impact of drying on structural performance of reinforced

Impact of Drying on Structural Performance of Reinforced Concrete Shear WallsHiroshi Sasano, Ippei Maruyama, Akihiro Nakamura, Yoshihito Yamamoto andMasaomi TeshigawaraJournal of Advanced Concrete Technology, volume 16 (2018), pp. 210-232

Prediction of Drying Shrinkage Cracks of Steel Chip Reinforced Polymer Cement MortarYuya Ida, Sunhee Hong, Shinya Minura, Yuichi Sato, Yoshio KanekoJournal of Advanced Concrete Technology, volume 14 (2016), pp. 739-752

Prediction of Drying Shrinkage Cracking of Eco-efficient Steel Chip Reinforced Cementitious Composite Considering Tensile CreepSunhee Hong , YuichiSato, Yoshio Kaneko, Shinya KimuraJournal of Advanced Concrete Technology, volume 13 (2015), pp. 393-402

Mechanism of Change in Splitting Tensile Strength of Concrete during Heating or Drying Up to 90°CMao Lin, Mitsuki Itoh, Ippei MaruyamaJournal of Advanced Concrete Technology, volume 13 (2015 ), pp. 94-102

Multi-scale based Simulation of Shear Critical Reinforced Concrete Beams Subjected to DryingEsayas Gebreyouhannes, Taiji Yoneda, Tetsuya Ishida, Koichi Maekawa Journal of Advanced Concrete Technology, volume 12 ( 2014 ), pp. 363-377

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Journal of Advanced Concrete Technology Vol. 16, 210-232, May 2018 / Copyright © 2018 Japan Concrete Institute 210

Scientific paper

Impact of Drying on Structural Performance of Reinforced Concrete Shear Walls Hiroshi Sasano1, Ippei Maruyama2*, Akihiro Nakamura3, Yoshihito Yamamoto4 and Masaomi Teshigawara5

Received 2 February 2018, accepted 11 May 2018 doi:10.3151/jact.16.210

Abstract The aim of this study is to experimentally investigate the effect of drying on a shear wall, and to clarify the mechanism of the changes in the structural performance due to drying. Two sufficiently hydrated wall specimens are prepared. Then, one is loaded without drying, while the other is tested after sufficient drying until the shrinkage of concrete reaches an equi-librium state. The results show a reduction in the initial stiffness and little change in the ultimate shear strength in the dry specimen, in spite of an increase in the compressive strength. Reproduction numerical analysis using Rigid Body Spring-network Model (RBSM) coupled with a truss network model for moisture transport is conducted, and an ac-ceptable agreement is confirmed in the ultimate strength and the crack patterns. From the numerical results, it is revealed that two factors are balanced in the ultimate shear strength after drying in this experiment: 1) an increase in the com-pressive strength due to aging (material scale), and 2) a strength reduction due to lateral strain, which is evaluated using the formula suggested by Vecchio and Collins (1986) (member scale). This indicates that the wall reinforcement ratio and concrete shrinkage have the influence on the ultimate strength through increasing/decreasing the number of cracks and the crack width.

1. Introduction

After demolding, it is inevitable for concrete to be ex-posed to ambient air to dry, and this drying process will take a long time until an equilibrium state or harmonic convergence is reached. In general reinforced concrete (RC) structures, concrete shrinkage due to drying is restrained by rebars and adjacent members, which can result in cracks.

In addition, drying affects the concrete in the multi-scale as well as the macro-scale, such as in drying shrinkage-induced cracking. On the nano-scale, changes in the physical characteristics of a calcium-silicate-hydrate (C-S-H) of cement paste have been reported (Maruyama et al. 2014a). On the sub-milli-scale, mi-crocracks occur due to the difference in the shrinkage of the aggregate and cement paste (Bisschop and Van Mier 2002; Idiart et al. 2012; Maruyama et al. 2012). As a result, macroscopic properties, such as the Young’s modulus and the compressive/tensile strength, change due to drying (Maruyama et al. 2014b). In particular, it

has been reported that the Young’s modulus of concrete decreases as drying progresses.

Meanwhile, a long-term decrease in the natural fre-quency has been observed in nuclear power plants and middle to high story RC buildings (Ikawa et al. 2012; Maruyama 2016; Morita et al. 2016). A theory to explain this phenomenon is the effect of drying on the RC structure (Maruyama 2016). As Maruyama has pointed out, a decrease in the Young’s modulus due to drying and drying shrinkage-induced cracks contribute to the stiff-ness reduction of the structure, which translates to a decline in the natural frequency. It is noteworthy that no stiffness change has been observed during small and medium earthquakes in 8 story steel-reinforced concrete (SRC) buildings (Li et al. 2014). This study revealed that a gradual decrease in the natural frequency is caused not by the small and medium earthquakes but by the other factors. Based on our existing data and research papers, it has been concluded that the influence of drying plays an important role on the reduction of natural frequency through the facts mentioned above (i.e., the decrease in Young’s modulus due to drying, and the decline in stiffness due to drying shrinkage-induced cracks).

Based on the above, in order to maintain the long-term safety of buildings, it is necessary to appropriately evaluate and predict the changes in the structural per-formance due to drying. The natural frequency reduction may cause unexpected resonance between structures and installments in important structures such as nuclear power plants, as well as unexpected excessive deforma-tion during earthquakes in medium to high story buildings.

Many experimental and numerical studies have been conducted on the influence of drying and the resultant

1Ph.D student, Graduate School of Environmental Studies, Nagoya University, Nagoya, Japan. 2Professor, Graduate School of Environmental Studies, Nagoya University, Nagoya, Japan. *Corresponding author, E-mail: [email protected] 3Researcher, Building Research Institute, Tsukuba, Japan4Associate Professor, Graduate School of Engineering, Nagoya University, Nagoya, Japan. 5Professor, Graduate School of Environmental Studies, Nagoya University, Nagoya, Japan.

H. Sasano, I. Maruyama, A. Nakamura, Y. Yamamoto and M. Teshigawara / Journal of Advanced Concrete Technology Vol. 16, 210-232, 2018 211

shrinkage on RC structural performance. For example, studies exist on the effect of shrinkage due to self-strain stress without considering concrete alternation (Umemura 1955; Aoyama 1958), the time dependent change in the stiffness of beams and slabs considering shrinkage, creep, and macroscopic cracks (Al-Deen et al. 2011; Gilbert 2013), tensile experiments of RC prisms (Bischoff 2001; Ema et al. 2002), the bending crack strength and ultimate bending strength of columns and beams (Iso et al. 1993; Tanimura et al. 2007; Lampropoulos and Dritsos 2011; Gribniak et al. 2013), and the shear strength (Sato and Kawakane 2008; Mitani et al. 2011; Nakarai et al. 2016; Nakarai et al. 2017). In tensile experiments of RC prisms, it was observed that drying shrinkage brought about a reduction in the ap-parent cracking load and made the softening steep (Gilbert 2013). With regard to the bending, a reduction in the bending crack strength has been commonly observed. In the ultimate bending strength, no significant changes have been reported. Iso et al. (1993) has reported that the standard formula could evaluate the bending strength of desiccated column specimens. Lampropoulos and Dritsos (2011) numerically confirmed that drying shrinkage decreased the ultimate bending strength of RC columns, and that simulation considering shrinkage re-produced the experimental result more precisely than that without shrinkage. Regarding the influence on the shear behavior, Nakarai et al. (2016) observed that the shear crack strength and ultimate strength of beams decreased in both cases with or without shear reinforcement as drying shrinkage increased. In numerical investigations, the changes in the structural performance of RC beams which show shear failure of RC beams (Gebreyouhannes and Maekawa 2011; Gebreyouhannes et al. 2014), and in the dynamic response of an 8 story RC building (Chijiwa and Maekawa 2015) were reproduced, using a multi-scale numerical model ’DuCOM-COM3’ devel-oped by Maekawa et al. (2003).

