A GENERIC MODEL OF A BASE-ISOLATED BUILDING

Transcription

1 Chapter 5 A GENERIC MODEL OF A BASE-ISOLATED BUILDING This chapter draws together the work o Chapters 3 and 4 and describes the assembly o a generic model o a base-isolated bilding. The irst section describes an existing two-dimensional model o a bilding, which is based on the dynamic-stiness method (DSM) and the same periodic strctre theory sed to model the piled ondation o Chapter 4. The copling o the bilding and ondation models is then described beore a virtal case stdy is presented to illstrate the practical application o the inal model. Along with some initial observations, the case o a pointload excitation o the ondation is sed to investigate three aspects o base-isolated bilding behavior: the added-mass eect associated with a bilding and the vibration o its ondation; the insertion perormance o typical isolation bearings; and the importance o acconting or pilesoil-pile interaction in the ondation model The Ininite Bilding Model In Chapter 3 the DSM was introdced as an appropriate means o modelling a typical bilding and this was illstrated with a simple portal-rame model. Real bildings contain many more colmns and loors and the generic base-isolated bilding model mst relect this. The chosen bilding model is that developed by Cryer [33]; see Figre 5.1. This is an ininitely long two-dimensional portal-rame model prodced by combining the DSM with the same periodic strctre theory sed to model the pile row o Chapter 4. The primary reason or choosing this approach is the comptational eiciency with which a mlti-story bilding may be modelled. It has also been 145

2 CAPTER 5. A GENERIC MODEL OF A BASE-ISOLATED BUILDING 146 validated by Cryer s experiments in Glocester Park, London, which show that predictions o vibration transmissibility agree well with measrements made in a real bilding. (b) (a) (b) = (c)... Figre 5.1: Cryer s ininitely long two-dimensional portal-rame model o a bilding, based on a combination o the dynamic-stiness method and periodic strctre theory. The central loaded nit (a) is copled to two semi-ininite strctres (b) to orm the complete model (c). The repeating nits are deined by dashed vertical lines. The mathematics describing the bilding model is very similar to that describing the pile-row model given in Section The key eqation again involves a transer matrix bt this now relates the generalised orces and displacements at the ends o each loor o the portal rame s repeating nit. The transer matrix is derived rom the repeating nit s reqency-response nction (FRF) matrix, as calclated by the DSM. Frther details may be ond in Cryer [33].

3 CAPTER 5. A GENERIC MODEL OF A BASE-ISOLATED BUILDING 147 When the model is sed to represent an isolated bilding the repeating nit has an isolation bearing added to the base o the colmn. This is modelled sing the approach described in Section Copling the Ininite Bilding and Pile-Row Models In principle, an ininitely long model o a bilding and its ondation may be prodced by sing the periodic strctre theory described in Section with a new orm o repeating nit. The nit wold be ormed by copling together the repeating nits o the bilding and pile-row models. This approach has the advantage o prodcing a lly copled model, with the base o every bilding colmn copled to a pile, bt the disadvantage o reqiring a new soltion to the entire model, inclding the ondation, whenever a parameter change is made. The approach chosen here is to solve the ininite bilding and pile-row models separately and then cople the two together at a inite nmber o pile heads, in a similar way to that sed or the initial model o Section The necessary nmber o copling points is determined by observing the convergence o the soltion as more piles are inclded. The advantage o this approach is that parameter changes may be made to the bilding model withot the need to resolve the pile-row model, which is by ar the more comptationally expensive component. A schematic diagram o the complete model is shown in Figre 5.2. The details o the copling procedre are as ollows. A general orm o Eqation 3.18 is sed to relate the generalised orces and displacements o the the bilding: or 1 2 N = N N N N 0 N pile heads that are to be copled to 1 2 N N 0 (5.1a) = + (5.1b) The 3 N x N 3 FRF matrix describes the behavior o the ondation and is assembled rom the 3 x 3 matrices describing the individal piles. The three 3 N x 1 vectors, o and

