# Numerical and Experimental Analysis of the Shear Behavior of Ultrahigh-Performance Concrete Construction Joints

Authors: Hyun-O. Jang; Han-Seung Lee; Keunhee Cho; Jinkyu Kim
Journal: Advances in Materials Science and Engineering
 (2018)

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## Abstract

Shear performance of plain UHPC (ultrahigh-performance concrete) construction joints is studied in both experimental and analytical ways. In push-off tests, three different contact surfaces of the construction joint were considered, while the case without any joint was provided for the reference. Test results indicate that the geometry of contact surfaces greatly affects shear performance of the construction joint. With simplifying structural behavior of contact surfaces and UHPC substrate, the finite-element analysis model is developed for every case studied by utilizing the ABAQUS software and validated against the test results. Agreement between experimental and numerical simulation results is excellent especially in terms of displacement, strength, and failure mechanism. It is expected that the present work provides a basis for further study on reinforced UHPC construction joints.


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## Body

## 1. Introduction

Ultrahigh-performance concrete (UHPC) is a class of concrete characterized by exceptionally high compressive/tensile strengths, ductility, toughness, flowability, and durability [1, 2]. Despite the various mix proportions of UHPC, it is widely known that higher strengths of the UHPC are obtained by the silica fume-cement mixture with a low water-cement ratio and the presence of very fine aggregates [3], while ductility has been enhanced by steel fibers [4]. Such remarkable enhanced material properties of UHPC now allow the real-world construction. Since the first UHPC bridge in Canada (1997), there have been some construction projects and design recommendations regarding the use of UHPC over the world [5–7]. As ordinary concrete, this UHPC can be either fabricated as precast members at a plant or cast in place at a construction site. In the aspect of controlling material qualities and accelerating construction speed, a precast-type UHPC is preferred. However, even in use of the precast-type UHPC, there still remain some components or joints of segments to be cast in place.A construction joint is provided when concrete pouring needs to be stopped and then is continued again—it is the most commonly experienced joint in concrete working with some typical shapes including vertical, horizontal, inclined, and key joints [8, 9]. At the construction site, preplanned construction joints are inevitable, and their locations are decided with consideration of casting amount, man power, curing methods, capability of construction equipment, and so on. When losing structural integrity, these joints usually cause problems such as cracks, water leaks, and corrosion of reinforcements [10]. In particular, construction joints must provide a well-bonded medium between the hardened and the fresh concrete so that ACI 224 [11] and concrete standard specification in Korea [12] recommend a desirable location for construction joints at points where shear force is small at the time of construction. In addition, to improve bonding behavior of concrete at the joint interface, some methods are suggested for using ordinary concrete materials: latency removal, waterjet, and sand blast. Thus, the main concern in concrete construction joints is in providing adequate shear transfer—notice that concrete’s capacity to take bending stresses is negligible [13, 14].So far, most research on the construction joint has described the case of ordinary reinforced concrete materials [15, 16]. For example, experiments and finite-element analysis have been carried out to quantify cracks and deformation characteristics at the joint by a simple method of reinforcements [17–19]. Furthermore, in current practice, bond strength of old-to-new concrete interfaces and mechanical behavior of high-strength concrete construction joints have been addressed with purely experimental ways [20–26]. In particular, Carbonell Muñoz et al. [24] carried out direct and indirect tension tests and the slant shear test to investigate bond performance between UHPC and normal-strength concrete with slightly brushed, chipped, brushed, sandblasted, grooved, and aggregate-exposed substrate surfaces. Shear performance of high-strength concrete (compressive strength above 80 MPa) construction joints was assessed by push-off tests: Walraven and Stroband [22] analyzed the engaging behavior of aggregates on the adhesion performance of concrete, and Kim et al. [23] confirmed that the shear strength of the high-strength concrete is highly correlated with the amount of aggregates friction in crack width. Also, the effect of the surface morphology of construction joints is recently investigated in an experimental way [27]. All these efforts are useful to account for shear transfer at the interface, but the absence of an analytical study undermines the efforts to draw general conclusions. Thus, both experimental and analytical studies are necessary for the study of construction joints with consideration of various interface morphologies.Over the past two decades, the UHPC material has been adopted in the construction of pedestrian and highway bridges over the world. However, currently, there is no specified design code for the use of UHPC materials (above 180 MPa strength) in the world, but only exist some recommendations. Eurocode 4 (2005) accounts for UHPC materials below 90 MPa, and AASHTO LRFD Bridge Design Specifications 4th Edition (2007) is applicable to UHPC up to 120 MPa strength. As part of ongoing activities to accelerate uses of UHPC in actual construction particularly for the further development of reinforced UHPC construction joints, in this study, shear performance of plain UHPC construction joints is investigated in both experimental and analytical ways. In experiments, a total of four specimens were tested under a monotonic uniaxial compressive test (push-off test), and shear performance among specimens is compared by identifying distinctive characteristics in shear bond strength, displacement responses, and failure mechanism. Finite-element models are also developed for every specimen, and these are validated through comparing numerical simulation results with test results. We would like to emphasize that every developed numerical model in the present work is based on simplified viewpoints on failure mechanisms, where models are developed as objective as possible with the help of the current design code and previous research and experiments.


## 2. Experimental Program

### 2.1. Outline

Table1 summarizes the list of specimens. Three cases of a construction joint and the case excluding any joint are considered in this study, where each specimen was named after the type of interface treatment and the size of an individual groove. For example, the MN-0 specimen represents the monolithic placement (the case without any construction joint), while the specimen “GR-20” represents the case having grooves with a size of 20 mm.Table 1
Characteristics of the UHPC construction joint specimens.
Specimen
Interface type
Groove size
MN-0
Monolithic pouring with no construction joint (MN)
No groove (0)
VC-0
Vertical construction joint (VC)
No groove (0)
GR-20
Construction joint with grooves (GR)
20 × 20 mm (20)
GR-30
Construction joint with grooves (GR)
30 × 30 mm (20)Figure1 shows configuration of each specimen. Dimensions of each specimen are given by 300 mm (width) × 640 mm (height) × 150 mm (thickness). Also, to investigate pure shear performance, 20 mm gap is placed at the top and the bottom in the center of each specimen. Grooves adopted in this study can be implemented in the connection of a segmental bridge with the match-cast method.Figure 1
Configuration of each specimen (reproduced from Jang et al. [29]): (a) monolithic case (MN-0); (b) joint with the smooth contact surface (VC-0); (c) joint with 20 mm size grooves (GR-20); (d) joint with 30 mm size grooves (GR-30).
(a)
(b)
(c)
(d)


### 2.2. UHPC Composition

The UHPC used in this study has mixed proportions given in Table2.Table 2
UHPC mix proportions.
Constituent
Mix proportions (kg for 1 m3)
Water
178
Cement
783
Zirconia silica fume
196
Filler
235
Expansive admixture
59
Shrinkage-reducing agent
8
Steel fibers (16.3 mm)
39
Steel fibers (19.5 mm)
78
Quartz sand
862
Superplasticizer (kg)
26.7
Antifoaming agent (kg)
0.78More specifically, type-1 ordinary Portland cement (a density of 3.15 g/cm3 [28]) without any coarse aggregate is used, and quartzose powder with an average particle size of 4.2 µm is adopted as a filler. High-strength straight steel fibers with two different lengths such as 16.3 and 19.5 mm (density of 7.18 kg/cm3, tensile strength of 2,500 MPa, and diameter of 0.2 mm) are mixed in the volume ratio of 1 : 2. Also, for fine aggregates, Australian silica sand with a specific gravity of 2.65, an average particle diameter of 0.5 mm, and an SiO2 content of 76% is used. Figure 2 shows grading curves of the fine aggregates adopted in the present study.Figure 2
Grading curve of fine aggregates.Tables3 and 4 show the chemical composition of the binder and main material properties of the superplasticizer, respectively. Particularly, the water-to-binder ratio (W/B) is 0.14, and superplasticizer (1.5 volume percent of mixing water) was used to enhance flowability. The more detailed manufacturing method of UHPC can be found in [30].Table 3
Chemical composition of the binder.
Division
SiO2 (%)
Al2O3 (%)
MgO (%)
TiO2 (%)
SO3 (%)
CaO (%)
Fe2O3 (%)
Na2O (%)
K2O (%)
Free lime
Insoluble (%)
Loss on ignition
Cement
19.47
5.24
3.72
—
2.49
61.80
2.69
0.18
0.87
—
—
Filler
99.47
0.40
0.009
0.04
—
0.01
0.05
0.008
0.006
—
—
—
Expansive admixture
4.0
10.0
0.6
—
28.3
52.5
1.2
—
—
16.0
1.4
1.0
Zirconia silica fume
96.00
0.25
0.10
—
—
0.38
0.12
—
—
—
—
—
Shrinkage-reducing agent
29.42
0.17
0.06
—
—
1.39
0.10
—
0.03
—
—
—Table 4
Material properties of the superplasticizer.
Main ingredient
Density (g/cm3)
pH
Alkali content (%)
Chloride content (%)
Appearance
Polycarboxylate
1.05
5.0 ± 2.0
0.01
0.008
Light brown liquidOverall, the UHPC material used in experiments is prepared by the procedure described in Figure3. Thus, first, the dry binder is mixed for 10 minutes. Then, water and superplasticizer are added and the mixture is mixed for 6 minutes. Finally, steel fibers are added and the mixture is mixed for another 6 minutes.Figure 3
Mixing process of UHPC: (a) dry mixing (mixing: 10 minutes), (b) adding water and superplasticizer (mixing: 6 minutes), and (c) putting steel fibers (mixing: 4 minutes).
(a)
(b)
(c)


