S.T. Sperbeck & H. Budelmann Institute of Building Materials, Concrete Construction and Fire Protection, TU Braunschweig, Braunschweig, Germany

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1 Structural Analysis of Historic Construction D Ayala & Fodde (eds) 2008 Taylor & Francis Group, London, ISBN Prestressing of asonry as strengthening easure against earthquake loading Experiental and nuerical investigations and influences on siulation results S.T. Sperbeck & H. Budelann Institute of Building Materials, Concrete Construction and Fire Protection, TU Braunschweig, Braunschweig, Gerany ABSTRACT: Local vertical prestressing is considered as strengthening easure to reduce the vulnerability of asonry structures in case of earthquake action. The shear strength and the ductility of asonry is iproved. This is shown in static cyclic tests. Static and dynaic behaviour is investigate for different asonry walls. To avoid an excessive aount of experiental tests, this paper is focused on nuerical siulations and ipacts on the results such as boundary conditions and different eans to odel prestressing. Previously, brief coparison of siulation techniques and aterial odels is given. The task is ainly copleted by eans of a suitable aterial odel for acro odelling of asonry. The researched paraeters which influence the nuerical results are discussed. Case studies are carried out to investigate the paraeters. The iportance to odel the tendons, especially for nonlinear dynaic analyses, is shown. The ipact of prestressing on the dynaic behaviour is investigated. 1 INTRODUCTION The resistance of asonry structures against earthquake action is liited by its low shear strength. Vertical prestressing is considered in order to iprove the shear capacity, and the ductility of asonry. Static and static cyclic tests have already shown the suitability of this ethod (Budelann et al. 2004). More research for different asonry constructions is recoended. In addition the dynaic behaviour should be investigate, before using the strengthening ethod against earthquake action. The large quantity of necessary experiental tests, especially dynaic ones with shaking tables, is very expensive. The final goal is to provide possibilities, based on nuerical ethods, to investigate the dynaic behaviour of prestressed asonry structures. Firstly, soe observed paraeters, which influence the nuerical results are investigated and discussed. 2 STATIC CYCLIC EXPERIMENTAL TEST OF PRESTRESSED SHEAR WALLS The experiental tests of prestressed shear walls briefly suarised below are described in detail in Budelann et al. (2004). Four walls were tested, with diensions and extra loads like walls used for stiffening of buildings with three floors. All walls had a height of and thickness of In these static cyclic tests only the ground floors were considered as they are ost critical under seisic action. W1 W2 W3 W4 Figure 1. Coplete experiental set-up for wall 1, wall 2, wall 3 and wall

2 For all walls, two tendons (strands) have been used for vertical prestressing. The coplete experiental set-up is depicted in Figure 1 on the left for wall 1. Furtherore, another position of the tendons closer to the iddle was investigated in wall 2. The influence of slenderness is taken into account by eans of wall 3 and wall 4. With wall 4, the floor slab is supported only on one end. The wall properties are listed in Table 1. A horizontal static cyclic displaceent was applied in the centre of the concrete slab. The crack patterns are shown in Figure 2. The diagonal crosses are very typical of earthquake daage. The load displaceent curves are displayed in Figure 3. Wall 2 had the ost useful behaviour. The shear capacity and the ductility are very high. The area enclosed by the hysteresis shows the energy dissipation, which is very good for wall 2 and wall 3. Measured values like the displaceent u and the horizontal load H are suarised in Table 2 for all walls. The index u eans the ultiate point of loading, whereas cr indicates the occurrence Table 1. W1 W2 W3 W4 Properties of the walls. Distance of tendon Length Height Thickness to edge Distance of tendons Support on 2 sides on 1 side of cracks. 2xP0 is the su of the initial prestressing forces of two tendons. The dead load of the wall and upper stories is expressed by G+F. In the last colun, the forces in the tendons after reaching the ultiate loading point (2xP0 )u are given. A significant decrease was observed. Moreover, it is listed where stone failure (partial collapse of the wall) occurred, or if axial displaceent of the testing equipent (vax ) was reached. 3 NUMERICAL SIMULATION TECHNIQUES AND MATERIAL MODELS 3.1 Theoretical background In the following, it is briefly discussed which siulation techniques and aterial odels are suitable to investigate the dynaic behaviour of prestressed asonry. In case of cyclic and dynaic loading, a degradation of stiffness and strength occur. The dynaic behaviour is effected strongly by the stiffness which is an iportant consideration. Usually, the accurate icro odelling is applied to investigate asonry in detail. The aterial odel by Oliveira (2003) includes degradation for this odelling strategy. It is based on the plasticity theory, described by Lourenço (1996) and Rots (1997). Due to the high calculation effort, the aterial odel is very tie consuing in the case of dynaic siulations of large structures. More suitable for such siulations is the aterial odel of Gabarotta & Lagoarsino (1997), which is based on fracture echanics and Figure 2. Crack pattern of wall 1, wall 2, wall 3 and wall 4. Figure 3. Horizontal load displaceent diagras (hysteresis) for wall

