SEISMIC STRENGTH REDUCTION FACTOR FOR SINGLE AND MULTI-STOREY SHEAR BUILDINGS CONSIDERING SOIL- STRUCTURE INTERACTION

Transcription

1 SEISMIC STRENGTH REDUCTION FACTOR FOR SINGLE AND MULTI-STOREY SHEAR BUILDINGS CONSIDERING SOIL- STRUCTURE INTERACTION Yang LU, Iman HAJIRASOULIHA * and Alec M. MARSHALL ABSTRACT A parametric analyi ha been performed to tudy the trength-ductility relationhip of building with different fundamental period conidering Soil-Structure Interaction (SSI). Multi-torey hear building are combined with the cone model that repreent a homogeneou oil half-pace to provide a implified SSI model. Thee building are deigned with the IBC lateral force ditribution and are then ubjected to a group of 6 imulated pectrum compatible earthquake. The effect of tructure to oil tiffne ratio, lenderne of the tructure and number of torey on the trength reduction factor and the modification factor have been invetigated. It i concluded that uing calculated baed on fixed-baed ytem in SSI deign would underetimate the required trength for a given target ductility demand and, therefore, i not uitable for practical deign purpoe. It i alo hown that the combined effect of and invariantly reult in an elongated period, while it can either increae or decreae the overall damping of SSI ytem when compared to their fixed-bae counterpart. The reult indicate that the modification factor for inelatic SSI ytem i mainly affected by the tructure to oil tiffne ratio, fundamental period and lenderne ratio of the building, but it i not enitive to the variation of ductility demand and number of torey. INTRODUCTION Modern eimic proviion allow tructure to diipate eimic energy by undergoing inelatic deformation in evere earthquake event. The expected level of inelaticity i uually achieved by reducing the elatic deign repone pectra. For example, the deign lateral trength can be much lower than that required to maintain a tructure in elatic tate during trong ground motion. Thi reduction in trength i quantified by a reduction factor given by Equation (Miranda, 997) R R R R M () where i aociated with the reduction in trength for a ingle-degree-of-freedom (SDOF) tructure due to it inelatic hyteretic behaviour; i a modification factor that take into account the multidegree-of-freedom (MDOF) effect; and account for the overtrength of tructural component and other afety factor. PhD candidate, The Univerity of Nottingham, Nottingham, evxyl7@nottingham.ac.uk Lecturer, The Univerity of Sheffield, Sheffield, i.hajiraouliha@sheffield.ac.uk Lecturer, The Univerity of Nottingham, Nottingham, alec.marhall@nottingham.ac.uk

