Numerical modelling of reinforced concrete flexural members strengthened using textile reinforced mortars

Abstract

Externally bonded (EB) and near-surface mounted (NSM) bonding are two widely adopted and researched strengthening methods for reinforced-concrete structures. EB composite substrates are easy to reach and repair using appropriate surface treatments, whereas NSM techniques can be easily applied to the soffit and concrete member sides. The EB bonded fiber-reinforced polymer (FRP) technique has a significant drawback: combustibility, which calls for external protective agents, and textile reinforced mortar (TRM), a class of EB composites that is non-combustible and provides a similar functionality to any EB FRP-strengthened substrate. This study employs a finite element analysis technique to investigate the failing failure of carbon textile reinforced mortar (CTRM)-strengthened reinforced concrete beams. The principal objective of this numerical study was to develop a finite element model and validate a set of experimental data in existing literature. A set of seven beams was modelled and calibrated to obtain concrete damage plasticity (CDP) parameters. The predicted results, which were in the form of load versus deflection, load versus rebar strain, tensile damage, and compressive damage patterns, were in good agreement with the experimental data. Moreover, a parametric study was conducted to verify the applicability of the numerical model and study various influencing factors such as the concrete strength, internal reinforcement, textile roving spacing, and externally-applied load span. The ultimate load and deflection of the predicted finite element results had a coefficient of variation (COV) of 6.02% and 5.7%, respectively. A strain-based numerical comparison with known methods was then conducted to investigate the debonding mechanism. The developed finite element model can be applied and tailored further to explore similar TRM-strengthened beams undergoing debonding, and the preventive measures can be sought to avoid premature debonding.

Graphical abstract

Keywords

fiber reinforced polymer / textile reinforced mortar / finite element analysis / concrete damage plasticity / calibration and validation / parametric study

1 Introduction

Textile reinforced mortars (TRMs) consist of a combination of cementitious mortar and fiber-reinforced polymer (FRP) textiles that can be applied to concrete and masonry substrates. The combination of FRP fibers with an inorganic matrix imparts a stiffness in the strengthening substrates that arises from the tensile strength of FRP fibers. The behavior of TRM composites has been well documented in Refs. [1–4], resulting in substantial interest from the research community. TRMs are used to strengthen structures to overcome the deficiencies of FRPs [5]. FRPs utilize epoxies for bonding because they provide excellent adhesion to concrete and masonry substrates. The minute pores on these substrates induce the absorption of epoxy into the substrate, which accelerates the realization of the optimum saturation required to easily lay FRPs. In addition, FRP fiber bundles can be uniformly wetted with the help of vacuum pumping techniques, making FRPs efficient for use. However, one of the most notable disadvantages of epoxy is that it is highly susceptible to deterioration at high temperatures. As soon as the epoxy reaches its glass-transition temperature, the bond deteriorates quickly. In practice, this can easily be achieved using sunlight in hot and arid countries. Hence, to alleviate this effect, TRM can be used as an alternative to FRP, and this has been showcased in the strengthening of different structural members such as beams, slabs, and columns [6–9]. However, experimental testing can be time- and resource-consuming, and many researchers have opted for finite element modelling to investigate the behavior of structures strengthened using TRMs. Finite element (FE) studies provide resource-effective method for studying a specimen’s expected behavior; however, a tradeoff needs to be considered in terms of the computational efforts.

