Proceedings Third UJNR Workshop on Soil-Structure Interaction, March 9-3, 4, Menlo Park, Caliornia, USA. Study on the Dynamic Characteristics o an Actual Large Size Wall Foundation by s and Analyses Masanobu Tohdo a) The dynamic behavior o a large size all oundation supporting a 54-story building is studied in this paper. The contents are on a response analysis ith soil-oundationsuperstructure interaction (SSI) applying SSI elements evaluated by a method proposed by the author and a vibratory experiment conducted ater the construction o oundation. The method to evaluate SSI elements rom soil consists o 4 steps : an equivalent linearlization o soil against a design earthquake, ormulation o orce-displacement relationship among nodal points or the all based on the Thin Layer method (TLM), condensation o the relationship to match ith a beam model o the oundation, and an evaluation o SSI elements o a Winkler type derived rom LSM. From the experiment it is ound that the all oundation has a high rigidity and the ave dissipation to soil increases ith requency. The simulation analyses or the experimental results veriy the validity o the method to evaluate SSI elements. INTRODUCTION A 54-story reinorced concrete building is no under construction at Tokyo bay area here deep soil deposits exist. The building is supported by a large size all oundation ith 46.5-meter square, 53-meter depth and 1.8-meter thickness. For the seismic design o this building, the seismic saety had been veriied by earthquake response analyses considering the eect o a soil-oundation-superstructure interaction (SSI). This paper presents on response behavior o the all oundation during a design earthquake ground motion applying a SSI model based on the Thin Layer method proposed by the author. a) Head o Structural Division, Technical Research Institute, Toda Corporation, masanobu.todo@toda.co.jp 5-34, Akasaka-8, Minato-ku, Tokyo, Japan 1
Just ater the construction o oundation, a vibratory experiment had been conducted by using a vibration generator. The experimental results on amplitudes and impedances are discussed in comparison ith the results o a simulation analysis. THE OBJECTIVE BUILDING AND FOUNDATION As shon in Fig.1, the objective is a 54-story reinorced concrete residence building o 174 meters high and the plan o 46.5 meters square ith inner void space. This building is constructed by members composed o high strength material o concrete o 1MN/mm and steel bar o 685MN/mm and others and applies a steel damper column o lo yielding stress o 5MN/mm or response control to earthquake excitations. The oundation is constructed by a reinorced concrete all o boxed type and piles shon in Fig. and supported by the depth o 53 meters rom ground surace. Figure 3 shos the proile o surrounding soil deposit hich has deep sot soil layers because the building is located at Tokyo bay area. RC rame ith steel damper all oundation Figure 1. Skeleton vie o the objective building 46.5m 9m 46.5m Basement Vs Vp( 1) Vs, Vp(m/ s) 3 6-46.5m 1.8m 44m 1.8m Depth (m) -4-6 -8 Figure. (a) Plan and (b) section o all and piles oundation - 1 Figure 3. Soil proile SEISMIC DESIGN In the seismic design, various earthquake response analyses against a e input motions had been perormed : 1) a push-over analysis o the super-structure to evaluate the
relationship beteen story shear orce and story drit, ) response analyses o the superstructure based on a 3-dimensional rame model including a vertical input excitation, 3) response analyses o soil-all oundationsuperstructure interaction system, and 4) a dynamic analysis due to an input excitation ith phase dierence i.e. a traveling seismic ave. This paper Super Structure presents the response analysis o a soil-all Steel Damper oundation-superstructure interaction system (SSI) o Column the analyses described above. Figure 4 is the analytical model or the SSI hich is composed o the super-structure ith a main structure and a steel damper column, the all oundation and supporting soil elements. The superstructure are modeled into an equivalent beam ith lexural-shear deormation converted rom the pushover analysis o the rame hich has a nonlinear restoring orce