Experimental study on the seismic behavior of RC shear walls after freeze-thaw damage

Engineering Structures 206 (2020) 110101

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Experimental study on the seismic behavior of RC shear walls after freezethaw damage

T

Xian-Liang Rong , Shan-Suo Zheng , Yi-Xin Zhang, Xiao-Yu Zhang, Li-Guo Dong ⁎

⁎

School of Civil Engineering, Xi’an University of Architecture and Technology, Xi’an 710055, China

ARTICLE INFO

ABSTRACT

Keywords: Frost-damaged RC shear wall Seismic performance FTCs Concrete strength Axial load ratio

Previous research shows that frost action represents one of the most dangerous threats to reinforced concrete (RC) structures. However, very few experimental studies have been performed on the seismic behavior of frostdamaged RC shear walls. Thus, this paper used the artificial climate rapid freeze-thaw technique to simulate the freeze-thaw environment. Successive freeze-thaw cycle tests and quasi-static tests were performed on eight RC shear wall specimens to investigate the seismic performance of frost-damaged RC shear walls. The key variables include the number of freeze-thaw cycles (FTCs), concrete strength and axial load ratio. The seismic behavior of test specimens was evaluated in terms of damage process, hysteretic behavior, load carrying capacity, deformation capacity, energy dissipation capacity, and shear deformation. The experimental results indicated that as the number of FTCs increased, the flexural-shear failure of the RC shear walls shifts from a flexure-dominated mode to a shear-dominated one. Meanwhile, the load carrying capacity, deformation capacity, and energy dissipation capacity gradually decreased. Furthermore, the freeze-thaw cycle can weaken the shear resistance of RC shear walls and can increase the average shear distortion and the ratio of shear deformation to the total deformation under different loading states. Based on the test results, a calculation equation was proposed for RC shear wall skeleton curves considering the influence of freeze-thaw damage and axial load ratio.

1. Introduction It is well known that frost action in cold regions is one of the main reasons for the decline in mechanical properties of concrete [1]. In Northeast China, the winter has a long duration with low temperatures and large temperature variations between day and night, reinforced concrete (RC) members are repeatedly subjected to a freeze-thaw cycle every year, and the deterioration of RC members caused by frost action is becoming increasingly significant [2]. Damage of RC members caused by frost action has attracted significant attention for several decades in Japan, Canada, and North America [3,4]. Meanwhile, these RC members may also locate in earthquake fortification regions. Therefore, it is necessary to study the seismic behavior of these deteriorated RC members. Most of the available relevant research studies mainly focused on the effect on the material scale. The widely accepted mechanism of frost damage [5,6] is that when the pore pressure generated by the expansion of pore water during freezing exceeds the concrete tensile stress, cracks initiate and lead to a series degradations of concrete properties. As stated in a series of experiments [7–12] that were conducted to investigate these degradations on the concrete material, their test results ⁎

concluded that as the number of freeze-thaw cycles (FTCs) increased, the strength and elastic modulus of confined and unconfined concrete [8] and the bond strength between concrete and steel [9,11,12] gradually decreased, whereas the peak strain of concrete gradually increased [7,8]. Moreover, high-strength concrete experiences less freezethaw damage than normal concrete under the same number of FTCs [8,12]. Compared with the deep insights on the properties of frost-damaged concrete materials, research on seismic performance of frost-damaged RC members is still limited, and the relevant research studies mainly focused on the RC columns [13–16]. Among them, Xu et al. [13], Qin et al. [14], Zhang et al. [16] used artificial climate environment simulation technology to subject concrete columns to various numbers of FTCs, after which the columns were subjected to quasi-static testing. Moreover, their test results concluded that the freeze-thaw cycle has a considerable impact on their strength, ductility, and energy dissipation. RC shear walls are the key structural elements widely used to resist lateral loads in medium- to high-rise buildings due to their capability to provide lateral strength, stiffness, and energy dissipation [17]. Many experimental studies have been conducted to investigate the effect of several parameters on the seismic performance of unfrozen RC shear

Corresponding author. E-mail addresses: [email protected] (X.-L. Rong), [email protected] (S.-S. Zheng).

https://doi.org/10.1016/j.engstruct.2019.110101 Received 12 August 2019; Received in revised form 14 December 2019; Accepted 14 December 2019 0141-0296/ © 2019 Elsevier Ltd. All rights reserved.

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walls [18–21]. For example, Su and Wong [18], Zhang and Wang [19], and Looi et al. [21] performed quasi-static tests to study the seismic performance of RC shear walls, wherein the axial load ratio and concrete strength were commonly used as test variables. However, considering freeze-thaw action, only Yang et al. [22] successively carried out freeze-thaw cycle test and quasi-static test on four shear walls specimens with a shear span ratio of 1.14 to investigate the seismic performance of frost-damaged squat RC shear walls that failed in shear. However, the shear span ratio of Yang’s [22] research under FTCs is limited to 1.14, in which failure with shear types and tests on frostdamaged RC shear wall specimens with other shear span ratios that might be flexural-shear and flexural failure types have not been studied. Moreover, in Yang’s [22] research, only one variable is the number of FTCs, and no research was performed on the effect of key parameters such as concrete strength and axial load ratio. Based on this, there is a need for more experimental studies on seismic behavior of frost-damaged RC shear walls with different shear span ratios and parameters. This paper aims to experimentally evaluate the effect of the of FTCs, concrete strength and axial load ratio on the seismic performance of frost-damaged RC shear walls dominated by flexural-shear failure. The test results discuss the damage process, load carrying capacity, deformation capacity, energy dissipation capacity, and shear deformation. Meanwhile, a skeleton curve calculation equation is proposed considering the effects of freeze-thaw damage and axial load ratio based on the test results. Moreover, a brief discussion on the experiment and skeleton curve calculation equation limitations is presented, followed by recommendations for the upcoming research.

horizontal web reinforcements were 6-mm-diameter HPB235 plain bars, and the percentage of reinforcements are shown in Table 1. Cantilever-type specimens fixed at an RC base were adopted, and the dimensions of the base were 400 mm (high) × 1500 mm (width) × 400 mm (thickness). The cross-section and reinforcement details of the test walls are shown in Fig. 1. It should be noted that the shear span ratio of the tested RC shear wall specimens under FTCs is limited to 2.14, and test on frost-damaged RC shear wall specimens with a shear span ratio of 1.14 (which might be dominated by shear failure) will be reported in the near future. To make the tensile longitudinal reinforcement yield, the reinforcement will not be pulled out, to ensure that the all test RC shear wall specimens can make full use of the tensile strength of the reinforcement. After the anchorage length is calculated according to standard GB50010-20010 [24] (lab = df y ft ), a hook of 90° with a length of 12d (d is the diameter of rebar) is added at the end of the longitudinal reinforcements of the boundary elements and vertical web reinforcements according to standard GB50010-20010 [24]. Fig. 2(e) shows the lap slice of reinforcement. Note that secondary concreting was adopted during the fabrication process due to the limited dimensions of the environmental chamber and to avoid frost damage in the wall-base joint. The detailed steps of the fabrication process are as follows: The wall webs were first cast and cured for 24 days under a natural environment (see Fig. 2(a)). Then, the samples were placed in 15–20 °C water for 4 days before being placed into the environmental chamber (see Fig. 2(b)). After the freeze-thaw exposure was finished, the foundation block and loading beam were cast (see Fig. 2(f)).