However, although some studies have reported the effect of drying on walls (Yoshida et al. 1987; Sashima et al. 2008; Hosoya et al. 2016; Maruyama 2016; Tadokoro et al. 2017), these are not sufficient to establish a com-mon view and little has been done to examine the mechanism of how the drying affects the structural per-formance of the wall. Sashima et al. (2008) conducted loading experiments on walls with drying shrink-age-induced cracks and reported a decrease in the initial stiffness and the same maximum load as non-drying walls. Hosoya et al. (2016) and Tadokoro et al. (2017) carried out a loading test of shear walls, simulating the cracks due to drying and earthquake using previously repeated-loads. They found that, compared with speci-mens without initial cracks, the wall with a wall rein-forcement ratio of 0.66% decreased in ultimate strength by 5%, while those with a ratio of 1.32% showed no change in strength. This indicates that the effect of drying changes depending on the reinforcement ratio. Maruyama (2016) pointed out that: 1) drying reduced the

initial stiffness by about 50% at the equilibrium of moisture transfer, 2) shrinkage-induced cracks contrib-uted more to stiffness reduction than to decreases in the Young’s modulus of concrete due to drying, based on 2D non-linear finite-element-method (FEM) coupled with a moisture transfer analysis. Kurihara et al. (2017) con-ducted a parametric study of a shear-wall dominant RC structure on the curing period and the scale-effect of drying numerically. As a conclusion, they pointed out that the natural frequency changes could be reproduced, and that the specimen scale significantly affected the aging changes of the initial stiffness due to drying, as well as the stiffness after long term drying (50 years).

To sum up, while an initial stiffness reduction has been commonly observed, the method to evaluate changes in the structural performance quantitatively and a common view on the effect of drying on the strength of walls have yet to be established. Furthermore, little has been re-ported on the mechanism of changes in ultimate strength due to drying.

Based on the previous research, the present study at-tempted to understand the effect of pure drying on a RC shear wall using experiments, after which its mechanism was analytically investigated. Two wall specimens were prepared for control and drying, with both being sub-jected to moist curing for about 100 days in order to avoid an additional progression of the hydration during drying. Subsequently, one was loaded without drying, and the other was loaded after being subjected to drying in ambient air for 1 year to achieve a moisture condition equilibrium. Experiment-reproducing numerical analy-ses were carried out, and the experimental results were discussed using the strain and stress of numerical analyses results. For the numerical study, the Rigid-Body-Spring-Model (RBSM) developed by Kawai (1978), coupled with moisture transfer using “Truss network model” (Bolander and Berton 2004; Nakamura et al. 2006), was adopted and the constitutive laws for repeated loading were introduced (Yamamoto et al. 2014).

2. Experimental outline

2.1 Concrete mixture properties and rebar properties Table 1 and Table 2 show the physical properties of the cement and aggregate, and the mixture proportions of the concrete. To investigate the effect of drying on the structural performance, the concrete mixture was de-signed to contain large amounts of water to promote drying shrinkage. The maximum size of the coarse ag-gregate was 15 mm, considering the workability, because the wall specimens are of a smaller scale than actual buildings.

As shown in Table 3, three types of rebar were used depending on their parts. Material properties of each rebar were obtained from direct tensile tests and 3 specimens were prepared for each type of rebar. In the


case of D4, a 0.2% offset yielding strength according to JIS Z 2241 was adopted because D4 did not show a clear yielding point. 2.2 RC wall specimen preparation and curing Table 4 and Fig. 1 show specifications and a schematic of the RC walls, respectively. The wall specimen was prepared at about a 1/3 scale and was designed to fail in shear. The thickness of the wall was 80 mm and the cross section of the column was 200×200 mm. The wall rein-forcement ratio was 0.35% and the longitudinal and transverse reinforcement of the columns were 2.85% and 0.32%, respectively, which meet the RC standard of Japan (AIJ 2010). In Table 4, calculated strength (i.e., a shear crack load, an ultimate shear strength, and an ul-timate bending strength) according to “Design Guide-lines for Earthquake Resistant Reinforced Concrete

Buildings Based on Inelastic Displacement Concept” (DGEI) (AIJ 1999) and Japanese RC standard (AIJ 2010) are shown. As shown in Fig. 4, the shear span ratio of the wall is 0.32, and the neutral axis was kept at the center of the wall height during the loading test. The shear span ratio was determined to make the shear deformation dominant.

In this study, two types of wall specimen, named “Sealed” and “Dried”, were prepared. Both specimens were cast at the same time, and then 7 days of sealed initial curing and moisture curing until the age of 87 days (Sealed specimen) or 104 days (Dried specimen) was reached. Afterwards, the Sealed specimen was loaded at the age of 94 days (exposed to ambient air for 7 days because of the measurement preparation). In the Dried case, the specimen was subjected to drying (ambient air in the experimental room) for approximately 1 year (until

Table 1 Physical properties of cement and aggregates. Material Notation Properties Cement C Ordinary Portland cement Water W -

Coarse aggregate G Seto Mountain gravel G: 60%, ρDRY: 2.55g/cm3, ρSAT: 2.58g/cm3 Maximum particle size: 15mm

Fine aggregate S Seto Mountain sand F:2.8%, ρDRY: 2.51g/cm3, ρSAT: 2.55g/cm3

Agent AE AE water reducing agent G: Solid volume percentage, F: Fineness modulus, ρDRY: Density at the oven dry condition, ρSAT: Density at the saturated surface dry condition

Table 3 Material properties of rebar. Position Type of steel Es (GPa) fy (MPa) εy (10-6) fu (MPa)

D4 Wall SD295A 177 367* 2073 523 D6 Column (stirrups) SD295A 182 347 1907 460

D10 Column (longitudinal reinforcement) SD345 199 382 1920 550

*0.2% offset yielding strength according to JIS Z 2241

Table 2 Mixture proportions and fresh properties of concrete. Mixture proportion Fresh Properties

Mass (kg/m3) W/C (%) s/a (%) W C G S AE Slump (cm)

Air (%)

Temp. (°C)

56.3 50 182 324 864 854 3.24 18 5.0 8

Table 4 Specimen specifications. Wall

Calculated value h (mm)

l (mm)

t (mm) Wall rebar pw

(%)

Shear span (mm)

Shear span ratio: a/d

(-) Shear crack load (kN)

Ultimate shear strength (kN)

Ultimate bending strength (kN)

1100 1300 80 2-D4@100 (26mm2) 0.35 550 0.32

(550/1700) 498*1 904*2 817*1 1830*3

*1DGEI formula (the mean formula for the effective compressive coefficient ν=0.8-σb/200 is used, σb: compressive strength of the cylinder (N/mm2)), *2Arakawa mean formula (*Shear span ratio is outside the scope (1<a/d<3)), *3AIJ standard