4 CAPTER 5. A GENERIC MODEL OF A BASE-ISOLATED BUILDING 148 are assembled, respectively, rom the 3 x 1 vectors containing the complex amplitdes o the generalised orces, and the generalised displacements beore and ater constrction o the bilding, o each pile-head. Bilding Model (Section 5.1) Isolation Bearings (Section 3.1.2) Y X Pile-Row Model (Section 4.2) Figre 5.2: Schematic isometric projection o the generic model o a base-isolated bilding. The ininitely long two-dimensional portal-rame model o a bilding is copled to the ininitely long three-dimensional model o a piled ondation. Becase the ondation comprises identical piles, the matrices ii along the diagonal o which contain the pile-head driving-point FRFs o each pile, are all eqal. The o-diagonal matrices describe the PSPI, and reciprocity and symmetry imply that: 1 1 1, ij ji = (5.2) 1 1 1

5 CAPTER 5. A GENERIC MODEL OF A BASE-ISOLATED BUILDING 149 where implies element-by-element matrix mltiplication. The orce and displacement amplitdes o the pile heads, ater constrction o the bilding, are also related throgh a general orm o Eqation 3.20: or 1 2 N = 11 b 21 b N b 1 12 b 22 b 1N b N b N 1 2 N (5.3a) = (5.3b) b Eliminating the orces rom Eqations 5.1 and 5.3 gives the inal displacements o the pile heads in terms o those prior to the constrction o the bilding, as in Eqation 3.21: 1 [ I + [ b ] ] 1 0 = (5.4) where I is a 3 N x N 3 identity matrix. For any chosen pre-constrction displacements o the pile-heads, the displacements given by Eqation 5.4 may be sed to ind the corresponding orces by inversion o Eqation 5.3. These orces are then applied, in the opposite sense, to the bilding model to determine the ll response. This concldes the mathematical description o the generic model. The model is lexible, comptationally eicient and there are many possible stdies that may now be ndertaken. These inclde investigations into the ollowing: the importance o the stiness vertical, horizontal and rotational and internal damping o isolation bearings in determining base-isolation perormance; the signiicance o dierent grond vibration ields when designing or maximm base isolation, and the eects o horizontal and rotational motion o a ondation in addition to vertical motion;

6 CAPTER 5. A GENERIC MODEL OF A BASE-ISOLATED BUILDING 150 the natre o the soil-strctre interaction between a bilding and its ondation and how this inlences isolation perormance; the natre o pile-soil-pile interaction in piled ondations and how this inlences isolation perormance. The next section presents three selected stdies as those o most immediate interest A Virtal Case Stdy This section discsses some initial observations along with three stdies ndertaken with the generic base-isolated bilding model. The reslts are presented in the orm o a virtal case stdy in order to illstrate the practical application o the model. =49 z Figre 5.3 shows a schematic elevation o a design or a new hospital. Emergency generator Figre 5.3: Schematic elevation o a design or a new hospital. An emergency generator located at grondloor level may lead to excessive levels o internal vibration and base isolation o the bilding is a potential soltion. The design is based on a typical concrete-ramed strctre onded on piles and incldes an emergency generator at grond-loor level located close to one o the central piles. It is recognised that the generator may lead to excessive vibration levels in the hospital. Conseqently,

7 CAPTER 5. A GENERIC MODEL OF A BASE-ISOLATED BUILDING 151 ollowing constrction o the ondation, a consltant is asked to simlate operation o the generator by sing a harmonic shaker monted on the pile head nearest to the location o the generator. Based on measrements o the reslting motion o the pile heads, the consltant concldes that vibration wold indeed be a problem in the completed hospital and that base isolation o the strctre shold be investigated. Three qestions are o primary concern: how signiicant is the added-mass eect, irst discssed in Section 3.2.2; what level o insertion perormance shold be expected rom the base isolation; and how important is the modelling o PSPI? These qestions are addressed in trn sing reslts rom the generic model. The reslts are all based on a model o a concrete-ramed bilding onded on concrete piles, with the parameter vales given in Table 5.1. Bilding property Vale Fondation property Vale Nmber o storeys 6 Length o piles [m] 7.5 eight o colmns [m] 3 Radis o piles [m] Length o loors [m] 1.5 Spacing o piles [m] 1.5 Bending stiness o elements [GPam 4 ] 0.4 Bending stiness o piles [GPam 4 ] 0.34 Axial stiness o elements [GPam 2 ] 5.0 Axial stiness o piles [GPam 2 ] 11.0 Yong s modls o elements [GPa] Yong s modls o piles [GPa] 28 Density o elements [kg/m 3 ] 2400 Density o piles [kg/m 3 ] 2667 Damping loss actor o elements 0.1 Yong s modls o soil [GPa] 0.28 Density o soil [kg/m 3 ] 2000 Poisson s ratio o soil 0.4 Damping loss actor o soil 0.02 Table 5.1: The parameter vales sed in the generic base-isolated bilding model or the virtal case stdy. The excitation rom the harmonic shaker is modelled as a vertical nit-amplitde orce applied to the central pile-head. This reslts in the pre-constrction pile-head vibration amplitdes 0, which are calclated sing the pile-row model alone. The piled ondation model ses the same bondary-element mesh as sed in the inal validated model o Section and an pper reqency limit o 80 z is chosen, which incldes the range o reqencies in which grondborne vibration levels typically peak. At 80 z the mesh provides six elements per S-wavelength, as recommended by Domingez [35] or se in elastodynamic analysis. When calclating the inal

