ML18192A851

a Comparison of Experimental and Theoretical Investigations of Embedment Effects on Seismic Response

ML18192A851
Person / Time
Site:	Palo Verde
Issue date:	09/30/1975
From:	Hadjian A, Howard G, Casey Smith - No Known Affiliation
To:	Office of Nuclear Reactor Regulation
References
Download: ML18192A851 (32)

Text

A. H. Hadjian A COMPARISON OF EXPERIMENTAL AND THEORETICAL INVESTIGATIONS OF EMBEDMENT EFFECTS ON SEISMIC RESPONSE Prepared for 3rd INTERNATIONAL CONFERENCE ON "Structural Mechanics in Reactor Technology" September 1975 by A. H. Hadjian, G. E. Howard, C. B. Smith I

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l. Introduction Dnc oi thc critical areas in the seismic design of nuclear power plant structures is thc estimation,of soil-'foundation interaction effects, parti-cularly whcr'c massive structures arc embcddcd. At thc present time this is qn area where improvements in thc .state-of-thc-art arc required [1]. Rcccnt work indicates that" errors can result if care is not paid to both thc para-meters and methods used in analysis [2]". To gain insight into this problem, I

expcrimcntal studies and analyses werc undertaken to study the cffcct of var-ious parameters on the dynamic rcspons'c of embedded structures [3,4].

'The first phase of the project involved dynamic testing of rigid model (4" - 12" high) structures. Thc models were founded on several types of soil under varying conditions of embedmcnt and horizontal and vertical shaking.

Shake table tests')I'ere conducted on families of geometric shapes to evaluate possible geometric, soil medium, and cmbedmcnt effects, as well as thc effects of combined horizontal-vertical accelerations upon model resonance.

In addition to resonant frequencies and damping values, overturning (or "brcak loose" ) from the supporting soil was investigated. Free field har.-

monic excitation tests of a selected model were conducted, at two different sites, to examine its response and the influcncc.of embedmcnt, soil, and amplitude upon the- modal frcquencics and damping.

The objectives of the seco'nd phase of the project were to perform field tests and additional studies on embedded"structures. In this phase, thc size of the model was increased by a factor of ten, from typically six incite. high in thc laboratory tests to seventy two inches high in the field tests.

The field test model was Eabricatcd from a concrete pipe 6 ft (1.8m) long and 42.S" (l.lm) outside diameter. A concrete plug was poured in thc bottom of the pipe to simulate the mass distribution of a concrete containment struc ture. A steel support structure was attached to the top of. the pipe for connecting an eccentric t))ass shaker.. The shaker was rigidly attached to the t'op of the cylinder. Accelcrometcrs were attached'o the structure and placed on the soil .at"appropriate locations. This assembly )Ias then embedded at different depths at a field site where the soil properties have been docu-mented by extensive testing. The objective of the project was'o establish the effect of cmbedmcnt under varying test conditions. The test results )I'erc thon compared with theoretical values obtained by various calculational pro-cedures.

2. Tost Methods The theory used tci11 first bc dcvclopcd for a it onc-degree-of-freedom'ystem.

l)'ith minor modifications, can be extended to multi-degree-of-frccdom systems. The differential- equation wi)ich defines thc dynamic re-sponse of this system is:

MR[t] + Cx[t] + Kx[t] - F[t] (1) where x[t] is the displacement of thc system from its equilibrium position, hl is the mass of the system Inc!roc)1<Inc fi<." )! ping ~ pirn<c s< I' cryo

0 t

l I

'. fl. Hadj ian C

l w>>.; i< r is thc coiffici'cnt"of'"viscous dampihg.

<<;t; > < 'i<>. <<.>'it> ~.".'> a>a)

K2/5 K is thc spring constant or stiffness, and Fft) is thc input or driving force.

Equation [1) can be transformed to thc frequency domain and written as a transfer function relating thc response of the system and input motion as de-scribed below:

~o r (2)

G [m]

x 1 - r z]' (2gr )z where 9 is C

the damping ratio, or fraction of critical damping,

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C c

= 2hf<o n being thc critical value of damping,"

n K/M is. the natural 'frcqucncy of the system, rn eo/u n " is the ratio of frequcncics, and x 1 = a reference acceleration which is proportional to thc applied force.

The transfer function given by equation {2) describes a resonant system.

