- Email: [email protected]
Finite element modelling of flexural behaviour of geosynthetic cementitious composite mat (GCCM)
Accepted Manuscript Finite element modelling of flexural behaviour of geosynthetic cementitious composite mat (GCCM) Tidarut Jirawattanasomkul, Nuttapong Kongwang, Pitcha Jongvivatsakul, Suched Likitlersunag PII:
S1359-8368(18)32099-7
DOI:
10.1016/j.compositesb.2018.07.052
Reference:
JCOMB 5819
To appear in:
Composites Part B
Received Date: 11 July 2018 Accepted Date: 23 July 2018
Please cite this article as: Jirawattanasomkul T, Kongwang N, Jongvivatsakul P, Likitlersunag S, Finite element modelling of flexural behaviour of geosynthetic cementitious composite mat (GCCM), Composites Part B (2018), doi: 10.1016/j.compositesb.2018.07.052. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
ACCEPTED MANUSCRIPT 1
Finite Element Modelling of Flexural Behaviour of Geosynthetic
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Cementitious Composite Mat (GCCM)
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Tidarut Jirawattanasomkul1, Nuttapong Kongwang2, Pitcha Jongvivatsakul3,* and
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Suched Likitlersunag4
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1. Assistant Professor, Department of Civil Engineering, Faculty of Engineering, Kasetsart
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University, Bangkok, Thailand. Email: [email protected]
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2. Master’s Candidate, Department of Civil Engineering, Faculty of Engineering, Kasetsart
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University, Bangkok, Thailand. Email: [email protected]
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3. Assistant Professor, Innovative Construction Materials Research Unit,
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Department of Civil Engineering, Faculty of Engineering, Chulalongkorn University,
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Bangkok, Thailand. Email: [email protected] (*Corresponding author)
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4. Professor, Geotechnical Research Unit, Department of Civil Engineering, Faculty of
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Engineering, Chulalongkorn University, Bangkok, Thailand. Email: [email protected]
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Abstract:
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This paper presents a finite element modelling of a new geosynthetic cementitious composite
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material called GCCM. The framework adopted a concept of concrete externally bonded by
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fibre-reinforced polymer (FRP). The existing bond-slip model was used to predict a flexural
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behaviour of GCCM, considering the effect of needle-punch process during manufacturing.
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The finite element modelling was calibrated against the experimental data of bending tests.
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The parameter optimisation was employed to define a set of the bond-slip model parameters.
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The analytical load-displacement curves predicted by the bond-slip model could agree well
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with those obtained from the experiments.
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Keywords: A. Fabrics/textiles; A. Layered structures; B. Fibre/matrix bond; C. Finite
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element analysis (FEA)
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No. of words in main text: 3,605
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No. of Tables: 8
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No. of Figures: 11
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ACCEPTED MANUSCRIPT Notation: bc bf
= Width of concrete prism
Ea Ef
= Elastic modulus of an adhesive = Elastic modulus of FRP or fabric woven material
' c
= Concrete cylinder compressive strength
ft Ga Gf
= Concrete tensile strength = Shear modulus of adhesive
Ka s sf
= Shear stiffness of adhesive layer = Local slip = Local slip when bond stress (τ ) reduces to zero
s0 ta
= Local slip at τ max
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= Interfacial fracture between fabric material and cement
= Thickness of an adhesive layer = Effective thickness of concrete/cement contributing to shear deformation
tc tf
= Thickness of FRP or fabric woven material = Width ratio factor = Local bond stress = Maximum local bond stress = Poisson’s ratio of adhesive
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βw τ τ max γa 33
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f
= Width of FRP or fabric woven material
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ACCEPTED MANUSCRIPT 1. Introduction
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Recently, a geosynthetic cementitious composite mat (GCCM) has been introduced by
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Paulson and Kohlman [1], Han et al. [2-4], Ramdit [5], and Jongvivatsakul et al. [6].
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According to this development, GCCM has many attractive properties such as high strength
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and stiffness after setting, and uniform thickness as well as it is simple to install in the field.
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Therefore, GCCM could be possibly used for slope stabilisation, erosion control, ditch lining,
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and containment. In addition, in early 2018, ASTM International has released a new standard
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guide for site preparation, layout, installation, and hydration of geosynthetic cementitious
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composite mats [7]. This event can be considered as a milestone to promote the GCCM in
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engineering applications.
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GCCM is a novel composite material comprised of two layers of geotextiles and a
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cement powder layer in the middle. After fabricating GCCM, its properties remarkably
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changed due to the needle-punched process [5, 6]. For example, although the fabric woven
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component shows the stiffness of 1,070 and 470 MPa in both length and width directions [5,
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6], these values were only from the fabric element test in which excludes the effect of needle
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punching. In reality, the needle punching significantly affects to the bond between fabric
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woven and cement in GCCM. Owing to this limitation in element test, the optimisation
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process is conducted to obtain the stiffness values of adhesive (representing needle-punched
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bond) and fabric materials for GCCM. Therefore, GCCM is assumed to exhibit behaviour
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similarly to that in concrete externally bonded with Fibre Reinforce Polymer (FRP) sheet.
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Since a fabric woven material is bonded with cement, GCCM therefore behaves like a
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composite material. As a result, FRP sheet can represent the woven materials both in width
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and length directions, whereas the interface between concrete and FRP sheet can represent
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the cement-to-woven fabric interface owing to needle-punching.
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ACCEPTED MANUSCRIPT In the Finite Element (FE) modelling, the existing modelling concept of FRP in
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GCCM is therefore adopt. In addition, the existing bond–slip models and some fundamental
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aspects of the behaviour of FRP-to-concrete interfaces [8-11] are used in the FE modelling.
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According to the previous experimental results [5, 6], a nonwoven material only helps water
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permeability and can rarely carry load. Consequently, such nonwoven layer can be ignored in
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the analysis of GCCM. In the FE analysis, optimised stiffness of both adhesive (Ea) and
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fabric woven (Ef) should carefully considered to account for needle-punched effect. The
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parametric optimisation with varied Ea and Ef was conducted to obtain the best fitted flexural
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load-displacement curves and crack patterns. From the analysis, the Ea-value is varied from
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100 to 600 MPa, whereas Ef-value is varied from 250 to 2,000 MPa. In addition, the
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analytical results show a good agreement when applied the bond-slip model proposed by Dai
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and Ueda [10].
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2. Geosynthetic cementitious composite mat
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2.1 Properties of GCCM components
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Geosynthetic cementitious composite mat (GCCM) is manufactured product comprised of
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two layers of geotextile and a dry cement layer bounded together with needle punching as
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shown in Fig. 1a. In practice, GCCM is formed into rolls with a dimension of 1 m in width
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and 3 m in length and weight of a roll about 30 kg, which can be carried by a person. Since
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the product is manufactured in the factory, the properties of GCCM are uniform comparing to
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the product that installed in the field. All components were bounded with needle-punching.
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The needle-punching with a density of 35 punches/cm2 caused some fibres from the top
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nonwoven geotextile to extend through the cement and bottom woven geotextile. GCCM is
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easy to install after spraying water on its surface for a certain curing time because of the
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hydration of cement in GCCM. After hardening GCCM becomes a solid material with high
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ACCEPTED MANUSCRIPT stiffness and tensile strength. In addition, the two geotextile layers at the top and bottom of
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GCCM can resist the large strain caused by the external load during operation. It is noted that
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the warp and weft directions in woven geotextile are associated with the length and width
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directions of the GCCM, respectively (see Fig. 1b). The detailed physical and mechanical
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properties of GCCM components are summarised in Table 1.
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2.2 Properties of GCCM
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2.2.1 Nominal thickness and mass per unit area
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To obtain a nominal thickness and mass per unit area, Jongvivatsakul et al. [6] prepared
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GCCM specimens using the ratio of water per GCCM weight (w/WGCCM) = 0.5, which is the
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saturated condition of GCCM. In their study, the GCCM was cured under water at ages of 1,
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3, and 7 days. The results showed that the nominal thickness were almost constant at 8.1 mm
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during 7 days, while the mass per unit area increased with curing time and was constant at
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1.35 g/cm2 after 7-day curing.
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2.2.2 Engineering properties of GCCM
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Engineering properties of GCCM were tested and reported as shown in Table 2. The GCCM
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can resist tensile, flexural, and puncher load. Figure 2a presents direct tensile test of GCCM.
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The tensile properties were different depending on loading direction (i.e. width direction or
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length direction). The tensile strength and stiffness of GCCM in width direction were higher
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than those of length direction. However, there was no difference of the maximum puncher
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load between the width and length directions. In addition, the GCCM is almost impermeable.
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2.2.3 Flexural behaviour of GCCM
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When the GCCM is used for slope protection, it will mainly resist bending stress under
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service condition. Therefore, the flexural behaviour of GCCM should be investigated. In the
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previous research [5, 6], the three-point bending tests of GCCM specimens with a size of 250
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ACCEPTED MANUSCRIPT × 250 mm specimens were performed as shown in Fig. 2b. In this test, nonwoven geotextile
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was on the upper side and woven geotextile was on the bottom of the GCCM specimens.
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Linear Variable Displacement Transducer (LVDT) was used for measuring mid-span
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deflection (Fig. 2b). The loading rate was 10 mm/min and load was applied until the mid-
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span deflection reached 40 mm. In the flexural test, a total of six specimens, Bending Length
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(denoted as BL.1-3) and Bending Width (denoted as BW.1-3), were tested.
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3. Finite Element modelling
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GCCM exhibited behaviour similarly to that in concrete externally bonded with Fibre
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Reinforce Polymer (FRP) sheet. Since a fabric woven material is bonded with cement,
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GCCM therefore behaves like a composite material. As a result, FRP sheet can represent the
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woven materials both in width and length directions, whereas the interface between concrete
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and FRP sheet can represent the cement-to-woven fabric interface owing to needle-punching.
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In the Finite Element (FE) modelling, the existing modelling concept of FRP in GCCM is
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therefore adopt. In addition, the existing bond–slip models and some fundamental aspects of
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the behaviour of FRP-to-concrete interfaces [8-10] are used in the FE modelling. According
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to the previous experimental results [5, 6], a nonwoven material only helps water
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permeability and can rarely carry load. Consequently, such nonwoven layer can be ignored in
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the analysis of GCCM.
