# Failure Mode Prediction of Unreinforced Masonry (URM) Walls Retrofitted with Cementitious Textile Reinforced Mortar (TRM)

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

#### 1.1. Literature Overview

#### 1.2. Brick Masonry Walls

#### 1.3. Cement Masonry Walls

#### 1.4. Stone Masonry Walls

#### 1.5. Research Gap and Novelty

## 2. Database Assembly

_{f}) ranging from 4 to 24 mm. The different composite strengthening materials were GTRM (with a modulus of elasticity E

_{GTRM}= 36.9–80 GPa), CTRM (E

_{CTRM}= 73–240 GPa), and BTRM (E

_{BTRM}= 72–89 GPa), orientated in various ways, e.g., horizontally, vertically, diagonally, grid, or full coverage of the exterior surface [41]. The majority of the textile reinforcement layouts coincided with the full coverage of the exterior surface. The masonry specimens provide thickness ranging from 85 mm to 560 mm, with an aspect ratio high/length of masonry walls (H/L) ranging from 0.3 to 3.25, while the masonry unit’s height ranges from 55 mm to 380 mm and the length from 185 mm to 400 mm, with the units’ compression capacity (f

_{unit}) ranging from 2 to 119 MPa, whereas for the masonry walls, the compression strength (f’

_{m}) was 1.27 to 68.25 MPa).

_{I}is designed by considering a uniform shear stress distribution within the panel, which leads to the below-mentioned central stress state: σ

_{y}= σ

_{x}= 0, τ = (1/√2) P/A

_{n}(A

_{n}is the cross-sectional area of the wall). Under these hypotheses, the diagonal tensile strength of the masonry f

_{dt}is calculated, in practice, as if the panel would be in a pure shear stress state (σ

_{I}/σ

_{II}= −1, for 45° loading slope angle) and is calculated as follows: f

_{dt}= σ

_{I}= 0.7 P/A

_{n}[42].

_{εjoint}and ε

_{joint}are the shear stress and strain of the binder mortar of the URM wall, τ

_{εmas}and ε

_{mas}are the shear stress and strain of the URM wall, τ

_{εjoint,d}, and ε

_{joint,d}are the shear stress and strain of the strengthening mortar at the contact level with the masonry wall, τ

_{εmortar}, and ε

_{mortar}are the shear stress and the shear strain of the strengthening mortar, and τ

_{TRM}and ε

_{TRM}are the shear stress and strain of the TRM textile.

## 3. Design Models

#### 3.1. Existing Models

_{m}–σ

_{n}), which is designed in terms of shear strength versus compressive stress [47,48,49].

#### 3.2. Proposed Model

_{m}is calculated, and is also proposed by the EC8 design model:

_{dt}is the diagonal tension, V

_{f}is the flexural capacity of the unreinforced masonry wall, and V

_{sf}is the shear friction and shear sliding capacity, where shear sliding and shear friction are combined due to the bond strength and friction resistance between the mortar joint and the blocks. Shear sliding and shear friction V

_{sf}are determined according to EC6:

_{fiber}+ V

_{mortar}).

_{dt}, according to EC8, for this failure mechanism is provided in the following equation, using the upper limit 0.065f

_{m}to ensure that failure in diagonal tension will occur in the compression area when subjected to a combined normal compressive and shear stress.

_{m}is the compressive strength of the masonry and N is the axial load. The proposed model innovates, compared to the existing models and regulations, in that it assumes the contribution of the strengthening mortar to the total shear strength of the TRM, and it is calculated according to the equation below:

_{fu}equal to the fabric or textile debonding strain ε

_{ffd}= 0.27‰. In contrast, existing regulations adopt the value of ε

_{fu}= 0.4‰. Further, the V

_{fiber}is calculated by the following expression:

_{f}is the area of the fabric or textile reinforcement by unit width, n is the number of layers of fabric, L

_{f}is the applied textile length over the wall, and E

_{f}is the tensile modulus of elasticity of the cracked TRM. The shear strength of the mortar V

_{mortar}is calculated using the following expression:

_{mortar}is the area by unit width, ε

_{tm}is the tensile strain of the coating mortar, and E

_{mortar}is the tensile modulus of elasticity of the cracked mortar of the TRM. The values of each tensile stain ε

_{tm}of the external cementitious strengthening mortar for different masonry substrates are depicted in Table 2.

## 4. Results

_{mpred}) with the experimental (V

_{mexp}). The failure mode derives from the condition that the predicted shear strength of the masonry substrate is lower than the experimental observation (V

_{mpred}< V

_{mexp}) within the same convergence range (25%). If the shear criterion is satisfied, the failure mode of the masonry substrate is categorized according to the agreement with the experimental observations and falls into the four characteristic modes (shear sliding, -SS; shear friction, -SF; diagonal tension, -DT; and toe crushing, -TC). Else, if V

_{mpred}> V

_{mexp}, the TRM system is damaged and leads to failure. The success of every model is defined as a percentage of the number of predictions that agree with the experimental observations.