### 2.3. Test Setup

#### 2.3.1. Test Specimens

Test specimens were normally prepared by a mold of 300 × 640 × 150 mm with different surface textures. Thickness of the steel mold is decided as 1 mm to avoid any excessive deformation during UHPC pouring, and Figure4 shows tolerance of actual steel molds used in experiments.Figure 4
Tolerance of steel molds: (a) VC-0; (b) GR-20; (c) GR-30.
(a)
(b)
(c)Figure5 describes the preparation process of specimens with a construction joint. That is, the mold was demolded 91 days after the first UHPC pouring (Figure 5(a))—the air-dry curing is adopted here with temperature and relative humidity variation specified in Figure 6.Figure 5
Specimen preparation: (a) removal of forms; (b) second portion of UHPC; (c) cured specimens.
(a)
(b)
(c)Figure 6
Curing conditions (the first part of UHPC specimens).Then, the hardened part was placed again in the steel mold, and the remaining part is filled with UHPC (Figure5(b)). After another 91 days with the air-dry curing condition specified in Figure 7, the mold is removed and each specimen is prepared (Figure 5(c)).Figure 7
Curing conditions (the remaining part of UHPC specimens).


#### 2.3.2. Measured Metrics

(1) Basic Properties of UHPC. In accordance with ASTM C143/143M [31], the slump flow test was performed to investigate flowability of the concrete in the fresh state. To account for compressive strength in detail, two sets of three circular UHPC specimens are prepared, where each set is cured for 91 days. Then, for each set, the compressive strength is computed as the average of three specimens’ test results [32]. Thus, here, the case with fully developed compressive strength is considered.(2) Push-Off Test. Figure 8 shows the test setup. A steel plate of 100 × 150 × 25 mm is placed at the top and the bottom of a specimen for load distribution, where the compressive load is applied until the upper part of a specimen initially contacts the lower part of the specimen. In experiments, the actuator with a 100-ton static capacity is run at a rate of 0.01 mm/sec, and main measurements are determined as the maximum shear strength and vertical displacement. More specifically, a set of two linear variable differential transducers (LVDTs) is installed on the top and the bottom of the specimen to measure relative deformation at the construction joint. Also, the maximum shear bond strength (fb) is computed by dividing the maximum load (F) by the vertical surface area (A): fb = F/A.Figure 8
Test setup and instrumentation (reproduced from Jang et al. [29]). (a) Set-up plan; (b) Real experiment.
(a)
(b)


## 2.1. Outline

Table1 summarizes the list of specimens. Three cases of a construction joint and the case excluding any joint are considered in this study, where each specimen was named after the type of interface treatment and the size of an individual groove. For example, the MN-0 specimen represents the monolithic placement (the case without any construction joint), while the specimen “GR-20” represents the case having grooves with a size of 20 mm.Table 1
Characteristics of the UHPC construction joint specimens.
Specimen
Interface type
Groove size
MN-0
Monolithic pouring with no construction joint (MN)
No groove (0)
VC-0
Vertical construction joint (VC)
No groove (0)
GR-20
Construction joint with grooves (GR)
20 × 20 mm (20)
GR-30
Construction joint with grooves (GR)
30 × 30 mm (20)Figure1 shows configuration of each specimen. Dimensions of each specimen are given by 300 mm (width) × 640 mm (height) × 150 mm (thickness). Also, to investigate pure shear performance, 20 mm gap is placed at the top and the bottom in the center of each specimen. Grooves adopted in this study can be implemented in the connection of a segmental bridge with the match-cast method.Figure 1
Configuration of each specimen (reproduced from Jang et al. [29]): (a) monolithic case (MN-0); (b) joint with the smooth contact surface (VC-0); (c) joint with 20 mm size grooves (GR-20); (d) joint with 30 mm size grooves (GR-30).
(a)
(b)
(c)
(d)


## 2.2. UHPC Composition

The UHPC used in this study has mixed proportions given in Table2.Table 2
UHPC mix proportions.
Constituent
Mix proportions (kg for 1 m3)
Water
178
Cement
783
Zirconia silica fume
196
Filler
235
Expansive admixture
59
Shrinkage-reducing agent
8
Steel fibers (16.3 mm)
39
Steel fibers (19.5 mm)
78
Quartz sand
862
Superplasticizer (kg)
26.7
Antifoaming agent (kg)
0.78More specifically, type-1 ordinary Portland cement (a density of 3.15 g/cm3 [28]) without any coarse aggregate is used, and quartzose powder with an average particle size of 4.2 µm is adopted as a filler. High-strength straight steel fibers with two different lengths such as 16.3 and 19.5 mm (density of 7.18 kg/cm3, tensile strength of 2,500 MPa, and diameter of 0.2 mm) are mixed in the volume ratio of 1 : 2. Also, for fine aggregates, Australian silica sand with a specific gravity of 2.65, an average particle diameter of 0.5 mm, and an SiO2 content of 76% is used. Figure 2 shows grading curves of the fine aggregates adopted in the present study.Figure 2
Grading curve of fine aggregates.Tables3 and 4 show the chemical composition of the binder and main material properties of the superplasticizer, respectively. Particularly, the water-to-binder ratio (W/B) is 0.14, and superplasticizer (1.5 volume percent of mixing water) was used to enhance flowability. The more detailed manufacturing method of UHPC can be found in [30].Table 3
Chemical composition of the binder.
Division
SiO2 (%)
Al2O3 (%)
MgO (%)
TiO2 (%)
SO3 (%)
CaO (%)
Fe2O3 (%)
Na2O (%)
K2O (%)
Free lime
Insoluble (%)
Loss on ignition
Cement
19.47
5.24
3.72
—
2.49
61.80
2.69
0.18
0.87
—
—
Filler
99.47
0.40
0.009
0.04
—
0.01
0.05
0.008
0.006
—
—
—
Expansive admixture
4.0
10.0
0.6
—
28.3
52.5
1.2
—
—
16.0
1.4
1.0
Zirconia silica fume
96.00
0.25
0.10
—
—
0.38
0.12
—
—
—
—
—
Shrinkage-reducing agent
29.42
0.17
0.06
—
—
1.39
0.10
—
0.03
—
—
—Table 4
Material properties of the superplasticizer.
Main ingredient
Density (g/cm3)
pH
Alkali content (%)
Chloride content (%)
Appearance
Polycarboxylate
1.05
5.0 ± 2.0
0.01
0.008
Light brown liquidOverall, the UHPC material used in experiments is prepared by the procedure described in Figure3. Thus, first, the dry binder is mixed for 10 minutes. Then, water and superplasticizer are added and the mixture is mixed for 6 minutes. Finally, steel fibers are added and the mixture is mixed for another 6 minutes.Figure 3
Mixing process of UHPC: (a) dry mixing (mixing: 10 minutes), (b) adding water and superplasticizer (mixing: 6 minutes), and (c) putting steel fibers (mixing: 4 minutes).
(a)
(b)
(c)


## 2.3. Test Setup

### 2.3.1. Test Specimens

Test specimens were normally prepared by a mold of 300 × 640 × 150 mm with different surface textures. Thickness of the steel mold is decided as 1 mm to avoid any excessive deformation during UHPC pouring, and Figure4 shows tolerance of actual steel molds used in experiments.Figure 4
Tolerance of steel molds: (a) VC-0; (b) GR-20; (c) GR-30.
(a)
(b)
(c)Figure5 describes the preparation process of specimens with a construction joint. That is, the mold was demolded 91 days after the first UHPC pouring (Figure 5(a))—the air-dry curing is adopted here with temperature and relative humidity variation specified in Figure 6.Figure 5
Specimen preparation: (a) removal of forms; (b) second portion of UHPC; (c) cured specimens.
(a)
(b)
(c)Figure 6
Curing conditions (the first part of UHPC specimens).Then, the hardened part was placed again in the steel mold, and the remaining part is filled with UHPC (Figure5(b)). After another 91 days with the air-dry curing condition specified in Figure 7, the mold is removed and each specimen is prepared (Figure 5(c)).Figure 7
Curing conditions (the remaining part of UHPC specimens).