TRM, textile-reinforced concrete (TRC), and fabric-reinforced cementitious mortar (FRCM) all have similar functionalities. Hence, textile/fabric is considered synonymously in this study, and the use of textiles is adopted to refer to studies wherein the term fabric is used. The most commonly used textiles are carbon, glass, and basalt. Steel is also used in a similar manner, and the composite is typically referred to as steel-reinforced grout (SRG). Steel-reinforced grout-strengthened reinforced concrete beams were modelled considering flexure and shear [10–12]. The contact between the SRG and reinforced concrete substrate was established using cohesive contact and traction separation laws. The ultimate load carried by the strengthened beams was evaluated within a difference of 5% from that of the experimental specimens. In another study, SRGs were applied to strengthen shear-deficient beams using FE analyses [13]. The study reported a difference of 1%, 10%, and 4.2% from the experimental results with regard to the load, displacement sustained by numerical specimens, and energy absorption capacities, respectively. Two-dimensional (2D) reinforced concrete beam models were employed in another study to investigate SRG-strengthened beams and a satisfactory comparison with the experimental results was obtained [14]. In a similar study, steel mesh laminates and epoxy were used to strengthen reinforced concrete beams [15]. The results were calculated for short- and long-term loading using a subroutine to define the creep and strain. The results of this study showed a better correlation between the experimental and numerical findings. Therefore, based on this brief review of existing literature, FE programs have a high capability for SRG modelling.

Similar to SRGs, carbon fibers are used to strengthen reinforced concrete beams [16]. TRM-strengthened beams were analyzed at ambient and elevated temperatures, and the ability of carbon TRM (CTRM) to increase the performance of reinforced concrete beams was studied. Mesoscale modelling of carbon textile fibers was carried out to model textile and mortar interactions in a uniaxial tensile test [17]. The shear strengthening effects of glass textiles in reinforced concrete beams have also been studied [18]. A 2D numerical study using a macroscopic constitutive law was applied to model glass TRMs. In another study [19], carbon fibers were modelled to evaluate various results in Ref. [20] using the Abaqus FE program. The study clearly demonstrated the capability of FE programs to capture the behavior of TRM-strengthened systems. Moreover, CFRP and CTRM have been applied to strengthen reinforced concrete beams in shear and flexure [21]. Similarly, shear-deficient and shear-resistant reinforced beams have been tested using CTRM, which revealed that the inclusion of a bond-slip model at the fabric-matrix interface reduces the contribution of carbon fibers to the shear capacity; hence, the results were slightly conservative [22]. In another study, basalt textile was applied as an external confining jacket to strengthen concrete cylinders coupled with Engineered Cementitious Composites (ECC), and the experimental results were in good agreement with the numerical results [23]. Basalt textiles have been applied in a unique study where normal and high-strength corroded reinforced concrete beams were strengthened [24]. In a similar study, carbon textiles were applied to strengthen rectangular columns, and a corresponding numerical study predicted results that were similar to those recorded in the respective experiments [25]. Similarly, glass textile fibers have been applied in sandwich structures [26]. An FE analysis of the sandwich structure with TRM modelled as a homogeneous material successfully captured the system’s global behavior, excluding the local deformation. Glass and carbon textiles have been modelled as a single composite in the layer-wise layup model. This study demonstrated that layered modelling is a viable approach for modelling such composites [27].

Several numerical studies have focused on concrete structures strengthened with TRMs [28,29]. Although modelling reinforced concrete structural members is generic, the main influencing factor that needs special attention is the interaction between the external strengthening layer and substrate. The applied strengthening composite can undergo premature debonding or rupture solely because of the interactions between the substrate and strengthening layer, and within the strengthening layer itself. Hence, some studies have used detailed modelling techniques in which the contact between the textile and mortar is explicitly established using cohesive contact laws [30–36]. In contrast, others have employed simple interface contact models [37–39] to capture this mechanism. These studies further demonstrate that FE modelling can be suitably applied to capture the strengthening process. Some studies on capturing the brittle behavior and fracture mechanics of concrete are available in the literature. Several studies, for example [39–46], present extensive analytical models coupled with FE validations that will aid in efficiently modeling the concrete behavior. Recently, an image-based neural network strategy [47,48] was applied to study concrete damage caused by concrete spalling due to fire. Similar studies can also be extended to obtain results using FE simulations.