=is obvious from a graph of. this function that the shape of. thc curve" is de-

't tcrmincd by the cigcnparameters {i.e., by the damping and natural frcqucncy) and that the higher values oE damping decrease the maximum response and cause a shift of the frequency at which thc maximum response occurs. Experi-

,e mental data obtained from tests could be graphed in thc same way and thc dyn-amic parameters could be evaluated Erom the data. F For a single-degree-of-freedom system with small damping values, the damping ratio is determined from thc width of the peak response as follows:

g <>

(3)

"n where->>>~ is'he bandwidth in frequency measured at 0.707 of thc peak response and u n is the natural frequency of thc system. For small values of damping, i.c., less than 20'. of. critical, the peak frequency is essentially equal to the eigenfrcqucncy. If thc damping is larger, morc elaborate techniques should be used. Equation (3) is true for steady-state input excitation of the type x 1 (f) ~ Asin~t where A is the constant, and u is the input motion 'frequency.

The laboratory tests werc performed using a Horizontal Natt's J.inkage (Hhl.) shake table. It was designed and built on thc principal of l(att>s

~

Linl age which develops linear horizontal motion over scvcral inches. Steady-statc sinusoidal motion of the table is induced by eccentric mass structural vibrators mounted directly on the table. This type of vibrator also has been extcnsivcly used to tost large'tructures [5). Thc vibrator used has an ad-justablc ccccntric moment with a maximum value of 45 lb-in. It is driven by a DC motor controlled by a solid-state fccdback system capable of frequency l>>slrnrti<<n> /i>r I!'mini - >< i>irmr s<'r >'rrso

I f

0 l

t g, i r (<.r D'f ~., I[ (r ~ <;>>u Ill'< ul IIadj ian control and mcssurcmcnt 'o +'0:01 IIz in thc range, o j' 30'z t

In a typical laboratory test, thc tcs t speci fmen was embcddcd in soil con-i

~.tained in a box mounted on thc shake table. Accclcromctcrs werc placed on thc

~.tableI and at selected locations on the test specimen. The frequency was

-'varied in the range 1-30 IIz in finite increments, while thc response was re-Icordcd on strip chart recorders. The eccentric moment, and hence the lcvcl ofI

excitation, was varied to cause different levels of rcsponsc and to -test the I

I

structure in greater detail. This was particularTy useful for examining non-'.

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linear effects'or field testing an eccentric mass vibrator was attached to the top of

,the model structure. A small compact vibrator was used with the small models;

.for the 1 8m high conrete model, thc same vibrator used to drive the shake

~

'table* was employed. During thc forced vibration tests, the response.of thc

~ :structure was measured using accelcromctcrs, strip-chart recorders and a real~

I time spectrum analyzer.

Thc entire data acquisition system was field calibrated using a tilt table I

, giving a 0 10 g or 1 .'0 g signal

~ ~ The til t table is leveled by reversing an l accelerometer t

in its level position. For greatest sensitivity, all of thc ro-,

'corder amplifiers can bc oporatcd at their maximum gain settings. This rc-I

suits in different sensitivities for each transducer depending upon the- par-

'icular combination o f acce 1 erome ter and recorder channel . Because o f thc '

I

range of frequencies covered in thc, tests, some acceleromcters were occasion-beyond the range in which their response is independent'f fre-I i ally operated 1

'qucncy. A calibration curve for each accelerometer has beep obtained. The I

I

computer programs used for data reduction automatically correct the data if

the accelcromcters have been used in the range in which 'their response is fre quency dependent.

As a guide to detailed testing, to verify that no significant range of frequcncics has been overlooked, and to establish the correct attenuator sct-'

tings for each recording channel, first a "s>>ccp" is made of the entire frc-i qucncy range attainable >>'ith a given sct-up. During the sweep, thc frequency of vibration was gradually but continuously varied and the response was con-tinuously recorded at some slow recorder speed. The cnvelopc of the result-

'ng record corresponds to thc desired response curve. Thc subsequent detail-,

ed testing was then concentrated in those ranges of frequency which were of most interest. During the detailed testing, the recorder was operated at a slow paper speed while incremental changes in frequency werc made. In this way,,the transition between one frequency setting and thc next >>'as monitored and thc frcqucncy increment was adjusted to study thc response with as much detail as was necessary.