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3.1 Stress-strain relationships
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3.1.1 Cement
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The stress-strain relationships of cement in compression are modelled with uniaxial
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behaviour based on CEB-FIP Model Code [12] and Hordijk [13], as shown in Fig. 3a. For
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cement in tension, the biaxial failure function for concrete proposed by Kupfer et al. [14] is
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ACCEPTED MANUSCRIPT applied (see Fig. 3b). In this study, the compressive strength of concrete at 7 days is equal to
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60 MPa from the compression test of the 50 mm × 50 mm in cube.
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3.1.2 Fabric woven materials
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The stress-strain relationships of woven material are according to both actual experimental
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result with a non-linear behaviour (Fig. 4a), and varied modulus of woven materials (Ef) for
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parametric optimisation with a linear behaviour (Fig. 4b). The actual experimental results
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show average value of Ef to be 470 MPa and 1,070 MPa for width and length direction,
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respectively. In the parametric optimisation, the Ef-values are varied from 250 to 2,000 MPa
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to represent stiffness of fabric woven materials with needle-punched effect.
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3.2 Bond-slip models
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3.2.1 Bond-slip model proposed by Nakaba et al. [8]
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Nakaba et al.’s stress-strain relationship is used to represent the local bond stress and slippage
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relationship with consideration of the concrete compressive stress-strain relationship. Their
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local bond stress-slip relationships, however, are not dependant on the type of fibre. They
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found that only increase of concrete compressive strength could lead to increase in the
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maximum local bond stress.
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In GCCM, the compressive strength of cement also controls the overall behaviour,
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especially in elastic stage. Therefore, the bond-slip relationship proposed by Nakaba et al.’s
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was used in the FEM and show nonlinear behaviour (see Fig. 5a). In Nakaba et al.’s
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experiment, the maximum local bond stress (τ max ) developed from 5.6 to 9.1 MPa with local
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bond slip at τmax ( s 0 ) developed approximately at 0.052 to 0.087 mm. From the best fitting
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analysis, τmax is equal to 3.5 f c'0.19 and s 0 is 0.065 mm. It is noted that their model is available
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only when concrete compressive strength ranges between 24-58 MPa. The stress-strain
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relationships [8] is shown in Eq. (1).
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ACCEPTED MANUSCRIPT 3 s s τ = τ max 3 / 2 + s0 s0
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(1)
where, τ max = 3.5 f c'0.19 and s0 = 0.065 mm.
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3.2.2 Bond-slip model proposed by Monti et al. [9]
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In Monti et al.’s model, uncracked and cracked concrete zones are considered. For uncracked
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zones, the effective bond length is used and the strain-bond fields are modelled along the
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anchorage length. For cracked zones, the model is used to predict the interaction between the
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two ends of a fabric material between two adjacent cracks.
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For the GCCM, the maximum bonding stress is calculated based on the ratio between
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width of the fabric woven material and cement as well as the tensile strength of cement. It
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should be noted that the slip at the maximum bonding strength depends on the thickness of
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adhesive ( t a ) as well as modulus of adhesive and cement ( E a and E c ). The local slip when
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bond stress reduces to zero (Sf) is calculated using the width of fabric woven and cement.
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Monti et al.’s model is expressed in Eqs. (2)-(3) and the bond-slip curve as a bilinear
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behaviour is shown in Fig. 5b.
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where,
s ; s ≤ s0 s0
τ = τ max
τ = τ max
sf − s s f − s0
; s > s0
(2)
(3)
t 50 τ max = 1.8β w f t , s0 = 2.5τ max a + , s f = 0.33β w , and E a Ec
βw =
1.5(2 − b f / bc ) 1 + b f / 100
.
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ACCEPTED MANUSCRIPT 3.2.3 Bond-slip model proposed by Dai and Ueda [10]
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Dai et al. [10, 11] found that not only increasing fabric stiffness but also decreasing
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adhesive’s shear stiffness affect to the enhancement of the interfacial performance of fabric
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sheets bonded to concrete. Dai and Ueda model [10] presented two separated equations to
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explain pre-peak and post-peak behaviours of the bond-slip interface, whereas Dai et al. [11]
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later simplified their former model to a unified equation. Owing to the experimental results
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[6], the pre-peak behaviour of GCCM is clearly dominated by cement, while the post-peak is
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mainly behaved by the woven geosynthetic. Therefore, bond-slip model proposed in Dai and
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Ueda [10] can be applied in the analysis to precisely characterise behaviour of GCCM. In
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their models, the interfacial fracture energy is applied owing to the good toughness and
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nonlinearity of low shear stiffness in adhesives. This leads to efficient use of the fabric woven
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material with high strength. A nonlinear interfacial bond stress-slip model is included. Their
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concerned parameters in the model are the fracture energy and two other empirical constants
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α and β, which govern the ascending and descending parts of the interfacial bond-stress slip
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curves, respectively.
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For GCCM, the compressive strength of cement are taken into account with the shear
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stiffness of adhesive in terms of the interfacial fracture ( G f ). The modulus and thickness of
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fabric woven material are included in the model. The bond-slip model proposed in Dai and
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Ueda [10] is expressed in Eqs. (4) - (5), while the bond-slip curve as a nonlinear behaviour is
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shown in Fig. 5c.
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s τ = τ max s0
0.575
; s ≤ s0
(4)
τ = τ max e − β ( s − s ) ; s > s0
(5)
0
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where,
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ACCEPTED MANUSCRIPT − 1.575αK a + 2.481α 2 K a2 + 6.3αβ 2 K a G f
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τ max =
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s0 = τ max /(αK a ) , β = 0.0035 K a ( E f t f / 1000 ) 0.34
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α = 0.028 ( E f t f / 1000 ) 0.254 , K a = Ga / t a , Ga =
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G f = 7.554 K a−0.449 ( f c' ) 0.343
2β
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Ea , 2(1 + γ a )
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4. Parameter optimisation
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After fabricating GCCM, its properties remarkably changed due to the needle-punched
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process [6]. Although the fabric woven component shows the stiffness of 1,070 and 470 MPa
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in both length and width directions (see Table 1), these values were only from the fabric’s
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element test in which excludes the effect of needle punching. In reality, the needle punching
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significantly affects to the bond between fabric woven and cement in GCCM. Therefore,
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optimised stiffness of both adhesive (Ea) and fabric woven (Ef) should carefully considered in
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the FE analysis. The parametric optimisation with varied Ea and Ef was conducted to obtain
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the best fitted flexural load-displacement curves and crack patterns. In the analysis, the Ea-
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value is varied from 100 to 600 MPa, whereas Ef-value is varied from 250 to 2,000 MPa.
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Table 3 is a summary of parameters considered in the FE modelling.
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In this research, the 2D ATENA program was implemented to perform FE analysis of
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GCCM. Figure 6 represents the finite element mesh with a size of 5 mm and a simple-support
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as a boundary condition. The model was developed based on the plane stress state in which
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three layers of GCCM’s component were combined, as shown in Fig. 6. Fabric woven and
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cement layers were bonded following the existing bond-slips models [8-11]. For concrete, the
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CC3DNonLinCementitious2 provided by ATENA was used with the fixed crack model. The
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compressive strength of cement (Fig. 3a) was specified in the numerical model. Then, the 11
ACCEPTED MANUSCRIPT other characteristics were automatically generated based on the stress-strain relationship used
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in the CC3DNonLinCementitious2 [15]. For a fabric woven, a discrete element was modelled
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based on truss element and connected to the cement layer using the existing bond behaviours.
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In addition, the nonwoven layer can be ignored in the analysis of GCCM since it cannot carry
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any load.
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4.1 Proposed bond-slip models
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Since needle-punched process affects to bonding and flexural behaviour of GCCM, existing
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models should be taken into account in the analysis. Bond-slip models proposed by Nakaba et
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al. [8], Monti et al. [9], and Dai et al. [10,11] were used to predict the load-displacement of
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GCCM subjected to a flexural load. In the FE modelling, the Ef-values in both length and
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width directions were 1,070 and 470 MPa based on the experimental results (see Table 1).
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Figure 7 shows load-displacement curves of GCCM under flexural load obtained from
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experiment and analysis. Regarding Nakaba et al. [8], their model is simplified, accounting
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for only compressive strength of cement or concrete (f’c). As a result, the analytical bond
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properties are lack of the effect of Ef- and Ea- values. Regarding Monti et al. [9], their model
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focuses only on a linear bond-slip behaviour so it insufficiently represent a nonlinear bond-
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slip of GCCM. Regarding Dai and Ueda [10], their model could capture nonlinear behaviour
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in both cracking and ultimate stages, while well explaining every characteristic of composite
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materials such as shear modulus of adhesive, interfacial fracture of and compressive strength
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of cement (see Eqs. (4) - (5) and Fig. 7). However, Figure 7 shows that using experimental
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value of Ef (1,070 and 470 for length and width) could still lead to discrepancies in load-
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deflection curve of the flexural test because of absence in needled-punch procedure.
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Therefore, in this parametric optimisation the bond-slip model proposed by Dai and Ueda
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[10] is carefully implemented with varied Ef- and Ea in the FE modelling.
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4.2 Optimised stiffness parameters from flexural test
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ACCEPTED MANUSCRIPT 4.2.1 Stiffness of adhesive bonding materials (Ea)
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As mentioned previously, the optimised stiffness of adhesive bonding materials (Ea) should
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be carried out in the analysis to obtain the best fitted flexural behaviour of GCCM. With
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varied Ea, the minimum value of Residual Sum of Square (RSS) and maximum value of
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coefficient of determination (R2) should be achieved. The RSS with unit of N2 is the sum of
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the squares of residuals, calculated from the discrepancies between the experimental and
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analytical results [16, 17], whereas the R2-value with non-unit used in this study is the
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estimation of the parameters in a linear regression model. The flexural loads at every
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incremental displacement of 5 mm are chosen to compare those discrepancies of results when
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the Ea as a main parameter is varied from 100 to 600 MPa for fabric woven materials in both
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length and width directions. This Ea can significantly represent different level of GCCM’s
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needle punching, leading to various bonding stresses between fabric woven and cement
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materials.
