Performance Based Review and Fine-Tuning of TRM-Concrete Bond Strength Existing Models

1. Introduction

Most of the concrete structures experience damages during their life time. These damages usually start with initial cracks and the these cracks propagate and will cause the whole structure to collapse [ 1 - 3 ]. To prevent such catastrophic collapses, the researcher proposed external bonded (EB) composite systems as useful techniques to strengthen the structural elements. Among different EB systems, the fiber reinforced polymer (FRP) composites are the most known strengthening systems with various advantages such as high strength to weight ratios, compatible geometrical features and easily installing procedure [ 4 - 7 ].

Although the FRP composites have a lot of merits, some of the disadvantages of them such as high sensitivity to fire, brittle manner in conditions with high temperature changes, non-environmental friendly manufacture process and their failure mode which is usually contains detachment a part of the concrete substrate with the FRP strips, make the researcher to find a more proper alternative for the FRP composites [ 8 ]. The textile reinforced mortar (TRM) composite was the selection of those researchers in which the epoxy resin in FRP composites was replaced with mineral mortar grouts. The TRM composites have all advantages of FRP composites and moreover reduce their side effects [ 9 ].

As the failure modes in TRM composites are more complicated with respect to FRP composites, most of researchers started to conduct deep experimental tests to undertake the bond behavior between TRM composites and different concrete substrates [ 10 , 11 ]. Most of the conducted test to study the TRM-concrete bond behavior were designated to direct shear (DS) tests. In DS tests, a strip of TRM composite should be attached to one face of a concrete block and by fixing the concrete block as the substrate, the strip of TRM composite should be pulled out until the detachment of the TRM composite from the concrete substrate or rupture of the fibers in the TRM composite. Various DS tests with different kinds of fibers such as carbon [ 12 ], glass [ 13 ], aramid [ 14 ], basalt [ 15 ], and PBO [ 16 ] were reported in previous studies. In many other investigations, the researchers proposed some empirical models to predict the bond strength between the TRM composite and the concrete substrate [ 17 - 20 ]. Most of the previously proposed TRM-concrete bond models were adopted from FRP-concrete bond models and were obtained based on some limited experimental data. As a result, the previous empirical TRM-concrete bond models can not be utilized as a general model and they have high values of errors. The goal of this paper is to calibrate a simplified TRM-concrete bond model based on a comprehensive complied DS tests data.

2. Research objective

Literature has shown that many experimental and analytical efforts have been conducted to investigate the bond behavior between textile reinforced mortar and concrete substrates. The most of existing analytical models provided to estimate the TRM-concrete bond strength originated from previous models proposed for predicting the FRP-concrete bond strength. Moreover, some analytical efforts have been done to propose updated models for estimating the TRM-concrete bond strength based on limited local experimental data. As a results, the performance of existing TRM-concrete bond strength models is still a challenging question for researchers. In this paper, it is tried to review the existing TRM-concrete bond strength models and select the simplest one to conduct the calibration based on soft computing techniques and improve its performance based on a comprehensive database including 221 experimental direct shear tests. As this paper aims to keep the original form of the selected existing model, the performance of the proposed model is not comparable to other calibration models without any limitation in the form of the proposed equation. The research flowchart is depicted in Fig. 1.

Fig. 1. The research flowchart in this study.

3. Existing TRM-concrete bond models

There are some known existing models to calculate the TRM-concrete bond strength. In this paper, to present a closed form simple equation, the simplest existing analytical model were chosen from the literature. Maeda et al. [ 20 ] had proposed the following equation to estimate the TRM-concrete bond strength:

$\begin{array}{cc}{P}_u=\mathrm{110.2}\times {\mathrm{10}}^{\mathrm{-2}}.E_f.t_f.b_f.l_e& \mathrm{(1)}\end{array}$

Where, in Eq. (1), the E_f, t_f, and the b_f are respectively the modulus of elasticity of fibers, thickness of fibers, and width of fibers in TRM composites. The l_e is the effective bonded length which can be calculated from the Eq. (2) presented below:

$\begin{array}{cc}{l}_e=e^{\mathrm{6.13}-\mathrm{0.580}\ln (E_f.t_f)};E_f\left(\mathrm{GPa}\right),t_f\left(\mathrm{mm}\right)& \mathrm{(2)}\end{array}$

In this paper, the Eq. (1) has been selected to be calibrated via different soft computing techniques. The performance of the resulted fine-tuning models will be compared to the original presented models by Maeda et al. [ 20 ].