3 ~ Laborator Tests Thc purpose of this phase of thc project was to obtain test data on thc response of cmbcddcd model structures under simulated conditions of ground 1

shaking. Thic laboratory tests involved a'crics of parametric studies using lntlrurrlDDtfi>r Irpiag ~ pIrn~r srr IrrsD

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s'mall wooden models. The areas examined in'cl6dcdi o An investigation of the effects of geometry on overturning of structures

~ Determination of the effoct of horizontal excitation versus combined horizontal-vertical'excitation.

o Evaluation of the influence of the aspect ratio (height-to-base ratio) on overturning.

a Evaluation of the effect of gross soil properties on test results.

o Determination of the effect associated with different amounts of embedment.

Nuclear power plant containment buildings have gross specific weights in

-the range of 40 to 5S lbf/ft'0.64 to 0.88 gm/cm'). The models cons'isted of

!spheres, cubes, cylinders, and right parallclepipeds made. from ash or mahogany,

with effective specific weights (including instrumentation) xn the range of 33 I

to 50 Ibf/ft~. There were 17 models of varying sizes ranging from 4 inches .

I (10 cm) diameter or width up to 10 inches (25:cm) maximum diameter or width and 12 inches (30 cm) maximum .height. Two types of "soils" were used; the first was a clean (noncohesive) No. 30 white silica sand. The second was natural soil from a. Los Angeles site. Both soils were subjected to direct shear tests to determine shear strengths at low normal loads. The input (shake table) motions occurred oyer the frequency range of 1 to 30 llz and had amplitudes of 0.7 g horizontal and 0.5 g vertical or greater.

,During testing the input (base)'otion .was gradually increased. It was observed that the response of the models increased gradually to a certain e point, and then sudden1y increased. The response', was similar to a nonlinear

! "jump" phenomenon l

and was followed by a

'verturning of the models.

still greater response and eventual Subsequ'cnt investigations indicated that overturning of the structural models during the shake table testing was preceded by local failure of the

'oil adjacent to the model. This phenomenon was called "break loose" and an attempt was made to determi !v the conditions under which it occurred. The tests indicated that lateral acceleration and percent embedment were the critical variables. Combined horizontal and vertical acceleration seemed to be only slightly more effective than strong horizontal shaking alone. Geo-metry had an effect on response, but it was a second order effect (except fo' the spheres, which were significantly less stable). The aspect ratio '(height to-base ratio) was an important parameter; low ratios performed better.

Based on these tests, the optimum model structure for avoiding "break loose" conditions would be a low profile, cylindrical geometry, with 1.0 <II/D

~ < 2.0 and embedment equal to 505 H.

The typo of soil had an important effect on both the dominant frequencies of'response and the amplitude (through damping and other effects), and in-creased soil motions resulted in increased'damping and a decrease in natural frequency.

In anticipation of future field studies of embedment effects upon partia-lly buried rigid bodies, a series of field tests were conducted with one model (the 12" high, 6" diameter cylinder) at two different sites. One.'site

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(yoni co Beach, Los Angeles) was selected to provide "an e'ffective 'sand hal I

similar to the No. 30 sand used in the laboratory vibration studies and f-'pace the other site was the location from which the second lot of soil (referred to

~

herein as "Los 'Angeles soil" ) gas obtained for the shake table study.'he model was mounted with both an accelerometer and an ANC hlark 10 shaker. ~

The field testing investigated two areas: (1) the effect of embedment upon the first soil media and (2) com-l mode response of the model in different parison of measured damping ratios for the two soil'media studied.

The first mode rocking-translation frequencies increased dramatically (in

'a nonlinear fashion) with percent embedment; for both sites, the frequency approximately tripled as the model went from zero embedment (surface tost) to 50: embedment. The frequencies for the Los Angeles soil were always lower I.

'than for the sand site. At the Los Angeles site for 50~'mbedment without backfill, a 23.5 Hz first mode and 40.8 Hz second mode were observed as

'opposed to surface results of 16.6 fIz and 21.1 Hz. This phenomenon was attri--

I

'uted to the hardened surface of the undisturbed soil.

The frequency response curves for two different force inputs illustrate

the nonlinear behavior of 'the soil. Increasing the input force by a factor o

3.3 produced a 20~ reduction in natural frequency, a factor of 3.95 increase

in amplitude and at least a 60'

increase '(to g "- 16:) in apparent damping.

