Sensitivity study on assessment of OOP behavior of URM walls

While chapter 5 presents the main body of the research in which the assessment of the OOP be-havior of URM walls in structure A is discussed, this chapter presents a sensitivity study in which adaptations are made to the original research. In this way, the influence of several aspects on the assessment of the OOP behavior of URM walls is included in the research. The sensitivity study aims for a better insight into the topic of investigation.

In the sensitivity study, the assessment process of the OOP behavior of URM walls is investigated for walls in two other types of Groningen typologies, which are referred to as structure B and C.

These structures are included in the sensitivity study in order to evaluate the influence of assessing the OOP behavior of URM walls in structures that differ from the original structure A. Whereas structure A consists of two RC floors, structure B consists of one RC floor and one timber diaphragm.

In structure B, large openings are present in the facade at BL1. Due to these large openings, a soft-story mechanism is likely to occur. The third two-soft-story structure, structure C, consists of two timber diaphragms, and therefore represents the most lightweight structure. The characteristics of both structure B and C are presented in Appendix G. In section 6.1 and 6.2, the assessment of the URM walls in respectively structure B and C is discussed.

Besides the influence of assessing URM walls in different types of Groningen typologies, the influence of the boundary conditions of the wall is examined. While both walls in structure A correspond to BC3, in which both the top and the bottom hinge are located at the wall’s edge, the sensitivity study includes the analysis of a URM wall that corresponds to BC0. In this case, the top and the bottom hinge of the wall are located at the wall’s center instead of at the wall’s edge. In section 6.3, the assessment of the OOP behavior of a URM wall with BC0 is discussed.

Lastly, the influence of the nonlinear behavior of the building layers of the overall structure on the wall’s OOP behavior is investigated. This last aspect that is included in the sensitivity study is presented in section 6.4.

Sensitivity study on assessment of OOP behavior of URM walls page 74

6.1 Structure B

Structure B consists of one RC floor, one timber diaphragm and a pitched timber roof. Due to the fact that a timber diaphragm is applied as second floor slab, the boundary conditions of the wall on BL2 of structure B differ from the boundary conditions of the walls in structure A. Whereas BC3 applies for both walls in structure A, BC1 applies for the wall on BL2 of structure B. Furthermore, structure B has large openings in the facade at BL1. Due to these large openings, a soft-story mechanism is likely to occur. In Appendix G.2, the characteristics of structure B are presented. The influence of the soft-story mechanism on the assessment process of the OOP behavior of the walls that are located within this structure is discussed in the current section.

In the sensitivity study on structure B, the OOP behavior of the walls in the structure is assessed for a PGA value of 0.15 g. Figures 6.1 and 6.2 show the derived UC values for the walls on respectively BL1 and BL2. The UC values for both structure A and B are included in order to discuss the impact of the soft-story mechanism in structure B, compared to the original structure A. Due to the fact that all depicted UC values do not approach the critical value of 1, the Tier 1 and Tier 2 method, on the one hand, and the Tier 3 methods, on the other hand, cannot be directly compared. Only the Tier 1 and the Tier 2 method can be compared to each other, as well as the UC values of the different Tier 3 methods. As a result of the absence of observed OOP failures in the NLTH analyses for both structure A and B, the UC values of the Tier 3 methods all represent the average of the total number of 11 UC values. The vertical lines depict the range of obtained UC values.

a) structure A b) structure B

Figure 6.1: Unity check values for wall on BL1 (PGA = 0.15 g).

For the wall on BL1, it can be seen that structure B generally corresponds to higher UC values than structure A. The obtained difference between structure A and B is less pronounced for the Tier 1 and the Tier 2 method than for the Tier 3b and the Tier 3c method. As described before, the Tier 3a method is disregarded.

