- Email: [email protected]
Shear behavior of a strain hardening cementitious composites (SHCC)-Grooved steel composite deck
Composites Part B 160 (2019) 195–204
Contents lists available at ScienceDirect
Composites Part B journal homepage: www.elsevier.com/locate/compositesb
Shear behavior of a strain hardening cementitious composites (SHCC)Grooved steel composite deck
T
Liqiang Yina, Changwang Yanb, Shuguang Liub,∗, Ju Zhangb, Mingyang Liangb a b
School of Materials Science and Engineering, Inner Mongolia University of Technology, Hohhot, 010051, PR China School of Mining and Technology, Inner Mongolia University of Technology, Hohhot, 010051, PR China
ARTICLE INFO
ABSTRACT
Keywords: Strain hardening cementitious composites (SHCC) Orthotropic steel deck pavement Interlayer shear resistance Digital image correlation method (DIC) Response surface method (RSM)
The deterioration and premature failure of an orthotropic steel deck pavement during its service period is a pressing issue. Strain hardening cementitious composites (SHCC) possess an extreme tensile ductility, in the range of 3%–5% (about 300–500 times that of concrete). Using SHCC as a steel deck pavement can enhance the overall stiffness of a deck system. In this paper, an SHCC-grooved steel composite structure is the research object, and the tooth spacing, tooth width, and tooth height are the parameters. The shear behavior of an SHCC-grooved steel composite structure was studied using a compression shear test and the digital image correlation method. The response surface method was used to analyze the significant influence of the test parameters on the shear capacity, and the response model of the shear capacity was established. The calculation formula of the shear capacity of an SHCC-grooved steel composite structure was established based on the theory of the diagonal compression strut. The experimental results show that the cracking of a shear diagonal SHCC leads to the ultimate failure of an SHCC-grooved steel composite structure. The angle between the main crack and the shear load direction ranges from 30 to 45°. The failure process of the composite structure can be divided into 4 stages: linear elasticity, elastic-plastic, slip hardening, and instability failure. The order of the influence of the test parameters on the shear capacity is the tooth spacing > tooth height > tooth width. The response surface model can optimize and predict the shear capacity of the composite structure under different parameters within a certain range. The calculated values of the shear capacity model based on the theory of the diagonal compression strut agree well with the experimental values, and the calculated values are favorable for safety. This research can provide a reference for the shear design of an SHCC-grooved steel composite structure.
1. Introduction Orthotropic steel decks have been widely used across the world because of their advantages, such as a light self-weight, high bearing capacity, superior integrity, and constructional convenience. A steel deck is usually made of 10–14 mm thick steel plates. The pavement layer is directly laid on the steel deck, and a 35–80 mm thick asphalt mixture is generally used [1]. Due to the limited improvement of the stiffness of the orthotropic steel bridge deck due to the asphalt mixture pavement layer, a steel bridge deck system is in a high stress amplitude state under a vehicle load, and the local stress and the deformation of the pavement layer are large. The cracking of the pavement layer directly leads to a significant decrease in the stiffness of the deck system, further increasing the local stress and the crack width [2]. Engineering practice shows that once the pavement is cracked, the occurrence of the failure of the deck system is
∗
only a matter of time. The Baishazhou Yangtze River Bridge in Wuhan, Hubei Province, China was built in 2000. The steel deck pavement was repaired 24 times in 10 years [3]. In order to solve the problem of a steel deck pavement being easy to damage, some researchers have proposed a rigid concrete paving scheme that uses pavement materials such as high performance concrete, reactive powder concrete, or fiber-reinforced concrete; this approach was expected to improve the stress state of the deck system [4,5]. Researchers have done a lot of research on rigid pavements. Their results show that a rigid pavement can enhance the overall stiffness of a steel deck, disperse the traffic load, improve the mechanical properties of the steel deck pavement, and reduce the occurrence of fatigue cracking [6,7]. It is impossible to fundamentally eliminate the occurrence of cracks due to the high brittleness of concrete materials, and the problem of the pavement layer being easy to damage still exists. A new type of
Corresponding author. School of Mining and Technology, Inner Mongolia University of Technology, Hohhot, 010051, PR China. E-mail address: [email protected] (S. Liu).
https://doi.org/10.1016/j.compositesb.2018.10.025 Received 1 September 2018; Received in revised form 7 October 2018; Accepted 9 October 2018 Available online 11 October 2018 1359-8368/ © 2018 Elsevier Ltd. All rights reserved.
Composites Part B 160 (2019) 195–204
L. Yin et al.
engineering material, polyvinyl alcohol fiber reinforced cementitious composites, or strain hardening cementitious composites (SHCC), have excellent properties such as a high ductility, a strong ability to control cracks, freeze-thaw resistance, and fatigue resistance [8,9]. SHCC have been successfully used in bridge deck repair, bridge expansion joints, pre-stressed concrete bridge deck connection plates, deck pavements, and other bridge pavement projects globally [10]. The local position of the pavement layer under the vehicle load will generate a large tensile stress and shear stress. When the vehicle brakes, the steel deck pavement will withstand a large horizontal shear load. If the braking occurs quickly, the horizontal shear load will act on the localized area. This phenomenon occurs often, especially in areas with large traffic volumes. If the inter-layer shear resistance is insufficient, it will directly lead to conditions such as slip delamination or cracking, which will cause the bridge deck to be corroded and affect the safety of the bridge [11,12]. Ding [13] designed a steel pavement underlying asphalt concrete meant to be replaced with SHCC, forming a combined deck structure of “an asphalt concrete upper layer + a rigid pavement lower layer + a steel deck”, and 4 rigid pavement materials, SHCC l, SHCC 2, ordinary concrete and mortar, were selected. A push shear test of an H type steelrigid pavement composite structure with a stud shear key was carried out. The results showed that the shear strength of the H type steel-SHCC pavement composite structure is higher than that of ordinary concrete and much higher than that of mortar. Moreover, the high ductility of the SHCC can disperse the stud shear load and improve the cooperative working ability between the SHCC pavement and the steel deck. Ma [14] studied the interlaminar shear behavior of an SHCC pavement/steel deck (without a shear key) composite structure using an oblique shear test. The finite element software ANSYS was used to analyze the stress state of the steel deck SHCC pavement under load, calculate the maximum tensile stress and the maximum shear stress between decks, and comprehensively evaluate the feasibility of the SHCC in the steel deck pavement. Based on the studies of SHCC by authors of this paper in the early stage, we comprehensively analyzed the mechanical characteristics and actual diseases of the pavement of an orthotropic steel deck, proposed a steel deck SHCC pavement composite system, and studied its interlayer shear resistance. This study will provide an experimental and theoretical basis for the design and application of steel deck SHCC pavements, which is of great importance for improving the service life of the pavement.
Table 1 Index properties of the PVA fiber. Tensile strength (MPa)
Young's modulus (Gpa)
Diameter (μm)
Length (mm)
Elongation (%)
1600
40
0.04
12
6
Table 2 Mix proportions of the SHCC. Cement (kg/m3)
Fly ash (kg/ m3)
Water (kg/m3)
Silica sand (kg/m3)
WaterRAE (kg/ m3)
Water binder ratio (mw/mb)
PVA fiber (vol. %)
378
880
302
457
16.37
0.24
2
mw, the weight of water, kg; mb, the weight of binder materials, cement and fly ash, kg.
2.2. Materials and specimen preparation
2. Experimental program
The designed SHCC binder system contained type I ordinary Portland cement, Class-I high calcium fly ash, a fine aggregate made of quartz sand with a maximum grain size of 0.2 mm, and Polycarboxylate Superplasticizer. Polyvinyl alcohol (PVA) fibers were incorporated into the mixture at a volume fraction of 2.0%, and the properties as shown in Table 1. The mix proportion is listed in Table 2; the fly ash accounted for 70% of the total cementitious material, and the ratio of water to binder was 0.24. The preparation process of the SHCC and the test methods of the basic mechanical properties are detailed in the authors' previous research [15]. The dumbbell specimen was used in a uniaxial tensile test with a size of 330 mm × 60 mm × 15 mm. The test was carried out on the MTS servo hydraulic loading system, and the loading rate was 0.1 mm/min. The deformation of the specimen was measured by a laser extensometer. The uniaxial tensile stress-strain curves of the SHCC and the development of cracks are shown in Fig. 2. A prism specimen with a size of 100 mm × 100 mm × 300 mm was used in the test of axial compressive strength, and the compressive strength was 47 MPa. A section of Q235 steel was used for the grooved steel plate and for sandblasting on the surface of the steel plate. The cleanliness reached Sa2.5 level and the roughness was 50–100 μm. The test parameters included the tooth spacing, s, the tooth width, w, and the tooth height, h (Fig. 1); s ranged from 30 mm to 50 mm, w ranged from 10 mm to 20 mm, and h ranged from 5 mm to 20 mm. The parameters of the specimen are shown in Table 3.
2.1. Specimen design
2.3. Experimental details
The SHCC-grooved steel composite deck structure was made up of SHCC pavement and a grooved steel plate. The form and size of the SHCC-grooved steel composite deck structure are shown in Fig. 1. The thickness of the SHCC pavement was 50 mm, and the thickness of the steel plate was 10 mm. The shear section area was 100 mm × 100 mm.