,The trend of all these effects are as would be expected for, an elasto-plastic I

I medium under dynamic loading. Of particular interest to seismic design is

the large increase in damping at the higher "1'evels of rcsporise.

4. Field Tests Three types of tests were performed at each depth of"embedment. The firs test was a low level test without backfill. The level of response was main-I tained at 0.025 inch or less. The second 'test was to install a compacted

-backfill I

and repeat the low level test, but now with the added restraining

'effect of the backfill. The maximum displacements at the top of the cylinder during the low level tests were in the range of 5-25 mils. 'The second series of tests, that is low level force with backfill, resulted in a roughly con-

,stant maximum displacement of 15 mils. The third series of tests involved in

'creasing the force by a factor of ten and repeating the test with, backfill.

~

Under these conditions, the top of the cylinder responded in the range of 0.75 to 1.25 g, The displacements ranged as high as 0.23 inch but were typically around 1/10 inch.

The 6 foot cylinder, tested ui>der actual field conditions, was iound to respond in a manner similar to the small models which were tested in the lab-oratory on the shake table [3]. As the frequency of shaking was'lowly in-creased, the response of the cylinder would increase slowly, until a critical t level was reached. At this point, the response would sud<lehly increase drama tically and the cylinder would undergo large amplitude respo>>se. Additional tests were performed to explore the significance of the "breakloose" fre-qucncy. These tests used the ANC h/K-10 vibrator., a'small low force, high J

1llSlfllCIAIIISfi>t l1'plllg c: p jg'VS('I('C <'CfSc7

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t f',fit (fslfal.n I(i 'C l L".n>

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'frequency shaker, to insure elastic response. The initial eccentricity was

~0.1 -in-lb. This was subsequentl> reduced to 0.03 in-lb. Tests were conduct" I

.ed on the 6'ylinder embedded 56 inches. At these low force levels (strain I, ~

= 10-~ "~), the soil-structure- system remained elastic and the response a typical resonance curve. hfodes were observed at 38, 50, and 80 I resembled

~

}lz. The first mode (rocking at 38 fiz) exhibited relative'amping of 64 of critical. Based on these results, it is concluded that the "breakloose" fre-

'uenc> characterizes response at the rocking mode when the applied force is I

sufiicient ot cause generalized yielding oi the soil around the embedded 1

structure'. Table I summarizes the experimental results.

Figure 1 illustrates how the rocking frequency varies as a function of em bedment for both. the high level and low level tests with and without backfill.

$ o long as the embedment is less than 70~>> of the diameter of the c>'linder the backfill has little effect: on the l

tionss,

(50m of the height of the cylinder),

high level test results. In other words, for shallow cmbedments (70~O of the diameter) when the soil surrounding the cylinder is underg'oing large deforms-the effect of the soil is. quite slight. At the higher level, the soil I

. undergoes greater responses and a large extent of yielding. It appears that I

the response of the system can be modeled by neglecting embedment effects.

In the low level,'no backfill case, the stiffness is primarily that of'the

~

I cylinder'rocking on its flat base, and the stiffness of the soil is one which

'orresponds to the small deflections being experienced.

b'hen back'.ill is provided and the level of excitation is still low, the rocking,freq>>ency increases in proportion to the depth of embedment. This is

~

~

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also true for high level tests when the depth of embedment is greater than 30 inches (70'f the'diameter), although the'rate,of increase is not so

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great as with the low level tests.

Using the applied'forces and measured displacements, effective stiffness-es can be found and compared >>ith calculated values (Table II). In the low level no backfill tests, the effective stiffness is attributed primarily-to rocking. It remains relatively constant with depth.' IS the soil was ideally uniform and isotropic, it would be expected to remain constant. During tho tests, it was observed that there were slight differences in the soil as a function of depth and this may explain, in part, the observed changes in the low level, no backfill stifinesses. The low level backfill curvo gives the highest values of effective stiffness, as would be expected, since the re-sponses under this condition are s'till low. The high level backfill results show effective stiSCnesses loss than the low lovel no backfill case for em-

~

bedments up to 30 inches. For embedments greater than 30 inches, the effect of the backfill is significant in increasing the effective stiffness of the system.