2 Y.Lu, I.Hajiraouliha and A.M.Marhall In the pat four decade, extenive tudie have been dedicated to (e.g. Riddell, et al., 989; Fichinger et al., 99) and (Santa-Ana and Miranda, ; Moghaddam and Mohammadi, ) that are ued in conventional deign for fixed-bae tructure. In thee tudie, and were obtained over a wind range of tructural period for different value of the ductility ratio. A comprehenive review of previou tudie on the relationhip wa made by Miranda and Bertero (99). On the other hand, the effect of oil flexibility have been een to increae the natural period of the Soil-Structure Interaction (SSI) ytem. Moreover, the oil that i introduced to a SSI ytem diipate ome of the eimic energy aborbed by the tructure through internal friction (hyteretic damping) and radiation damping. The period lengthening and damping effect have been regarded a beneficial and are coded into ome of the deign proviion (NERHP, 997; ATC -6; FEMA 5). A a conequence, the above-mentioned reduction factor hould be modified accordingly. While a number of analye have been performed to tudy the trength reduction factor of SDOF SSI ytem (Avilé and Pérez-Rocha, 5; Ghannad and Jahankhah, 7; Jarernpraert, ), le attention ha been paid to the inelatic force demand of multi degree-of-freedom (MDOF) SSI ytem. In thi tudy, the trength reduction factor and the modification factor for SSI ytem are calculated and compared to thoe obtained from their fixed-bae counterpart. Analyi i performed on a implified SSI model ubjected to a group of 6 imulated earthquake compatible with IBC- deign pectra for Site E (oft oil profile). Effect of oil flexibility, fundamental period and lenderne ratio of the tructure, target ductility demand and number of torey are invetigated. MODELLING AND ASSUMPTIONS The multi-torey building in thi tudy are modelled a hear building, conitent with previou eimic analye of building tructure (e.g. Hajiraouliha and Pilakouta, ). The reliability and accuracy of thee model can be found in Lai et al. (99). In hear-building model, the ma of each floor i aumed to be lumped at the centre of the beam and i connected by an elatic-perfectly-platic pring that model the hear deformation. Each building i conidered to have a torey height of and a total ma which i uniformly ditributed along the height. The trength and tiffne ditribution i aumed to be proportional to the torey hear force ditribution in accordance with the IBC lateral force pattern. The homogeneou oil half-pace i modelled by a dicrete-element model baed on the concept of the cone model (Ehler, 9). Thi model ha been found to be adequate for practical application (Meek and Wolf, 99). A Sway-Rocking SSI model coniting of a tranlational and a rotational cone that upport a hear building i hown in Figure a. Both cone are contructed a an interconnection of a mall number of mae, pring, and damper whoe propertie are given by Wolf, (99). k h 8 r, ch r () k 8 r pr, c () 5 M r 9 p 8 () where and are the coefficient of pring (denoted by ) and radiation damping dahpot (denoted by ) for the horizontal (denoted with ubcript ) and rocking (denoted with ubcript ) motion, repectively, a illutrated in Figure a. The propertie of the homogeneou oil half-pace include it ma denity, Poion ratio, hear wave velocity and dilatational wave

3 Y.Lu, I.Hajiraouliha and A.M.Marhall velocity. The equivalent radiu of the hallow foundation i aumed to be r. To account for the frequency dependence of the rocking component of the cone model in the time domain analyi, an additional rotational degree of freedom, with it own ma moment of inertia, i introduced a hown in Figure a. a Spectral Acceleration (g) b Deign Spectrum IBC- Soil Type E Average of 6 Synthetic Eq Period (ec) Figure. (a) Simplified Soil-Structure Interaction model; (b) Comparion of the IBC- repone pectrum for oil type E with the average pectrum of the ynthetic earthquake Six pectrum-compatible ynthetic earthquake are generated to repreent the elatic deign repone pectra of IBC- correponding to oil type E (Figure b), which i decribed a a very oft oil profile with. Thi deign repone pectrum i aumed to be an envelope of the poible ground motion that could occur at the ite. MODELLING PARAMETERS The main propertie of a SSI ytem can be well decribed by the following non-dimenional parameter:. The tructure-to-oil tiffne ratio, which i defined a wnh a (5) where i the circular frequency of the fixed-bae tructure correponding to it firt mode of vibration, with being the fundamental period, and the effective height of the tructure i approximated a.7 time the total height ( ). indicate the degree of influence of SSI and generally varie from zero, for fixed-bae tructure, to about two, where the oil become very flexible compared to the tructure.. The lenderne ratio of the tructure, which i given by. The tructure-to-oil ma ratio that i H (6) r