The experiment was made up of a loading system and a digital image correlation (DIC) system, as shown in Fig. 3. An electro-hydraulic servo universal testing machine with a range of 100 KN was used as loading device for the compression shear test. The clamping device was designed and made independently, and 2 steel roll shafts with a diameter of 20 mm were arranged between the upper clamping device and
Fig. 1. Specimen geometry: (a) front elevation; (b) side elevation. 196
Composites Part B 160 (2019) 195–204
L. Yin et al.
Fig. 2. Uniaxial tensile stress-strain curve of the SHCC and the cracks.
of 2 CCD cameras, a light source, an image acquisition system, and an image analysis system. The speckle images of the specimen surface were collected continuously by the CCD cameras during the loading process, and the displacement and strain fields were calculated by the image analysis system. The maximum resolution of a CCD camera was 1624(H) × 1224(V) pixels, the maximum frame number was 30 fps, and the strain accuracy was less than 50 με. In order to make a good contrast for the speckle, the dummy black lacquer was used to make the surface speckle of the specimen. Because the digital image correlation method is a full-field measurement technique, the correlation function has a significant effect on the result of calculation. Therefore, it was necessary to select correlation functions that are simple in operation, small in computation, and good at anti-interference. The zero mean normalized least square distance correlation function was adopted in this paper [16]:
Table 3 Test parameters and specimens (unit: mm). Specimens
s
w
h
Specimens
s
w
h
Specimens
s
w
h
s1w1h1 s1w1h2 s1w1h3 s1w2h1 s1w2h2 s1w2h3 s1w3h1 s1w3h2 s1w3h3
30 30 30 30 30 30 30 30 30
10 10 10 15 15 15 20 20 20
5 10 20 5 10 20 5 10 20
s2w1h1 s2w1h2 s2w1h3 s2w2h1 s2w2h2 s2w2h3 s2w3h1 s2w3h2 s2w3h3
40 40 40 40 40 40 40 40 40
10 10 10 15 15 15 20 20 20
5 10 20 5 10 20 5 10 20
s3w1h1 s3w1h2 s3w1h3 s3w2h1 s3w2h2 s3w2h3 s3w3h1 s3w3h2 s3w3h3
50 50 50 50 50 50 50 50 50
10 10 10 15 15 15 20 20 20
5 10 20 5 10 20 5 10 20
the bearing. The angle of the compression shear test α was 45°. Taking into account the actual braking load is mainly concentrated on the upper surface of the pavement. Therefore, the shear load cross section of the SHCC pavement was raised to 3/10 at the height of the composite structural specimen in the compression shear test; the shear load cross section of the SHCC layer was 18 mm × 100 mm. The displacement control method was adopted, and the loading rate was 2 mm/min. The interlaminar shear displacement was measured by 2 LVDTs at the top of the SHCC layer and at the steel plate. The shear load was measured by a load transducer. The data for the load and the displacement was collected continuously by a DH3820 high-speed static strain test and analysis system. The displacement field and the strain field of composite structural specimen surface during loading were measured continuously using a digital image correlation technique. As shown in Fig. 3(a), the DIC testing system was mainly composed
C (p ) =
[f (x , y ) [f (x , y )
fm ][g(x , y ) fm
]2
[g(x , y )
gm] gm]2
(1)
where, C (P) is the correlation coefficient. f (x, y) is the gray value of the coordinates of each point in the reference subset and g (x', y') is the gray value of the coordinates of each point in the target subset. fm and gm refer to the average value of the gray level for the reference subset and the target subset, respectively. p is the deformation parameter vector describing the location and shape of the target subset before and after deformation.
Fig. 3. Scheme of the loading device and the DIC testing system. 197
Composites Part B 160 (2019) 195–204
L. Yin et al.
Fig. 4. Shear failure mode of an SHCC-grooved steel composite structure.
weakened for specimens with s values of 40 mm and 50 mm. Therefore, no cracking was present in the shear diagonal area to the tooth II; it is usually manifested as the shear diagonal area of tooth I cracking. In general, the influence law of the tooth width on the specimen failure code is not obvious. As shown in Fig. 4(d)–(f), 3 groups of specimens with values of s equal to 40 mm, h equal to 10 mm, and w equal to 10 mm, 15 mm, and 20 mm, were selected as examples for comparison and analysis. With the decrease of w, the possibility of forming 2 parts of the strut mechanism increase only when s and the h are constant. As shown in Fig. 4(d), the number of cracks increases. However, the change of w has little effect on the main crack angle. The influence of different tooth heights on the specimen failure mode was studied through the contrast analysis of 3 groups of specimens with values of s equal to 50 mm, w equal to 15 mm, and h equal to 5 mm, 10 mm and 20 mm, as shown in Fig. 4(g)–(i). Consistent with the tooth width, the influence of the tooth height on the failure modes of the specimens was also focused on the mechanism of the forming strut at the shear diagonal area of the right tooth II. With the increase of h, the cross-sectional area of the shear-compression area of the SHCC pavement increased. Therefore, its resistance to the diagonal pressure increased, and the shear capacity of the specimen was improved. The tooth height had an influence on the angle of the main crack. With the increase of tooth height, the main crack angle tended to decrease. The main reason is that the increase of tooth height leads to the reduction of the height of the characteristic shear span, which affects the change of the angle of the inclined crack.
3. Experimental results and analysis of the shear performance 3.1. Shear failure modes and analysis of an SHCC-grooved steel composite structure The typical shear failure mode of the SHCC-grooved steel composite structural specimen is shown in Fig. 4(a)-(i). The ultimate failure modes of each group of specimens were mostly the debonding and slippage of the interface between SHCC and steel plate near tooth I, as shown in Fig. 4(e), and the shear cracks that ran through the SHCC pavement. The angle between the main crack and the shear load direction ranges from 30° to 45°. It was observed that multiple cracks developed near the main crack when the SHCC was racked and damaged. The width of the crack is constant at the micron level. The SHCC-grooved steel composite structural specimen showed obvious ductile failure characteristics. The influence of different tooth spacings on the specimen failure mode was studied through the contrast analysis of 3 groups of specimens, namely, with values of w equal to 10 mm, h equal to 5 mm, and s equal to 30 mm, 40 mm, and 50 mm, as shown in Fig. 4(a)–(c). There are 2 main cracks in the SHCC layer corresponding to the specimen with a tooth spacing of 30 mm. The cracks are distributed in the shear diagonal region, and the angle between the cracks and the shear load direction ranges from 40° to 45°. There is only one main crack in the SHCC layer corresponding to the 2 specimens with s values of 40 mm, and 50 mm. The angle between the crack and the shear load direction is about 35°. The general rule is as follows: large tooth spacing, small angle of main crack. With the reduction of the tooth spacing, the number of main cracks increased, and the characteristic of the multiple cracks of the SHCC was brought into full play. After analysis, it was possible that the total size of the specimen was a constant value, and with the decrease of the distance between the teeth, the angle between the teeth and the diagonal bar that formed between the shear diagonal and the shear diagonal increased. With the decrease of s, the inclination of the diagonal portion of the strut towards shear load direction increased. The action of the tooth II diagonal compression strut was further strengthened, and it could bear a greater normal load and shear load. The shear diagonal crack occurred when the principal tensile stress reached the SHCC tensile strength. The action of the strut formed between the diagonal of the shear and tooth II under a load was
3.2. Shear failure process and analysis of an SHCC-grooved steel composite structure The full field displacement Ux and strain εx can be obtained with the digital image correlation method. The specimen s1w3h1 was selected in order to list the full field tangential displacement Ux cloud image and the strain εx cloud image at 6 typical moments (Fig. 5) during the experimental process, as shown in Figs. 6(a)–(f) and 7(a)–(f), respectively. The displacement along the positive direction of the x-axis is a tangential positive displacement. Conversely, it is a tangential negative displacement. The direction of the coordinate axis is detailed in Fig. 3(b). The tangential (x axial) tensile strain is positive and the 198
Composites Part B 160 (2019) 195–204
L. Yin et al.
SHCC is gradually perceptible. The blue-green relative displacement abruptly-appearing belt appeared in the specimen bounded by a diagonal shear line, as shown in Fig. 6(c) (corresponding to Pc). This indicates that the area near the relative displacement abrupt belt may crack first and become a vulnerable section. When the load reaches the Pd point (Fig. 5), as shown in Fig. 6 (d), the relative displacement difference between the 2 parts of the area on the left and right sides of the abrupt belt is especially obvious, the maximum displacement value is 2.844 mm, and the minimum displacement value is 2.470 mm. Macro slight debonding and slippage begin to occur between the left surface and the top surface of tooth I, the steel plate on the left side of tooth I, and the SHCC. In addition, fine cracks appear in the SHCC near the abrupt belt. However, the micro-cracks do not break suddenly due to the super-strong anti-cracking effect of PVA fiber in the SHCC, but rather expand steadily in a short time. When the load reaches its maximum value, as shown in Fig. 6 (e) (corresponding to Pe), the development of the debonding, slippage, and crack propagation reaches its limit. At this point, the critical state of the composite structural specimen is to resist the shear load. When the load begins to decrease after exceeding the maximum value, as shown in Fig. 6 (f) (corresponding to Pf), the macro crack crosses over the composite structural specimen, and the pavement of the composite structure is completely destroyed. Corresponding to the tangential displacement Ux cloud image, there are 6 typical moments in the process of change of the tangential strain εx cloud image. At the initial stage of loading, as shown in Fig. 7 (a) (corresponding to the point Pa on the curve in Fig. 5), the εx cloud image shows the distribution with a blue-green stripe and a local scatter point. The strain stripes appear alternately with the increase of the load, and it is the stage of the internal micro-crack dispersion and stress adjustment. The main reason for this phenomenon is that the heterogeneity of the SHCC and the interface discontinuity between the SHCC layer and grooved steel plate layer lead to the stress concentration. The phenomenon will first occur at the tip of the micro-crack in the SHCC, then the weak interface area between the layers, and then quickly reach
Fig. 5. Typical shear load slip curve (Fv -δ) of an SHCC-grooved steel composite structure specimen (s1w3h1).
tangential compressive strain is negative. The typical Fv -δ curve of an SHCC-grooved steel composite structural specimen is shown in Fig. 5. Six typical moments corresponding to the Pa - Pf points on the curve were selected for analysis. As shown in Fig. 6(a) (corresponding to the point Pa on the curve in Fig. 5), the tangential displacement Ux cloud image of the specimen is distributed with a scattered point and a strip phenomenon during the initial stage of loading. Although the specimen was subjected to a tangential load, the value is small. At this time, the development of the stress and deformation of each point in the composite structure is not uniform because of the discontinuities of the stress of each phase material and the internal defects. With the increase of the load, as shown in Fig. 6(b) (corresponding to Pb), there is a general change in the Ux cloud image. The relative displacement between the 2 teeth and the
Fig. 6. The full field displacement Ux of an SHCC-grooved steel composite structural specimen corresponding to 6 typical moments. 199
Composites Part B 160 (2019) 195–204
L. Yin et al.
Fig. 7. The full field strain εx of an SHCC-grooved steel composite structural specimen corresponding to 6 typical moments.