2. Experimental program

2.2. Properties of materials

2.1. Specimen design

The designed concrete strength grades of the specimens were C30, C40 and C50, respectively. The water cement ratio of C30, C40 and C50 concrete is 0.53, 0.48, and 0.40, respectively. The stone has a maximum particle size of 15 mm, the sand has a modulus of fineness above 2.6, and no air-entraining agent is added, while the mix ratio used in this study is shown in Table 2. Three cube concrete specimens with the same cured and freezethaw cycle conditions as RC shear wall specimens are taken as a group (the side length is 150 mm), and the compression tests of the concrete cubes were carried out when the freeze-thaw exposures were finished, with the average results given in Table 3. Fig. 3 shows the relative compressive strength (ratio of compressive strength of concrete with and without frost-damaged) under different numbers of FTCs. It shows that the compressive strength decreased as the number of FTCs increased, and the decreasing rate gradually increases. This phenomenon could be attributed to the freeze-thaw damage concrete gel that is lost, such that the hydration product gradually changes from a dense block to a loose needle [22]. Moreover, the periodic freezing pressure formed by the pore water causes microcracks to appear in the middle of the

The experimental work assesses the response of RC shear walls when subjected to in-plane axial compressive stress and cyclic lateral excitations. The main variables considered were the number of FTCs, concrete strength grade and axial load ratio. Table 1 summarizes the design parameters details of the tested walls. Note that the axial load N was kept at a constant value instead of the axial load ratio n because the actual axial load ratio changed as the concrete strength decreased in response to the freeze-thaw attack. According to the Chinese standard and code [23,24], eight rectangular cross-section RC shear wall specimens with the same geometry and structural details were designed. The dimensions of specimens were 1400 mm (high) × 700 mm (width) × 100 mm (thickness), the thickness of the concrete cover was 10 mm, boundary elements in the form of beams were set for the shear walls, and the shear span ratio of the walls was 2.14. The reinforcement of the specimens is symmetrically arranged and well distributed around the cross-section. The longitudinal reinforcements of the boundary elements were four 12mm-diameter HRB335 deformed bars, the stirrup, vertical and

Table 1 Design parameters of the shear wall specimens. Specimen number

Shear span ratio

ρh (%)

ρv (%)

ρbs (%)

ρbe (%)

Concrete strength grade

Axial load ratio n

Axial load N (kN)

FTCs

SW-9 SW-10 SW-11 SW-12 SW-13 SW-14 SW-15 SW-16

2.14 2.14 2.14 2.14 2.14 2.14 2.14 2.14

0.283 0.283 0.283 0.283 0.283 0.283 0.283 0.283

0.377 0.377 0.377 0.377 0.377 0.377 0.377 0.377

0.377 0.377 0.377 0.377 0.377 0.377 0.377 0.377

4.524 4.524 4.524 4.524 4.524 4.524 4.524 4.524

C50 C30 C40 C50 C50 C50 C50 C50

0.2 0.2 0.2 0.2 0.1 0.2 0.3 0.2

586.05 293.35 379.53 526.68 235.62 471.25 706.87 397.94

0 100 100 100 200 200 200 300

Notes: ρh and ρv are the percentages of the horizontal web reinforcement and vertical web reinforcement, respectively; ρbe and ρbs are the percentages of the longitudinal reinforcement and the stirrup in the boundary elements, respectively. 2

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Fig. 1. Dimensions and reinforcement details of the shear walls (units: mm).

Fig. 2. Test procedure.

hydration product, and with the number of FTC increases, the width of microcracks gradually increases. Under the same FTCs, with the increased concrete strength, the relative concrete strength gradually increased, and the increasing rate gradually increased, indicating that the increase of concrete strength can enhance the frost resistance of concrete. This phenomenon could be attributed to the high-strength of the cement paste of the high-strength concrete, which enables the ability of the concrete to bear the tensile stress caused by the expansion of pore

water to be high. Moreover, for high-strength concrete whose hydration products are dense, the total internal microporous content is small, while the cracks in the cement paste and the cracks in the interface between the aggregate and cement paste are few and narrow. According to Chinese code GB/T228-2010 [25], three bars of the same diameter and type are taken as a group to carry out the tensile test, and the average mechanical properties index of the reinforcement are shown in Table 4.

Table 2 Mixing ratio of the concrete. Concrete strength grade

Water cement ratio

Type of cement

Cement (kg)

Water (kg)

Medium sand (kg)

Stone (kg)

Fly ash (kg)

C30 C40 C50

0.53 0.48 0.40

P.O 32.5R P.O 42.5R P.O 42.5R

383 425 515

205 205 205

566 540 427

1146 1091 1112

60 75 90

3

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Table 3 Mechanical properties of the concrete. Concrete strength grade

fcu0 (MPa)

fcu100 (MPa)

fcu200 (MPa)

fcu300 (MPa)

fcu100/fcu0

fcu200/fcu0

fcu300/fcu0

C30 C40 C50

32.00 40.30 55.08

28.53 36.48 51.70

24.10 31.18 45.72

17.92 24.18 37.45

0.89 0.91 0.94

0.75 0.77 0.83

0.56 0.60 0.68

Notes: fcu0 and fcu100, fcu200, fcu300 are the cubic compressive strength values of the unfrozen concrete and the concrete after 100, 200, 300 freeze-thaw cycles, respectively.

Relative compressive strength

1.2

C30 C40 C50

1.0

0.8

0.6

0.4

0

100

200

300

FTCs Fig. 3. Relative compressive strength. Fig. 4. Application of temperature variation during each cycle.

2.3. Details of the freeze-thaw exposure

64 °C/h, respectively. Moreover, to produce better freeze-thaw effects, five spray cycles were maintained for 15 min at the end of the maximum temperature phase, and one spraying cycle lasted for 3 min, i.e., 1 min of spraying, followed by 2 min without spraying.

The artificial climate rapid freeze-thaw technique is used to simulate the freeze-thaw environment. A model ZHT/W2300 environmental chamber was used for freeze-thaw cycle testing at the component level, as shown in Fig. 2(c). The freeze-thaw condition is simulated through variation in temperature and humidity cycles, of which parameters are pre-set in the chamber according to the Chinese standard [26]. The temperature and humidity technical specifications are as follows.