8 CAPTER 5. A GENERIC MODEL OF A BASE-ISOLATED BUILDING 152 response, observations o the convergence o the varios reslts show that, or the particlar parameter vales chosen, the nmber o piles that mst be copled to the bilding is Initial Observations Figres 5.4 and 5.5 illstrate the predicted response o the hospital in the event that it is let nisolated and the colmns o the bildings are directly copled to the piles. In this case it is clear that the bilding and ondation experience comparable vibration amplitdes and behave as one system. It is also clear that the piles ndergo horizontal, as well as vertical, motion.

9 CAPTER 5. A GENERIC MODEL OF A BASE-ISOLATED BUILDING 153 Figre 5.4: Vibration o an nisolated hospital as predicted by the generic base-isolated bilding model. The 50 z excitation corresponds to a vertical nit-amplitde orce applied to the central pile-head prior to the constrction o the bilding. All displacements are magniied by 1 x ; a side elevation is shown in Figre 5.5.

10 CAPTER 5. A GENERIC MODEL OF A BASE-ISOLATED BUILDING 154 Figre 5.5: Side elevation o Figre 5.4 showing the vibration o an nisolated hospital as predicted by the generic base-isolated bilding model. The 50 z excitation corresponds to a vertical nit-amplitde orce applied to the central pile-head prior to the constrction o the bilding. All displacements are magniied by 1 x. Figres 5.6 and 5.7 illstrate the eqivalent reslts when the bilding is base-isolated with an isolation reqency o 5 z; the damping loss actor o the bearings is The same displacement magniication actor is sed in Figres 5.5 and 5.7 (a), and it is clear that the isolation signiicantly redces the vibration amplitdes o the bilding. This is achieved by the isolation bearings allowing relative motion between the pile heads and the bases o the bilding colmns. The latter is clear in Figre 5.7 (b) where the displacement magniication actor is an order o magnitde greater than in the other igres: the bending o the grond-loor colmns either side o the applied load is as thogh they were reely vibrating cantilevers.

11 CAPTER 5. A GENERIC MODEL OF A BASE-ISOLATED BUILDING 155 Figre 5.6: Vibration o a 5 z base-isolated hospital as predicted by the generic base-isolated bilding model. The 50 z excitation corresponds to a vertical nit-amplitde orce applied to the central pile-head prior to the constrction o the bilding. All displacements are magniied by 1 x ; a side elevation is shown in Figre 5.7.

12 CAPTER 5. A GENERIC MODEL OF A BASE-ISOLATED BUILDING 156 (a) (b) 26 x 3 [m] x [m] 1 (Fondation not shown) Figre 5.7: Side elevation o Figre 5.6 showing the vibration o a 5 z base-isolated hospital as predicted by the generic base-isolated bilding model. The 50 z excitation corresponds to a vertical nitamplitde orce applied to the central pile-head prior to the constrction o the bilding. The displacements 11 are magniied by (a) 1 x and (b) 1 x.

