# Tensile Capacity of Adhesive Anchors in Damaged Masonry
## 4 Discussion
### Comparison of Experimental Results with Prediction Equations  
To use post-installed bonded anchors in masonry in Europe, the assessment of the adhesive performance must be performed according to EAD 330,076 (European Assessment Document) [13] issued by EOTA. The associated document to design anchor connections is the TR054 [14] which requires the evaluation of all possible failure modes (considering even joint influence), under tension loading namely: steel failure, pull-out failure of the anchor, brick breakout failure, pull-out of one brick. The document gives formulations only for steel (N\({}_{\text{rk,s}}\)) and pull-out of one brick (N\({}_{\text{rk,pb}}\)) characteristic failure loads, while other failure modes must be experimentally assessed according to EAD and are reported in the ETA (European Technical Assessment) of the anchor system. For the considered case it results:  
\[\text{N}_{\text{rk,s}}=\text{A}_{\text{s}}\text{f}_{\text{uk}}=27.1\text{ kN} \tag{1}\]  
\[\text{N}_{\text{rk,pb}}=2\text{l}_{\text{brick}}\text{b}_{\text{brick}}\text{ (}0.5\text{ f}_{\text{rk,0}}+0.4\text{ \sigma}_{\text{d}}\text{)}+2\text{ h}_{\text{brick}}\text{b}_{\text{brick}}\text{ 0.5 f}_{\text{rk,0}}=12.1\text{ kN} \tag{2}\]  
where A\({}_{\text{s}}\) and f\({}_{\text{uk}}\) are the bar area and the ultimate steel strength, b\({}_{\text{brick}}\), b\({}_{\text{brick}}\), h\({}_{\text{brick}}\) are the length, width, and height of the brick, f\({}_{\text{rk,0}}\) is the initial shear strength of the masonry mortar and \(\text{\sigma}_{\text{d}}\) is the compressive stress perpendicular to the bed joint.  
Several brick breakout formulations, based mainly on the concrete capacity design (CCD) method developed for anchors in concrete [21], can be found in literature. Usually, the proposed methods [36; 37] consider a constant tensile strength acting on the projected area of the failure cone to evaluate the ultimate mean load. The main difference among models is related to the evaluation of the tensile strength (which is correlated to compressive strength f\({}_{\text{m}}\)) and on the projected area which can be assumed in different ways (cone or pyramid with an angle of 35\({}^{\circ}\) or 45\({}^{\circ}\)). Those models overestimate the expected ultimate load (range of about 18-70 kN). In [18] another approach is proposed for brick breakout failure of clay bricks, which is based on results with perforated bricks and considers a linear influence of the embedment depth. The characteristic resistance is calculated as follows (with f\({}_{\text{b}}\) the average brick compressive strength and h\({}_{\text{ef}}\) the effective embedment depth):  
\[\text{N}_{\text{b}}=11.4\text{ }\sqrt{\text{f}_{\text{b}}}\text{ h}_{\text{ef}} \tag{3}\]  
\[\text{N}_{\text{b}}=9.7\text{ kN from Equation (3)}\]  
The available formulations seem to be unsuitable to predict the ultimate load, in some cases it is overestimated (with the CCD approach overestimate [36; 37]) or underestimated as in Equation (3), presumably because of the linear approach. In addition, it should be considered that the formulations do not consider cracking and damage level of the wall.  
From experimental evidence the resistance for anchor pull-out failure can be predicted from Table 1, neglecting the anchors that exhibited steel or brick failure.  
Figure 13: Stiffness of the linear branch of the load-displacement curves vs. crack width.  
By considering all tests, it results a characteristic value (5% fractile)  
\[\text{N}_{\text{rk,p}}=4.0\text{ kN (19 tests; cov}=35\%)\]  
While considering only test of anchors in crack width lower than 1.0 mm, it results  
\[\text{N}_{\text{rk,p}}=10.9\text{ kN (15 tests; cov}=21\%)\]  
This last result suggests that anchors that underwent a limited cyclic damage (limited crack width) are still able to sustain a high carrying capacity.