Numerical modeling for damaged reinforced concrete slab strengthened by ultra-high performance concrete (UHPC) layer

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Numerical modeling for damaged reinforced concrete slab strengthened by ultra-high performance concrete (UHPC) layer ⁎

Yanping Zhua,b, Yang Zhanga, , Husam H. Husseinc, Genda Chenb a

Key Laboratory for Wind and Bridge Engineering of Hunan Province, College of Civil Engineering, Hunan University, Changsha 410082, China Civil, Architectural and Environmental Engineering, Missouri University of Science and Technology, MO 65401, USA c Department of Civil Engineering, Stocker Center 102, Ohio University, Athens, OH 45701-2979, USA b

A R T I C LE I N FO

A B S T R A C T

Keywords: Ultra-high performance concrete UHPC Reinforced concrete slab Strengthen Cracks Interface model Finite element model

Ultra-high performance concrete (UHPC) has been developed as an innovative cementitious based material. It can be used for repairing and strengthening existing reinforced concrete (RC) structures because of its excellent mechanical performance, such as high tensile and compressive strengths, long-term durability, and low permeability. However, when using UHPC to strengthen existing RC structures for flexure members, there is limited information on simulating existed cracks in RC structures and considering interface modeling between RC substrate and UHPC overlay. This research developed a finite element (FE) model to investigate flexural behaviors of UHPC-RC composite slab with introducing existed cracks in RC substrate by geometry discontinuous, approximately matched with experimental results previously published by the authors. Meanwhile, based on recent research on the bond strength of UHPC to concrete, a UHPC-RC interfacial model was included in the FE model. The FE model was validated with experimental laboratory results previously published by the authors, and a good agreement was obtained between numerical and experimental results. Finally, a parameter study was conducted to investigate the strengthening effects and optimizing strengthening parameters by using the developed FE model. Results showed that the effect of existing cracks on the ultimate flexure capacity of UHPC-RC cannot be neglected, and the interface model has a precise accuracy in FE modeling.

1. Introduction Recently, the use of ultra-high performance concrete (UHPC) for rehabilitation and strengthening of reinforced concrete (RC) beams has been considered by researchers and engineers [1–7]. The material properties of UHPC, such as super-high tensile and compressive strengths, ductility, and good durability make UHPC attractive for various engineering structures, especially in bridge engineering [8–10]. Many studies, either numerically or experimentally, have been done to investigate the behavior of RC elements with UHPC in recent decades. However, most studies [11–13] of UHPC-rehabilitation have been conducted on virgin and uncracked specimens to estimate the ultimate strengthening capacity. A few experimental studies [4,14,15] exist on pre-damaged specimens. Neglecting the effects of cracks due to the existing pre-damage maybe lead the designers to incorrect retrofit or strengthening. On the other hand, finite element (FE) models developed in some literature [11,13–16] to study the behavior of strengthened structures especially for flexure behavior might not be accurate without considering the bond strength of UHPC and slip occurred in the UHPC-

⁎

RC interface. Hussein et al. [17] investigated the flexural and shear capacities of UHPC-uncracked NSC/HSC (normal or high strength concrete) composite prisms and beams, respectively. Stirrups were not used in the left span of composite beams. UHPC was located in tension while NSC/HSC was in compression. Additional parameters, such as shear connectors and fiber volume content, were discussed. Results showed that flexural and shear capacities of the strengthened composite members were enhanced, and all beams failed in shear. Also, the bond strengths between UHPC and NSC/HSC obtained by splitting tests were significantly high, with a maximum value of 11.97 and 12.86 MPa for UHPC-NSC and UHPC-HSC, respectively. Prem et al. [4] experimentally studied the flexural behavior of damaged RC beams (up to 80% and 90% of the failure load of control RC beam) strengthened with UHPC overlay under different curing conditions for UHPC. Results indicated that there was a significant increase in ductility and load capacity by 30% and 25.8% for 80% and 90% damage degree, respectively, under high-temperature curing. In a study by Safdar et al. [11], the flexural behavior of RC beams

Corresponding author. E-mail addresses: [email protected] (Y. Zhu), [email protected] (Y. Zhang).

https://doi.org/10.1016/j.engstruct.2019.110031 Received 5 May 2019; Received in revised form 30 October 2019; Accepted 29 November 2019 0141-0296/ © 2019 Elsevier Ltd. All rights reserved.

Please cite this article as: Yanping Zhu, et al., Engineering Structures, https://doi.org/10.1016/j.engstruct.2019.110031

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degrees of roughness (smooth, mid-rough and rough).

retrofitted with the UHPC layer was investigated in the tensile or compressive side with varying thickness. Results showed that with the increase of UHPC layer thickness, the ultimate flexural capacity of UHPC-RC was increased regardless of UHPC location. Also, a 3-D FE model was developed to investigate the influence of UHPC tensile strength as well as yield strength of tensile steel bars inside the UHPC layer on the ultimate flexural capacity of UHPC-RC. A perfect bond between RC and UHPC layers was assumed in the FE model. The perfect bond assumption was also used in other literature [12,14,15], and the model (perfect bond) was unable to capture bond failure at the joint interface. Al-Osta et al. [12] investigated the efficiency of intact RC beams strengthened by UHPC layers with three different strengthening configurations. Two different techniques for interfacial preparation were used: (1) sandblasting RC beams surfaces then casting UHPC insitu, and (2) bonding prefabricated UHPC strips to the RC using epoxy adhesive. A FE model was developed to study the behavior of the composite beams with reasonable accuracy. In the FE model, concrete damage-plasticity (CDP) model was used to model the nonlinear behavior of both concrete and UHPC. Steel was simulated using an elasticperfectly plastic relationship. Also, a perfect bond was assumed with a tie constraint used to fuse the UHPC and RC beam at the interface, and the behavior at the interface between components was not considered in the model. Ramachandra et al. [14,15] studied a new methodology for the repair of damaged RC beams using UHPC strip. Also, the researchers developed an integrated FE model accounting for pre-damage degree and nonlinearities of concrete and steel. The pre-damage severity for initial beams was induced by load step, say preloading before strengthening of UHPC and loading on strengthened structures in different steps in numerical software. However, the primary assumption made in the analysis was that the bond between the damaged beam and the UHPC strip was perfect. Lampropoulos et al. [16] focus on using UHPC jackets to strengthen existing RC beams. A numerical investigation was conducted to compare beams strengthened by conventional concrete with that by UHPC jackets. It should be noted that early shrinkage in UHPC was included and simulated by correcting concrete elements in the FE model. The interface between RC and UHPC was modeled by using a special 2-D element. Interfacial parameters such as friction coefficient equal to 1.5 and cohesion equal to 1.9 MPa were preset, representing a well-roughened interface. From the experimental and numerical results, it can be observed that in all strengthened cases, the slip occurred, and the maximum slip occurred near the ends of composite beams. Paschalis et al. [13] conducted UHPC-RC flexural tests and FE analysis. The interface between RC and UHPC layers was modeled using 2-D contact elements. Interfacial parameters such as friction coefficient equal to 1.0 and cohesion equal to 1.8 MPa were defined. The crucial parameters, such as the thickness of the UHPC layer and the steel ratio inside were investigated using FE modeling. Also, small slip at the interface with roughened RC substrate were found from experimental results. Yin et al. [18] conducted numerical modeling for predicting the structural response of composite UHPCconcrete members. A technique using equivalent beam elements at the interface was proposed for the consideration of the bond strength at the interface. The material properties of the equivalent beam elements were defined to represent the equivalent bond characteristics of NSC. Results showed that the bond strength should be taken into account in numerical models, whereas UHPC and NSC would not form a perfect bond interface. However, until now, there are limited published studies on simulation of existing cracks in RC in UHPC-RC composite structures strengthened by the UHPC layer. Past research in FE modeling of UHPCRC composites has either neglected the effect of slip on the interfacial bond between concrete materials or considered slip effect simulated in different ways [16–18]. On the other hand, recent research [13] has shown that the slip at the interface indeed occurred during loading. Meanwhile, recent research [19–21] has developed a new kind of model for simulation of flexure-shear interface connection with consideration of adhesion and friction between UHPC and concrete with different