2.4. Loading scheme and test point arrangement The cantilever test setup and measurement configuration are shown in Fig. 5. Axial and lateral loads were transferred to the walls through the beams constructed over the wall webs. The specific loading process is as follows: first, the target constant axial load was exerted on the specimens via hydraulic jacks; then, a horizontal cyclic lateral load is applied by an MTS actuator fixed on the reaction wall until the specimen obviously fails or the lateral load drops to 0.85 times the peak load. The horizontal cyclic lateral loading point is at the center of the top beam, and its detailed loading scheme is according to the Chinese National Standard JGJ101-96 [23] as follows: before yielding, the lateral load was exerted in the load-control mode, wherein the load increment was set at 20 kN for each step, and each load level was repeated once; after yielding, three loading cycles were conducted in displacement-control mode, wherein the displacement increment was 3 mm for each step. The horizontal cycle lateral loading procedure is shown in Fig. 6. In addition, the axial load N and horizontal lateral load P were measured by a vertical pressure sensor and a horizontal pull-pressure sensor installed on the top of the wall. The horizontal displacements at

(1) Temperature control: the heating rate and cooling rate (without heating samples) are 0.7–1 °C/min, the temperature variation range is −20 to 80 °C, the temperature departure is ± 2 °C, and the temperature fluctuation is ≤ ± 0.5 °C. (2) Humidity control: the humidity range is 30–98% RH without heating samples, and the humidity departures are 2 to −3% (> 75% RH) and ± 5% (≤75% RH). The freeze-thaw exposure of the shear wall specimens is stopped when the design number of FTCs is reached, and the design FTCs of eight specimens are shown in Table 1. The environmental parameters of the freeze-thaw cycle are shown in Fig. 4, and the detailed control scheme of each FTC is as follows [26]. One FTC lasted 5.5 h, wherein the minimum temperature was −17 °C, which was maintained for 2 h, and the maximum temperature was 15 °C, which was maintained for 1 h. The temperature ramp rates to reach the minimum and maximum temperatures were 16 °C/h and Table 4 Mechanical properties of the reinforcement. Type

Appearance

Diameter (mm)

Yield strength fy (MPa)

Ultimate strength fu (MPa)

Elastic modulus Es (MPa)

Elongation (%)

HPB235 HRB335

Plain Deformed

6 12

270 409

470 578

2.1 × 105 2.0 × 105

10.52 7.41

4

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Reaction beam

Sliding support Rigidity beam

Hydraulic jack

RC top beam

LVDTs

MTS actuator

Shear wall

Reaction wall

700 mm

LVDTs

Rolled screw

Threaded rod

RC foundation

Strong floor

Fig. 5. Test setup and instrument arrangement.

the loading point were measured with linear variable displacement transducers (LVDTs) installed on the wall surface. The shear deformation was measured with two 45° crossed LVDTs attached to the wall specimen. The LVDT arrangement is shown in Fig. 5.

cracks continue to increase, while transverse cracks widened and extended to the center of wall SW-16, as shown in Fig. 7(c). It is worth noting the slow crack growth of concrete [27,28]. This phenomenon could be attributed to the freeze-thaw action changing the internal crystal structure of the concrete, thereby changes from flake to needle shape occur [22], which reduces the chemical bond of the concrete and thus reduces the toughness. The capacity of the concrete to anchor embedded reinforcement decreases with the decrease of toughness, and the bond force causes the microcracks in the concrete slow crack growth. A comparison of frost-heave cracks of specimens SW-9, SW-12, SW14 and SW-16 shows that before 200 cycles of freeze-thaw, the frostheave cracks are primarily around the edge of the boundary zone and are basically lengthwise frost-heave cracks. As the number of FTCs increased, horizontal frost-heave cracks gradually appear, the number and width of frost-heave cracks and the surface damage gradually increased, and the distribution of cracks developed from the wall edges to the center. This phenomenon could be attributed to the theory of osmotic pressures and hydrostatics, such that when the inner tensile stress

3. Analysis of quasi-static test results 3.1. Crack patterns of the specimens after freeze-thaw exposure Fig. 7 shows the surface and partially enlarged maps of the RC shear wall specimens, which were composed of different numbers of FTCs after freeze-thaw exposure. The surface of the unfrozen specimen SW-9 is smooth and flat and has no visible cracks. A small amount of lengthwise hairline visible cracks appear along the boundary zone in wall SW-12 (FTCs = 100), as shown in Fig. 7(a). As the number of FTCs increased to 200 (SW-14), the number of hairline vertical cracks along the boundary zone increased, the width increased, and the transverse cracks begin to appear, as shown in Fig. 7(b). When the number of FTCs increased to 300, the number of lengthwise cracks and the width of

Displacement-controlled step (mm)

Load (kN) / Displacement (mm)

Load-controlled step (kN)

20 0

40

-20

60

-40

140

...

-60

...

...

Py

-140 ...

Δy+3

Δy+6

...

Δy+15

Δu

...

Pull

Push -Δy

-Δy-3

-Δy-6 Load cycles

Fig. 6. Loading protocol. 5

... -Δy-15

...

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Towards the center wall edges Longitudinal crack

Coarse transverse crack

Transverse crack

(a) SW-12 (FTCs=100)

(b) SW-14 (FTCs=200)

(c) SW-16 (FTCs=300)

Fig. 7. RC shear wall surfaces after freeze-thaw applications.

A comparison of specimens SW-9, SW-12, and SW-14 shows that as the number of FTCs increased, the initial horizontal crack and the vertical bond-slip crack at the bottom of the wall gradually formed earlier. The early appearance of bond-slip cracks is mainly due to the weakening of bond strength between reinforcement and concrete due to the following three reasons. First, after freezing, the water in the pores of concrete freezes and expands, and forces the unfrozen pore solution to move outward from the frozen area, resulting in compressive stress. When the generated pressure exceeds the concrete tensile stress, the compressive and tensile strength of concrete will be reduced. Because the mechanical interlocking is positively related to the concrete strength [29], the freeze-thaw thus reduces the mechanical interlocking at the interface between the reinforcement and the concrete. Second, after being frozen, the water in the concrete pores will freeze and expand, and the internal stress produced in the concrete will directly act on the pore wall, resulting in irreversible microcrack damage in the concrete interior. Under the action of multiple FTCs, the internal stress repeatedly acts on the pore wall, which makes the microcrack damage of the concrete continue to accumulate and expand, and eventually lead to loosening, cracks and volume expansion of the concrete. The loosening, cracks and volume expansion in the concrete reduce the friction coefficient of the interface [30], and weaken the restraint effect of the concrete cover, thereby reducing the friction between the reinforcement and the concrete interface. Last, after being frozen, the internal cement paste cracks and is separated from the aggregate interface, and the gel is lost, which weakens the role of cement gel in the concrete, resulting in the reduction of chemical adhesion [31] between the reinforcement and surrounding concrete. After cracking, the horizontal crack spacing and width at the bottom of the wall gradually increased. This increase in horizontal crack spacing and width may occur because the freeze-thaw cycle weakens the bond performance between the rebar and the concrete [9,11,12], which increases the required length of force transfer when the stress in the rebar is transmitted to the concrete through the bond. When failure occurred, the width of the primarily flexural-shear crack gradually increased, which indicates that the increase in freeze-thaw damage can shift the specimen response from flexure-dominated to shear-dominated. This phenomenon could be attributed to the freeze-thaw action that decreased the toughness of concrete, thus reducing the bond strength, which leads to the decrease rate of the tensile strength of the concrete greater than that of the compressive strength. After specimen SW-16 (FTCs = 300) yielded, more short cracks appeared within 500 mm of the bottom of the wall. As the horizontal displacement of the wall top increased, the short cracks gradually linked to each other. When the horizontal displacement of the wall top reached 10.76 mm, the concrete in the compression zone at the end of the wall was crushed into crisp granules (Fig. 9(b)), and both the flexural reinforcements in the boundary elements and the vertical web reinforcements were compressed to buckling, as shown in Fig. 9(c). Then, the specimen lost its load carrying capacity and exhibited an obvious brittle failure. After removing the spalling concrete, a significant boundary was found between the frostdamaged and intact portions of the wall section, as shown in Fig. 9(d). Moreover, an observation of the spalling concrete block showed that

