Literature review
2.2 Unreinforced masonry
A significant part of the buildings in the province of Groningen is constructed of unreinforced masonry (URM). URM is a composite material, consisting of brick units that are interconnected by mortar. The basic material properties of both individual elements are presented in section 2.2.1.
Then, section 2.2.2 introduces several mechanical properties of the composite material. Afterwards, section 2.2.3 describes common failure mechanisms of URM walls. Eventually, in section 2.2.4, the hysteretic behavior of URM structures is described.
2.2.1 Material properties of individual elements
Brick units can be made out of different materials. The majority of the building stock in Groningen comprises structures that contain either clay (CL) units or calcium silicate (CS) units [19]. The units generally show brittle behavior in compression, as can be seen in Figure 2.6a. Their tensile strength is relatively small compared to the compressive strength, which is common for brittle materials.
Nevertheless, the tensile strength generally still exceeds the bond strength between the units and the mortar [20]. Due to the fact that the tensile strength of the units will not be normative when applied in a masonry structure, the compressive strength of the units is of main interest. In order to connect the brick units, mortar is applied. In the majority of the masonry structures in Groningen that are constructed using CL brick units, general purpose mortar is applied [21]. For masonry structures that are constructed using CS brick units, the type of applied mortar generally depends on the construction year of the structure [22]. Mortars are classified by their compressive strength, although they show significantly more ductility than brick units, as shown in Figure 2.6b.
a) CL units b) mortar
Figure 2.6: Compressive stress-strain relationship of both brick units and mortar [23].
The individual material properties of both the brick units and the mortar have quite a significant influence on the eventual behavior of the composite material. However, also the adhesion between both components is of great importance, because the level of adhesion determines the initial shear strength and the flexural bond strength of the masonry [24].
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2.2.2 Mechanical properties Compressive strength
Figure 2.7 shows compressive stress-strain relationships for three types of masonry, that are con-structed using one type of clay brick units and three different types of mortar: (a) weak, (b) strong;
and (c) intermediate mortar. The masonry prisms show a response that can be categorized in between the brittle response of the brick units and the more ductile response of the mortar. Furthermore, the significant influence of the applied type of mortar can be seen.
Figure 2.7: Compressive stress-strain relationship of units, mortar and masonry [23].
Shear strength
The shear strength of masonry is influenced by the normal stress that is present in a masonry wall, which depends on the weight and the loading conditions of the structure that is surrounding the masonry wall of interest. Therefore, no single value can be derived that describes the shear strength of a masonry wall on itself.
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Figure 2.8 shows the failure envelope of masonry, subjected to a shear force and an axial load, for different ratios between the shear stress and the normal stress in the wall. Three different failure mechanisms, as illustrated in Figure 2.9, can be distinguished from the failure envelope [24]:
a. Sliding shear failure
The maximum shear stress increases for an increasing normal stress, until the bed joints fail in shear. This type of failure is shown in Figure 2.9a;
b. Diagonal tension cracks
For a further increase of normal stress, the maximum principle tensile stress exceeds the diagonal tensile stress of the masonry, which results in a diagonal crack [25]. This crack can either run via the joints or in a straight diagonal line through the brick units. The type of diagonal tension crack that will occur depends on the relative material properties of the brick units and the mortar. This type of failure is shown in Figure 2.9b;
c. Failure in compression
For an even further increase of normal stress, the masonry wall will fail in compression at the toe, i.e. the masonry in the bottom right corner will crush. This type of failure is shown in Figure 2.9c.
Figure 2.8: Failure envelope of masonry, subjected to a shear force and an axial load [24].
a) sliding shear failure b) diagonal tension cracks c) failure in compression Figure 2.9: Failure mechanisms of masonry, subjected to a shear force and an axial load [26].
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Flexural strength
The flexural strength having a plane of failure parallel to the bed joints (bending around horizontal axis) differs from the flexural strength having a plane of failure perpendicular to the bed joints (bending around vertical axis). Both planes of failure are shown in Figure 2.10.
a) bending around horizontal axis b) bending around vertical axis Figure 2.10: Planes of failure of masonry in bending [27].