the limit and cause destruction and the stress release at the stress concentration, and then move on to the next section. The stress concentration is formed at the next weak place, so that it alternates repeatedly. With the increase of the load, as shown in Fig. 7(b) (corresponding to Pb), there is a general change in the εx cloud image. The red tensile strain concentration begins to appear in the tooth I and tooth II parts of the steel plate, while the purple compressive strain concentration is mainly distributed in the upper part of the SHCC. At this time, the yellowish-red elliptical area with the local tensile strain concentration appears in the SHCC on the upper right part of tooth I along the shear diagonal direction, for the first time. When the load reaches the Pc point (Fig. 5), as shown in Fig. 7 (c), the strain concentration of tooth I is more obvious, while tooth II is relatively weakened. The yellowish-red elliptical area in the SHCC is further enlarged, and its color changes from yellowish-red to red, accompanied by the increase of the strain value from 1.640 to 3.200. When the load increases to the point where a slight debonding and slippage occurs between the left area of tooth I and the SHCC (the corresponding εx cloud image is shown in Fig. 7 (d)), the debonding and slippage lead to a failure of the pixel recognition and the missing εx cloud image at the corresponding positions. Fig. 7 (e) is a tangential strain εx cloud image during the peak load, corresponding to the Pe point on the curve in Fig. 5. At this point, the tangential strain in the diagonal shear zone is the largest, the strain value is 16.00, and the shear capacity of the composite structure reaches the limit. When the load begins to decrease after exceeding the maximum value, as shown in Fig. 7 (f) (corresponding to Pf), a macro crack crosses over the composite structural specimen, and the pavement of the composite structure is completely destroyed. Based on the typical Fv -δ curve (Fig. 5), combined with the tangential displacement Ux cloud image and the s strain εx cloud image, it can be seen that the shear failure process of the SHCC-grooved steel composite structure shows 4 stages of development. I: The linear elastic stage occurs at the initial stage of loading, when the micro-cracks in the specimen are in the state of stress adjustment and dispersion, and the tangential load is uniformly distributed in the shear zone. The shear
load increases linearly. II: The elastic-plastic deformation stage occurs when the tangential load reaches the linear elastic limit value and enters the elastic-plastic process, and fine cracks appear in the shear diagonal area of the SHCC. The growth rate of the tangential load decreases, and the interfacial shear modulus decreases. III: The slip hardening stage occurs when the tangential load reaches its peak value; it does not drop suddenly as the macro crack and the interface slip continue to grow. The load can remain near a peak value due to the excellent performance of the SHCC, showing the pseudo strain hardening characteristic. However, this process is relatively short. IV: The failure stage occurs when the slip hardening reaches the critical point, cracks are suddenly destabilized, and the interface slip failure takes place. 3.3. Significance analysis of shear capacity based on response surface methodology (RSM) In order to clarify the significance of the influence of tooth spacing, tooth width, and tooth height on the shear capacity of the composite structure, a response surface methodology (RSM) was used. Taking the tooth spacing, tooth width, and tooth height as the independent variables and the shear capacity of the composite structure as the dependent variable (that is, the response value), a response surface analysis test with 3 factors and 3 levels was designed using the method of BoxBehnken test design. In total, seventeen sets of test points were used along with 5 replications of the center test point, and the actual number of test points was thirteen groups. The Box-Behnken test design and results are shown in Table 4. According to the data listed in Table 4, the response relationship between the test parameters and the shear capacity was regressively fitted using Design-Expert 8.0 analysis software. The response surface multivariate quadratic regression model is shown in Eq. (2). Fv = 470.63–17.94s-18.82w+11.87h + 0.12sw-0.16sh-0.047wh + 0.24s2+0.54w2-0.078h2 (2) The ANOVA results of the response surface regression model are 200
Composites Part B 160 (2019) 195–204
L. Yin et al.
Table 4 Box-Behnken test design and experimental values of the shear capacity. Run
Specimens
Factor 1 s (mm)
Factor 2w (mm)
Factor 3 h (mm)
Experimental shear capacity (KN)
Response predicted shear capacity (KN)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
s3w2h1 s3w3h2 s2w2h2 s1w1h2 s2w2h3 s2w1h3 s1w3h2 s2w3h1 s3w2h3 s2w1h1 s1w2h3 s2w2h2 s2w2h2 s3w1h2 s1w2h1 s2w2h2 s2w2h2
50 50 40 30 40 40 30 40 50 40 30 40 40 50 30 40 40
15 20 15 10 20 10 20 20 15 10 15 15 15 10 15 15 15
5 10 10 10 20 20 10 5 20 5 20 10 10 10 5 10 10
106.5 167.3 92.5 105.2 130.0 116.1 106.9 106.6 144.8 83.7 152.4 92.5 92.5 141.2 76.0 92.5 92.5
123.5 161.55 92.5 110.9 136.4 124.4 115.5 97.3 142.2 78.2 140.2 92.5 92.5 132.6 73.8 92.5 92.5
Table 5 ANOVA for the response surface quadratic model. Source
Sum of Squares
DF
Mean Square
F Value
P Value (Prob > F)
Model s w h sw sh wh s2 w2 h2
10199.52 1777.366 670.9243 801.1307 148.84 600.4238 13.32237 2473.501 757.4533 61.0221
9 1 1 1 1 1 1 1 1 1
1133.28 1777.366 670.9243 801.1307 148.84 600.4238 13.32237 2473.501 757.4533 61.0221
8.92885 14.00345 5.286056 6.311922 1.172676 4.730599 0.104964 19.48814 5.967798 0.480779
0.0043 0.0072 0.0551 0.0403 0.3147 0.0661 0.7554 0.0031 0.0446 0.5104
significant significant significant
shown in Table 5. The Model F-value of 8.93 implies the model is significant. There is only a 0.43% chance that a Model F-Value this large could occur due to noise. The F value can be used to assess the significance of each model term or factor. Values of Prob > F less than 0.0500 indicate model terms are significant. Values greater than 0.1000 indicate the model terms are not significant. In this case s, h, and w2 are significant model terms, and s (P = 0.0072 < 0.01) is extremely significant. However, the influence of the tooth width w (P = 0.0551 > 0.05) and the 3 interaction terms on the shear capacity are not significant. Therefore, considering only a single factor, the significance of the influence of the test parameters on the shear capacity is s > h > w. The 3-dimensional (3D) surfaces of the response surface model are presented in Figs. 8(a) - (c). The interactions among the various factors were analyzed from the graph. The influence of each factor on the response value (shear capacity) is not a simple linear relationship, but there is an extreme point. The steeper the slope of the 3D surface is (where contours tend to ellipse), the more sensitive the response value to the change of the interaction factors is. In addition, the interaction factor has a greater effect on the shear capacity. The gentler the slope of 3D surface is (where contours tend to circle), the less influence the interaction factors have on the shear capacity [17,18]. The 3D surface of the interaction term of the tooth spacing and tooth height in Fig. 8 (b) is the steepest, and the value range of the Zaxis is larger, followed by the interaction term of the tooth spacing and tooth width in Fig. 8 (a). The 3D surface of Fig. 8 (c) is relatively gentle, and the value range of the Z-axis is relatively small. It can be concluded that the influence of the interaction term of the tooth spacing and tooth
Fig. 8. 3D surfaces of the response surface model.
height on the shear capacity is the most obvious, followed by the interaction of the tooth spacing and tooth width, and the interaction of the tooth height and tooth width is the weakest, which is consistent with the results of the variance analysis. The comparison of the 13 sets of the design experimental values and the response model predicted values is shown in Fig. 9 (a). The 13 sets of data correspond to the actual number of the design experimental groups. In order to further evaluate the effectiveness of the response model, the model was used to calculate and analyze the other 14 groups of test values. The comparison of the 14 sets of response model calculated values and the experimental values is shown in Fig. 9 (b). From the graph, it is that the predicted value of the shear capacity of the response surface model is in good agreement with the experimental value. The optimal values of the model were calculated using the Numerical Function of Optimization in the Design-Expert 8.0 software. The optimum parameters were as follows: tooth spacing s = 50 mm, tooth width w = 20 mm, tooth height h = 18.99 mm. Under these conditions, we found that the optimum Fv predictive value (shear capacity) of the model is 167.834 KN. In summary, the prediction model of the shear capacity based on the response surface method is accurate and reliable and has a practical application value. Within a certain range, the response surface model can be used to optimize and predict the shear capacity of the SHCC/ 201
Composites Part B 160 (2019) 195–204
L. Yin et al.
diagonal compression strut is mainly formed in 1 tooth groove, and the shear capacity of the specimen is relatively small. However, the strut is mainly formed in 2 tooth grooves (the tooth groove between tooth I and tooth II and the non-complete tooth groove on the right side of tooth II) when the tooth spacing is small, and at this time, the shear capacity of the specimen is relatively large. Taking the right section of tooth I in the composite structural specimen as the shear characteristic area and the distance a from the top surface of the SHCC layer to the top surface of the tooth as the shear span of the composite structure, the ratio of the shear span a to the effective width w0 of the shear characteristic area is called the shear span ratio, and it is expressed by λ0. λ0 = a/w0
(3)
The shear span is a = H-h, and the effective width is w0 = 50 + s/2, resulting in the formula below: λ0 = (H-h)/(s + w) Fig. 9. Comparison of the predicted and experimental values of the RSM.
(4)
4. Calculation and analysis of the shear capacity
It is calculated that the shear span ratio of the 27 sets of composite structural specimens is between 0.4 and 0.69. Therefore, the influence of the bending moment caused by the shear span ratio is not considered when calculating the shear capacity. It is assumed that the compressive strength of the SHCC in the diagonal compression strut is fc [21].
4.1. Force model
fc = fc′/(0.8 + 170ε0)
groove steel composite structural specimen under different parameters, and provide reference for the shear design of a composite structure.