From the literature above, it can be observed that there is a need to establish a simplified model for capturing the response of CTRM-strengthened reinforced concrete beams. Hence, this study has the following vital contributions. Textile reinforcement within cementitious mortars can be modelled as either shell or truss elements. Shell elements modelled as 3D elements can be used to investigate the contact between adjacent mortar layers using specialized contact laws to capture the slip effects. In contrast, 2D truss elements can be modelled as embedded in the cementitious mortar, or special spring contacts can be used to connect the truss element nodes with the surrounding mortar nodes before defining the required contact laws. However, this process is slightly complicated. Therefore, a combined approach was adopted in this study by modelling textiles as embedded and using a cohesive surface to establish contact between the CTRM and reinforced concrete beam soffit. Using this technique, the model was simplified, and the desired response of the specimens was accurately captured using the FEM program.

The main objective of this study is in line with this idea, where the focus is analyzing flexural members failing via bending, particularly composite debonding failure, that is, beams strengthened by TRM using an FE model. The secondary objectives of this study is to evaluate the application of the validated FE model to members failing in flexure and to generate a working model that can be used to carry out parametric studies.

2 Objectives of the current study

It is clear from the studies mentioned thus far that the experimental results on TRMs can be efficiently modelled using a numerical method. Hence, with this background, the current research was carried out to provide FE validations of existing experimental data using Abaqus FE software [49]. This study explores the application of FE modelling on beams strengthened using TRMs to achieve the following: i) to verify the applicability of concrete damage plasticity parameters to TRM-strengthened flexural members; ii) to model textile and mortar as discrete elements rather than via the smeared technique, where textile and mortar are considered as single elements discretely; iii) to verify the bond-slip relationship at the TRM concrete interface; iv) to carry out parametric studies on different factors influencing the generated model; and iv) to compare the debonding strain obtained from numerical analysis with that in existing literature.

3 Summary of the experimental setup adopted

A set of experimental data strengthened in flexure was selected from literature as the target of the FE validation. The reason for this was to capture the debonding phenomenon occurring in all specimens. In addition, different layers of textiles were tested to determine their effect on the load-carrying capacity of the specimens. The data consisted of reinforced concrete beams strengthened in flexure using CTRM [50]. Experimental data were available for seven specimens including the control beam. All the specimens had a length, beam cross section width, and depth of 3000, 170, and 300 mm, respectively. Six beam specimens were divided into Type-A and Type-B, strengthened using Carbon-A and Carbon-B type textile fibers. The experimental parameters considered were the textile layers and areas. Carbon fiber-A had a cross-section of 1.8 mm², and carbon fiber-B had a cross-section of 2.7 mm². The properties of the carbon fibers are listed in Tab.1. A single concrete mix with a cylindrical compressive strength of 28 MPa, was used to cast all the specimens tested with a single reinforcement of type, that is, 10 mm bars acting as the bottom tensile and top compression bars. Shear links were provided as 8 mm diameter bars placed 150 mm center to center. The loading span was 900 mm and a span length of 2600 mm was selected for strengthening. A 45 MPa cylindrical compressive strength mortar with an elastic modulus of 40 GPa was applied as a matrix to reinforce the carbon fibers. All the specimens failed via TRM end debonding, except for the control beam. A typical sketch of a test specimen is shown in Fig.1.

4 Finite element model development

Abaqus FE software [49] was used to model all specimens considered in this study. The developed model considered the full size of the members. Fig.2 shows a schematic of the finite element model of the beam. The developed FE model was a replica of a typical sketch of the experimental specimens shown in Fig.1. In the experiments, the load was applied using a circular bar that was in contact with the concrete beam, and the loading pins were idealized as rectangular bars in the FE model to simplify the model. A similar technique was used to model the support. The following subsections discuss the modelling procedure used in this analysis in detail.

4.1 Adopted finite element types

The concrete and mortar were modelled as C3D8R, 8-node linear brick, reduced integration, and hourglass control solid elements. The rebars and textiles were modelled using T3D2, a 2-node linear 3-D truss element. The supports and loading plates were modelled as C3D8R solid elements with properties similar to those of the rebar.

