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Confining elements of reinforced concrete
Masonry is a brittle material that resists small deformations. Then concrete elements with thickness equal to the wall thickness and width ranging from 0.15 m to 0.20 m are in general added to improve its behavior. The compressive strength of these elements must be greater or equal than 15.0 MPa and the percentage of the longitudinal steel ratio must be greater (or equal) than 0.2f’c/fy, where f’c is the concrete compressive strength and fy is the steel yield strength [42].
In Mexico, concrete elements commonly used have four longitudinal bars 9.5 mm diameter yield stress equal to 42 MPa and stirrups 6.5 mm diameter yield stress equal to 23 MPa [48] [107]. Besides, in the market there are prefabricated rebar formed by three or four longitudinal smooth or rough wire and stirrups of the same material with steel yield stress greater than 50 MPa [33]. Figure 2.1 shows the components of confined masonry walls, which tie-columns should be located at maximum distance of 3.0 m or 1.5H. For any wall opening with length greater than one quart of wall length confining elements should be used [42].
Failure modes of confined masonry walls
From damage observed after earthquakes and tests’ results of confined masonry walls have been identified several mechanisms of failure under in-plane lateral loads. Among many other variables, the resistance of masonry (combination of masonry units and joints), the resistance of the concrete columns, the quality of workmanship and steel reinforcement ratio define the failure pattern [66] [85] [106]. The following paragraphs describe four main failure modes.
1. Flexion failure. This failure mode appears on slender walls, where the tension is high and causes the yield of the longitudinal steel and the compression failure on the wall’s corners [20], Figure 2.4a.
2. Sliding shear failure. Sliding of a portion of the wall along to the horizontal joint occurs when the shear stress is greater than the shear strength. Sliding produces the short column effect on the concrete elements that generates plastic hinges [106], Figure 2.4b.
3. Diagonal tension failure. This failure mode occurs because the stress along the wall diagonal exceeds the masonry tensile strength causing diagonal cracking. [106][107], Figure 2.4c.
4. Splitting failure by diagonal compression. It happens when there is separation between masonry and concrete columns on discharged corners. A compression strut is then formed. This generates compression at the loaded corners and causes crushing of the masonry units [106], Figure 2.4d.
In two last failures modes, masonry may fail for a combination of the units cracking and joints sliding. In general, the failure occurs in the units when they are weaker than the joints. Indeed, the failure appears in the vertical or horizontal joints, Figure 2.5.In this context, it is important to define the state-of-the art of the experimental research guided to evaluate the behavior of masonry units and confined masonry walls. It is worth to notice that some experimental results were used to define the parameters required in the building codes. In addition, this information was useful to define the experimental program presented herein and to compare their results (chapter 4), in order to elaborate the numerical models (chapters 5 and 6). Figure 2.6 shows the different sites where have been developed full-scale masonry walls tests.
Experimental and numerical study of confined masonry walls under in-plane loads
Experimental research in Mexico City
In Mexico City and its surroundings, where a quarter of the Mexican population lives, there are areas with records of large damage caused by earthquakes in 1957 and 1985. Then, the pioneering studies about the masonry walls behavior were carried out at the National Autonomous University of Mexico (UNAM). The more important experimental studies are:
• Meli and Salgado (1969) tested 34 confined masonry walls under monotonous and cyclic loading. They used the same mortar to glue hollow concrete blocks, hollow and solid bricks, whereas the reinforced concrete elements had different longitudinal reinforcement ratios. All walls were fixed to a bottom massive concrete beam and most of them had vertical and horizontal movement on top. The results showed the failure types, the load-deformation characteristics, the influence of the vertical load and established criteria to seismic design. The walls with low longitudinal reinforcement ratio showed horizontal cracks at the bottom concrete beam-masonry interface and at the top joints while the presence of vertical loads reduced by flexural cracks. At the end, cracks appeared along the wall diagonal.
• Meli and Hernandez (1971) and Meli and Reyes (1971) developed an extensive program on different pieces and mortars to evaluate the compressive strength and other statistical parameters. Besides, compression tests on prisms built from different units to measure the axial stress vs. strain relationship were carried out. Shear tests on three-piece prisms were also performed for assessing the joint cohesion under different confining stress. Diagonal tension test on masonry panels were also developed. Some results are still used by building local codes [42] [45].
• Alcocer, Muria and Peña (1999) tested in shaking table three models of reduced scale 1:3, two models ratio H/L = 1 (Height/Length) and other model ratio H/L = 1.5. These represented the ground floor of a four-level building, which were constituted by two parallel walls fixed by an upper reinforced concrete slab. From the results, it could be concluded that the shear deformations were more important for models H/L = 1, while the flexural deformations predominated for the model H/L = 1.5, Figure 2.7.