For the flexural strength around the horizontal axis, the adhesion between the brick units and the mortar is normative. For the flexural strength around the vertical axis, the eventual failure mechanism will depend on several factors, such as the relative strengths of the mortar and the brick units, the adhesion between both elements and the applied masonry bond [24].
2.2.3 Failure mechanisms
URM structures often suffer damage due to earthquake loading. The observed damages can be categorized in the following common failure modes [28]:
• lack of anchorage;
• anchor failures;
• in-plane failures;
• out-of-plane failures;
• combined in-plane and out-of-plane effects;
• diaphragm-related failures.
These failure modes are shortly described in the following sections [28,29].
Lack of anchorage
In URM structures, beams and floor slabs often simply rest on walls. In such a structure, there is an absence of positive anchorage of floors and roofs to the URM walls. In case ground motions do occur, the exterior URM walls therefore can behave as cantilevers over the total height of the building. This behavior results in high flexural stresses at the base of the walls, which increases the risk of out-of-plane failure. In case the beams slip from their supports, this can even yield global failure of the URM structure.
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Anchor failures
In case any anchorage of beams and floors to walls is present in URM structures, these anchors are often not designed for seismic reasons. Therefore, anchor failure is likely to occur as a result of earthquake loading. The type of failure naturally depends on the type of anchors that is used:
failure of the anchor itself can occur, as well as rupture at the connection points between the anchor and its base.
In-plane failures
In-plane (IP) failures can occur due to shear or bending. The first type of IP failure, due to shear, is most common for URM structures. The failure mechanisms sliding shear failure and diagonal tension cracks, as illustrated in Figure 2.9a and b, concern IP failures due to shear. Due to the nature of earthquakes, the direction of the corresponding lateral loading fluctuates over time. Therefore, double-diagonal (X) cracks are regularly observed in seismic zones, as shown on the left side in Figure 2.11.
The latter type of IP failure, due to bending, mainly occurs to slender piers. Due to bending, flexural tensile cracks arise at the base of the pier. For an increasing lateral load, the pier starts to rotate around the compression zone. This relatively ductile phenomenon is called rocking. In case the compressive stresses in the compression zone exceed the compressive strength of the masonry, so-called toe-crushing of the masonry occurs at the pier’s toe. This is illustrated in Figure 2.9c.
Failure of the ends of a specific URM pier causes the pier to behave as a loose rigid body that is isolated from the adjacent structural elements. Therefore, the pier does not provide any lateral resistance anymore to the rest of the structure. This type of failure is shown on the right side in Figure 2.11. Generally, IP failures do not directly endanger the load-bearing capacity of the wall.
a) In-plane shear failure [30] b) In-plane bending failure [31]
Figure 2.11: In-plane failures of URM walls.
The IP failure behavior of a URM wall is influenced by several factors, among others by the aspect ratio. The aspect ratio is defined as the ratio between the height and the length of a (part of a) URM wall. A slender pier tends to fail in bending, whereas a stocky pier tends to fail in shear [32].
The residual lateral resistance of a URM wall is relatively high in case an IP shear failure is present, compared to a situation in which an IP bending failure is present [33]. Due to the fact that the
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aspect ratio of a URM wall has a significant influence on the type of IP failure that will most likely occur, the aspect ratio also influences the lateral resistance of a URM wall.
Generally, numerous openings are present in URM facades. The positioning of the openings deter-mines the geometry and the corresponding aspect ratios of the URM wall and, therefore, influences the type of failure that will tend to occur. Adapting the configuration of openings in URM walls can change the ductility and the seismic capacity of walls significantly [34].
Out-of-plane failures
URM structures are most vulnerable to flexural out-of-plane (OOP) failure. Due to the unstable nature of this type of failure, the load-bearing capacity of a URM wall will be endangered in case an OOP failure occurs. The vulnerability of a wall to an OOP failure depends, among other things, on the level of anchorage between the floors in a structure and the wall.