4. The experimental TRM-concrete bond database

In this study, a database including 221 experimental direct shear tests were compiled from various researchers. As presented in Fig. 2, the input parameters in the compiled database were modulus of elasticity of fibers (E_f), thickness of fibers (t_f), the width (b_f) and bonded length (L_b) of fibers in TRM composites, the compressive strength of concrete substrate (f_c), and the width of concrete block (b); Whereas the output is the bond strength between TRM composite and the concrete substrate (P_u). Table 1 presents the input and output ranges and the number of specimens in each reference, and the Table 2 reports the statistical features of the compiled database in this paper.

Fig. 2. The inputs and output parameters considered in this study.

5. Calibrated TRM-concrete bond strength models

New TRM-concrete bond strength models were proposed in this section based on the compiled experimental direct shear tests database reported in Table 1. The proposed models were aimed to improve the accuracy and performance of the selected existing TRM-concrete bond strength model (Maeda et al. [ 20 ]). Thus, for calibrating the general simplified models, P_{u_Cal_I} and P_{u_Cal_II} as presented in Eqs. (3) and (4) respectively, a generalized reduced gradient nonlinear approach was implemented to provide the best coefficients (C, α and β) that minimize the root mean square error (RMSE) as the objective function. The achieved results are presented in Table 3.

$P_{\mathrm{u\_Cal\_I}}={C.110.2\times {\mathrm{10}}^{\mathrm{-6}}.E_f.t_f.b_f.l_e}^{\alpha }$

$\begin{array}{cc}{l}_e=e^{\beta \mathrm{6.13}-\mathrm{0.580}\ln (E_f.t_f)};E_f\left(\mathrm{GPa}\right),t_f\left(\mathrm{mm}\right)& \mathrm{(3)}\end{array}$

$P_{\mathrm{u\_Cal\_II}}=C.110.2\times {\mathrm{10}}^{\mathrm{-6}}.E_f.t_f.b_f.l_e$

$\begin{array}{cc}{l}_e=e^{\alpha -\beta \ln (E_f.t_f)};E_f\left(\mathrm{GPa}\right),t_f\left(\mathrm{mm}\right)& \mathrm{(4)}\end{array}$

By applying the results of Table 3, the generalized reduced gradient nonlinear method as the calibration method for P_{u_Cal_I} and P_{u_Cal_II} proposed models are presented in Eqs. (5) and (6), respectively.

$P_{\mathrm{u\_Cal\_I}}={\mathrm{0.1517}\times \mathrm{110.2}\times {\mathrm{10}}^{\mathrm{-6}}.E_f.t_f.b_f.l_e}^{\mathrm{1.4129}}$

$\begin{array}{cc}{l}_e=e^{\mathrm{1.2374}\times \mathrm{6.13}-\mathrm{0.580}\ln (E_f.t_f)};E_f\left(\mathrm{GPa}\right),t_f\left(\mathrm{mm}\right)& (5)\end{array}$

$P_{\mathrm{u\_Cal\_II}}=\mathrm{1.0037}\times \mathrm{110.2}\times {\mathrm{10}}^{\mathrm{-6}}.E_f.t_f.b_f.l_e$

$\begin{array}{cc}{l}_e=e^{\mathrm{6.2637}-\mathrm{0.6448}\ln (E_f.t_f)};E_f\left(\mathrm{GPa}\right),t_f\left(\mathrm{mm}\right)& \mathrm{(6)}\end{array}$

To compare the performance of the two proposed calibration models (P_{u_Cal_I} and P_{u_Cal_II}) with other statistical methods, a multi linear regression (MLR) technique is also applied to estimate the TRM-concrete bond strength via reported database in Table 1. The general equation for the MLR technique (P_{u_MLR}) is presented in Eq. (7):

$\begin{array}{cc}{P}_{\mathrm{u\; \_MLR}}=\alpha .b_c+\beta .f_c+\phi .t_f+\delta .b_f+\lambda .l_b+\eta .E_f+C& \mathrm{(7)}\end{array}$

The obtained parameters in MLR technique are presented in Table 4. Eq. (8) shows the simplified MLR proposed model (P_{u_MLR}).