caused by osmotic and hydrostatic pressures exceeded the tensile stress of concrete, internal microcracks in the concrete began to spread as the number of FTCs increased; the microcracks then began to extend and interconnect such that the number of cracks increased more rapidly, while the cracks widened [4,22]. Meanwhile, the wall edges were subjected to three-dimensional freeze-thaw action, and the wall webs were subjected to two-dimensional freeze-thaw action during the FTCs; thus, the frost cracks propagated from the wall edges to the center of the wall. 3.2. Damage process and failure pattern The loading process of all specimens were similar, wherein three stages were observed: elastic, elastic-plastic and failure. Taking SW-9 as an example, the failure process of the specimens is described in detail. During the initial loading, the wall was in an elastic working state. When the lateral load on the top of the wall reached 119.6 kN (the corresponding displacement and drift ratio were 2.76 mm and 1/543, respectively), the first horizontal crack appeared at the bottom of the wall boundary zone. As the horizontal load amplitude of the wall top increased, new short horizontal cracks were detected from the bottom to the top of the specimen along the two sides of the boundary zone, and some inclined cracks first emerged on the bottom of the walls. The initial horizontal crack extended along the horizontal direction, and its width gradually increased. This result indicated that the response of wall SW-9 was initially dominated by flexural cracking. When the lateral load of the wall top reached 179.41 kN (the corresponding displacement and drift ratio were 7.31 mm and 1/205, respectively), the longitudinal reinforcement of the boundary elements yielded under tension, and the specimen began to enter the elastic-plastic working stage. At this time, the control mode of the lateral load was switched from the force-control mode to the displacement-control mode. As the horizontal displacement amplitude of the wall top increased, the horizontal crack at the edge of the boundary elements continued to extend obliquely to the bottom of the web wall, and the initial inclined cracks became longer and wider and intersected with each other. When the horizontal displacement of the wall top reached 15.39 mm (the corresponding load and drift ratio were 214.55 kN and 1/97, respectively), the specimen reached the peak load, the horizontal web reinforcement intersecting the inclined crack yielded, and the specimen began to enter the failure working stage. As the horizontal displacement amplitude of the wall top continued to increase, the existing inclined crack rapidly extended and the width continued to increase, and the area of crushing and spalling concrete at the bottom of the wall gradually increased. Finally, due to concrete crushing and spalling in the bottom of the boundary elements, the longitudinal reinforcement of the boundary elements buckled (seen in Fig. 9(a)), the section was further weakened, the horizontal load on the top of the wall rapidly dropped, and the specimens exhibited typical flexural-shear failure. The final damage states and crack maps of the eight specimens are shown in Fig. 8. Although all the walls exhibited flexural yielding followed by shear failure, due to different test parameters, the speed and degree of the damage progression were different, and the specific performance is as follows. 6

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Fig. 8. Failure status of the shear wall specimens.

the concrete in the surface area was earth-yellow and gradually faded to the interior area until it disappears, as shown in Fig. 9(e). A comparison of specimens SW-10, SW-11, and SW-12 shows that as the concrete strength grade increased, the initial horizontal cracks and vertical bond-slip cracks at the bottom of the wall gradually formed later. After cracking, the crack spacing and width of the horizontal crack at the bottom of the wall were gradually reduced. When failure occurred, the width of the primarily flexural-shear crack gradually increased, whereas the area of crushing and spalling concrete at the bottom of the wall gradually decreased. A comparison of specimens SW-13, SW-14, and SW-15 shows that as the axial load ratio increased, the initial horizontal and inclined cracks gradually formed later, and the extension rate of horizontal and inclined cracks gradually decreased. The angle between the intersecting inclined crack and the horizontal direction gradually increased, and the length of the vertical bond-slip crack at the bottom of the wall gradually decreased. When failure occurred, the height of the plastic hinge first

(a) Longitudinal reinforcement buckling

(b) Concrete spalling

increased and then decreased, the area of crushing and spalling concrete at the bottom of the wall gradually decreased, and the brittleness characteristics gradually became more obvious. 3.3. Hysteretic behavior The hysteresis loops of the lateral load vs. the top displacement for the eight specimens are shown in Fig. 10. Each sample exhibited similar hysteretic behavior, and a detailed description of this behavior is given hereafter. Before cracking, the specimen was in the elastic working stage, and the hysteresis curve was approximately a straight line passing through the origin. There was no residual deformation at the end of the unloading paths, and the area of the hysteresis loop was approximately zero. After cracking, as the cyclic lateral load at the wall top increased, the hysteresis curve slightly approached the horizontal axis, and the area of the hysteresis loop and the residual deformation began to appear and increased. After the longitudinal reinforcement of the

(c) Sectional longitudinal reinforcement buckling

(d) Concrete layering

Fig. 9. Damage details for the shear wall samples. 7

(e) Boundary between the frost-damaged and intact portions of the wall

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Fig. 10. Hysteresis loops of the shear wall top horizontal force versus displacement.

Drift (%)

Drift (%)

Drift (%)

200

200

200

150

150

150

100

100

100

50 0

-50

50 0

-50

-100

SW-9 (0) SW-12 (100) SW-14 (200) SW-16 (300)

-150 -200 -250 -25 -20 -15 -10

P (kN)

-1.7 -1.3 -1.0 -0.7 -0.3 0.0 0.3 0.7 1.0 1.3 1.7 250

P (kN)

-1.7 -1.3 -1.0 -0.7 -0.3 0.0 0.3 0.7 1.0 1.3 1.7 250

P (kN)

-1.7 -1.3 -1.0 -0.7 -0.3 0.0 0.3 0.7 1.0 1.3 1.7 250

-5

0

5

Δ (mm)

10

15

20

(a) Different numbers of FTCs

25

0

-50

-100

-100 SW-10 (C30) SW-11 (C40) SW-12 (C50)

-150 -200 -250 -25 -20 -15 -10

50

-5

0

5

Δ (mm)

10

15

20

(b) Different concrete strength

SW-13 (0.1) SW-14 (0.2) SW-15 (0.3)

-150 -200 25

-250 -25 -20 -15 -10

-5

0

5

Δ (mm)

10

15

20

25

(c) Different axial load ratios

Fig. 11. Hysteresis loop envelopes.

boundary elements yielded, as the horizontal displacement of the wall top increased, the plastic deformation, the area of the hysteresis loop and the residual deformation gradually increased, while the stiffness of the loading and unloading gradually decreased, and the hysteresis curve was pinched. After the peak value, as the horizontal displacement of the wall top continued to increase, the stiffness of the loading and unloading was more significantly degraded, the residual deformation was further increased, the hysteresis curve was no longer stable, and the applied load rapidly decreased. Due to the nonuniform distribution of freeze-thaw damage [32] and the directionality of the initial loading, the degree of wall damage caused by pull loading and push loading under the same loading level was different, which resulted in the obvious asymmetry of the hysteresis curves. In addition, due to the different experimental design parameters, each specimen exhibited different hysteretic behaviors, which are described hereafter. When the other design parameters were kept the same, as the number of FTCs increased, the width and area of the hysteresis loop under the same horizontal displacement of the wall top gradually decreased, and the residual deformation gradually increased. The pinched hysteretic behavior gradually became more obvious, and the length of the yield platform of the hysteresis curve gradually decreased. When failure occurred, the horizontal displacement of the top of the wall and

the total area enclosed by the hysteresis curve gradually decreased. When the other design parameters were kept the same, as the concrete strength grade increased, the width of the hysteresis loop and the residual deformation under the same horizontal displacement of the wall top gradually increased, and the length of the yield platform of the hysteresis curve increased. When failure occurred, the total area enclosed by the hysteresis curve gradually increased. When the other design parameters were kept the same, as the axial load ratio increased, the width of the hysteresis loop and the residual deformation under the same horizontal displacement of the wall top gradually decreased. The pinched hysteretic behavior gradually became more obvious, and the length of the yield platform of the hysteresis curve gradually decreased. When failure occurred, the horizontal displacement of the top of the wall and the total area enclosed by the hysteresis curve gradually decreased. 3.4. Skeleton curves and characteristic values The skeleton curves of specimens with different design parameters are shown in Fig. 11. Because the hysteresis loops of specimens under low cyclic loading are not perfectly symmetrical, the characteristic values are calculated as the average of the absolute values of the pull and push directions, as shown in Table 5. Moreover, the displacement 8