characteristics on the basis o structural experiments. Wall Foundation EI,GA r a b Figure 4. Model or response analyses o soil-all oundationsuperstructure system A METHOD FOR MODELING OF SOIL AND WALL FOUNDATION INTERACTION SYSTEM In order to perorm earthquake response analyses o soil-all oundation-superstructure interaction (SSI) system, the soil and all oundation are modeled into a kind o the beam on continuous springs as the Winkler type. The all oundation is modeled into a beam ith lexural-shear deormation using FEM explained later. The modeling makes possible to perorm nonlinear response analyses o a SSI system. The analytical steps to convert a soil medium into springs connecting ith a beam o all oundation are as ollos and the schematic vie is illustrated in Fig.5. Step.1 : To perorm an earthquake response analysis o a soil deposit only considering strain dependency o soil i.e. nonlinearity and obtain the equivalent soil rigidity and hysteresis damping o soil due to equivalent linearlization. 3
Nodal points ithin soil CL CL Wall a CL Rigid 一 plane EI GA b P U (b) Step.3 Condensation by (c) Step.4.Winkler (a) Step. Relationship o t t in soil by 3D-TLM rigid plane assumption type modeling Figure 5. Procedure to evaluate spring and dashpot constants o interaction elements represented by Winkler type based on the 3D-Thin Layer method or nonlinear response analyses r Step. : To evaluate the relationship at a requency excited by the unction o beteen orces and displacements among any nodal points ithin the equivalent soil medium shon in Fig.5(a) here the objective all oundation is settled, by applying 3- dimensional Thin Layer method called as TLM (Tajimi 198). in hich P t and { } [ ]{ P } t t t i t e ω U = (1) U t are nodal orces and displacements ith the reedoms o nodal points multiplied by 3D, respectively and [ ] is a ull lexibility matrix in complex. t Step.3 : To make the condensation o the relationship o Eq.(1) in step. into the reedoms o translation and rotation in x-y-z o planes hich are assumed to move as rigidbody shon in Fig.5(b) and locate at the same depth ith the points discretizing all oundation. Using the displacements, displacements, becomes as ollos. U can be expressed as { } [ A]{ } t U r representing the movement o plane, the U =, thereore the condensed relationship t U r T { P } [ ]{ U }, [ ] = [ A] [ ] [ A] r = () s r s t 1 4
here [ s ] is a ull stiness matrix in complex. The Eq.() might be a rigorous expression based on the TLM. Step.4 : To evaluate spring constants (includes dashpots) o the Winkler type as shon in Fig.5 (c). We assume that the springs in horizontal response ith rotation consist o a, b and r or axial, shear and rotational delection o soil, respectively and those are vertically in vertical response. Using the springs, the relationship beteen orces and displacements is expressed as in hich the stiness matrix is given by [ { } [ ]{ U } P = (3) r s s a b + r r ] = [ ] + [ ] [ ] (4) here [ a ] and [ r ] are diagonal matrixes in complex and [ b ] is a tri-diagonal one ithout damping. The spring constants o the Winkler type are estimated rom [ s ] o Eq.() in the olloing. Let us consider the condition that a all oundation, the dynamic stiness o hich is represented by [ ], is subjected by external orces, { } F and soil responses in ree ield, { U s }. Under the condition, the equation o motion o the all oundation, { } expressed as ollos. ({U } {U }) {F } s = in hich [ s ] indicates [ s ] in Eq.() or [ s ] to { F } T = { Q,,,} o all top orce and { } U is [ ]{U } + [ ] s (5) o Eq.(4). The reaction orces o soil due U are ormulated by s here { } Q { F } and { s } s s { R sq } = [ ]{U Q }, {R sg } = [ ]({U G} {Us}) (6) U and { U } are the solutions due to { F } and { U } G U are given, the solutions o { U } and { } Q G s, respectively. When U are obtained using the 5