$\begin{array}{cc}{P}_{\mathrm{u\; \_MLR}}=-\mathrm{0.0766}{b}_c-\mathrm{0.1554}{f}_c+\mathrm{19.2451}{t}_f+\mathrm{0.1937}{b}_f-\mathrm{0.0156}{l}_b+\mathrm{0.0058}{E}_f+\mathrm{13.0192}& \mathrm{(8)}\end{array}$

Some of the regular performance and error evaluation parameters such as the correlation coefficient (R), the coefficient of determination (R²), Mean Squared Error (MSE), Root Mean Square Error (RMSE), Mean Absolute Error (MAE), Mean Absolute Percentage Error (MAPE), Normalized Mean Squared Error (NMSE) and Normalized Mean Absolute Error (NMAE) presented in Eqs. (9) to (16) [ 43 - 48 ], were selected to evaluate the performance of existing and proposed models. The evaluation results are presented in Table 5 for various TRM-concrete bond strength models.

$\begin{array}{cc}R=\frac{\sum _{\mathrm{i=1}}^n(A_i-\stackrel{-}{A})(F_i-\stackrel{-}{F})}{\sqrt{\sum _{\mathrm{i=1}}^n{(A_i-\stackrel{-}{A})}^2\sum _{\mathrm{i=1}}^n{(F_i-\stackrel{-}{F})}^2}}& \mathrm{(9)}\end{array}$

$\begin{array}{cc}{R}^2={\left(\frac{\sum _{\mathrm{i=1}}^n(A_i-\stackrel{-}{A})(F_i-\stackrel{-}{F})}{\sqrt{\sum _{\mathrm{i=1}}^n{(A_i-\stackrel{-}{A})}^2\sum _{\mathrm{i=1}}^n{(F_i-\stackrel{-}{F})}^2}}\right)}^2& \mathrm{(10)}\end{array}$

$\begin{array}{cc}\mathrm{MSE}=\frac{1}{n}\sum _{\mathrm{i=1}}^n{(A_i-F_i)}^2& \mathrm{(11)}\end{array}$

$\begin{array}{cc}\mathrm{RMSE}=\sqrt{\frac{1}{n}\sum _{\mathrm{i=1}}^n{(A_i-F_i)}^2}& \mathrm{(12)}\end{array}$

$\begin{array}{cc}\mathrm{MAE}=\frac{1}{n}\sum _{\mathrm{i=1}}^n|A_i-F_i|& \mathrm{(13)}\end{array}$

$\begin{array}{cc}\mathrm{MAPE}=\frac{1}{n}\left[\frac{\sum _{\mathrm{i=1}}^n|A_i-F_i|}{\sum _{\mathrm{i=1}}^n\left|A_i\right|}\right]\times \mathrm{100}& \mathrm{(14)}\end{array}$

$\begin{array}{cc}\mathrm{NMSE}=\frac{\frac{1}{n}\sum _{\mathrm{i=1}}^n{(A_i-F_i)}^2}{\max \left(A_i\right)-\min \left(A_i\right)}\times \mathrm{100}& \mathrm{(15)}\end{array}$

$\begin{array}{cc}\mathrm{NMAE}=\frac{\frac{1}{n}\sum _{\mathrm{i=1}}^n|A_i-F_i|}{\max \left(A_i\right)-\min \left(A_i\right)}\times 100& \mathrm{(16)}\end{array}$

where A_i represents the obtained experimental value, and F_i shows the predicted value, n is equal to the number of the studied data, $\stackrel{-}{A}$ is the mean observed values, and $\stackrel{-}{F}$ is the mean predicted values. The comparison of predicted TRM-concrete bond strength values with corresponding experimental results for direct shear tests and the measured to predicted ratios are presented in Figs. 3 and 4, respectively. In Fig. 3, the ideal fit line (shown with a continuous purple line) indicates how the results were located accurately.