### 2.3.2. Measured Metrics

(1) Basic Properties of UHPC. In accordance with ASTM C143/143M [31], the slump flow test was performed to investigate flowability of the concrete in the fresh state. To account for compressive strength in detail, two sets of three circular UHPC specimens are prepared, where each set is cured for 91 days. Then, for each set, the compressive strength is computed as the average of three specimens’ test results [32]. Thus, here, the case with fully developed compressive strength is considered.(2) Push-Off Test. Figure 8 shows the test setup. A steel plate of 100 × 150 × 25 mm is placed at the top and the bottom of a specimen for load distribution, where the compressive load is applied until the upper part of a specimen initially contacts the lower part of the specimen. In experiments, the actuator with a 100-ton static capacity is run at a rate of 0.01 mm/sec, and main measurements are determined as the maximum shear strength and vertical displacement. More specifically, a set of two linear variable differential transducers (LVDTs) is installed on the top and the bottom of the specimen to measure relative deformation at the construction joint. Also, the maximum shear bond strength (fb) is computed by dividing the maximum load (F) by the vertical surface area (A): fb = F/A.Figure 8
Test setup and instrumentation (reproduced from Jang et al. [29]). (a) Set-up plan; (b) Real experiment.
(a)
(b)


## 2.3.1. Test Specimens

Test specimens were normally prepared by a mold of 300 × 640 × 150 mm with different surface textures. Thickness of the steel mold is decided as 1 mm to avoid any excessive deformation during UHPC pouring, and Figure4 shows tolerance of actual steel molds used in experiments.Figure 4
Tolerance of steel molds: (a) VC-0; (b) GR-20; (c) GR-30.
(a)
(b)
(c)Figure5 describes the preparation process of specimens with a construction joint. That is, the mold was demolded 91 days after the first UHPC pouring (Figure 5(a))—the air-dry curing is adopted here with temperature and relative humidity variation specified in Figure 6.Figure 5
Specimen preparation: (a) removal of forms; (b) second portion of UHPC; (c) cured specimens.
(a)
(b)
(c)Figure 6
Curing conditions (the first part of UHPC specimens).Then, the hardened part was placed again in the steel mold, and the remaining part is filled with UHPC (Figure5(b)). After another 91 days with the air-dry curing condition specified in Figure 7, the mold is removed and each specimen is prepared (Figure 5(c)).Figure 7
Curing conditions (the remaining part of UHPC specimens).


## 2.3.2. Measured Metrics

(1) Basic Properties of UHPC. In accordance with ASTM C143/143M [31], the slump flow test was performed to investigate flowability of the concrete in the fresh state. To account for compressive strength in detail, two sets of three circular UHPC specimens are prepared, where each set is cured for 91 days. Then, for each set, the compressive strength is computed as the average of three specimens’ test results [32]. Thus, here, the case with fully developed compressive strength is considered.(2) Push-Off Test. Figure 8 shows the test setup. A steel plate of 100 × 150 × 25 mm is placed at the top and the bottom of a specimen for load distribution, where the compressive load is applied until the upper part of a specimen initially contacts the lower part of the specimen. In experiments, the actuator with a 100-ton static capacity is run at a rate of 0.01 mm/sec, and main measurements are determined as the maximum shear strength and vertical displacement. More specifically, a set of two linear variable differential transducers (LVDTs) is installed on the top and the bottom of the specimen to measure relative deformation at the construction joint. Also, the maximum shear bond strength (fb) is computed by dividing the maximum load (F) by the vertical surface area (A): fb = F/A.Figure 8
Test setup and instrumentation (reproduced from Jang et al. [29]). (a) Set-up plan; (b) Real experiment.
(a)
(b)


## 3. Experimental Results

### 3.1. Material Test Results

Figure9 shows test results of compressive strength (fc) and corresponding strain (ε) of all the specimens, and these are summarized in Table 5. As shown in Table 5, both cases satisfy the strength requirement of 180 MPa.Figure 9
Stress-strain curves of UHPC: (a) first pouring part; (b) second pouring part.
(a)
(b)Table 5
Measured compressive strengths for the UHPC.
Case
Compressive strength (MPa)
Average compressive strength (MPa)
Standard deviation (MPa)
Coefficient of variation
1 (min)
2
3 (max)
First pouring
202.0
204.7
207.2
204.6
2.12
0.010
Second pouring
185.2
187.0
188.8
187.0
1.47
0.007For each set of UHPC specimen, flowability of concrete in the fresh state is also checked. The slump flow of the UHPC for the first pouring is 710 mm and that of the UHPC for the second pouring is 690 mm. Such a result satisfies the target slump flow of 700 ± 50 mm.


### 3.2. Push-Off Test Results

Figure10 and Table 6 show load-vertical displacement responses and shear strength observed in each specimen. The order of shear strength capacity is identified as MN-0 > GR-30 > GR-20 > VC-0.Figure 10
Load-vertical displacement results.Table 6
Measured shear strengths for the UHPC construction joint specimens.
Number
Specimen
Maximum load (kN)
Shear strength (MPa)
Shear strength reduction rate (%)
0
MN-0
624.14
20.80
Reference
1
VC-0
21.74
0.72
96.52
2
GR-20
321.20
10.70
48.53
3
GR-30
481.40
16.05
22.87For the MN-0, linear response in load-vertical displacement was found until the load reached about 50 kN. Afterwards, a gentle slope up to the maximum load appeared, followed by the fracture at the middle of the specimen when the maximum load reached about 624 kN. The main factor for this nonlinear strength-increasing response may result from the UHPC substrate damaged plasticity resulting from tensile fracture and shear/axial strength of steel fibers. Thus, after initiation of tensile cracks, the UHPC loses strength and stiffness in part, where steel fibers at cracked parts entirely endure complete fracture in shear and axial directions with respect to their standing position. However, it must be noted that MN-0 shows lack of ductility compared to reinforced cases—previously, Waseem and Singh [33] investigated shear strength of reinforced concrete for the monolithic pouring case. In their tests, there are two different types of reinforcement such as transversely unreinforced and reinforced cases along with two different types of concrete such as normal (30 MPa) and high strength (70 MPa). All their specimens show better ductility than the present MN-0. Thus, one can think that even steel fibers enhance ductility behavior of the UHPC, and their effects are relatively small compared to reinforcements. Other than reinforcements, there are other effects on shear performance when using the ordinary/high-strength concrete rather than the UHPC. The most distinctive difference would be effects of coarse aggregates interlock. Next, VC-0 shows sudden debonding (adhesive failure) at the vertical interface with the maximum load of 21.7 kN due to the effect of the joint with the smooth contact surface—at the interface, the failure mechanism may get involved with friction, but the main factor is adhesive failure at the interface: the complete failure surfaces at the interface in the VC-0 specimen remain smooth without any debris. Regarding groove-shaped construction joints, the GR-30 shows similar responses to the MN-0, while GR-20 suffers from both shear and deformation capacities. Such results may come from different amounts of steel fibers and interlocking effects in grooves. Clearly, one can assume that there exist a less amount of steel fibers per one groove in the GR-20 than the GR-30, where a total volume of grooves with respect to the centerline for each specimen is computed as 540,000 mm3 (=20 mm × 20 mm × 9EA × 150 mm) and 675,000 mm3 (=30 mm × 30 mm × 5EA × 150 mm) for the GR-20 and GR-30, respectively. Also, on the aspect of interlocking effects, the enveloping length of cracks required for the fracture at each groove is less in the GR-20 than the GR-30. With consideration of stress concentration and the crack propagation until the complete fracture, interlocking effects at grooves get worse in the GR-20 than the GR-30. In addition, the most evident difference between grooved-shaped construction joints (GR-30 and GR-20) and the vertical construction joint (VC-0) may indicate constraining effects. Compared to the VC-0, constraining effects in each groove can enhance horizontal friction, vertical bearing, and bonding capacities, resulting in the increase of the shear strength. In particular, the GR-30 has about twice the shear strength capacity as the GR-20, which shows that an individual groove size of 20 mm may not be sufficient for vertical bonding/bearing and horizontal friction at the construction joint.Also, crack patterns and fracture behavior of all the specimens are checked during the test. Figure11 describes crack propagation in each specimen with respect to marked points in Figure 7. When the compression loading reaches about 492 kN, diagonal cracks initiate at left and right sides especially in the middle height of the MN-0. As the loading increases around 538 kN, vertical cracks also initiate at the middle of the specimen, and these spread gradually upward and downward. Finally, complete shear fracture occurs in the middle of the MN-0. The GR-30 has similar crack patterns and fracture behavior found in the MN-0—diagonal cracks at left and right sides of the specimen initiate at the loading of 376 kN. However, vertical cracks occur in the middle top and the middle bottom of the specimen when loading reaches 391 kN. The upper part contacts the lower part at the loading of 481 kN, leaving partial fracture at the middle of the specimen. Compared to the GR-30, the GR-20 shows somewhat a different fracture mechanism. In particular, there is no diagonal crack on the body of the specimen. Also, at the loading of about 281 kN, vertical cracks simultaneously initiate at the middle of the specimen in the region of top, bottom, and center. These cracks vertically spread and finally lead to complete fracture.Figure 11
Crack pattern in each specimen: (a) a-1 (crack initiation); (b) a-2 (crack development); (c) a-3 (complete fracture); (d) b-1 (adhesion failure on the external surface); (e) b-2 (development of inner surface detachment); (f) b-3 (complete separation); (g) c-1 (crack initiation); (h) c-2 (crack development); (i) c-3 (complete fracture); (j) d-1 (crack initiation); (k) d-2 (crack development); (l) d-3 (complete fracture).
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
(j)
(k)
(l)Overall, based on failure mode criteria presented in [34] which are summarized in Table 7, four types of failure modes are observed in push-off tests as shown in Figure 12.Table 7
Failure mode classifications.
Type
Description
Type A
Interfacial failure (a complete debonding at the transition zone)
Type B
Interfacial failure and substrate cracking or minor substrate damage
Type C
Interfacial failure and substrate fracture
Type D
Complete substratum failure with good interfaceFigure 12
Failure modes: (a) MN-0; (b) VC-0; (c) GR-20; (d) GR-30.
(a)
(b)
(c)
(d)


