7.1 Conclusions
In the presented research, the assessment process of the OOP behavior of URM walls is investigated for walls in a typical terraced house in the Groningen area. The research aims for a better and more clear view on the assessment process, in which the balance between the efficiency of the overall assessment process and the accuracy of the assessment outcomes is of particular interest. Therefore, the main research question is formulated in the following manner:
How can the out-of-plane (OOP) behavior of unreinforced masonry (URM) walls, as a result of earthquake loading, be assessed in an efficient, but sufficiently accurate manner?
In order to investigate the described assessment process while considering both the efficiency of the method, as well as the accuracy of the outcome, the current research evaluates three Tier 3 methods that utilize a relatively simple macro-NLTH analysis, referred to as the Tier 3a, the Tier 3b and the Tier 3c method. Due to the absence of complex micro-NLTH analyses, the application of the three Tier 3 methods requires relatively little time and effort. Hence, it can be stated that the three methods correspond to a relatively high efficiency. Besides the inclusion of the three Tier 3 methods, the basic Tier 1 and Tier 2 method are included in the research as well.
It must be noted that the results of the current research can only be used to conclude on the relative functioning of the different evaluated assessment methods. Due to the fact that the current research does not include more accurate assessment methods with higher complexities, no statements can be made concerning the ‘position’ of the Tier 3 methods within the imaginary accuracy vs. efficiency spectrum. Furthermore, no conclusions can be drawn concerning the actual functioning of the evaluated Tier 3 methods. More research is required before the analyzed idealized systems can be defined as valid and sufficiently accurate. Hence, the focus of the conducted research is on the relative functioning of the different assessment methods.
In the first place, it can be concluded that the Tier 2 method yields slightly smaller wall responses than the Tier 1 method. This is in accordance with the expectations.
Then, conclusions are drawn concerning the three different Tier 3 methods. The first Tier 3 method, the Tier 3a method, investigates the influence of the usage of a simplified SDOF system for the representation of the analyzed URM wall. In this method, the analyzed wall is subjected to the average dynamic response of the floors at the top and the bottom side of the specific wall, compared to the usual situation in which both sides of the wall are subjected to different displacement time histories. The Tier 3a method is considered unsuitable for the assessment of the OOP behavior of URM walls. The application of the average displacement time history yields a reduced input load for situations in which the two floors that enclose the analyzed wall show different horizontal displacements. Thus, the method results in non-conservative OOP demands for the wall. Combined with the high capacity that applies to the single spring that is incorporated in the simplified SDOF
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system, the Tier 3a method yields unrealistically low UC values.
The second Tier 3 method, the Tier 3b method, incorporates a SDOF system with two springs that are connected in parallel. In this way, the influence of differences in horizontal displacements of the two floor levels that enclose the analyzed wall is taken into account, in contrast to the Tier 3a method. Using the Tier 3b method, the influence of performing a simplified analysis in which the so-called cascade approach is applied is evaluated. When employing this cascade approach, an uncoupled analysis is performed. In such an analysis, first, the dynamic response of the overall structure is determined. Afterwards, the wall’s dynamic response is evaluated. In the Tier 3b method, the dynamic response of the URM wall therefore does not affect the dynamic response of the overall structure.
Within the third Tier 3 method, the Tier 3c method, the influence of differences in movements of the floor level at the top and at the bottom side of the wall is again incorporated. In contrast to the Tier 3b method, however, the analyzed wall is already included in the initial idealized system, resulting in a single analysis of a 3DOF system. In this method, the response of the overall structure is dependent on the response of the analyzed URM wall. The 3DOF system, as utilized in the Tier 3c method, is expected to best reflect the actual structure. From the results, it can be stated that the Tier 3c method generally results in somewhat lower UC values than the Tier 3b method. Combined with the fact that a single, ‘coupled’ analysis applies for the Tier 3c method, this assessment method is expected to yield the most accurate results. When considering the efficiency of the different assessment methods, the Tier 3c method again seems to be successful: the fact that the assessment method does not implement the cascade approach is not seen as a major increase of the complexity of the assessment method.
Although the Tier 3c method seems to yield the most favorable balance in terms of the efficiency of the assessment process, on the one hand, and the accuracy of the assessment outcomes, on the other hand, the method does not, by definition, constitute an improved assessment method compared to the Tier 2 method. When comparing the Tier 3c method against the Tier 1 and the Tier 2 method, it can be seen that the Tier 3c method in several cases yields more conservative outcomes. It should be noted that the Tier 1 and the Tier 2 method, as evaluated in the current research, yield lower UC values than the original Tier 1 and Tier 2 method, as prescribed in Annex H of the NPR, due to the usage of the updated formula for the derivation of the wall’s effective thickness tef f, which results in higher OOP capacities for the Tier 1 and the Tier 2 method.