Fig. 3.The predicted vs. obtained TRM-concrete bond strength in different models: a) P_{u_Cal_I}; b) P_{u_Cal_II}; c) Maeda et al. and d) P_{u_MLR}.

Fig. 4. The measured to predicted ratios of TRM-concrete bond strength in different models.

The presented result in Table 5 and Figs. 3 and 4 show that for TRM-concrete bond strength, proposed P_{u_Cal_I} model resulted in R value of 0.6909 and NMAE value of 12.62%, which can be included as the most accurate model. Additionally, the proposed P_{u_Cal_I} model obtained better R value of 0.6902 but gained more NMAE error value of 13.17% in comparison to existing Maeda et al. model (respectively equal to 0.6676 and 13.10%). Based on the results, the P_{u_MLR} model was not successful to outperform the existing Maeda et al. model. The outcomes can be confirmed by the histogram of absolute percentage error frequencies shown in Fig. 5.

Fig. 5. The histogram of absolute percentage error frequency in different TRM-concrete bond strength models.

6. Conclusions

In this paper, new TRM-concrete bond models were calibrated to predict the bond strength between various TRM composites and the concrete substrate. Two calibrated models named P_{u_Cal_I} and P_{u_Cal_II} as well as a multi regression model named P_{u_MLR} model were conducted to estimate the TRM-concrete bond strength. To achieve this goal, a database including 221 experimental direct shear tests were compiled and a simple existing model was selected to be calibrated via soft computing techniques. Based on the achieved results, the following conclusion could be drawn:

Among the calibrated models, the P_{u_Cal_I} model outperforms all other models with R value of 6909 and NMAE error value of 12.62%. The calibrated P_{u_Cal_II} model gained more R value of 0.6902 but higher NMAE error value of 13.17% in comparison to existing Maeda et al. model (0.6676 and 13.10%, respectively).

Opposite to the obtained result from calibrated models conducted by a generalized reduced gradient nonlinear approach by minimizing the root mean square error (RMSE), the proposed multilinear regression model (P_{u_MLR}) was not successful to outperform the existing Maeda et al. model. The obtained R and NMAE values for P_{u_MLR} model was 0.6398 and 13.73% respectively.

The proposed generalized reduced gradient nonlinear approach by minimizing RMSE values was a capable technique to calibrate the existing Maeda et al. model to estimate the TRM-concrete bond strength with higher accuracy and lower error values.

Acknowledgments

The authors declare that no funding was received for this study.

Funding

This research received no external funding.

Conflicts of interest

The authors declare no conflict of interest.

Authors contribution statement

HJ, ZN, DRE: Conceptualization; HJ, ZN: Data curation; HJ, DRE: Formal analysis; ZN, HJ: Investigation; HJ, DRE: Methodology; MRE: Project administration; ZN: Resources; DRE: Software; MRE: Supervision; HJ, DRE: Validation; HJ, DRE: Visualization; HJ: Roles/Writing - original draft; HJ, DRE: Writing - review & editing.