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4.2.2 Stiffness of woven materials (Ef)
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The Ef can represent properties of woven fabric after needle punching. Similarly to Ea, the
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same optimisation procedure is also implemented for Ef with a range of 250-2,000 MPa. The
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optimisation of both Ea and Ef were performed simultaneously in the FE modelling. The Ea-
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and Ef- values are altered until the minimum RSS and maximum R2 are achieved. Tables 4-7
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show RSS- and R2- values obtained from FE models of GCCM in both length and width
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directions. The optimised Ea of 450 MPa can achieve minimum RSS of 3,281 and 1,076 N2
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for the optimised Ef of 750 and 1,750 MPa in both length and width, respectively. At the
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same time, such Ea–and Ef–values lead to the maximum R2 values of 0.902 and 0.987 in both
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length and width, respectively. It can be concluded that the optimised Ea representing needle-
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punched bonding in GCCM should be equal to 450 MPa. Opposite to the fabric woven test,
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ACCEPTED MANUSCRIPT the optimised Ef in the length direction (750 MPa) is smaller than that from the test (1,070
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MPa), whereas the optimised Ef in the width direction (1,750 MPa) is higher than that in the
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test (470 MPa). This is because the GCCM’s behaviour changed after fabricating with
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needle-punched procedure.
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5. Results and discussions
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5.1 Load-displacement curves of flexural test
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The experimental and analytical results using bond-slip model by Dai et al. [10] with varied
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Ea are compared, as shown in Fig. 8. These varied Ea of 100, 450 and 600 MPa were input in
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the FE modelling. Decreasing Ea to 100 MPa leads to fluctuated load-deflection curves in
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both length and width (see Fig. 8). Increasing Ea to 450 MPa with Ef of 750 and 1,750 MPa in
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length and width directions, the analytical load-deflection curves agree well with that
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obtained from experiment in all specimens.
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Figure 9 shows comparison of the experiment and analytical results using bond-slip
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model by Dai et al. [10,11] with varied Ef. With Ea of 450 MPa, the optimised Ef of 750 and
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1,750 MPa in length and width directions can provide good analytical load-deflection curves,
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especially in specimen BL.2 (Fig. 9a) and BW.2 (Fig. 9b). It is found that increasing of Ef to
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1,000 MPa in length direction causes over-estimation of the peak load, whereas decreasing of
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Ef to 500 MPa in width direction leads to under-estimation of the peak load.
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Overall, Ea of 450 MPa with the optimised Ef of 750 and 1,750 MPa in length and
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width directions can also help predict both loads at first crack (Pfirst-crack) and ultimate
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(Pultimate) very well. In Table 8, the percent differences of Pfirst-crack between experiment and
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FEM are only 23.9% and 19.4% when optimised Ea is equal to 450 MPa, and optimised Ef is
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750 and 1,750 MPa for length and width directions, respectively. With same optimised
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values, the percent differences of Pultimate is 6.0% and 7.9% for length and width directions,
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respectively.
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5.2 Crack patterns and failure modes
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A crack patterns and failure modes of the bending specimens BL.2 and BW.2 at first crack is
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presented in Figs. 10a and 11a. It can be seen that the crack patterns from analysis agree well
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with that from experiment (see Figs. 10 and 11). In the optimised procedure, it is also found
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that crack width becomes smaller with better crack distribution when increasing Ef. For
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example, increasing Ef to 2,000 MPa in width direction can cause absence of major cracks
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owing to higher maximum local bond stress (τmax). In Dai and Ueda [10], such higher τmax
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leads to higher local bond stress (τ), causing difficulty of slip between fabric woven and
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cement materials.
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6. Conclusions
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The work has presented an optimisation study on the flexural of GCCM as well as the
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modelling of this behaviour by 2D Nonlinear FEM. The GCCM analysed in the study is
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expected to resist the bearing load during the slope protection, causing the flexural stress.
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Based on the results and discussions presented in the paper, the following conclusions can be
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drawn up:
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1) During fabricating process of GCCM, the needle-punched process changed GCCM
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properties drastically. Therefore, optimisation for stiffness of adhesive (representing needle
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punching) and stiffness of fabric woven material were conducted. From the analytical results,
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GCCM can be modelled using the concept of concrete externally bonded by FRP. In the
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models, FRP represents fabric woven layer whereas cement represents concrete layer. The
317
interface between fabric woven and cement was based on using existing bond-slip models.
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2) The existing bond-slip model by Dai and Ueda [10] could successfully predict
319
flexural behaviour of GCCM, considering needle-punched effect. This needle-punched effect
320
was included in terms of the stiffness of adhesive material. The analytical load-displacement
321
curves with the bond-slip model could agree well with that obtained from the experiment. 3) To represent needle-punched effect, two parametersstiffness of adhesive, Ea and
323
stiffness of fabric material, Efwere optimised to achieve prediction of flexural behaviour as
324
well as crack patterns. From the optimisation process, the optimised Ea is 450 MPa whereas
325
the optimised Ef are 750 and 1,750 MPa for GCCM in both length and width direction. These
326
values will be useful for future prediction of GCCM behaviours when the material testing
327
results are very limited.
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4) In the current study, the calculation is still based on a small strain analysis
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constraining by cracking of cement. In real geotechnical application, large strain analysis may
330
be required for slope stability and deformation analysis. This should be considered in the
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future.
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Acknowledgements
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The research was supported by the Thailand Research Fund Grant No. DBG-6180004 and the
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Ratchadapisek Sompoch Endowment Fund (2017), Chulalongkorn University (760003-CC).
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Authors would like to thank Siam Cement Group (SCG) for supporting materials during tests.
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Endorsement by SCG is not implied and should not be assumed. The first author would also
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like to acknowledge the TRF grant No. TRG5880266. The second author would also like to
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acknowledge Master’s scholarship granted from Faculty of Engineering, Kasetsart
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University, Thailand.
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References
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[1]
Paulson J, Kohlman R. The geosynthetic concrete composite mat (GCCM). In: Current
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and Future Practices for the Testing of Multi-Component Geosynthetic Clay Liners.
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STP
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doi:10.1520/STP156220120087 [2]
Pennsylvania:
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p.146–154.
Han FY, Chen HS, Jiang KF, Zhang WL, Lv T, Yang YJ. Influences of geometric
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1562.
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patterns of 3D spacer fabric on tensile behavior of concrete canvas. Constr Build Mat
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2014;65:620-629. doi:10.1016/j.conbuildmat.2014.05.041 [3]
Han FY, Chen HS, Li XY, Bao BC, Lv T, Zhang WL, Duan WH. Improvement of
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mechanical properties of concrete canvas by anhydrite modified calcium sulfoaluminate
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cement. J Compos Mater 2016;50(14):1937-1950. doi:10.1177/0021998315597743
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[4]
Han FY, Chen HS, Zhang WL, Lv T, Yang YJ. Influence of 3D spacer fabric on drying
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shrinkage
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doi:10.1177/1528083714562087 [5]
concrete
canvas.
Journal
In:
Text
2016;45(6):1457-1476.
Ramdit T. Laboratory Investigation of Geosynthetic Cement Ccomposite Properties. Master Thesis. Chulalongkorn University; 2017.
357 358
of
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Jongvivatsakul P, Ramdit T, Ngo TP, Likitlersuang S. Experimental investigation on mechanical properties of geosynthetic cementitious composite mat (GCCM). Constr
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Build Mat 2018;166:956–965. doi:10.1016/j.conbuildmat.2018.01.185 [7]
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ASTM-D8173. Site Preparation, Layout, Installation, and Hydration of Geosynthetic
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Cementitious Composite Mats. ASTM International, West Conshohocken, PA, USA,
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2018.
364 365
[8]
Nakaba K, Kanakubo T, Furuta T, Yoshizawa H. Bond behavior between fiberreinforced polymer laminates and concrete. ACI Struct J 2001;98(3):359-367.
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[9]
Monti G, Renzelli M, Luciani P. FRP adhesion in uncracked and cracked concrete
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zones. In: Fibre-Reinforced Polymer Reinforcement for Concrete Structures: (In 2
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Volumes), 2003. p. 183-192. [10] Dai JG, Ueda T. Local bond stress slip relations for FRP sheets-concrete interfaces. In:
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Proceeding of 6th international symposium on FRP reinforcement for concrete
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structures. Singapore: World Scientific Publications, 2003. p.143-152.
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[11] Dai JG, Ueda T, and Sato Y. Development of the nonlinear bond stress–slip model of
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fiber reinforced plastics sheet–concrete interfaces with a simple method. Journal of
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composites for construction, 2005;9(1): 52-62.
379 380 381 382 383 384 385 386
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[13] Hordijk, PA. Local approach to fatigue of concrete. Doctoral Thesis, Delft University. 1991.
[14] Kupfer H, Hilsdorf HK, and Rusch H. Behavior of concrete under biaxial stresses. In:
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1991; 87-109.
Journal Proceedings of American Concrete Institute, 1969;66(8):656-666. [15] Cervenka V, Jendele L, and Cervenka J. ATENA Program Documentation, Part 1: Theory. Cervenka Consulting, Prague, 2007. p. 231.
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[12] CEB-FIP, CEB-FIP Model Code 1990. Comitee Euro-International Du Beton, Paris,
[16] Rawlings JO, Pantula SG, and Dickey DA. Applied regression analysis: a research tool.
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Springer Science & Business Media, 2001. [17] Devore JL. Probability and Statistics for Engineering and the Sciences. Brooks/Cole, Cengage Learning, Boston, 2015.