2. Objectives This study aimed to develop a high-fidelity 3D FE model capable of accurately simulating flexure behaviors of UHPC-RC composite slab in terms of load-deflection relations, ultimate moment capacity, and failure mode. Then, the FE model was used to investigate the effect of key strengthening parameters on the flexural capacity of UHPC-RC slab under a negative bending moment (NBM) or positive bending moment (PBM). In order to verify the FE model, experimental results were presented, whereas other specific analyses on experiments referred to another journal [22]. The damaged RC slab was modeled by introducing geometry discontinuous in the original RC slab. Different interfacial models based on the concept in the AASHTO LRFD Bridge Design Specifications [23] and the American Concrete Institute (ACI) [24] for the UHPC-RC interface modeling were compared and discussed. Comparing the FE results with experimental results, a relatively accurate model for simulation of the interface between UHPC-RC components and the cracked RC slab were validated. Finally, a parameter study was conducted to obtain the effects of geometry discontinuous in the RC model on ultimate moment capacity and to optimize the key factors for the strengthened slab. 3. Summary of the experimental program In previous experimental work [22], two full-scale damage RC slabs strengthened by UHPC and one intact RC slab as a baseline were tested. The detailed parameters for the specimens are listed in Table 1. To investigate the flexure performance of strengthened slabs with the UHPC layer at tension zone and compression zone, load patterns of NBM and PBM were conducted. Fig. 1 shows the specimens with the main parameters. The RC slabs had a rectangular cross-section with a height of 28 cm, a width of 200 cm, and a total length of 320 cm and were reinforced with two layers of steel reinforcement mesh spaced at 150 mm with 16 mm and 20 mm diameter bars (in the left of Fig. 1). The UHPC, with a depth of 50 mm, was reinforced with one layer of steel reinforcement mesh spaced at 37.5 mm with 10 mm diameter bar. A stud with a height of 150 mm was used as a connector between the UHPC layer and RC slab. A 115 mm stud length was embedded into damaged RC slabs and spaced at 300 mm center to center (in the right of Fig. 1). In preparation of the test specimens, the three RC slabs were cast at laboratory temperature. After demolding on the second day, the slabs were cured under normal temperature for 28 days with water spraying two times every day. Then, the two RC slabs were subjected to preloading to produce diagonal cracks, as shown in Fig. 2. The diagonal cracks were achieved by the flexure-torsion loading method, where the loading point was in the middle of the diagonal line. For reinforcement slab with UHPC under PBM (H-UC-2), a 0.4 mm crack width in the RC slab was formed at the highest applied load of 266 kN, corresponding with 12.9 mm of displacement in the middle. After unloading, the maximum width became 0.18 mm. However, for reinforcement slab with UHPC under NBM (N-UC), a 0.2 mm crack width in the RC slab was formed at the highest applied load of 145 kN with a maximum displacement of 5.7 mm in the middle. Then, after unloading, 0.08 mm of maximum crack width was obtained. Also, an epoxy resin was Table 1 Description of test specimens.

2

Specimen

Curing conditions

Composite materials

Load directions

N-RC N-UC H-UC-2

NC NC HC

RC RC + UHPC RC + UHPC

/ Negative moment Positive moment

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spreader beam to distribute the load to the slab along the transverse direction. Hydraulic jack with a constant loading rate of 0.1kN/s applied loads at an initial loading stage and with an imposed deflection rate of 0.008 mm/s after all the tested slabs reached the ultimate load. The loads and vertical displacements of slabs were recorded during the test. 4. Finite element modeling The finite element software package ABAQUS [25], which can accurately capture nonlinear behavior of materials and structures, was employed to establish the FE model in this research in order to better investigate and understand the flexural response of the tested full-scale damaged RC strengthened by UHPC layer. The following subsections show the modeling procedures to replicate load-deflection behavior and ultimate load capacity as well as crack patterns of RC damaged slabs strengthened by the UHPC layer. The intact RC slab was first modeled for a pre-damage degree under flexure-torsion loading as well as the verification of material properties of NSC and steel reinforcement used under flexure loading. Then, the strengthened slab under a NBM and the other strengthened slab under a PBM were modeled. 4.1. Uniaxial tension and compression nonlinear behavior of NSC and UHPC

Fig. 1. Dimensions and reinforcement details of specimens (unit: cm).

The details of a mix design of NSC (Class C55) and UHPC used in experiments can be referred to the literature [22]. The popularly employed Concrete Damaged Plasticity (CDP) model available in ABAQUS [25] was used to model the nonlinear behavior of both NSC and UHPC in compression and tension. Stress-strain curves of NSC (Class C55) under uniaxial tension and compression were derived by the design code of concrete structures (GB50010-2010) in China [26]. Equations (1)-(4) give the derivation procedures for NSC tensile and compressive stress-strain relationships. Stress-strain curves of UHPC under uniaxial tension and compression were obtained by Zhang et al. [27] and by Yang [28], respectively. Eqs. (5) and (6) give the calculated procedures for UHPC tensile and compressive stress-strain relationships. It should be noted that the ultimate tensile and compressive strengths in Eqs. (5) and (6) were obtained by using material mechanical tests. Calculated stress-strain relationships for UHPC and NSC in tension and compression were shown in Fig. 4. According to the ABAQUS user manual [25], stress-strain relations of both NSC and UHPC need to be converted to stress-inelastic strain relations, which can be suitable for analysis using CDP in ABAQUS. The inelastic strain was calculated by the following Eq. (7) and (8). The stress-inelastic strain values of NSC and UHPC are listed in Table 2.