In case there is no or insufficient anchorage between floors and walls, no OOP support is provided to the walls over their height. This results in cantilever behavior over the total height of the building instead of over the individual story heights.
The same principle applies to parapets, which are non-structural URM elements, at the top of the building, that vertically extend beyond the roof line [28]. Such a URM part often is supported at the bottom side only and, therefore, behaves as a cantilever. In combination with the fact that parapets are subjected to the greatest amplification of the ground motions, due to their high position in a structure, OOP failures of parapets are commonly observed. Figure 2.12 shows a parapet failure due to the Christchurch earthquake in 2011.
Figure 2.12: Out-of-plane failure of parapet [35].
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In case a sufficient number of anchors is present between floors and a specific URM wall, the total wall can be schematized as several individual walls that span in between the floors of the structure.
In this situation, the URM walls are supported at both ends by the floors at the bottom and the top of the wall. In case of an earthquake, the movements of the structure will be introduced to the URM walls via the floors, so at the two supports of the URM walls. This configuration will be evaluated in this research.
Combined in-plane and out-of-plane effects
URM walls are loaded in both their in-plane and their out-of-plane direction, due to the bidirectional nature of earthquakes. Therefore, combined IP and OOP effects do occur. For example, an IP failure, resulting in diagonal cracks, can change the configuration and the supporting conditions of a URM wall, making the wall more vulnerable to OOP failure. Identification of this combined failure mode, however, is complex. Generally, such failures will therefore be wrongly attributed to OOP loading only.
Diaphragm-related failures
The flexibility of floor diaphragms within a URM structure can have a substantial impact on walls that are surrounding the diaphragms. IP rotation of the ends of a diaphragm can induce damage to the adjacent walls. Also, a lack of shear anchors between floors and adjacent walls can yield diaphragm-related failures. For example, a lack of shear anchors between a floor diaphragm and a wall that is positioned parallel to a ground motion can yield damage in an adjacent wall that is positioned perpendicular to the ground motion. The shortage of anchors prevents a full transmission of IP shear forces in the floor diaphragm to the shear wall, resulting in a transfer of the residual forces perpendicular to the other wall. This type of failure mainly occurs in long, narrow buildings.
2.2.4 Hysteresis
At larger deformations, URM structures dissipate energy due to their nonlinear behavior. In case of cyclic forces or deformations, which is the case for earthquake loading, this behavior results in a force-deformation hysteresis loop. The area within a singe hysteresis loop indicates the amount of damping energy that has been dissipated within the corresponding deformation cycle [15]. In order to account for the energy dissipation due to nonlinear behavior, the nonlinear relationship between force and deformation must be implemented in the stiffness component in the EOM.
Due to the complexity of predicting the exact behavior of URM structures, it is desirable to obtain the correct nonlinear relationship between force and deformation through experiments. Therefore, many experiments have been performed in which URM components are subjected to cyclic loading conditions. The obtained nonlinear behavior depends on the type of failure, and thus on related influencing factors such as the applied materials, the aspect ratio and the normal stress that is present [29]. Figure 2.13 shows qualitative force-deformation loops that correspond to the aforementioned IP failure mechanisms, as illustrated in Figures 2.8 and 2.9. Differences in the areas of the hysteresis loops can be obtained, indicating the significant influence of the factors on the eventual energy dissipation in the system.
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a) sliding shear failure b) diagonal tension cracks c) failure in compression Figure 2.13: Qualitative force-deformation loops for different IP failure mechanisms URM walls [36].
While a considerable amount of energy dissipation can apply for IP loaded URM components, the energy dissipation for OOP loaded URM walls is negligible. Figure 2.14 shows force-deformation loops that correspond to an OOP loaded wall. It can be seen that the areas of the hysteresis loops are insignificant. Therefore, the OOP behavior of URM walls is often represented by a perfect rigid body (RB) mechanism, in which no energy dissipation is included: the unloading curve then follows the loading curve.
Figure 2.14: Force-deformation loops for OOP behavior URM wall [37].
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