The difference in the assessment outcomes of the Tier 1 and the Tier 2 method, on the one hand, and the Tier 3 methods, on the other hand, can be attributed to the substantial difference in the nature of the incorporated seismic analysis methods. The NLTH analyses that are utilized in the Tier 3 methods appear to be highly sensitive to nonlinear response of the analyzed URM walls. Due to the so-called butterfly effect, excessive nonlinear behavior is easily obtained, yielding OOP failure of the analyzed wall. The butterfly effect, which is inherent to nonlinear dynamic problems, also causes an increase in fluctuations between the obtained UC values for the different ground motion records. Despite the high sensitivity of the Tier 3 methods, the methods still have potential to yield improved methods for the assessment of the OOP behavior of URM walls.
Whether the Tier 3c method is more accurate or less accurate than the Tier 2 method, can only be concluded after a verification of the Tier 3c method. A verification check can be performed
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by comparing the numerical results against experimental results, as well as against results of more complex micro-NLTH analyses.
Further research is needed to investigate the actual accuracy of the Tier 3 methods. Only then, a statement can be made on the ability of the proposed methods to assess the OOP behavior of URM walls in an efficient, yet sufficiently accurate manner. After the description of the limitations of the conducted research in section 7.2, the recommendations for further research are described in section 7.3.
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7.2 Limitations
In this section, the limitations of the conducted research are described. Different categories can be distinguished. First, the inaccuracies that concern the analyzed idealized systems are presented.
Afterwards, the simplifications that are made in the construction of the material models are listed.
Eventually, the drawbacks of the method that is applied to compare the different assessment methods are described.
Regarding the idealized systems that represent the analyzed walls, no validation check using exper-imental data has been performed. Hence, the ability of the systems to represent the actual OOP behavior of URM walls can be considered as an uncertain aspect in the conducted research. A fur-ther important limitation is related to the damping that is assigned to the systems that represent the analyzed URM walls. The damping coefficients are defined using the wall’s effective stiffness kef f. Hence, a conservative, low degree of damping is incorporated in the idealized system, as described in Appendix D.2.2. This underestimated damping level is expected to significantly contribute to the excessive nonlinear behavior that is observed in the NLTH analyses. Due to the assumption that the modeled damping has an important effect on the obtained results, the simplification of using the effective stiffness kef f for the derivation of the damping coefficient is seen as a limitation.
Concerning the idealized 3DOF system that is incorporated in the Tier 3c method, the stiffness of the spring that represents the building layer within which the analyzed wall is located is not reduced as a result of the separately modelled springs that represent the URM wall. Although this concerns only a negligible reduction, it can be seen as a limitation.
In order to perform a dynamic analysis of the idealized systems, material models must be assigned to the different springs. In the construction of the material models, several simplifications are made.
The simplifications are listed for the two types of material models that are used in the current research: the material model Hysteretic and the material model ElasticBilin.
The first material model, Hysteretic, represents the lateral behavior of the building layers. This material model is constructed, as well as ‘calibrated’ using a single experimental dataset. However, experimental data may contain noise and inaccuracies. Moreover, experimental data correspond to a very specific situation, which makes the data not generally applicable in other situations. Hence, it is a limitation that only a single dataset is used for the construction of all applied hysteretic material models. Furthermore, the method of transforming the experimentally derived backbone curves (BBCs) into the BBCs for structures for which no experimental data are available includes several simplifications that may be seen as limitations. In the first place, the BBC in the material models is scaled using a single scale factor that is based on the axial load that acts on a building layer. Of course, more factors influence the BBC of a structure’s actual hysteretic behavior. Hence, the usage of the axial load as the only influencing factor is a simplification. Secondly, the scale factor is only applied to scale the BBC along the vertical axis. Therefore, only the forces are scaled, while the deformations of the building layers are assumed to be constant. This can also be seen as a simplification. The last limitation that corresponds to the hysteretic material model concerns the ‘calibration process’. This process is based on checking the orders of magnitude only. No quantification is incorporated, which can be seen as a limitation.
The second material model, ElasticBilin, represents the OOP behavior of the URM walls. In this material model, no energy dissipation is incorporated. Hence, the unloading curve follows the
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loading curve, which corresponds to the perfect rigid body mechanism. This mechanism, however, is an approximation of the actual OOP behavior of URM walls. Therefore, it can be seen as a limitation.
After assigning the material models to the springs in the idealized systems, the OOP behavior of the walls is assessed using the different assessment methods. The results are presented in terms of UC values. The method that is applied to compare the outcomes of the different assessment methods has some drawbacks.
First, the substantial difference between the determination of the UC value for the Tier 1 and the Tier 2 method, on the hand, and the determination of the UC value for the Tier 3 methods, on the other hand, makes it impossible to directly compare the different UC values in all situations.
Statements on the different assessment outcomes can only be made relative to the critical UC value of 1. This can be seen as a limitation of the current research: the comparison procedure must be handled with care.