3 acro odelling. Also, this odel is able to describe the post-peak behaviour and the dynaic behaviour. Daage odelling is used in which the inelastic strains are described by eans of two internal daage variables which express the daage evolution in the bricks and ortar. The odel of Gabarotta & Lagoarsino (1997) works efficiently also in the case of dynaic nonlinear analyses and probabilistic analyses of large scale asonry structures. 4 IMPACTS ON NUMERICAL RESULTS It is iportant to know which paraeters have a significant influence on the nuerical results. The findings of a literature review and of siulations ade for this contribution are discussed as follows. Due to the great ipact of boundary conditions, the different conditions are separately explained in the next subchapter. 4.1 Boundary conditions of shear walls The boundary conditions influence the behaviour and failure echaniss strongly. This is explained in ore Table 2. Loading and results of the experiental tests. 2xP0 G+F Hcr kn kn kn W W W W Ucr Hu kn Uu Type (2xP0)u of fail. kn 17 vax Stone vax Stone 140 detail in Ötes & Löring (2006) as well as other literature. Two extree cases are given. For case BC 1, the top of the wall is constrained, because of that it stays horizontal. Mainly shear loading occurs. For case BC 2, the top of the wall is free and can rotate. Thus, the wall behaves like a cantilever, and bending loading occurs. Below it is designated as BC 2. Figure 4 shows walls with these boundary conditions and shapes. In reality, the support of the wall is between these extree cases, depending on the behaviour of the floor slabs. To predict the behaviour realistically, beas should be odelled, as depicted in Figure 4 in iddle. Below, the ipacts are explained in ore detail. 4.2 Case study of static analyses To gain deeper insight, a case study was perfored in which the following paraeters were varied to investigate their ipacts. Four variations of slenderness S (0.5, 1, 2, 3) are ade. For the different slenderness values, different heights of 1.25,, 5 and 7.5 are obtained. The boundary conditions on the top of the wall BC 1 (constrained), odelled by eans of a ridge L-fraework, and BC 2 (free) are used. Furtherore, for BC 2 walls with tendons close to the iddle are investigated. Two eans to odel prestressing are applied (external forces and tendons), illustrated in Figure 5. Its outcoe are the ipacts on: the change of prestressing forces in the tendons, the restoring forces, the rotation of the top, the shear capacity, the ductility as well as the suitability of the tendons location. The subsequent values are fixed for all variations of the odels: the width of the walls is, thickness 0.175, prestressing force per each tendon is 189 kn, and vertical load of upper stories is kn. Furtherore, the aterial paraeters are the sae for all odels as listed in Table 3. Below, soe iportant results of this case study are briefly suarised. In general, the eans to si- Figure 4. Left: BC 1 (constrained), iddle: real boundary conditions, right: BC 2 (free). 1045

4 ulate prestressing is iportant for BC 2, especially when the tendons are close to the edges. For BC 1 this phenoenon can often be neglected. Restoring forces occur and can be siulated when the prestressing is odelled by eans of tendons. The restoring forces have to be divided into horizontal and vertical coponents. The last one is iportant only for BC 2. Here, the vertical oveent of the corners during the top rotation leads to changes of tendons length. The result is a variation of the prestressing forces in the tendons, which decrease in the tendons on the lower corner and increase in the tendons on the upper corner. In the case of low walls, the top rotation leads to significant differences in the prestressing forces. These differences decrease as the walls becoe higher as illustrated in Figure 6. The reason is siple. An equal change of length of a long and short bar gives high stresses in the saller bar, but only sall stresses in the longer. For odels with tendons close to the edges, the rotation of the top edge is saller, but the tendons have to be odelled to notice this effect. If only external forces are used to odel prestressing, no significant differ- Figure 5. Investigated walls in dependency of the slenderness, boundary conditions, eans to odel the prestressing and position of tendons. 1046