4.2 Mesh and boundary conditions

A mesh size study was conducted before the selection of an appropriate mesh for all models. This study showed that a mesh size of 30 mm was adequate, and the same mesh size was adopted in all the subsequent analyses for both models. The contact between the concrete beam supports and loading plate was modelled using tie constraints. In contrast, the rebar and textile reinforcement were embedded using embedded constraints within the concrete and mortar, respectively, because this constraint smears the contact between the rebar/textile-concrete/mortar interfaces. The applied load was displacement controlled using two reference points, as shown in Fig.2, which were coupled to the loading plates to transfer the loads using coupling constraints. The simulated support conditions were modelled as hinges and rollers constrained along the U1 = 0 and U2 = 0 directions, respectively. The contact between the TRM and concrete interface was modelled using a bilinear traction separation law. A cohesive surface was utilized between the top surface of the TRM composite and underneath the concrete beam in all specimens. This contact modelling was chosen to obtain the debonding effect, which was observed in the experiments. A bond-slip relationship was used to define the cohesive surface contact between the two interfaces, which is discussed in Subsection 4.5.

4.3 Material properties

4.3.1 Compressive stress−strain modelling of the concrete damage plasticity parameters

The concrete and cement mortar compressive stress versus strain curves were generated using Alfarah’s model [51], and modelled as shown in Fig.3 and Fig.4. The stress versus strain model includes three stages: an initial linear stage 1 defined as 0.4 f_cm, a nonlinear stage 2 extending into concrete compression stress and strain, and stage 3, a softening region where the curve descends to a minimum compressive stress/strain similar to that in reference [51]. The Abaqus input was in the form of inelastic strain versus compressive stress, with the subtraction of the elastic part being done directly, as shown in Fig.3(b). The corresponding compression damage variables were input as inelastic compressive strain to completely capture the concrete damage from the FE program, as shown in Fig.5(a).

Because the models required to estimate the cementitious/polymer mortar compressive stress versus strain were limited in literature, the same model was applied to generate the cementitious mortar compressive stress versus strain/inelastic strain and compressive damage versus inelastic strain curves, as shown in Fig.3(a) and Fig.3(b), respectively [53].

4.3.2 Concrete-tensile stress−strain modelling

Concrete tension can be modelled using various methods, such as those by Nayal and Rasheed [53] and Wahalathantri et al. [54]. However, because Alfarah’s study included tension modelling, the same model was utilized. This model was based on Hordijk’s equation [55] presented in Eq. (1) below. The concrete fracture energy can be estimated using MC2010 [56] and Eq. (2).

(1)\frac{\sigma t\left(w\right)}{f_{\mathrm{t}\mathrm{m}}} =\left[1+c1{\left(\frac{w}{w_{\mathrm{c}}}\right)}^3\right]{\mathrm{e}}^{-c2\left(\frac{w}{w_{\mathrm{c}}}\right)}- \left(\frac{w}{w_{\mathrm{c}}}\right)\left(1+c{1}^3\right){\mathrm{e}}^{-c2},

(2)G_{\mathrm{f}}= 0.073\ast f_{\mathrm{c}\mathrm{m}}^{0.18},

where σt(w) denotes the stress at the crack opening displacement w, c1 = 3, c2 = 6.93, w_c is the crack opening at fracture, G_f is the fracture energy per unit area, and f_cm is the concrete compressive strength.

The concrete tensile stress versus strain was modelled in two stages: an initial stage comprising a linear curve up to cracking, followed by stage two comprising a nonlinear softening stage (Fig.4(a) and Fig.4(b)). The corresponding damage variables were input to capture the tensile damage, as shown in Fig.5(a) and 5(b). Tab.2 contains the plasticity parameters adopted in the modelling of the two experiment data.

4.4 Steel rebar and textile reinforcement modelling

The steel rebar stress−strain curves required for Abaqus modelling were modeled using Han’s equations [57]. The stress and strain were input as the corresponding stress versus plastic strain by converting the nominal strains into plastic strains. As reported in the experiments, a 10 mm rebar was used as the bottom and top rebar bars along with 8 mm diameter shear links. A representative stress versus strain curve is shown in Fig.6.