_{Rdpred}) is compared to the corresponding experimental shear strength taken from the database assembled (V

_{Rdexp}). A deviation of 25% in terms of the experimental observation was used again as a success criterion of the predictions. If this criterion is not met, then the predicted failure mode presents low accuracy and is not taken into account. In the cases that the deviation criterion is met and the predicted total shear strength is lower than the experimental value (V

_{Rdpred}< V

_{Rdexp}), then the model is considered accurate.

_{tm}= 0.055%), which is the limit of the first crack in the mortar layer. What is more, the contribution of the TRM system calibrated with the factor k (Table 1) is proven to be essential for the success of the predictions.

_{tm}= 0.112%). The CTRM systems exhibit an increased value of factor k, meaning that after the extensive cracking of the mortar beyond the transition point (ε

_{tm}), the carbon fiber grid develops tensile resistance, contributing to the shear resistance of the strengthened wall at a greater level than glass.

_{tm}. These values of tensile strains permit better collaboration between the substrate, mortar layer, and fiber grid. All of the above is taken into consideration in the model, which is multiplied by the factor k, denoting the shear transfer through the interfaces that leads to TRM failure.

## 5. Conclusions

_{t1}) and the debonding strains rather than the ultimate strain of the textile. What is more, the matrix strength is calibrated in relation to the substrate’s mechanical performance to predict if the failure happens in the substrate or in the strengthening system. The model’s provisions are compared not only to each specimen that is contained in the database but also to the provisions of the existing design/prediction models. The criterion of accuracy is ±25% convergence to the experimental observations, both for the shear failure mode of the masonry substrate as well as the retrofitted wall.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

**Table A1.**Failure mode prediction with existing regulations of strengthened URM made of brick, concrete, or stone with TRM reinforcement.

Authors | Type of Masonry | Type of TRM | Specimen Code | Experimental Failure Mode | ACI | CNR (2018) | CNR (2013) | TA 2000 | Trantafillou 1998 | Trantafillou 2016 | EC6 | EC8 | Proposed Model |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

[12] | brick | G | SO-UMG1 | TRM | SF | NA | NA | NA | NA | NA | NA | NA | TRM |

brick | G | SO-UMG2 | TC | TRM | M | M | M | M | M | M | TRM | TC | |

brick | G | SO-UMG3 | TC | NA | NA | NA | NA | NA | NA | NA | NA | TC | |

[30] | brick | G | 1GRW^{N}25 | TC | NA | NA | NA | NA | NA | NA | NA | NA | TC |

brick | G | 2GRW^{N}15 | DT | NA | NA | NA | NA | NA | NA | NA | NA | NA | |

brick | G | 2GRW^{N}25 | TC | NA | NA | NA | NA | NA | NA | NA | NA | NA | |

brick | G | 2GRW^{N}25 | TC | NA | NA | NA | NA | NA | NA | NA | NA | NA | |

[29] | brick | G | W16-G | TRM/DT | TRM | NA | NA | NA | NA | NA | NA | NA | TRM |

brick | G | W17-G | TRM/DT | TRM | NA | NA | NA | NA | NA | NA | NA | TRM | |

brick | G | W18-G | TRM/DT | TRM | NA | NA | TRM | NA | NA | NA | NA | TRM | |

G | |||||||||||||

[32] | concrete | G | T1F-3 | DT/TRM | TRM | NA | NA | NA | NA | NA | NA | NA | TRM |

concrete | G | T1F-4 | DT/TRM | TRM | NA | NA | NA | NA | NA | NA | NA | TRM | |

concrete | C | T1F-5 | DT/TRM | TRM | NA | NA | NA | NA | NA | NA | NA | TRM | |

concrete | C | T1F-6 | DT/TRM | TRM | NA | NA | NA | NA | NA | NA | NA | TRM | |

concrete | B | T1F-7 | TC/ DT | TRM | NA | NA | TC | NA | NA | NA | NA | TRM | |

concrete | B | T1F-8 | TC DT | NA | NA | NA | TC | NA | NA | NA | NA | TRM | |

concrete | B | T1F-9a | TC/ DT | TRM | NA | TC | TC | NA | NA | NA | NA | TRM | |

concrete | G | T2F-10 | DT/TC | DT | NA | NA | TC | NA | NA | NA | NA | TC | |

concrete | G | T2F-11 | DT/TC | DT | NA | NA | TC | NA | NA | NA | NA | TC | |

concrete | C | T2F-12 | DT-TRM | DT | NA | NA | NA | NA | NA | NA | NA | TRM | |

concrete | C | T2F-13 | TC | NA | NA | NA | NA | NA | NA | NA | NA | TC | |

concrete | B | T2F-14 | DT/TRM | TRM | NA | NA | NA | NA | NA | NA | NA | TRM | |

concrete | B | T2F-15 | DT/TRM | TRM | NA | NA | NA | NA | NA | NA | NA | TRM | |