(5)
where ε0 is the average maximum principal tensile strain corresponding to the cracking of the SHCC. In this study, the maximum measured strain, ε0 is 0.004; fc′ is the compressive strength of the SHCC. We find that
Based on the analysis of the failure process and failure characteristics of the composite structural specimen, and referring to the relevant research results, the shear capacity calculation model of the SHCC/ grooved steel composite deck was established by using the theory of the diagonal strut [19,20]. The basic assumptions were as follows:
fc = 0.67fc′
(6)
Therefore, the shear capacity Fv of the composite structural specimen is
(1) The tangential load was mainly borne by the SHCC of the diagonally sheared area of tooth I and tooth II in the composite structural specimen. (2) The teeth of the composite structural specimen were not deformed when the composite structural specimen was finally destroyed. (3) The frictional shear resistance between the SHCC and the grooved steel plate was not considered.
Fv = fc Acs cosθ
(7)
where Fv is the shear capacity of the composite structural specimen based on the strut mechanism in KN, Acs is the average cross-sectional area of the diagonal portion of the strut in mm2, and θ is the inclination of the diagonal portion of the strut towards the shear horizontal direction.
Under a test load, the diagonal compression strut is formed along the diagonally sheared area of tooth I and tooth II in the SHCC pavement in order to resist the tangential shear force and the normal pressure. The force diagram is shown in Fig. 10, and the green area is the formed diagonal strut. The 2 blue rectangular dashed frames in the figure represent the range of changes in tooth parameters. From the diagram analysis, it can be seen that when the tooth spacing is large, the
4.2. Determination of model parameters The effective width of the cross-section of the diagonal portion of the strut is assumed to be b. According to Rizkala [21], it is calculated using Eq. (6). b = b1+b2 = h cosθ + (s + w) sin θ is
(8)
The average cross-sectional area of the diagonal portion of the strut
Acs = b t = h t cosθ + (s + w) t sin θ
(9)
The inclination of the diagonal portion of the strut towards the shear horizontal direction is θ = tan−1(H/ (50 + s/2))
(10)
where b is the effective width of the cross-section of the diagonal portion of the strut in mm, t is the effective length of the cross-section of the diagonal portion of the strut, that is, the length of the composite structural specimen, 100 mm, h is the tooth height of the composite structural specimen in mm, s is the tooth spacing of the composite structural specimen in mm, w is the tooth width of the composite structural specimen in mm, and H is the thickness of the SHCC
Fig. 10. Force model of the diagonal strut of the SHCC/grooved steel composite structure. 202
Composites Part B 160 (2019) 195–204
L. Yin et al.
Table 6 Experimental values and calculated values of the shear capacity. Specimen
Exp.
Cal.
FEV/FCV
Specimen
Exp.
Cal.
FEV/FCV
Specimen
Exp.
Cal.
FEV/FCV
s1w1h1 s1w1h2 s1w1h3 s1w2h1 s1w2h2 s1w2h3 s1w3h1 s1w3h2 s1w3h3
69.6 105.2 118.0 76.0 111.5 152.4 108.5 106.9 141.4
67.9 79.3 101.9 75.0 86.3 109.0 82.1 93.4 116.1
1.02 1.33 1.16 1.01 1.29 1.40 1.32 1.14 1.22
s2w1h1 s2w1h2 s2w1h3 s2w2h1 s2w2h2 s2w2h3 s2w3h1 s2w3h2 s2w3h3
83.7 132.6 116.1 101.4 92.5 153.2 106.6 89.2 130.0
78.9 90.9 115.0 85.6 97.6 121.7 92.2 104.3 128.3
1.06 1.46 1.01 1.19 0.95 1.26 1.16 0.86 1.01
s3w1h1 s3w1h2 s3w1h3 s3w2h1 s3w2h2 s3w2h3 s3w3h1 s3w3h2 s3w3h3
72.3 141.2 127.7 106.5 135.3 144.8 101.9 167.3 182.5
88.2 100.8 126.0 94.5 107.1 132.3 100.8 113.4 138.6
0.82 1.40 1.01 1.13 1.26 1.09 1.01 1.48 1.32
angle between the main crack and the shear load direction ranges from 30° to 45°. (2) The shear failure process of the SHCC-grooved steel composite structural specimen can be divided into 4 stages: the linear elastic stage, the elastic-plastic stage, the slip hardening stage, and the failure stage. A digital image correlation technique can be used to describe the failure process of a composite structural specimen. (3) The response surface model of the shear capacity is extremely significant. The tooth spacing s (P = 0.0072 < 0.01) and the tooth height h (P = 0.0403 < 0.05) have a significant influence on the shear capacity, and the tooth spacing s is extremely significant. However, the influence of the tooth width w (P = 0.0551 > 0.05) and the interaction term for the shear capacity are not significant. (4) The calculated values of the shear capacity model based on theory of the diagonal strut agree well with the experimental values. The model can be used to predict the shear capacity of a SHCC/grooved steel composite structure under different parameters, and provide a basis for the shear design of a composite structure. Fig. 11. Comparison of experimental and calculated values.
Acknowledgements
pavement, or 50 mm.
This research was funded by National Natural Science Foundation of China (Grant No. 51768051), the Natural Science Foundation of the Inner Mongolia Autonomous Region of China (Grant No. 2017MS0505), and the Science and Technology Innovation Project of Inner Mongolia Autonomous Region of China (Grant No. KCBJ2018016). Their financial support is highly appreciated. We thank LetPub (www.letpub. com) for its linguistic assistance during the preparation of this manuscript.
4.3. Calculation results and analysis The shear capacity of a SHCC/grooved steel composite structural specimen can be calculated by Eq. (7), and the calculation results are shown in Table 6. The average value of the ratio of experimental values to calculated values is 1.16. The comparison between the experimental value of the shear capacity and the calculated value is shown in Fig. 11. It can be seen from the figure that the calculated value agrees well with the experimental value, and the calculated value is lower than the experimental value as a whole. The calculated value of the shear capacity is favorable for safety. Therefore, the shear capacity formula proposed in this paper can be used to predict the shear capacity of a SHCC/ grooved steel composite structure under different parameters and provide a basis for the shear design of a composite structure. In this paper, the composite structural specimen has 2 teeth and only 1 complete tooth groove. The shear behavior and the calculation model of large size specimen with more than 3 teeth and 2 grooves need to be further studied.
Appendix A. Supplementary data Supplementary data to this article can be found online at https:// doi.org/10.1016/j.compositesb.2018.10.025. References [1] Ma J, Sun SZ, Qi Y. Review on China's bridge engineering research. China J Highw Transp 2014;27(5):1–96. [2] Shao XD, Yi DT, Huang ZY, Zhao H. Basic Performance of the composite deck system composed of orthotropic steel deck and ultrathin RPC layer. J Bridge Eng 2013;18(5):417–28. [3] Wei J, Zha X, Zheng JL, Wang BJ. Cracks resisting mechanism analysis of large stone asphalt mixture base structure. Highways 2008;4:6–10. [4] Kakuma K, Matsumoto T, Hayashikawa T, He X. An analytical study on the composite effect of steel deck with ECC overlay reinforcement. J Jpn Soc Civ Eng 2010;56:1282–91. [5] Walter R, Olesen JF, Stang H, Vejrum T. Analysis of an orthotropic deck stiffened with a cement-based overlay. J Bridge Eng 2007;12(3):350–63. [6] Abe T, Kawai Y, Yamashita T, Ichinose Y. Decreasing effect of stress in orthotropic steel decks by SFRC pavement with ordinary Portland cement and low shrinkage type mixture material. J Pavement Eng JSCE 2015;71(2):47–62. [7] Dieng L, Marchand P, Gomes F, Tessiera C, Toutlemondec F. Use of UHPFRC overlay to reduce stresses in orthotropic steel decks. J Constr Steel Res 2013;89(5):30–41. [8] Liu H, Zhang Q, Gu C, Su H, Li VC. Influence of micro-cracking on the permeability of engineered cementitious composites. Cement Concr Compos 2016;72(9):104–13. [9] Wang B, Xu S, Liu F. Evaluation of tensile bonding strength between UHTCC repair
5. Conclusions Based on the compression-shear test of a SHCC/grooved steel composite structure, combined with a digital image correlation technique, the response surface method, and the theory of the diagonal strut, the interlayer shear performance and shear capacity of a SHCC/ grooved steel composite structure under different test parameters were studied in this paper. The following conclusions were drawn: (1) The failure mode of the SHCC-grooved steel composite structural specimen is the diagonal shear cracking of the ECC pavement. The 203
Composites Part B 160 (2019) 195–204
L. Yin et al. materials and concrete substrate. Construct Build Mater 2016;112(6):595–606. [10] Dhawale AW, Joshi VP. Engineered cementitious composites for structural applications. Int J Appl Innovat Eng Manag 2013;2:198–205. [11] Cao J, Shao X, Deng L, Gan Y. Static and fatigue behavior of short-headed studs embedded in a thin ultrahigh-performance concrete layer. J Bridge Eng 2017;22(5):04017005. [12] Cao J, Shao X, Zhang Z, Zhao H. Retrofit of an orthotropic steel deck with compact reinforced reactive powder concrete. Struct Infrastruct E 2016;12(3):411–29. [13] Ding B. Research of interface characteristics of early-strength ECC steel deck pavement structure based on stud connection. NJ: Southeast University; 2015. [14] Ma H. Research of early-strength ECC applying on long-span steel bridge deck pavement. NJ: Southeast University; 2014. [15] Liu SG, Zhang DX, Yan CW, Deng YD. Experimental study on the tensile properties of PVA-ECC with high-calcium fly ash. Bull Chin Ceramic Soc 2016;35(1):52–60.
[16] Pan B, Xie HM, Hua T, Anand A. Measurement of coefficient of thermal expansion of films using digital image correlation method. Polym Test 2009;28(1):75–83. [17] Asadzadeh S, Khoshbayan S. Multi-objective optimization of influential factors on production process of foamed concrete using Box-Behnken approach. Construct Build Mater 2018;170:101–10. [18] Li W, Cai L, Wu Y, Liu Q, Yu H, Zhang C. Assessing recycled pavement concrete mechanical properties under joint action of freezing and fatigue via RSM. Construct Build Mater 2018;164:1–11. [19] Zhang X, Ma J, Han P, Niu S, Zhang S. Shear behavior on prefabricated shear wall alveolar type connection. J Build Struct 2017;38(11):93–100. [20] Collins MP, Mitchell D. Prestressed concrete basics. Ottawa, Ontario: Canadian Prestressed Concrete Institute; 1987. p. 318–20. [21] Rizkala SH. Multiple shear key connections for precast shear wall panels. PCI J 1989;34(2):104–20.
