# 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.

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**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 |

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## 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