References

1. Daneshvar MH, Saffarian M, Jahangir H, Sarmadi H. Damage identification of structural systems by modal strain energy and an optimization-based iterative regularization method. Eng Comput. 2022; :1-21. https://doi.org/10.1007/s00366-021-01567-5. Publisher Full Text
2. Jahangir H, Khatibinia M, Mokhtari Masinaei M. Damage Detection in Prestressed Concrete Slabs Using Wavelet Analysis of Vibration Responses in the Time Domain. J Rehabil Civ Eng. 2022; 10:37-63. https://doi.org/10.22075/jrce.2021.23385.1510. Publisher Full Text
3. Jahangir H, Khatibinia M, Kavousi M. Application of Contourlet Transform in Damage Localization and Severity Assessment of Prestressed Concrete Slabs. J Soft Comput Civ Eng. 2021; 5:39-67. https://doi.org/10.22115/scce.2021.282138.1301. Publisher Full Text
4. Bagheri M, Chahkandi A, Jahangir H. Seismic Reliability Analysis of RC Frames Rehabilitated by Glass Fiber-Reinforced Polymers. Int J Civ Eng. 2019. https://doi.org/10.1007/s40999-019-00438-x. Publisher Full Text
5. Jahangir H, Esfahani MR. Bond Behavior Investigation Between Steel Reinforced Grout Composites and Masonry Substrate. Iran J Sci Technol Trans Civ Eng. 2022. https://doi.org/10.1007/s40996-022-00826-9. Publisher Full Text
6. Kamgar R, Naderpour H, Komeleh HE, Jakubczyk-Gałczyńska A, Jankowski R. A proposed soft computing model for ultimate strength estimation of FRP-confined concrete cylinders. Appl Sci. 2020; 10. https://doi.org/10.3390/app10051769Publisher Full Text
7. Tahir M, Wang Z, Ali KM, Isleem HF. Shear behavior of concrete beams reinforced with CFRP sheet strip stirrups using wet-layup technique. Structures. 2019; 22:43-52. https://doi.org/10.1016/j.istruc.2019.08.001. Publisher Full Text
8. Cerniauskas G, Tetta Z, Bournas DA, Bisby LA. Concrete confinement with TRM versus FRP jackets at elevated temperatures. Mater Struct Constr. 2020; 53:1-14. https://doi.org/10.1617/s11527-020-01492-x. Publisher Full Text
9. Jahangir H, Esfahani MR. Numerical Study of Bond - Slip Mechanism in Advanced Externally Bonded Strengthening Composites. KSCE J Civ Eng. 2018; 22:4509-18. https://doi.org/10.1007/s12205-018-1662-6. Publisher Full Text
10. Escrig C, Gil L, Bernat-Maso E, Puigvert F. Experimental and analytical study of reinforced concrete beams shear strengthened with different types of textile-reinforced mortar. Constr Build Mater. 2015; 83. https://doi.org/10.1016/j.conbuildmat.2015.03.013Publisher Full Text
11. Raoof SM, Koutas LN, Bournas DA. Bond between textile-reinforced mortar (TRM) and concrete substrates: Experimental investigation. Compos Part B Eng. 2016; 98:350-61. https://doi.org/10.1016/j.compositesb.2016.05.041. Publisher Full Text
12. Trapko T. Fibre reinforced cementitious matrix confined concrete elements. Mater Des. 2013; 44:382-91. https://doi.org/10.1016/j.matdes.2012.08.024. Publisher Full Text
13. Leone M, Aiello MA, Balsamo A, Carozzi FG, Ceroni F, Corradi M, et al. Glass fabric reinforced cementitious matrix: Tensile properties and bond performance on masonry substrate. Compos Part B Eng. 2017; 127:196-214. https://doi.org/10.1016/j.compositesb.2017.06.028. Publisher Full Text
14. De Santis S, Carozzi FG, de Felice G, Poggi C. Test methods for Textile Reinforced Mortar systems. Compos Part B Eng. 2017; 127. https://doi.org/10.1016/j.compositesb.2017.03.016Publisher Full Text
15. Ahmed ER, Mohamed-Amine A, Radhouane M. Bond Performance of Basalt Fiber-Reinforced Polymer Bars to Concrete. J Compos Constr. 2015; 19:4014050. https://doi.org/10.1061/(ASCE)CC.1943-5614.0000487. Publisher Full Text