As can be seen in Figure 6.1a, a negligible difference is obtained in UC values that correspond to the three Tier 3 methods for structure A, suggesting the absence of nonlinear behavior of the wall on BL1 of structure A for the applied PGA value of 0.15 g. For the wall on BL1 of structure B, however, nonlinear behavior does apply as a result of this PGA value. The occurrence of this nonlinear wall behavior is expected to be the reason for the higher degree of variation in the UC values that result

6.1 Structure B page 75

a) structure A b) structure B Figure 6.2: Unity check values for wall on BL2 (PGA = 0.15 g).

from the application of the 11 different ground motion records. This variation is illustrated by means of the vertical lines in the graphs, which depict the range of derived UC values.

For the wall on BL2, the Tier 1 and the Tier 2 method yield higher UC values for structure B than for structure A, while the Tier 3b and the Tier 3c method yield lower UC values. As can be seen in Figure 6.2b, no significant differences can be obtained when comparing the results of the different Tier 3 methods for structure B. It is expected that this is caused by the relatively low deformations of the spring that represents the lateral behavior of BL2. Due to a small deformation of BL2, no major differences apply between the displacement time histories that are subjected to the two wall springs that are connected in parallel. Hence, it is expected that the wall on BL2 of structure B shows mainly linear behavior for the PGA value of 0.15 g, or only a small degree of nonlinear behavior. For the wall on BL2 of structure A, however, the depicted UC values suggest the occurrence of nonlinear wall behavior.

When comparing the UC values for the walls on both BL1 and BL2 according to the Tier 3 methods, it can be stated that the soft-story mechanism in structure B results in more critical UC values for the wall on BL1, while less critical UC values are obtained for the wall on BL2. The soft-story mechanism applies to BL1, yielding significant deformations of the specific building layer. As a result of the occurrence of this soft-story mechanism, it is expected that BL2 does only experience minor deformations. Hence, the observed difference in assessment outcomes for the walls on the BL1 and BL2 is in line with the expectations.

For the Tier 1 and the Tier 2 method, the high increase in UC values for the wall on BL2, compared to the wall on BL1, as a result of the soft-story mechanism in structure B, is expected to be attributed to the significant reduction in OOP capacity for the wall on BL2, due to the different boundary condition type that applies for this wall: BC1. The OOP demand, on the other hand, hardly changes.

By means of providing an example, Appendix H.1 presents the evaluation of the wall on BL1 and BL2 for both structure A and B, according to the Tier 3c method. The depicted analyses correspond to the first and the tenth ground motion record, GM1 and GM10, respectively, and a PGA value of 0.15 g.

6.1 Structure B page 76

6.2 Structure C

Structure C consists of two timber diaphragms and a pitched timber roof. Due to the relatively flexible nature of the timber diaphragms in structure C, compared to the stiff RC floors in structure A, the boundary conditions that apply to the walls within structure C differ from the boundary conditions of the walls in structure A. Whereas BC3 applies for both walls in structure A, BC1 and BC0 apply for the walls on, respectively, BL1 and BL2 of structure C. Furthermore, the application of timber diaphragms, rather than RC floors, results in a significantly reduced total mass of structure C, compared to the total mass of structure A. The reduction corresponds to a percentage of over 35%. In Appendix G.3, the characteristics of structure C are presented. The influence of the mass of the total structure on the assessment process of the OOP behavior of the walls that are located within this structure is discussed in the current section.

In the sensitivity study on structure C, the OOP behavior of the walls in the structure is assessed for a PGA value of 0.15 g. Figures 6.3 and 6.4 show the derived UC values for the walls on respectively BL1 and BL2. The UC values for both structure A and C are included in order to discuss the impact of the reduced mass of structure C, compared to the original structure A. For the wall on BL1 of both structure A and C, as well as for the wall on BL2 of structure A, the depicted UC values do not approach the critical value of 1. Hence, the Tier 1 and Tier 2 method, on the one hand, and the Tier 3 methods, on the other hand, cannot be directly compared. Only the Tier 1 and the Tier 2 method can be compared to each other, as well as the UC values of the different Tier 3 methods. For the wall on BL2 of structure C, instead, the UC values of the Tier 3 methods do reach the critical value of 1, while the UC values of the Tier 1 and the Tier 2 method do not reach the critical value.