The selected steel rebar has a yield strength similar to the concrete inelastic strain input steel rebar inelastic values that should be input to completely capture the plastic deformation of the specimens. The model comprises three parts: an initial elastic ascending curve followed by a plateau of the strain-hardening phase with a further nonlinear increase in stress and strain. Textile reinforcement was modelled as linearly ascending with stress and strain increasing proportionally without considering an explicit plastic stage, as shown in Fig.7. The reported values of carbon textiles were directly used with the ultimate strain reported in Tab.2 and Tab.3. A representative stress versus strain curve is shown in Fig.7.

4.5 Interface modelling

The interaction between the concrete beams and TRM was modelled as a cohesive contact for all the specimens from the literature using the traction separation relationship [50] as mentioned in Subsection 3.2. Using general contact interaction, a contact pair was chosen between the concrete bottom surface and TRM top surface. The contact between the two surfaces was formulated as pure master/slave assignments. Tangential frictionless contact and hard contact were also chosen along with the cohesive behavior as inputs for K_nn, K_ss, and K_tt. Cohesive damage was defined using normal and shear forces along the two directions using the maximum criterion, and the calculated values were calibrated as necessary from the idealized curve presented in Fig.7. Typical values of the cohesive surface parameters are listed in Tab.4 for reference.

The bilinear bond-slip model adopted was obtained from a study by Lu et al. [58]. The model requires the use of the following parameters while defining the FE program according to Eqs. (3)−(7).

(3){\tau }_{\mathrm{m}\mathrm{a}\mathrm{x}}=1.5{\beta }_{\mathrm{w}}{f}_{\mathrm{t}},

(4)S_{\mathrm{d}}= 0.01955{\beta }_{\mathrm{w}}{f}_{\mathrm{t}},

(5)S_{\mathrm{u}}= 2G{f}_{\mathrm{t}}/{\tau }_{\mathrm{m}\mathrm{a}\mathrm{x}},

(6)G_{\mathrm{f}}= 0.308{\beta }_{\mathrm{w}}^2\sqrt{f_{\mathrm{t}}},

(7){\beta }_{\mathrm{w}}= \frac{\sqrt{2.25-{\displaystyle \frac{b_{\mathrm{f}}}{b_{\mathrm{c}}}}}}{\sqrt{1.25+{\displaystyle \frac{b_{\mathrm{f}}}{b_{\mathrm{c}}}}}},

where {\tau }_{\mathrm{m}\mathrm{a}\mathrm{x}} is the maximum shear stress (MPa), S_{\mathrm{d}} is the slip at the maximum bond stress, S_{\mathrm{u}} is the slip at failure, G_{\mathrm{f}} is the fracture energy at the TRM concrete beam interface, {\beta }_{\mathrm{w}} is the width coefficient factor, b_{\mathrm{f}} is the width of the TRM, b_{\mathrm{c}} is the width of the concrete substrate, and f_{\mathrm{t}} is the concrete tensile strength.

5 Validation of the finite element model

With the material properties described thus far, the generated model was subjected to multiple runs to calibrate the control specimens of the respective experimental data. After arriving at a suitable model with fixed concrete damage plasticity parameters, especially the dilation angle, the same value was extended in modelling the strengthened specimens. The FE versus experimental comparisons included the percentage difference in the ultimate load, load versus mid-span deflection curves, load versus textile strain curves [50] and failure modes. Tab.5 lists the ultimate load from the experimental testing and FE simulations for each of the seven beams and shows that the coefficient ofvariation (COV) of the experimental to FE ultimate load values and ultimate deflections ranged between 6.02% and 5.07%, reflecting the robustness of the model in capturing the beam load capacity.

5.1 Use of the explicit solver

A dynamic explicit solver was used in this study to maintain cost-efficiency and convergence of the computational solution. The internal and kinetic energies were kept at a minimum by limiting their ratio to less than 10%. This is a crucial aspect of ensuring that the solutions obtained using the dynamic explicit solution method will always remain static. Hence, checks were performed to maintain this ratio after each simulation ended. A history output was created using ALLIE and ALLKE output variables available in the FE software to store the energies, which were then plotted against each other. The following sections discuss in detail the various parameters validated against the chosen experiments.