Fig. 2. Typical distribution and shape of cracks in RC slab by preloading.

injected into cracks with a width more than 0.1 mm, and cement paste was used to close cracks with a width less than 0.1 mm; then the damaged RC slabs were placed for five days until the epoxy resin hardened. For substrate interface roughness, roughening substrate with the macrotexture depths of about 1.0–4.0 mm was combined before pouring UHPC. The contacting surfaces were cleaned of any debris before casting UHPC. Also, spraying water for more than 4 h to make concrete substrate dampened sufficiently to minimize the water loss in the UHPC due to absorption by the unsaturated normal concrete deck. After substrate processing, reinforcement mesh was placed at the top of the RC slab, and then UHPC was cast. The surface of the UHPC was covered by plastic wraps, sprayed with water periodically for 48 h. After that, the N-UC strengthened slab was continued to be cured at normal laboratory temperature, with water sprayed periodically for another 28 days while the H-UC-2 strengthened slab was cured by applying steam at a temperature of 60 °C for 72 h. Then, all of them were placed in the laboratory environment until testing. The test setup and measurement layout of the tested slabs under PBM and NBM are presented in Fig. 3(a) and (b), respectively. All slabs were simply supported and subjected to three-point bending. The clear span of the slabs was 300 cm and carried a concentrated load at mid-span, using a steel

σ = (1 − dc ) Ec ε ;

dc =

⎧1 − ⎨1 − ⎩

ρc n n − 1 + xn ρc α c (x − 1)2 + x

where, x =

(1)

x ≤ 1⎫ x > 1⎬ ⎭

(2)

fc, r Ec εc, r ε , ρc = , n= , fc, r = 25.3MPa, εc, r Ec εc, r − fc, r Ec εc, r εc , r

= 920με

σ = (1 − dt ) Ec ε ;

dt =

5 ⎧1 − ρt [1.2 − 0.2x ] x ≤ 1⎫ ρt x > 1⎬ ⎨1 − α (x − 1)1.7 + x t ⎩ ⎭

where, x =

3

ft , r ε , ρt = , ft , r = 1.96MPa, εt , r = 94με Ec εt , r εt , r

(3)

(4)

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Fig. 3. Loading setup and measurement layout of the test slabs: (a) PBM test; (b) NBM test.

σ (ε ) =

⎧ fc

nξ − ξ 2 1 + (n − 2) ξ

tension and compression was captured in the FE model. The NSC and UHPC compressive and tensile damage parameters used in the model are given in [29] and calculated by Eq. (9) and (10) for compression and tension, respectively.

0 < ε ≤ ε0 ⎫

ξ ⎨f ε > ε0 2 c ⎩ 2(ξ − 1) + ξ

⎬ ⎭

(5)

where, ξ = ε / ε0, ε0 = 3500με, fc = 143.2MPa. σ (ε ) =

⎧

fc, t ε εca

⎨f ⎩ ct

0 < ε ≤ εca ⎫ εca

< ε ≤ εpc ⎬ ⎭

∊in c = ∊ − σc / Ec

(7)

∊in t = ∊ − σt / Ec

(8)

(6)

Dc = 1 −

where, fct = 8.10MPa, εca = 193με, εpc = 776με fc, r represents compressive strength of NSC, εc, r represents a compressive strain of NSC at fc, r , Ec represents elastic modulus of NSC, dc represents a compressive factor of concrete. ft , r represents tensile strength of NSC, εt , r represents a tensile strain of NSC at ft , r , dt represents a tensile factor of concrete. fc represents compressive strength of UHPC, ε0 represents a compressive strain of UHPC at fc . fct represents tensile strength of UHPC, εca represents a tensile strain of UHPC at fct , εpc represents an ultimate tensile strain of UHPC.

Dt = 1 −

σc Ec−1 ∊cpl

(

1 bc

∊tpl

(

1 bt

)

− 1 + σc Ec−1

(9)

σt Ec−1

)

− 1 + σt Ec−1

(10)

where, Dc and Dt are concrete compression and tension damage parameter respectively; σc and σt are compression stress and tensile stress, respectively; Ec is concrete elastic modulus; ∊cpl and ∊tpl are plastic strains corresponding to compressive stress and tensile stress, respectively; pl in ∊cpl = bc ∊in c ; ∊t = bt ∊t , bc and bt are constants both with range 0 < bc , bt < 1. Additionally, the CDP model requires five additional parameters: flow potential eccentricity (∊), a viscosity parameter that defines viscoplastic regularization ( μ ), the ratio of the second stress invariant on

To observe the crack propagation, the damage parameter in tension and compression can be assumed to activate when the peak strength is achieved. In this manner, the degradation of NSC and UHPC under both

Fig. 4. Uniaxial stress-strain relationships of UHPC and NSC: (a) Tension; (b) Compression. 4

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bars. A 2-node linear 3-D truss element was used to model the steel reinforcements. This element is a long, slender structural member that transmits only axial load. Two kinds of elements (beam element and solid element with a detailed description of these elements in 4.3.3)) for studs modeling were compared and discussed later.

Table 2 Properties of NSC and UHPC in Compression and Tension. Compression behavior of NSC

Tension behavior of NSC

Comp. stress, MPa

Tensile stress, MPa

Inelastic strain

Damage parameter

Crack strain

Damage parameter

4.3. UHPC-NSC interface model 22.52 0.000000 0.000 23.27 4.864E-05 0.015 24.02 0.000118 0.034 25.30 0.000531 0.133 24.56 0.000846 0.201 21.78 0.001410 0.321 19.71 0.001794 0.400 16.89 0.002359 0.506 13.90 0.003082 0.619 11.20 0.003942 0.720 8.99 0.004932 0.801 Compression behavior of UHPC

1.96 0.000000 1.94 7.61E-06 1.77 3.57E-05 1.21 0.000132 0.94 0.000204 0.72 0.000305 0.63 0.000369 0.49 0.000526 0.38 0.000731 0.34 0.000884 0.29 0.001086 Tension behavior of UHPC

0.000 0.069 0.276 0.674 0.803 0.888 0.917 0.953 0.972 0.980 0.986

Comp. stress, MPa

Inelastic strain

Damage parameter

Tensile stress, MPa

Crack strain

Damage parameter

130.86 150.00 144.82 133.09 119.31 105.96 83.74 75.00 61.31 51.36 47.38

0.000000 0.000251 0.000551 0.001330 0.002159 0.002977 0.004506 0.005214 0.006540 0.007777 0.008371

0.000 0.029 0.064 0.153 0.246 0.336 0.492 0.556 0.658 0.732 0.761

7.99 8.10 7.72 7.11 6.44 5.85 5.12 4.74 3.79 2.87 2.81

0.0000000 0.0017709 0.0019309 0.0023868 0.0030239 0.0035787 0.0044590 0.0048391 0.0057046 0.0065056 0.0068297