concrete | B | T2F-16 | DT/TRM | DT | NA | NA | NA | NA | NA | NA | NA | TRM | |

[29] | brick | G | W4 | TRM | NA | NA | NA | NA | NA | NA | NA | NA | TRM |

brick | G | W5 | TRM | NA | NA | NA | NA | NA | NA | NA | NA | TRM | |

brick | G | W6 | TRM | NA | NA | NA | NA | NA | NA | NA | NA | TRM | |

[23] | brick | C | FRMCom_01 | DT | NA | NA | NA | NA | NA | NA | NA | NA | NA |

[25] | brick | C | CFRCM 01 | SS | TC | NA | NA | NA | NA | NA | M | NA | SS-SF |

brick | G | CFRCM 02 | SS | TC | NA | NA | NA | NA | NA | M | NA | SS-SF | |

[24] | brick | C | CD_FRCM | TRM | NA | TRM | TRM | NA | NA | NA | NA | NA | NA |

[40] | brick | G | A-3 | DT | TC | M | TC | TC | TC | M | TRM | TRM | TC |

[34] | stone | G | CD-07-U-IP | SF | NA | NA | NA | NA | NA | NA | NA | NA | NA |

[38] * | stone | G | 7 | DT/TRM | NA | NA | NA | NA | NA | NA | M | DT | DT |

stone | G | SM-10S | DT/TRM | SF/SS | NA | TRM | NA | NA | TRM | NA | DT | DT | |

[35] | brick | G | CD-11-S-IP | TRM | SF | TRM | TRM | TC | TC | TRM | TRM | TRM | TRM |

stone | G | CD-12-P-IP | DT/TRM | NA | NA | TRM | TRM | TRM | NA | TRM | NA | TRM | |

stone | G | CD-13-P-IP | DT-TRM | NA | NA | TRM | TRM | TRM | NA | TRM | NA | TRM | |

[26] | brick | G | B2A-F33S-1 | DT/TRM | NA | NA | NA | NA | NA | NA | NA | TRM | TRM |

brick | G | B2A-F33S-2 | DT/TRM | NA | NA | NA | NA | NA | NA | NA | TRM | TRM | |

brick | G | B2A-F66S-1 | DT/TRM | NA | NA | NA | NA | NA | NA | NA | TRM | TRM | |

brick | G | B2A-F66S-2 | DT/TRM | NA | NA | NA | NA | NA | NA | NA | TRM | TRM | |

brick | G | B2A-F99S-1 | DT/TRM | NA | NA | NA | NA | NA | NA | NA | TRM | TRM | |

brick | G | B2A-F99S-2 | DT/TRM | NA | NA | NA | NA | NA | NA | NA | TRM | TRM | |

brick | G | B2C-F33S-1 | DT/TRM | NA | NA | NA | NA | NA | NA | NA | TRM | TRM | |

brick | G | B2C-F33S-2 | DT/TRM | NA | NA | NA | NA | NA | NA | NA | TRM | TRM | |

brick | G | B2C-F66S-1 | DT/TRM | NA | NA | NA | NA | NA | NA | NA | TRM | TRM | |

brick | G | B2C-F66S-2 | DT/TRM | NA | NA | NA | NA | NA | NA | NA | TRM | TRM | |

brick | G | B2C-F99S-1 | DT/TRM | NA | NA | NA | NA | NA | NA | NA | TRM | TRM | |

brick | G | B2C-F99S-2 | DT/TRM | NA | NA | NA | NA | NA | NA | NA | TRM | TRM | |

brick | G | B3A-F33S-1 | DT/TRM | NA | NA | NA | NA | NA | NA | NA | TRM | TRM | |

brick | G | B3A-F33S-2 | DT/TRM | NA | NA | NA | NA | NA | NA | NA | TRM | TRM | |

brick | G | B3A-F66S-1 | DT/TRM | NA | NA | NA | NA | NA | NA | NA | TRM | TRM | |

brick | G | B3A-F66S-2 | DT/TRM | NA | NA | NA | NA | NA | NA | NA | TRM | TRM | |

brick | G | B3A-F66D-1 | DT/TRM | NA | NA | NA | NA | NA | NA | NA | TRM | TRM | |

brick | G | B3A-F66D-2 | DT/TRM | NA | NA | NA | NA | NA | NA | NA | TRM | TRM | |

brick | G | B3A-F99D-1 | DT/TRM | NA | NA | NA | NA | NA | NA | NA | TRM | TRM | |

brick | G | B3A-F99D-2 | DT/TRM | NA | NA | NA | NA | NA | NA | NA | TRM | TRM | |

rub stone | G | RA-F33S-1 | DT/TRM | NA | NA | TRM | NA | NA | NA | NA | TRM | TRM | |

rub stone | G | RA-F33S-2 | DT/TRM | NA | NA | TRM | NA | NA | NA | NA | TRM | TRM | |

rub stone | G | RA-F66S-1 | DT/TRM | NA | NA | TRM | NA | NA | NA | NA | TRM | TRM | |

rub stone | G | RA-F66S-2 | DT/TRM | NA | NA | TRM | NA | NA | NA | NA | TRM | TRM | |

rub stone | G | RA-F66D-1 | DT/TRM | NA | NA | TRM | NA | NA | NA | NA | TRM | TRM | |

rub stone | G | RA-F66D-2 | DT/TRM | NA | NA | TRM | NA | NA | NA | NA | TRM | TRM | |