rigorous stiness [ s ] in Eq.(), that are converted into { R sq} and { sg } e consider on { R sq} and { R sg } expressed by using the unkon stiness o [ s ] and substituting { U Q } and { U } into Eq.(6). The square errors beteen { R } and { } G L=Q and G, can be expressed as ollos. R by Eq.(6). Here in Eq.(4) sl R, sl ε = L L= Q,G T ({R } {R }) ({R } {R }) sl sl sl sl (7) in hich L is eighting actors and the superscript o () indicates the conjugate complex values. The Eq.(7) leads to a least square method (LSM) or the unknon spring and dashpot constants o a and b as: ε ε min, = in any x i o ai and bi (8) x i Consequently, the unknons o a and b in Fig.5(c) can be estimated. Here e obtain r or rotation rom reaction moment in Eq.() due to independently given rotation beore the procedure described above. The method to evaluate spring constants rom TLM solutions described above can be applied or pile oundations as ell (Tohdo ). AN EARTHQUAE RESPONSE ANALYSIS An earthquake ground motion is synthesized or the veriication o seismic perormance o the objective structure shon in Fig.1. The design earthquake is assumed to be a anto earthquake shon in Fig.6 hich has the seismic moment o 7. 6 1 dyne cm and the ault plane o 13km 7km. The procedure to estimate earthquake ground motions is a semiempirical ave synthesis method using observed accelerograms by a small event (Tohdo et al. 199). Figure 7 is the acceleration ave orms o horizontal and vertical earthquake ground motions at an engineering bed-rock at the site. 7 6
Delection (µm / MN) 1 3-1 δ δ s δ t Depth (m) - -3 In order to model the all oundation shon in Fig. into a beam, an analysis by FEM is carried out, the condition o hich is taking the pure all oundation o boxed-type ithout soil and a support ixed at bottom as shon in Fig.8(a). The total displacement distribution, δ t due to a top orce is shon by a solid line in Fig.8(b) and the shear-like displacement, δ s by a dashed line hich is obtained under the condition o eb-all only and restriction vertically at top. The shear and lexural rigidities o the modelled beam are determined rom δ s and δ = δ t δ s ix support Figure 8. (a) Mesh and (b) delection o FEM analysis o the pure all oundation to model into a beam ith lexure-shear deormation -4-5, respectively. It is noted here that pile oundations shon in Fig. are 4 Horizontal Comp. (33 gals, 38cm/ s) Gal Site Fault Plane or anto Earthquake -4 4 Gal Vertical Comp. (187gals, 17cm/ s) M o 7.6 1 7 dyne cm L W 13 km 7km dip angke 34 degree Figure 6. Desgin earthquake - 4 4 6 8 1 Time (sec.) Figure 7. Accelerations at engneering bed-rock or design earthquake synthesized by a ault model 7
ignored in the SSI analysis because e ind the act derived rom the FEM analysis o a allpile-soil model that piles share less than 1% o stresses against a top orce. a /( Gs H ) 1 b /( Gs H ) 5 1-1 -1 Depth (m) - -3 Depht (m) - -3-4 -5 Real Imag -4-5 Real (a) a or axial spring (b) b or shear spring Figure 9. Spring constants or interaction elements connecting ith all oundation against design earthquake ground motions shon in Fig.7 The step.1 analysis o soil shon in Fig.3 against the base-rock input o Fig.7 is carried out applying a modiied R-O model or restoring orce characteristics o soil. The relative displacement and acceleration are shon in Fig.1. The spring constants o SSI elements due to equivalent linearlized soil are evaluated on the basis o the method explained in step. through step.4. In the step.4, the conditions are assumed : 1) { U s } shon in Fig.1(a) and some top Q o { F } Q and G as to be Q { R sq} G { R sg } max max b and the imaginary part o, and ) eighting actors o = by Eq.(6). The real part o o a and a are analyzed at the requency o almost, i.e. statically, and the 1st requency o SSI system, respectively. The results are shon in Fig.9, hich are normalized by shear rigidity o soil and element thickness in discretization. The real parts are spring constants and the imaginary parts are converted into dashpots. 8