4 Y.Lu, I.Hajiraouliha and A.M.Marhall m mtot (7) H r tot Where i the totoal ma of the tructure. Additional parameter ued in thi tudy include the tructural ductility ratio, which i the imum inter-torey ductility at the critical torey; the foundation-to-tructure ma ratio, where i the ma of the foundation that determine the ma moment of inertia of the foundation ( ; the damping ratio of the tructure ; number of torey ; and Poion ratio of the oil. The value of the parameter ued in thi tudy are preented in Table. Table. Modelling parameter ued in thi tudy Parameter a m μ m f m tot,,,,,,,6,8.5,,,6. N ζ v ρ (kg m ) h ( ),,5,, RESULTS AND DISCUSSIONS Strength Reduction Factor For a SDOF ytem, i a factor which reduce the elatic bae hear to that required to avoid the imum ductility larger than the deign target ductility. R SDOF SDOF t (8) where and are the bae hear demand of SDOF tructure to remain elatic ( ) and to limit their imum ductility ratio to the target value ( ), repectively. In the preent tudy, factor are calculated from contant ductility pectra obtained for given and value. The mean factor, hown in Figure, are calculated by averaging the reduction factor obtained from the ix pectrum compatible earthquake. A mentioned earlier, i a factor that control the everity of the SSI phenomena, and i the lenderne of the building. It i oberved from Figure that in general, regardle of and, for nearly rigid tructure (i.e. ) tend to one and increae with increaing the flexibility of the building. For fixed-bae tructure ( ) having a long natural period (i.e. very flexible tructure), approache the target ductility ratio. Thee obervation are conitent with the evidence preented by Miranda and Bertero (99). Figure alo how that increaing (including SSI) reduce of flexibly-upported tructure when compared to their fixed-bae counterpart. The reduction i more obviou when the value i maller than, and i up to 75% for a tructure with predominant SSI effect ( ) a een in Figure (f). Unlike the rigidly-upported tructure whoe factor are not affected by the lenderne ratio in SSI ytem, for lender tructure i maller than quatty tructure. However, the trength reduction factor i mainly influenced by the relative tiffne, and to a leer degree, by the lenderne of the tructure. Thi indicate that uing fixed-bae to deign a lender building conidering SSI can be unconervative.

5 Y.Lu, I.Hajiraouliha and A.M.Marhall 5 a = a = a = a =.5.5 R (a) = =.5 (b) = = R R 5 (c) = = 8 (e) =6 = 6 5 (d) = = 8 (f) =6 = 6 T n (ec) Figure. Strength reduction factor T n (ec) for SDOF SSI ytem, average of ix pectrum compatible earthquake It hould be noticed that the factor i not only a function of the dynamic propertie of the SSI ytem, but alo related to ite condition and the ground input motion. However, the mean factor for a SSI ytem ubjected to a given et of earthquake ground motion (ignoring any trength hardening or oftening) can be expreed a a function of the effective ytem period, damping ratio and the target ductility demand. The period and damping ratio of SSI ytem can be calculated from their fixed-bae counterpart and uing the modified expreion baed on the work of eleto and Meek (97) T T n ma ma (9) T T n 56 ma 9 () The effectivene of thee relationhip i demonterated in Figure, where the predicted curve from Equation (9) and () match very well with the data obtained from an Eigen analyi.

6 Y.Lu, I.Hajiraouliha and A.M.Marhall 6 = = =6 =8 Eq. (9) & () T/T n a Figure. Comparion of the obtained and predicted effective period and damping ratio of SSI ytem One of the controverial iue concerning the trength reduction factor i that obtained from a number of earthquake may not be applicable to all cae given the variability of the ground motion and ite condition. It i worth mentioning that Ordaz and Pérez-Rocha (998) propoed the following reduction rule, where i dependent on the elatic diplacement pectra. R R D T, n DT,,, n D t () D where i the elatic pectral diplacement; i the peak ground diplacement and i a curve fitting variable a a function of the ductility. The effect of damping, ite condition and ground motion are implicitly incorporated in the hape of the diplacement pectra, which can account for the cae-to-cae variability. Thi rule wa further extended to SSI ytem by Avilé and Pérez-Rocha (5). Modification Factor For multi-torey building, it i propoed that the factor in Equation (8) be multiplied by a modification factor to account for the poible concentration of the ductility in certain floor. Thi modification factor, denoted by i propoed a: a R M F SDOF MDOF t t () where i the bae hear trength that i required to limit the imum inter-torey ductility of a MDOF ytem to the target ductility. The imum ductility i defined a: u u ui u N MAX,,,,, () uy u y uiy u Ny where and are the imum and yield lateral deformation exhibited by the floor during an earthquake, repectively. By ubtituting Equation (8) and () into Equation () and ignoring the overtrength of tructural component (i.e., the bae hear trength demand of a MDOF ytem ( ) to achieve the target ductility can be calculated by:

7 Y.Lu, I.Hajiraouliha and A.M.Marhall 7 F MDOF SDOF t () R RM The modification factor wa tudied by Santa-Ana and Miranda () where eight multitorey teel moment-reiting frame building were ubjected to 8 earthquake ground motion recorded on different ite. They found that to achieve a target ductility demand, elatic MDOF ytem experienced le bae hear when compared with their correponding SDOF ytem wherea inelatic MDOF tructure attracted higher bae hear than that of the equivalent SDOF tructure. They alo oberved that the modification factor wa mainly affected by the number of torey, and to a mall extent by the ite condition and fundamental period of the tructure. In thi tudy, i obtained for SSI ytem by uing Equation (), where the bae hear trength of MDOF ytem and their correponding SDOF ytem (having the ame total ma) are calculated for the ame and under a given excitation. The average reult from the ix pectrum compatible earthquake are plotted againt the number of torey a preented in Figure. The data in Figure (a) how that (i.e. / ) for (fixed-bae) fall below, which agree with the previouly mentioned obervation that elatic MDOF ytem require lower bae hear capacity than SDOF ytem. Similar reult are oberved for tructure under moderate SSI effect (i.e. ). On the contrary, for evere SSI effect (e.g. and ), higher bae hear trength are required by MDOF ytem than that of SDOF ytem to remain elatic. Similar to, the modification can alo be expreed a a function of the ytem period, damping ratio and the target ductility demand. Beide, may be affected by the number of torey. a = a = a = a = MDOF / SDOF /R M = F MDOF / SDOF /R M = F MDOF / SDOF /R M = F.5.5 (a) = = (c) = = (e) = = 5 5 Number of torey.5.5 (b) = = (d) =6 = (f) =6 = 5 5 Number of torey Figure. Modification factor for MDOF SSI ytem ( )

8 Y.Lu, I.Hajiraouliha and A.M.Marhall 8 The natural period and overall damping of SSI ytem depend on the combined effect of and. It i hown in Figure that the period of a SSI ytem increae with an increae in and. By increaing, the damping ratio increae for quatty tructure, while it decreae for lender tructure. For example, the damping ratio of a SSI ytem with and i five time larger than that of the fixed-bae tructure. On the other hand, if the lenderne ratio had been increaed to four, the overall damping ratio would reduce by up to thirty percent. Thi can be explained by the fact that increaing increae the flexibility and damping of the ytem, while increaing decreae the radiation damping by reducing the contact area between the foundation and oil. Thi will hinder the geometric attenuation of wave energy ariing from the inertial interaction. Conidering the reult in Figure (b) (f), the modification factor for inelatic ytem i mainly affected by and, but it i not enitive to the variation of target ductility demand and number of torey. Generally, decreae with increaing The reult how that doe not change monotonically with increaing, and in general, and lead to a higher trength demand for MDOF ytem. MDOF / SDOF /R M = F.5.5 (a) a = = 5 5 Number of torey T =. T =.5 T =. T =.5 n n n n.5.5 (b) a = = 5 5 Number of torey Figure 5. Effect of period on modification factor for MDOF SSI ytem ( ) The effect of fundamental period of tructure on the modification factor i illutrated in Figure 5. The reult indicate that i coniderably more enitive to the variation of for SSI ytem compared to fixed-bae ytem. Generally, increae with increaing for SSI ytem, while it i almot unaffected by for fixe-baed ytem. The reult preented in Figure and 5 indicate that, for the tructure with imilar fundamental period and lenderne ratio, the modification factor i not enitive to the number of torey. CONCLUSIONS Thi tudy aimed to invetigate the effect of effect of Soil-Structure Interaction (SSI) on the trength-ductility relationhip of SDOF and MDOF ytem. Baed on the reult from thi tudy, the following concluion can be drawn: Soil tructure interaction in general reduce the trength reduction factor. Thi reduction can be up to 75% and decreae with increaing flexibility of the oil relative to the tructure a well a the lenderne of the tructure. Therefore, value which are calculated baed on fixedbaed ytem in SSI deign underetimate the required trength for a given target ductility demand and, therefore, are not uitable for practical deign purpoe. The combined effect of and, though reulting in an elongated period, can either increae or decreae the overall damping of SSI ytem when compared to their fixed-bae counterpart. Generally, damping for flexibly-upported lender building i maller than that of rigidlyupported tructure, while SSI ytem with quatty building have larger damping ratio than thoe of fixed-bae building.