[22] | concrete | C | CMU-1 ply-1 | TC | NA | NA | NA | NA | NA | NA | M | NA | NA |

concrete | C | CMU-1 ply-2 | TC | NA | TC | NA | NA | NA | NA | M | NA | NA | |

concrete | C | CMU-1 ply-3 | TC | NA | TC | NA | NA | NA | NA | M | NA | NA | |

concrete | C | CMU-4 ply-1 | TC | NA | NA | NA | NA | NA | NA | M | NA | NA | |

concrete | C | CMU-4 ply-2 | TC | NA | NA | NA | NA | NA | NA | M | NA | NA | |

concrete | C | CMU-4 ply-3 | TC | NA | NA | NA | NA | NA | NA | M | NA | NA | |

clay brick | C | 1 ply-1 | TRM | TRM | NA | NA | NA | NA | NA | NA | NA | TRM | |

clay brick | C | 1 ply-2 | TRM | TRM | NA | NA | NA | NA | NA | NA | NA | TRM | |

clay brick | C | 1 ply-3 | TRM | TRM | NA | NA | NA | NA | NA | NA | NA | TRM | |

clay brick | C | 4 ply-1 | TC | NA | NA | NA | NA | NA | NA | M | NA | NA | |

clay brick | C | 4 ply-2 | TC | NA | NA | NA | NA | NA | NA | M | NA | NA | |

clay brick | C | 4 ply-3 | TC | NA | NA | NA | NA | NA | NA | M | NA | NA | |

[37] | tuff | G | PRR1 | SF/SS | NA | NA | NA | NA | NA | NA | M | NA | NA |

tuff | G | PRR2 | DT | NA | NA | NA | NA | NA | NA | M | NA | NA | |

[39] * | clay brick | C | I10%_SW_RC1 | TRM | NA | TRM | NA | NA | NA | TRM | NA | NA | NA |

clay brick | C | I10%_SW_RC2 | TC | NA | NA | TC | NA | NA | NA | NA | NA | NA | |

clay brick | C | I_SC_PC1 | TRM | NA | NA | NA | NA | NA | TRM | NA | NA | NA | |

clay brick | C | I_SC_PC2 | DT | NA | NA | NA | NA | NA | NA | NA | NA | NA | |

clay brick | C | I25%_F_PC1 | DT | NA | NA | NA | NA | NA | NA | NA | NA | NA | |

clay brick | C | I25%_F_PC2 | DT | NA | NA | NA | NA | NA | NA | NA | NA | NA | |

stone blocks | B | I3%_SW_LB1 | TC | NA | NA | NA | NA | NA | NA | NA | NA | NA | |

stone blocks | B | I3%_SW_FB1 | TC | NA | NA | NA | NA | NA | NA | NA | NA | NA | |

[21] | clay brick | C | specimen#4 | DT | NA | NA | NA | NA | NA | NA | NA | NA | NA |

clay brick | C | specimen#5 | TRM | NA | NA | NA | NA | NA | TRM | NA | TRM | NA | |

clay brick | C | specimen#6 | TRM | NA | NA | NA | NA | NA | TRM | NA | TRM | NA | |

clay brick | C | specimen#7 | DT | NA | NA | NA | NA | NA | NA | NA | NA | NA | |

clay brick | C | specimen#8 | DT | NA | NA | NA | NA | NA | NA | NA | NA | NA | |

clay brick | C | specimen#9 | TRM | NA | NA | NA | NA | NA | TRM | NA | TRM | NA | |

[33] | tuff | G | PS#3 | TC | NA | NA | NA | TC | NA | NA | NA | NA | NA |

tuff | G | PS#4 | TC | NA | NA | TC | TC | NA | NA | NA | NA | NA | |

tuff | G | PS#1 | TC | NA | NA | NA | TC | NA | NA | NA | NA | NA | |

tuff | G | PS#2 | TC | NA | NA | NA | TC | NA | NA | NA | NA | NA | |

[14] | tuff | G | PS#1 | DT | NA | NA | NA | NA | NA | NA | NA | NA | DT |

tuff | G | PS#2 | DT | NA | NA | NA | NA | NA | NA | NA | NA | DT | |

tuff | G | PS#3 | SS/DT/TRM | NA | NA | NA | NA | NA | NA | TRM | NA | NA | |

tuff | G | PS#4 | SS/DT | NA | NA | NA | NA | NA | NA | TRM | NA | DT | |

tuff | G | PT#1 | SS/TRM | NA | NA | NA | NA | NA | NA | TRM | NA | NA | |

tuff | G | PT#2 | SS/TRM | NA | NA | NA | NA | NA | TRM | TRM | NA | TRM | |

tuff | G | PT#3 | SS | NA | NA | NA | NA | NA | NA | NA | NA | NA | |

tuff | G | PT#4 | SS, out-of-plane | NA | NA | NA | NA | NA | NA | NA | NA | NA |

**Note:**C: CTRM; G: GTRM; B: BTRM: shear sliding; SF: shear friction; DT: diagonal tension; TC: toe crushing; TRM: failure of TRM system; NA: Not Accurate, *: shear test, without * diagonal compression test.