13 CAPTER 5. A GENERIC MODEL OF A BASE-ISOLATED BUILDING 157 These initial observations indicate qalitatively that base-isolation wold be beneicial or the hospital, at least at 50 z. A qantitative measre o this, or dierent isolation bearings and over a range o reqencies, is considered in Section The Added-Mass Eect In Section it was demonstrated, sing simple models, how the constrction o a bilding acts to constrain its ondation and redce the original ondation vibration levels. It was also demonstrated how the level o this added-mass eect depended on whether or not the bilding is base-isolated, the eect being less signiicant with a base-isolated bilding de to the decopling o the bilding rom its ondation. It is important to investigate this eect with the more comprehensive generic model. To qantiy the eect, comparisons are made o the vertical pile-head displacement amplitdes beore and ater the constrction o the hospital bilding. Figre 5.8 smmarises the reslts in the event that the bilding is let nisolated. In this case the added-mass eect leads to a redction in the pile-head amplitde o the loaded pile o approximately 4 db, which is approximately constant over the reqency range considered. Piles downstream o the loaded pile, in general, experience an ampliication o vibration levels, which is greatest at low reqencies, and the level o ampliication increases the rther downstream the pile. This is de to the bilding transmitting vibration to the pile heads in addition to that propagating throgh the soil, the lower reqencies being more eiciently transmitted along the bilding. The eect is more noticeable with the more distant piles de to their lower pre-constrction vibration levels. The troghs in the crves are believed to occr when the vibration transmitted via the bilding arrives ot-o-ase with that transmitted via the grond.

14 CAPTER 5. A GENERIC MODEL OF A BASE-ISOLATED BUILDING v/v 0 mag. [db] Pile nmber Freqency [z] Figre 5.8: Soil-strctre interaction o an nisolated hospital, as predicted by the generic base-isolated bilding model. The ratio o the inal vertical pile-head displacement amplitdes v to those prior to the constrction o the bilding v 0 is plotted against reqency or the central loaded pile (no.12) and those at increasing distances rom it (nos.11-1). Only one hal o the ondation is considered de to the symmetry o the response. Figre 5.9 smmarises the reslts or the case o a 5 z isolation reqency; the damping loss actor o the bearings is The change in vibration levels is now negligible except or a small amont o ampliication o the downstream pile amplitdes at low reqencies. Note that neither the isolated nor the nisolated reslts show the peaks and troghs de to ondation and grond resonances, as discssed in Section This is de to the natre o the ininite model.

15 CAPTER 5. A GENERIC MODEL OF A BASE-ISOLATED BUILDING v/v 0 mag. [db] Pile nmber Freqency [z] Figre 5.9: Soil-strctre interaction o a 5 z base-isolated hospital, as predicted by the generic baseisolated bilding model. The ratio o the inal vertical pile-head displacement amplitdes v to those prior to the constrction o the bilding v 0 is plotted against reqency or the central loaded pile (no.12) and those at increasing distances rom it (nos.11-1). Only one hal o the ondation is considered de to the symmetry o the response. These reslts conirm the general conclsions drawn in Section that constrcting a bilding modiies the original, ondation vibration ield and that the eect is less signiicant when the bilding is decopled rom the ondation by the se o base isolation. owever, whether or not this leads to a redction in ondation vibration levels depends on the natre o the excitation. When sbject to localised excitation, as investigated here, the additional vibration transmission path throgh the bilding leads, in general, to an increase in ondation vibration at points remote rom the excitation. In the case o distribted excitation, where pre-constrction vibration levels are comparable across the whole ondation, the added-mass eect is expected to lead to a general redction in ondation vibration levels.

