness is shown in Fig. 11; the elastic stage (0-1) and theelastic stiffness K1; the elastic-plastic stage (1-7), the stiffness K2 before yield (1-3) and K3 after
yield (3-7); the failure stage (7-15) and the negative stiffness K4. According to the test results andstatistical data, the stiffness of every stage could adopt the recommendation in section 5.2. The
initial crack point, yield point, maximum point, ultimate point were determined respectively
according to the preceding definition and statistical data.
5.4.2 The unloading stiffness
This paper has chosen the degrading quadrilinear model for the restoring model walls. The
degrading rule of stiffness is mainly related to the unloading stiffness shown in Fig. 7. Based on thenormal hysteretic loops obtained from the statistical data at the yield point, the maximum point, theultimate point, and the model walls unloading stiffness constructed at three stages were interpolated.
To calculate the described conditions the following formulas were considered (For an explanation of
the symbols referring to 3.2)
0.5

Kr1 = ( ∆cr ⁄ ∆r ) K1(∆cr < ∆r < ∆y)(11)Table 7 The calculation results of stiffness
Specimens

K

K1

K2

K3

EW1-1

88.70

75.40

60.32

12.06

EW1-2

88.67

75.37

60.30

12.06

EW2-1

89.36

75.96

60.77

12.15

EW2-2

88.94

75.60

60.48

12.10

EW3-1

90.04

76.53

61.22

12.24

EW3-2

88.87

75.54

60.43

12.09

Experimental hysteretic behavior of in-plane loaded reinforced grouted multi-ribbed aerated concrete blocks masonry walls 109
Table 8 Comparison of the test and calculation results for the significant points of the skeleton curve∆cr (mm)

Pcr (kN)

Specimens∆y (mm)Py (kN)

Pcr.e

Pcr.c

∆cr.e

∆cr.c

Py.e

Py.c

∆y.e

∆y.c

EW1-1

83.0

86.47

1.12

1.15

165.7

170.94

3.06

2.55

EW1-2

125.0

104.26

1.80

1.38

172.5

170.43

2.30

2.48

EW2-1

90.1

93.91

1.18

1.24

180.0

185.64

2.54

2.75

EW2-2

122.5

128.02

1.59

1.69

213.4

209.27

3.13

3.03

EW3-1

96.8

108.53

1.26

1.42

196.1

214.54

2.76

3.15

EW3-2

133.2

140.35

1.77

1.86

222.1

229.42

3.26

3.33

Specimens∆m (mm)Pm (kN)∆u (mm)Pu (kN)

Pm.e

Pm.c

∆m.e

∆m.c

Pu.e

Pu.c

∆u.e

∆u.c

EW1-1

203.7

201.1

5.56

5.05

173.2

170.94

9.77

8.13

EW1-2

207.8

200.5

5.32

4.97

174.6

170.43

8.62

8.04

EW2-1

207.7

218.4

4.89

5.45

—

185.64

—

8.77

EW2-2

253.9

246.2

6.03

6.08

214.5

209.27

9.15

9.84

EW3-1

221.4

252.4

5.60

6.24

187.9

214.54

7.17

10.05

EW3-2

272.0

269.9

7.79

6.68

230.8

229.42

10.92

10.80

Kr2 = ( ∆y ⁄ ∆r )0.61

Kr3 = ( ∆m ⁄ ∆r )

K1

0.63

K1

(∆y < ∆r < ∆m)(12)(∆m < ∆r < ∆u)(13)

Where Kri (i = 1, 2, 3) represents the unloading stiffness and ∆r represents the lateral displacementof the model walls when unloaded.
5.5 Fitting of feature points of skeleton curve
Based on the method in section 5.2 and 5.3, the flexural stiffness and feature points of theskeleton curve of RGMACBMW have been calculated. The results of the flexural stiffness areshown in Table 7.
The test results and calculations of the feature points are shown in Table 8. In table 8 thesubscript e represents the experimental values and subscript c represents the calculation results
respectively.
The Comparison of the calculated and test results are shown in Fig. 12. Through observation thetest results are fairly close to the calculated values for the skeleton curves in this paper.

110

Sheng-Cai Li, Jian-Xi Dong and Li-Feng Li

Fig. 12 Comparison on skeleton curves of calculation and test results

6. Conclusions(1) The ductility factor of the average lateral displacement for RGMACBMW is 3.16 which was
calculated and supported by the test results. This value illustrates that the model walls rationallydesigned can meet the seismic requirements of the structure. Therefore, the general failure modeof the model walls was due to the shear failure under the low-cycle reversed lateral loads.
However, the model walls that are rationally designed would possess certain deformation capacity.
(2) Through the accurate experimental data of RGMACBMW, the degradation quadrilinear
restoring model was obtained for the model walls, which by comparison correctly reflect thehysteretic property and skeleton curves of the model walls. Therefore, the restoring model can beapplied to the time-history analysis of the reinforced grouted multi-ribbed aerated concrete blocks
masonry structure.

Experimental hysteretic behavior of in-plane loaded reinforced grouted multi-ribbed aerated concrete blocks masonry walls 111(3) Based on the Pseudo Static Test the restoring model proposed in this paper could notcomprehensively reflect the real dynamic performance of RGMACBMW. It is recommended thata more comprehensive study of the seismic performance of the pseudo dynamic test or theshaking table test to be carried out.

Acknowledgments
The authors acknowledge the financial contribution by Grant of national natural science
foundation (50948036); Key scientific and technological planning project of Fujian province(2008H0029); Natural science foundation planning project of Fujian province (E0810022).

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