At irst, the pure all oundation is subjected to earthquake ground motions due to the input in Fig.7 hich in ree ield are the time histories o response acceleration at base-rock, and velocity and displacement o surace soil ground rom top to bottom. Here the vertical response analysis o soil is carried out by assuming P-ave traveling in surace soil (Tohdo et al. 1998). The maximum response displacements and accelerations o all vary little at depth as shon in Fig.1. Figure 11(a) is maximum shear by horizontal input and axial stress by vertical input hich are normalized by eight o all itsel summed rom top to the depth. The shear stresses are strongly aected by the dierence o response displacement beteen all and soil as shon in Fig.1(a). Figure 11(b) shos response spectra by the response acceleration at all top to be a oundation input motion, and the ree ield motion at ground surace. The eect o high rigidity o all oundation appears that the oundation input motions at the period less than undamental period o soil ground become smaller than ree ield motions. Displacement (cm) 4 6 8 1 Acceleration (gal) 1 3 4-1 -1 Depth (m) - -3-4 -5 Wall Soil Depth (m) - -3-4 -5 Wall Soil Figure 1. (a) Maximum displacements and (b) accelerations o all oundation and soil due to response analyses against horizontal earthquake ground motions shon in Fig.7 9
Shear and axial stress coeicients.5 1 1.5.5 1 Hor. at WF Hor. at GL UD at WF UD at GL h=5% Depth (m) -1 - -3 psv(cm/s) 1 1-4 -5 shear axial stress 1.1.1 1 1 Period (sec.) Figure 11. (a) Maximum shear and axial stresses o all oundation normalized by all eight, and (b) response spectra obtained by accelerations at the top o all and ree ield surace, due to horizontal and vertical earthquake ground motions shon in Fig.7 The earthquake response analysis o the soil-all oundation-superstructure interaction system is perormed. The results o maximum story drit are shon in Fig.1 in comparison ith the results by the input o ree ield surace overall SSI analysis Fixed model by GL input acceleration. It is recognized in this analysis that the response o the structure becomes airly small due to the SSI eect, that is, the structure has such seismic perormance against this design earthquake. VIBRATORY EXPERIMENT An investigation by microtremor observation in ree ield at the site had been carried out to clariy the elastic ave velocity proile o the soil ground. The spectral ratios o horizontal components to vertical one o microtremors (H/V.5.1 Story drit angle(rad.) Figure 1. Maximum story drit angles o super-structure due to horizontal earthquake ground motion shon in Fig.7 spectrum) are shon in Fig.13., hich have the 1
peak amplitude at requency o about.9hz and the lo amplitude around Hz. Using the soil proile obtained rom P-S loggings shon in Fig.3, an analysis derived rom the Rayleigh surace ave theory is done and its H/V spectrum due to the undamental mode is shon by a dashed line in Fig.13. Comparing the spectrum by the theory ith one by observation, both o the spectrum have similar variation in terms o requency, that is, the soil proile shon in Fig.3 is accurate. A vibratory experiment had been conducted just ater construction o the oundation by using a vibration generator ith unbalanced masses shon in Photo 1 hich have the maximum orce o.3mn and is settled at.the 1st loor. The accelerogragh sensors o horizontal and vertical components are arranged on the all. Since the order o observed vibration is 1 micron meter, the sensitive vibration o all oundation is extracted by analyzing the correlation beteen the signal o excitation and vibratory measurement. 6 Microtremors Amplitude 4 Rayleigh ave theory 1 3 4 Figure 13. H/V spectrum due to microtremors and Rayleigh ave theory based on the soil proile shon in Fig.3 Photo 1. Vibration generator The circle marks in Fig.14 sho the amplitudes and phase dierences taken out or horizontal translation and Figure 15 is the rotational ones obtained rom vertical measurement on the eb o all. These amplitudes are converted or excitation orce as to be 1MN. It is ound in these results that the horizontal and rotational amplitudes are so small and do not have evident resonance, it seems the characteristics o all oundation ith high rigidity, and the phase dierences increase gradually as requency becomes large, that is, the ave dissipation rom all to surrounding soil increases. 11