9 Y.Lu, I.Hajiraouliha and A.M.Marhall 9 Elatic MDOF ytem with moderate SSI effect require lower bae hear capacity than SDOF ytem. However, for evere SSI effect, higher bae hear trength are required by MDOF ytem than that of SDOF ytem to remain elatic. The modification factor for inelatic SSI ytem i mainly affected by the tructure to oil tiffne ratio, fundamental period and lenderne of the building, while it i not enitive to the variation of ductility demand and number of torey. REFERENCES Avilé J and Pérez-Rocha LE (5) Influence of Foundation Flexibility on Rμ and Cμ Factor, Journal of tructural engineering, (), - BSSC () The NEHRP Recommended proviion for new building and other tructure, Part : proviion (FEMA 5) Ehler G (9) The effect of oil flexibility on vibrating ytem, Beton und Eien, (/), 97- Fichinger M, Fajfar P and idic T (99) Factor contributing to the repone reduction, Proc., Fifth US Nat. Conf. Earthq. Eng, Chicago Ghannad MA and Jahankhah H (7) Site-dependent trength reduction factor for oil-tructure ytem, Soil Dynamic and Earthquake Engineering, 7(), 99- Hajiraouliha I and Pilakouta K () General eimic load ditribution for optimum performance-baed deign of hear-building. Journal of Earthquake Engineering, 6(), -6. IBC- () International Building Code, International Code Council, Country Club Hill, USA Jarernpraert S, Bazan-Zurita E, and Bielak J () Seimic oil-tructure interaction repone of inelatic tructure, Soil Dynamic and Earthquake Engineering Lai M, Li Y and Zhang C (99) Analyi method of multi-rigid-body model for earthquake repone of heartype tructure, In Proc., th WCEE Conf -8 Meek JW & Wolf JP (99) Cone model for homogeneou oil, I, Journal of geotechnical engineering, 8(5), Miranda E (997) Strength reduction factor in performance-baed deign, In Proceeding of the EERC- CUREe Sympoium, Berkeley, California (ol. 6) Miranda E & Bertero (99) Evaluation of trength reduction factor for earthquake-reitant deign, Earthquake Spectra, (), Moghaddam H and Mohammadi RK () Ductility reduction factor of MDOF hear-building tructure, Journal of earthquake engineering, 5(), 5- Ordaz M and Pérez Rocha LE (998) Etimation of trength reduction factor for elato-platic ytem: a new approach, Earthquake engineering & tructural dynamic, 7(9), Riddell R, Hidalgo P & Cruz E (989) Repone modification factor for earthquake reitant deign of hort period building. Earthquake Spectra, 5(), Santa-Ana PR and Miranda E () Strength reduction factor for multi-degree-of-freedom ytem, In Proceeding of the th world conference on Earthquake Engineering eleto AS & Meek JW (97) Dynamic behaviour of building foundation ytem, Earthquake Engineering & Structural Dynamic, (), -8 Wolf JP (99) Foundation ibration Analyi Uing Simple Phyical Model, Englewood Cliff: Prentice Hall