## References

- ACI 549-20; Guide to Design and Construction of Externally Bonded Fabric-Reinforced Cementitious Matrix (FRCM) and Steel-Reinforced Grout (SRG) Systems for Repair and Strengthening Masonry Structures. ACI 549.6R. ACI: Farmington Hills, MI, USA, 2020.
- CNR-DT 215; Istruzioni per la Progettazione, l’Esecuzione ed il Controllo di Interventi di Consolidamento Statico mediante l’utilizzo di Compositi Fibrorinforzati a Matrice Inorganica. Consiglio Nazionale delle Ricerche: Roma, Italy, 2018.
- Triantafillou, T. Strengthening of Existing Masonry Structures: Design Models. In Textile Fibre Composites in Civil Engineering; Elsevier Inc.: Amsterdam, The Netherlands, 2016; pp. 375–388. [Google Scholar]
- CNR-DT 200 R1/2012; Guide for the Design and Construction of Externally Bonded FRP Systems for Strengthening Existing Structures. National Research Council: Rome, Italy, 2013.
- Triantafillou, T.C. Strengthening of masonry structures using epoxy-bonded FRP laminates. J. Compos. Constr. ASCE
**1998**, 2, 96–104. [Google Scholar] [CrossRef] - Triantafillou, T.C.; Antonopoulos, C.P. Design of concrete flexural members strengthened in shear with FRP. J. Compos. Constr. ASCE
**2000**, 4, 198–204. [Google Scholar] [CrossRef] - Eurocode 6; Design of Masonry Structures, Part 1-1: General Rules for Building-Rules for Reinforced and Unreinforced Masonry. European Committee for Standardization, CEN: Brussels, Belgium, 2005.
- EN 1998-3; Design of Structures for Earthquake Resistance, Part 3: Assessment and Retrofitting of Buildings. European Standard: Brussels, Belgium, 1998.
- Thomoglou, A.K.; Rousakis, T.C.; Achillopoulou, D.V.; Karabinis, A.I. Ultimate shear strength prediction model for unreinforced masonry retrofitted externally with textile reinforced mortar. Earthq. Struct.
**2020**, 19, 4411–4425. [Google Scholar] - Roca, P.; Lourenço, P.B.; Gaetani, A. Damage and collapse mechanisms in masonry buildings. In Historic Construction and Conservation; Routledge: England, UK, 2019; pp. 239–293. [Google Scholar]
- Thomoglou, A.K.; Rousakis, T.C.; Karabinis, A.I. Investigation of failure modes of URM walls strengthened with TRM subjected to in-plane seismic loads. In Proceedings of the 2nd International Conference on Natural Hazards & Infrastructure, Chania, Greece, 23–26 June 2019. [Google Scholar]
- Thomoglou, A.K.; Rousakis, T.C.; Karabinis, A.I. Experimental Investigation of Shear Behavior of URM strengthened with TRM. In Proceedings of the 4nd Hellenic Conference Mechanical Seismology, Athens, Greece, 5–7 September 2019. [Google Scholar]
- Viskovic, A.; Zuccarino, L.; Kwiecień, A.; Zając, B. Masonry panels composite reinforcements with epoxy matrix, inorganic mortar matrix and PS polymer matrix. Key Eng. Mater.
**2015**, 624, 214–221. [Google Scholar] [CrossRef] - Prota, A.; Marcari, G.; Fabbrocino, G.; Manfredi, G.; Aldea, C. Experimental In-Plane Behavior of Tuff Masonry Strengthened with Cementitious Matrix–Grid. Composites. J. Comp. Constr. ASCE
**2006**, 10, 223–233. [Google Scholar] [CrossRef] - Papanicolaou, C.G.; Triantafillou, T.C.; Karlos, K.; Papathanasiou, M. Textile-reinforced mortar (TRM) versus FRP as strengthening material of URM walls: In-plane cyclic loading. Mater. Struct.
**2007**, 40, 1081–1097. [Google Scholar] [CrossRef] - Del Zoppo, M.; Di Ludovico, M.; Prota, A. Analysis of FRCM and CRM parameters for the in-plane shear strengthening of different URM types. Compos. B Eng.
**2019**, 171, 20–33. [Google Scholar] [CrossRef] - Saleh, H.M.; Eskander, S.B.; Fahmy, H.M. Mortar composite based on wet oxidative degraded cellulosic spinney waste fibers. Int. J. Environ. Sci. Technol.
**2014**, 11, 1297–1304. [Google Scholar] [CrossRef][Green Version] - Saleh, H.M.; Salman, A.A.; Faheim, A.A.; Abeer, A.E. Influence of aggressive environmental impacts on clean, lightweight bricks made from cement kiln dust and grated polystyrene. Case Stud. Constr. Mater.
**2021**, 15, e00759. [Google Scholar] [CrossRef] - Eskander, S.B.; Saleh, H.M. Cement mortar-degraded spinney waste composite as a matrix for immobilizing some low and intermediate level radioactive wastes: Consistency under frost attack. J. Nucl. Mater.
**2012**, 420, 491–496. [Google Scholar] [CrossRef] - Thomoglou, A.K.; Falara, M.G.; Gkountakou, F.I.; Elenas, A.; Chalioris, C.E. Smart Cementitious Sensors with Nano-, Micro-, and Hybrid-Modified Reinforcement: Mechanical and Electrical Properties. Sensors
**2023**, 23, 2405. [Google Scholar] [CrossRef] [PubMed] - Faella, C.; Martinelli, E.; Nigro, E.; Paciello, S. Shear capacity of masonry walls externally strengthened by a cement-based composite material: An experimental campaign. Constr. Build. Mater.
**2010**, 24, 84–93. [Google Scholar] [CrossRef] - Babaeidarabad, S.; De Caso, F.; Nanni, A. URM Walls Strengthened with Fabric-Reinforced Cementitious Matrix Composite Subjected to Diagonal Compression. J. Compos. Constr.