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ACCEPTED MANUSCRIPT Table captions Table 1 Mechanical and physical properties of GCCM component [5, 6] Table 2 Mechanical and physical properties of GCCM [5, 6] Table 3 Parameters in FEM program Table 4 Residual Sum of Square (RSS) of Length direction models
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Table 5 Residual Sum of Square (RSS) of Width direction models Table 6 Coefficient of determination ( R 2 ) of Length direction models Table 7 Coefficient of determination ( R 2 ) of Width direction models
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Table 8 Summary of experimental and FEM results with varied Ef
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Table 1 Mechanical and physical properties of GCCM Component [5, 6] GCCM Fabrics Properties Cement Woven paste Non-woven Width (Weft) Length (Warp) Thickness (mm) 3.87 0.48 3.75 2 Weight (g/m ) 279 168 1.31x104 Punch density (punch/cm2) 35 35 35 Ultimate elongation (%) 118.62 45.98 32.66 Tensile strength (MPa) 1.00 72.05 71.70 Compressive strength at 7 days (MPa) 60.9 Young’s modulus (MPa) 470 1,070
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Table 2 Mechanical and physical properties of GCCM [5, 6] GCCM* Properties Width Direction Length Direction Thickness (mm) 8.10 ± 0.05 2 Mass per unit (g/cm ) 1.35 ± 0.07 2 35 Punch density (punch/cm ) Tensile strength** (kN/m) 26.50 ± 0.42 16.25 ± 0.84 Tensile stiffness (MPa) 710.30 219.79 Bending strength (MPa) 11.28 ± 0.15 7.75 ± 0.28 Maximum puncture load (kN) 1.60 ± 0.02 Permeability (cm/s) 7.03 ± 0.89 x 10-7 Note: *Properties of GCCM at 28 days are reported. **Tensile strength is defined as maximum tensile force per unit width of material.
ACCEPTED MANUSCRIPT Table 3 Parameters in FEM program Specimen Parameters Length and Width Direction
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100 200 300 E a (MPa ) 400 450 500 600 250 500 750 1,000 E f (MPa ) 1,250 1,500 1,750 2,000 Note: E a and E f are stiffness modulus of bonding and woven materials, respectively.
ACCEPTED MANUSCRIPT Table 4 Residual Sum of Square (RSS) of Length direction models E f (MPa )
E a (MPa )
100 200 300 400 450 500 600
250
500
750
1,000
1,250
1,500
1,750
2,000
69,510 68,589 84,552 82,035 105,281 101,685 107,588
6,956 14,019 17,783 14,433 33,063 30,124 34,407
5,764 5,619 4,989 4,490 3,281 3,493 5,236
25,304 39,660 11,469 7,530 9,291 6,877 4,851
65,838 55,427 44,659 39,509 20,851 18,782 44,906
140,589 75,653 99,678 108,742 115,814 80,868 108,529
149,237 134,043 131,144 96,909 132,643 102,360 113,775
189,017 44,090 298,995 306,139 242,546 288,471 283,740
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Parameters
Table 5 Residual Sum of Square (RSS) of Width direction models 250
500
750
1,000
372,730 373,519 408,515 404,708 456,303 448,490 458,177
180,784 215,216 229,432 213,715 277,940 272,305 281,784
87,354 86,454 159,326 156,813 152,067 154,062 159,114
46,406 27,432 73,546 82,030 81,714 95,448 102,435
∧
1,250
1,500 1,750
2,000
11,417 18,156 24,215 28,559 53,350 57,085 25,726
3,137 8,969 3,997 1,940 1,291 6,990 1,974
11,453 26,364 38,689 42,043 19,333 34,563 32,477
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E f (MPa )
Parameters
4,235 1,597 1,664 6,208 1,076 4,467 1,580
∧
Note: RSS = ∑ ( y i − y i ) 2 Where yi is the experiment values and the modelled value is y i i
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-1.069 -1.042 -1.517 -1.442 -2.134 -2.027 -2.203
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E a (MPa )
100 200 300 400 450 500 600
E f (MPa )
500
750
1,000
1,250
1,500
1,750
2,000
0.793 0.583 0.471 0.570 0.016 0.103 -0.024
0.828 0.833 0.851 0.866 0.902 0.896 0.844
0.247 -0.181 0.659 0.776 0.723 0.795 0.856
-0.960 -0.650 -0.330 -0.176 0.379 0.441 -0.337
-3.186 -1.252 -1.968 -2.237 -2.448 -1.408 -2.231
-3.443 -2.991 -2.904 -1.885 -2.949 -2.047 -2.387
-4.627 -0.313 -7.901 -8.114 -6.221 -7.588 -7.447
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Table 6 Coefficient of determination ( R 2 ) of Length direction models
ACCEPTED MANUSCRIPT Table 7 Coefficient of determination ( R 2 ) of Width direction models Parameters
E f (MPa )
250
500
750
1,000
1,250
1,500
1,750
2,000
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-1.187 -0.057 0.438 0.862 0.962 0.949 0.861 100 -3.510 -1.604 -0.046 0.668 0.780 0.891 0.981 0.681 200 -3.520 -1.776 -0.928 0.110 0.707 0.952 0.980 0.532 300 -3.943 E a (MPa ) 400 -3.897 -1.586 -0.897 0.007 0.654 0.977 0.925 0.491 -2.363 -0.840 0.011 0.354 0.984 0.987 0.766 450 -4.521 -4.427 -2.295 -0.864 -0.155 0.309 0.915 0.946 0.582 500 -2.410 -0.925 -0.239 0.689 0.976 0.981 0.607 600 -4.544 RSS Note: R 2 = 1 − In which RSS = the residual sum of square can be computed from RSS = TSS ∧
∧
i _
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∑ ( y i − y i ) 2 where yi is the experiment values and the modelled value is y i ; TSS = the total sum of square can be computed from TSS = ∑ ( y i − y i ) 2 where yi is the experiment values i
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Table 8 Summary of experimental and FEM results with varied Ef ACCEPTED MANUSCRIPT Ef
(MPa)
(MPa) 500 750 1000 1500 1750 2000
Specimen Length direction
450
Width direction
450
Pfirst-crack Experiment (N) 174.6 174.6 174.6 184.3 184.3 184.3
Pfirst-crack FEM (N) 215.5 216.4 217.3 219.1 220.0 220.9
Pultimate Experiment (N) 334.1 334.1 334.1 478.0 478.0 478.0
Pultimate FEM (N) 264.7 354.2 414.5 521.9 515.8 635.0
wfirst-crack FEM (mm) 8.499x10-4 8.456x10-4 8.414x10-4 8.334x10-4 8.296x10-4 8.260x10-4
Difference of Pfirst-crack (%) 23.4 23.9 24.5 18.9 19.4 19.9
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Ea
Difference of Pultimate (%) -20.8 6.0 24.1 9.2 7.9 32.8
Note: Pfirst-crack and wfirst-crack = loads and crack widths at the first-crack stage, and Pfirst − crack ( FEM ) − Pfirst − crack ( Experiment) × 100 and Difference of Pfirst-crack and Pultimate are calculated from Pfirst − crack ( Experiment)
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Pultimate ( FEM ) − Pultimate ( Experiment ) × 100 , respectively. Pultimate ( Experiment )
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Figure captions Figure 1
Geosynthetic Cementitious Composite Mat (GCCM) [5,6]
Figure 2
Experimental programs [5,6]
Figure 3
Stress-strain relationships of concrete in compression and tension [12-14]
Figure 4
Stress-strain relationship of the woven material (Ef) in experiment and FEM model Bond-slip models for the bonding material
Figure 6
2D Nonlinear Finite Element Modelling
Figure 7
Load-deflection curve of the flexural test with varied bond-slip models
Figure 8
Comparison of the experiment and analytical results using bond-slip model by Dai and Ueda [10] with varied Ea
Comparison of the experiment and analytical results using bond-slip model by Dai and Ueda [10] with varied Ef
Crack width of the analytical GCCM of Length Direction at first crack (Ea =450
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MPa) Figure 11
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Figure 9
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Crack width of the analytical GCCM of Width Direction at first crack (Ea =450
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MPa)
Woven
Width direction
Needle-punched GCCM Cross section
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Cement powder layer
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Length direction
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b) Final product of GCCM
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Figure 1 Geosynthetic Cementitious Composite Mat (GCCM) [5, 6]
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b) Bending Test Setup
a) Tensile Test Setup
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Figure 2 Experimental programs [5, 6]
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Tensile failure
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f ‘c from experiment = 60 MPa at 7 days 50 mm x 50 mm in cube
Compressive failure
b) Biaxial stress failure criterion according to Kupfer et al. [14]
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a) Stress-strain relationships of concrete in compression and tension [12, 13]
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Figure 3 Stress-strain relationships of concrete in compression and tension [12-14]
ACCEPTED MANUSCRIPT Stress
Stress
Ef–FEM varied from 250-2,000 MPa
Ef-exp average = 470 MPa
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(width), 1070 MPa (length)
Strain
Strain
b) FEM model – linear behavior
a) Experiment – nonlinear behavior
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Figure 4 Stress-strain relationship of the woven material (Ef) in experiment and FEM model
MANUSCRIPT Bond stress, ACCEPTED τ 3 s s τ = τ max 3 / 2 + s0 s0
τmax
where,
τ max = 3.5 f c'0.19
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S0
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a) Nakaba et al. [8] Bond stress, τ
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b) Monti et al. [9]
Bond stress, τ
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τmax
S0
c) Dai and Ueda [10] Figure 5 Bond-slip models
; s ≤ s0 ; s > s0
Slip, s
ACCEPTED MANUSCRIPT 215 mm
8.1 mm Non-woven 3.87 mm thickness Cement 3.75 mm thickness Woven 0.48 mm thickness y
2
y
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x
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Figure 6 2D Nonlinear Finite Element Modelling
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600 500
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Load (N)
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Monti et al. [9]
100 0 0
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[8] Nakaba et al. (2001)
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Experiment (BL.2)
[9] Monti et al. (2003)
Experiment (BL.3)
Dai and [10] Ueda andUeda Dai (2004)
a) Length direction (Ef = 1,070 MPa)
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Experiment (BW.1)
[8] Nakaba et al. (2001)
Experiment (BW.2)
[9] Monti et al. (2003)
Experiment (BW.3)
Dai and [10] Ueda andUeda Dai (2004)
b) Width direction (Ef = 470 MPa) Figure 7 Load-deflection curve of the flexural test with varied bond-slip models
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Ea = 600 Ea= 450
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Experiment (BL.1) Experiment (BL.2) Experiment (BL.3)
FEM Model (Ea 100) FEM Model (Ea 450) FEM Model (Ea 600)
a) Length direction (Ef = 750 MPa) 600
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Experiment (BW.2)
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Experiment (BW.3) FEM Model (Ea 600) b) Width direction (Ef = 1,750 MPa) Figure 8 Comparison of the experiment and analytical results using bond-slip model by Dai and Ueda [10] with varied Ea
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Ef = 1000
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a) Actual failure of BL.2
Maximum Crack Width = 0.0045 mm.
