dynamic response of block foundations

8/22/2019 Dynamic Response of Block Foundations

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!!! roceedings: Third International Conference on Case Histories in Geotechnical Engineering, St. Louis, Missouri,June 1-4, 1993, Paper No. 4.08 .==Dynamic Response of Block Foundations

Vijay K. PuriAssociate Professor, Department of Civil Engineering andMechanics, Southern Illinois University, Carbondale, Illinois

Braja M. DasAssociate Vice President, Academic Affairs and Research,Southern Illinois University, Carbondale, Illinois

SYNOPSIS This paper presents the results of comparison of the computed and observed response of twoblock foundations made of concrete. The tes t blocks measuring 3.0m x 1.5m x 0.7m and l.Sm x 0.7Sm x0.70m were cast on level ground. The blocks were excited into ver t ical vibrations using a speedcontrolled mechanical oscil lator . The amplitudes of vibration at different frequencies ofexcitat ion were measured in each case using acceleration transducers mounted on appropriate faces ofthe block. Dynamic shear modulus at th is s i te was also determined b conducting in-si tu testsnamely the wave propagation tes t , the cyclic plate load tes t , and the standard penetration tests.From this data the dynamic shear modulus versus shear strain plot was obtained. The ~ a t u r a l .frequencies and the vibration amplitudes of the tes t blocks were then calculated by th e l ~ n e a rspring method, ( i i) the elastic half space method. A comparison was then made of the o b s e ~ e d andcomputed natural frequencies and the vibrati?n a m p ~ i t u d ~ s of th e blocks. The r e s ~ l t s . o f t ~ 1 scomparison showed that for the cases of vert1cal v ~ b r a t ~ o n s , the natural frequenc1es 1n th1s casecould be reasonably predicted b either of the methods used. The calculated and observed .amplitudes, however, showed a wide variation. The detai ls of tests performed and th e a n a l y s ~ s arediscussed in this paper.INTRODUCTIONRigid concrete blocks are commonly used asfoundations for supporting reciprocatingmachines. In order to ensure long termsatisfactory performance of a foundationsupporting a machine, i ts design should meetthe cr i te r ia for stat ic and dynamic s tabi l i ty .The cr i te r ia for stat ic design are the same asfor an ordinary foundation namely, no shearfailure in soil , and no excessive settlement ofthe footing. The cr i te r ia for dynamics tabi l i ty requires that the natural frequencyof the foundation soi l system should be faraway from the operating frequency of themachine, and the amplitude of vibrat ion undernormal operating conditions should not exceedthe specified l imits. The vibrations produceddue to operation of the machine should not beharmful to th e people working in the vicini tyof the machine, and to the adjacent s t ructures .The design of the machine foundations i sgenerally made either by the l inear springmethod (Barkan, 1962) or by th e elastic halfspace method (Richart, Hall and Woods, 1970;Prakash and Puri, 1988; Das, 1992). Veryl i t t l e data is however available on thecalculated response of a machine foundation andi t s actual performance. In fact no attentionis paid to the measurement of vibrationamplitudes unti l some problem develops.This paper presents the results of a comparisonof the computed and observed response of twoblock foundations made of concrete. The t es tblocks were excited into vertical vibrationsand the i r natural frequencies and amplitudeswere measured. The pertinent soi l propertieswere determined b conducting in-situ tes ts andoscillatory shear tests in the laboratory. Theresponse of the two tes t blocks was then

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computed by the (i) l inear weightless springmethod, and (ii) elast ic half space method. Acomparison was made of th e observed andpredicted response of the test blocks. Thedetai ls of the tes ts conducted, data obtained,and comparison of the observed and computedresponse are discussed here.