**2014**, 18, 04013045. [Google Scholar] [CrossRef] - Almeida, J.A.P.P.; Pereira, E.B.; Barros, J.A.O. Assessment of Overlay Masonry Strengthening System Under In-Plane 1 Monotonic and Cyclic Loading Using the Diagonal Tensile Test; 2, ISISE, University of Minho, Department of Civil Engineering, School of Engineering: Guimarães, Portugal, 2015. [Google Scholar]
- Ferretti, F.; Tilocca, A.R.; Ferracuti, B.; Mazzotti, C. In situ diagonal compression tests on masonry panels strengthened by FRP and FRCM. In Proceedings of the 12th International Symposium on Fiber Reinforced Polymers for Reinforced Concrete Structures (FRPRCS-12) & 5th Asia-Pacific Conference on Fiber Reinforced Polymers in Structures (APFIS-2015) Joint Conference, Nanjing, China, 14–16 December 2015. [Google Scholar]
- Mazzotti, C.; Ferretti, F.; Ferracuti, B.; Incerti, A. Diagonal Compression Tests on Masonry Panels Strengthened by FRP and FRCM; © Taylor & Francis Group: London, UK, 2016; ISBN 978-1-138-02951-4. [Google Scholar]
- Gattesco, N.; Boem, I. Experimental and analytical study to evaluate the effectiveness of an in-plane reinforcement for masonry walls using GFRP meshes. Constr. Build. Mater.
**2015**, 88, 94–104. [Google Scholar] [CrossRef] - Ismail, N.; Ingham, J.M. In-plane and out-of-plane testing of unreinforced masonry walls strengthened using polymer textile reinforced mortar. Eng. Struct.
**2016**, 118, 167–177. [Google Scholar] [CrossRef] - Tomaževič, M.; Gams, M.; Berset, T. Seismic strengthening of brick masonry walls with composites: An experimental study. In Proceedings of the 4th Structural Engineering World Congress, International Association for Shell and Spatial Structures, Madrid, Spain, 2011; p. 307. [Google Scholar]
- Mustafaraj, E.; Yardim, Y. In-plane Shear Strengthening of Unreinforced Masonry Walls Using GFRP Jacketing. Period. Polytech. Civ. Eng.
**2018**, 62, 330–336. [Google Scholar] [CrossRef][Green Version] - Shabdin, M.; Zargaran, M.; Attari, N.K.A. Experimental DT (shear) test of Un-Reinforced Masonry (URM) walls strengthened with textile reinforced mortar (TRM). Constr. Build. Mater.
**2018**, 164, 704–715. [Google Scholar] [CrossRef] - Babaeidarabad, S.; Arboleda, D.; Loreto, G.; Nanni, A. Shear strengthening of un-reinforced concrete masonry walls with fabric-reinforced-cementitious-matrix. Constr. Build. Mater.
**2014**, 65, 243–253. [Google Scholar] [CrossRef] - Ismail, N.; El-Maaddawy, T.; Khattak, N.; Najmal, A. In-plane shear strength improvement of hollow concrete masonry panels using a fabric-reinforced cementitious matrix. J. Compos. Constr.
**2018**, 22, 04018004. [Google Scholar] [CrossRef] - Lignola, G.; Prota, A.; Manfredi, G. Nonlinear analyses of tuff masonry walls strengthened with cementitious matrix-grid composites. J. Compos. Constr.
**2009**, 13, 243–251. [Google Scholar] [CrossRef] - Borri, A.; Corradi, M.; Castori, G.; Sisti, R. Reinforcement of masonry panels with GFRP grids. In Proceedings of the SAHC2014, 9th International Conference on Structural Analysis of Historical Constructions, Mexico City, Mexico, 14–17 October 2014. [Google Scholar]
- Corradi, M.; Borri, A.; Castori, G.; Sisti, R. Shear strengthening of wall panels through jacketing with cement mortar reinforced by GFRP grids. Compos. B Eng.
**2014**, 64, 33–42. [Google Scholar] [CrossRef][Green Version] - Mustafaraj, E. External Shear Strengthening of Unreinforced Damaged Masonry Walls. Ph.D. Thesis, Epoka University, Tirana, Albania, 2016. [Google Scholar]
- Parisi, F.; Iovinella, I.; Balsamo, A.; Augenti, N.; Prota, A. In-plane behaviour of tuff masonry strengthened with inorganic matrix-grid composites. Compos. Part B
**2013**, 45, 1657–1666. [Google Scholar] [CrossRef] - Gams, M.; Kwiecien, A.; Zajac, B.; Tomacevic, M. Seismic Strengthening of Brick Masonry Walls with Flexible Polymer Coating. In Proceedings of the 9th International Masonry Conference, Guimarães, Portugal, 7–9 July 2014; ISBN 978-972-8692-85-8. ID 1502. [Google Scholar]
- Tomaževič, M.; Gams, M.; Berset, T. Strengthening of stone masonry walls with composite reinforced coatings. Bull. Earthq. Eng.