Therefore, for this wall, the five assessment methods can be compared in a more valid manner. It must be stated, however, that OOP failures are observed in several NLTH analyses for the wall on BL2 of structure C. For these analyses, no UC value could be extracted. The depicted ‘average’ UC values for the Tier 3 methods therefore represent the average value of less than the total number of 11 UC values. The numbers in Figure 6.4b show the number of UC values that is included in the average UC values. Although the average UC values are still incorporated in the graph, it must be emphasized that the values must be considered invalid. The vertical lines depict the range of obtained UC values.

a) structure A b) structure C

Figure 6.3: Unity check values for wall on BL1 (PGA = 0.15 g).

6.2 Structure C page 77

a) structure A b) structure C Figure 6.4: Unity check values for wall on BL2 (PGA = 0.15 g).

It can be seen that that all five assessment methods yield higher UC values for the walls on both BL1 and BL2 of structure C, compared to the walls in the original structure A. The impact of the reduced mass of the overall structure seems to be more pronounced for the wall on BL2 than for the wall on BL1, in particular for the Tier 3 methods. A reason for this can be the substantial difference in the capacity curve for the wall on BL2 of structure A and the wall on BL2 of structure C, as shown in Figure G.4. The NLTH analyses that are incorporated in the Tier 3 methods show a significant increase in the wall’s OOP demand as a result of this difference in the capacity curve.

The reduced capacity curve of the wall is expected to be the reason for the increased variation in Tier 3 assessment outcomes as well, due to the reduced stiffness of the wall and the more frequent occurrence of nonlinear wall behavior.

As mentioned before, the depicted UC values concerning the wall on BL2 of structure C for the Tier 3 methods may not be considered valid due to the presence of observed OOP failures. Hence, it must be stated from the results that the Tier 3 methods yield less accurate assessment outcomes than the Tier 1 and the Tier 2 method, in contrast to the expectations of more complex assessment methods yielding lower UC values, as described in chapter 5.

By means of providing an example, Appendix H.2 presents the evaluation of the wall on BL1 and BL2 for both structure A and C, according to the Tier 3c method. The depicted analysis corresponds to the first ground motion record, GM1, and a PGA value of 0.15 g.

6.2 Structure C page 78

6.3 BC0

The influence of the boundary conditions of the analyzed URM wall is examined by means of a comparison between the assessment of the OOP behavior of a wall that corresponds to BC3, as applies for the original structure A, and a wall that corresponds to BC0. This latter boundary condition type represents the most unfavorable situation in which both the eccentricities eb and eP

are equal to zero, as shown in Table 3.4.

In the sensitivity study, the OOP behavior of the wall on BL1 of structure A is assessed for both BC0 and BC3 as a result of a PGA value of 0.15 g. Figure 6.5 shows the derived UC values for the walls that correspond to the original BC3 and the adapted BC0. Due to the fact that all depicted UC values do not approach the critical value of 1, the Tier 1 and Tier 2 method, on the one hand, and the Tier 3 methods, on the other hand, cannot be directly compared. Only the Tier 1 and the Tier 2 method can be compared to each other, as well as the UC values of the different Tier 3 methods. As a result of the absence of observed OOP failures in the NLTH analyses for both the wall with BC0 and the wall with BC3, the UC values of the Tier 3 methods all represent the average of the total number of 11 UC values. The vertical lines depict the range of obtained UC values.

a) BC3 b) BC0

Figure 6.5: Unity check values for wall on BL1 of structure A for different BCs (PGA = 0.15 g).

It can be seen that all five assessment methods yield higher UC values as a result of BC0. The influence of the adapted boundary conditions seems to be more pronounced for the Tier 3 methods, compared to the Tier 1 and the Tier 2 method. The considerable increase in UC values for the Tier 3 methods can be explained by the fact that the capacity curve of the wall that corresponds to BC0, as implemented in the utilized NLTH models, is significantly reduced compared to the capacity curve of the wall with BC3, as shown in Figure 6.6. Hence, a major increase in the OOP demand of the wall is observed for the Tier 3 methods. For the Tier 1 and the Tier 2 method, instead, no noteworthy change is observed in the OOP demand of the adapted wall. Although the application of BC0 significantly affects the OOP capacity for the Tier 1, the Tier 2 and the Tier 3 methods, the OOP demand thus gets affected to varying degrees.