## 3.1. Material Test Results

Figure9 shows test results of compressive strength (fc) and corresponding strain (ε) of all the specimens, and these are summarized in Table 5. As shown in Table 5, both cases satisfy the strength requirement of 180 MPa.Figure 9
Stress-strain curves of UHPC: (a) first pouring part; (b) second pouring part.
(a)
(b)Table 5
Measured compressive strengths for the UHPC.
Case
Compressive strength (MPa)
Average compressive strength (MPa)
Standard deviation (MPa)
Coefficient of variation
1 (min)
2
3 (max)
First pouring
202.0
204.7
207.2
204.6
2.12
0.010
Second pouring
185.2
187.0
188.8
187.0
1.47
0.007For each set of UHPC specimen, flowability of concrete in the fresh state is also checked. The slump flow of the UHPC for the first pouring is 710 mm and that of the UHPC for the second pouring is 690 mm. Such a result satisfies the target slump flow of 700 ± 50 mm.


## 3.2. Push-Off Test Results

Figure10 and Table 6 show load-vertical displacement responses and shear strength observed in each specimen. The order of shear strength capacity is identified as MN-0 > GR-30 > GR-20 > VC-0.Figure 10
Load-vertical displacement results.Table 6
Measured shear strengths for the UHPC construction joint specimens.
Number
Specimen
Maximum load (kN)
Shear strength (MPa)
Shear strength reduction rate (%)
0
MN-0
624.14
20.80
Reference
1
VC-0
21.74
0.72
96.52
2
GR-20
321.20
10.70
48.53
3
GR-30
481.40
16.05
22.87For the MN-0, linear response in load-vertical displacement was found until the load reached about 50 kN. Afterwards, a gentle slope up to the maximum load appeared, followed by the fracture at the middle of the specimen when the maximum load reached about 624 kN. The main factor for this nonlinear strength-increasing response may result from the UHPC substrate damaged plasticity resulting from tensile fracture and shear/axial strength of steel fibers. Thus, after initiation of tensile cracks, the UHPC loses strength and stiffness in part, where steel fibers at cracked parts entirely endure complete fracture in shear and axial directions with respect to their standing position. However, it must be noted that MN-0 shows lack of ductility compared to reinforced cases—previously, Waseem and Singh [33] investigated shear strength of reinforced concrete for the monolithic pouring case. In their tests, there are two different types of reinforcement such as transversely unreinforced and reinforced cases along with two different types of concrete such as normal (30 MPa) and high strength (70 MPa). All their specimens show better ductility than the present MN-0. Thus, one can think that even steel fibers enhance ductility behavior of the UHPC, and their effects are relatively small compared to reinforcements. Other than reinforcements, there are other effects on shear performance when using the ordinary/high-strength concrete rather than the UHPC. The most distinctive difference would be effects of coarse aggregates interlock. Next, VC-0 shows sudden debonding (adhesive failure) at the vertical interface with the maximum load of 21.7 kN due to the effect of the joint with the smooth contact surface—at the interface, the failure mechanism may get involved with friction, but the main factor is adhesive failure at the interface: the complete failure surfaces at the interface in the VC-0 specimen remain smooth without any debris. Regarding groove-shaped construction joints, the GR-30 shows similar responses to the MN-0, while GR-20 suffers from both shear and deformation capacities. Such results may come from different amounts of steel fibers and interlocking effects in grooves. Clearly, one can assume that there exist a less amount of steel fibers per one groove in the GR-20 than the GR-30, where a total volume of grooves with respect to the centerline for each specimen is computed as 540,000 mm3 (=20 mm × 20 mm × 9EA × 150 mm) and 675,000 mm3 (=30 mm × 30 mm × 5EA × 150 mm) for the GR-20 and GR-30, respectively. Also, on the aspect of interlocking effects, the enveloping length of cracks required for the fracture at each groove is less in the GR-20 than the GR-30. With consideration of stress concentration and the crack propagation until the complete fracture, interlocking effects at grooves get worse in the GR-20 than the GR-30. In addition, the most evident difference between grooved-shaped construction joints (GR-30 and GR-20) and the vertical construction joint (VC-0) may indicate constraining effects. Compared to the VC-0, constraining effects in each groove can enhance horizontal friction, vertical bearing, and bonding capacities, resulting in the increase of the shear strength. In particular, the GR-30 has about twice the shear strength capacity as the GR-20, which shows that an individual groove size of 20 mm may not be sufficient for vertical bonding/bearing and horizontal friction at the construction joint.Also, crack patterns and fracture behavior of all the specimens are checked during the test. Figure11 describes crack propagation in each specimen with respect to marked points in Figure 7. When the compression loading reaches about 492 kN, diagonal cracks initiate at left and right sides especially in the middle height of the MN-0. As the loading increases around 538 kN, vertical cracks also initiate at the middle of the specimen, and these spread gradually upward and downward. Finally, complete shear fracture occurs in the middle of the MN-0. The GR-30 has similar crack patterns and fracture behavior found in the MN-0—diagonal cracks at left and right sides of the specimen initiate at the loading of 376 kN. However, vertical cracks occur in the middle top and the middle bottom of the specimen when loading reaches 391 kN. The upper part contacts the lower part at the loading of 481 kN, leaving partial fracture at the middle of the specimen. Compared to the GR-30, the GR-20 shows somewhat a different fracture mechanism. In particular, there is no diagonal crack on the body of the specimen. Also, at the loading of about 281 kN, vertical cracks simultaneously initiate at the middle of the specimen in the region of top, bottom, and center. These cracks vertically spread and finally lead to complete fracture.Figure 11
Crack pattern in each specimen: (a) a-1 (crack initiation); (b) a-2 (crack development); (c) a-3 (complete fracture); (d) b-1 (adhesion failure on the external surface); (e) b-2 (development of inner surface detachment); (f) b-3 (complete separation); (g) c-1 (crack initiation); (h) c-2 (crack development); (i) c-3 (complete fracture); (j) d-1 (crack initiation); (k) d-2 (crack development); (l) d-3 (complete fracture).
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
(j)
(k)
(l)Overall, based on failure mode criteria presented in [34] which are summarized in Table 7, four types of failure modes are observed in push-off tests as shown in Figure 12.Table 7
Failure mode classifications.
Type
Description
Type A
Interfacial failure (a complete debonding at the transition zone)
Type B
Interfacial failure and substrate cracking or minor substrate damage
Type C
Interfacial failure and substrate fracture
Type D
Complete substratum failure with good interfaceFigure 12
Failure modes: (a) MN-0; (b) VC-0; (c) GR-20; (d) GR-30.
(a)
(b)
(c)
(d)


## 4. Numerical Analysis of UHPC Construction Joints

Only limited numerical and analytical studies on the UHPC structural member have been reported until now. In particular, most studies focus on flexural elements such as the beam and girder. For example, Chen and Graybeal [35] focused on predicting the load deflection (strain) response of UHPC girders subjected to two-point loads. Mahmud et al. [36] conducted two-dimensional plane stress finite-element analysis of unreinforced notched UHPC beams to study size effects on flexural capacity.In order to address shear performance of plain UHPC construction joints numerically with lack of previous attempts, in this study, failure mechanism is simplified as much as possible. Three mechanisms including damaged plasticity in the plain UHPC substrate, friction in horizontal contact surfaces, and cohesive failure in vertical contact surfaces are considered to provide a simplified model of the corresponding construction joint, where material parameters are determined from design codes, previous research, experiments, and reasonable posteriori.