5 ence can be observed. Of course, the shear capacity and the ductility depend decisively on the slenderness and boundary conditions, as already noted and described above. To get inforation about the shear capacities and ductilities it is necessary to apply a horizontal loading Table 3. Material paraeters used for the case study. Sybol Variable Value µ σr Friction coefficient Tensile strength of ortar joints Shear strength of ortar joints Copressive strength of asonry Shear strength of asonry Poissons ratio Density Young s odulus Softening ortar Softening brick Inelastic deforation paraeter for ortar Inelastic deforation paraeter for brick N/2 τr σbr τbr η ρ E β βb ct cb t 0.20 N/2 3.5 N/2 1.5 N/ kg/ N/ higher than 5. Figure 8 depicts greater stiffness and shear capacities for walls with BC 1 than for BC 2, but saller ductilities. Especially for slender walls the differences in ductility are significant. It is found in case of BC 2, when the tendons are odelled, the shear capacity is higher (Fig. 7 left) and the ductility is a bit saller. This eans of odelling leads to saller horizontal displaceent. Figure 7 left also shows higher stiffness for walls odelled with tendons. If the tendons are placed close to the iddle, no significant difference can be observed, as shown in Figure 7 right. The post-peak behaviour of odels with tendons near the edges is ore useful, where higher forces can be applied. Obviously, the tendons carry tensile loads after tensile failure has occurred in the asonry wall. If the tendons are close to the iddle, only a sall iproveent regarding the post-peak behaviour can be observed. A coparison of Figure 7 left and right shows this. The findings of this case study regarding the ipact of slenderness cannot be generalised since the width of the walls is constant.the height of the wall has an iportant influence, because it is equal to the basic length of the tendons. Sall changes of length lead to large differences of the forces inside short tendons. For long tendons, uch higher differences in length are necessary to reach significant changes of such inner forces. As shown, any reasons exist to odel tendons, such as the tendon forces that Figure 6. Forces in tendons in dependency on the horizontal top displaceent of walls for BC 2 and tendons close to the edges. 1047

6 change during static horizontal loading. This ipact is significant for BC 2 and copact walls. The shear capacity depends considerably on the vertical loads. Another iportant reason for odelling the tendons, is the decreasing of the prestressing force in the tendons during static cyclic and seisic loading. This was observed in experiental tests (Budelann et al. 2004), probably caused by the reduction in height of bed joints due to slipping in the joints. The static siulations show horizontal and vertical restoring forces lead to saller horizontal displaceent and saller rotations as well as to increased stiffness (Fig. 7 left). Figure 7. Left: Horizontal load displaceent diagra for BC 2 and tendons close to the edges, right: horizontal load displaceent diagra for BC 2 and tendons close to the iddle. Figure 8. Horizontal load displaceent diagra for odels with tendons for BC 1 and for BC 2 for different tendon positions (edges and iddle). 1048

7 4.3 Case Study of nonlinear dynaic analyses The increasing of stiffness, as entioned above, affect the dynaic behaviour. A sall case study was perfored to investigate further. The vibration behaviour of prestressed walls odelled with external forces, tendons, and for walls without prestressing, is calculated in nonlinear dynaic siulations. A ground displaceent is applied as an ipulse for all entioned siulations below. The tie for the ipulse is 0.12 s to ove ground and return back to the original position. The three different load functions are tie dependent as identified in Figure 9 with dashed lines. Table 4 gives a short overview of the carried out dynaic analyses, the level of the applied displaceent, and whether it was possible to receive convergence. For these odels the sae values for width, thickness and aterial paraeters (Table 3) are used as for the static case study above. All have a static Table 4. Overview of the carried out analyses with ipulse loading. Means to odel prestressing Ipulse displaceent External forces Tendons Without prestressing vertical load of kn. The variations external forces and tendons have an additional prestressing force of 189 kn per each tendon. The results for the vibration behaviour regarding the horizontal top displaceent are depicted in Figure 9. For all of the wall odels and load levels, the biggest value for the roof displaceent is reached after 0.12 s. The highest displaceent reaches 34 for the nonprestressed wall. As expected prestressing leads to a reduction of the vibration aplitude. For the odels with external forces the displaceent aounts to 32 and for the odels with tendons The observed difference between the axiu horizontal roof displaceent of tendons and external forces are saller for lower load levels. The horizontal displaceent of the prestressed walls is insignificantly saller than the prestressed walls for lower vertical load levels (5 and 10 ). Nevertheless, the ortar daage is uch less for prestressed walls, than for the non-prestressed wall (Fig. 10). This indicates that vertical prestressing can be a useful strengthening easure also for dynaic loading. More detailed investigations are still in progress. The dynaic behaviour is different for all considered walls, as periods vary significantly.the walls with tendons vibrates faster. This eans they are stiffer. Observations of experiental tests lead to a probable reason. Ötes et al. (2002) observe that in the range of high horizontal loading, the stiffness of the wall is ainly affected due to the spring properties of the tendons after the occurrence of gaping joints. This Figure 9. Horizontal displaceent of the top tie-dependent for odelling of prestressing by eans of external forces, tendons, and without prestressing in case of BC