Column

h (mm) b d Longitudinal rebar pgc (%) Stirrup pwc (%)

1100 200 200 16-D10 (1136mm2) 2.85 2-D6@100 (64mm2) 0.32


the age of 462 days was reached) and then loaded. As shown in Fig. 2, an average temperature and relative humidity during the drying period were 18.4°C and 58.7% R.H., and the maximum and minimum tempera-tures were 34.3°C and 3.1°C; that is, the room which the walls were stored has no temperature and humidity con-trol. For measuring temperature of concrete, two ther-mocouples were embedded in the columns as shown in Fig. 1(a). Little difference between ambient air and in-wall temperature was observed. 2.3 Concrete properties Material property testing and drying shrinkage meas-urements were conducted. The compressive strength, Young’s modulus, and tensile-splitting strength were tested at the age of loading with a cylinder of concrete of

φ100×200mm, according to the Japanese Industrial Standard (JIS A 1108, JIS A 1149, and JIS A 1113, re-spectively). Tensile fracture energy tests were conducted using 100×100×400 mm concrete specimens with a notch of 30 mm in depth, according to JCI-S-001-2003 (JCI 2003).

Drying shrinkage was measured with 2 types of specimen: one 1000×1000×80 mm concrete plate specimen, which imitate a wall specimen (dummy specimen), as shown Fig. 3, and two φ100×200 mm cylinder specimens. One dummy specimen and two cylinder-specimens were prepared and desiccated in ambient air (same condition as the wall specimen). The four sides of the dummy specimen were sealed using aluminum tape, and the shrinkages were measured using 2 embedded strain gauges. In the case of cylinder

(a) Overall (b) Details of the wall and column Fig. 1 Schematic of the RC wall specimen.

Fig. 2 History of temperature and humidity.


specimens, shrinkage was measured using a height gauge (QM-Height 350, accuracy: (±2.8+5L/1000) μm， L: measuring length (mm); Mitutoyo, Kawasaki, Japan) without any sealing, and acrylic plates were attached to the head of the specimens for measurements.

The properties of the specimens are shown in Table 5. All specimens were cured and tested in the same condi-tions as each wall.

2.4 Loading tests of the RC wall specimens As shown in Fig. 4, the wall specimens were loaded so as to generate a reverse symmetric moment, and a panto-graph keeps upper and lower stubs parallel during load-ing; that is, the pantograph restrained both top and bot-tom stubs for rotation. The shear span ratio was fixed at 0.32. An axial force of 360 kN was applied during loading, which was associated with an axial force ratio of 0.15 in each column for the designed compressive strength of 30 MPa. The axial force was kept constant during loading. The loading process started from a story drift angle of ±1/3200, and then doubled. From the drift

angle of ±1/400, the cycle was repeated twice. In Sealed case, ±1/3200 cycle was repeated twice in order to adjust the wall to the equipment (i.e., ±1/3200 → (±1/3200(2): only Sealed) → ±1/1600 → ±1/800 → ±1/400 → ±1/400(2) → ±1/200 (Sealed failed at 1/220) → 1/170: Dried failed).

The measurement system is shown in Fig. 1(a) and Fig. 5. Measurement of the rebar strain was conducted from the time of casting, and the drift angle of the wall was calculated based on the horizontal deformation be-tween stubs using contact type displacement meters and a frame attached behind the stub.

1000

mm

450mm

Embedded Strain Gauge

1000mm

100mm 450mm (a) Strain gauge position

Sealed

80mm

Drying Surface

(b) Drying condition Fig. 3 Dummy specimen for shrinkage measurement.

Fig. 4 Loading device.

Fig. 5 Measurement system.

Table 5 Measured material properties of concrete at the age of the RC loading test.

Age (days) fc (MPa) Ec (GPa) n Ft (MPa) n Gft (N/m) n Cal.*

Sealed 87 35.5±0.24 30.4±0.27 3 3.1±0.29 4 87.9±4.4 4 81.1

Dry 462 39.0±0.44 (1.10)

26.0±0.88 (0.86) 5 3.0±0.57

(0.97) 5 128.7±11.7 (1.46) 4 -

*Calculated according to JSCE standard (JSCE 2002)


3. Experimental results

3.1 Material properties and drying shrinkage of concrete Table 5 shows the compressive strength (fc), Young’s modulus (Ec), tensile splitting strength (ft), and tensile fracture energy (Gft) before and after drying with stan-dard deviation (n in the table represents the number of specimen). The number in brackets shows the normal-ized properties (Dried properties/Sealed properties). In Dried specimens, a 10% increase in compressive strength and a 14% decrease in the Young’s modulus were ob-served. Although a mature concrete strength reduction of around 15% at the R.H. equilibrium state was reported (Maruyama et al. 2014b), in this study, the increase in strength seemed to be caused by C-S-H agglomeration bonding which mainly caused above 60% RH at room temperature (Maruyama et al. 2014b) and/or slight additional hydration of cement. On the other hand, the Young’s modulus reduction can be interpreted as the influence of the microcrack. It may be worth mentioning here that the compressive strength, 36.5±0.5 MPa (n=3), was also measured at the age of 28 days under standard water curing, which was almost same as for 87 days (Sealed). For the tensile splitting strength, almost no change was observed between the Sealed and Dried

specimens. The tensile fracture energy of the Dried specimens was 46% higher than for the Sealed. This may have been caused by microcracks: microcracks yielded during drying due to the difference of shrinkage strain between aggregate and cement paste should create mul-tiple cracks under bending moment, and resultantly, it is considered to increase the total mechanical work. In addition, similar result about the fracture energy has been reported (Matsuzawa and Kitsutaka 2013).

The shrinkage of the wall dummy and cylinder specimens during the drying period is shown in Fig. 6. From Fig. 6(a), it is clear that the drying shrinkage of the dummy specimen had reached the equilibrium state, which implies that the wall specimen also reached equi-librium because it was of the same thickness. The aver-age ultimate shrinkage was -903 μ in the dummy speci-men, and a similar result was found for the average -965 μ shrinkage in the cylinder specimen.

3.2 Shrinkage induced cracks of the wall Figure 7 shows the drying shrinkage-induced crack pattern, which was observed just before loading. The values in Fig. 7 indicate the crack width (unit: mm); cracks without value indicate the width of the entire crack was less than 0.03 mm. The maximum crack width was 0.15 mm, which locations were the upper left (front

(a) Dummy: average -901 μ (b) Cylinder: average -965 μ

Fig. 6 Drying shrinkage of concrete.

0 . 03 0 . 030 . 08

0 . 060 . 03

0 . 06

0 . 04

0 . 060 . 04

0 . 06

0 . 10

0 . 08

0 . 05

0 . 15

0 . 08

0 . 04

0 . 06

0 . 06

0 . 06

0 . 03

0 . 100 . 10

0 . 05

0 . 06 0 . 06

0 . 06 0 . 06 0 . 06 0 . 06 0 . 060 . 100 . 080 . 04

0 . 04

0 . 04

0 . 08

0 . 04

0 . 04 0 . 04

0 . 04

0 . 04

0 . 150 . 10

0 . 15

0 . 06 0 . 100 . 04 0 . 040 . 06

Front (right side is north) Back (right side is south) Fig. 7 Drying shrinkage-induced crack at the end of drying (at the age of 462 days).


side) and lower left corner (back side) of the wall re-strained by the stub and column. Crack widths were measured at 86 points in total using crack scale (average interval was about 10 cm), and the average crack width was about 0.05 mm.