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cracking displacement gradually decreased, and the displacement ductility coefficient significantly increased at first and then slightly decreased. Among the samples, the peak load increased from 145.52 to 157.65 kN (8.34%) and the ductility coefficient increased from 1.73 to 2.72 (57.53%) when the concrete strength grade increased from C30 to C40. The peak load increased from 157.65 to 185.37 kN (17.58%) and the ductility coefficient decreased from 2.72 to 2.48 (8.82%) when the concrete strength grade increased from C40 to C50. These findings indicate that when the concrete strength grade increased, the peak load increased significantly, which might be attributed to substantial increases in the bonding strength, and the freeze-thaw damage decreased [8,12]. In conclusion, increasing the strength of concrete can improve the load carrying capacity of freeze-thaw damaged RC shear walls, and the corresponding increasing rate of the load carrying capacity obviously increased. Fig. 11(c) and Table 5 show that the initial stiffness and stiffness degradation rate of specimens increased as the axial load ratios increased, which could be attributed to the axial compressive restraining the development of horizontal cracks in the wall, and the P-Δ effect gradually increased. As the axial load ratio increased, the load carrying capacities under different loading stages and cracking displacement gradually increased, and the peak displacement, ultimate displacement and displacement ductility coefficient gradually decreased. Among the samples, the peak loads increased by 22.08% (SW-14 compared to SW13) and 2.90% (SW-15 compared to SW-14) separately, and the ultimate displacements decreased by 9.66% (SW-14 compared to SW-13) and 36.51% (SW-15 compared to SW-14). These findings indicate that as the axial load ratio increased, the increasing rate of the peak load significantly decreased, and the decreasing rate of the ultimate displacement significantly increased. In conclusion, increasing the axial load ratio can improve the load carrying capacity and reduce the deformation capacity of the freeze-thaw damaged RC shear walls. Furthermore, the increasing rate of the load carrying capacity obviously decreases, whereas the decreasing rate of deformation capacity and energy dissipation capacity obviously increase.

Fig. 12. Definition of the yielding point.

ductility coefficient µ is used as an index to measure the plastic deformation capacity of the specimen, and this coefficient is calculated as follows:

µ=

u

(1)

y

where Δy is the yield displacement, which is defined based on the equivalent energy method (the calculation diagram for the yield displacement is shown in Fig. 12), and Δu is the ultimate displacement. Fig. 11(a) and Table 5 show that the skeleton curve of the unfrozen specimens basically contained the skeleton curve of the frozen-thawed specimens, and the initial stiffness of the frozen-thawed specimens was lower than that of the unfrozen specimens. Furthermore, as the number of FTCs increased, the stiffness of the specimens gradually decreased under the same loading displacement, which might be attributed to the lower elasticity modulus, more internal microcracks and faster crack development of the concrete specimens. As the number of FTCs increased, the load carrying capacities under different loading stages, ultimate displacement, and ductility coefficient of the RC shear walls gradually reduced. Among the RC shear walls, the ultimate displacements were reduced by 10.21% (SW-12 compared to SW-9), 12.34% (SW-14 compared to SW-12) and 30.77% (SW-16 compared to SW-14), which indicates that the declining rate in the ultimate displacement gradually increases. This phenomenon could be attributed to substantial decreases in concrete strength and bonding strength and increases in freeze-thaw damage after exposure to a larger number of FTCs [8,9]. The peak load increased from 140.79 to 213.45 (34.04%) when the number of FTCs increased from 0 to 300. In conclusion, when the number of FTCs increased, the load carrying capacity and deformation capacity of the RC shear walls gradually weakened, and the declining rate of the deformation capacity gradually increased. Fig. 11(b) and Table 5 show that as the concrete strength grade increased, the initial stiffness and the horizontal load on the wall top under different characteristic stages continuously increased, the

3.5. Energy dissipation capacity The cumulative energy dissipation E was adopted to characterize the energy absorption capability of the walls after the frost damage, as shown in Eq. (2):

E=

n

Ei

(2)

i=1

where Ei is the area of the hysteresis loop of the i-th cycle and n is the number of cycles of load reversals before the specimens reached the failure standard. Based on this information, the energy consumption of the specimens under each cycle load was calculated, and the results are shown in Fig. 13. Fig. 13(a) shows that before the 9th cyclic loading, the cumulative energy dissipation of the freeze-thaw damaged specimens was greater than that of the unfrozen specimen SW-9 under the same number of

Table 5 Characteristic parameters of the skeleton curves. Specimen number

SW-9 SW-10 SW-11 SW-12 SW-13 SW-14 SW-15 SW-16

Cracking point

Yielding point

Peak point

Ultimate point

Pc (kN)

Δc (mm)

Py (kN)

Δy (mm)

Pm (kN)

Δm (mm)

Δu (mm)

120.16 80.36 80.87 99.88 80.82 99.31 129.49 78.36

2.64 2.76 2.41 2.34 2.03 2.33 2.78 2.46

178.47 121.80 132.46 152.73 120.65 142.37 150.59 116.33

7.26 7.93 5.97 7.06 6.65 7.07 6.50 5.86

213.45 145.52 157.65 185.37 140.32 171.30 176.27 140.79

15.37 13.68 12.40 14.34 16.98 15.34 8.65 10.62

19.49 13.68 16.23 17.50 16.98 15.34 9.74 10.62

9

Ductility coefficient μ

2.69 1.73 2.72 2.48 2.55 2.17 1.50 1.81

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Fig. 13. Cumulative energy dissipation vs. loading cycles.

loading cycles, which was attributed to the frozen-thawed specimens having larger residual deformation (refer to Fig. 10). As the number of FTCs increased, the cumulative energy dissipation values at wall failure decreased by 7.51% (SW-12 compared to SW-9), 33.79% (SW-14 compared to SW-12) and 43.58% (SW-16 compared to SW-14). These findings indicate that increasing the number of FTCs can weaken the energy dissipation capacity of RC shear walls and that the weakening degree of energy dissipation capacity obviously increases. Fig. 13(b) shows that as the concrete strength grade increased, the cumulative energy dissipation first decreased and then increased with the same number of loading cycles. As the concrete strength grade increased, the cumulative energy dissipation values at wall failure increased by 15.81% (SW-11 compared to SW-10) and 29.48% (SW-12 compared to SW-11). These findings indicate that increasing the concrete strength can enhance the energy dissipation capacity of frost-damaged RC shear walls and that the increasing degree of energy dissipation capacity obviously increases. Fig. 13(c) shows that before the 14th cyclic loading, the cumulative energy dissipation gradually decreased as the axial load ratio increased under the same number of loading cycles, and the corresponding reduction degree decreased significantly. As the axial load ratio increased, the cumulative energy dissipation values at wall failure decreased by 21.50% (SW-14 compared to SW-13) and 48.78% (SW-15 compared to SW-14). These findings indicate that increasing the axial load ratio can weaken the energy dissipation capacity of frost-damaged RC shear walls and that the weakening degree of energy dissipation capacity obviously increases.