Although a sufficient number of experimental studies have been carried out to experimentally report the advantages and disadvantages of TRMs, numerical studies on strengthened structures act as an essential tool to obtain different behaviors of the strengthened structural system with simple modelling techniques [9,10]. Generally, most FE models utilize elements such as solids to model cementitious polymer mortars, alkali-activated mortars [11,12], and textiles, which can be modelled as two-node truss elements and shell elements [12,61]. Contact between textiles and mortar can be established using cohesive elements, cohesive surfaces, or embedding textiles in a mortar. In contrast, the substrate concrete and rebar were modelled using solid and truss elements with specialized contact laws between the rebar and concrete. Textiles were modelled as linear 2D rather than 3D elements, which can be tedious to run owing to the type of FE chosen. However, with a two-node truss element, the textile roving and its exact grid nature of textiles can be realized with mortar penetrating the grid spaces, allowing realistic modelling. However, when the textiles were modelled as shell elements, this realistic feature could not be achieved because of the inherent nature of this element.

The chosen FE play a vital part in the numerical study, whereas selecting the appropriate FE solver is as crucial as satisfying the convergence criterion and efficient computational time required. Most studies utilize static and dynamic methods to solve a particular problem. A static solver sometimes results in non-convergence, coupled with increased time, owing to the minimum time increments chosen to solve a problem. On the other hand, a dynamic solver attempts the same problem with minimum computation time but with large increment sizes; if the internal energies generated while using this kind of solver are considered, the solutions obtained can then be treated as static. Given this background, the current study adopted a dynamic approach to model different specimens.

5.2 Comparison of the load versus mid-span deflection

The specimen terminology used in the original publication was retained with FEA appended at the end to indicate the FE and Exp for experimental results; that is, A/B-L-here A/B represents carbon-type and L-layers. The unstrengthened control specimen (unstrengthened) from Jung et al. [50] was chosen to study the effects of the mesh size and dilation angle. Initially, two mesh sizes were selected 25 and 30 mm; 30 mm size was chosen owing to its best fit in terms of load versus deflection curve obtained against control specimens; Fig.8 and Fig.9 reports this study. The dilation angles were varied to investigate their effect on the load versus deflection curve. A set of dilation angles, namely 31°, 35°, 40°, and 45°, was chosen to examine its impact; although these different dilation angle values present a similar trend in observation, a dilation angle of 40° gave the best and closest response to the control specimen; hence, the same was adopted in all the models. The load and deflection values obtained from the FE analysis are presented in Tab.5 and in Fig.10 and Fig.11 for easy understanding. The ratio of experimental values reported over FE values was calculated for the simulated beams, and COV of 6.02% and 5.7% were reported for the ultimate load and ultimate deflection, respectively. In addition, a linear correlation of the experimental and FE ultimate loads was carried out, and an R² value equal to 0.98 was obtained, indicating that the simulated results obtained in this study were reasonably good and in agreement with the experimental outcome. To further understand the simulated results, a bar plot comparison of the experimental and FE simulation results were carried out. This figure shows the difference between the predicted and the experimental results. The horizontal dotted line shows the capacity of the unstrengthened specimen, and the portion above this line can be visualized as the capacity gain achieved by strengthening the specimens along with the contribution of the individual layers to the overall strength gain. A further simple analysis of the applied external strengthening scheme with respect to the internal reinforcement was carried out. These data show that, as the external strengthening ratio with respect to the internal reinforcement increases, the load capacity of the strengthening system increases, which is an obvious outcome. However, this figure shows the individual capacity increase contribution from different layers, with the highest observed in the three-layered specimens; the one- and two-layered specimens provide almost similar load increments. This result is particularly useful for determining the optimum number of strengthening layers required for a practical strengthening job.