### 4.1. Development of Analytical Models

#### 4.1.1. Modeling UHPC Substrate

By referring to a recent modeling technique in nonlinear behavior of ordinary concrete [37–41], the substrate UHPC is described by the elastoplastic damage model “concrete damaged plasticity (CDP).” Compared to other concrete material models available in ABAQUS such as the smeared crack concrete model and brittle crack concrete model, this CDP model is taken in the present study because it has the potential to represent complete inelastic behaviour of concrete in both tension and compression including damage characteristics. Also, this is the only model in ABAQUS that can be used for both static and dynamic analysis—the further application of the current numerical model to dynamic analysis is taken into account.Two failure mechanisms in the CDP model are tensile cracking and compressive crushing of the concrete, where uniaxial tensile and compressive behavior is characterized by damaged plasticity. Figure13 shows a one-dimensional schematic view of the plastic model and plastic damage model, respectively.Figure 13
(a) Plastic model. (b) Damaged plastic model.
(a)
(b)As shown in Figure13, for the CDP model, stress-strain relations under uniaxial compression and tension are expressed as(1)σc=1−dcE0ε−εcpl,σt=1−dtE0ε−εtpl,where E0 is the initial (undamaged) elastic stiffness of the material and σc,εcpl,σt,andεtpl are compressive stress, compressive plastic strain, tensile stress, and tensile plastic strain, respectively. Two damage variables such as dc and dt characterize the degradation of elastic stiffness on the strain-softening branch of the stress-strain curve. These variables can take values from zero to one, where zero represents the undamaged material and one represents total loss of strength. If such damage variables are not specified, the CDP model behaves as a plasticity model. For example, if the compression damage variable dc is not specified, then the compressive plastic strain εcpl takes the value of the inelastic compressive strain εcin. It must be noted that the tensile damage in the CDP model can be specified by either stress-strain relation or stress-displacement response (again, this is an optional choice), while the strain-softening behavior for cracked concrete must be specified by either stress-strain relation or fracture energy-cracking criterion GF (mandatory requirement).Regarding plasticity, the CDP model considers the isotropic hardening with the yield function developed by Lubliner et al. [42] and elaborated by Lee and Fenves [43]. Parameters determining the shape of this yield function and nonassociated plastic flow rule are the dilation angle ψ, the ratio of initial equibiaxial compressive yield stress to initial uniaxial compressive yield stress fb0/fc0, the eccentricity of the plastic potential surface ε, and the ratio of the second stress invariant on the tensile meridian to compressive meridian K. For more detailed description of this CDP model, readers can refer to ABAQUS manuals.Overall, for a full definition of the UHPC substrate with the CDP model, stress-strain relations in compression/tension and strain-softening behavior for cracked UHPC as a set of points laying on the stress-strain curve or optional fracture energyGF are required for characterizing damage along with plasticity parameters including ψ, fb0/fc0, ε, and K.In the present study, the compressive stress-strain relation of UHPC is identified as the average value of experimental results given in Table8, where the evolution of damage is assumed to occur only in tension after initiating fracture. That is, Table 8 is the reinterpretation of Figure 9 in average sense with differentiating inelastic stress-strain.Table 8
Average compressive inelastic stress-strain test results for the UHPC.
First pouring
Second pouring
Stress (MPa)
Inelastic strain
Stress (MPa)
Inelastic strain
180
0
176
0
193
0.0002
185
0.0002
199
0.0003
187
0.0003
204.6
0.00039
186.5
0.0004
202
0.0005
186
0.0005
201
0.0006
185.4
0.0006
200.5
0.0007
184.3
0.0007
200
0.001
182
0.00075
172
0.002
170
0.003572Also, the tensile damage is described by stress-displacement relation from the previous study [43]—Kusumawardaningsih et al. [44] investigated stress-crack opening behavior of UHPC through axial tension and bending tension tests. Table 9 shows their tensile test results indicating that UHPC has a mean maximum tensile strength of 4.0263 MPa with the crack opening length of 7.8 µm and that a total loss of tensile strength occurs linearly with the crack opening length of 0.2 mm. This result is adopted in the present study by excerpting tendency with strength reduction damage parameters: the maximum tensile strength drops linearly from the zero crack opening length to the crack opening length of 0.2 mm.Table 9
Parameters for modeling tension damage.
Damage parameters
Displacement (mm)
0
0
0.5
0.1
0.99
0.2For the strain softening of cracked UHPC, the extended version of Euro design code [45] is used. In Euro design code, for ordinary concrete, main parameters such as the fracture energy GF and the tensile strength of ordinary concrete ft are given by(2)ft=1.4f′c−8102/3MPa,and(3)GF=0.0469da2−0.5da+26f′c100.7N/mm.These equations are adopted in the present study for computing tensile strength of UHPC and fracture energy: a nominal compressive strength of UHPC is taken to bef′c (=180 MPa) and a maximum size of UHPC aggregates is assumed to be da (20 mm). The main reason for taking da (20 mm) despite the absence of coarse aggregates in UHPC is that the design code for UHPC materials is not currently available—in order to account for improved material properties of UHPC in the current code, a generally accepted size of the maximum aggregate in ordinary concrete is considered here (the most common size of coarse aggregates in construction).All other material parameters of substrate UHPC are related with the yield surface and nonassociated potential plastic flow, where recommendation (default) values of the ordinary concrete material in the ABAQUS are taken [46–48]: ψ=36.31°, ε = 0.1, fb0/fc0 = 1.16, and K = 0.67.Apart from these, basic material properties such as Poisson’s ratio and modulus of elasticity are taken as 0.19 and 98,000 MPa—Poisson’s ratio of 0.19 is taken through reference [49] and the modulus of elasticity is the measured value from cylindrical tests.


#### 4.1.2. Modeling Contact Surfaces at the Joint

For the sake of simplicity, the friction mechanism is presumed to occur only on horizontal contact surfaces, where a friction coefficient of the surface between the first and the second placements of UHPC is taken asμ = 0.4 based upon Table 11 (concrete-to-concrete) in the research report [50]. In addition, a shear stress limit at the horizontal interface is computed as 104 MPa corresponding to the upper-bound estimate of f′c/3 in the ABAQUS analysis manual: this means that sliding at the interface initiates when exceeding the compressive strength of UHPC.For the development of analytical models, vertical contact surfaces play key roles. In the present approach, cohesive effects at the vertical interface are modeled with a surface-based behavior. This surface-based cohesive behavior initially defines a traction-separation model followed by the initiation and evolution of damage. Thus, the contact surface is assumed to show linear elastic response in terms of a constitutive matrix, tractions, and separations by(4)tntstt=Knn000kss000Kttδnδsδt,for the uncoupled traction-separation case, where tn, ts, and tt represent normal (along the global Z-axis), shear (along the global X-axis), and tangential (along the global Y-axis) tractions, while the corresponding separations are denoted by δn,δs, and δt.Subsequently, degradation and failure of the bond at the interface are described by damage modeling, where the damage initiation refers to the beginning of degradation of the cohesive response at each contact point, while the damage evolution describes the rate at which the cohesive stiffness is degraded once the corresponding initiation criterion is reached.Figure14 shows a schematic viewpoint on traction-separation response described in the ABAQUS analysis manual, where peak values of traction and those of separation in normal, shear, and tangential directions are identified as sets of tn0,ts0,tt0 and δn0,δs0,δt0 with a set of δnf,δsf,δtf representing each separation at complete failure.Figure 14
Typical traction-separation response.Among some criteria available in the ABAQUS, the following quadratic traction criterion for the damage initiation at the interface is considered:(5)tntn02+tsts02+tttt02=1,where . denotes the Macaulay bracket signifying that a purely compressive displacement (i.e., a contact penetration) or a purely compressive stress state does not initiate damage.In Figure14, damage evolution corresponding to each traction-separation response can be modeled with scalar variables of Dn, Ds, and Dt as(6)tn=1−Dntn0,ts=1−Dsts0,tt=1−Dtt0,where every D monotonically increases from 0 to 1 upon further loading after the initiation of damage.In order to describe the damage evolution under a combination of normal and other separations across the interface, an effective separationδm,(7)δm=δn2+δs2+δt2,is considered along with a single damage variable D:(8)D=1−δm0δmmax1−1−exp−αδmmax−δm0/δmf−δm01−exp−α,where δm0 is the effective separation at damage initiation and δmf is the effective separation at complete failure. Also, δmmax refers to the maximum value of the effective separation attained during the loading history, and α is a nondimensional parameter that defines the rate of damage evolution.Overall, cohesive failure in the vertical contact surface is modeled with uncoupled stiffness coefficientsKnn,Kss,Ktt, peak values of traction tn0,ts0,tt0, an effective separation at complete failure δmf, and a nondimensional parameter α. For every analysis model, α is fixed as 2, while other parameters are chosen differently as presented in Table 10. As shown in Table 10, the vertical interface is differentiated as to whether constrained or not. Also, a factor of 2 is considered when vertical contact surfaces are constrained with the concave-convex geometry. Such posteriori and values are found to be the best fit to experiment results.Table 10
Parameters for modeling vertical contact surfaces.
Configurations
Parameters (N, mm)
K
nn
,
K
ss
,
K
tt
t
n
0
,
t
s
0
,
t
t
0
δ
m
f
Geometry with no concave-convex interface
(490, 490, 490)
(0.7, 0.7, 0.7)
0.7
Geometry with concave-convex interfaces
(980, 980, 980)
(1.4, 1.4, 1.4)
1.4