were less than 10%. The ratio of shear deformation to total deformation under the yielding state was lower than that under the cracking state and was significantly increased in the peak state. A comparison of specimens SW-9, SW-12, SW-14 and SW-16 shows that the average shear distortion γ and the ratio of shear deformation to total deformation Δs/Δ under different loading states of the frost-damaged specimens were higher than those of the unfrozen specimen SW9. As the number of FTCs increased, the average shear distortion and the ratio of shear deformation to total deformation Δs/Δ under different loading states gradually increased. Among the samples, the contribution of the shear displacement at the peak point was 65.608% for wall SW-16, i.e., shear deformation became the main deformation for this specimen. The above change rule indicates that frost damage can weaken the shear resistance of RC shear walls and that the shear resistance gradually decreased as the number of FTCs increased. A comparison of specimens SW-10, SW-11 and SW-12 shows that as the concrete strength grade increased, the average shear distortion and its ratio to total deformation of the frost-damaged RC shear walls first decreased and then increased in the yielding state and gradually increased in the peak state. The contributions of the shear displacement at the peak points were 31.658%, 36.855%, and 37.202% for walls SW 10, SW-11, and SW-12, respectively. A comparison of specimens SW-13, SW-14 and SW-15 shows that as the axial load ratio increased, the average shear distortion and its ratio to the total deformation of the frost-damaged RC shear walls gradually decreased at the yielding points. At the peak points, as the axial load ratio increased, the average shear distortion gradually decreased and its ratio to the total specimen deformation gradually increased. This phenomenon could be attributed to the axial load restraining the development of shear inclined cracks and significantly reducing the peak displacement of the specimens. Therefore, while reducing the shear deformation of the specimens, the ratio of the shear deformation to the total deformation at the peak state increased. Among the samples, the contribution of the shear displacement at the peak point was 55.736% for wall SW-15, i.e., shear deformation became the main deformation for this specimen.

3.6. Shear deformation According to the data from the instruments attached to the tested wall (the instrument layout is shown in Fig. 5), the shear deformation Δs [33] and the average shear distortion γ can be estimated with Eqs. (3) and (4), and the calculation diagram is shown in Fig. 14. s

=

=

1 [ (d + D1)2 2 s

l

l2

(d + D2) 2

l2 ]

(3)

4. Calculation equation of the skeleton curve feature points

(4)

The mechanical and deformation properties of frost-damaged RC shear walls are affected not only by decreasing the concrete strength [7–9] and increasing the peak strain [8] but also by many factors, such as the degradation in bond strength [9,11,12] and the increase in the number of microcracks [22] in the wall. Therefore, it is difficult to reasonably characterize the characteristic parameters of skeleton curves with theoretical methods. However, the experimental fitting method can comprehensively consider the effects of the above factors on the mechanical and deformation properties of RC shear walls under certain accuracy conditions. Thus, this paper first used existing theoretical

where d1 and d2 are the original lengths of the two diagonal sensors, D1 and D2 are the displacements measured from these diagonal sensors, and l is the height of the diagonal sensors. Based on this information, the shear distortion γ and contributions of shear displacement to the total displacement Δs/Δ at the cracking, yielding and peak points are shown in Figs. 15 and 16. Table 6 lists the shear distortion and its proportion of total displacement for eight specimens. Table 6 shows that the average shear distortions γ of the RC shear walls under cracking and yielding states were less than 1 × 10−3, and their respective contributions to the total specimen deformation (Δs/Δ) 10

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Fig. 14. Calculation diagram of shear displacement.

damage in the concrete, and the equation for the freeze-thaw damage parameter D is established as follows:

results [35–38] to establish an equation of load and displacement at characteristic points of the skeleton curve of an unfrozen RC shear wall. Then, based on the pseudo-static test data of the eight RC shear walls mentioned above, a calibration method for the characteristic parameters of the RC shear wall skeleton curve considering the effects of frost damage and axial load ratio was established through the combination of theoretical analysis and multiparameter regression.

D=1

RDME = 0.003632f cu0.4494 F

(5)

where F is the number of FTCs and fcu is the compressive strength of the concrete cube, for which the value is shown in Table 3. The results of the quasi-static test mentioned above show that as the freeze-thaw damage degree and axial load ratio increased, the load carrying capacity and deformation capacity of the RC shear walls under different loading states changed to different degrees. Therefore, considering the effects of the freeze-thaw damage degree and axial load ratio on the mechanical and deformation properties of RC shear walls, this paper selected n and D as parameters to modify the characteristic parameters of the skeleton curve of unfrozen RC shear walls. The revised equations are as follows:

4.1. Calculation equation of the unfrozen RC shear wall skeleton curve Based on the results of the previous quasi-static tests, the skeleton curves of unfrozen and frost-damaged RC shear walls were simplified to four-polyline models with similar geometric shapes, as shown in Fig. 17. In Fig. 17, points A (A'), B (B'), C (C') and D (D') correspond to the cracking point, yielding point, peak point and ultimate point of the skeleton curve of the unfrozen (frost-damaged) RC shear walls, respectively. The load and displacement at the characteristic points of the skeleton curves of the unfrozen RC shear walls were calculated by the equation in Table 7.

(6)

Pi = fi (D , n) Pi i

= gi (D, n)

i

(7)

where Pi and Pi' are the lateral load on the wall top at the characteristic point i of the unfrozen and frost-damaged specimens, respectively; Δi and Δi' are the displacement corresponding to Pi and Pi', respectively; fi(D,n) is the load revised function of characteristic point i considering the effects of freeze-thaw damage and axial load ratio; and gi(D,n) is the corresponding displacement revised function of fi(D,n). According to the normalized coefficients of the test values in Table 5, a suitable

4.2. Calculation equation of the freeze-thaw damaged RC shear wall skeleton curve Based on the results of the concrete material property tests and Refs. [39,40], this paper used the relative dynamic elastic modulus (RDME) as an index to quantitatively characterize the degree of freeze-thaw

Fig. 15. Shear distortion γ at the different characteristic points. 11

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Fig. 16. Contributions of shear displacement to total displacement Δs/Δ.