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b) Crack pattern Length Direction Model Ef = 500
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a) Actual failure of BW.2
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d) Crack pattern of Width Direction Model Ef = 2000
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Figure 11 Crack width of the analytical GCCM of Width Direction at first crack (Ea = 450 MPa)
S1359-8368(18)32099-7
DOI:
10.1016/j.compositesb.2018.07.052
Reference:
JCOMB 5819
To appear in:
Composites Part B
Received Date: 11 July 2018 Accepted Date: 23 July 2018
Please cite this article as: Jirawattanasomkul T, Kongwang N, Jongvivatsakul P, Likitlersunag S, Finite element modelling of flexural behaviour of geosynthetic cementitious composite mat (GCCM), Composites Part B (2018), doi: 10.1016/j.compositesb.2018.07.052. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
ACCEPTED MANUSCRIPT 1
Finite Element Modelling of Flexural Behaviour of Geosynthetic
2
Cementitious Composite Mat (GCCM)
3
Tidarut Jirawattanasomkul1, Nuttapong Kongwang2, Pitcha Jongvivatsakul3,* and
5
Suched Likitlersunag4
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1. Assistant Professor, Department of Civil Engineering, Faculty of Engineering, Kasetsart
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University, Bangkok, Thailand. Email: [email protected]
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2. Master’s Candidate, Department of Civil Engineering, Faculty of Engineering, Kasetsart
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University, Bangkok, Thailand. Email: [email protected]
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3. Assistant Professor, Innovative Construction Materials Research Unit,
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Department of Civil Engineering, Faculty of Engineering, Chulalongkorn University,
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Bangkok, Thailand. Email: [email protected] (*Corresponding author)
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4. Professor, Geotechnical Research Unit, Department of Civil Engineering, Faculty of
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Engineering, Chulalongkorn University, Bangkok, Thailand. Email: [email protected]
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Abstract:
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This paper presents a finite element modelling of a new geosynthetic cementitious composite
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material called GCCM. The framework adopted a concept of concrete externally bonded by
20
fibre-reinforced polymer (FRP). The existing bond-slip model was used to predict a flexural
21
behaviour of GCCM, considering the effect of needle-punch process during manufacturing.
22
The finite element modelling was calibrated against the experimental data of bending tests.
23
The parameter optimisation was employed to define a set of the bond-slip model parameters.
24
The analytical load-displacement curves predicted by the bond-slip model could agree well
25
with those obtained from the experiments.
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Keywords: A. Fabrics/textiles; A. Layered structures; B. Fibre/matrix bond; C. Finite
28
element analysis (FEA)
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No. of words in main text: 3,605
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No. of Tables: 8
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No. of Figures: 11
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2
ACCEPTED MANUSCRIPT Notation: bc bf
= Width of concrete prism
Ea Ef
= Elastic modulus of an adhesive = Elastic modulus of FRP or fabric woven material
' c
= Concrete cylinder compressive strength
ft Ga Gf
= Concrete tensile strength = Shear modulus of adhesive
Ka s sf
= Shear stiffness of adhesive layer = Local slip = Local slip when bond stress (τ ) reduces to zero
s0 ta
= Local slip at τ max
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= Interfacial fracture between fabric material and cement
= Thickness of an adhesive layer = Effective thickness of concrete/cement contributing to shear deformation
tc tf
= Thickness of FRP or fabric woven material = Width ratio factor = Local bond stress = Maximum local bond stress = Poisson’s ratio of adhesive
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ACCEPTED MANUSCRIPT 1. Introduction
35
Recently, a geosynthetic cementitious composite mat (GCCM) has been introduced by
36
Paulson and Kohlman [1], Han et al. [2-4], Ramdit [5], and Jongvivatsakul et al. [6].
37
According to this development, GCCM has many attractive properties such as high strength
38
and stiffness after setting, and uniform thickness as well as it is simple to install in the field.
39
Therefore, GCCM could be possibly used for slope stabilisation, erosion control, ditch lining,
40
and containment. In addition, in early 2018, ASTM International has released a new standard
41
guide for site preparation, layout, installation, and hydration of geosynthetic cementitious
42
composite mats [7]. This event can be considered as a milestone to promote the GCCM in
43
engineering applications.
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GCCM is a novel composite material comprised of two layers of geotextiles and a
45
cement powder layer in the middle. After fabricating GCCM, its properties remarkably
46
changed due to the needle-punched process [5, 6]. For example, although the fabric woven
47
component shows the stiffness of 1,070 and 470 MPa in both length and width directions [5,
48
6], these values were only from the fabric element test in which excludes the effect of needle
49
punching. In reality, the needle punching significantly affects to the bond between fabric
50
woven and cement in GCCM. Owing to this limitation in element test, the optimisation
51
process is conducted to obtain the stiffness values of adhesive (representing needle-punched
52
bond) and fabric materials for GCCM. Therefore, GCCM is assumed to exhibit behaviour
53
similarly to that in concrete externally bonded with Fibre Reinforce Polymer (FRP) sheet.
54
Since a fabric woven material is bonded with cement, GCCM therefore behaves like a
55
composite material. As a result, FRP sheet can represent the woven materials both in width
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and length directions, whereas the interface between concrete and FRP sheet can represent
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the cement-to-woven fabric interface owing to needle-punching.
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GCCM is therefore adopt. In addition, the existing bond–slip models and some fundamental
60
aspects of the behaviour of FRP-to-concrete interfaces [8-11] are used in the FE modelling.
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According to the previous experimental results [5, 6], a nonwoven material only helps water
62
permeability and can rarely carry load. Consequently, such nonwoven layer can be ignored in
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the analysis of GCCM. In the FE analysis, optimised stiffness of both adhesive (Ea) and
64
fabric woven (Ef) should carefully considered to account for needle-punched effect. The
65
parametric optimisation with varied Ea and Ef was conducted to obtain the best fitted flexural
66
load-displacement curves and crack patterns. From the analysis, the Ea-value is varied from
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100 to 600 MPa, whereas Ef-value is varied from 250 to 2,000 MPa. In addition, the
68
analytical results show a good agreement when applied the bond-slip model proposed by Dai
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and Ueda [10].
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2. Geosynthetic cementitious composite mat
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2.1 Properties of GCCM components
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Geosynthetic cementitious composite mat (GCCM) is manufactured product comprised of
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two layers of geotextile and a dry cement layer bounded together with needle punching as
75
shown in Fig. 1a. In practice, GCCM is formed into rolls with a dimension of 1 m in width
76
and 3 m in length and weight of a roll about 30 kg, which can be carried by a person. Since
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the product is manufactured in the factory, the properties of GCCM are uniform comparing to
78
the product that installed in the field. All components were bounded with needle-punching.
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The needle-punching with a density of 35 punches/cm2 caused some fibres from the top
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nonwoven geotextile to extend through the cement and bottom woven geotextile. GCCM is
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easy to install after spraying water on its surface for a certain curing time because of the
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hydration of cement in GCCM. After hardening GCCM becomes a solid material with high
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GCCM can resist the large strain caused by the external load during operation. It is noted that
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the warp and weft directions in woven geotextile are associated with the length and width
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directions of the GCCM, respectively (see Fig. 1b). The detailed physical and mechanical
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properties of GCCM components are summarised in Table 1.
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2.2 Properties of GCCM
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2.2.1 Nominal thickness and mass per unit area
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To obtain a nominal thickness and mass per unit area, Jongvivatsakul et al. [6] prepared
92
GCCM specimens using the ratio of water per GCCM weight (w/WGCCM) = 0.5, which is the
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saturated condition of GCCM. In their study, the GCCM was cured under water at ages of 1,
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3, and 7 days. The results showed that the nominal thickness were almost constant at 8.1 mm
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during 7 days, while the mass per unit area increased with curing time and was constant at
96
1.35 g/cm2 after 7-day curing.
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2.2.2 Engineering properties of GCCM
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Engineering properties of GCCM were tested and reported as shown in Table 2. The GCCM
99
can resist tensile, flexural, and puncher load. Figure 2a presents direct tensile test of GCCM.
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The tensile properties were different depending on loading direction (i.e. width direction or
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length direction). The tensile strength and stiffness of GCCM in width direction were higher
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than those of length direction. However, there was no difference of the maximum puncher
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load between the width and length directions. In addition, the GCCM is almost impermeable.
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2.2.3 Flexural behaviour of GCCM
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When the GCCM is used for slope protection, it will mainly resist bending stress under
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service condition. Therefore, the flexural behaviour of GCCM should be investigated. In the
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previous research [5, 6], the three-point bending tests of GCCM specimens with a size of 250
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was on the upper side and woven geotextile was on the bottom of the GCCM specimens.
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Linear Variable Displacement Transducer (LVDT) was used for measuring mid-span
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deflection (Fig. 2b). The loading rate was 10 mm/min and load was applied until the mid-
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span deflection reached 40 mm. In the flexural test, a total of six specimens, Bending Length
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(denoted as BL.1-3) and Bending Width (denoted as BW.1-3), were tested.
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3. Finite Element modelling
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GCCM exhibited behaviour similarly to that in concrete externally bonded with Fibre
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Reinforce Polymer (FRP) sheet. Since a fabric woven material is bonded with cement,
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GCCM therefore behaves like a composite material. As a result, FRP sheet can represent the
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woven materials both in width and length directions, whereas the interface between concrete
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and FRP sheet can represent the cement-to-woven fabric interface owing to needle-punching.