16 CAPTER 5. A GENERIC MODEL OF A BASE-ISOLATED BUILDING 160 It is clear that the consltant concerned with the hospital needs a comprehensive model to make predictions o base-isolation perormance. It is not possible to make these predictions by simply taking measrements o ondation vibration and sing them as the inpts to a bilding model: the bilding and ondation act as one system and mst be modelled as sch. It shold be noted that this case stdy has avoided the need to consider the eect o a ondation on a pre-existing grond vibration ield. In practice, this is a common problem and is the sbject o rther work; see Section Predictions o Insertion Perormance The most important qestion or any base-isolated bilding project is what level o insertion perormance shold be expected. The consltant s predictions have signiicant implications or the hospital project, rom the speciication o the isolation reqency to a potential redesign o major parts o the bilding strctre. In Section power low insertion gain (PFIG) was introdced as a more sel measre o insertion perormance than those crrently sed, which are based on vibration amplitdes. Predictions o PFIG rom the generic model are discssed here. Figre 5. shows the variation with reqency in the PFIG when the hospital is base-isolated on bearings giving isolation reqencies o 5, and 15 z, with internal damping loss actors o 0.1 and This range o parameters is typically ond in practice: a 15 z isolation with a loss actor o 0.1 is representative o high-hysteresis rbber bearings while a 5 z isolation with a loss actor o 0.01 is representative o ndamped steel springs. The irst thing to note abot Figre 5. is the smoothness o the crves; the series o resonant peaks predicted by the initial model o Section 3.3, as in Figre 3.14, are no longer evident. This is de to the ininite natre o the model, which radiates energy away rom the excitation and prevents resonances rom being established. This behavior was originally noted by Cryer [33] when developing the ininite bilding model and was ond to be more representative o real bildings, which do not exhibit the strong resonant behavior o inite models.

17 CAPTER 5. A GENERIC MODEL OF A BASE-ISOLATED BUILDING η = 0.1 η = PFIG [db] isol = 15 z isol = z isol = 5 z Freqency [z] Figre 5.: Variation with reqency in the power low insertion gain o a base-isolated hospital, as predicted by the generic base-isolated bilding model. Isolation reqencies o 5, and 15 z are considered, provided by bearings with internal damping loss actors o 0.1 and The excitation corresponds to a vertical nit-amplitde orce applied to the central pile-head prior to the constrction o the bilding. The peaks that are evident in Figre 5. are de to peaks in the total mean vibrational power low into the isolated bilding; see Figre The irst o these occrs near the isolation reqency and corresponds, in essence, to the global bonce mode o the bilding on the isolation bearings, althogh the response is localised arond the excitation; see or example Figre The smaller peaks in the region o 30, 40 and 50 z appear to occr at reqencies when vibration can propagate reely along the strctre in the region o the bilding-ondation interace; see or example Figres 5.13 and 5.14.

18 CAPTER 5. A GENERIC MODEL OF A BASE-ISOLATED BUILDING P total [db re 1 W] nisolated isol = 15 z isol = z isol = 5 z Freqency [z] Figre 5.11: Variation with reqency in the total mean power low P total into a base-isolated hospital, as predicted by the generic base-isolated bilding model. Isolation reqencies o 5, and 15 z are considered, provided by bearings with an internal damping loss actor o The excitation corresponds to a vertical nit-amplitde orce applied to the central pile-head prior to the constrction o the bilding. O interest to the consltant is the act that the choice o isolation reqency makes a large dierence to the eiciency o the isolation. The dierences are not as great as predicted by the initial model approximately 15 db, rather than 20 db, between a 5 and 15 z isolation bt they are nevertheless signiicant and wold certainly inlence a design decision. It mst be stressed that the predictions are expected to depend on the natre o the excitation and that a dierent conclsion may be drawn or less localised excitation.

19 CAPTER 5. A GENERIC MODEL OF A BASE-ISOLATED BUILDING 163 Figre 5.12: Side elevation showing the vibration o a z base-isolated hospital, as predicted by the generic base-isolated bilding model. A vertical nit-amplitde orce is applied to the central pile-head prior to the constrction o the bilding at a reqency o 7 z. This corresponds to a peak in the PFIG crve o Figre 5.. All displacements are magniied by 1 x. In general, the level o internal damping in the bearings has a negligible eect on the PFIG. owever, it does have an eect at reqencies when relative motion between the pile heads and the bases o the bilding colmns is signiicant, that is, when the isolation bearings ndergo signiicant deormation. This is evident in Figres 5.12 to The relative vertical motion at 7 z (Figre 5.12) and that in the horizontal direction at 41 z (Figre 5.14) is large: increasing the internal damping thereore increases the power dissipation in the bearings and redces the total power low into the bilding. When the bearing deormation is small, sch as at 34 z (Figre 5.13) the internal damping has little eect on the eiciency o the isolation.