16. D’Ambrisi A, Feo L, Focacci F. Experimental analysis on bond between PBO-FRCM strengthening materials and concrete. Compos Part B Eng. 2013; 44:524-32. https://doi.org/10.1016/j.compositesb.2012.03.011. Publisher Full Text
17. Wu Y, Zhou Z, Yang Q, Chen W. On shear bond strength of FRP-concrete structures. Eng Struct. 2010; 32:897-905. https://doi.org/10.1016/j.engstruct.2009.12.017. Publisher Full Text
18. Neubauer U, Rostasy. FS. Design aspects of concrete structures strengthened with externally bonded CFRP-plates. Proc. SEVENTH Int. Conf. Struct. FAULTS REPAIR, 8 JULY 1997., CONCRETE AND COMPOSITES; 1997.
19. Tanaka T. Shear resisting mechanism of reinforced concrete beams with CFS as shear reinforcement. Hokkaido University, Japan, 1996.
20. Maeda T, Asano Y, Sato Y, Ueda T, Kakuta Y. A study on bond mechanism of carbon fiber sheet. Non-Metallic Reinf. Concr. Struct. Proc. 3rd Int. Symp., Tokyo, Japan: Japan Concrete Institute; 1997, p. 279-85.
21. Iorfida A, Verre S, Candamano S, Ombres L. Tensile and Direct Shear Responses of Basalt-Fibre Reinforced Mortar Based Materials, 2018, p. 544-52. https://doi.org/10.1007/978-94-024-1194-2_63.Publisher Full Text
22. Awani O, Refai A El, El-Maaddawy T. Bond characteristics of carbon fabric-reinforced cementitious matrix in double shear tests. Constr Build Mater. 2015; 101:39-49. https://doi.org/10.1016/j.conbuildmat.2015.10.017. Publisher Full Text
23. D’Antino T, Carloni C, Sneed LH, Pellegrino C. Matrix-fiber bond behavior in PBO FRCM composites: A fracture mechanics approach. Eng Fract Mech. 2014; 117. https://doi.org/10.1016/j.engfracmech.2014.01.011Publisher Full Text
24. Tran CTM, Stitmannaithum B, Ueda T. Investigation of The Bond Behaviour Between PBO-FRCM Strengthening Material and Concrete. J Adv Concr Technol. 2014; 12:545-57. https://doi.org/10.3151/jact.12.545. Publisher Full Text
25. D’Antino T, Pellegrino C, Carloni C, Sneed LH, Giacomin G. Experimental analysis of the bond behavior of glass, carbon, and steel FRCM composites. Key Eng. Mater., vol. 624, 2015, p. 371-8.
26. Sneed LH, D’Antino T, Carloni C, Pellegrino C. A comparison of the bond behavior of PBO-FRCM composites determined by double-lap and single-lap shear tests. Cem Concr Compos. 2015; 64:37-48. https://doi.org/10.1016/j.cemconcomp.2015.07.007. Publisher Full Text
27. Ombres L. Analysis of the bond between Fabric Reinforced Cementitious Mortar (FRCM) strengthening systems and concrete. Compos Part B Eng. 2015; 69:418-26. https://doi.org/10.1016/j.compositesb.2014.10.027. Publisher Full Text
28. D’Antino T, Sneed LH, Carloni C, Pellegrino C. Influence of the substrate characteristics on the bond behavior of PBO FRCM-concrete joints. Constr Build Mater. 2015; 101:838-50. https://doi.org/10.1016/j.conbuildmat.2015.10.045. Publisher Full Text
29. Raoof SM, Koutas LN, Bournas DA. Bond between textile-reinforced mortar (TRM) and concrete substrates: Experimental investigation. Compos Part B Eng. 2016; 98:350-61. https://doi.org/10.1016/j.compositesb.2016.05.041. Publisher Full Text
30. Carloni C, Antino TD, Sneed LH, Pellegrino C. Three-Dimensional Numerical Modeling of Single-Lap Direct Shear Tests of FRCM-Concrete Joints Using a Cohesive Damaged Contact Approach. 2018; 22:1-10. https://doi.org/10.1061/(ASCE)CC.1943-5614.0000827. Publisher Full Text
31. Sneed LH, D’Antino T, Carloni C, Pellegrino C. A comparison of the bond behavior of PBO-FRCM composites determined by double-lap and single-lap shear tests. Cem Concr Compos. 2015; 64:37-48. https://doi.org/10.1016/j.cemconcomp.2015.07.007. Publisher Full Text