The National Center for Disaster Prevention (CENAPRED) has developed a large number of full-scale walls tests under cyclic loading. The following experiments are the more important:
• Alcocer, Flores and Sanchez (1993) tested three systems built from two confined masonry walls, 2.5 m height. An upper system beam-concrete slab cast in-situ linked the walls and created the space of a door, Figure 2.8. Different reinforcements in horizontal joints of two systems were placed and the third un-reinforced system was the control specimen. A compression stress equal to 0.50 MPa simulated the gravitational load and cyclic lateral loads were applied. All systems showed cracks in X. Besides, the edge wall above the diagonal wall displaced with respect to the inferior edge wall generating cracking at both ends of the tie-columns for the maximum load.
• Sanchez, Alcocer and Flores (1996) developed the first full-scale test of a two-level building in Mexico. Two parallel systems of identical walls with perpendicular restriction in order to eliminate torsion effects composed each level. The main conclusion were: a) the structure resistance was satisfactory with respect to that proposed by the local code, b) the shear deformation and diagonal tension cracking of the masonry dominated the building behavior, b) hysteretic cycles were symmetric and stables. In addition, it could be seen that the resistance of the three-dimensional structure can be extrapolated from the walls’ individual resistance.
• Aguilar (1997) tested, under cyclic load, four masonry walls built with solid clay bricks, 2.5 m X 2.5 m. Three walls were reinforced with different percentages of steel ratio inside the horizontal joints. A fourth un-reinforced wall was the control specimen, which failed by diagonal cracking. The results showed resistance evolution, high deformation capacity of reinforced walls and identification of three behavior stages. The first stage is linear behavior and ends with the presence of the first cracks due to diagonal tension, the second stage finishes at the peak load, and the third stage shows resistance degradation and the distortion increment until the longitudinal steel failure, Figure 2.9. From wall instrumentation, it can be seen that the tie-columns resist 70% of the vertical load.
Experimental research outside Mexico City
Additional to Mexico City, two sites have evidence of tests on confined masonry walls. The first site is the Structures Laboratory at the Autonomous University of Nuevo Leon (UANL) in the Northern, where there is not seismic hazard. The second site is the Structures Laboratory at the University of Guadalajara (UG) located in high seismic hazard zone, Figure 2.6. The following paragraphs describe these experimental programs.
• Trevino et. al (2004) tested eight confined masonry walls built with hollow concrete blocks, 2.5 m X 2.5 m, under cyclic loading. Four longitudinal bars 9 mm diameter linked through stirrups reinforced the columns of four walls and prefabricated steel reinforcing frames were used on the columns of the remaining walls. The lateral load was applied in two series under constant vertical stress equal to that applied at the ground floor of a five-level building. Loading control for the first series and control displacement for the second series were applied. Symmetrical hysteretic, typical of the confined masonry were measured. In the same way, the tie-columns failure and the longitudinal reinforcement yield happened after the masonry units’ failure. The authors found no significant behavioral differences between the two sets of walls, Figure 2.10.
• Hernandez and Urzua (2002) built three masonry walls by using lightweight lime-cement blocks commonly used to construct residential buildings. Size of the walls, 2.50 m X 2.5 m, represented the dimension of a building wall with vertical loads similar to those applied at the ground floor of a two-level building. The concrete columns had four longitudinal bars 9 mm diameter. Tests on prisms and masonry panels were also carried out to evaluate the compressive strength, shear strength, and modulus of elasticity. Dynamic loads corresponding to displacement associated to El Centro accelerogram were applied. The main conclusions were: a) the walls have shear failure mode, b) the walls fail due to diagonal tension of masonry units, and c) the resistance of the three specimens was identical, Figure 2.11. They proposed an expression to evaluate the stiffness degradation in function of the walls rotation, R.
In other way, the influence area of this project is Guerrero State, where the experimental programs have focused on evaluation of the mechanical characteristics of masonry specimens and masonry units. For example, Salgado (2000) conducted a field study among the building workers for assessing the characteristics of mortars, masonry units, as well as the compressive strength of the concrete elements. Additionally, he tested eighteen panels of 0.80 m X 0.80 m reinforced with metallic reinforcement mesh and mortar.
A second study developed by Navez (2002) included tests on twenty-one panels of solid clay bricks, three panels of hollow concrete blocks, and three panels of solid concrete blocks. Mortars type I and II were used according to local code. The shear strength of solid clay bricks and hollow concrete blocks panels was slightly less than the specified value, while the shear strength of concrete block panels was adequate with respect to the normative value. In addition, tests on masonry prisms in order to evaluate the compressive strength were carried out with satisfactory results.
To determine the influence of the manual fabrication process on mechanical properties of solid clay bricks, Jorge (2005) conducted an experimental study to measure the physical properties of the raw material, the compressive strength of masonry units and the modulus of rupture. The two last parameters had mean values equal to 5.6 MPa and 1.2 MPa.