204
Contents lists available at ScienceDirect
Composites Part B journal homepage: www.elsevier.com/locate/compositesb
Shear behavior of a strain hardening cementitious composites (SHCC)Grooved steel composite deck
T
Liqiang Yina, Changwang Yanb, Shuguang Liub,∗, Ju Zhangb, Mingyang Liangb a b
School of Materials Science and Engineering, Inner Mongolia University of Technology, Hohhot, 010051, PR China School of Mining and Technology, Inner Mongolia University of Technology, Hohhot, 010051, PR China
ARTICLE INFO
ABSTRACT
Keywords: Strain hardening cementitious composites (SHCC) Orthotropic steel deck pavement Interlayer shear resistance Digital image correlation method (DIC) Response surface method (RSM)
The deterioration and premature failure of an orthotropic steel deck pavement during its service period is a pressing issue. Strain hardening cementitious composites (SHCC) possess an extreme tensile ductility, in the range of 3%–5% (about 300–500 times that of concrete). Using SHCC as a steel deck pavement can enhance the overall stiffness of a deck system. In this paper, an SHCC-grooved steel composite structure is the research object, and the tooth spacing, tooth width, and tooth height are the parameters. The shear behavior of an SHCC-grooved steel composite structure was studied using a compression shear test and the digital image correlation method. The response surface method was used to analyze the significant influence of the test parameters on the shear capacity, and the response model of the shear capacity was established. The calculation formula of the shear capacity of an SHCC-grooved steel composite structure was established based on the theory of the diagonal compression strut. The experimental results show that the cracking of a shear diagonal SHCC leads to the ultimate failure of an SHCC-grooved steel composite structure. The angle between the main crack and the shear load direction ranges from 30 to 45°. The failure process of the composite structure can be divided into 4 stages: linear elasticity, elastic-plastic, slip hardening, and instability failure. The order of the influence of the test parameters on the shear capacity is the tooth spacing > tooth height > tooth width. The response surface model can optimize and predict the shear capacity of the composite structure under different parameters within a certain range. The calculated values of the shear capacity model based on the theory of the diagonal compression strut agree well with the experimental values, and the calculated values are favorable for safety. This research can provide a reference for the shear design of an SHCC-grooved steel composite structure.
1. Introduction Orthotropic steel decks have been widely used across the world because of their advantages, such as a light self-weight, high bearing capacity, superior integrity, and constructional convenience. A steel deck is usually made of 10–14 mm thick steel plates. The pavement layer is directly laid on the steel deck, and a 35–80 mm thick asphalt mixture is generally used [1]. Due to the limited improvement of the stiffness of the orthotropic steel bridge deck due to the asphalt mixture pavement layer, a steel bridge deck system is in a high stress amplitude state under a vehicle load, and the local stress and the deformation of the pavement layer are large. The cracking of the pavement layer directly leads to a significant decrease in the stiffness of the deck system, further increasing the local stress and the crack width [2]. Engineering practice shows that once the pavement is cracked, the occurrence of the failure of the deck system is
∗
only a matter of time. The Baishazhou Yangtze River Bridge in Wuhan, Hubei Province, China was built in 2000. The steel deck pavement was repaired 24 times in 10 years [3]. In order to solve the problem of a steel deck pavement being easy to damage, some researchers have proposed a rigid concrete paving scheme that uses pavement materials such as high performance concrete, reactive powder concrete, or fiber-reinforced concrete; this approach was expected to improve the stress state of the deck system [4,5]. Researchers have done a lot of research on rigid pavements. Their results show that a rigid pavement can enhance the overall stiffness of a steel deck, disperse the traffic load, improve the mechanical properties of the steel deck pavement, and reduce the occurrence of fatigue cracking [6,7]. It is impossible to fundamentally eliminate the occurrence of cracks due to the high brittleness of concrete materials, and the problem of the pavement layer being easy to damage still exists. A new type of
Corresponding author. School of Mining and Technology, Inner Mongolia University of Technology, Hohhot, 010051, PR China. E-mail address: [email protected] (S. Liu).
https://doi.org/10.1016/j.compositesb.2018.10.025 Received 1 September 2018; Received in revised form 7 October 2018; Accepted 9 October 2018 Available online 11 October 2018 1359-8368/ © 2018 Elsevier Ltd. All rights reserved.
Composites Part B 160 (2019) 195–204
L. Yin et al.
engineering material, polyvinyl alcohol fiber reinforced cementitious composites, or strain hardening cementitious composites (SHCC), have excellent properties such as a high ductility, a strong ability to control cracks, freeze-thaw resistance, and fatigue resistance [8,9]. SHCC have been successfully used in bridge deck repair, bridge expansion joints, pre-stressed concrete bridge deck connection plates, deck pavements, and other bridge pavement projects globally [10]. The local position of the pavement layer under the vehicle load will generate a large tensile stress and shear stress. When the vehicle brakes, the steel deck pavement will withstand a large horizontal shear load. If the braking occurs quickly, the horizontal shear load will act on the localized area. This phenomenon occurs often, especially in areas with large traffic volumes. If the inter-layer shear resistance is insufficient, it will directly lead to conditions such as slip delamination or cracking, which will cause the bridge deck to be corroded and affect the safety of the bridge [11,12]. Ding [13] designed a steel pavement underlying asphalt concrete meant to be replaced with SHCC, forming a combined deck structure of “an asphalt concrete upper layer + a rigid pavement lower layer + a steel deck”, and 4 rigid pavement materials, SHCC l, SHCC 2, ordinary concrete and mortar, were selected. A push shear test of an H type steelrigid pavement composite structure with a stud shear key was carried out. The results showed that the shear strength of the H type steel-SHCC pavement composite structure is higher than that of ordinary concrete and much higher than that of mortar. Moreover, the high ductility of the SHCC can disperse the stud shear load and improve the cooperative working ability between the SHCC pavement and the steel deck. Ma [14] studied the interlaminar shear behavior of an SHCC pavement/steel deck (without a shear key) composite structure using an oblique shear test. The finite element software ANSYS was used to analyze the stress state of the steel deck SHCC pavement under load, calculate the maximum tensile stress and the maximum shear stress between decks, and comprehensively evaluate the feasibility of the SHCC in the steel deck pavement. Based on the studies of SHCC by authors of this paper in the early stage, we comprehensively analyzed the mechanical characteristics and actual diseases of the pavement of an orthotropic steel deck, proposed a steel deck SHCC pavement composite system, and studied its interlayer shear resistance. This study will provide an experimental and theoretical basis for the design and application of steel deck SHCC pavements, which is of great importance for improving the service life of the pavement.
Table 1 Index properties of the PVA fiber. Tensile strength (MPa)
Young's modulus (Gpa)
Diameter (μm)
Length (mm)
Elongation (%)
1600
40
0.04
12
6
Table 2 Mix proportions of the SHCC. Cement (kg/m3)
Fly ash (kg/ m3)
Water (kg/m3)
Silica sand (kg/m3)
WaterRAE (kg/ m3)
Water binder ratio (mw/mb)
PVA fiber (vol. %)
378
880
302
457
16.37
0.24
2
mw, the weight of water, kg; mb, the weight of binder materials, cement and fly ash, kg.
2.2. Materials and specimen preparation
2. Experimental program
The designed SHCC binder system contained type I ordinary Portland cement, Class-I high calcium fly ash, a fine aggregate made of quartz sand with a maximum grain size of 0.2 mm, and Polycarboxylate Superplasticizer. Polyvinyl alcohol (PVA) fibers were incorporated into the mixture at a volume fraction of 2.0%, and the properties as shown in Table 1. The mix proportion is listed in Table 2; the fly ash accounted for 70% of the total cementitious material, and the ratio of water to binder was 0.24. The preparation process of the SHCC and the test methods of the basic mechanical properties are detailed in the authors' previous research [15]. The dumbbell specimen was used in a uniaxial tensile test with a size of 330 mm × 60 mm × 15 mm. The test was carried out on the MTS servo hydraulic loading system, and the loading rate was 0.1 mm/min. The deformation of the specimen was measured by a laser extensometer. The uniaxial tensile stress-strain curves of the SHCC and the development of cracks are shown in Fig. 2. A prism specimen with a size of 100 mm × 100 mm × 300 mm was used in the test of axial compressive strength, and the compressive strength was 47 MPa. A section of Q235 steel was used for the grooved steel plate and for sandblasting on the surface of the steel plate. The cleanliness reached Sa2.5 level and the roughness was 50–100 μm. The test parameters included the tooth spacing, s, the tooth width, w, and the tooth height, h (Fig. 1); s ranged from 30 mm to 50 mm, w ranged from 10 mm to 20 mm, and h ranged from 5 mm to 20 mm. The parameters of the specimen are shown in Table 3.
2.1. Specimen design
2.3. Experimental details
The SHCC-grooved steel composite deck structure was made up of SHCC pavement and a grooved steel plate. The form and size of the SHCC-grooved steel composite deck structure are shown in Fig. 1. The thickness of the SHCC pavement was 50 mm, and the thickness of the steel plate was 10 mm. The shear section area was 100 mm × 100 mm.