Figure 8 shows the rebar strain after drying (slashed area means there was no data because of disconnection). Almost all the measurement points (25 out of 28) showed shrinkage strain, and the maximum shrinkage was -827 μ in the horizontal direction at the center of the wall. The wall reinforcement at the lower and upper left corner showed tensile strain; these regions corresponded to the location of drying shrinkage-induced cracks shown in Fig. 7. The maximum tensile strain was 323 μ in the vertical direction at the lower left corner of the wall.

3.3 Loading test results (1) Overall results Figures 9 and 10 show the load-deformation relationship obtained by the loading test with the theoretical stiffness (Kcal). A theoretical stiffness (Kcal) and a shape factor (κSF) for shear stiffness was calculated by Eqs. (1)-(2) (AIJ 2016).

13 1 , 2.215 3

allSF

aw

At l

κ η η= + = ≤⋅

(1)

3

1 1 1 121/ 1/ allSF

cal b s

GAEIK K K hh

κ⎛ ⎞⎛ ⎞= + = +⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠ (2)

where Aall: total cross-sectional area of wall and columns

Fig. 8 Rebar strain of the wall after drying and the load rebar yielding.


(mm2), t: thickness of wall (mm), law (= l + 2d in Table 4): total length of wall and columns (mm), Kb: theoretical bending stiffness (N/mm), Ks: theoretical shear stiffness (N/mm), E: Young’s modulus of concrete (N/mm2), G:Shear modulus of concrete (Poisson’s ratio of 1/6 was used) (N/mm2), h: length of specimens as shown in Table 4 (mm). Since the both walls showed brittle failure, few

data points in the post-peak were measured. Table 6 shows a list of load and displacement at significant stages. Compared with the Sealed specimen, a reduction was seen in the initial stiffness, the shear crack load (de-creased by 160 kN), and the yielding load of the column reinforcement (decreased by 85 kN). The ultimate strength was slightly lower (decreased by 40 kN, Dried/Sealed: 0.96) and the deformation at the ultimate strength increased by 1.1 times more than the Sealed specimen: 1/220 rad in the Sealed and 1/200 rad in the Dried. The deformation at the shear cracking load and the rebar yielding load of the column was almost the same between the Sealed and Dried specimens. It should be noted that despite a 10% increase in the compressive strength after drying (see Table 5) the ultimate strength of the Dried wall was almost the same. This phenomenon cannot be explained by existing standard formulas of the ultimate shear strength (e.g., Arakawa formula (AIJ 2010), the DGEI formula (AIJ 1999). This point is ar-gued in Section 5 using numerical results.

Table 7 indicates the stiffness of each cycle. The initial stiffness was calculated using a linear least-squares (a) Sealed

(b) Dried Fig. 9 Load-deformation relationships. Fig. 10 Envelopes of each specimen.

Table 6 Load and displacement at significant stages of loading.

Shear crack Yielding of wall rebar Bending crack Yielding of

column rebar Ultimate strength

Load Disp. Load Disp. Load Disp. Load Disp. Load Disp.

Sealed 435 0.37 (1/2970)

-464 -0.62 (1/1770) -610 -1.46

(1/753) 889 3.95 (1/278)

980 5.02 (1/220)

Dry 273 0.435 (1/2530)

-362 -0.95 (1/1160) 562 1.94

(1/567) 804 3.88 (1/284)

942 5.51 (1/200)

*Values in brackets shows drift angle. (Unit of “Load”: kN, Unit of “Disp.”: mm)

Table 7 Stiffness of each cycle.

Sealed Dry Theoretical stiff-ness*2

Dry /Sealed

Dry /Theoretical

Initial Stiffness (kN/mm) 1226 663 1330 0.54 0.50 1/800 459 333 0.73 0.25 1/400 289 236 0.82 0.18 Equivalent Stiffness

(kN/mm) 1/200 196*1 165 -

0.84 0.12 *1: Calculated by the least squares method of the load deformation relation from 0 kN to the failure (1/220) *2: Shape factor is calculated by the “AIJ standard for Lateral Load-carrying Capacity Calculation of Reinforced Concrete Struc-tures (Draft)” (AIJ 2016)


method using data from the origin to the positive peak in the 1/3200 cycle. The equivalent stiffness of each cycle was the average of the two slopes connecting the origin and the positive/negative peak. In this table, it is clearly observed that the initial stiffness after drying decreased by half; as deformation increased, the difference in the equivalent stiffness became smaller.

The crack pattern after failure is illustrated in Fig. 11; the gray parts indicate spalling at failure. Both the Sealed and Dried specimens showed brittle failure, and no change in the failure mode was observed. Clearly, more cracks were observed in the Dried wall, as Fig. 11 shows. This can be explained as the initial stress and shrink-age-induced cracks promoting the generation of new cracks at the time of loading. In the Dried specimen, the progress of cracks induced by drying shrinkage (initial cracks) were observed during the first cycle (1/3200), and it seemed to contribute to the initial stiffness reduc-tion and the occurrence of shear cracks. Focusing on the cracks at failure, it was observed that new cracks had occurred connecting to the existing cracks, which led to failure; that is, cracks at failure appeared independently of the shrinkage-induced cracks.

In short, drying and cracks induced by shrinkage had significant influence on the initial stiffness and the shear crack strength of the wall. On the contrary, little changes or slight decreases in the ultimate strength were observed despite the 10% increase in compressive strength. This is discussed fully in Chapter 5.

(2) Comparison of the initial stiffness The initial stiffness reduction of 0.54 times is compatible with the natural frequency reduction of 0.73 times fol-lowing equation by assuming the elastic response and the same vibration mode:

0 0/ /f f E E= (3)

where f: natural frequency after drying (Hz), f0: initial natural frequency (Hz), E: initial stiffness (kN/mm), and E0: initial stiffness before drying (kN/mm). In this equa-tion, weight of a building is assumed to change little by

aging. The value of 0.73 times in natural frequency is quite

close to the values shown in the previous reports con-cerning the natural frequency change of the existing buildings (i.e., the SRC building, and the nuclear power plants) which age are more than 10 years (Maruyama 2016; Morita et al. 2016). It was concluded that the im-pact of drying on the stiffness of RC wall and resultant natural frequency change was experimentally confirmed in this study.

4. Analytical study

4.1 RBSM In this study, the Rigid Body Spring Model (RBSM), developed by Kawai (1978), was adopted. The RBSM employs a discrete numerical analysis method, and deals with the crack propagation of concrete directly, since the RBSM represents a continuum material as an assembly of rigid particle elements interconnected by springs along their boundaries. To obtain the strain of the springs, relative displacement between the two elements con-nected springs is divided by the initial distance of the two elements (i.e., the distance between two Voronoi bary-center as shown in Fig. 5). Based on the nonlinear be-havior of these springs, the cracking behavior of a con-tinuum material can be simulated.

In the present modeling, each interface between two rigid particles was divided into several triangles formed by the barycenter and vertices of the interface, with each triangle having three individual springs: one for the normal force and two for the orthogonal tangential forces, as shown in Fig. 12. In some studies (Saito and Hikosaka 1999; Nagai et al. 2004, 2005), a rotation spring is in-stalled to bear the moment, while in the present study, the moment was borne by several normal springs, with the number corresponding to the vertices on a face (Yamamoto et al. 2008). In other words, the nonlinearity of the bending behavior was reproduced by the nonlin-earity of the vertical springs.