TESTS CONDUCTED

Block Vibration Tests:The block vibration tests were conducted onr igid concrete blocks. The sizes of th e testblocks were 1.5m x 0.7Sm x 0.70m and 3.0m x1.5m x 0.7m. The blocks were cast on levelground. Vertical vibration tests wereconducted on each of these two blocks. Thesetes ts were conducted by exciting the block inth e ver t ical direction with the help of amechanical oscillator. A speed controlled D.C.motor was used to operate the osci l la tor . Theoscillator-motor assembly was mounted centrallyon the to p of the test block, and rigidlyattached to i t . The block was set intovert ical vibrations by operating the mechanicaloscil lator . The vibrations of the block weremeasured with an acceleration transducermounted on the to p of the block and oriented soas to sense vertical vibrat ions. The outputfrom the accelerometers was amplified andrecorded. A schematic sketch of the tes t setup is shown in Figure 1. Records of vibrationwere obtained for different frequencies ofexcitation. The tests were repeated bychanging '9 ' th e angle of set t ing of theeccentric masses. From the recorded data, thefrequency and the corresponding amplitudes weredetermined. The data was then plotted in the


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0.04

Fig.2

Motor oscillatorassembly

Test BlockAccelerationtransducers 1.5m

1Fig.1 Test setup For Block VibrationTests.

Eccentricity

180

Frequency HzAmplitude versus Frequency Plotsfor vertical Vibration Test on1.5 m x o.75m x0.7 m High Block.

form of amplitude-frequency plots . Typical.amplitude versus frequency plots are shown 1nFigures 2 and 3.Tests for Determination of Dynamic SoilPropertiesThe dynamic properties of the soi l used in th eanalysis of machine foundation may be . .

d e t e ~ i n e d by a number of laboratory or 1n-s1tutes ts . These properties are affected b anumber of factors which should be accounted forwhen selecting th e design values. The mostimportant parameters which affect ~ h e s e . .properties are (1) the mean effect1ve conf1n1ng

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8 Eccentricity

26 30 34 38 42 4.4Frequency HzFig. 3 Amplitude versus Frequency Plotsfor vert ical Vibration Test on3.0 m x 1.5m x0.7 m High Block.

pressure, (2) the shear s t ra in amplitude, and(3 density in the soi l . A good discussion onthese corrections has been presented by Prakashand Puri (1977), Nandakumaran et a l (1977),Prakash and Puri (1981) and Indian StandardCode (IS 5249 - 1977).In-situ Soil investigations consisted of (1)wave propagation tests, (2) cyclic plate loadtes ts and (3) standard penetrat ion tes ts . Fromthe cyclic plate load t e s t data , values ofdynamic shear modulus "G" were computed. Fromthe uncorrected standard penetration (N) valuesshear wave velocity V8 a t a par t icular depthwas d e t e ~ i n e d from equation (1) Imai (1977)and dynamic shear modulus "G" was computed fromequation (2)

Vs = 91.0 NJ337G = V82 x p

(1 )(2 )

in which p=y/g =mass density of soi l . Valuesof "G" from different tes ts were corrected for(1) effect ive confinement in each case an dcomputed for an effect ive overburden pressureof 100kN/m2 using equation (3).

in which G1 = shear modulus at an effect iveoverburden pressure of Gv1and G2 = shear modulus at an effectiveoverburden pressure of


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Testo Wave PropagationC standard PenetrationA cyclic Plate Load0 oscillatory Shear

Shear Strain y 8Fig.4 Dynamic Shear Modulus versus Shearstrain

modulus 'G ' versus shear strain 'Ye' wasobtained as shown in Figure 4.

PREDICTED RESPONSE OF THE TEST BLOCKSThe methods commonly used for the analysis anddesign of foundations for machines are (1 )Barkan's approach and (2) elast ic hal f spaceapproach. In the Barkan's approach or thel inear spring method (Barkan, 1962) thefoundation soi l system is represented as aspring-mass system. The spring s t i f fness dueto the soi l and mass of the foundation andsupported equipment only are considered andiner t ia of the soi l and damping are neglected.In the elast ic half space approach thevibrating footing is treated as resting on thesurface of an elas t ic , semi-infinite,homogenous, isotropic half space (Richart,1962). The elast ici ty of the soi l an d theenergy carried into the half space by wavestravelling away from the vibrating footing(geometric damping) are thus accounted for andthe response of such a system may be predictedusing a mass-spring-dashpot model (Richart andWhitman (1967) and Richart, Hall and Woods(1970)) .The dynamic response of the foundation wascomputed using both the above methods ofanalysis . The values of dynamic shear moduluswere selected depending on th e effectiveoverburden pressure and th e shear s t ra ininduced in the soi l by th e vibrating block.Effective overburden pressure a t a depth equalto one half of the width of tes t block was usedand was obtained from equation (4) .Ov = Ovl + Ov2 (4)

in which Ov1 Overburden due to weight of soi lVert ical stress intensity at adepth equal to ~ width du e tosuperimposed load of machine andfoundation and may be computedusing Boussinesq theory.