The experiment was made up of a loading system and a digital image correlation (DIC) system, as shown in Fig. 3. An electro-hydraulic servo universal testing machine with a range of 100 KN was used as loading device for the compression shear test. The clamping device was designed and made independently, and 2 steel roll shafts with a diameter of 20 mm were arranged between the upper clamping device and
Fig. 1. Specimen geometry: (a) front elevation; (b) side elevation. 196
Composites Part B 160 (2019) 195–204
L. Yin et al.
Fig. 2. Uniaxial tensile stress-strain curve of the SHCC and the cracks.
of 2 CCD cameras, a light source, an image acquisition system, and an image analysis system. The speckle images of the specimen surface were collected continuously by the CCD cameras during the loading process, and the displacement and strain fields were calculated by the image analysis system. The maximum resolution of a CCD camera was 1624(H) × 1224(V) pixels, the maximum frame number was 30 fps, and the strain accuracy was less than 50 με. In order to make a good contrast for the speckle, the dummy black lacquer was used to make the surface speckle of the specimen. Because the digital image correlation method is a full-field measurement technique, the correlation function has a significant effect on the result of calculation. Therefore, it was necessary to select correlation functions that are simple in operation, small in computation, and good at anti-interference. The zero mean normalized least square distance correlation function was adopted in this paper [16]:
Table 3 Test parameters and specimens (unit: mm). Specimens
s
w
h
Specimens
s
w
h
Specimens
s
w
h
s1w1h1 s1w1h2 s1w1h3 s1w2h1 s1w2h2 s1w2h3 s1w3h1 s1w3h2 s1w3h3
30 30 30 30 30 30 30 30 30
10 10 10 15 15 15 20 20 20
5 10 20 5 10 20 5 10 20
s2w1h1 s2w1h2 s2w1h3 s2w2h1 s2w2h2 s2w2h3 s2w3h1 s2w3h2 s2w3h3
40 40 40 40 40 40 40 40 40
10 10 10 15 15 15 20 20 20
5 10 20 5 10 20 5 10 20
s3w1h1 s3w1h2 s3w1h3 s3w2h1 s3w2h2 s3w2h3 s3w3h1 s3w3h2 s3w3h3
50 50 50 50 50 50 50 50 50
10 10 10 15 15 15 20 20 20
5 10 20 5 10 20 5 10 20
the bearing. The angle of the compression shear test α was 45°. Taking into account the actual braking load is mainly concentrated on the upper surface of the pavement. Therefore, the shear load cross section of the SHCC pavement was raised to 3/10 at the height of the composite structural specimen in the compression shear test; the shear load cross section of the SHCC layer was 18 mm × 100 mm. The displacement control method was adopted, and the loading rate was 2 mm/min. The interlaminar shear displacement was measured by 2 LVDTs at the top of the SHCC layer and at the steel plate. The shear load was measured by a load transducer. The data for the load and the displacement was collected continuously by a DH3820 high-speed static strain test and analysis system. The displacement field and the strain field of composite structural specimen surface during loading were measured continuously using a digital image correlation technique. As shown in Fig. 3(a), the DIC testing system was mainly composed
C (p ) =
[f (x , y ) [f (x , y )
fm ][g(x , y ) fm
]2
[g(x , y )
gm] gm]2
(1)
where, C (P) is the correlation coefficient. f (x, y) is the gray value of the coordinates of each point in the reference subset and g (x', y') is the gray value of the coordinates of each point in the target subset. fm and gm refer to the average value of the gray level for the reference subset and the target subset, respectively. p is the deformation parameter vector describing the location and shape of the target subset before and after deformation.
Fig. 3. Scheme of the loading device and the DIC testing system. 197
Composites Part B 160 (2019) 195–204
L. Yin et al.
Fig. 4. Shear failure mode of an SHCC-grooved steel composite structure.
weakened for specimens with s values of 40 mm and 50 mm. Therefore, no cracking was present in the shear diagonal area to the tooth II; it is usually manifested as the shear diagonal area of tooth I cracking. In general, the influence law of the tooth width on the specimen failure code is not obvious. As shown in Fig. 4(d)–(f), 3 groups of specimens with values of s equal to 40 mm, h equal to 10 mm, and w equal to 10 mm, 15 mm, and 20 mm, were selected as examples for comparison and analysis. With the decrease of w, the possibility of forming 2 parts of the strut mechanism increase only when s and the h are constant. As shown in Fig. 4(d), the number of cracks increases. However, the change of w has little effect on the main crack angle. The influence of different tooth heights on the specimen failure mode was studied through the contrast analysis of 3 groups of specimens with values of s equal to 50 mm, w equal to 15 mm, and h equal to 5 mm, 10 mm and 20 mm, as shown in Fig. 4(g)–(i). Consistent with the tooth width, the influence of the tooth height on the failure modes of the specimens was also focused on the mechanism of the forming strut at the shear diagonal area of the right tooth II. With the increase of h, the cross-sectional area of the shear-compression area of the SHCC pavement increased. Therefore, its resistance to the diagonal pressure increased, and the shear capacity of the specimen was improved. The tooth height had an influence on the angle of the main crack. With the increase of tooth height, the main crack angle tended to decrease. The main reason is that the increase of tooth height leads to the reduction of the height of the characteristic shear span, which affects the change of the angle of the inclined crack.
3. Experimental results and analysis of the shear performance 3.1. Shear failure modes and analysis of an SHCC-grooved steel composite structure The typical shear failure mode of the SHCC-grooved steel composite structural specimen is shown in Fig. 4(a)-(i). The ultimate failure modes of each group of specimens were mostly the debonding and slippage of the interface between SHCC and steel plate near tooth I, as shown in Fig. 4(e), and the shear cracks that ran through the SHCC pavement. The angle between the main crack and the shear load direction ranges from 30° to 45°. It was observed that multiple cracks developed near the main crack when the SHCC was racked and damaged. The width of the crack is constant at the micron level. The SHCC-grooved steel composite structural specimen showed obvious ductile failure characteristics. The influence of different tooth spacings on the specimen failure mode was studied through the contrast analysis of 3 groups of specimens, namely, with values of w equal to 10 mm, h equal to 5 mm, and s equal to 30 mm, 40 mm, and 50 mm, as shown in Fig. 4(a)–(c). There are 2 main cracks in the SHCC layer corresponding to the specimen with a tooth spacing of 30 mm. The cracks are distributed in the shear diagonal region, and the angle between the cracks and the shear load direction ranges from 40° to 45°. There is only one main crack in the SHCC layer corresponding to the 2 specimens with s values of 40 mm, and 50 mm. The angle between the crack and the shear load direction is about 35°. The general rule is as follows: large tooth spacing, small angle of main crack. With the reduction of the tooth spacing, the number of main cracks increased, and the characteristic of the multiple cracks of the SHCC was brought into full play. After analysis, it was possible that the total size of the specimen was a constant value, and with the decrease of the distance between the teeth, the angle between the teeth and the diagonal bar that formed between the shear diagonal and the shear diagonal increased. With the decrease of s, the inclination of the diagonal portion of the strut towards shear load direction increased. The action of the tooth II diagonal compression strut was further strengthened, and it could bear a greater normal load and shear load. The shear diagonal crack occurred when the principal tensile stress reached the SHCC tensile strength. The action of the strut formed between the diagonal of the shear and tooth II under a load was
3.2. Shear failure process and analysis of an SHCC-grooved steel composite structure The full field displacement Ux and strain εx can be obtained with the digital image correlation method. The specimen s1w3h1 was selected in order to list the full field tangential displacement Ux cloud image and the strain εx cloud image at 6 typical moments (Fig. 5) during the experimental process, as shown in Figs. 6(a)–(f) and 7(a)–(f), respectively. The displacement along the positive direction of the x-axis is a tangential positive displacement. Conversely, it is a tangential negative displacement. The direction of the coordinate axis is detailed in Fig. 3(b). The tangential (x axial) tensile strain is positive and the 198
Composites Part B 160 (2019) 195–204
L. Yin et al.
SHCC is gradually perceptible. The blue-green relative displacement abruptly-appearing belt appeared in the specimen bounded by a diagonal shear line, as shown in Fig. 6(c) (corresponding to Pc). This indicates that the area near the relative displacement abrupt belt may crack first and become a vulnerable section. When the load reaches the Pd point (Fig. 5), as shown in Fig. 6 (d), the relative displacement difference between the 2 parts of the area on the left and right sides of the abrupt belt is especially obvious, the maximum displacement value is 2.844 mm, and the minimum displacement value is 2.470 mm. Macro slight debonding and slippage begin to occur between the left surface and the top surface of tooth I, the steel plate on the left side of tooth I, and the SHCC. In addition, fine cracks appear in the SHCC near the abrupt belt. However, the micro-cracks do not break suddenly due to the super-strong anti-cracking effect of PVA fiber in the SHCC, but rather expand steadily in a short time. When the load reaches its maximum value, as shown in Fig. 6 (e) (corresponding to Pe), the development of the debonding, slippage, and crack propagation reaches its limit. At this point, the critical state of the composite structural specimen is to resist the shear load. When the load begins to decrease after exceeding the maximum value, as shown in Fig. 6 (f) (corresponding to Pf), the macro crack crosses over the composite structural specimen, and the pavement of the composite structure is completely destroyed. Corresponding to the tangential displacement Ux cloud image, there are 6 typical moments in the process of change of the tangential strain εx cloud image. At the initial stage of loading, as shown in Fig. 7 (a) (corresponding to the point Pa on the curve in Fig. 5), the εx cloud image shows the distribution with a blue-green stripe and a local scatter point. The strain stripes appear alternately with the increase of the load, and it is the stage of the internal micro-crack dispersion and stress adjustment. The main reason for this phenomenon is that the heterogeneity of the SHCC and the interface discontinuity between the SHCC layer and grooved steel plate layer lead to the stress concentration. The phenomenon will first occur at the tip of the micro-crack in the SHCC, then the weak interface area between the layers, and then quickly reach
Fig. 5. Typical shear load slip curve (Fv -δ) of an SHCC-grooved steel composite structure specimen (s1w3h1).
tangential compressive strain is negative. The typical Fv -δ curve of an SHCC-grooved steel composite structural specimen is shown in Fig. 5. Six typical moments corresponding to the Pa - Pf points on the curve were selected for analysis. As shown in Fig. 6(a) (corresponding to the point Pa on the curve in Fig. 5), the tangential displacement Ux cloud image of the specimen is distributed with a scattered point and a strip phenomenon during the initial stage of loading. Although the specimen was subjected to a tangential load, the value is small. At this time, the development of the stress and deformation of each point in the composite structure is not uniform because of the discontinuities of the stress of each phase material and the internal defects. With the increase of the load, as shown in Fig. 6(b) (corresponding to Pb), there is a general change in the Ux cloud image. The relative displacement between the 2 teeth and the
Fig. 6. The full field displacement Ux of an SHCC-grooved steel composite structural specimen corresponding to 6 typical moments. 199
Composites Part B 160 (2019) 195–204
L. Yin et al.
Fig. 7. The full field strain εx of an SHCC-grooved steel composite structural specimen corresponding to 6 typical moments.