0.000 0.988 0.990 0.992 0.994 0.996 0.997 0.997 0.998 0.999 0.999

Two different basic mechanisms contribute to the minimum shear resistance at the UHPC-NSC interface. One is given in AASHTO LRFD Bridge Design Specifications [23] to define shear stress at the interface between concrete cast at different times as:

vu = cAcv (cohesion) + μ (Avf f y + Pc )(friction)

where Acv is the area of concrete at the shear interface; Avf is the area of shear reinforcement; c is the cohesion; μ is the friction coefficient; fy is the yield stress of the reinforcement, and Pc is the compressive force normal to the shear interface. If the interface is in tension, Pc is zero, and Eq. (11) gives the minimum tensile resistance. It should be noted that the values of c and μ in Eq. (11) represent cohesion and friction in the bonded materials, or adhesion and friction at the material interface, depending on the location of the failure. AASHTO provides values for c and μ for a concrete-to-concrete interface with varying degrees of roughness. The values depend on the surface condition as follows: (1) the cohesion and friction coefficient are 1.65 MPa and 1.0, respectively, for the clean rough surface, roughened to amplitude of 6.35 mm; (2) the cohesion and friction coefficient are 0.5 MPa and 0.6, respectively, for the clean smooth condition. For an interface other than concrete-toconcrete, c and μ should be determined through laboratory testing according to ASTM standards. The same mechanisms were reported by [31], namely concrete-to-concrete cohesion, concrete-to-concrete friction, and in the case of reinforced interfaces, the connecting action from shear connectors placed across the interface between concrete and concrete. The other is given in the ACI [24] that specifies the minimum shear resistance at the interface between two materials. However, the ACI shear calculation is more conservative as the cohesive strength at the interface between two concretes cast at different times is neglected. Also, ACI assumes that there is already a crack along the interface plane. Therefore, only two parameters (the friction coefficient and the shear-friction reinforcement) are considered in the calculation of the shear strength. According to the literature [21,32], there are two types of interfacial model in ABAQUS corresponding to cohesion/adhesion and friction as following: traction-separation model and ‘hard’ contact with friction penalty, respectively. In this research, studs exist as connectors for enhancing the bond strength at the interface. Also, studs were simulated using solid elements or beam elements. Then, the efficiency of these two elements was compared. Meanwhile, two different concepts mentioned in AASHTO and ACI standards to model UHPC-RC interface were also considered for comparison, and the better model in terms of prediction of load–deflection response and failure mode was obtained to conduct parameter study later.

the tensile meridian to that on the compressive meridian such that the maximum principal stress is negative (K c ), the ratio of the initial equibiaxial compressive yield stress to the initial uniaxial compressive yield stress (σb0 /σc0 ), and the dilation angle in degrees (Ψ ). For both UHPC and NSC materials, these parameters were defined as 0.1, 0.0, 0.67, 1.16, and 15°, respectively [12]. Moreover, the modulus of elasticity for NSC and UHPC were 35.20 GPa and 42.45 GPa, respectively, used in FE models, but need to be further calibrated by linear elastic response of the tested slabs. The Poisson’s ratio (υ) of 0.19 was assumed for both materials. A three-dimensional stress 8-node linear brick element C3D8R (Cube Three Dimensional eight-node Reduced integration) was used to model both the NSC and UHPC components. This element type is suitable for both complex nonlinear analysis besides linear analysis. 4.2. Steel bar and stud material models The reinforcement bars used in this study were HRB400 [30] grade having a yield stress of 450 MPa. The post-yield stress-strain relationship of reinforcement bars was shown in Table 3. All the bars had the same elastic modulus of 210 GPa and Poisson’s Ratio of 0.3. Steel studs used for connecting the UHPC layer and the RC layer had a yielding strength of 240 MPa with a length of 150 mm and a diameter of 13 mm. The elastic modulus and Poisson’s Ratio were as same as reinforcement

4.3.1. Traction-separation model for UHPC-RC interface ABAQUS provides two methods to simulate the interface connection using the traction-separation model. The first method of the tractionseparation constitutive model is using cohesive elements with a certain thickness of the interface element to represent a transition zone between UHPC and NSC. Another method is considering modeling interfaces with zero thickness using surface to surface (here is UHPC and NSC faces) property. Here the latter was used because no adhesion material was added at the interface between UHPC and NSC during the experiment, and the adhesion thickness can be assumed zero. The traction-separation constitutive properties used are shown in Fig. 5. The primary law of traction-separation behaviors is as following:

Table 3 Plastic Properties of Steel Bars. Plastic parameter Yield stress (MPa)

Plastic Strain

450 450 1

0 0.01 0.02

(11)

5

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was allowed [34]. The value for friction coefficient inputted as tangent behavior in ABAQUS can be seen in Table 4. This friction coefficient was derived by back-calculated using the results of the slant-shear and direct tension test with more details shown in [19,20] and [23]. 4.3.3. Studs modeling Studs with a length of 150 mm and a diameter of 13 mm were used at the interface between UHPC overlay and RC slab. A length of 115 mm was planted in the RC slab, and 35 mm was embedded in the UHPC overlay. The studs were arranged with a spacing of 300 mm center to center. In the FE modeling, the constraint between studs and UHPC or NSC was simulated by ‘embedded technique’ in ABAQUS. Two different elements were used for the simulation of studs. One is the solid element with an 8-node linear brick, reduced integration, hourglass control element [25]. Average strain in a kinematic split and secondorder accuracy were chosen, while other element characteristics were controlled by default. Gauss integration is almost always used with second-order isoparametric elements because it is efficient at the Gauss points corresponding to reduced integration. Also, according to the ABAQUS manual [25], the strains are most accurately predicted if the elements are well-shaped. The other model is a beam element with a 2node linear element in space. The type of beam is shear-flexible, which corresponds to the stress state of studs at the interface subjected to shear and flexural forces. The scaling factor of linear bulk viscosity is 1.0.

Fig. 5. Uniaxial stress-displacement curve of the interface. Table 4 Mechanical Properties of UHPC-NSC Interface [19] Properties

Rough 3

Kn (N/mm ) Ks and Kt (N/mm3) tn , ts andtt (MPa) Total/plastic displacement (mm) Stabilization Friction coefficient

1358 20,358 5.63 0.241 0.001 1.44

4.4. Cracking modeling The whole process of composite slabs strengthened by UHPC includes two stages: one is a preloading stage to obtain damage degree in original RC slab; the other is to apply load on the UHPC-RC slabs after strengthening by UHPC. These two stages can be modeled in ABAQUS with a multi-step strategy. However, discrete cracks in RC produced in the preloading stage after unloading cannot be well modeled in ABAQUS. This can be manifested from the numerical results in the literature [14,15] that seem not very close to experimental results using a multistep strategy in ABAQUS to analyze flexure behavior and fatigue behavior of the damaged beams strengthened by UHPC. On the other hand, in the experiment conducted by the authors [22], steel reinforcement strain almost recovered after unloading. Therefore, initial stresses in steel reinforcement in RC slabs can be neglected, and just cracks in RC slab are considered for simulating the reduction of stiffness. Therefore, in order to mimic existing cracks in RC slabs, cracks were modeled as a geometry entity or geometry discontinues [35]. Based on previous experimental observations for cracks in the preloading stage [22], crack parameters including the amounts of cracks, crack spacing, crack width, and crack length in RC slabs were assumed. The assumed parameter for cracks was listed in Table 5. Fig. 7 shows some of the geometry discontinuous explored in RC slabs in FE modeling. Relatively reasonable crack parameters were identified by comparing numerical and experimental results.