A simulation analysis against experimental results is conducted on the basis o the method described in the above section. Applying the condensed stiness in Eq.() based on Amplitude 15 1 5 1 3 4 135 9 45-45 1 3 4 Figure 14. (a) Amplitude and (b) phase dierence o horizontal displacement subjected to a lateral orce at the top o all Phase di. (Degree) Amplitude ( 1^-6rad/MN) 15 1 5 1 3 4 135 9 45-45 1 3 4 Figure 15. (a) Amplitude and (b) phase dierence o rotational displacement subjected to a lateral orce at the top o all Phase di. (Degree) the TLM, the movement o all oundation can be ritten by ( ] [ ]{U ) } = {F } [ s + (9) From Eq.(9), the impedance unction beteen orces and displacements at the top o the all oundation is obtained as ollos. P = M HH RH HR RR U Θ (1) here =. Thereore the displacements due to a orce, P o the generator are HR expressed by RH 1
U = Θ HH RH HR RR 1 P (11) The solid lines in Figs.14 and 15 are the simulated results by Eq.(11) hich agree ell ith the observed results. Next, e discuss on the impedance unctions derived rom the observed data. It is noted here that the unknon 3-components o the impedance can not be obtained directly rom observed data, because the excitation by generator is horizontal only, i.e. the equations are composed o -unknons only ith shortage. So e assume the relationship o Eq.(1) hich is obtained using the analytical impedance o Eq.(1). HR r = (1) Using this relation, the diagonal terms o impedance can be obtained by HH RR Real(HH) (MN/mm) 15 1 75 5 5-5 1 3 4 Imag.(HH) (MN/mm) 15 1 75 5 5-5 1 3 4 Figure 16. (a) Real and (b) imaginary parts o horizontal translation impedance, HH Real(RR) ( 1^1MN mm/rad) 1 8 6 4-1 3 4 Imag.(RR) ( 1^1MN mm/rad) 1 8 6 4-1 3 4 Figure 17. (a) Real and (b) imaginary parts o rotational impedance, RR 13
HH P 1 =, U 1 r RR r 1 r PU = (13) Θ in hich P is a excited orce, and U and Θ are observed displacements. The resulted impedances are shon by circles in Figs.16 and 17 in comparison ith the analytical impedance. Although RR horizontal excitation, both o has rather dierences because o the indirect part due to HH have ell agreement. From these comparisons beteen observed data by experiments and the analytical results, it is recognized that the method applied here on the basis o TLM is appropriate or SSI analyses in seismic design. CONCLUSIONS The study on the dynamic behavior o a large size all oundation supporting a 54-story building as presented, hich considers the eect o a soil-oundation-superstructure interaction (SSI). The contents are summarized as ollos. From an earthquake response analysis o the SSI system in the seismic design, it is recognized that the structure is strongly inluenced by SSI eects such that the response displacements o the all oundation are remarkable smaller than those o soil ground in ree ield, and a oundation input motion into the super-structure is suppressed, consequently the response o the super-structure becomes small. A vibratory experiment or the all oundation has made clear the dynamic characteristics such that horizontal and rotational amplitudes at the top o all are so small and do not have evident resonance and the phase dierences increase gradually ith requency, that is, the ave dissipation rom all to surrounding soil increases. The results are simulated ell by the method hich as applied or the earthquake response analysis. This might sho that the method applied or SSI analyses in seismic design is appropriate. ACNOWLEDGEMENT The author ould like to thank Dr.Izumi o chie structural designer o this building or collaboration in the seismic design and my colleagues o the Technical Research Institute or cooperation o the experiment. 14
REFERENCES Tajimi H., 198, A contribution to theoretical prediction o dynamic stiness o surace oundations, Proceedings o the 7th World Conerence on Earthquake Engineering, pp.15-11 Tohdo, M.,, Study on earthquake response behavior o all oundation, Proceedings o the 11th Japan Earthquake Engineering Symposium, 33(CD ROM) (in Japanese) Tohdo M., Chiba O., Fukuzaa R., 199, Estimation o Earthqauke ground motions during large earthquakes by superposing the element aves due to small events ith stochastic parameters, Journal o Structural Engineering, Vol.B, AIJ, pp.85-9 (in Japanese) Tohdo M., Hatori, T., Chiba O., Takahashi., obayashi Y., 1998, A role o sedimentary layers or the ave propagation o vertical seismic motions, The eects o Surace Geology on Seismic Motion, Balkema, pp.371-378 15