- freely available
Materials 2019, 12(7), 1151; https://doi.org/10.3390/ma12071151
2. State of the Art on Retrofitting Techniques for Masonry Structures
2.1. Active and Passive Strengthening
2.2. Some Recent Active Retrofitting Techniques For Masonry Buildings
2.2.1. Punctual Retrofitting Techniques
2.2.2. Continuous Retrofitting Techniques
- It is no longer necessary to anchor the ties into the masonry, because the ribbons close on themselves. This eliminates the problem of the excessive concentrations of stresses induced by the anchorages.
- The straps are made of stainless steel. This avoids the typical corrosion problems of tie rods , which need of a suitable covering or galvanization zinc plating.
- The cross-section of the straps is very small. This allows a moderate increase in the total weight of the structure, useful to not increase the attraction of seismic forces too much.
- Each strap is a bi-dimensional device. This allows the ribbons to provide in-plane and transversal post-compression at the same time.
- The steel ribbons continue to wrap masonry even after masonry crushing. This is of fundamental importance for safeguarding life, as people do not risk that some part of the structure hits them, due to building collapse.
3. An in-Depth Study of the Three-Dimensional Continuous Systems: The Actual Strengthening Mechanisms
3.1. The Φ System
- (Figure 16): the greatest circle is associated with the plane (blue circle). Both the red and blue circles become smaller and move away from the limit surface. This increases the minimum distance between the greatest circle and the limit surface, which provides a measure of the safety factor. Thus, the higher the value of in this interval, the higher the safety factor. In other words, the retrofitting intervention is effective in this field. More precisely, it is all the more effective the higher the out-of-plane post-compression. At the end of the interval, when , the red circle degenerates into a point and the blue circle superimposes onto the green circle.
- (Figure 17): the greatest circle is associated with the plane (green circle). When the out-of-plane compression, , increases from the value to the value (in absolute value), the radius of the red circle increases while the radius of the blue circle decreases. It could seem that the safety factor does not change in this interval: since the radius of the greatest (green) circle does not modify, the safety factor does not seem to depend on the value of . In fact, the discussion about the safety factor is a bit more complex. As a matter of fact, retrofitting the masonry wall modifies the overall behavior of the wall, that is, modifies the limit surface, all the more greater as the stress of the threaded bars increases. The new limit surface is a combination of the two limit surfaces of masonry and steel. Thus, it seems reasonable that the new limit surface is wider and flatter than the limit surface in Figure 17. In conclusion, if computed as the minimum distance between the greatest circle and the combined limit surface, the safety factor slightly increases even in this interval. At the end of the interval, when , the red circle superimposes onto the green circle and the blue circle degenerates into a point.
- (Figure 18): the greatest circle is associated with the plane (red circle). Both the red and blue circles become greater. In particular, the red circle grows closer to the limit surface of masonry. This decreases the minimum distance between the greatest circle and the masonry limit surface. The minimum distance between the greatest circle and the combined limit surface also decreases, but slower than the previous one. In conclusion, in the third interval the combined safety factor decreases. Moreover, there are two limit values of : the first limit value of makes the red circle tangent to the masonry limit surface (Figure 19) and the second limit value, , higher than the previous one (in absolute value), makes the red circle tangent to the combined limit surface. The crisis takes place for the second limit value and occurs in a plane parallel to the z axis. Thus, the retrofitting system modifies the crisis mechanism.
3.2. The CAM System
- (Figure 25), where is the modified lateral stress, the greatest circle is associated with the plane (blue circle). As increases (in absolute value), even increases (in absolute value), but , the variation of , is lower than , the variation of , because the constraint degree along the vertical direction is higher than the constraint degree along the transverse direction:
- (Figure 26), where and are the modified lateral and vertical stresses, the greatest circle is associated with the plane (green circle). As increases, and increase as for the previous interval:
- (Figure 27), where is the modified vertical stress, the greatest circle is associated with the plane (red circle). , , and increase according to the inequalities (5). All the circles become greater, with the red circle that grows closer to the limit surface of masonry (and to the combined limit surface). This decreases the safety factor but, for each given , the safety factor of the CAM system is higher than that achievable with the Φ system. The crisis takes place when the red circle becomes tangent to the combined limit surface and occurs for a value of that is higher than the of the Φ system. Even for the CAM system, the retrofitting modifies the crisis mechanism, since the new sliding plane is parallel to the z axis.
4. A Critical Analysis of the Design Criteria for the CAM System
- is the design compressive strength of the unreinforced masonry (URM);
- is a dimensionless coefficient of strength increase, which depends on the mass density, , through the relationship:
- is the effective confinement pressure, that is, the confinement pressure reduced by a coefficient of efficiency, , defined as the ratio between the effectively confined volume of the masonry wall, , and the volume of the masonry wall, :
- , in the absence of proven experimental results, is equal to 0.5.
- The orange plot is the limit domain for unreinforced masonry;
- The blue plot is the limit domain for confined masonry (only horizontal straps);
- The red plot is the limit domain for masonry reinforced by the CAM system (both horizontal and vertical straps).
- For masonry units of the lower stories, where the constraint degree is very high—at the limit, infinite—along the in-plane directions, the two continuous retrofitting systems perform almost the same way. In particular, both provide the maximum increase of the safety factor for low values of .
- For masonry units of the upper stories, where the constraint degree is low—but never equal to zero—along the in-plane directions, the effectiveness of the continuous systems depends on the additional transverse stress provided by retrofitting. In particular, for low values of the Φ system is more effective than the CAM system in increasing the safety factor, for intermediate values of the safety factor achieved after retrofitting depends on the single intervention and deserves further deepening and, lastly, for high values of the maximum advantage in terms of safety factor is given by the CAM system.
6. Further Developments
Conflicts of Interest
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|Label||Damage Level||Description||Masonry Buildings||Reinforced Concrete (RC) Buildings|
|DS1||Negligible to slight damage||No structural damage, slight nonstructural damage|
|DS2||Moderate damage||Slight structural damage, moderate nonstructural damage|
|DS3||Substantial to heavy damage||Moderate structural damage, heavy nonstructural damage|
|DS4||Very heavy damage||Heavy structural damage, very heavy nonstructural damage|
|DS5||Destruction||Very heavy structural damage|
|Label||Building Class||No. of Stories|
|IMA1||Masonry—irregular layout—flexible floors—with tie rods and/or tie beams||1–2|
|IMA2||Masonry—irregular layout—flexible floors—without tie rods and tie beams||1–2|
|RMA2||Masonry—regular layout—flexible floors—without tie rods and tie beams||1–2|
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