function form was selected and obtained by multiparameter nonlinear surface regression analysis. The specific determination method is described hereafter. The load and displacement of the characteristic points in Table 5 were divided by the load and displacement of the characteristic points of the unfrozen specimens under the same axial load ratio and concrete strength, and the corresponding revised coefficients were obtained. Then, the freeze-thaw damage parameter D and the axial load ratio n were taken as the abscissa and the revised coefficient was taken as the ordinate, and the change rules of the load and displacement revised coefficients of each characteristic point with respect to the freeze-thaw damage parameter D and axial load ratio n were plotted, as shown in Fig. 18 and Fig. 19, respectively. Figs. 18(a) and 19(a) show that when the axial load ratio was kept the same, as the freeze-thaw damage parameter D increased, the load revised coefficients at each characteristic point and the displacement revised coefficients at the cracking and yielding states exhibited a polygonal trendline. The displacement revised coefficients at the peak and ultimate states exhibited an approximately linear decreasing trend. Figs. 18(b) and 19(b) show that when the freeze-thaw damage degree was kept the same, as the axial load ratio n increased, the load revised coefficient of each characteristic point and the displacement revised coefficient under the peak and ultimate states exhibited a linear trend, whereas the displacement revised coefficient under the cracking and yielding states exhibited no obvious regularity. Therefore, to ensure a high accuracy of the fitting results, the load revised function fi(D,n) of each characteristic point was assumed to be a quadratic function form of the freeze-thaw damage parameter D and a linear function form of the axial load ratio n. The displacement revised function gi1(D,n) under the cracking and yielding states was assumed to be a quadratic function of the freeze-thaw damage parameter D and the axial load ratio n. The displacement revised function gi2(D,n) under the peak and ultimate states was assumed to be a linear function of the freeze-thaw damage parameter D and the axial load ratio n. Considering the boundary conditions at the same time, the revised functions are expressed as follows.

fi (D , n) = (aD 2 + bD)(cn+ d ) + 1

(8)

gi1 (D , n) = (aD 2 + bD)(cn2 + dn + e ) + 1

(9) (10)

gi 2 (D , n) = D (an + b) + 1

where a, b, c, d, and e are fitting parameters, and their values are shown in Fig. 20. Then, the equation of the characteristic point load and displacement of the freeze-thaw damaged RC shear wall skeleton curve and its goodness of fit R2 were obtained as follows. (1) Cracking load and corresponding displacement

Pc = [( 1.473D 2

0.275D )( 37.642n + 10.762) + 1] Pc (R2 = 0.872) (11a)

c

= [(22.878D 2

4.131D)(2.441n2

0.995n + 0.128) + 1]

c

(11b)

(R2 = 0.752) (2) Yielding load and corresponding displacement

Py = [(- 1.463D2 - 0.350D)(- 13.302n + 5.948) + 1] Py (R2 = 0.889) (12a) y

= [( 8.955D 2 + 0.684D)( 3.521n2 + 1.305n

0.132) + 1]

y

(12b)

(R2 = 0.904) (3) Peak load and corresponding displacement

Pm = [(1.915D 2 + 0.606D) ( 5.585n

= [( 22.582n + 3.143) D + 1]

m

0.817) + 1] Pm (R2 = 0.953) 2 m (R

= 0.958)

(13a) (13b)

(4) Ultimate load and corresponding displacement (14a)

Pu = 0.85Pm = [( 15.4786n + 0.801) D + 1]

u

u

(R2

= 0.921)

(14b)

According to Table 7 and Eqs. (11)–(14), the theoretical values of

Table 6 Shear deformation and its proportion of the total specimen deformation under different conditions. Specimen number

Cracking point γ (10

SW-9 SW-10 SW-11 SW-12 SW-13 SW-14 SW-15 SW-16

0.192 0.193 0.205 0.196 0.174 0.224 0.270 0.288

−3

)

Yielding point Δsc/Δ (%)

γ (10

5.085 4.891 5.944 5.865 5.985 6.727 6.799 8.201

0.400 0.436 0.392 0.507 0.681 0.647 0.556 0.747

12

−3

)

Peak point −3

Δsy/Δ (%)

γ (10

3.852 4.112 3.802 5.027 7.172 6.348 5.987 8.927

5.104 6.187 6.529 7.621 10.156 9.794 6.887 9.954

)

Δsm/Δ (%) 23.245 31.658 36.855 37.202 41.866 44.674 55.736 65.608

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Fig. 17. Four-polyline skeleton curves.

load and displacement at the characteristic points of the RC shear wall skeleton curves and their ratios to experimental values were calculated, and the results are listed in Tables 8 and 9. Tables 8 and 9 show that the calculated values of load and displacement at each characteristic point agree well with the experimental values. This finding indicates that the load and displacement calculation equation of the characteristic points proposed in this paper can accurately reflect the mechanical and deformation properties of frostdamaged RC shear walls. The calculated values of individual specimens are in poor agreement with the experimental values, which could be attributed to the variability in the concrete material itself and the uncertainty of the distribution of the freeze-thaw damage.

is 2.48%, which is nearly half of the mass loss rate of 5% when the specimens experience freeze fracture. Therefore, it is necessary to further study the seismic behavior of RC shear walls with freezethaw damage under FTCs > 300. (2) Increasing the strength of concrete can improve the frost resistance of concrete specimens. This paper studies only three types of shear walls that do not exceed the C50 strength level, and the seismic performance of high-strength concrete shear walls with freeze-thaw damage above the C50 strength level needs further study. (3) Air-entraining agents can improve the frost resistance of concrete, and air-entrained concrete is often used during construction in severely cold regions. Therefore, it is necessary to study the seismic performance of RC shear walls with air-entraining agents in freezethaw environments. For ordinary nonaerated concrete, the air content is approximately 1–2% [7]. Therefore, the calculation equation in this paper is applicable to concrete with air contents below 2%. (4) One of the main types of damage due to freeze-thaw action is the decrease in bond strength. However, we have not separately studied the effect of the decrease in bond strength on the seismic performance of RC shear walls. Meanwhile, it should be noted that the

5. Discussion on the experiment and model limitations (1) There are many differences between the freeze-thaw conditions during testing and actual freeze-thaw conditions, such as temperature range and freezing rate. Moreover, the manner in which to use the test results to predict actual freeze-thaw damage needs further research. In addition, the mass loss rate of the specimens under the maximum freeze-thaw damage degree (FTCs = 300, C30) Table 7 Equation for the skeleton curve of an unfrozen RC shear wall. Feature points Cracking point

Equation

Pc = 4 fc 1 +

Py

2.05

y

Peak point

3 Hw 3Ec I

= Pc

c

Yielding point

Parameter description

Py Hw Gc A

Ultimate point

=

+

=

Hw is the height from the loading point to the bottom of the wall (1500 mm); Ec is the concrete elastic modulus (the value is listed in Table 2); I is the moment of inertia of the shear wall section; μ is the coefficient of nonuniformity of the shear stress distribution, which is 1.2 for a rectangular section; and Gc is the concrete shear modulus, where Gc = 0.4Ec. n is the axial load ratio; λv is the stirrup characteristic value of the boundary elements, where λv = ρfsy/fc, in which fsy and ρ are the stirrup yield strength and the volumetric stirrup ratio, respectively; and λ is the shear span ratio. fy and Es are the yield strength and elastic modulus of the longitudinal reinforcement of the boundary elements, respectively, and h is the height of the shear wall section.

0.6

0.34

[35]

Hw2 [36]

y [1

0.5 A f yh hw sh sh

+ (4.25

0.27 Pu = 0.85Pm u

Hw Gc A

fy Es h

fc is the compressive strength of concrete, N is the axial load, and A is the cross-sectional area of the shear wall.

[34]

ft is the tensile strength of the concrete, b is the thickness of the shear wall, hw is the effective height of the shear wall section (650 mm), Aw is the area of wall web (700 mm × 100 mm), and fyh, sh and Ash are the tensile strength, spacing and cross-sectional area of the horizontal web reinforcement, respectively.