Fig. 6. NSC interface roughness before adding UHPC layer.

linearly and elastically increase until up to the maximum traction or separation and start to decrease after initiation of damage. In Fig. 5, Kn Ks and Kt are the normal and tangential stiffness components that relate to the normal and shear separation across the interface before the initiation of damage. The contact stresses (tn , ts andtt ) at the interface are the normal stress and other two shear stresses, corresponding to the deformation normal to the interface, paralleled with the first shear direction and the second shear direction, respectively. The contact stresses (tn , ts andtt ) have the same assumed value, which is equal to direct tensile strength obtained by direct tensile test or equal to adhesion/cohesion value between UHPC and NSC. All these parameters are listed in Table 4 [19]. Due to the roughening of RC face before strengthening of UHPC, the property for the rough surface was chosen to be consisted with the experimental tests. Fig. 6 shows the interface roughness of the experimental NSC substrate.

Table 5 Parametric values to determine the crack properties.

4.3.2. Hard contact and friction coefficient Hard contact implies that: (1) the surfaces transmit no contact pressure unless the nodes of the slave surface contact the master surface; (2) no penetration is allowed at each constraint location (depending on the constraint enforcement method used, this condition will either be strictly satisfied or approximated); (3) There is no limit to the magnitude of contact pressure that can be transmitted when the surfaces are in contact. Hard contact can be set in normal behavior [33] in ABAQUS. A friction model considering a friction coefficient was implemented in which little slip between the interfaces (NSC and UHPC) 6

n (amounts of cracks)

s (crack spacing)

w (crack width)

l (crack length)

1 3 3 5 5 5 9 9 9 9 0

0 80 mm 80 mm 80 mm 80 mm 80 mm 80 mm 80 mm 100 mm 100 mm 0

2 1 2 1 2 2 1 2 1 2 2

0.50 0.85 0.85 0.85 0.85 0.99 0.85 0.85 0.85 0.85 1.00

mm mm mm mm mm mm mm mm mm mm mm

h h h h h h h h h h h

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Fig. 7. Geometry discontinuous (side view) for simulation of NSC cracking in RC slab (a) Five, 80 mm, 1 mm, 0.85 h (desired model) (b) Five, 80 mm, 1 mm, 0.99 h (c) Nine, 100 mm, 2 mm, 0.85 h (h denotes the height of RC slab).

5. Results and discussion

The N-UC under NBM and H-UC-2 under PBM were modeled with proposed geometry discontinuous for damaged RC slab. A total of 88 models (N-UC and H-UC-2) with each type of crack parameter listed in Table 5 for simulation of cracking in RC slab was run in ABAQUS. Comparing numerical and experimental load-deflection responses of NUC and H-UC-2 slabs, crack parameters with five cracks, crack width of 1 mm, crack spacing of 80 mm and crack length of 0.85h were selected for further parameters analysis. It should be noted that the accuracy of crack parameters selected directly affects the reliability of numerical results. Specific discussion of accuracy between numerical and experimental results was given in Section 5.

5.1. RC slab prior to strengthening: Numerical modeling and experimental validation 5.1.1. Preloading stage modeling Prior to strengthening, the preloading stage on the RC slab was simulated for the experimental test. The flexure-torsion loading pattern was conducted as shown in Fig. 8(a). The maximum load was applied to the specimen to produce the depth of cracks in the RC slab. CDP model was used for NSC constitutive modeling, as mentioned before. For the simulation of steel bars, linear truss elements with bilinear behavior were used. The tensile damage was shown in Fig. 10. Comparing Fig. 10 with Fig. 2, FE modeling can capture the crack pattern in terms of crack depth and crack direction in NSC at the preloading stage. Meanwhile, the characteristics of cracks proposed in Table 5 for simulation of the cracked RC slab by geometry discontinuous were approximately consistent with numerical results.

4.5. Finite element models The FE models used to simulate the experimental unstrengthened slab and strengthened slabs are shown in Figs. 8 and 9, respectively. Fig. 8(a) shows the model for simulation of RC slab at the preloading stage under flexure-torsion loading. In Fig. 8(b), the FE model was used for the intact control RC slab under flexure loading. The steel sketch in the control RC slab was embedded in the whole model. The cracked RC slab was assembled as shown in Fig. 9(a) and (b) for N-UC slab under NBM and H-UC-2 slab under PBM, respectively. These figures show the crack tip region in RC slabs based on experimental observations in order to make models closer to experimental cases.

5.1.2. Intact RC slab The initial intact slab examined in this study under flexure loading is based on the experimental program. The numerical results are compared to the corresponding experimental results, and the results are presented in Figs. 11 and 12. From the results presented in Fig. 11, good agreement between the numerical and the corresponding experimental load-displacement curve was observed except some fluctuation in the first phase. Although the modulus of elasticity was already calibrated, this fluctuation may be related to the variance between the simulated boundary condition and the actual boundary condition. In other words, the simulated contact areas between the supports and the concrete slab are fully contacted and uniformed, but in the actual condition, these

Fig. 8. FE model for unstrengthened slab (a) Under flexure-torsion loading (preloading stage) (b) Under flexure loading (control RC slab). 7

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Fig. 9. (a) Assembled N-UC slab and (b) Assembled H-UC-2 slab.

areas were not fully uniformed. Therefore, in this study, the calibration of Young's modulus of NSC and UHPC was conducted to match as much as the response of tested slabs. Also, the maximum load (678 kN) predicted by the FE model was almost equal to the experimental one (677 kN). Both numerical and experimental curves show a hardening phase after steel reinforcement yielded. From Fig. 12, the damage of NSC was displayed. Many vertical cracks started from the tensile side and propagated the concrete compression zone downwards. The main cracks spacing is close to the spacing of vertical steel reinforcement in the RC slab about 15 cm. Therefore, the assumptions of material properties presented in RC layers and steel bars were relatively reasonable and can be used for the modeling in the following parts. 5.2. Strengthened slab under NBM (N-UC) Fig. 11. Comparison of load-deflection for unstrengthened slab.