In discrete analysis models, the element division de-termines the position of the crack. In order to deal with

(a) Sealed: failure at 5.03 mm (1/220) (b) Dried: failure at 6.44 mm (1/170)

Fig. 11 Crack pattern at failure.


this problem, a random geometry using Voronoi dia-grams was applied, as described by Bolander and Saito (1998).

(1) Concrete model The tensile behavior of concrete was modeled using the linear elasticity until the stress reaches the tensile strength, followed by a bilinear softening branch of a 1/4 model, as shown in Fig. 13(a). The parameters for the concrete behavior in the tension field are the tensile strength (ft), the tensile fracture energy (Gft), and the distance between the Voronoi generators (h) (centroid of the rigid particle).

The behavior in the compression field is shown in Fig. 13(b), where the S-type curve is derived from the stress-volumetric strain relationship under hydrostatic pressure loading (Yamamoto et al. 2008). The skeleton curve is described by the fallowing equations:

20 0 1

21 1 1 1

( )( )

c

c

a ba b c

ε ε ε εσ ε ε ε ε⎧ + >= ⎨ + + ≤⎩

(4)

11

2(1 )

cc

c c

fE a

ε = −+

(5)

10

1

(1 )2

c c

c

E aa

ε−

= − (6)

0 cb E= (7)

2 11

2 1

( )2( )

c c c

c c

E a aa

ε ε−

=−

(8)

1 2 2 11

2 1

( )c c c c c

c c

E a ab

ε εε ε

−=

− (9)

21 1 1 1 1c c cc a b fε ε= − − − (10)

where fc, Ec, εc2, αc1, αc2 are the material parameters of concrete, and are determined as shown in Table 8.

Tangential springs represent the shear transfer mecha-nisms of the cracked (a normal spring strain exceed the cracking strain) and un-cracked concrete matrices (Fig. 13(c)). The softening process was modeled by the fol-

Barycenter of interface Position of springs

Shear spring

Shear springNormal spring Fig. 12 Schematic of the elements in RBSM and springs connecting rigid bodies.

(a) Tensile model of the normal spring (b) Compression model for the normal spring

(c) Shear spring model (d) Mohr-Coulomb criteria (e) Softening coefficient of shear spring

Fig. 13 Constitutive models for concrete (Yamamoto et al. 2008).


lowing equations:

( )max( ( ),0.1 ) ( )

f

f f f f

GK

γ γ γτ τ γ γ τ γ γ<⎧= ⎨ + − <⎩

(11)

where τ: shear stress (N/mm2), G: shear stiffness (N/mm2), τf: shear strength (N/mm2), γf: strain at the maximum stress in the shear strain and shear-stress rela-tionship, and K: shear softening coefficient (negative value). A linear relationship between the shear strain and stress was assumed until the stress reached the peak. Following the peak, the softening process was defined as a function of the shear strain and the normal spring stress on the same face, while the minimum value was assumed to be 0.1 τf. For the shear strength, the Mohr–Coulomb type criterion was adopted, as shown in Fig. 13(c), and is represented by the following equations:

{ tan ( )tan ( )

bf

b b

cc

σ φ σ στ σ φ σ σ− > −= + < − (12)

where c: cohesion parameter (N/mm2), φ : angle of in-ternal friction (degrees), and hσ : maximum shear strength of a normal spring (N/mm2). As shown in Fig. 13(e), the softening process of shear springs is a function of the normal stress:

K Gβ= (13)

0 maxmin( ( / ), )bβ β χ σ σ β= + (14)

where 0β , maxβ , and χ are parameters for shear sof-tening. Equations (11)–(14) are common to cracked and un-cracked concrete elements.

The shear transfer is reduced when the strain in the direction normal to the plane that the shear stress acts upon is in the post-peak region. This process is repre-sented by the coefficient crβ as shown in Eqs. (15)–(17). Equation (15) means that after a normal spring softened, stress of tangential spring is multiplied by the coefficient

crβ which is dependent on the tensile strain of normal spring.

( )max( ( ),0.1 ) ( )

cr f

cr ft f ft f

GK

γβ γ γτ β τ γ γ τ γ γ<⎧= ⎨ + − <⎩

(15)

exp ( )tcr t

tu

ε κβ ε εε ε

⎧ ⎫= −⎨ ⎬

⎩ ⎭ (16)

tanf tt c fτ φ= − (17)

where βcr: shear stress reduction factor due to normal spring (0 1)crβ< ≤ which was proposed by Saito and Hikosaka (1999), ε : strain of normal spring (positive: tensile strain), tε : cracking strain of normal spring, tuε : ultimate strain of normal spring (see in Fig. 13(a)), κ: constant parameter, and tf : tensile strength of normal spring (N/mm2).

It should be noted that, in the applied numerical model, the compression softening behavior from the macro-scopic view (i.e., stress-strain relationships in uniaxial compression tests) is reproduced by the shear spring softening behavior, and the stress of the normal springs determined the shear strength in the Mohr-Coulomb criteria. This material model makes it possible to repro-duce the failure process under multiaxial stresses pre-cisely (Gedik et al. 2011).

Figure 14(a) shows the typical hysteresis loop of a normal spring under reversed cyclic loading, which was implemented based on the model described above. The stiffness of the unloading, both in the compressive and tensile zone, is the initial elastic modulus. After the stress reaches zero, the normal spring keeps zero stresses. The reloading paths in the tension and compressive zone pass toward the starting point of the unloading. Fig. 14(b) shows the typical hysteresis loop of the shear spring. The stiffness of the unloading is the initial elastic modulus. In addition, after the stress reaches zero on the unloading path, the stress stays zero until the strain reaches the residual strain of the opposite sign.

(2) Rebar and bond-slip model For rebar and bond-slip modeling, the discrete rebar model proposed by Saito and Hikosaka (1999) was ap-plied. This model uses zero size link elements, which are connected to Voronoi generators (concrete elements) with a spring. For the axial behavior of reinforcing bars, the formula developed by Shima et al. (1987) was adopted. In the other direction, it is assumed to be elastic.

The bond-slip relationship between the concrete ele-ment and the link element is shown in Fig. 15. Equation (18) (Suga et al. 2001) is applied up to peak strength.

Table 8 Applied values of springs in the numerical calculation. (a) Normal spring

Young’s modulus Tension field Compression field Ec (N/mm2) ft (N/mm2) Gft (N/mm) fc (N/mm2) εc2 αc1 αc2 1.4Ec

* 0.8ft* 0.5Gft

* 1.5fc* -0.015 0.15 0.25

(b) Shear spring

Shear modulus Failure criteria Softening behavior η=G/Ec c (N/mm2) φ (degree) σb (N/mm2) β0 βmax χ κ 0.35 0.14fc

* 37 fc* -0.05 -0.025 -0.01 -0.3

An asterisk in this table means experimental properties (e.g., Ec* means the experimental value of Young’s modulus).