**2014**, 13, 2003–2027. [Google Scholar] [CrossRef] - Papanicolaou, C.; Triantafillou, T.; Lekka, M. Externally bonded grids as strengthening and seismic retrofitting materials of masonry panels. Constr. Build. Mater.
**2011**, 25, 504–514. [Google Scholar] [CrossRef] - Wang, X.; Lam, C.C.; Iu, V.P. Comparison of different types of TRM composites for strengthening masonry panels. Constr. Build. Mater.
**2019**, 219, 184–194. [Google Scholar] [CrossRef] - Calderini, C.; Cattari, S.; Lagomarsino, S. In-plane strength of unreinforced masonry piers. Earthq. Eng. Struc.
**2009**, 38, 243–267. [Google Scholar] [CrossRef] - Carozzi, F.G.; Milani, G.; Poggi, C. Mechanical properties and numerical modeling of Fabric Reinforced Cementitious Matrix (FRCM) systems for strengthening of masonry Structures. Compos. Struct.
**2014**, 117, 711–725. [Google Scholar] [CrossRef] - Ferrara, G.; Pepe, M.; Martinelli, E. Influence of fibres impregnation on the tensile response of flax textile reinforced mortar composite systems. In Fiber Reinforced Concrete: Improvements and Innovations, RILEM-Fib International Symposium on FRC (BEFIB); Serna, P., Llano-Torre, A., Vargas, J.R.M., Navarro-Gregori, J., Eds.; Springer: Valencia, Spain, 2021. [Google Scholar]
- Gaetani, A.; Fascetti, A.; Nistico, N. Parametric investigation on the tensile response of GFRP elements through a discrete lattice modeling approach. Compos. B Eng.
**2019**, 176, 107254. [Google Scholar] [CrossRef] - De Santis, S.; Hadad, A.; De Caso, B.; De Felice, G.; Nanni, A. Acceptance Criteria for Tensile Characterization of Fabric-Reinforced Cementitious Matrix Systems for Concrete and Masonry Repair. ASCE J. Compos. Constr.
**2018**, 22, 04018048. [Google Scholar] [CrossRef] - Türkmen, Ö.S.; De Vries, B.T.; Wijte, S.N.M.; Vermeltfoort, A.T. In-plane behaviour of clay brick masonry wallettes retrofitted with single-sided fabric-reinforced cementitious matrix and deep mounted carbon fibre strips. Bull. Earthq. Eng.
**2020**, 18, 725–765. [Google Scholar] [CrossRef][Green Version] - Mann, W.; Müller, H. Failure of shear-stressed masonry—An enlarged theory. Tests and application to shear walls. Proc. Br. Ceram. Soc.
**1982**, 30, 223–235. [Google Scholar] - Li, T.; Galati, N.; Tumialan, J.G.; Nanni, A. Analysis of unreinforced masonry concrete walls strengthened with glass fiber-reinforced polymer bars. Aci. Struct. J.
**2005**, 102, 569–577. [Google Scholar] - D’Ambrisi, F.A.; Focacci, F. Experimental and analytical investigation on bond between Carbon-FRCM materials and masonry. Compos. B Eng.
**2013**, 46, 15–20. [Google Scholar] [CrossRef] - Sagar, S.L.; Singhal, V.; Rai, D.C.; Gudur, P. Diagonal shear and out-of-plane flexural strength of fabric-reinforced cementitious matrix-strengthened masonry wallets. J. Compos. Constr.
**2017**, 21, 04017016. [Google Scholar] [CrossRef] - Ferrara, G.; Caggegi, C.; Martinelli, E.; Gabor, A. Shear capacity of masonry walls externally strengthened using Flax–TRM composite systems: Experimental tests and comparative assessment. Constr. Build. Mater.
**2020**, 261, 120490. [Google Scholar] [CrossRef] - Trochoutsou, N.; Di Benedetti, M.; Pilakoutas, K.; Guadagnini, M. Mechanical characterisation of flax and jute textile-reinforced mortars. Constr. Build. Mater.
**2021**, 271, 121564. [Google Scholar] [CrossRef] - Trochoutsou, N.; Di Benedetti, M.; Pilakoutas, K.; Guadagnini, M. Bond of flax textile-reinforced mortars to masonry. Constr. Build. Mater.
**2021**, 284, 122849. [Google Scholar] [CrossRef] - Papadopoulos, N.A.; Naoum, M.C.; Sapidis, G.M.; Chalioris, C.E. Cracking and Fiber Debonding Identification of Concrete Deep Beams Reinforced with C-FRP Ropes against Shear Using a Real-Time Monitoring System. Polymers
**2023**, 15, 473. [Google Scholar] [CrossRef] - Zapris, A.G.; Naoum, M.C.; Kytinou, V.K.; Sapidis, G.M.; Chalioris, C.E. Fiber Reinforced Polymer Debonding Failure Identification Using Smart Materials in Strengthened T-Shaped Reinforced Concrete Beams. Polymers
**2023**, 15, 278. [Google Scholar] [CrossRef] - Ali, A.H.; Mohamed, H.M.; Chalioris, C.E.; Deifalla, A. Evaluating the shear design equations of FRP-reinforced concrete beams without shear reinforcement. Eng. Struct.
**2021**, 235, 112017. [Google Scholar] [CrossRef] - Askouni, P.D.; Papanicolaou, C.G. Experimental investigation of bond between glass textile reinforced mortar overlays and masonry: The effect of bond length. Mater. Struct.
**2017**, 50, 164. [Google Scholar] [CrossRef] - Hojdys, Ł.; Krajewski, P. Tensile Behaviour of FRCM Composites for Strengthening of Masonry Structures—An Experimental Investigation. Materials
**2021**, 14, 3626. [Google Scholar] [CrossRef] - Yardim, Y.; Lalaj, O. Shear strengthening of unreinforced masonry wall with different fiber reinforced mortar jacketing. Constr. Build. Mater.
**2016**, 102, 149–154. [Google Scholar] [CrossRef] - Tarek, D.; Ahmed, M.M.; Hussein, H.S.; Zeyad, A.M.; Al-Enizi, A.M.; Yousef, A.; Ragab, A. Building envelope optimization using geopolymer bricks to improve the energy efficiency of residential buildings in hot arid regions. Case Stud. Constr. Mater.
**2022**, 17, e01657. [Google Scholar] [CrossRef] - Jagadesh, P.; Nagarajan, V.; Karthik prabhu, T.; Karthik Arunachalam, K. Effect of nano titanium di oxide on mechanical properties of fly ash and ground granulated blast furnace slag based geopolymer concrete. J. Build. Eng.
**2022**, 61, 105235. [Google Scholar]