the limit and cause destruction and the stress release at the stress concentration, and then move on to the next section. The stress concentration is formed at the next weak place, so that it alternates repeatedly. With the increase of the load, as shown in Fig. 7(b) (corresponding to Pb), there is a general change in the εx cloud image. The red tensile strain concentration begins to appear in the tooth I and tooth II parts of the steel plate, while the purple compressive strain concentration is mainly distributed in the upper part of the SHCC. At this time, the yellowish-red elliptical area with the local tensile strain concentration appears in the SHCC on the upper right part of tooth I along the shear diagonal direction, for the first time. When the load reaches the Pc point (Fig. 5), as shown in Fig. 7 (c), the strain concentration of tooth I is more obvious, while tooth II is relatively weakened. The yellowish-red elliptical area in the SHCC is further enlarged, and its color changes from yellowish-red to red, accompanied by the increase of the strain value from 1.640 to 3.200. When the load increases to the point where a slight debonding and slippage occurs between the left area of tooth I and the SHCC (the corresponding εx cloud image is shown in Fig. 7 (d)), the debonding and slippage lead to a failure of the pixel recognition and the missing εx cloud image at the corresponding positions. Fig. 7 (e) is a tangential strain εx cloud image during the peak load, corresponding to the Pe point on the curve in Fig. 5. At this point, the tangential strain in the diagonal shear zone is the largest, the strain value is 16.00, and the shear capacity of the composite structure reaches the limit. When the load begins to decrease after exceeding the maximum value, as shown in Fig. 7 (f) (corresponding to Pf), a macro crack crosses over the composite structural specimen, and the pavement of the composite structure is completely destroyed. Based on the typical Fv -δ curve (Fig. 5), combined with the tangential displacement Ux cloud image and the s strain εx cloud image, it can be seen that the shear failure process of the SHCC-grooved steel composite structure shows 4 stages of development. I: The linear elastic stage occurs at the initial stage of loading, when the micro-cracks in the specimen are in the state of stress adjustment and dispersion, and the tangential load is uniformly distributed in the shear zone. The shear
load increases linearly. II: The elastic-plastic deformation stage occurs when the tangential load reaches the linear elastic limit value and enters the elastic-plastic process, and fine cracks appear in the shear diagonal area of the SHCC. The growth rate of the tangential load decreases, and the interfacial shear modulus decreases. III: The slip hardening stage occurs when the tangential load reaches its peak value; it does not drop suddenly as the macro crack and the interface slip continue to grow. The load can remain near a peak value due to the excellent performance of the SHCC, showing the pseudo strain hardening characteristic. However, this process is relatively short. IV: The failure stage occurs when the slip hardening reaches the critical point, cracks are suddenly destabilized, and the interface slip failure takes place. 3.3. Significance analysis of shear capacity based on response surface methodology (RSM) In order to clarify the significance of the influence of tooth spacing, tooth width, and tooth height on the shear capacity of the composite structure, a response surface methodology (RSM) was used. Taking the tooth spacing, tooth width, and tooth height as the independent variables and the shear capacity of the composite structure as the dependent variable (that is, the response value), a response surface analysis test with 3 factors and 3 levels was designed using the method of BoxBehnken test design. In total, seventeen sets of test points were used along with 5 replications of the center test point, and the actual number of test points was thirteen groups. The Box-Behnken test design and results are shown in Table 4. According to the data listed in Table 4, the response relationship between the test parameters and the shear capacity was regressively fitted using Design-Expert 8.0 analysis software. The response surface multivariate quadratic regression model is shown in Eq. (2). Fv = 470.63–17.94s-18.82w+11.87h + 0.12sw-0.16sh-0.047wh + 0.24s2+0.54w2-0.078h2 (2) The ANOVA results of the response surface regression model are 200
Composites Part B 160 (2019) 195–204
L. Yin et al.
Table 4 Box-Behnken test design and experimental values of the shear capacity. Run
Specimens
Factor 1 s (mm)
Factor 2w (mm)
Factor 3 h (mm)
Experimental shear capacity (KN)
Response predicted shear capacity (KN)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
s3w2h1 s3w3h2 s2w2h2 s1w1h2 s2w2h3 s2w1h3 s1w3h2 s2w3h1 s3w2h3 s2w1h1 s1w2h3 s2w2h2 s2w2h2 s3w1h2 s1w2h1 s2w2h2 s2w2h2
50 50 40 30 40 40 30 40 50 40 30 40 40 50 30 40 40
15 20 15 10 20 10 20 20 15 10 15 15 15 10 15 15 15
5 10 10 10 20 20 10 5 20 5 20 10 10 10 5 10 10
106.5 167.3 92.5 105.2 130.0 116.1 106.9 106.6 144.8 83.7 152.4 92.5 92.5 141.2 76.0 92.5 92.5
123.5 161.55 92.5 110.9 136.4 124.4 115.5 97.3 142.2 78.2 140.2 92.5 92.5 132.6 73.8 92.5 92.5
Table 5 ANOVA for the response surface quadratic model. Source
Sum of Squares
DF
Mean Square
F Value
P Value (Prob > F)
Model s w h sw sh wh s2 w2 h2
10199.52 1777.366 670.9243 801.1307 148.84 600.4238 13.32237 2473.501 757.4533 61.0221
9 1 1 1 1 1 1 1 1 1
1133.28 1777.366 670.9243 801.1307 148.84 600.4238 13.32237 2473.501 757.4533 61.0221
8.92885 14.00345 5.286056 6.311922 1.172676 4.730599 0.104964 19.48814 5.967798 0.480779
0.0043 0.0072 0.0551 0.0403 0.3147 0.0661 0.7554 0.0031 0.0446 0.5104
significant significant significant
shown in Table 5. The Model F-value of 8.93 implies the model is significant. There is only a 0.43% chance that a Model F-Value this large could occur due to noise. The F value can be used to assess the significance of each model term or factor. Values of Prob > F less than 0.0500 indicate model terms are significant. Values greater than 0.1000 indicate the model terms are not significant. In this case s, h, and w2 are significant model terms, and s (P = 0.0072 < 0.01) is extremely significant. However, the influence of the tooth width w (P = 0.0551 > 0.05) and the 3 interaction terms on the shear capacity are not significant. Therefore, considering only a single factor, the significance of the influence of the test parameters on the shear capacity is s > h > w. The 3-dimensional (3D) surfaces of the response surface model are presented in Figs. 8(a) - (c). The interactions among the various factors were analyzed from the graph. The influence of each factor on the response value (shear capacity) is not a simple linear relationship, but there is an extreme point. The steeper the slope of the 3D surface is (where contours tend to ellipse), the more sensitive the response value to the change of the interaction factors is. In addition, the interaction factor has a greater effect on the shear capacity. The gentler the slope of 3D surface is (where contours tend to circle), the less influence the interaction factors have on the shear capacity [17,18]. The 3D surface of the interaction term of the tooth spacing and tooth height in Fig. 8 (b) is the steepest, and the value range of the Zaxis is larger, followed by the interaction term of the tooth spacing and tooth width in Fig. 8 (a). The 3D surface of Fig. 8 (c) is relatively gentle, and the value range of the Z-axis is relatively small. It can be concluded that the influence of the interaction term of the tooth spacing and tooth
Fig. 8. 3D surfaces of the response surface model.
height on the shear capacity is the most obvious, followed by the interaction of the tooth spacing and tooth width, and the interaction of the tooth height and tooth width is the weakest, which is consistent with the results of the variance analysis. The comparison of the 13 sets of the design experimental values and the response model predicted values is shown in Fig. 9 (a). The 13 sets of data correspond to the actual number of the design experimental groups. In order to further evaluate the effectiveness of the response model, the model was used to calculate and analyze the other 14 groups of test values. The comparison of the 14 sets of response model calculated values and the experimental values is shown in Fig. 9 (b). From the graph, it is that the predicted value of the shear capacity of the response surface model is in good agreement with the experimental value. The optimal values of the model were calculated using the Numerical Function of Optimization in the Design-Expert 8.0 software. The optimum parameters were as follows: tooth spacing s = 50 mm, tooth width w = 20 mm, tooth height h = 18.99 mm. Under these conditions, we found that the optimum Fv predictive value (shear capacity) of the model is 167.834 KN. In summary, the prediction model of the shear capacity based on the response surface method is accurate and reliable and has a practical application value. Within a certain range, the response surface model can be used to optimize and predict the shear capacity of the SHCC/ 201
Composites Part B 160 (2019) 195–204
L. Yin et al.
diagonal compression strut is mainly formed in 1 tooth groove, and the shear capacity of the specimen is relatively small. However, the strut is mainly formed in 2 tooth grooves (the tooth groove between tooth I and tooth II and the non-complete tooth groove on the right side of tooth II) when the tooth spacing is small, and at this time, the shear capacity of the specimen is relatively large. Taking the right section of tooth I in the composite structural specimen as the shear characteristic area and the distance a from the top surface of the SHCC layer to the top surface of the tooth as the shear span of the composite structure, the ratio of the shear span a to the effective width w0 of the shear characteristic area is called the shear span ratio, and it is expressed by λ0. λ0 = a/w0
(3)
The shear span is a = H-h, and the effective width is w0 = 50 + s/2, resulting in the formula below: λ0 = (H-h)/(s + w) Fig. 9. Comparison of the predicted and experimental values of the RSM.
(4)
4. Calculation and analysis of the shear capacity
It is calculated that the shear span ratio of the 27 sets of composite structural specimens is between 0.4 and 0.69. Therefore, the influence of the bending moment caused by the shear span ratio is not considered when calculating the shear capacity. It is assumed that the compressive strength of the SHCC in the diagonal compression strut is fc [21].
4.1. Force model
fc = fc′/(0.8 + 170ε0)
groove steel composite structural specimen under different parameters, and provide reference for the shear design of a composite structure.
(5)
where ε0 is the average maximum principal tensile strain corresponding to the cracking of the SHCC. In this study, the maximum measured strain, ε0 is 0.004; fc′ is the compressive strength of the SHCC. We find that
Based on the analysis of the failure process and failure characteristics of the composite structural specimen, and referring to the relevant research results, the shear capacity calculation model of the SHCC/ grooved steel composite deck was established by using the theory of the diagonal strut [19,20]. The basic assumptions were as follows:
fc = 0.67fc′
(6)
Therefore, the shear capacity Fv of the composite structural specimen is
(1) The tangential load was mainly borne by the SHCC of the diagonally sheared area of tooth I and tooth II in the composite structural specimen. (2) The teeth of the composite structural specimen were not deformed when the composite structural specimen was finally destroyed. (3) The frictional shear resistance between the SHCC and the grooved steel plate was not considered.