#### 4.1.3. Other Considerations

In every finite-element analysis, an 8-node linear brick element with reduced integration (C3D8R) is used as a basic element, while contact surfaces are modeled as the surface-to-surface contact with either tangential friction (horizontal surfaces) or cohesive with damage evolution (vertical surfaces). Also, following the static loading condition in real experiments, the displacement-controlled method is adopted at a rate of 1 mm/min at the upper part, while boundary conditions are assigned to the bottom part by setting all the displacements to zero.Figure15 describes the finite-element model used in analysis. In particular, the model was constructed by using the solid meshing capability in ABAQUS, where the vertical contact surface is densely divided into a size of 10 mm, leaving other parts to be divided into a size of 20 mm. The main reason to have such a different-sized control is that the stress distribution is expected to change dramatically at the vertical contact surface. For every analysis, the Newton iterative procedure with the specific step-time increment is adopted. Thus, the maximum number of time increments is set to 10000, while the initial increment size and minimum increment size are set to 0.01 and 1E− 8 with convergence criteria in Table 11.Figure 15
FEA model description (GR-20): (a) mesh; (b) vertical surface; (c) horizontal surface; (d) boundary condition.
(a)
(b)
(c)
(d)Table 11
Finite-element analysis model convergence criteria tolerances.
Criterion for residual force in a nonlinear problem
5E− 03
Criterion for displacement correction in a nonlinear problem
1E− 02
Initial value of time average force
1E− 02
Alternate criterion for residual force in a nonlinear problem
2E− 02
Criterion for zero force relative to time average force
1E− 05
Criterion for residual force when there is zero flux
1E− 05
Criterion for displacement correction when there is zero flux
1E− 03
Criterion for residual force for a linear increment
1E− 08
Field conversion ratio
1.00
Criterion for zero force relative to time average
1E− 05
Criterion for zero displacement relative to characteristic length
1E− 08


### 4.2. Simulation Results

Figure16 shows vertical displacement versus vertical reaction force in experiments and analysis, where the percentile error E is computed as(9)E=A−TT×100%,where T and A represent experimental and analytical results. As shown, each analytical model yields comparable results to experiments. In particular, every analytical model predicts the maximum shear capacity with less than 10% error.Figure 16
Comparison between analytical and experimental results: (a) MN-0; (b) VC-0; (c) GR-20; (d) GR-30.
(a)
(b)
(c)
(d)Figure17 (unit: sec−1) presents analytical results of the maximum principal strain rate at integration points. With comparison of Figure 14 to Figures 11 and 12, one can check that each analysis model is able to account for debonding behavior at the vertical interface with crack propagation.Figure 17
Analysis results (maximum principal strain rate): (a) MN-0; (b) VC-0; (c) GR-20; (d) GR-30.
(a)
(b)
(c)
(d)


## 4.1. Development of Analytical Models

### 4.1.1. Modeling UHPC Substrate

By referring to a recent modeling technique in nonlinear behavior of ordinary concrete [37–41], the substrate UHPC is described by the elastoplastic damage model “concrete damaged plasticity (CDP).” Compared to other concrete material models available in ABAQUS such as the smeared crack concrete model and brittle crack concrete model, this CDP model is taken in the present study because it has the potential to represent complete inelastic behaviour of concrete in both tension and compression including damage characteristics. Also, this is the only model in ABAQUS that can be used for both static and dynamic analysis—the further application of the current numerical model to dynamic analysis is taken into account.Two failure mechanisms in the CDP model are tensile cracking and compressive crushing of the concrete, where uniaxial tensile and compressive behavior is characterized by damaged plasticity. Figure13 shows a one-dimensional schematic view of the plastic model and plastic damage model, respectively.Figure 13
(a) Plastic model. (b) Damaged plastic model.
(a)
(b)As shown in Figure13, for the CDP model, stress-strain relations under uniaxial compression and tension are expressed as(1)σc=1−dcE0ε−εcpl,σt=1−dtE0ε−εtpl,where E0 is the initial (undamaged) elastic stiffness of the material and σc,εcpl,σt,andεtpl are compressive stress, compressive plastic strain, tensile stress, and tensile plastic strain, respectively. Two damage variables such as dc and dt characterize the degradation of elastic stiffness on the strain-softening branch of the stress-strain curve. These variables can take values from zero to one, where zero represents the undamaged material and one represents total loss of strength. If such damage variables are not specified, the CDP model behaves as a plasticity model. For example, if the compression damage variable dc is not specified, then the compressive plastic strain εcpl takes the value of the inelastic compressive strain εcin. It must be noted that the tensile damage in the CDP model can be specified by either stress-strain relation or stress-displacement response (again, this is an optional choice), while the strain-softening behavior for cracked concrete must be specified by either stress-strain relation or fracture energy-cracking criterion GF (mandatory requirement).Regarding plasticity, the CDP model considers the isotropic hardening with the yield function developed by Lubliner et al. [42] and elaborated by Lee and Fenves [43]. Parameters determining the shape of this yield function and nonassociated plastic flow rule are the dilation angle ψ, the ratio of initial equibiaxial compressive yield stress to initial uniaxial compressive yield stress fb0/fc0, the eccentricity of the plastic potential surface ε, and the ratio of the second stress invariant on the tensile meridian to compressive meridian K. For more detailed description of this CDP model, readers can refer to ABAQUS manuals.Overall, for a full definition of the UHPC substrate with the CDP model, stress-strain relations in compression/tension and strain-softening behavior for cracked UHPC as a set of points laying on the stress-strain curve or optional fracture energyGF are required for characterizing damage along with plasticity parameters including ψ, fb0/fc0, ε, and K.In the present study, the compressive stress-strain relation of UHPC is identified as the average value of experimental results given in Table8, where the evolution of damage is assumed to occur only in tension after initiating fracture. That is, Table 8 is the reinterpretation of Figure 9 in average sense with differentiating inelastic stress-strain.Table 8
Average compressive inelastic stress-strain test results for the UHPC.
First pouring
Second pouring
Stress (MPa)
Inelastic strain
Stress (MPa)
Inelastic strain
180
0
176
0
193
0.0002
185
0.0002
199
0.0003
187
0.0003
204.6
0.00039
186.5
0.0004
202
0.0005
186
0.0005
201
0.0006
185.4
0.0006
200.5
0.0007
184.3
0.0007
200
0.001
182
0.00075
172
0.002
170
0.003572Also, the tensile damage is described by stress-displacement relation from the previous study [43]—Kusumawardaningsih et al. [44] investigated stress-crack opening behavior of UHPC through axial tension and bending tension tests. Table 9 shows their tensile test results indicating that UHPC has a mean maximum tensile strength of 4.0263 MPa with the crack opening length of 7.8 µm and that a total loss of tensile strength occurs linearly with the crack opening length of 0.2 mm. This result is adopted in the present study by excerpting tendency with strength reduction damage parameters: the maximum tensile strength drops linearly from the zero crack opening length to the crack opening length of 0.2 mm.Table 9
Parameters for modeling tension damage.
Damage parameters
Displacement (mm)
0
0
0.5
0.1
0.99
0.2For the strain softening of cracked UHPC, the extended version of Euro design code [45] is used. In Euro design code, for ordinary concrete, main parameters such as the fracture energy GF and the tensile strength of ordinary concrete ft are given by(2)ft=1.4f′c−8102/3MPa,and(3)GF=0.0469da2−0.5da+26f′c100.7N/mm.These equations are adopted in the present study for computing tensile strength of UHPC and fracture energy: a nominal compressive strength of UHPC is taken to bef′c (=180 MPa) and a maximum size of UHPC aggregates is assumed to be da (20 mm). The main reason for taking da (20 mm) despite the absence of coarse aggregates in UHPC is that the design code for UHPC materials is not currently available—in order to account for improved material properties of UHPC in the current code, a generally accepted size of the maximum aggregate in ordinary concrete is considered here (the most common size of coarse aggregates in construction).All other material parameters of substrate UHPC are related with the yield surface and nonassociated potential plastic flow, where recommendation (default) values of the ordinary concrete material in the ABAQUS are taken [46–48]: ψ=36.31°, ε = 0.1, fb0/fc0 = 1.16, and K = 0.67.Apart from these, basic material properties such as Poisson’s ratio and modulus of elasticity are taken as 0.19 and 98,000 MPa—Poisson’s ratio of 0.19 is taken through reference [49] and the modulus of elasticity is the measured value from cylindrical tests.