{ }2

0.530.4 0.9( ) 1 exp 40( )cf s Dτ ⎡ ⎤= ⋅ − −⎣ ⎦ (18)

where s: slip displacement (mm), and D: rebar diameter (mm). (3) Truss network model for moisture transfer Water diffusion in the concrete was modeled using a random lattice, whose mesh was defined by a Voronoi diagram, originally developed by Bolander and Berton (2004). Lineal conduit elements connect the Voronoi generators and special nodes set on the boundary sur-faces, which are named the “surface truss nodes”, are the centroid of the surfaces of the Voronoi mesh facing the boundary. The governing equation of the potential flow of Eq. (19) was modeled assuming a potential flow in the linear conduit as described in Eq. (20):

1 ( ( ) )R div D R grad R Wtω

∂= ⋅ +

∂ (19)

1 1

2 2

1

2

/1 1 2 1( ) 1

/1 1 1 26R 0

R 0

e e

env

b m

env

R R tA D R A L

R R tLR

A aR

ω

∂ ∂−⋅ ⋅+

∂ ∂−−

+ ⋅ =−

⎧ ⎫ ⎧ ⎫⎡ ⎤ ⎡ ⎤⎨ ⎬ ⎨ ⎬⎢ ⎥ ⎢ ⎥⎣ ⎦ ⎣ ⎦⎩ ⎭ ⎩ ⎭

⎧ ⎫ ⎧ ⎫⎨ ⎬ ⎨ ⎬

⎩ ⎭⎩ ⎭

(20)

where R: relative water content (-); ω: volumetric con-version factor (Nakamura et al. 2006); W : water con-sumption by cement hydration (g/mm3); D(R): moisture transfer coefficient (mm2/s); R1, R2: relative water con-

tent in conduit nodes 1 and 2, respectively (-); R env: relative water content at the equilibrium state with the environment (-); and t: time (s). In Eq. (20), the third term in the left-hand formula represents the flow on the boundary surface. Ae is the area of the Voronoi facet between the contiguous nodes i and j; L is the length of the conduit from node 1 to 2; αm: moisture transmission coefficient (mm/s), and Ab is the area of the boundary (mm2). The moisture transfer model was determined based on the research of Akita et al. (1994). 4.2 Outline of the analysis (1) Element Figure 16 shows the elements used in the analysis. The number of elements was approximately 35000, and the average distance between Voronoi barycenter of wall and column parts (the length of spring) was approximately 30 mm. Plate elements were installed on the top, bottom, and side of stubs. In RBSM, a plate element is generally applied to introduce boundary condition (e.g., a fixed boundary, a boundary given displacement) since an element of RBSM is assumed to be rigid, such element enable to fix all surfaces of the target elements. A dis-placement was given to the plate on the top stub. Re-garding the spring properties between the plate and Vo-ronoi surface, the Young’s modulus was sufficiently higher than the concrete, and they were assumed to be elastic. Boundary conditions are also shown in Fig. 16 (“fixed(x)” means direction x is fixed). To simulate the experimental condition, the vertical displacement was free and the rotation of the upper stub was fixed at the loading. (2) Spring properties The numerical parameters for the normal and shear springs of the concrete element are shown in Table 8. The material properties of rebar are the same as Table 3. Since in the RBSM, unlike FEM, spring properties do not have physical meanings, each parameter in Table 8 has been decided by conducting parametric analyses com-paring the specimen test results of the uniaxial tension, the uniaxial compression, the hydrostatic compression, and the triaxial compression (Yamamoto et al. 2008).

5

6 11

3,10

12

4

7 8

9

12

σ

ε

1

2

3

4,14

5

9

7

8

6

10

11

12

13 15

16

17

τ l

γ l

(a) Normal spring (b) Shear spring (σ = constant)

Fig. 14 Hysteresis of the stress-strain relationship (Yamamoto et al. 2014).

Fig. 15 Bond stress – slip model (Yamamoto et al. 2014).


Moreover, concrete properties during drying (moisture transfer analysis) were regarded as constant, for sim-plicity; that is, in the Dried case analysis, the results of the strength test (see Table 5) were initially introduced.

(3) Moisture transfer properties In the Dried case, the moisture transfer analysis is carried out first, and then the drying shrinkage is introduced into a normal spring as stress, which causes a deformation equivalent to the drying shrinkage. The drying shrinkage was modeled as a linear function of the relative water content (R=w/w0) as shown in the following equation:

sh sha RεΔ = Δ (21)

where αsh: coefficient of conversion from the relative water content to the shrinkage strain and R: relative water content (i.e., the ratio of the water content (w) to the maximum water content (w0)). The moisture transfer parameter is shown in Table 9. In Table 9, shrinkage and relative water content at 60% R. H. were obtained from the specimens, then αsh was calculated (i.e., -900×10-6/(0.55 – 1.0) = 2000×10-6 (αsh)). The tempera-ture analysis was not introduced in this study. Generally, temperature variation has impacts on rate of water transport and concrete shrinkage, but in our experiment, variation of temperature was gradual and not broad, and this means that consideration of temperature is not sig-nificant from a view point of structural performance. Consequently, to understand the impact of drying on the structural performance, our calculation objectives will be accomplished sufficiently, if both the drying rate and

shrinkage of concrete were reproduced in the calculation.

4.3 Analytical result (1) Moisture transfer analysis Figures 17 and 18 show a comparison of the water loss and shrinkage between the experiment and analysis. A good correlation was seen in both the water loss and shrinkage, therefore, a calibration of the parameter of moisture transfer was thought to be appropriate. The difference between two analytical strain shown in Fig. 18 is due to the angular variation of Voronoi surface.

Figure 19 shows a distribution of the relative water content just before loading (drying age: 370 days), the wall part completely reached the equilibrium state in ambient air, and the center of the columns retained a higher relative water content. It may be worth mention-ing that, in addition to the dummy specimen result (see Fig. 6(a)), this result provides the evidence that the wall specimen reached the equilibrium state in the experi-ment.

Figure 20 shows cracks induced by drying shrinkage with widths higher than 0.05 mm. Diagonal cracks at four corners of the wall were reproduced. However, their widths seem to be higher than the experimental result; in the numerical result, many parts of the cracks showed widths of more than 0.15 mm, and some parts had widths more than 0.25 mm. On the other hand, in the experi-mental result, many parts showed widths of 0.03～0.1 mm, and the maximum width was 0.15 mm. One possible explanation is that ignoring creep and property changes during drying affected the crack width.

Table 9 Material properties for moisture transfer and drying shrinkage. Shrinkage at equilibrium

Water content at saturation w0 (g/mm3)

Moisture transfer coefficient at saturation (m2/s) *1

Moisture transmittancecoefficient (m/s) *1 αsh

Renv: Relative water content at R.H. 60% equilibrium state

0.0736 3.47×10-9 1.74×10-5 -900μ 2000×10-6 0.55

*1Calculated according to Akita et al. (1994)’s formula

x

y

z x

y θy

θx θz (a) Concrete elements (b) Plate elements (colored parts) (c) Rebar elements

Fig. 16 Element for analysis.


(a) Water loss (b) Shrinkage

Fig. 17 Analytical result: water loss and shrinkage of cylinder specimen.

1.0 0.91 0.82 0.73 0.64 0.55RelativeWater Content(-)

(a)Cross section in the middle of the depth

(b)Cross section in the middle of the height Fig. 20 Analytical result: distribution of the relative water content after drying.

0.20.1 0.25(mm)0.05 0.15

Fig. 19 Analytical result of the cracks induced by drying shrinkage.

Fig. 18 Analytical result: shrinkage of dummy wall specimen.