Fv = fc Acs cosθ
(7)
where Fv is the shear capacity of the composite structural specimen based on the strut mechanism in KN, Acs is the average cross-sectional area of the diagonal portion of the strut in mm2, and θ is the inclination of the diagonal portion of the strut towards the shear horizontal direction.
Under a test load, the diagonal compression strut is formed along the diagonally sheared area of tooth I and tooth II in the SHCC pavement in order to resist the tangential shear force and the normal pressure. The force diagram is shown in Fig. 10, and the green area is the formed diagonal strut. The 2 blue rectangular dashed frames in the figure represent the range of changes in tooth parameters. From the diagram analysis, it can be seen that when the tooth spacing is large, the
4.2. Determination of model parameters The effective width of the cross-section of the diagonal portion of the strut is assumed to be b. According to Rizkala [21], it is calculated using Eq. (6). b = b1+b2 = h cosθ + (s + w) sin θ is
(8)
The average cross-sectional area of the diagonal portion of the strut
Acs = b t = h t cosθ + (s + w) t sin θ
(9)
The inclination of the diagonal portion of the strut towards the shear horizontal direction is θ = tan−1(H/ (50 + s/2))
(10)
where b is the effective width of the cross-section of the diagonal portion of the strut in mm, t is the effective length of the cross-section of the diagonal portion of the strut, that is, the length of the composite structural specimen, 100 mm, h is the tooth height of the composite structural specimen in mm, s is the tooth spacing of the composite structural specimen in mm, w is the tooth width of the composite structural specimen in mm, and H is the thickness of the SHCC
Fig. 10. Force model of the diagonal strut of the SHCC/grooved steel composite structure. 202
Composites Part B 160 (2019) 195–204
L. Yin et al.
Table 6 Experimental values and calculated values of the shear capacity. Specimen
Exp.
Cal.
FEV/FCV
Specimen
Exp.
Cal.
FEV/FCV
Specimen
Exp.
Cal.
FEV/FCV
s1w1h1 s1w1h2 s1w1h3 s1w2h1 s1w2h2 s1w2h3 s1w3h1 s1w3h2 s1w3h3
69.6 105.2 118.0 76.0 111.5 152.4 108.5 106.9 141.4
67.9 79.3 101.9 75.0 86.3 109.0 82.1 93.4 116.1
1.02 1.33 1.16 1.01 1.29 1.40 1.32 1.14 1.22
s2w1h1 s2w1h2 s2w1h3 s2w2h1 s2w2h2 s2w2h3 s2w3h1 s2w3h2 s2w3h3
83.7 132.6 116.1 101.4 92.5 153.2 106.6 89.2 130.0
78.9 90.9 115.0 85.6 97.6 121.7 92.2 104.3 128.3
1.06 1.46 1.01 1.19 0.95 1.26 1.16 0.86 1.01
s3w1h1 s3w1h2 s3w1h3 s3w2h1 s3w2h2 s3w2h3 s3w3h1 s3w3h2 s3w3h3
72.3 141.2 127.7 106.5 135.3 144.8 101.9 167.3 182.5
88.2 100.8 126.0 94.5 107.1 132.3 100.8 113.4 138.6
0.82 1.40 1.01 1.13 1.26 1.09 1.01 1.48 1.32
angle between the main crack and the shear load direction ranges from 30° to 45°. (2) The shear failure process of the SHCC-grooved steel composite structural specimen can be divided into 4 stages: the linear elastic stage, the elastic-plastic stage, the slip hardening stage, and the failure stage. A digital image correlation technique can be used to describe the failure process of a composite structural specimen. (3) The response surface model of the shear capacity is extremely significant. The tooth spacing s (P = 0.0072 < 0.01) and the tooth height h (P = 0.0403 < 0.05) have a significant influence on the shear capacity, and the tooth spacing s is extremely significant. However, the influence of the tooth width w (P = 0.0551 > 0.05) and the interaction term for the shear capacity are not significant. (4) The calculated values of the shear capacity model based on theory of the diagonal strut agree well with the experimental values. The model can be used to predict the shear capacity of a SHCC/grooved steel composite structure under different parameters, and provide a basis for the shear design of a composite structure. Fig. 11. Comparison of experimental and calculated values.
Acknowledgements
pavement, or 50 mm.
This research was funded by National Natural Science Foundation of China (Grant No. 51768051), the Natural Science Foundation of the Inner Mongolia Autonomous Region of China (Grant No. 2017MS0505), and the Science and Technology Innovation Project of Inner Mongolia Autonomous Region of China (Grant No. KCBJ2018016). Their financial support is highly appreciated. We thank LetPub (www.letpub. com) for its linguistic assistance during the preparation of this manuscript.
4.3. Calculation results and analysis The shear capacity of a SHCC/grooved steel composite structural specimen can be calculated by Eq. (7), and the calculation results are shown in Table 6. The average value of the ratio of experimental values to calculated values is 1.16. The comparison between the experimental value of the shear capacity and the calculated value is shown in Fig. 11. It can be seen from the figure that the calculated value agrees well with the experimental value, and the calculated value is lower than the experimental value as a whole. The calculated value of the shear capacity is favorable for safety. Therefore, the shear capacity formula proposed in this paper can be used to predict the shear capacity of a SHCC/ grooved steel composite structure under different parameters and provide a basis for the shear design of a composite structure. In this paper, the composite structural specimen has 2 teeth and only 1 complete tooth groove. The shear behavior and the calculation model of large size specimen with more than 3 teeth and 2 grooves need to be further studied.
Appendix A. Supplementary data Supplementary data to this article can be found online at https:// doi.org/10.1016/j.compositesb.2018.10.025. References [1] Ma J, Sun SZ, Qi Y. Review on China's bridge engineering research. China J Highw Transp 2014;27(5):1–96. [2] Shao XD, Yi DT, Huang ZY, Zhao H. Basic Performance of the composite deck system composed of orthotropic steel deck and ultrathin RPC layer. J Bridge Eng 2013;18(5):417–28. [3] Wei J, Zha X, Zheng JL, Wang BJ. Cracks resisting mechanism analysis of large stone asphalt mixture base structure. Highways 2008;4:6–10. [4] Kakuma K, Matsumoto T, Hayashikawa T, He X. An analytical study on the composite effect of steel deck with ECC overlay reinforcement. J Jpn Soc Civ Eng 2010;56:1282–91. [5] Walter R, Olesen JF, Stang H, Vejrum T. Analysis of an orthotropic deck stiffened with a cement-based overlay. J Bridge Eng 2007;12(3):350–63. [6] Abe T, Kawai Y, Yamashita T, Ichinose Y. Decreasing effect of stress in orthotropic steel decks by SFRC pavement with ordinary Portland cement and low shrinkage type mixture material. J Pavement Eng JSCE 2015;71(2):47–62. [7] Dieng L, Marchand P, Gomes F, Tessiera C, Toutlemondec F. Use of UHPFRC overlay to reduce stresses in orthotropic steel decks. J Constr Steel Res 2013;89(5):30–41. [8] Liu H, Zhang Q, Gu C, Su H, Li VC. Influence of micro-cracking on the permeability of engineered cementitious composites. Cement Concr Compos 2016;72(9):104–13. [9] Wang B, Xu S, Liu F. Evaluation of tensile bonding strength between UHTCC repair
5. Conclusions Based on the compression-shear test of a SHCC/grooved steel composite structure, combined with a digital image correlation technique, the response surface method, and the theory of the diagonal strut, the interlayer shear performance and shear capacity of a SHCC/ grooved steel composite structure under different test parameters were studied in this paper. The following conclusions were drawn: (1) The failure mode of the SHCC-grooved steel composite structural specimen is the diagonal shear cracking of the ECC pavement. The 203
Composites Part B 160 (2019) 195–204
L. Yin et al. materials and concrete substrate. Construct Build Mater 2016;112(6):595–606. [10] Dhawale AW, Joshi VP. Engineered cementitious composites for structural applications. Int J Appl Innovat Eng Manag 2013;2:198–205. [11] Cao J, Shao X, Deng L, Gan Y. Static and fatigue behavior of short-headed studs embedded in a thin ultrahigh-performance concrete layer. J Bridge Eng 2017;22(5):04017005. [12] Cao J, Shao X, Zhang Z, Zhao H. Retrofit of an orthotropic steel deck with compact reinforced reactive powder concrete. Struct Infrastruct E 2016;12(3):411–29. [13] Ding B. Research of interface characteristics of early-strength ECC steel deck pavement structure based on stud connection. NJ: Southeast University; 2015. [14] Ma H. Research of early-strength ECC applying on long-span steel bridge deck pavement. NJ: Southeast University; 2014. [15] Liu SG, Zhang DX, Yan CW, Deng YD. Experimental study on the tensile properties of PVA-ECC with high-calcium fly ash. Bull Chin Ceramic Soc 2016;35(1):52–60.
[16] Pan B, Xie HM, Hua T, Anand A. Measurement of coefficient of thermal expansion of films using digital image correlation method. Polym Test 2009;28(1):75–83. [17] Asadzadeh S, Khoshbayan S. Multi-objective optimization of influential factors on production process of foamed concrete using Box-Behnken approach. Construct Build Mater 2018;170:101–10. [18] Li W, Cai L, Wu Y, Liu Q, Yu H, Zhang C. Assessing recycled pavement concrete mechanical properties under joint action of freezing and fatigue via RSM. Construct Build Mater 2018;164:1–11. [19] Zhang X, Ma J, Han P, Niu S, Zhang S. Shear behavior on prefabricated shear wall alveolar type connection. J Build Struct 2017;38(11):93–100. [20] Collins MP, Mitchell D. Prestressed concrete basics. Ottawa, Ontario: Canadian Prestressed Concrete Institute; 1987. p. 318–20. [21] Rizkala SH. Multiple shear key connections for precast shear wall panels. PCI J 1989;34(2):104–20.
204