4.1 Com arison with Thcor Two methods were used to calculate both the eignefrequencies and damping of the structure at different levels of embedment. The first method [6],

ltllllllCllilltSfiPf l1'plI'g as pt(WC SCP 4'CfJO

IJ 1f l

h, f

1 I 1t v

I A. H. Hadj ian K2/5

'or f

simplicity of analysis, increases the impedance coefficients of the sur-

'ace structure by a factor as given in Figure 1. The curves in this figure are derived from the solution of the embedded structure as reported by Dere-dugo and Novak [7,8] with certain modifications. The second approach used the methodology of References 7 and 8 without any modifications. The strain de-pendent soil properties were estimated based on generalized curves published for this purpose by Seed and Idriss [9].

a. Eigenfrequencies Figure 2 compares experimental eigenfrequencies >>'ith calculated values for various embedments. The theoretical values using geophysical soil data overestimated the measured values in all cases. Thi's was attributed to the fact that even the low lovel tests resulted in leigh strain levels and 'inelast-ic response.

To check this hypothesis', a supplemental test was performed (see Figure).

In this test, a smaller shaker was used and the strain level was about 2 x 10 ~~, or well in the elastic range. This point falls in the midband of the results obtained with the two theoretical models used.

In the 56 inch embedded cases; where results were obtained at three force levels, ranging from 5 lbf to 1250 lbf, the nonlinear softening effect of the soils is clearly evident.

Equation 17 of Ref. [6] gave the best prediction of the deeply embedded test results, while Beredugo and Novak's [7,8] mo'del was more accurate for P

embcdments less than 30 inches. For embedm<<nts greater than SOS of the OD, and for high strain levels, either method could overestimate the natural fre'-

quency by 100: or more unless appropriate strain dependent parameters are used [6]. Neglecting the 'effect of the backfill, on the other hand, >>ould overestimate (12.5 Hz vs. 7-8 Hz) the high level results for embedments up to about 30 inches (70~ of OD), and at the greatest embedment, would underesti-mate the frequency by about 2S': (12.5 Hz vs. 16.5 Hz).

b. Damping Values Calculated damping values for rocking range from 3.8$ to 21: depend.--

ing on embedment (see Table III). The experimental values ranged from, 3': to 145. In general, the low level,backfilled results >>'ere higher than the low level no backfill results (typically 7': vs. 3':) although this was not true in every case. The high level tests showed the highest damping values (7-14~)

but in one case showed only 3'.. The damping data'is limited because some of the peaks are not sufficiently well defined. In other cases, once the system "broke loose", the resulting clearance may have caused less energy dissipa-tion.

5. Conclusions These tests investigated the effects of embedment on structural models of nuclear power plant containment structures. Experimental results were com-pared with theoretical models in which equivalent impedance coefficients.

.which depended on depth >>ere computed.

0 I

~[, lladjian Thc cxperimcntal results sho>>cd substantial increases in resonant fre-quency as thc amount of embedment increased. hhcn soil paramctcrs (shear mod-ulus principally) werc evaluated at strain lcvcls consistent with those ex-perienced during thc test, satisfactory agrccment with experimental values was obtained.

a ~ These results emphasize the importance of using strain-dcpcndcnt soil parameters in the seismic analysis of nuclear power plants. Additionally the effect of embedment was negligible for'mbcdmcnts less than about 70~ of

.thc diameter of the cylinder during the high strain level tests. hfore import-antly,,the analytical methods used were adequate when strain dependent soil parameters were, used.

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A. EE. Eladj ian K2/5 I

References

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[2]

3

~ sl=~

Applied Nucleonics Co., Seismic Design of Nuclear Power Plants - A No. 2, pp. 151-233, January 19

[3) Applied Nucleonics Co., parametric Studies of Embedded Structures Subl ected to Simulated Groun Ilotxons, aport No. 1iE~ ',Lento Ifonica,

~ax~ecemexcr 1

[4) Applied Nucleonics Co., Ex)ierimental and Anal tical Soil-Structure Interaction Studies for limbed e Structures, aport N~lo. 1 S-lo, Santa IIonxca, Calx ., Decem er P S.

[5l See the special issue of Nuclear En ineerin and Desi n, Vol. 25, No.. 1, June 1973.