5.3 Comparison of the load versus rebar strain at mid-span

The rebar strain sustained by the internal longitudinal rebar was recorded as the logarithmic strain output from the mid-span of the rebar to obtain the strain increment as the specimens maintained loads. In Fig.12(a) and Fig.12(b), it is clear that the rebar strain follows the default load versus deflection trend with pronounced stiffness, similar to the load−deflection behavior. As the control specimen strain was not reported in the reference paper, only the strengthened specimens were evaluated using the FE model.

5.4 Flexural stiffness degradation

Flexural stiffness degradation provides an idea of the behavior of strengthened beams after cracking. This parameter is essential because the serviceability of strengthened members is significantly affected when the stiffness changes. The evolution of the flexural stiffness degradation graph consists of an EI-kN·m² versus load plotted on x and y, respectively. EI was calculated using Eq. (8) [60], where EI is the stiffness of the beam, a is the shear span from the loading point to the support, L is the support span, and P and Δ are the load and deflection, respectively. From the plot, it is noticeable that each plot of EI versus load can be discretely divided into three regions. The first region can be considered the onset of cracking, followed by the second stage, where a gradual EI reduction was observed. The third stage begins soon after steel yielding, as the curve flattens and grows continuously. Fig.13(a) and Fig.13(b) show that the FE curves of the three-layered specimens present the highest flexural stiffness in the case of specimens strengthened with Type-A and Type-B fibers. However, in specimens strengthened with Type-A and Type-B fibers, the three-layered experimental specimen curves showed less stiffness compared to the two layers and one layer in the case of Type-B and Type-A fibers, respectively, which could be an experimental record error. In contrast, all reported FE curves exhibit a clear trend in the stiffness increment corresponding to the number of layers.

(8)EI=\frac{P}{\mathrm{\Delta }}\frac{a}{48}(3 L^2- 4a).

5.5 Finite element damage assessment

The tensile and compressive damages, defined as inputs at the time of material definition, provide a visual realization in the form of tensile damage-DAMAGET and compressive-DAMAGEC. It can be observed that the crack patterns sustained by the specimens match well with the numerical models, that is, the control specimen and strengthened specimens in terms of the tensile damage patterns recorded and are reported in Fig.14-Fig.19. TRM end debonding can extend until point loads are applied in all the cases.

5.6 Parametric analysis

A set of parameters, including the concrete strength, rebar diameter size, shear span, and textile spacing, were chosen to evaluate their effects on the experimental specimens. Cylindrical compressions of 15 and 45 MPa were selected to imitate low- and medium-high concrete strength grades and the respective load versus deflection responses are presented in Fig.20-Fig.23. A set of bars with diameters of 8 and 12 mm were chosen as the tension and compression steel, respectively, with a diameter of 8 mm as the shear links throughout the parametric study which is reported in Fig.22 and Fig.23. The shear span was varied in two lengths: 225 and 900 mm. Textile grid spacings of 8 and 34 mm were adopted to study the fabric roving arrangement effect. The following sections describe the parametric analysis in detail.

5.6.1 Concrete strength

TRM strengthening applied to reinforced beams with a concrete cylindrical compressive strength of 15 MPa resulted in a 12.45% lower ultimate load-carrying capacity when three layers were used. A common observation is that, as the concrete strength increases, the ultimate load increases. The load increment was linear for the one- and two-layered specimens but not for the three-layered specimens. It is evident from the load versus displacement curves that the three-layered specimens are prone to brittle failure, and adequate measures should be taken in the form of supplementary anchorages to maximize the effect of the increased textile layers. In addition, the one-layered specimen exhibited a lower load capacity than the two-layered specimens for both A- and B-type fibers, as shown in Fig.24(a) and Fig.24(b).

5.6.2 Rebar percentage

Two types of rebar bar diameters of 8 and 12 mm were simulated to observe their effects while keeping all other parameters the same, that is, concrete and cementitious mortar compressive strength. The rebar percentage was calculated as the area over the width and the effective depth. Fig.25(a) and Fig.25(b) show a clear linear pattern for the ultimate load increment. Type-A showed a proper linear trend in load increment, whereas Type-B fibers with three layers showed a linear trend, whereas one and two layers showed almost similar load increments.