20 CAPTER 5. A GENERIC MODEL OF A BASE-ISOLATED BUILDING 164 Figre 5.13: Side elevation showing the vibration o a z base-isolated hospital, as predicted by the generic base-isolated bilding model. A vertical nit-amplitde orce is applied to the central pile-head prior to the constrction o the bilding at a reqency o 34 z. This corresponds to a peak in the PFIG crve o Figre 5.. All displacements are magniied by 1 x.

21 CAPTER 5. A GENERIC MODEL OF A BASE-ISOLATED BUILDING 165 Figre 5.14: Side elevation showing the vibration o a z base-isolated hospital, as predicted by the generic base-isolated bilding model. A vertical nit-amplitde orce is applied to the central pile-head prior to the constrction o the bilding at a reqency o 41 z. This corresponds to a peak in the PFIG crve o Figre 5.. All displacements are magniied by 1 x. Beore leaving the discssion on power low it is worth noting again the signiicance o horizontal motion. Figre 5.15 shows the variation with reqency in the three components o the mean power low entering the hospital as percentages o the total low. It is clear that horizontal motion can contribte a signiicant proportion o the total power low and this shold not be ignored.

22 CAPTER 5. A GENERIC MODEL OF A BASE-ISOLATED BUILDING P /P v total P /P total P /P θ total P/P total [%] Freqency [z] Figre 5.15: Variation with reqency in the vertical P v, horizontal P and rotational P θ components o the mean power low entering a z base-isolated hospital, as predicted by the generic base-isolated bilding model. The excitation corresponds to a vertical nit-amplitde orce applied to the central pilehead prior to the constrction o the bilding. The reslts are presented as percentages o the total mean power low P total The Importance o Pile-Soil-Pile Interaction Chapter 4 was concerned entirely with the development o a new piled-ondation model, which, most signiicantly, lly acconts or the eects o PSPI. It is now important to establish whether or not the extra eort this involves is necessary. This is investigated here by comparing reslts rom the generic base-isolated bilding model with those rom a model that disregards PSPI. The latter is identical to the generic model in all respects except that the ondation is based on the single-pile model o Section 4.1. The ondation FRF matrix is thereore a banded matrix, ij since = 0, and incldes only the pile-head driving-point FRFs o the single-pile. Figre 5.16 illstrates qalitatively the eect o PSPI on the response o the hospital in the nisolated state.

23 CAPTER 5. A GENERIC MODEL OF A BASE-ISOLATED BUILDING 167 (a) x 3 [m] x [m] 1 (b) x 3 [m] (Fondation 30 not shown) x [m] 1 Figre 5.16: Side elevation showing the vibration o an nisolated hospital, as predicted by (a) the generic base-isolated bilding model and (b) a model that disregards PSPI. The 50 z excitation corresponds to a vertical nit-amplitde orce applied to the central pile-head prior to the constrction o the bilding. All displacements are magniied by 1 x.

24 CAPTER 5. A GENERIC MODEL OF A BASE-ISOLATED BUILDING 168 In this example, neglecting the interaction between piles signiicantly redces the response o the colmns either side o the loaded pile. Disregarding PSPI ignores hal o the vibration transmission path rom the loaded pile and vibration o neighboring piles is de solely to vibration transmission throgh the bilding. The eect o this on the predictions o insertion perormance are shown in Figres 5.17 and Generic model PSPI disregarded nisolated 90 P total [db re 1 W] isol = 15 z isol = z isol = 5 z Freqency [z] Figre 5.17: Variation with reqency in the total mean power low P total into a base-isolated hospital, as predicted by the generic base-isolated bilding model and a model that disregards PSPI. Isolation reqencies o 5, and 15 z are considered, provided by bearings with an internal damping loss actor o The excitation corresponds to a vertical nit-amplitde orce applied to the central pile-head prior to the constrction o the bilding. Figre 5.17 shows how PSPI leads primarily to a change in the total power low into the isolated bilding. At reqencies below approximately 40 z, PSPI leads to an increase in power low; at higher reqencies there is a small decrease. This may be de to the more eective propagation o