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In the Finite Element (FE) modelling, the existing modelling concept of FRP in GCCM is
122
therefore adopt. In addition, the existing bond–slip models and some fundamental aspects of
123
the behaviour of FRP-to-concrete interfaces [8-10] are used in the FE modelling. According
124
to the previous experimental results [5, 6], a nonwoven material only helps water
125
permeability and can rarely carry load. Consequently, such nonwoven layer can be ignored in
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the analysis of GCCM.
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3.1 Stress-strain relationships
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3.1.1 Cement
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The stress-strain relationships of cement in compression are modelled with uniaxial
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behaviour based on CEB-FIP Model Code [12] and Hordijk [13], as shown in Fig. 3a. For
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cement in tension, the biaxial failure function for concrete proposed by Kupfer et al. [14] is
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60 MPa from the compression test of the 50 mm × 50 mm in cube.
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3.1.2 Fabric woven materials
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The stress-strain relationships of woven material are according to both actual experimental
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result with a non-linear behaviour (Fig. 4a), and varied modulus of woven materials (Ef) for
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parametric optimisation with a linear behaviour (Fig. 4b). The actual experimental results
139
show average value of Ef to be 470 MPa and 1,070 MPa for width and length direction,
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respectively. In the parametric optimisation, the Ef-values are varied from 250 to 2,000 MPa
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to represent stiffness of fabric woven materials with needle-punched effect.
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3.2.1 Bond-slip model proposed by Nakaba et al. [8]
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Nakaba et al.’s stress-strain relationship is used to represent the local bond stress and slippage
146
relationship with consideration of the concrete compressive stress-strain relationship. Their
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local bond stress-slip relationships, however, are not dependant on the type of fibre. They
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found that only increase of concrete compressive strength could lead to increase in the
149
maximum local bond stress.
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In GCCM, the compressive strength of cement also controls the overall behaviour,
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especially in elastic stage. Therefore, the bond-slip relationship proposed by Nakaba et al.’s
152
was used in the FEM and show nonlinear behaviour (see Fig. 5a). In Nakaba et al.’s
153
experiment, the maximum local bond stress (τ max ) developed from 5.6 to 9.1 MPa with local
154
bond slip at τmax ( s 0 ) developed approximately at 0.052 to 0.087 mm. From the best fitting
155
analysis, τmax is equal to 3.5 f c'0.19 and s 0 is 0.065 mm. It is noted that their model is available
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only when concrete compressive strength ranges between 24-58 MPa. The stress-strain
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relationships [8] is shown in Eq. (1).
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(1)
where, τ max = 3.5 f c'0.19 and s0 = 0.065 mm.
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3.2.2 Bond-slip model proposed by Monti et al. [9]
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In Monti et al.’s model, uncracked and cracked concrete zones are considered. For uncracked
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zones, the effective bond length is used and the strain-bond fields are modelled along the
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anchorage length. For cracked zones, the model is used to predict the interaction between the
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two ends of a fabric material between two adjacent cracks.
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For the GCCM, the maximum bonding stress is calculated based on the ratio between
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width of the fabric woven material and cement as well as the tensile strength of cement. It
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should be noted that the slip at the maximum bonding strength depends on the thickness of
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adhesive ( t a ) as well as modulus of adhesive and cement ( E a and E c ). The local slip when
169
bond stress reduces to zero (Sf) is calculated using the width of fabric woven and cement.
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Monti et al.’s model is expressed in Eqs. (2)-(3) and the bond-slip curve as a bilinear
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behaviour is shown in Fig. 5b.
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where,
s ; s ≤ s0 s0
τ = τ max
τ = τ max
sf − s s f − s0
; s > s0
(2)
(3)
t 50 τ max = 1.8β w f t , s0 = 2.5τ max a + , s f = 0.33β w , and E a Ec
βw =
1.5(2 − b f / bc ) 1 + b f / 100
.
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ACCEPTED MANUSCRIPT 3.2.3 Bond-slip model proposed by Dai and Ueda [10]
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Dai et al. [10, 11] found that not only increasing fabric stiffness but also decreasing
177
adhesive’s shear stiffness affect to the enhancement of the interfacial performance of fabric
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sheets bonded to concrete. Dai and Ueda model [10] presented two separated equations to
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explain pre-peak and post-peak behaviours of the bond-slip interface, whereas Dai et al. [11]
180
later simplified their former model to a unified equation. Owing to the experimental results
181
[6], the pre-peak behaviour of GCCM is clearly dominated by cement, while the post-peak is
182
mainly behaved by the woven geosynthetic. Therefore, bond-slip model proposed in Dai and
183
Ueda [10] can be applied in the analysis to precisely characterise behaviour of GCCM. In
184
their models, the interfacial fracture energy is applied owing to the good toughness and
185
nonlinearity of low shear stiffness in adhesives. This leads to efficient use of the fabric woven
186
material with high strength. A nonlinear interfacial bond stress-slip model is included. Their
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concerned parameters in the model are the fracture energy and two other empirical constants
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α and β, which govern the ascending and descending parts of the interfacial bond-stress slip
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curves, respectively.
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For GCCM, the compressive strength of cement are taken into account with the shear
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stiffness of adhesive in terms of the interfacial fracture ( G f ). The modulus and thickness of
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fabric woven material are included in the model. The bond-slip model proposed in Dai and
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Ueda [10] is expressed in Eqs. (4) - (5), while the bond-slip curve as a nonlinear behaviour is
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shown in Fig. 5c.
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s τ = τ max s0
0.575
; s ≤ s0
(4)
τ = τ max e − β ( s − s ) ; s > s0
(5)
0
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where,
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τ max =
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s0 = τ max /(αK a ) , β = 0.0035 K a ( E f t f / 1000 ) 0.34
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α = 0.028 ( E f t f / 1000 ) 0.254 , K a = Ga / t a , Ga =
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G f = 7.554 K a−0.449 ( f c' ) 0.343
2β
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Ea , 2(1 + γ a )
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4. Parameter optimisation
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After fabricating GCCM, its properties remarkably changed due to the needle-punched
203
process [6]. Although the fabric woven component shows the stiffness of 1,070 and 470 MPa
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in both length and width directions (see Table 1), these values were only from the fabric’s
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element test in which excludes the effect of needle punching. In reality, the needle punching
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significantly affects to the bond between fabric woven and cement in GCCM. Therefore,
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optimised stiffness of both adhesive (Ea) and fabric woven (Ef) should carefully considered in
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the FE analysis. The parametric optimisation with varied Ea and Ef was conducted to obtain
209
the best fitted flexural load-displacement curves and crack patterns. In the analysis, the Ea-
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value is varied from 100 to 600 MPa, whereas Ef-value is varied from 250 to 2,000 MPa.
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Table 3 is a summary of parameters considered in the FE modelling.
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In this research, the 2D ATENA program was implemented to perform FE analysis of
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GCCM. Figure 6 represents the finite element mesh with a size of 5 mm and a simple-support
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as a boundary condition. The model was developed based on the plane stress state in which
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three layers of GCCM’s component were combined, as shown in Fig. 6. Fabric woven and
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cement layers were bonded following the existing bond-slips models [8-11]. For concrete, the
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CC3DNonLinCementitious2 provided by ATENA was used with the fixed crack model. The
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compressive strength of cement (Fig. 3a) was specified in the numerical model. Then, the 11
ACCEPTED MANUSCRIPT other characteristics were automatically generated based on the stress-strain relationship used
220
in the CC3DNonLinCementitious2 [15]. For a fabric woven, a discrete element was modelled
221
based on truss element and connected to the cement layer using the existing bond behaviours.
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In addition, the nonwoven layer can be ignored in the analysis of GCCM since it cannot carry
223
any load.
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4.1 Proposed bond-slip models
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Since needle-punched process affects to bonding and flexural behaviour of GCCM, existing
226
models should be taken into account in the analysis. Bond-slip models proposed by Nakaba et
227
al. [8], Monti et al. [9], and Dai et al. [10,11] were used to predict the load-displacement of
228
GCCM subjected to a flexural load. In the FE modelling, the Ef-values in both length and
229
width directions were 1,070 and 470 MPa based on the experimental results (see Table 1).
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Figure 7 shows load-displacement curves of GCCM under flexural load obtained from
231
experiment and analysis. Regarding Nakaba et al. [8], their model is simplified, accounting
232
for only compressive strength of cement or concrete (f’c). As a result, the analytical bond
233
properties are lack of the effect of Ef- and Ea- values. Regarding Monti et al. [9], their model
234
focuses only on a linear bond-slip behaviour so it insufficiently represent a nonlinear bond-
235
slip of GCCM. Regarding Dai and Ueda [10], their model could capture nonlinear behaviour
236
in both cracking and ultimate stages, while well explaining every characteristic of composite
237
materials such as shear modulus of adhesive, interfacial fracture of and compressive strength
238
of cement (see Eqs. (4) - (5) and Fig. 7). However, Figure 7 shows that using experimental
239
value of Ef (1,070 and 470 for length and width) could still lead to discrepancies in load-
240
deflection curve of the flexural test because of absence in needled-punch procedure.
241
Therefore, in this parametric optimisation the bond-slip model proposed by Dai and Ueda
242
[10] is carefully implemented with varied Ef- and Ea in the FE modelling.
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4.2 Optimised stiffness parameters from flexural test
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245
As mentioned previously, the optimised stiffness of adhesive bonding materials (Ea) should
246
be carried out in the analysis to obtain the best fitted flexural behaviour of GCCM. With
247
varied Ea, the minimum value of Residual Sum of Square (RSS) and maximum value of
248
coefficient of determination (R2) should be achieved. The RSS with unit of N2 is the sum of
249
the squares of residuals, calculated from the discrepancies between the experimental and
250
analytical results [16, 17], whereas the R2-value with non-unit used in this study is the
251
estimation of the parameters in a linear regression model. The flexural loads at every
252
incremental displacement of 5 mm are chosen to compare those discrepancies of results when
253
the Ea as a main parameter is varied from 100 to 600 MPa for fabric woven materials in both
254
length and width directions. This Ea can significantly represent different level of GCCM’s
255
needle punching, leading to various bonding stresses between fabric woven and cement
256
materials.