Furthermore, it can be noted that the application of BC0 corresponds to more fluctuations in the derived UC values for the Tier 3 methods. Due to the significant difference in the capacity curves that correspond to the two analyzed walls, a higher extent of nonlinear wall behavior is observed as

6.3 BC0 page 79

a result of BC0. Since the NLTH analyses in the Tier 3 methods appear to be highly sensitive to nonlinear response of the analyzed wall, an increased variation in assessment outcomes is observed for the wall with BC0.

Figure 6.6: Positive displacement range of OOP capacity curves of analyzed URM walls.

By means of providing an example, Appendix H.3 presents the evaluation of the wall on BL1 for both the original BC3 and the adapted BC0, according to the Tier 3c method. The depicted analysis corresponds to the first ground motion record, GM1, and a PGA value of 0.15 g.

6.3 BC0 page 80

6.4 Linear behavior of BL1 and BL2

The influence of nonlinear behavior of the building layers in the overall structure on the wall’s OOP behavior is investigated. This is done by comparing the assessment of walls within the original structure A, in which the nonlinear hysteretic material model is applied, against the assessment of walls within an adapted structure, in which only elastic behavior applies to the springs that represent the lateral behavior of the building layers. The stiffnesses of BL1 and BL2 of the latter structure equal the initial stiffnesses of BL1 and BL2 of the nonlinear material model.

In the sensitivity study, the OOP behavior of the wall on BL1 of structure A is assessed for both nonlinear and linear BL behavior as a result of a PGA value of 0.25 g. Figure 6.7 shows the derived UC values. Due to the fact that all depicted UC values do not approach the critical value of 1, the Tier 1 and Tier 2 method, on the one hand, and the Tier 3 methods, on the other hand, cannot be directly compared. Only the Tier 1 and the Tier 2 method can be compared to each other, as well as the UC values of the different Tier 3 methods. As a result of the absence of observed OOP failures in the NLTH analyses for structure A for both linear and nonlinear BL behavior, the UC values of the Tier 3 methods all represent the average of the total number of 11 UC values. The vertical lines depict the range of obtained UC values.

a) nonlinear behavior BLs b) linear behavior BLs

Figure 6.7: Unity check values for wall on BL1 of structure A for different BL behavior (PGA = 0.25 g).

It can be seen that the Tier 1 and the Tier 2 method yield higher UC values as a result of linear BL behavior. This can be explained by the fact that no hysteretic damping ζ_hys is incorporated in the determination of the spectral reduction factor ηζ for the structure with linear BL behavior. The elastic response spectrum S_a(T), as well as the ADRS-curve, are thus not reduced, as described in section 3.2. This eventually causes higher OOP demands according to the Tier 1 and the Tier 2 method, yielding higher UC values.

For the Tier 3 methods, instead, it can be noted that linear BL behavior generally results in lower UC values. This can be explained by the fact that the floor displacements remain limited. The idealized systems that represent the analyzed URM walls are therefore subjected to lower displacements. As a result of the lower loading conditions for the wall systems, the wall springs show less nonlinear behavior than the wall springs in the original structure A. This yields a reduction in eventual wall

6.4 Linear behavior of BL1 and BL2 page 81

deformations, and thus a reduction in the obtained UC values. As can be seen in Figure 6.7b, the Tier 3 methods show similar results, which suggests linear wall behavior.

When comparing the range of obtained UC values for the original structure with nonlinear BL behavior and the adapted structure with only linear BL behavior, the different UC values that correspond to the first structure show significantly more variation. It is expected that this is the

In document Assessment of the seismic out-of-plane behavior of unreinforced masonry walls (pagina 90-99)