Two different interfacial models (ACI and AASHTO) were conducted with and without consideration of cohesion/adhesion contribution between UHPC and NSC layers. Also, two different elements (solid and beam elements) were used for the simulation of studs between UHPC and RC components at the interface. All cases are listed in Table 6. In Fig. 13, with cracked RC slabs simulated, as can be seen from FEM-N-UC-STS and FEM-N-UC-BTS, the FE model with AASHTO concept interface model shows a good agreement with experimental results in terms of initial loading stage with displacement smaller than 5 mm, as shown in Fig. 13(a). However, in the first 1 mm of displacement, they show a difference with experimental stiffness higher than numerical stiffness. Because using cement paste and epoxy resin repaired the cracks, this procedure was not included in FE modeling. After their contributions lost, numerical and experimental development of loaddisplacement curves was almost overlapped along with the increase of load until the load close to the maximum. For solid and beam elements used for modeling studs existed at the interface, the slight effect of different elements for studs on load-displacement response was found. For FEM-N-UC-SHF and FEM-N-UC-BHF models with the ACI concept used for the modeling of the interface, the results are not wellmatched with experimental results. From the comparison of FEM-N-UCSTS and FEM-N-UC-SHF, the effectiveness of the interface bond strength (adhesion and friction) was examined for interface modeling, and there are some differences in the maximum load, as summarized in Table 7. The ultimate flexure capacity for N-UC produced by the FE model using the AASHTO interface concept with beam and solid elements for studs is 10.2% and 8.6% less than experimental values,

respectively. Moreover, the post-peak behaviors of load-displacement can be reproduced in models of FEM-N-UC-STS and FEM-N-UC-BTS. Somewhat difference between them in post-peak responses was observed. FEM-N-UC-BTS curve was much closer to the experimental result (almost parallel with the experimental curve in the phase of postpeak behavior). However, using ACI interfacial concept cannot capture the post-peak response of N-UC in ABAQUS, so the accuracy of the AASHTO interface model was further verified. In Fig. 14, N-UC without cracks included was modeled with different interface models and different studs’ elements. Generally, all modeling results showed a higher flexure ultimate capacity and stiffness compared with the experimental one as expected. In the first 5 mm displacement, as shown in Fig. 14(a), the load-displacement curves of FEM-N-UC-STS and FEM-N-UC-HTS are slightly higher than EXP-N-UC. This may be because, at a lower load, uncracked RC slab cracked, which was similar to cracking of cement paste or epoxy resin used for repair of existing cracks in preloading. However, their load-displacement curves gradually deviate from the experimental one with the load over around 800 kN without consideration of stiffness reduction in cracked RC slabs. This might be due to after cracking in intact RC slab, the newly casting UHPC placed at the tension side restrained further development of cracks in the RC slab. While in experimental damaged RC slab, all existed cracks opened immediately and rapidly after the strength of cement paste or epoxy resin reached. Therefore, preloaded cracks in NSC in the RC slab reduced the ultimate flexure capacity in N-UC. Fig. 15

Fig. 10. Tensile damage in NSC in deformed RC slab after preloading. 8

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Fig. 12. Typical flexural damage pattern for deformed unstrengthened slab. Table 6 Cases for FE Modeling under NBM and PBM. Cases

Interface model

Interface concept

Stud element

FEM-N-UC (H-UC-2)-SHF FEM-N-UC-BHF FEM-N-UC-BTS FEM-N-UC (H-UC-2)-STS

Friction only Friction only Adhesion and friction Adhesion and friction

ACI ACI AASHTO AASHTO

Solid element (S) Beam element (B) Beam element (B) Solid element (S)

Fig. 13. Comparison of load-deflection for N-UC slab with cracked RC slab (a) displacement less than 5 mm (b) the whole process of loading.

influence of solid and beam elements for modeling studs can be neglected. Therefore, using solid elements only in the H-UC-2 slab did not interfere the further validation. The comparison for two different interface models with cracked RC slab is shown in Fig. 16. The results of FEM-H-UC-2-STS show a good agreement with experimental results in terms of the initial phase until yielding steel reinforcement at a load of around 600 kN. After that, some deviations are observed in the curve. This might be explained by the accuracy of the cracked RC slab simulated by geometry discontinuous [35]. Although this difference is not as expected, AASHTO interfacial concept still provides relatively better accurate results. In Fig. 17, the comparison was presented for two interface models with uncracked RC slab. Without consideration of reduction in initial stiffness in the RC slab, the ACI interfacial concept still performed underevaluated results compared with the experimental results. It should be noted that from the curves produced by FE modeling in Fig. 17, the initial stage deviated from the experimental curve as expected. The experimental results did not have initial linear-elastic phase because the cracks have already existed. Then, the development of initial cracks in RC would trace the existed cracks in the bottom of the H-UC-2 slab [22] after loading. However, the response of FEM-HUC2-STS (Fig. 17) is very close to the experimental curve at a later stage. This may be qualitatively explained that when H-UC-2 was subjected to PBM, the RC slab was in tension. Therefore, the contribution of NSC in flexure capacity can be neglected after cracking. As a result, the experimental postcracking behavior of H-UC-2 can be according to the numerical result of the strengthened slab without consideration of cracks in RC after NSC

Table 7 Comparison of Ultimate Flexure Moment Values Obtained by Experiments and FE Modeling. Specimens

Experimental (kN)

Numerical (kN) Solid element

N-RC N-UC H-UC-2

677 (6 7 8) 1340 860

Beam element

AASHTO

ACI

AASHTO

ACI

– 1225 756

– 1228 672

– 1203 –

– 1204 –

shows compression and tension damage in NSC in RC slab and tension damage in the UHPC overlay obtained from numerical simulations. Comparing numerical results with experimental ones, crack distribution and crushed concrete zone were well reproduced by FE modeling, which indicates that FE modeling can approximately reflect experimental observations. 5.3. Strengthened slab under PBM (H-UC-2 slab) Figs. 16 and 17 show the comparison of load-deflection for H-UC-2 slab with cracked RC slab and uncracked RC slab and analyzed cases referred to Table 6. In Figs. 16 and 17, the results with the studs modeled by beam element in because convergence cannot be achieved in the H-UC-2 slab. However, from the modeling results of N-UC, the 9

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Fig. 14. Comparison of load-deflection for N-UC slab with uncracked RC slab (a) Displacement less than 5 mm (b) The whole process of loading.

Fig. 15. Compression and tension damage in NSC and UHPC and comparison with experimental failure mode of N-UC.

Fig. 16. Comparison of load-deflection for H-UC-2 slab with cracked RC slab (a) Displacement less than 5 mm (b) The whole process of loading.

Fig. 17. Comparison of load-deflection for H-UC-2 slab with uncracked RC slab (a) Displacement less than 5 mm (b) The whole process of loading.