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4.2.2 Stiffness of woven materials (Ef)
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The Ef can represent properties of woven fabric after needle punching. Similarly to Ea, the
260
same optimisation procedure is also implemented for Ef with a range of 250-2,000 MPa. The
261
optimisation of both Ea and Ef were performed simultaneously in the FE modelling. The Ea-
262
and Ef- values are altered until the minimum RSS and maximum R2 are achieved. Tables 4-7
263
show RSS- and R2- values obtained from FE models of GCCM in both length and width
264
directions. The optimised Ea of 450 MPa can achieve minimum RSS of 3,281 and 1,076 N2
265
for the optimised Ef of 750 and 1,750 MPa in both length and width, respectively. At the
266
same time, such Ea–and Ef–values lead to the maximum R2 values of 0.902 and 0.987 in both
267
length and width, respectively. It can be concluded that the optimised Ea representing needle-
268
punched bonding in GCCM should be equal to 450 MPa. Opposite to the fabric woven test,
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270
MPa), whereas the optimised Ef in the width direction (1,750 MPa) is higher than that in the
271
test (470 MPa). This is because the GCCM’s behaviour changed after fabricating with
272
needle-punched procedure.
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5. Results and discussions
275
5.1 Load-displacement curves of flexural test
276
The experimental and analytical results using bond-slip model by Dai et al. [10] with varied
277
Ea are compared, as shown in Fig. 8. These varied Ea of 100, 450 and 600 MPa were input in
278
the FE modelling. Decreasing Ea to 100 MPa leads to fluctuated load-deflection curves in
279
both length and width (see Fig. 8). Increasing Ea to 450 MPa with Ef of 750 and 1,750 MPa in
280
length and width directions, the analytical load-deflection curves agree well with that
281
obtained from experiment in all specimens.
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Figure 9 shows comparison of the experiment and analytical results using bond-slip
283
model by Dai et al. [10,11] with varied Ef. With Ea of 450 MPa, the optimised Ef of 750 and
284
1,750 MPa in length and width directions can provide good analytical load-deflection curves,
285
especially in specimen BL.2 (Fig. 9a) and BW.2 (Fig. 9b). It is found that increasing of Ef to
286
1,000 MPa in length direction causes over-estimation of the peak load, whereas decreasing of
287
Ef to 500 MPa in width direction leads to under-estimation of the peak load.
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Overall, Ea of 450 MPa with the optimised Ef of 750 and 1,750 MPa in length and
289
width directions can also help predict both loads at first crack (Pfirst-crack) and ultimate
290
(Pultimate) very well. In Table 8, the percent differences of Pfirst-crack between experiment and
291
FEM are only 23.9% and 19.4% when optimised Ea is equal to 450 MPa, and optimised Ef is
292
750 and 1,750 MPa for length and width directions, respectively. With same optimised
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values, the percent differences of Pultimate is 6.0% and 7.9% for length and width directions,
294
respectively.
295
5.2 Crack patterns and failure modes
297
A crack patterns and failure modes of the bending specimens BL.2 and BW.2 at first crack is
298
presented in Figs. 10a and 11a. It can be seen that the crack patterns from analysis agree well
299
with that from experiment (see Figs. 10 and 11). In the optimised procedure, it is also found
300
that crack width becomes smaller with better crack distribution when increasing Ef. For
301
example, increasing Ef to 2,000 MPa in width direction can cause absence of major cracks
302
owing to higher maximum local bond stress (τmax). In Dai and Ueda [10], such higher τmax
303
leads to higher local bond stress (τ), causing difficulty of slip between fabric woven and
304
cement materials.
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6. Conclusions
307
The work has presented an optimisation study on the flexural of GCCM as well as the
308
modelling of this behaviour by 2D Nonlinear FEM. The GCCM analysed in the study is
309
expected to resist the bearing load during the slope protection, causing the flexural stress.
310
Based on the results and discussions presented in the paper, the following conclusions can be
311
drawn up:
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1) During fabricating process of GCCM, the needle-punched process changed GCCM
313
properties drastically. Therefore, optimisation for stiffness of adhesive (representing needle
314
punching) and stiffness of fabric woven material were conducted. From the analytical results,
315
GCCM can be modelled using the concept of concrete externally bonded by FRP. In the
316
models, FRP represents fabric woven layer whereas cement represents concrete layer. The
317
interface between fabric woven and cement was based on using existing bond-slip models.
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ACCEPTED MANUSCRIPT 318
2) The existing bond-slip model by Dai and Ueda [10] could successfully predict
319
flexural behaviour of GCCM, considering needle-punched effect. This needle-punched effect
320
was included in terms of the stiffness of adhesive material. The analytical load-displacement
321
curves with the bond-slip model could agree well with that obtained from the experiment. 3) To represent needle-punched effect, two parametersstiffness of adhesive, Ea and
323
stiffness of fabric material, Efwere optimised to achieve prediction of flexural behaviour as
324
well as crack patterns. From the optimisation process, the optimised Ea is 450 MPa whereas
325
the optimised Ef are 750 and 1,750 MPa for GCCM in both length and width direction. These
326
values will be useful for future prediction of GCCM behaviours when the material testing
327
results are very limited.
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4) In the current study, the calculation is still based on a small strain analysis
329
constraining by cracking of cement. In real geotechnical application, large strain analysis may
330
be required for slope stability and deformation analysis. This should be considered in the
331
future.
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Acknowledgements
334
The research was supported by the Thailand Research Fund Grant No. DBG-6180004 and the
335
Ratchadapisek Sompoch Endowment Fund (2017), Chulalongkorn University (760003-CC).
336
Authors would like to thank Siam Cement Group (SCG) for supporting materials during tests.
337
Endorsement by SCG is not implied and should not be assumed. The first author would also
338
like to acknowledge the TRF grant No. TRG5880266. The second author would also like to
339
acknowledge Master’s scholarship granted from Faculty of Engineering, Kasetsart
340
University, Thailand.
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Springer Science & Business Media, 2001. [17] Devore JL. Probability and Statistics for Engineering and the Sciences. Brooks/Cole, Cengage Learning, Boston, 2015.
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ACCEPTED MANUSCRIPT Table captions Table 1 Mechanical and physical properties of GCCM component [5, 6] Table 2 Mechanical and physical properties of GCCM [5, 6] Table 3 Parameters in FEM program Table 4 Residual Sum of Square (RSS) of Length direction models
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Table 5 Residual Sum of Square (RSS) of Width direction models Table 6 Coefficient of determination ( R 2 ) of Length direction models Table 7 Coefficient of determination ( R 2 ) of Width direction models
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Table 8 Summary of experimental and FEM results with varied Ef
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Table 1 Mechanical and physical properties of GCCM Component [5, 6] GCCM Fabrics Properties Cement Woven paste Non-woven Width (Weft) Length (Warp) Thickness (mm) 3.87 0.48 3.75 2 Weight (g/m ) 279 168 1.31x104 Punch density (punch/cm2) 35 35 35 Ultimate elongation (%) 118.62 45.98 32.66 Tensile strength (MPa) 1.00 72.05 71.70 Compressive strength at 7 days (MPa) 60.9 Young’s modulus (MPa) 470 1,070
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Table 2 Mechanical and physical properties of GCCM [5, 6] GCCM* Properties Width Direction Length Direction Thickness (mm) 8.10 ± 0.05 2 Mass per unit (g/cm ) 1.35 ± 0.07 2 35 Punch density (punch/cm ) Tensile strength** (kN/m) 26.50 ± 0.42 16.25 ± 0.84 Tensile stiffness (MPa) 710.30 219.79 Bending strength (MPa) 11.28 ± 0.15 7.75 ± 0.28 Maximum puncture load (kN) 1.60 ± 0.02 Permeability (cm/s) 7.03 ± 0.89 x 10-7 Note: *Properties of GCCM at 28 days are reported. **Tensile strength is defined as maximum tensile force per unit width of material.
ACCEPTED MANUSCRIPT Table 3 Parameters in FEM program Specimen Parameters Length and Width Direction
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100 200 300 E a (MPa ) 400 450 500 600 250 500 750 1,000 E f (MPa ) 1,250 1,500 1,750 2,000 Note: E a and E f are stiffness modulus of bonding and woven materials, respectively.