(2) Loading analysis This section states the results of the loading analysis. The load-deformation relationships of the experimental and numerical results are compared in Fig. 21. The crack patterns of each cycle are shown in Figs. 22 and 23. As

shown in these figures, a good correspondence between the experiment and analysis was generally seen for fol-lowing factors: the initial stiffness in the Sealed case; the maximum strength (although a little bit lower than the experimental result) and its tendency to change before

(a)Sealed (b)Dried

Fig. 21 Analytical result of load-deformation.

Sealed Experiment Analysis

1/800

1/400

Failure (1/220)

0.40.2 0.50.1 0.3Crack

Width(mm) Fig. 22 Crack comparison between the experiment and the analysis (Sealed).


and after dying; the crack pattern and its tendency to change before and after drying (the number of cracks increase after drying); and the cracks at shear failure, which connect existing shear cracks.

However, numerical results of the initial stiffness after drying were significantly lower than the experimental result. One explanation for this result may be that the width of shrinkage-induced cracks obtained by the analysis was much larger, which reduced the stress borne

by the shear springs, as shown in Eq. (16). In other words, this numerical model might overestimate the effect of drying, from the perspective of initial stiffness. Yet, with regard to the ultimate strength of RC wall, the analytical results show acceptable agreement with the experimental values, therefore, the ultimate strength is discussed in the next chapter.

Dried Experiment Analysis

1/800

1/400

1/200(1) (maximum load)

Failure (1/170)

0.40.2 0.50.1 0.3Crack

Width(mm) Fig. 23 Crack comparison between the experiment and the analysis (Dried).


5. Discussion

In this chapter, the mechanism of the drying effect on the ultimate shear strength is discussed; that is, to investigate the reason why the ultimate strength did not change despite the increase in the compressive strength after drying. Figure 24 shows the factors, assumed in this paper, contributing to the wall strength.

For simplification, this discussion considers only the arch mechanism (the truss mechanism is left aside) be-cause the shear span ratio is as low as 0.32, and 77% of the strength is attributed to the arch mechanism from the DGEI (AIJ 1999) formula. It should be noted that the discussion including the truss mechanism, according to the DGEI formula, is also described in Appendix 3, and the assumption does not affect the conclusion.

Based on the theory of the arch mechanism, the wall strength is determined by the concrete strength and the compressive strut width. In addition, the concrete strength in the wall is not only determined by the material strength (i.e., strength of the uniaxial compression test) but is also affected by the strain perpendicular to the compressive strut due to cracking (Vecchio and Collins 1986; Miyahara et al. 1987).

Hence, as a working hypothesis, we suppose that the rise of the material strength and other factors that cause a decline in wall strength (i.e., narrow strut width, increase in lateral strain) were balanced; consequently, the strength of the walls before and after drying became equal. To investigate this hypothesis, we use the stress and strain distribution obtained by the RBSM.

5.1 Strut width The strut widths were estimated based on three methods: the neutral axis, the minimum principal stress, and the theoretical value (AIJ 1999). The element stress was calculated from the force generation on the element surface (the force borne by springs). With regard to the neutral axis, elements were cut at a 5 mm height from the lower end of the wall, and the stress was calculated. For the principal stress, in order to acquire the stress tensor, each element at the center in the depth direction (z-direction) was cut along a plane perpendicular to the width, height, and depth direction of the wall, which are associated with x, y, and z direction as shown in Fig. 16 respectively, so as to pass through the barycenter of elements (Bolander et al. 2001), and then the stress was calculated according to Cauchy’s formula (Iwamoto et al. 2017).

Figure 25 shows the vertical (in the height direction) stress at the maximum load, which was averaged at 50 mm intervals. Figure 26 shows the minimum principal stress. In both the Sealed and Dried case of Fig. 25, the neutral axis is between 500～550 mm from the end of the column and Fig. 26 indicates almost the same result. From these results, it was confirmed that drying had no effect on the strut width. Furthermore, it should be noted that the position of the neutral axis corresponded to the theoretical value at the maximum load of the arch mechanism (Fig. 27 and Eq. (22)-(24)), as shown in Table 10.

U ltim ate strength

of shear w all

Arch

M echan ism

Stru t W id thEvalu ated by num erica l resu lt:

Section 5.1

Concrete

Strength

Cylind er

Strength

After d ryin g , 10% increase w as

ob served (a lready g iven ) : Tab le 5

Strength

Reduction

due to Crack ing

Evaluated by num erica l resu lt and

Vecch io et a l’s form u la : Section 5.2

Truss

M echan ism

Ignored in th is chap ter.

In Appendix 3 , the exam ina tion considering

Truss M echanism is conducted.

Eva lua tion results

Fig. 24 The factors that determine the shear wall strength.

Fig. 25 Analytical result: stress distribution of the wall section.


2maxl (1 tan )neutral L x θ= − + (22)

max / 2x L= (23)

2 2max max maxtan ( / 2 ) ( / 1) /(2 )h x L x h xθ = + − − (24)

where lneutral: the position of neutral axis (mm), xmax: x at the maximum load (mm), L: width (mm), h: height (mm), and θ: angle of strut (rad). In Appendix 2), the derivation of the Eq. (23) is described. Therefore, the position of the neutral axis was set to 600 mm in the later calculations. 5.2 Concrete strength Based on the previous section, the effect of cracking on the concrete strength is assumed to balance the increase of the uniaxial strength. As shown in Eq. (25), Vecchio and Collins (1986) suggested an empirical formula of the relationship between the lateral strain and the compres-sive strength of the RC plate. Miyahara et al. (1987) also reported the same result. In addition, recently, Nanri et al. (2016) reported that this strength reduction was due to the crack itself.

In this section, the strain perpendicular to the com-pressive strut is calculated from the RBSM result, and an estimate of the wall strength can be obtained based on the arch mechanism using Eq. (25):

1 , 0.0020.8 0.34 /h c

a εε ε

= = −−

(25)

where α: reduction ratio of compressive strength (-), εh: the lateral strain perpendicular to the compression strut at the maximum load, and εh: strain at the compressive strength of the uniaxial test. It should be noted that the wall reinforcement ratio of Miyahara’s experiment was 0.3～0.6%, which is considered to be applicable to this experiment where the reinforcement ratio was 0.35%.

Table 11 shows the lateral strain of the compression strut at the maximum load (εh) and the calculation proc-ess of the ultimate shear strength (Qsu_cal), which is based on the arch mechanism and the concrete strength reduc-tion due to the lateral strain. Qsu_cal was calculated fol-lowing Eq. (26). This formula was derived from the assumption that the maximum load was consistent with when the entire cross section reached the compressive strength, while considering the reduction factor:

_ sinsu cal cQ t w a f θ= ⋅ ⋅ ⋅ (26)

where t: wall thickness (mm), and w: width of strut as shown in Fig. 27 (mm).

The lateral strain was the average of the three strains along the lines shown in Fig. 26 (each strain was calcu-lated using deformation of elements at the end of the line). As shown in Table 11, the Qsu_cal agree with the ultimate strength of the experimental and analytical result. Par-ticularly, it should be emphasized that the wall subjected to drying has a large lateral strain because of the increase of cracks, which leads to a larger strength reduction than the sealed specimen. Therefore, an increase of the cyl-inder strength and the strength reduction due to the lat-eral strain balance each other. As a result, the ultimate strength before and after drying shows almost the same value.