10

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initial behavior cannot be reproduced. The main reason for this phenomenon may also stem from the accuracy of cracks modeled in RC slab by geometry discontinuous before strengthened. However, both with and without consideration of cracks in NSC in RC can reflect the actual flexure behavior of H-UC-2 in different aspects to a certain degree, such as serviceability and ultimate state criterion. Therefore, when conducting parameter study for strengthened slab under PBM, the RC slab without cracks was modeled due to in this way modeled ultimate flexure capacity close to the experimental one. Besides, Fig. 18 shows the simulated crack pattern compared with the failure mode obtained by the experiments. The propagation of vertical cracks in the RC slab obtained by FE modeling was basically in accordance with experimental observations. No damage was observed in the UHPC layer due to high compressive strength and steel reinforcement inside the UHPC overlay. These comparisons further demonstrated that FE modeling reproduces the response of UHPC-RC well.

Fig. 18. comparing crack pattern obtained by numerical simulation with experimental failure mode of H-UC-2.

Table 8 Comparison of Efficiency of Different Interface Models and Different Simulations for Studs in FE Modeling. Interface Modeling

Timing cost

UHPC-RC interface

Studs simulation

Adhesion/cohesion and friction (AASHTO concept) Friction (ACI concept)

solid element beam element solid element beam element

High Highest High Higher

6. Parametric study

Convergence NBM

PBM

Y Y Y Y

Y N Y N

After the comparison of experimental and numerical results with two interface models and two elements (solid and beam element) for studs, the reliability of FE modeling is verified. The computation efficiency of different numerical models with existing cracks in the RC slab was compared, as summarized in Table 8. From this table, the AASHTO interfacial model along with studs simulated by the solid element can achieve convergence and save timing cost, also having good accuracy with experimental ones. Therefore, the AASHTO interfacial model and studs simulated by solid elements were used for further analysis of parameters, which affect the ultimate flexure capacity of the strengthened slab under NBM and PBM. Due to the high cost of UHPC material, constructing and testing several scaled slab specimens are not economically possible. A series of strengthened slabs under the NBM or PBM with different UHPC thickness layers, rebar diameters in UHPC overlay, and RC layer were numerically modeled for optimization parameters for construction. Meanwhile, the effects of existing cracks on the ultimate load capacity of strengthened slabs were presented with corresponding strengthened slabs without consideration of existing cracks in the RC slab. Table 9 gives the specific parameters prepared to investigate. Three different layer depths were investigated; 30 mm, 50 mm, and 70 mm, and each layer depth was reinforced with steel bars with diameters of 8 mm, 10 mm, and 12 mm (see Table 9). Furthermore, the steel bars with diameters of 16 mm, 20 mm, and 25 mm in RC slabs were also investigated. The grade and shape of the steel bars were the same as the experimental investigation, namely HRB400.

Table 9 Parameters for Investigation of the Effects of Existence of Cracks in the Models. Groups

UHPC depthhU / mm

Rebar diameter DU in UHPC/mm

Rebar diameter DR in RC/mm

Group1

30

8 10 12

16 20 25

Group2

50

8 10 12

16 20 25

Group3

70

8 10 12

16 20 25

cracking. Therefore, a conflict exists here that says, with considering the existence of cracks in RC, initial behavior of strengthened slab under PBM can be better modeled. Then, the stiffness was reduced after the load over yielding load; without considering initial cracks in RC, the

Table 10 Results of Parametric Study for the Strengthened Slab under NBM. Variables

Group 1 hU = 30

Group 2 hU = 50

Group 3 hU = 70

DU /mm

DR /mm

Fmax / kN

Fcmax / kN

Fcmax / Fmax

Fmax / kN

Fcmax / kN

Fcmax / Fmax

Fmax / kN

Fcmax / kN

Fcmax / Fmax

8

16 20 25

953 1134 1418

912 1051 1288

1.045 1.079 1.101

1072 1234 1495

1014 1138 1349

1.057 1.084 1.108

1217 1367 1604

1115 1219 1415

1.091 1.121 1.134

10

16 20 25

1187 1365 1632

1072 1202 1396

1.107 1.136 1.169

1301 1457 1734

1155 1296 1463

1.126 1.124 1.185

1447 1601 1836

1249 1350 1501

1.159 1.186 1.223

12

16 20 25

1462 1619 1879

1192 1313 1484

1.227 1.233 1.266

1581 1741 1968

1271 1386 1547

1.244 1.256 1.272

1725 1881 2107

1377 1484 1640

1.253 1.268 1.285

Note: Fmax denotes the result simulated by the FE model without consideration of cracking in RC; FCmax denotes the result simulated by the FE model with consideration of cracking in RC. 11

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Table 11 Results of Parametric Study for the Strengthened Slab under PBM. Variables

Group 1 hU = 30

Group 2 hU = 50

Group 3 hU = 70

DU /mm

DR /mm

Fmax /kN

Fcmax /kN

Fcmax / Fmax

Fmax /kN

Fcmax /kN

Fcmax / Fmax

Fmax /kN

Fcmax /kN

Fcmax / Fmax

8

16 20 25

552.8 795.6 1153.3

452 687 1051

1.223 1.158 1.097

596.1 867.1 1257.9

501 757 1154

1.189 1.145 1.090

638.9 928.9 1362.3

540 820 1250

1.183 1.133 1.090

10

16 20 25

548.8 800.1 1157.9

453 688 1054

1.211 1.163 1.099

596.3 867.2 1259.4

501 757 1154

1.190 1.145 1.091

639.3 928.9 1362.1

540 820 1250

1.182 1.133 1.090

12

16 20 25

552.5 798.9 1153.5

454 689 1057

1.217 1.160 1.091

597.9 868.1 1257.4

501 758.6 1156

1.157 1.144 1.088

641.2 929.2 1361.2

539 820 1253

1.190 1.133 1.086

14

16

553.9

454

1.220

596.8

501

1.191

642.1

539

1.191

Note: Fmax denotes the result simulated by the FE model without consideration of cracking in RC; FCmax denotes the result simulated by the FE model with consideration of cracking in RC.

8.6% to 22.3% of Fmax (relatively real value).

6.1. Strengthened slab under NBM Generally, with an increase in the UHPC layer thickness and the diameter of steel reinforcement in UHPC and RC, the flexure capacity of the UHPC-RC slab under NBM is increased, as shown in Table 10. However, the degree of influence for the three parameters on the ultimate flexure capacity varies. As the amount of steel reinforcement in RC is fixed, the area of steel reinforcement in UHPC is a more critical parameter affecting the ultimate flexure capacity than the depth of the UHPC layer having the same conclusion in literature [13]. Similarly, when the diameter of steel in UHPC is fixed, the area of steel in RC also has a better effect on flexure capacity compared with the depth of UHPC layer. This is due to the increase of the reinforcement ratio of steel existing in RC in tension zone. This increase can provide more flexure resistance on the UHPC-RC members under NBM. Additionally, when the depth of the UHPC layer is constant, the effect of the steel area in the UHPC on flexure capacity is more significant compared with the steel area in the RC slab. This is because the steel in UHPC layer is far away from the neutral axis, which can provide much more flexure resistance as well. With the introduction of existing cracks in the RC slab, ultimate flexure capacity decreases comparing with composite members with intact RC in the range of 4.5% to 28.5%, as shown in Table 10.