8 Figure 10. Mortar daage for ipulse loading of 10, left: external forces, iddle: tendons, right: without prestressing. Figure 11. Mortar daage for ipulse loading of 17, left: external forces, iddle: tendons, right: without prestressing. would explain also the bigger difference between tendons and external forces in case of higher shaking levels. Also, presented static siulations show that the post-peak behaviour varies with the prestressing is odelled as external forces or tendons (Fig. 7 left). Modelling of tendons leads to higher resistances. In general, the walls vibrates slower, when the ground acceleration is higher. A reason is higher daage of the walls leading to saller stiffness, and lower frequencies. For a higher load level (horizontal ground displaceent of 17 ) also the prestressed walls are significantly daaged (Fig. 11). Here, the difference between the two eans to odel prestressing becoe larger, but not iportant. In all these siulations the ortar daage, as well as the brick daage, is a bit higher for tendons, than for external forces. 1050

9 5 CONCLUSIONS The static cyclic experiental tests on internal prestressed shear walls indicate the functionality of this ethod to strengthen asonry against earthquake loading. Useful aterial odels were discussed and used for nuerical investigations. Many reasons to odel the tendons were pointed out, e.g. the restoring force and the ipact on the dynaic behaviour. Deeper investigations especially regarding the dynaic behaviour of prestressed walls are recoended. This has been done by eans of first dynaical nonlinear siulations. The entioned iportant factors have to be considered carefully in further siulations. ACKNOWLEDGEMENTS We would like to thank Prof. Lagoarsino and Dr. Calderini fro the Università degli Studi di Genova for their perission and support in including their aterial odel into our research. Also we have to express deepest gratitude to Prof. Bartoli fro the Università degli Studi di Firenze. großforatige MW it hohe Erdbebenwiderstand, Abschlussbericht, ibmb der TU Braunschweig, Gerany Gabarotta, L. & Lagoarsino, S Daage Models for the seisic response of brick asonry shear walls, Part I and II, Earthquake Engineering and Structural Dynaics, Vol. 26, 1997: Lourenço, P.B Coputational strategies for asonry structures, Ph.D. Thesis, Delft University of Technology, Netherlands Oliveira, D.V Experiental and nuerical analysis of blocky asonry structures under cyclic loading, Ph.D. Thesis, University of Minho, Portugal Ötes, A., Löring, S. & Elsch, B Erhöhung der Schubtragfähigkeit von KS-Wänden unter Erdbebenlasten durch schlaf bewehrte Beton-stützen in Forsteinen bzw. durch Vorspann-ung der Wand, Forschungsvereinigung Kalk- Sand e.v. Ötes, A. & Löring, S Zu Tragverhalten von Mauerwerksbauten unter Erdbebenbelastung, Bautechnik, No. 83, Heft 2, 2006: Rots, J.G Structural Masonry: An Experiental /Nuerical Basis for Practical Design Rules, Balkea, Rotterda, Netherlands, ISBN Verfeltfoort, A.Th. & Raijakers, T.M.J Deforation controlled eso shear tests on asonry piers, Part 2, Draft report, TU Eindhoven, dept. BKO, Netherlands. REFERENCES Budelann, H., Gunkler, E., Huseann, U. & Becke, A Rationell hergestellte Wände aus vorgespannte 1051