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(a) Barkan's MethodNatural frequency of ver t ica l vibrationsCOnz is given by

- ~ u A - ~J)nz - --- - ---m m (5)and amplitude of vert ical vibrat ion A. isgiven by

A . = - ~ " ' " " ~ " " - - ~m ( (J)nz2 - ro2)in which,

m = mass of the foundation and machinek. stiffness of vertical soi l springro operating frequency, andCu the coefficient of elast ic uniformcompression and i s given by equation(7 ) .

(6 )

Cu = 1.13 X 2 G ~ 1 +V) 1(1 - v > F. . . . . . . . (7 )in which v = Poissons rat io (assumed 0.337) .The computed values of undamped naturalfrequencies and undamped amplitudes ofvibration as obtained from the l inear springmethod, for the two tes t blocks, are given inTables 1 and 2 (b) Elastic Half Space MethodThe natural frequency of the foundation invert ical vibrations i s computed by equation(5) . The soil spring is computed as follows(Prakash and Puri, 1988) and Richart, Hall andWoods, 1970):

Kz = 4Gro1-Vin which, r 0 = Equivalent radius of thefoundation and i s obtained as follows:For vert ical vibrations or sliding

ro = ~

(8)

(9)The damped amplitude of ver t ica l vibrations isgiven by

Where,

an dDamping rat io = 0.425~ -

B. = Modified mass rat io = (1-vlm4pro3

(10)

(11)

(12)The computed values of undamped naturalfrequencies and damped amplitudes of vibrationobtained from th e elast ic half space method forthe two tes t blocks are given in Tables 1 and2.


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Table 1 comparison of Observed and Computed Response of l.Sm x 0.75m x 0.70m Block in Vert icalV'b t'ra ~ o n sObserved Data Computed Data

Coeff ic ient Linear Spring Elas t i c HalfAngle Amplitude Shear Shear Method Space Analogof Natural Strain Modulus of Methodrequency Az G kN/m2 Ela.sticccentr- Yei c i ty Hz mm Uniform Natural Undamped Natural Dampede Compression Freq- Ampli- Freq- Ampli-Cu kN/m3 uency tude uency tudeHz Az Hz Azmm mm

25 38.5 0.031 4.13 X 35,500 266,600 44.8 0.36 41.4 0.127lo-s50 37.5 0.069 9.2 X 29,000 288,800 40.5 1. 067 37.1 0.2710-s75 37.0 0.0975 1 . 3 x 26,000 196,000 38.5 4.94 35.2 0.40610'4

125 36.7 0.182 2.43 X 22,100 166,500 35.3 3.23 33.1 0.53110'4180 35.0 0.240 3.3 X 18,100 136,400 31.0 1.38 29.3 0. 72010 '4

Table 2 Comparison of Observed and Computed Response of 3.0m x 1.5m x 0.70m Block in Vert icalVibrationsObserved Data

Angle Shear Shearof Natural Amplitude Strain ModulusFrequency Az G kN/m2ccentr- Hz 'Yei c i ty mma

25 36.0 0.006 4 X 70,00010' 650 34.5 0.012 8 X 67,50010 675 37.0 0.018 1 . 2 x 66,000lo-s

100 37.0 0.024 1 . 6 x 65,00010-5125 35.0 0.030 2.0 X 61,00010-5150 34.5 0.036 2.4 X 60,000lo-s180 33.5 0.053 3.5 X 56,00010-7

CONCLUSIONS ANQ DISCUSSION1. I t i s observed from Tables 1 and 2, thatthe na tura l frequencies of the two t e s t blockscalculated by using the l i nea r spring methodan d the e las t i c half space method are generallyof the same order. Also these calculated