7. Conclusions This research conducted FE modeling to simulate two full-scale flexural UHPC-RC strengthened members under PBM and NBM. Specific modeling procedures were discussed, and some conclusions can be drawn as follows: (1) Traction-separation model with friction penalty (AASHTO interfacial concept) can achieve relatively accurate results in flexural response of UHPC-RC compared with experimental ones, while using ACI interfacial concept (only friction) still performed an under-evaluated results compared with the experimental results due to the neglected adhesive strength at the interface between two concretes cast at different times. (2) Existing cracks in RC slab preloaded were simulated by geometry discontinuous, which can roughly reflect the damage degree in reality and the stiffness reduction of RC slab in experiments. Many attempts based on experimentally known cracks distribution show five, 80 mm, 1 mm, 0.85 h for the number of cracks, crack spacing, crack width, and crack height respectively can capture the structural response and ultimate flexure capacity well. (3) Compared to intact RC slab, preloaded cracks in NSC in RC cannot influence the initial loading stage while it has an influence on ultimate flexure capacity in the strengthened slab under NBM. However, in the strengthened slab under PBM, preloaded existing cracks in NSC in RC influence both the initial loading stage and ultimate flexure capacity. (4) Studs were modeled by beam and solid elements, and the results show that the type of stud elements did not influence the response of UHPC-RC under NBM, while beam elements influenced the convergence of simulation of UHPC-RC under PBM. (5) Parameter study with factors affecting the ultimate flexure capacity of UHPC-RC was conducted after verification of FE modeling. With the increase of thickness of UHPC and diameter of steel reinforcement in UHPC and RC, the flexure capacity of UHPC-RC slab under NBM is increased while for UHPC-RC under PBM, the diameter of steel reinforcement in UHPC does not affect maximum force capacity. Both show that existing cracks cannot be neglected, affecting ultimate flexure capacity.

6.2. Strengthened slab under PBM The numerical results for parameter analysis of the strengthened slab under a PBM are shown in Table 11. From this table, the diameter of steel reinforcement inside the UHPC layer does not affect the maximum flexural capacity. This may be because the UHPC layer is located at a compression zone, and the failure mode for the PBM slab was controlled by the tension capacity of the NSC and steel reinforcement in the RC slabs. Therefore, a higher area of steel reinforcement in UHPC cannot improve any ultimate capacity. However, with an increase of the steel reinforcement diameter in RC, the ultimate flexure capacity increases the same as the strengthened slab with the NBM. On the contrary, with the increase of the steel reinforcement diameter in RC, the influence of existing cracks in RC on ultimate capacity gradually weakens. This may be because the steel reinforcement with larger diameter can better control cracks growth and propagation. It should be noted that as mentioned in section 5.3, the strengthened slab under PBM without simulation of cracking in RC slab get a closer result to the experimental one. Therefore, in Table 10, Fmax represents value close to experimental one while existing cracks induced in RC encourage FE modeling results much more close to the initial stage of experimental results with compromising ultimate flexure capacity in the range of

To sum up, the adhesion/cohesion strength between UHPC and NSC in strengthened slab should be taken account, and recent development in interfacial properties between UHPC and NSC without damage provides relatively accurate numerical results. Moreover, geometry 12

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discontinuous presents a certain degree of accuracy for simulation of cracked RC slab, explaining the stiffness reduction in damaged RC slabs strengthened by UHPC. However, more research on the effect of existing damage in NSC on interfacial properties of UHPC-NSC (such as the effect of the stress state of interface at the location of existing crack tips on interfacial conditions and crack initiation and propagation in the UHPC overlay) need to be conducted. Also, other more accurate alternative ways for simulation of existing cracks in RC slab need to be explored in the future.

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Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgments This research was made possible with the support of the National Natural Science Foundation of China Project (Grant 51578226 51578226 and 51778221). References [1] Noshiravani T, Brühwiler E. Rotation capacity and stress redistribution ability of RUHPFRC-RC composite continuous beams: an experimental investigation. Mater Struct Constr 2013;46:2013–28. https://doi.org/10.1617/s11527-013-0033-5. [2] Oesterlee C. Structural analysis of a composite bridge girder combining UHPFRC and reinforced concrete. High Perform Concr 2008:1–8. [3] Pimentel M, Nunes S. Experimental tests on RC beams reinforced with a UHPFRC layer failing in bending and shear. Proc 4th Int Symp Ultra-High Perform Concr High Perform Mater. 2016. [4] Prem PR, Murthy AR, Ramesh G, Bharatkumar BH, Iyer NR. Adv Struct Eng 2015. https://doi.org/10.1007/978-81-322-2190-6. [5] Habel K, Denarié E, Brühwiler E. Experimental investigation of composite ultrahigh-performance fiber-reinforced concrete and conventional concrete members. ACI Struct J 2007;104:93–101. https://doi.org/10.14359/18437. [6] Habel K, Denarié E, Brühwiler E. Time dependent behavior of elements combining ultra-high performance fiber reinforced concretes (UHPFRC) and reinforced concrete. Mater Struct Constr 2006;39:557–69. https://doi.org/10.1617/s11527-0059045-0. [7] Makita T. Modelling of fatigue behaviour of bridge deck slab elements strengthened with reinforced UHPFRC. Labmas 2014;12:2472–9. [8] Lee MG, Wang YC, Te Chiu C. A preliminary study of reactive powder concrete as a new repair material. Constr Build Mater 2007;21:182–9. https://doi.org/10.1016/j. conbuildmat.2005.06.024. [9] Graybeal B. Ultra-high performance concrete. Res Dev Technol Turner-Fairbank Highw Res Center 2011. FHWA Publi:8. doi:01342247. [10] Rossi P. Ultra-high performance fibre reinforced concretes UHPFRC an overview. Fifth RILEM Symp Fibre-Reinforced Concr – BEFIB’ 2000, 3036. 2004. p. 87–100. https://doi.org/10.5075/epfl-thesis-3036. [11] Safdar M, Matsumoto T, Kakuma K. Flexural behavior of reinforced concrete beams repaired with ultra-high performance fiber reinforced concrete (UHPFRC). Compos Struct 2016;157:448–60. https://doi.org/10.1016/j.compstruct.2016.09.010. [12] Al-Osta MA, Isa MN, Baluch MH, Rahman MK. Flexural behavior of reinforced concrete beams strengthened with ultra-high performance fiber reinforced concrete. Constr Build Mater 2017;134:279–96. https://doi.org/10.1016/j.conbuildmat. 2016.12.094. [13] Paschalis SA, Lampropoulos AP, Tsioulou O. Experimental and numerical study of the performance of ultra high performance fiber reinforced concrete for the flexural strengthening of full scale reinforced concrete members. Constr Build Mater 2018;186:351–66. https://doi.org/10.1016/j.conbuildmat.2018.07.123.

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