5.02.0

-1.0-4.0-7.0-10.0-13.0-16.0-19.0-22.0

-25.0

σp_min(N/mm2)

(a)Sealed (b)Dried

Fig. 26 Analytical result: principal stress of the middle section.

Table 10 Calculation results of the neutral axis position (lneutral).

Stress distribu-tion

(From Fig.25)

Principal stress (From Fig.26)

Theoretical*1

(From Eqs. (22)-(24))

500～550mm 600mm 598mm

These values correspond to lneutral in Fig.27, and indicate the distance from the left end of the column. *1According to DGEI (AIJ 1999)


As a conclusion of this discussion, the following mechanism is proposed to explain the experimental re-sults of this study: an increase in the compressive strength due to additional aging (in the material scale) and the strength reduction due to an increase of the horizontal strain (in the member scale) were balanced, consequently, little change in the ultimate shear strength was observed.

6. Conclusion

In the present study, so as to reveal the influence of drying and the resultant cracks on the structural per-formance of RC shear walls, experiments and analyses were conducted.

First, a loading experiment on a matured RC wall, which had been kept sealed until loading, and on a wall which was subjected to drying, after moisture curing during almost the same period as the sealed specimen, was carried out. In this experiment, the influence of hydration was eliminated to the upmost (i.e., the mois-ture curing period was more than 87 days) and the drying period was sufficient for the moisture content of the wall to reach the equilibrium state. The results were as fol-lows: 1) With regard to concrete properties after drying, the

compressive strength was 10% higher, the Young’s modulus was 14% lower, the tensile splitting strength was almost same, and the tensile fracture energy was

46% higher than the sealed one. 2) The initial stiffness of the wall after drying decreased

46% compared with the sealed specimen, and the initial stiffness of the sealed specimen corresponded with the theoretical stiffness.

3) Both the sealed and dry walls showed shear failure and the same failure mechanism. The ultimate strength was almost same: 980 kN for the Sealed and 942 kN for the Dried. Furthermore, the horizontal displacement at the ultimate strength was increased after drying: 1/220 rad in the Sealed and 1/200 rad in the Dried.

Next, an analytical study using the Rigid-Body Spring Model (RBSM) was conducted in order to clarify the reason why the ultimate strength was almost same before and after drying, even though the compressive strength after drying increased by 10%. In RBSM, a truss network model for solving the moisture diffusion, with cracking due to drying, was implemented. Thus, the flow of analysis is the following: i) moisture diffusion analysis, ii) introducing shrinkage as the equivalent nodal force and the mechanical analysis, and iii) mechanical analysis of the loading after repeating i) and ii) for a predeter-mined period. The acquired results and discussion are as follows: 4) The experimental results were almost reproduced

by the RBSM excepting for the initial stiffness after drying. Changes in the cracking pattern as well as the ultimate shear strength agreed with the experi-mental results.

5) A mechanism to explain why the ultimate shear strength did not change due to drying was suggested. From the analytical investigation, we concluded that the increase of the compressive strength in the uniaxial condition and the reduction of the com-pressive strength due to cracking in the wall bal-anced each other. To calculate the reduction ratio, Vecchio and Collins (1986) empirical formula was adopted and the lateral expansion of compressive strut at the ultimate strength was acquired from the RBSM results. Moreover, we confirmed that no change occurred in the width of compressive strut before and after drying.

6) Based on the mechanism of 5), the factors, such as the wall reinforce ratio and shrinkage, is assumed to affect the ultimate strength of shear walls strongly. We would like to investigate what factors have a large effect on structural performance as future subjects.

θ

x

wh

L (= l + 2b)

x(1+tan2θ)

θ

L - x

lneutral

Fig. 27 Schematic of the arch mechanism.

Table 11 Calculation process of ultimate strength considering strength reduction factor.

Arch mechanism Strength reduction Experiment & Analysis Fc

(MPa) t

(mm) xmax

(mm) tanθ Q’*3

(kN) εH (μ) α

Qsu_cal (kN) Qsu_exp

(kN) Qsu_rbsm

(kN) Sealed 35.5 1313 3395 0.73 954 980 898

Dry 39.0 80 850*2 0.54*3 1443 4616 0.63 910 942 877

*1w=xmax/cosθ, *2 From Eq. (23), *3Q’=t・w・Fc・sinθ(=Qsu_cal/α)


Acknowledgements This work was supported by a Grant-in-Aid for Scientific Research (B) (Grant No. 15H04077), and a Grant-in-Aid for Scientific Research (S) (Grant No. 16H06363) from the Japan Society for the Promotion of Science. A part of this paper (up to Chapter 3 in this paper) was registered in “NAGOYA Repository” (an academic institution re-pository of Nagoya University) as a preprint (Sasano and Maruyama 2018). References AIJ, (2010). “AIJ standard for structural calclation of

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Appendix 1. Material data and analytical model

(a) D4 (b) D6 (c) D10

Fig. B Rebar tensile test results.

(a) Compressive test (b) Fracture energy test

Fig. A Concrete test results.


2. Theoretical strut width at maximum strength based on the arch mechanism

As shown in Fig. 27, w (strut width) can be arranged as the following Equation.

/ cosw x θ= (27)

Equation (26) can be arranged as follows by combin-ing Equations (24) and (27):

{ }_

2 2 2

( tan )

( / 2) ( / 2) ( / 2) / 2su cal c

c

Q t x f

t x L L h h f

θ′ = ⋅ ⋅ ⋅

= − − + + − (28)

From Equation (28), the strut width when the arch mechanism bears the highest shear force (xmax) is L/2. In this study, L/2 is 850 mm. 3. Qsu_cal considering the truss mechanism based on the formula from the Design Guidelines for Earthquake Resistant Reinforced Concrete Buildings

In Chapter 5, the truss mechanism was ignored for simplicity. In this section, the maximum load considering the truss mechanism is investigated based on the formula from the “Design Guidelines for Earthquake Resistant

Reinforced Concrete Buildings Based on Inelastic Dis-placement Concept” (DGEI).

With regard to the arch and truss mechanism, the concept is widely accepted that the surplus calculated by subtracting the stress generated by the truss mechanism from the compressive strength is regarded as the stress borne by the arch mechanism. In DGEI, the truss mechanism force at the maximum load and the ratio of the stress distributed to the truss mechanism are ex-pressed as follows:

cottruss wb w syQ t l p σ φ= ⋅ ⋅ (29) 2(1 cot ) /( )s sy cp vfβ φ σ= + (30)

0.8 / 200cv f= − (31)

where t: wall thickness (mm), lwb: effective wall length (mm), pw: wall reinforcement ratio (-), σsy: tensile strength of rebar (N/mm2), φ : compressive strut angle of the truss mechanism ( cot 1.0φ = ), ν: effective compres-sive strength coefficient (-), and fc: compressive strength of the cylinder (N/mm2). As shown in Table A, the cal-culated strength roughly agreed with the experimental result and the trend was the same. Therefore, considering the truss mechanism did not affect the result of the sug-gested mechanism.

Table A Calculation of the ultimate strength considering the truss mechanism. Arch mechanism Experiment & Analysis

Qtruss (kN) ν β (1-β)Qsu_cal

(kN)

Qtruss+(1-β)Qsu_cal (kN) Qsu_exp

(kN) Qsu_rbsm

(kN) Sealed 190 0.62 0.13 833 1023 980 898

impact of drying on structural performance of reinforced

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