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Computed DataCoeff ic ient Linear Spring Elast ic Halfof Method Space AnalogElast ic MethodUniform Natural Undamped Natural DampedCompression Freq- Ampli- Freq- Ampli-Cu kN/m3 uency tude uency tudeHz Az Hz Az

mm mm222,615 42.0 0.0954 42.0 0.0261214,660 41.2 0.157 41.3 0.0478209,900 40.8 0.449 40.7 0.0852206,700 40.5 0.616 40.4 0.109193,900 39.1 0.566 39.2 0.119190,800 38.8 0.578 38.8 0.127178,100 37.5 0.63 37.5 0.133

natural frequencies are in reasonable agreementwith the observed natural frequencies. Thecalculated undamped natu ra l frequencies aregeneral ly within 20% of the experimentallyobserved na tura l frequencies.


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2. The undamped amplitudes of ver t ica lvibrat ion calculated py using the l inear springmethod are much higher than the observedamplitudes. This i s to be expected sincedamping has been omitted in this method.3. The damped vibration amplitudes asobtainedfrom the elas t ic half space method aresmaller than those calculated by the l inearspring method. However, the amplitudescalculated by the elas t ic half space methodalso do not show any reasonable agreement withthe observed amplitudes and are la rger than theobserved amplitudes.

REFERENCESBarkan, D.D. (1962), "Dynamics of Bases andFoundations, McGraw Hil l Book Company.Das, B.M. (1992), "Principles of SoilDynamics, PWS Kent, Boston, MA.Imai T. (1977), velocit ies of p- and s- Wavesin ' sub-surface Layers of Ground in J a p a n ~ ,Proc IX: International Conference on S o ~ lMechanics and Foundation Engineering, Vol. 2,

pp 257-260.IS : 5249-1977. Code of Practic7 for .Determination of In-si tu D y n ~ c P r o p e r t ~ e sof Soil . Indian Standards Inst i tu te , NewDelhi, Firs t Revision.Nandakumaran, P. , Puri, V. K. , Joshi , V. H. an dMukerjee, s. (1977), "Investigations forEvaluation of Dynamic Shear Modulus ofSoils" , Bulle t in, Indian Society of Earthquake Technology, Vol.14, No.2, June, PP39-54.

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Prakash, s . and Puri, V.K. ( 1 9 7 7 ) ~ Cri t ica lEvaluation of IS 5249-1969, I n d ~ a n StandardCode of Practice for In-si tu Dynami?Properties of Soil, Indian G e o t e c h n ~ c a lJournal, Vol. VIII , No. 1, January, 43-56.Prakash, s . and Puri, V.K. (1981), "DynamicProperties of Soils from In-si tu .Tests ,Proc: ASCE, journal of G e o t e c h n ~ c a l Engr.Div., Vol. 107, No. GT7, July, PP 943-964.Prakash, s . and Puri, V.K. (1981),. "Observedan d Predicted Response of a Mach1neFoundation, Proc X: InternationalConference on SM & FE Stockholm, Vol. 3,pp 209-273.Prakash s. and Puri, V.K. (1988), "Foundationsfor M ~ c h i n e s Analysis and Design, Wileyser ies in Geotechnical Engineering, JohnWiley, NY.Richart, F.E. (1962), "Foundation Vibrations,Transactions: ASCE, Vol. 127, Part 1, PP863-898.Richart, F.E., Hall, J.R. and Woods, R.D.(1970), "Vibrations of Soils and

Foundations, Prentice Hall, Inc. , NewYork, NY.Richart, F.E. and Whitman, R.V. (1967a),"Design Procedures for Dynamically LoadedFoundations , Journal SMF, Proc: ASCE,Vol. 93, SM6, Nov., PP 168-193.Richart, F.E. and W h i ~ n , _R.v. ( 1 9 6 7 ~ ) ,"Comparison of Foot1ng V 1 b r a t ~ o n s w ~ t hTheory, Journal SMF, Proc: ASCE,Vol. 93, NOSM6, Nov., pp 143-167.

dynamic response of block foundations

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