Another difficulty of the comparison procedure concerns the important effect of the observed OOP failures on the depicted UC values. In case NLTH analyses observe OOP failure, no UC values are obtained. The UC values that correspond to these NLTH analyses are thus not incorporated in the averaging, which means that the depicted UC values that correspond to these analyses are the average of all other ground motion records that did yield results. Although the average UC values are still incorporated in the graphs, the assessment outcome must be considered invalid. Namely, the NPR states that not a single analysis is allowed to yield a UC value higher than the critical value of 1 [21]. This must be carefully considered during the discussion of the results.
It can be stated that the results that are obtained in the conducted research are not presented in an easy-to-use, or easy-to-compare, format.
Lastly, the comparison of the assessment methods would be more valid, as well as more interesting, in case more accurate assessment methods with higher complexities would be included. In case an assessment method that includes a micro-NLTH analysis would have been included in the compari-son, more could have been said on the actual functioning of the proposed Tier 3 methods and their
‘position’ within the imaginary accuracy vs. efficiency spectrum. Only a comparison with the Tier 1 and the Tier 2 method is included in the current research, which can be seen as a limitation.
Besides, due to the absence of a more accurate method, the UC values of the Tier 3a, the Tier 3b and the Tier 3c method are not validated or checked. Low UC-values are assumed to be accurate, however, the values can also be too low. Hence, false pass predictions might be present within the presented results. This is an important limitation of the current research.
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7.3 Recommendations
The conducted research presents methods to assess the OOP behavior of URM walls in which a relatively simple macro-NLTH analysis is applied. The methods, which can be categorized as Tier 3 methods, can potentially serve as improved assessment methods, considering the balance between the efficiency of the assessment process, on the one hand, and the accuracy of the assessment outcomes, on the other hand. The application of the proposed Tier 3 methods requires much less time and effort than Tier 3 methods that utilize more complex, micro-NLTH analyses. Therefore, the methods can be considered to be efficient. From the results of the research, it seems like the Tier 3 methods yield more conservative results than the more simple Tier 2 method does. This in contrast to the expectations. Further research is needed to find out if the Tier 3 methods can serve as improved assessment methods. In the first place, it is recommended to further examine and verify the general ability of the idealized systems that are used to represent the analyzed walls. In case the idealized systems indeed appear adequate to represent the OOP behavior of URM walls, the inaccuracies in the applied idealized systems must be minimized. Also, the material models must be constructed in a more reliable manner. Eventually, more accurate methods must be included in the research for a valid comparison. The different recommendations are described below.
First of all, it is recommended to reexamine the general ability of the idealized systems that are used to represent the analyzed walls. It is advised to verify the SDOF system with two springs, which is used to model the analyzed URM wall in the Tier 3b and the Tier 3c method, using experimental data. Shaking table tests have been performed on one-way bending URM walls [71].
The corresponding data are perfectly suitable for the validation of the SDOF systems. In case it can be concluded from the reconsideration of the idealized systems that the proposed systems can adequately represent the OOP behavior of URM walls, a further recommendation applies. Namely, it is important to minimize the inaccuracies in the idealized systems. Especially the assignment of damping needs improvement in order to yield more accurate results.
Besides the optimization of the idealized systems, it is desirable to improve the material models that are assigned to the different springs in the idealized systems. In this way, the reliability of the eventual assessment outcomes increases.
The first material model, Hysteretic, represents the lateral behavior of the building layers. This material model can be optimized in several ways. In the first place, the material model can be set up in a more reliable manner by the usage of different datasets to construct and calibrate the material model, rather than just a single dataset. Furthermore, the applied method of transforming the experimentally derived BBCs into the BBCs for structures for which no experimental data are available can be improved. This can be done by the implementation of additional parameters for the determination of the scale factor, instead of using only the axial load that acts on the building layers.
Besides, it is desirable to incorporate the influence of the different parameters on both the force capacity and the deformation capacity of the building layers. Preferably, the transformation method is based on experimental data. For further research, it might even be interesting to investigate the option of constructing the hysteretic material models based on codes instead of on experimental data, due to the inherent noise in actual data, as well as the fact that experimental data apply for a specific analyzed structure, while codes are generally applicable for all types of structures. In this way, formulas that describe the lateral behavior of URM building layers in a rather general manner
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can be constructed. Herein, several scale factors can be incorporated to adapt the general formula to different structures, for example for structures with varying axial loads or boundary conditions.
The second material model, ElasticBilin, represents the OOP behavior of the URM walls. This material model does not incorporate energy dissipation. For further research, it is recommended to investigate the suitability of (the parallel usage of) other material models in OpenSees, that do take into account the dissipation of energy, for the representation of the URM wall. In line with the main research goal, it is important to not choose a material model that results in a significant increase of the complexity of the eventual assessment method.
The above mentioned recommendations will yield more reliable results for the Tier 3 methods.
However, in order to make a statement on the actual functioning of the methods, it is important to
However, in order to make a statement on the actual functioning of the methods, it is important to