Bechtel Power Corporation, To ical Re ort: Seismic Anal 'ses of Struc-.

tures and E ui ment for Ebfuclear ower lants, C-T(H'- 4ev. une

'll/ E

[7) Beredugo, Y.O., hl. Novak, "Coupled Horizontal and Rocking Vibration of Embedded Footing>g", Canadian Geotechnical Journal, Vol. 9, p. 474,. 1972.

[8) Novak, M., Y.O. Beredugo, "Vertical Vibration of Embedded Footings",

ASCE, Proceedings Paper No. 9412, Journal of Soil hlechanics Foundation Division, Vol. 98, No. Shl12, p. 12 , Decem er

[9l Seed, ll.B. and Idriss, I.hf., "Soil Moduli and Damping Factors for Dynamic Response Analysis", Report No. EERC 70-10, Earthquake Engineer-ing Research Center, Univ. of. Calif., Berkeley, Calif., 1970.

I I

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TABL SU&v&RY OF VIBRATION TEST RESULTS Embedment Low Level, Low Level . High Level (inches) No Backfill Nith Backfill Nith Bac'kfill( ~

f 'f

~Hz) g

(:) ~lbf F Y

("3 ~(H z F

~(lb t ~) ~Hz ~lbt'(':)

F 0 10 46 0. 003 6.5 . 3-7 194 0.026 9.3 39 0.018 13.5 84 0. 017 6.5 3-11 194 0.32 30 42 56 10 8.9 8.0 7

4 37 29 G. 028

0. 033 0.035 19 23 24.5

'43 166 276

0. 021

0. 019

0. 013 8.3 13 3 16.

~

5 14 7

312 689 1250 0.22

0. 13

0. 096 inmates:

(1) Symbols: f= rocking frequency; 5 = damping factor; F applied force; y = soil strain (2) No "backfill" on surface.

TABLE 1X CALCULATED li>iPEDANCE COEFFICIENTS Enb edr.ent (inches) Rocking Sti fnesses, K>~, lb-ft/radian x 10 Trans 1 at ional S t iffnes s es K, lb/ ft x 10-.

Based on ';Strain Based on Strain 'ased on Geophysical Data Dependent Data Based on Geophysical Data. Dependent Data Ref. 7 fj 8 Ref. 6 Ref. 6 Ref. 758 Ref. 6 Ref. 6 0 6.37 1.47 0.9 5.3 3.5 14 8. 95 2. 16 0.35 8.2 7.5 1.2 30 10. 2 3. 52 P 7 11.4 1.9 42 10. 7 5. 34 1.2 13. 9 10. 8 2.5 56 13.7 8. 69 2.6 16. 7 12.4 3.7 Embedment i~measured Rocking Stiffness with Backfill K>~ lb-ft/radian x 10 (inches) Low Level Tests High Level Tests 0"

"'0 3-5 5.0 42 9.0 3.5 56

ll V.

(

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TABLE III DAMPING FACTORS' (~o) t Embedment Rocking Mode Translation Mode (inches) Sy .

I'x 0 3.8 27 14 5.9 31

• 30 9.5 35 42 14 37 56 40

lt FIGURE 2: COhfPARISON OF CALCULATED AND MEASURED EIGEHI'REQUENCIES--

FIGURE 1: MODIFICATION FACTORS DUE TO EhfBEDMENT FOR EQUIVALENT FOUNDATION INTERACTION SPRINGS AT UNIFOIN SOIL SITES

'I

'l

'f

3 Vert'cal Tran 1 at,ion 2 Late al Trans ation x 3 Rock ing Q

~ Pt cO 9A 2

~ Ct CQ d 0 6 U

'4 1 0

0 0

~ R 0.1 0.3 .5 EmbedIIiont De th (h)

~ase Diameter i'.t7

j 0

l I Theory (Low Level) 50

---Theory (Bigh Leueli Ref. 6) i BXPBBl!1BNT '" (with haclcfill) 0 (Low Level) t ]

Q {High Level)

Ref 7,8 0 (Supplementary Test) 40 C3 Encreasin Force CY VQ Re 6 30 V) 20 Pv 10 Avera g e J

calculated value (12 5 Hz) for low level soil inches) parameters, no backfill 0 2i0 0 60 90 75 . 100

('. of Diameter)

EMBEDMENT

il to P

I P

I t

l