**Figure 1.**Experimental test setup of masonry walls under diagonal compression test (denoted as load P in the Figure) ASTM E519/2010 or in-plane shear test (denoted as loads N and V).

**Figure 2.**(

**a**) Compression stresses and shear stresses in terms of principal stresses (

**b**) Three-linear stress–strain curve of TRM coupon tensile strength.

**Figure 3.**Ranges of experimental shear stresses and strains of binder mortar, masonry wall, strengthening mortar, and TRM textile.

**Figure 5.**Algorithm for defining model accuracy in predicting the failure mode of URM walls retrofitted with a TRM jacket based on the shear strengths (V

_{Rd}, V

_{m}).

**Figure 6.**Estimator charts for (

**a**) the shear capacity predictions of non-strengthened and (

**b**) strengthened URM with different TRM systems for design models and regulations.

**Figure 7.**Accuracy of model predictions for strengthened URM: (

**a**) with the different substrate material, (

**b**) failure modes in masonry substrate, and (

**c**) TRM strengthening system failure.

**Table 1.**Ranges of experimental values of shear stresses and strains of binder mortars, masonry walls, strengthening mortars, and TRM textiles of the strengthened specimens.

τ_{exp} | Range (MPa) | ε | Range (mm/mm) | Failure Mode | Type of TRM | |
---|---|---|---|---|---|---|

Masonry substrate | τ_{εjoint} | 0.041–0.088 | ε_{joint} | 0.000095–0.000410 | SS-SF | GTRM-CTRM |

τ_{εmas} | 0.056–0.058 | ε_{mas} | 0.000330–0.000830 | DT-TC | GTRM-CTRM | |

TRM | τ_{εjoint,d} | 0.041–0.108 | ε_{joint,d} | 0.000009–0.000110 | TRM Failure | GTRM-CTRM |

τ_{εmortar} | 0.049–0.057 | ε_{mortar} | 0.000288–0.003590 | TRM Failure | GTRM-CTRM | |

τ_{TRM} | 0.070–0.151 | ε_{TRM} | 0.004100–0.011700 | TRM Failure | CTRM-CTRM |

Types of Masonry Units | Types of Textile Reinforcement | Coefficient k | ε_{tm} (%) |
---|---|---|---|

brick | glass | 0.55 | 0.057 |

carbon | 0.60 | 0.112 | |

cement | glass | 0.52 | 0.038 |

carbon | 0.52 | 0.015 | |

stone | glass | 0.59 | 0.038 |

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |

© 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Thomoglou, A.K.; Karabini, M.A.; Achillopoulou, D.V.; Rousakis, T.C.; Chalioris, C.E.
Failure Mode Prediction of Unreinforced Masonry (URM) Walls Retrofitted with Cementitious Textile Reinforced Mortar (TRM). *Fibers* **2023**, *11*, 53.
https://doi.org/10.3390/fib11060053

**AMA Style**

Thomoglou AK, Karabini MA, Achillopoulou DV, Rousakis TC, Chalioris CE.
Failure Mode Prediction of Unreinforced Masonry (URM) Walls Retrofitted with Cementitious Textile Reinforced Mortar (TRM). *Fibers*. 2023; 11(6):53.
https://doi.org/10.3390/fib11060053

**Chicago/Turabian Style**

Thomoglou, Athanasia K., Martha A. Karabini, Dimitra V. Achillopoulou, Theodoros C. Rousakis, and Constantin E. Chalioris.
2023. "Failure Mode Prediction of Unreinforced Masonry (URM) Walls Retrofitted with Cementitious Textile Reinforced Mortar (TRM)" *Fibers* 11, no. 6: 53.
https://doi.org/10.3390/fib11060053