### 4.1.2. Modeling Contact Surfaces at the Joint

For the sake of simplicity, the friction mechanism is presumed to occur only on horizontal contact surfaces, where a friction coefficient of the surface between the first and the second placements of UHPC is taken asμ = 0.4 based upon Table 11 (concrete-to-concrete) in the research report [50]. In addition, a shear stress limit at the horizontal interface is computed as 104 MPa corresponding to the upper-bound estimate of f′c/3 in the ABAQUS analysis manual: this means that sliding at the interface initiates when exceeding the compressive strength of UHPC.For the development of analytical models, vertical contact surfaces play key roles. In the present approach, cohesive effects at the vertical interface are modeled with a surface-based behavior. This surface-based cohesive behavior initially defines a traction-separation model followed by the initiation and evolution of damage. Thus, the contact surface is assumed to show linear elastic response in terms of a constitutive matrix, tractions, and separations by(4)tntstt=Knn000kss000Kttδnδsδt,for the uncoupled traction-separation case, where tn, ts, and tt represent normal (along the global Z-axis), shear (along the global X-axis), and tangential (along the global Y-axis) tractions, while the corresponding separations are denoted by δn,δs, and δt.Subsequently, degradation and failure of the bond at the interface are described by damage modeling, where the damage initiation refers to the beginning of degradation of the cohesive response at each contact point, while the damage evolution describes the rate at which the cohesive stiffness is degraded once the corresponding initiation criterion is reached.Figure14 shows a schematic viewpoint on traction-separation response described in the ABAQUS analysis manual, where peak values of traction and those of separation in normal, shear, and tangential directions are identified as sets of tn0,ts0,tt0 and δn0,δs0,δt0 with a set of δnf,δsf,δtf representing each separation at complete failure.Figure 14
Typical traction-separation response.Among some criteria available in the ABAQUS, the following quadratic traction criterion for the damage initiation at the interface is considered:(5)tntn02+tsts02+tttt02=1,where . denotes the Macaulay bracket signifying that a purely compressive displacement (i.e., a contact penetration) or a purely compressive stress state does not initiate damage.In Figure14, damage evolution corresponding to each traction-separation response can be modeled with scalar variables of Dn, Ds, and Dt as(6)tn=1−Dntn0,ts=1−Dsts0,tt=1−Dtt0,where every D monotonically increases from 0 to 1 upon further loading after the initiation of damage.In order to describe the damage evolution under a combination of normal and other separations across the interface, an effective separationδm,(7)δm=δn2+δs2+δt2,is considered along with a single damage variable D:(8)D=1−δm0δmmax1−1−exp−αδmmax−δm0/δmf−δm01−exp−α,where δm0 is the effective separation at damage initiation and δmf is the effective separation at complete failure. Also, δmmax refers to the maximum value of the effective separation attained during the loading history, and α is a nondimensional parameter that defines the rate of damage evolution.Overall, cohesive failure in the vertical contact surface is modeled with uncoupled stiffness coefficientsKnn,Kss,Ktt, peak values of traction tn0,ts0,tt0, an effective separation at complete failure δmf, and a nondimensional parameter α. For every analysis model, α is fixed as 2, while other parameters are chosen differently as presented in Table 10. As shown in Table 10, the vertical interface is differentiated as to whether constrained or not. Also, a factor of 2 is considered when vertical contact surfaces are constrained with the concave-convex geometry. Such posteriori and values are found to be the best fit to experiment results.Table 10
Parameters for modeling vertical contact surfaces.
Configurations
Parameters (N, mm)
K
nn
,
K
ss
,
K
tt
t
n
0
,
t
s
0
,
t
t
0
δ
m
f
Geometry with no concave-convex interface
(490, 490, 490)
(0.7, 0.7, 0.7)
0.7
Geometry with concave-convex interfaces
(980, 980, 980)
(1.4, 1.4, 1.4)
1.4


### 4.1.3. Other Considerations

In every finite-element analysis, an 8-node linear brick element with reduced integration (C3D8R) is used as a basic element, while contact surfaces are modeled as the surface-to-surface contact with either tangential friction (horizontal surfaces) or cohesive with damage evolution (vertical surfaces). Also, following the static loading condition in real experiments, the displacement-controlled method is adopted at a rate of 1 mm/min at the upper part, while boundary conditions are assigned to the bottom part by setting all the displacements to zero.Figure15 describes the finite-element model used in analysis. In particular, the model was constructed by using the solid meshing capability in ABAQUS, where the vertical contact surface is densely divided into a size of 10 mm, leaving other parts to be divided into a size of 20 mm. The main reason to have such a different-sized control is that the stress distribution is expected to change dramatically at the vertical contact surface. For every analysis, the Newton iterative procedure with the specific step-time increment is adopted. Thus, the maximum number of time increments is set to 10000, while the initial increment size and minimum increment size are set to 0.01 and 1E− 8 with convergence criteria in Table 11.Figure 15
FEA model description (GR-20): (a) mesh; (b) vertical surface; (c) horizontal surface; (d) boundary condition.
(a)
(b)
(c)
(d)Table 11
Finite-element analysis model convergence criteria tolerances.
Criterion for residual force in a nonlinear problem
5E− 03
Criterion for displacement correction in a nonlinear problem
1E− 02
Initial value of time average force
1E− 02
Alternate criterion for residual force in a nonlinear problem
2E− 02
Criterion for zero force relative to time average force
1E− 05
Criterion for residual force when there is zero flux
1E− 05
Criterion for displacement correction when there is zero flux
1E− 03
Criterion for residual force for a linear increment
1E− 08
Field conversion ratio
1.00
Criterion for zero force relative to time average
1E− 05
Criterion for zero displacement relative to characteristic length
1E− 08


## 4.1.1. Modeling UHPC Substrate

By referring to a recent modeling technique in nonlinear behavior of ordinary concrete [37–41], the substrate UHPC is described by the elastoplastic damage model “concrete damaged plasticity (CDP).” Compared to other concrete material models available in ABAQUS such as the smeared crack concrete model and brittle crack concrete model, this CDP model is taken in the present study because it has the potential to represent complete inelastic behaviour of concrete in both tension and compression including damage characteristics. Also, this is the only model in ABAQUS that can be used for both static and dynamic analysis—the further application of the current numerical model to dynamic analysis is taken into account.Two failure mechanisms in the CDP model are tensile cracking and compressive crushing of the concrete, where uniaxial tensile and compressive behavior is characterized by damaged plasticity. Figure13 shows a one-dimensional schematic view of the plastic model and plastic damage model, respectively.Figure 13
(a) Plastic model. (b) Damaged plastic model.
(a)
(b)As shown in Figure13, for the CDP model, stress-strain relations under uniaxial compression and tension are expressed as(1)σc=1−dcE0ε−εcpl,σt=1−dtE0ε−εtpl,where E0 is the initial (undamaged) elastic stiffness of the material and σc,εcpl,σt,andεtpl are compressive stress, compressive plastic strain, tensile stress, and tensile plastic strain, respectively. Two damage variables such as dc and dt characterize the degradation of elastic stiffness on the strain-softening branch of the stress-strain curve. These variables can take values from zero to one, where zero represents the undamaged material and one represents total loss of strength. If such damage variables are not specified, the CDP model behaves as a plasticity model. For example, if the compression damage variable dc is not specified, then the compressive plastic strain εcpl takes the value of the inelastic compressive strain εcin. It must be noted that the tensile damage in the CDP model can be specified by either stress-strain relation or stress-displacement response (again, this is an optional choice), while the strain-softening behavior for cracked concrete must be specified by either stress-strain relation or fracture energy-cracking criterion GF (mandatory requirement).Regarding plasticity, the CDP model considers the isotropic hardening with the yield function developed by Lubliner et al. [42] and elaborated by Lee and Fenves [43]. Parameters determining the shape of this yield function and nonassociated plastic flow rule are the dilation angle ψ, the ratio of initial equibiaxial compressive yield stress to initial uniaxial compressive yield stress fb0/fc0, the eccentricity of the plastic potential surface ε, and the ratio of the second stress invariant on the tensile meridian to compressive meridian K. For more detailed description of this CDP model, readers can refer to ABAQUS manuals.Overall, for a full definition of the UHPC substrate with the CDP model, stress-strain relations in compression/tension and strain-softening behavior for cracked UHPC as a set of points laying on the stress-strain curve or optional fracture energyGF are required for characterizing damage along with plasticity parameters including ψ, fb0/fc0, ε, and K.In the present study, the compressive stress-strain relation of UHPC is identified as the average value of experimental results given in Table8, where the evolution of damage is assumed to occur only in tension after initiating fracture. That is, Table 8 is the reinterpretation of Figure 9 in average sense with differentiating inelastic stress-strain.Table 8
Average compressive inelastic stress-strain test results for the UHPC.
First pouring
Second pouring
Stress (MPa)
Inelastic strain
Stress (MPa)
Inelastic strain
180
0
176
0
193
0.0002
185
0.0002
199
0.0003
187
0.0003
204.6
0.00039
186.5
0.0004
202
0.0005
186
0.0005
201
0.0006
185.4
0.0006
200.5
0.0007
184.3
0.0007
200
0.001
182
0.00075
172
0.002
170
0.003572Also, the tensile damage is described by stress-displacement relation from the previous study [43]—Kusumawardaningsih et al. [44] investigated stress-crack opening behavior of UHPC through axial tension and bending tension tests. Table 9 shows their tensile test results indicating that UHPC has a mean maximum tensile strength of 4.0263 MPa with the crack opening length of 7.8 µm and that a total loss of tensile strength occurs linearly with the crack opening length of 0.2 mm. This result is adopted in the present study by excerpting tendency with strength reduction damage parameters: the maximum tensile strength drops linearly from the zero crack opening length to the crack opening length of 0.2 mm.Table 9
Parameters for modeling tension damage.
Damage parameters
Displacement (mm)
0
0
0.5
0.1
0.99
0.2For the strain softening of cracked UHPC, the extended version of Euro design code [45] is used. In Euro design code, for ordinary concrete, main parameters such as the fracture energy GF and the tensile strength of ordinary concrete ft are given by(2)ft=1.4f′c−8102/3MPa,and(3)GF=0.0469da2−0.5da+26f′c100.7N/mm.These equations are adopted in the present study for computing tensile strength of UHPC and fracture energy: a nominal compressive strength of UHPC is taken to bef′c (=180 MPa) and a maximum size of UHPC aggregates is assumed to be da (20 mm). The main reason for taking da (20 mm) despite the absence of coarse aggregates in UHPC is that the design code for UHPC materials is not currently available—in order to account for improved material properties of UHPC in the current code, a generally accepted size of the maximum aggregate in ordinary concrete is considered here (the most common size of coarse aggregates in construction).All other material parameters of substrate UHPC are related with the yield surface and nonassociated potential plastic flow, where recommendation (default) values of the ordinary concrete material in the ABAQUS are taken [46–48]: ψ=36.31°, ε = 0.1, fb0/fc0 = 1.16, and K = 0.67.Apart from these, basic material properties such as Poisson’s ratio and modulus of elasticity are taken as 0.19 and 98,000 MPa—Poisson’s ratio of 0.19 is taken through reference [49] and the modulus of elasticity is the measured value from cylindrical tests.