Retrofitting and rehabilitation of masonry
After an earthquake occurrence, an inspection to evaluate the residual safety of the buildings must be done. It has three possible outcomes: the building is safe, the construction should be repaired, and the building should be destroyed. For the second case, the reparation process called “retrofit” can apply in order to recover the original seismic resistance. A different situation occurs in those structures which resistance should be improved to achieve an acceptable level of safety, as is the current case for historic structures. This process is called “rehabilitation” [105].
Types of reinforcement
There are two main forms to place the reinforcement, one placed on the wall faces, called herein external reinforcement, and another placed inside the joints[18] [87][106], Figure 2.12. Although other types of reinforcement exist, such as fiber reinforced polymer [37] [94] and plastics straps [91], next paragraphs describe the particular case of two experimental researches with similar reinforcements to those used herein. This information will be useful to compare the results in chapter 4.
Table of contents :
Chapter 1 ntroduction
1.1 Justification
1.2 Main objective and goals
1.3 Study contents
Chapter 2 Masonry review
2.1 Introduction
2.2 Confined masonry
2.2.1 Masonry units
2.2.2 Mortars
2.2.3 Confining elements of reinforced concrete
2.3 Failure modes of confined masonry walls
2.4 Experimental research in Mexico
2.4.1 Experimental research in Mexico City
2.4.2 Experimental research outside Mexico City
2.5 Retrofitting and rehabilitation of masonry
2.5.1 Types of reinforcement
2.5.1.1 External reinforcement
2.5.1.1 Reinforcement of mortar joints
2.6 Design of masonry buildings in Guerrero State
2.7 Conclusions
Chapter 3 Masonry modeling review
3.1 Introduction
3.2 Types of masonry models
3.3 Masonry micro-models
3.4 Masonry macro-models
3.4.1 Level-one macro-models
3.4.1 Level-two macro-models
3.5 Simplified models
3.6 Conclusions
Chapter 4 Experimental program and results
Experimental and numerical study of confined masonry walls under in-plane loads
4.1 Introduction
4.2 Description of the experimental program
4.3 Tests on elements
4.3.1 Compressive strength of solid clay bricks
4.3.2 Mortars
4.4 Test on specimens
4.4.1 Mechanical properties of mortar joints
4.4.2 Shear strength of masonry panels
4.4.2.1 Behavior of unreinforced panels
4.4.2.2 Behavior of reinforced panels
4.4.2.3 Panels associated to masonry walls
4.4.3 Compressive strength of masonry prisms
4.5 Test on confined masonry walls
4.5.1 Description of the mechanical-electronic devices and apparatus
4.5.2 Building process and characteristics of walls
4.5.3 Instrumentation of walls
4.5.4 Test on wall MUR1
4.5.5 Test on wall MUR2
4.5.6 Test on retrofitted wall MRM2
4.5.6.1 Retrofit process
4.5.6.2 Description of behavior and failure mode
4.5.7 Test on rehabilitated wall MMR3
4.5.7.1 Rehabilitation process
4.5.7.2 Description of behavior and failure mode
4.5.8 Comments about the behavior of confined masonry walls
4.6 Conclusions
Chapter 5 Numeric simulations of masonry walls behavior
5.1 Introduction
5.2 Masonry modeling by using micro-models
5.2.1 Behavior of the mortar joint
5.2.1.1 Shear slipping mode
5.2.1.2 Tension cut-off mode
5.2.1.3 Compression cap mode
5.2.1.4 Corners
5.2.2 Behavior of masonry units
5.2.3 Behavior of concrete elements
5.3 Micro-models for the masonry panels
5.3.1 Unreinforced masonry panel MM1
5.3.1.1 Modeling
5.3.1.2 Mechanical properties
5.3.1.3 Results
5.3.2 Reinforced masonry panel
5.3.2.1 Modeling
5.3.2.2 Results
5.4 Micro-model of confined masonry wall
5.4.1 Model of the wall MUR2
5.4.1.1 Description and modeling
5.4.1.2 Mechanical properties
5.4.1.3 Results
5.4.2 Model of the wall MUR2 with metallic reinforcement mesh inside the joints
5.5 Masonry modeling by using a macro-model level two
5.5.1 Background
5.5.1.1 Behavior of masonry
5.5.1.2 Behavior of concrete columns
5.6 Analysis procedure and results
5.6.1 Results of the wall MUR2
5.6.2 Results for other walls
5.7 Conclusions
Chapter 6 Simplified models to asses the lateral masonry walls bearing capacity
6.1 Introduction
6.2 Experimental information
6.3 Vertical load supported by the masonry
6.4 Shear failure model
6.4.1 Masonry wall resistance
6.4.1.1 Masonry resistance
6.4.1.2 Vertical load effect
6.4.1.3 Columns resistance
6.4.2 Results
6.5 Induced tension failure model
6.5.1 Masonry wall resistance
6.5.2 Results
6.6 Comparison of results for both models
6.7 Limits of application
6.8 Conclusions
Chapter 7 Conclusions and perspectives