ACCEPTED MANUSCRIPT Table 4 Residual Sum of Square (RSS) of Length direction models E f (MPa )
E a (MPa )
100 200 300 400 450 500 600
250
500
750
1,000
1,250
1,500
1,750
2,000
69,510 68,589 84,552 82,035 105,281 101,685 107,588
6,956 14,019 17,783 14,433 33,063 30,124 34,407
5,764 5,619 4,989 4,490 3,281 3,493 5,236
25,304 39,660 11,469 7,530 9,291 6,877 4,851
65,838 55,427 44,659 39,509 20,851 18,782 44,906
140,589 75,653 99,678 108,742 115,814 80,868 108,529
149,237 134,043 131,144 96,909 132,643 102,360 113,775
189,017 44,090 298,995 306,139 242,546 288,471 283,740
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Parameters
Table 5 Residual Sum of Square (RSS) of Width direction models 250
500
750
1,000
372,730 373,519 408,515 404,708 456,303 448,490 458,177
180,784 215,216 229,432 213,715 277,940 272,305 281,784
87,354 86,454 159,326 156,813 152,067 154,062 159,114
46,406 27,432 73,546 82,030 81,714 95,448 102,435
∧
1,250
1,500 1,750
2,000
11,417 18,156 24,215 28,559 53,350 57,085 25,726
3,137 8,969 3,997 1,940 1,291 6,990 1,974
11,453 26,364 38,689 42,043 19,333 34,563 32,477
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E a (MPa )
100 200 300 400 450 500 600
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E f (MPa )
Parameters
4,235 1,597 1,664 6,208 1,076 4,467 1,580
∧
Note: RSS = ∑ ( y i − y i ) 2 Where yi is the experiment values and the modelled value is y i i
250
-1.069 -1.042 -1.517 -1.442 -2.134 -2.027 -2.203
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E a (MPa )
100 200 300 400 450 500 600
E f (MPa )
500
750
1,000
1,250
1,500
1,750
2,000
0.793 0.583 0.471 0.570 0.016 0.103 -0.024
0.828 0.833 0.851 0.866 0.902 0.896 0.844
0.247 -0.181 0.659 0.776 0.723 0.795 0.856
-0.960 -0.650 -0.330 -0.176 0.379 0.441 -0.337
-3.186 -1.252 -1.968 -2.237 -2.448 -1.408 -2.231
-3.443 -2.991 -2.904 -1.885 -2.949 -2.047 -2.387
-4.627 -0.313 -7.901 -8.114 -6.221 -7.588 -7.447
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Parameters
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Table 6 Coefficient of determination ( R 2 ) of Length direction models
ACCEPTED MANUSCRIPT Table 7 Coefficient of determination ( R 2 ) of Width direction models Parameters
E f (MPa )
250
500
750
1,000
1,250
1,500
1,750
2,000
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-1.187 -0.057 0.438 0.862 0.962 0.949 0.861 100 -3.510 -1.604 -0.046 0.668 0.780 0.891 0.981 0.681 200 -3.520 -1.776 -0.928 0.110 0.707 0.952 0.980 0.532 300 -3.943 E a (MPa ) 400 -3.897 -1.586 -0.897 0.007 0.654 0.977 0.925 0.491 -2.363 -0.840 0.011 0.354 0.984 0.987 0.766 450 -4.521 -4.427 -2.295 -0.864 -0.155 0.309 0.915 0.946 0.582 500 -2.410 -0.925 -0.239 0.689 0.976 0.981 0.607 600 -4.544 RSS Note: R 2 = 1 − In which RSS = the residual sum of square can be computed from RSS = TSS ∧
∧
i _
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∑ ( y i − y i ) 2 where yi is the experiment values and the modelled value is y i ; TSS = the total sum of square can be computed from TSS = ∑ ( y i − y i ) 2 where yi is the experiment values i
1 ∑ y i where n is number of data. n i =1
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and y i =
n
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Table 8 Summary of experimental and FEM results with varied Ef ACCEPTED MANUSCRIPT Ef
(MPa)
(MPa) 500 750 1000 1500 1750 2000
Specimen Length direction
450
Width direction
450
Pfirst-crack Experiment (N) 174.6 174.6 174.6 184.3 184.3 184.3
Pfirst-crack FEM (N) 215.5 216.4 217.3 219.1 220.0 220.9
Pultimate Experiment (N) 334.1 334.1 334.1 478.0 478.0 478.0
Pultimate FEM (N) 264.7 354.2 414.5 521.9 515.8 635.0
wfirst-crack FEM (mm) 8.499x10-4 8.456x10-4 8.414x10-4 8.334x10-4 8.296x10-4 8.260x10-4
Difference of Pfirst-crack (%) 23.4 23.9 24.5 18.9 19.4 19.9
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Ea
Difference of Pultimate (%) -20.8 6.0 24.1 9.2 7.9 32.8
Note: Pfirst-crack and wfirst-crack = loads and crack widths at the first-crack stage, and Pfirst − crack ( FEM ) − Pfirst − crack ( Experiment) × 100 and Difference of Pfirst-crack and Pultimate are calculated from Pfirst − crack ( Experiment)
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Pultimate ( FEM ) − Pultimate ( Experiment ) × 100 , respectively. Pultimate ( Experiment )
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Figure captions Figure 1
Geosynthetic Cementitious Composite Mat (GCCM) [5,6]
Figure 2
Experimental programs [5,6]
Figure 3
Stress-strain relationships of concrete in compression and tension [12-14]
Figure 4
Stress-strain relationship of the woven material (Ef) in experiment and FEM model Bond-slip models for the bonding material
Figure 6
2D Nonlinear Finite Element Modelling
Figure 7
Load-deflection curve of the flexural test with varied bond-slip models
Figure 8
Comparison of the experiment and analytical results using bond-slip model by Dai and Ueda [10] with varied Ea
Comparison of the experiment and analytical results using bond-slip model by Dai and Ueda [10] with varied Ef
Crack width of the analytical GCCM of Length Direction at first crack (Ea =450
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Figure 10
MPa) Figure 11
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Figure 9
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Figure 5
Crack width of the analytical GCCM of Width Direction at first crack (Ea =450
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MPa)
Woven
Width direction
Needle-punched GCCM Cross section
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Cement powder layer
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Non-woven
Length direction
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b) Final product of GCCM
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a) Components of GCCM
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Figure 1 Geosynthetic Cementitious Composite Mat (GCCM) [5, 6]
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b) Bending Test Setup
a) Tensile Test Setup
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Figure 2 Experimental programs [5, 6]
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Tensile failure
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f ‘c from experiment = 60 MPa at 7 days 50 mm x 50 mm in cube
Compressive failure
b) Biaxial stress failure criterion according to Kupfer et al. [14]
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a) Stress-strain relationships of concrete in compression and tension [12, 13]
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Figure 3 Stress-strain relationships of concrete in compression and tension [12-14]
ACCEPTED MANUSCRIPT Stress
Stress
Ef–FEM varied from 250-2,000 MPa
Ef-exp average = 470 MPa
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(width), 1070 MPa (length)
Strain
Strain
b) FEM model – linear behavior
a) Experiment – nonlinear behavior
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Figure 4 Stress-strain relationship of the woven material (Ef) in experiment and FEM model
MANUSCRIPT Bond stress, ACCEPTED τ 3 s s τ = τ max 3 / 2 + s0 s0
τmax
where,
τ max = 3.5 f c'0.19
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s0 = 0.065
S0
Slip, s
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a) Nakaba et al. [8] Bond stress, τ
s s0
; s ≤ s0
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τ = τ max τ = τ max
s f − s0
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τmax
sf − s
S0
; s > s0
Slip, s
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b) Monti et al. [9]
Bond stress, τ
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0.575
s τ = τ max s0 τ = τ max e − β ( s − s 0 )
τmax
S0
c) Dai and Ueda [10] Figure 5 Bond-slip models
; s ≤ s0 ; s > s0
Slip, s
ACCEPTED MANUSCRIPT 215 mm
8.1 mm Non-woven 3.87 mm thickness Cement 3.75 mm thickness Woven 0.48 mm thickness y
2
y
5
6
9
3
1 3
7
x
8
4
x
Truss element (woven)
Loading point
X
Roller support
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Plane elements (cement)
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Y
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Hinged support
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Figure 6 2D Nonlinear Finite Element Modelling
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600 500
300 Dai and Ueda [10]
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Load (N)
400
200
Monti et al. [9]
100 0 0
5
10
15
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Nakaba et al. [8]
20 25 Deflection (mm)
35
40
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[8] Nakaba et al. (2001)
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Experiment (BL.1)
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Experiment (BL.2)
[9] Monti et al. (2003)
Experiment (BL.3)
Dai and [10] Ueda andUeda Dai (2004)
a) Length direction (Ef = 1,070 MPa)
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600 500
Dai and Ueda [10]
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300 200
Monti et al. [9]
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Load (N)
400
Nakaba et al. [8]
100 0
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5
10
15
20 25 Deflection (mm)
30
35
40
Experiment (BW.1)
[8] Nakaba et al. (2001)
Experiment (BW.2)
[9] Monti et al. (2003)
Experiment (BW.3)
Dai and [10] Ueda andUeda Dai (2004)
b) Width direction (Ef = 470 MPa) Figure 7 Load-deflection curve of the flexural test with varied bond-slip models
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ACCEPTED MANUSCRIPT
600 500
Ea = 100
300
Ea = 600 Ea= 450
200
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100 0 5
10
15
20 25 Deflection (mm)
30
35
40
45
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Load (N)
400
Experiment (BL.1) Experiment (BL.2) Experiment (BL.3)
FEM Model (Ea 100) FEM Model (Ea 450) FEM Model (Ea 600)
a) Length direction (Ef = 750 MPa) 600
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500
300
Ea = 600
Ea = 100
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Load (N)
400
Ea = 450
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5
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20 25 Deflection (mm)
30
35
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Experiment (BW.1)
FEM Model (Ea 100)
Experiment (BW.2)
FEM Model (Ea 450)
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Experiment (BW.3) FEM Model (Ea 600) b) Width direction (Ef = 1,750 MPa) Figure 8 Comparison of the experiment and analytical results using bond-slip model by Dai and Ueda [10] with varied Ea
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600 500
Ef = 1000
300
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Load (N)
400
Ef = 750
200
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100 0 5
10
15
20 25 Deflection (mm)
30
35
40
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Experiment (BL.1) FEM Model (Ef 500) Experiment (BL.2) FEM Model (Ef 750) Experiment (BL.3) FEM Model (Ef 1000) a) Length direction (Ea =450 MPa) 600
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Ef = 2000
500
Ef = 1750
Ef = 1500
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Load (N)
400 300
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200 100 0
0
5
10
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20 25 Deflection (mm)
Experiment (BW.1) Experiment (BW.2) Experiment (BW.3)
30
35
40
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FEM Model (Ef 1500) FEM Model (Ef 1750) FEM Model (Ef 2000)
b) Width direction (Ea = 450 MPa) Figure 9 Comparison of the experiment and analytical results using bond-slip model by Dai and Ueda [10] with varied Ef
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a) Actual failure of BL.2
Maximum Crack Width = 0.0045 mm.
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b) Crack pattern Length Direction Model Ef = 500
Maximum Crack Width = 0.0022 mm.
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c) Crack pattern Length Direction Model Ef = 750
Maximum Crack Width = 0.0019 mm.
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d) Crack pattern Length Direction Model Ef = 1000
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Figure 10 Crack width of the analytical GCCM of Length Direction at first crack (Ea = 450 MPa)
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a) Actual failure of BW.2
Maximum Crack Width = 0.0017 mm.
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b) Crack pattern of Width Direction Model Ef = 1500
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Maximum Crack Width = 0.0016 mm.
c) Crack pattern of Width Direction Model Ef = 1750
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Maximum Crack Width = 0.0015 mm.
d) Crack pattern of Width Direction Model Ef = 2000
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Figure 11 Crack width of the analytical GCCM of Width Direction at first crack (Ea = 450 MPa)