## 4.1.2. Modeling Contact Surfaces at the Joint

For the sake of simplicity, the friction mechanism is presumed to occur only on horizontal contact surfaces, where a friction coefficient of the surface between the first and the second placements of UHPC is taken asμ = 0.4 based upon Table 11 (concrete-to-concrete) in the research report [50]. In addition, a shear stress limit at the horizontal interface is computed as 104 MPa corresponding to the upper-bound estimate of f′c/3 in the ABAQUS analysis manual: this means that sliding at the interface initiates when exceeding the compressive strength of UHPC.For the development of analytical models, vertical contact surfaces play key roles. In the present approach, cohesive effects at the vertical interface are modeled with a surface-based behavior. This surface-based cohesive behavior initially defines a traction-separation model followed by the initiation and evolution of damage. Thus, the contact surface is assumed to show linear elastic response in terms of a constitutive matrix, tractions, and separations by(4)tntstt=Knn000kss000Kttδnδsδt,for the uncoupled traction-separation case, where tn, ts, and tt represent normal (along the global Z-axis), shear (along the global X-axis), and tangential (along the global Y-axis) tractions, while the corresponding separations are denoted by δn,δs, and δt.Subsequently, degradation and failure of the bond at the interface are described by damage modeling, where the damage initiation refers to the beginning of degradation of the cohesive response at each contact point, while the damage evolution describes the rate at which the cohesive stiffness is degraded once the corresponding initiation criterion is reached.Figure14 shows a schematic viewpoint on traction-separation response described in the ABAQUS analysis manual, where peak values of traction and those of separation in normal, shear, and tangential directions are identified as sets of tn0,ts0,tt0 and δn0,δs0,δt0 with a set of δnf,δsf,δtf representing each separation at complete failure.Figure 14
Typical traction-separation response.Among some criteria available in the ABAQUS, the following quadratic traction criterion for the damage initiation at the interface is considered:(5)tntn02+tsts02+tttt02=1,where . denotes the Macaulay bracket signifying that a purely compressive displacement (i.e., a contact penetration) or a purely compressive stress state does not initiate damage.In Figure14, damage evolution corresponding to each traction-separation response can be modeled with scalar variables of Dn, Ds, and Dt as(6)tn=1−Dntn0,ts=1−Dsts0,tt=1−Dtt0,where every D monotonically increases from 0 to 1 upon further loading after the initiation of damage.In order to describe the damage evolution under a combination of normal and other separations across the interface, an effective separationδm,(7)δm=δn2+δs2+δt2,is considered along with a single damage variable D:(8)D=1−δm0δmmax1−1−exp−αδmmax−δm0/δmf−δm01−exp−α,where δm0 is the effective separation at damage initiation and δmf is the effective separation at complete failure. Also, δmmax refers to the maximum value of the effective separation attained during the loading history, and α is a nondimensional parameter that defines the rate of damage evolution.Overall, cohesive failure in the vertical contact surface is modeled with uncoupled stiffness coefficientsKnn,Kss,Ktt, peak values of traction tn0,ts0,tt0, an effective separation at complete failure δmf, and a nondimensional parameter α. For every analysis model, α is fixed as 2, while other parameters are chosen differently as presented in Table 10. As shown in Table 10, the vertical interface is differentiated as to whether constrained or not. Also, a factor of 2 is considered when vertical contact surfaces are constrained with the concave-convex geometry. Such posteriori and values are found to be the best fit to experiment results.Table 10
Parameters for modeling vertical contact surfaces.
Configurations
Parameters (N, mm)
K
nn
,
K
ss
,
K
tt
t
n
0
,
t
s
0
,
t
t
0
δ
m
f
Geometry with no concave-convex interface
(490, 490, 490)
(0.7, 0.7, 0.7)
0.7
Geometry with concave-convex interfaces
(980, 980, 980)
(1.4, 1.4, 1.4)
1.4


## 4.1.3. Other Considerations

In every finite-element analysis, an 8-node linear brick element with reduced integration (C3D8R) is used as a basic element, while contact surfaces are modeled as the surface-to-surface contact with either tangential friction (horizontal surfaces) or cohesive with damage evolution (vertical surfaces). Also, following the static loading condition in real experiments, the displacement-controlled method is adopted at a rate of 1 mm/min at the upper part, while boundary conditions are assigned to the bottom part by setting all the displacements to zero.Figure15 describes the finite-element model used in analysis. In particular, the model was constructed by using the solid meshing capability in ABAQUS, where the vertical contact surface is densely divided into a size of 10 mm, leaving other parts to be divided into a size of 20 mm. The main reason to have such a different-sized control is that the stress distribution is expected to change dramatically at the vertical contact surface. For every analysis, the Newton iterative procedure with the specific step-time increment is adopted. Thus, the maximum number of time increments is set to 10000, while the initial increment size and minimum increment size are set to 0.01 and 1E− 8 with convergence criteria in Table 11.Figure 15
FEA model description (GR-20): (a) mesh; (b) vertical surface; (c) horizontal surface; (d) boundary condition.
(a)
(b)
(c)
(d)Table 11
Finite-element analysis model convergence criteria tolerances.
Criterion for residual force in a nonlinear problem
5E− 03
Criterion for displacement correction in a nonlinear problem
1E− 02
Initial value of time average force
1E− 02
Alternate criterion for residual force in a nonlinear problem
2E− 02
Criterion for zero force relative to time average force
1E− 05
Criterion for residual force when there is zero flux
1E− 05
Criterion for displacement correction when there is zero flux
1E− 03
Criterion for residual force for a linear increment
1E− 08
Field conversion ratio
1.00
Criterion for zero force relative to time average
1E− 05
Criterion for zero displacement relative to characteristic length
1E− 08


## 4.2. Simulation Results

Figure16 shows vertical displacement versus vertical reaction force in experiments and analysis, where the percentile error E is computed as(9)E=A−TT×100%,where T and A represent experimental and analytical results. As shown, each analytical model yields comparable results to experiments. In particular, every analytical model predicts the maximum shear capacity with less than 10% error.Figure 16
Comparison between analytical and experimental results: (a) MN-0; (b) VC-0; (c) GR-20; (d) GR-30.
(a)
(b)
(c)
(d)Figure17 (unit: sec−1) presents analytical results of the maximum principal strain rate at integration points. With comparison of Figure 14 to Figures 11 and 12, one can check that each analysis model is able to account for debonding behavior at the vertical interface with crack propagation.Figure 17
Analysis results (maximum principal strain rate): (a) MN-0; (b) VC-0; (c) GR-20; (d) GR-30.
(a)
(b)
(c)
(d)


## 5. Conclusions

Surface roughness of concrete-to-concrete interfaces has been the interesting research topic in materials science; however, there is lack of research with both experimental and analytical ways on shear performance of concrete-to-concrete interfaces. As preliminary study for the further development of UHPC construction joints with reinforcement, the present work investigates shear performance of plain UHPC construction joints in both analytical and experimental approaches. Three different configurations of a construction joint integrated with the 180 MPa UHPC are considered with the reference case of monolithic UHPC pouring, and the static push-off test is performed for each case. Based upon experimental results, the failure mechanism and the relation between vertical displacement and shear bond strength for each specimen are investigated. Some noteworthy comments are as follows:(1)
The monolithic pouring case (MN-0) had the maximum shear strength of 20.80 MPa with both interfacial failure and substrate cracks (failure mode B).(2)
The vertical joint case (VC-0) had the maximum shear strength of 0.72 MPa with complete interfacial failure (failure mode A).(3)
For the grooved joint cases, the maximum shear strength is 16.05 MPa for GR-30 with the failure mode B, and the maximum shear strength is 10.70 MPa for GR-20 with the failure mode A.The paper also presents a simplified three-dimensional finite-element analysis model for each case. In particular, three failure mechanisms including (a) damaged plasticity in the plain UHPC substrate, (b) friction in horizontal contact surfaces, and (c) cohesive failure in vertical contact surfaces are considered. All the developed analytical models result in responses well matched to experiments in displacement responses, maximum shear strength, and failure mode.Overall, it is anticipated that the present work will provide a basis for further study on reinforced UHPC construction joints.



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*Source: 6429767-2018-08-28.xml*