5.6.3 Loading span/shear span

The loading span was varied to study its influence on TRM composite debonding. Increasing the load span typically increases the capacity of the beam owing to the arching action mechanism developed with the beam [57]. Shear spans of 225 and 450 mm were adopted and compared with the experimental span of 900 mm to evaluate the strengthened load capacities of the specimens. A schematic of the load span is shown in Fig.26 as a reference. It can be seen from Fig.27(a)–Fig.27(b) and Fig.28(a)–Fig.28(b) that a reduction in the shear span will increase the load capacity owing to the arching effect.

5.6.4 Textile grid spacing

The textile grid spacing, particularly along the warp, was carefully chosen because the weft fibers were unaffected or did not participate in taking the effective tensile force beneath the reinforced concrete beam substrate. The weft fibers add rigidity along the length and width of the beams. A similar observation can also be made from the textile stress distribution recorded during the FE analysis and is reported in Fig.14–Fig.17, textile stress contour. A similar force distribution develops in TRM-strengthened columns, where the textile rovings running along the length of the column do not show any sign of stress, in contrast to the hoop stress generated along the cross-sectional circumference. From the textile grid parametric study, it was clear that textile grids with smaller spacing subsequently carried higher loads than larger grid sizes (Fig.29(a) and Fig.29(b)). However, the effect is not as profound as that shown in Fig.29(a); doubling the grid spacing from 17 to 34 mm resulted in similar load capacities.

5.7 Comparison of the finite element strain with existing strain formula

The debonding strain was evaluated using three approaches and was compared with the recorded FE strain. Ceroni and Salzano [62], Mandor and Refai [63], and ACI 549.4-20 [64] were selected, and the debonding/rupture strain was calculated accordingly. Although these formulae are used to calculate the debonding strain of FRCM composites bonded to non-reinforced specimens, the same can be applied to evaluate the strain sustained by a reinforced concrete member.

The textile strain was evaluated using five approaches and compared with the FE strain. The approaches from Ceroni and Mandor presented formulae to predict the debonding strain from concrete substrates, and ACI 549.4-20 with a maximum strain of textile limit of ≤ 0.012 was selected, and the textile strain was calculated correspondingly at the ultimate load, as shown in Fig.30. The ultimate load obtained from the FE method, Ceroni’s method, and Mandor’s second and third approaches, ACI549.4-20, show predictions similar to the experiment, with Ceroni’s formula matching closely with the FE strain. However, Mandor’s first method overestimated the strain and was found to be conservative in this study.

6 Conclusions

In this study, an FE model was developed to numerically validate the experimental outcomes in existing literature using the Abaqus FE software [49]. The selected experimental data were modelled and validated, and the predicted results were found to match the experimental results; hence, the modelling technique was sufficiently accurate in terms of the concrete damage plasticity (CDP) calibration and solution method adopted. The obtained numerical results were further validated using a parametric study to extend the application of the developed model. The following conclusions were drawn from this study.

1) The calibrated concrete damage plasticity parameters provided FE model predictions that were closer to the experimental results. The layer and textile area effects captured during the experiment showed the same results as those of the numerical models.

2) The adopted bilinear traction separation law showed reasonable agreement with the experimental outcome, capturing the debonding phenomenon.

3) The debonding behavior of single/multi-layered TRM composite-strengthened reinforced concrete beams shows that if suitable end anchorages are applied, imminent debonding can be postponed, which results in reasonable utilization of the TRM composite.

4) The parametric study showed that applying a TRM composite to low-strength concrete beams could enhance and restore its strength, which can be exploited to strengthen old structures. By contrast, high-strength concrete is more prone to brittle failure, as observed in this study.

5) The textile strain predicted at the ultimate loads using available formulae and codal provisions shows that FE strain prediction produces a closer outcome to the experimental results.

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