(1.1912ft bhw + 0.1447NAw A)

+ m

+µ

Pm 0.31n + 0.40 v

= 1.2

Pm =

fc N 4A fc

2 2 y Hw 3h

+

[37]

2.50n + 7.19

v

11.39ra)]

(

2H 0.0675lp 3

0.5lp

)

[35]

h [38]

ra is the ratio of the boundary element area to the cross-sectional area. Pm is the peak load. εy is the yielding strain of the longitudinal reinforcement of the boundary elements, lp is the height of the plastic hinge region, and H is the height of the shear wall.

13

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Fig. 18. Load correction factor.

shear span ratio of the tested RC shear wall of this research and Yang’s [22] research are limited to 2.14 and 1.14. Furthermore, some conclusions of Yang’s [22] findings are contrary to those of this study. Moreover, other aspects that affect the seismic performance of frost-damaged RC shear walls may exist. Therefore, it is necessary to further study the seismic behavior of frost-damaged RC shear walls. (5) The calculation equation in this paper is obtained by a shear span ratio regression, and the practicality of other similar shear span ratios of RC shear walls needs further verification.

whereas the declining rate of deformation capacity and energy dissipation capacity, the average shear distortion and the ratio of shear deformation to the total specimen deformation under different loading states gradually increase. (2) As the concrete strength grade improve, the load carrying capacity, energy dissipation capacity, peak shear distortion and its contribution to the total specimen deformation gradually increase. Furthermore, the rate of improvement of load carrying capacity and energy dissipating capacity is more obvious, and the ductility coefficient first increases and then decreases. (3) As the axial load ratio increases, the load carrying capacity of the RC shear walls progressively strengthened, whereas the deformation capacity, energy dissipation capacity, yielding and peak shear distortion gradually deteriorate. Moreover, the increasing rate of the load carrying capacity obviously reduces, whereas the decreasing rate of deformation capacity and energy dissipation capacity obviously increase. The ratio of shear deformation to the total specimen deformation gradually decreases in the yielding state and gradually increases in the peak state. (4) The calculation equation of the RC shear wall skeleton curve considering the influence of freeze-thaw damage and axial load ratio is established, and the degree of calibration accuracy of the calculation equation is verified through comparison with the experimental values.

6. Conclusion In this paper, the influence of different design parameters on the seismic performance of frost-damaged RC shear walls is studied through quasi-static tests, and based on the test results, a calculation equation is proposed for RC shear wall skeleton curves. The results of this research can be summarized by the following conclusions. (1) As the number of FTCs growth, the flexural-shear failure of the RC shear walls shifts from a flexure-dominated mode to a sheardominated one. Moreover, the load carrying capacity, deformation capacity and energy dissipation capacity gradually weakened,

Fig. 19. Displacement correction factor.

14

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(a) C racking load

(b) Yielding load

(c) Peak load

(d) C racking displacement

(e) Yielding displacement

(f) Peak displacement

(g) Ultimate displacement

Fig. 20. The fitting results of load and displacement correction factor.

15

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Table 8 Calculated load values of the characteristic points of the skeleton curve. Specimen number

Cracking load (kN)

SW-9 SW-10 SW-11 SW-12 SW-13 SW-14 SW-15 SW-16

Yielding load (kN)

Peak load (kN)

Calculation

Calculation/test

Calculation

Calculation/test

Calculation

Calculation/test

119.43 79.11 91.25 111.01 65.61 98.49 122.87 81.88

0.99 0.98 1.13 1.11 0.82 0.99 0.95 1.05

176.08 112.80 131.16 160.91 107.90 139.60 158.21 112.17

0.98 0.93 0.99 1.05 0.89 0.98 1.05 0.96

225.34 146.72 169.48 206.50 171.99 181.66 169.04 150.81

1.06 1.01 1.08 1.11 1.23 1.06 0.96 1.07

Note: The test values of the characteristic points are shown in Table 5. Table 9 Calculated displacement values of the characteristic points of the skeleton curve. Specimen number

SW-9 SW-10 SW-11 SW-12 SW-13 SW-14 SW-15 SW-16

Cracking displacement (mm)

Yielding displacement (mm)

Peak displacement (mm)

Ultimate displacement (mm)

Calculation

Calculation/test

Calculation

Calculation/test

Calculation

Calculation/test

Calculation

Calculation/test

2.58 1.85 1.98 2.22 2.02 2.22 2.54 2.64

0.90 0.67 0.82 0.95 1.00 0.95 0.91 1.07

6.89 6.76 6.81 6.87 6.27 6.49 6.21 5.66

0.94 0.91 0.94 0.97 0.94 0.91 0.96 0.97

16.80 16.33 15.86 15.40 15.87 13.54 11.38 11.24

1.09 1.19 1.28 1.07 0.93 0.99 1.32 1.06

20.88 17.19 17.57 18.00 19.01 15.13 11.25 12.26

1.07 1.26 1.08 1.03 1.12 0.99 1.16 1.15

Note: The test values of the characteristic points are shown in Table 5.

CRediT authorship contribution statement

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Xian-Liang Rong: Conceptualization, Methodology, Investigation, Data curation, Writing - original draft, Writing - review & editing. Shan-Suo Zheng: Resources, Writing - original draft, Writing - review & editing, Supervision, Funding acquisition. Yi-Xin Zhang: Formal analysis, Writing - original draft, Writing - review & editing. Xiao-Yu Zhang: Writing - original draft. Li-Guo Dong: Writing - original draft. Acknowledgments The authors are grateful for the financial support received from the National Nature Science Foundation of China (No. 51678475), the Research Fund of Shaanxi Province in China (2017ZDXM-SF-093), the Industrialization Project of Shaanxi Education Department (No. 18JC020), and the Xi’an Science and Technology Project (No. 2019113813CXSF016SF026). The authors would like to thank the reviewers’ for their efforts in reading the manuscript. References [1] Mehta PK. Concrete durability-fifty years progress. Proceedings of the 2nd international conference on concrete durability. 1991. p. 1–31. [2] Cao DF, Zhou M, Ge WJ. Study of the shear behaviors of RC beams after freeze-thaw cycles. Indust Constr 2015;45(2):32–7. [3] Green MF, Dent AJS, Bisby LA. Effect of freeze-thaw cycling on the behavior of reinforced concrete beams strengthened in flexure with fiber reinforced polymer sheets. Can J Civ Eng 2003;30(6):1081–8. [4] Yazdani F. Damage assessment, characterization, and modeling for enhanced design of concrete bridge decks in cold regions PhD dissertation North Dakota State: North Dakota State University; 2015 [5] Powers TC. A working hypothesis for further studies of frost resistance of concrete. J ACI 1945;16(4):245–72. [6] Powers TC, Helmuth RA. Theory of volume change in hardened Portland cement paste during freezing. Proceedings of the Thirty-second annual meeting of the highway research board. 1953. p. 285–97. [7] Hasan M, Okuyama H, Sato Y, et al. Stress-strain model of concrete damaged by freezing and thawing cycles. J Adv Concr Technol 2004;2(1):89–99. [8] Duan A, Jin WL, Qian JW. Effect of freeze-thaw cycles on the stress-strain curves of unconfined and confined concrete. Mater Struct 2011;44(7):1309–24.

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