32. Ombres L, Verre S. Experimental and Numerical Investigation on the Steel Reinforced Grout (SRG) Composite-to-Concrete Bond. J Compos Sci. 2020; 4. https://doi.org/10.3390/jcs4040182Publisher Full Text
33. Carozzi FG, Arboleda D, Asce AM, Poggi C, Nanni A, Asce F. Direct Shear Bond Tests of Fabric-Reinforced Cementitious Matrix Materials. 2020; 24. https://doi.org/10.1061/(ASCE)CC.1943-5614.0000991Publisher Full Text
34. Gonzalez-libreros J, Antino TD, Pellegrino C. Experimental Behavior of Glass-FRCM Composites Applied onto Masonry and Concrete Substrates. 2017; 747:390-7. https://doi.org/10.4028/www.scientific.net/KEM.747.390. Publisher Full Text
35. Gonzalez J, Antino TD, Pellegrino C. Bond behaviour of basalt FRCM composites applied on RC elements. 2015.
36. Sneed LH, D’Antino T, Carloni C. Investigation of Bond Behavior of Polyparaphenylene Benzobisoxazole Fiber-Reinforced Cementitious Related papers Investigation of Bond Behavior of PBO Fiber-Reinforced Cementitious Matrix Composite-Concrete Interface n.d.
37. Sneed LH, Verre S, Carloni C, Ombres L. Flexural behavior of RC beams strengthened with steel-FRCM composite. Eng Struct. 2016; 127:686-99.
38. Zou X, Sneed LH, Antino TD, Carloni C. Analytical Bond-Slip Model for Fiber-Reinforced Cementitious Matrix-Concrete Joints Based on Strain Measurements. 2019;31:-.
39. Zou X, Sneed LH. Bond Behavior Between Steel Fiber Reinforced Polymer (SRP) and Concrete. Int J Concr Struct Mater. 2020; 14:46. https://doi.org/10.1186/s40069-020-00420-1. Publisher Full Text
40. Younis A, Ebead U. A study on the bond behavior of different FRCM systems. 2018; 09003:1-5.
41. Younis A, Ebead U. Bond characteristics of different FRCM systems. Constr Build Mater. 2018; 175:610-20. https://doi.org/10.1016/j.conbuildmat.2018.04.216. Publisher Full Text
42. D’Antino T, Gonzalez J, Pellegrino C, Carloni C, Sneed LH. Experimental investigation of glass and carbon FRCM composite materials applied onto concrete supports. 2016; 847:60-7. https://doi.org/10.4028/www.scientific.net/AMM.847.60. Publisher Full Text
43. Jahangir H, Bagheri M, Delavari SMJ. Cyclic Behavior Assessment of Steel Bar Hysteretic Dampers Using Multiple Nonlinear Regression Approach. Iran J Sci Technol Trans Civ Eng. 2021; 45:1227-51. https://doi.org/10.1007/s40996-020-00497-4. Publisher Full Text
44. Rezazadeh Eidgahee D, Jahangir H, Solatifar N, Fakharian P, Rezaeemanesh M. Data-driven estimation models of asphalt mixtures dynamic modulus using ANN, GP and combinatorial GMDH approaches. Neural Comput Appl. 2022; 34:17289-314. https://doi.org/10.1007/s00521-022-07382-3. Publisher Full Text
45. Isleem HF, Tayeh BA, Alaloul WS, Musarat MA, Raza A. Artificial Neural Network (ANN) and Finite Element (FEM) Models for GFRP-Reinforced Concrete Columns under Axial Compression. Materials (Basel). 2021; 14:7172. https://doi.org/10.3390/ma14237172. Publisher Full Text
46. Ghanizadeh AR, Delaram A, Fakharian P, Armaghani DJ. Developing Predictive Models of Collapse Settlement and Coefficient of Stress Release of Sandy-Gravel Soil via Evolutionary Polynomial Regression. Appl Sci. 2022; 12:9986. https://doi.org/10.3390/app12199986. Publisher Full Text
47. Naderpour H, Rezazadeh Eidgahee D, Fakharian P, Rafiean AH, Kalantari SM. A new proposed approach for moment capacity estimation of ferrocement members using Group Method of Data Handling. Eng Sci Technol an Int J. 2020; 23:382-91. https://doi.org/10.1016/j.jestch.2019.05.013. Publisher Full Text
48. Naderpour H, Sharei M, Fakharian P, Heravi MA. Shear Strength Prediction of Reinforced Concrete Shear Wall Using ANN, GMDH-NN and GEP. Soft Comput Civ Eng. 2022; 6:66-87. https://doi.org/10.22115/SCCE.2022.283486.1308. Publisher Full Text