25 CAPTER 5. A GENERIC MODEL OF A BASE-ISOLATED BUILDING 169 vibration throgh the ondation, and sbseqently into the bilding, at lower reqencies; at higher reqencies, as the wavelengths approach the diameter o the piles, there is an increased tendency o wave scattering and propagation along the ondation is more diiclt. Figre 5.18 shows how these changes are relected in the predictions o PFIG. The increase in power low into the isolated bilding reslts in vales o PFIG below 40 z that are approximately 4 db greater, althogh this can be as mch as 7 db. Neglecting PSPI thereore leads to an over-prediction o the isolation eiciency, and by an amont that is signiicant or the consltant working to meet a noise or vibration standard. It is again worth noting that these reslts are or the particlar case o point excitation and a dierent conclsion may be drawn or other grond vibration ields. 5 0 Generic model PSPI disregarded 5 PFIG [db] isol = 15 z isol = z isol = 5 z Freqency [z] Figre 5.18: Variation with reqency in the power low insertion gain o a base-isolated hospital, as predicted by the generic base-isolated bilding model and a model that disregards PSPI. Isolation reqencies o 5, and 15 z are considered, provided by bearings with an internal damping loss actor o The excitation corresponds to a vertical nit-amplitde orce applied to the central pile-head prior to the constrction o the bilding.

26 CAPTER 5. A GENERIC MODEL OF A BASE-ISOLATED BUILDING Conclsions Bilding on the work o Chapters 3 and 4, this chapter has described the assembly o a generic base-isolated bilding model, comprising an ininitely long two-dimensional model o a bilding copled to an ininitely long three-dimensional model o a piled ondation. By considering the speciic case o a grond vibration ield de to a point-load excitation o the ondation, three aspects o base-isolated bilding behavior have been investigated. The main conclsions o these are smmarised below. 1. The bilding and ondation act as one system: changes to the bilding aect the ondation and vice versa. This means that it is impossible to make good predictions o bilding behavior by modelling the bilding alone. 2. Constrcting a bilding on a ondation modiies any pre-existing vibration ield de to the constraining eect o the added mass together with the vibration transmission within the bilding. The ormer leads to a redction in ondation vibration, while the latter can lead to an increase i the excitation is localised and the bilding is able to transmit vibration to remote parts o the ondation that originally experienced little vibration. In either case, the eect is less signiicant when the bilding is base-isolated. 3. The choice o isolation reqency can make p to a 15 db dierence to the eiciency o the isolation or typical bearing designs. This is signiicant or the design o a particlar bilding bt the dierence may depend on the natre o the excitation, in particlar, whether or not the grond vibration ield is small compared to the size o the bilding. 4. In general, the level o internal damping in the isolation bearings has a negligible eect on the PFIG. owever, it does increase internal power dissipation at reqencies when the isolation bearings ndergo signiicant deormation. It is thereore important or controlling local resonant behavior o the base o the bilding strctre, which wold otherwise lead to an increase in the vibrational power entering the bilding.

27 CAPTER 5. A GENERIC MODEL OF A BASE-ISOLATED BUILDING The comprehensive modelling o a piled ondation is important. orizontal, and to a lesser extent, rotational motion o the pile heads can contribte signiicant proportions o the total vibrational power low entering a bilding. Interaction between piles throgh wave propagation in the srronding soil shold be inclded as an important vibration transmission path. Neglecting this pile-soil-pile interaction can reslt in an nder-prediction o the power low entering an isolated bilding and conseqently an over-prediction, o p to 7 db, o the isolation eiciency. Again this may depend on the natre o the excitation. These conclsions are based on a speciic grond vibration ield and it is not yet possible to say whether they are applicable to base-isolation in general. The reqency range considered extends p to 80 z, which incldes the range in which grond-borne vibration levels typically peak bt excldes the pper reqencies o interest. Frthermore, as noted in Section 4.3, the accracy o the ondation model with the crrent bondary-element mesh is expected to decrease with reqency above 50 z. These represent the primary limitations o the reslts presented in this chapter and are the sbject o rther work, as discssed in Chapter 7. This dissertation has discssed in detail the advantages o a theoretical power-based approach to predicting base-isolation perormance. In the next chapter the practical easibility o these ideas is considered by exploring the possibility o a orce-sensitive vibration isolation bearing.