DAMPING CAPACITY OF SOIL DURING DYNAMIC LOADING

M ISC E LL A N E O U S PAPER S-72-II

DAMPING CAPACITY OF SOIL DURING DYNAMIC LOADING

Report 2

REVIEW OF LABORATORY METHODS OF DETERMINING DAMPING

by

W. F. Marcuson III

T A7.W34m S-72-11 1973 Vol. 2

May 1973

Sponsored by Office, Chief of Engineers, U. S. Army

Conducted by U. S. Army Engineer Waterways Experiment Station

Soils and Pavements Laboratory

Vicksburg, Mississippi

APPROVED FOR PUBLIC RELEASE; DISTRIBUTION UNLIMITED

l

DBRARY

JAN 1 8 1974

Bureau of Reclamation Denver, Colorado

Destroy th is report when no longer needed. Do not return it to the originator.

T h e findings in th is report are not to be construed as an o ff ic ia Department of the Army posit ion un less so designated

by other authorized documents.

BUREAU OF RECLAMATIOI IENVER LIBRARY

y

n•' M ISCELLANEOUS PAPER S-72-II <7

DAMPING CAPACITY OF SOIL DYNAMIC LOADING J

Report 2 )

92098889

DURING

REVIEW OF LABORATORY METHODS OF DETERMINING DAMPING3,

by

W. F. MarcusonJII

I D II Q Iof®

I D ID I D I

^ May 1973 ^

Sponsored by Office, Chief of Engineers, U. S. Army Project 4A06II02B52E , Task 01, Work Unit 012

Conducted by U. S. Army Engineer Waterways Experiment Station Soils and Pavements Laboratory

Vicksburg, Mississippi

R M Y - M R C V I C K S B U R G , M I S S

APPROVED FOR PUBLIC RELEASE; DISTRIBUTION UNLIMITED

92098889

FOREWORD

T h is i n v e s t i g a t i o n was c o n d u c te d by th e U. S . Army E n g in e e r W a te r­ways E x p e rim e n t S t a t i o n (WES) u n d e r th e s p o n s o r s h ip o f th e O f f i c e , C h ie f o f E n g in e e r s , D e p a rtm e n t o f t h e Army, a s a p a r t o f P r o j e c t UA06ll02B52E, " E v a lu a t io n o f th e Damping C a p a c i ty o f S o i l s U nder Dynamic L o a d s ,"T ask 0 1 , Work U n i t 0 1 2 .

The i n v e s t i g a t i o n was c o n d u c te d b y D r. W. F . M arcuson I I I d u r in g th e p e r io d A p r i l - J u n e 1971 u n d e r t h e g e n e r a l d i r e c t i o n o f M e s s rs . J . P . S a l e , R. W. C unny, R . F . B a l l a r d , J r . , and D r . L. W. H e l l e r o f th e S o i l s and P avem en ts L a b o r a to r y . M r. S . J . Jo h n so n p a r t i c i p a t e d in th e re v ie w o f th e r e p o r t an d made s e v e r a l h e l p f u l com m ents. T h is r e p o r t was w r i t t e n by D r. M arcu so n .

D i r e c t o r o f WES d u r in g th e p r e p a r a t i o n and p u b l i c a t i o n o f t h i s r e p o r t was COL E r n e s t D. P e i x o t t o , CE. T e c h n ic a l D i r e c t o r was M r. F . R . B row n.

iii

CONTENTSPage

FOREWORD...................................................... iiiS U M M A R Y .................................. vilPART I: INTRODUCTION............ 1

Background .............................................. 1Objective .............................................. 1Scope of W o r k ........................................ . 2

PART II: THEORY.............................................. 3Single-Degree-of-Freedom S y s t e m .................. .. . . 3Hysteresis Curve...................... 7

PART III: LABORATORY T E S T I N G ............................... 9Resonant Column Testing ............................... 9Cyclic Triaxial Testing . . . . ....................... 12Uniaxial-Triaxial Stress-Strain Testing ................. 13Other Methods . . . .......... ................... .. . lU

PART IV: MECHANICS THEORY USED TO ASSESS SOIL DAMPING......... 15Resonant Column T e s t s ................................. 15Cyclic Triaxial Tests ................. 15Uniaxial-Triaxial T e s t s .............. ............... .. 16

PART V: CONCLUSIONS AND RECOMMENDATIONS...................... 17Conclusions................... ........................ 17Recommendations........................................ 17

LITERATURE CITED.............................................. l8

v

SUMMARY

In predicting the response of soils subjected to dynamic loads, the pertinent soil properties must be known. This report discusses the various laboratory methods for determining the damping value for a soil, resonant column testing, cyclic triaxial testing, and uniaxial- triaxial stress-strain testing. The procedures for calculating the damping values are given.

vii

DAMPING CAPACITY OF SOIL DURING DYNAMIC LOADING

REVIEW OF LABORATORY METHODS OF DETERMINING DAMPING

PART I: INTRODUCTION

Background

1. Report 1̂ ~ of this series reviewed the various mathematical models used to simulate the soil; the first report is based on methods of continuum mechanics and contains a summary of the available mathe­matical material models and their general functional representation.In predicting the response of soil specimens subjected to dynamic loads in the laboratory, two basic approaches have been used: the theory ofelasticity and the single-degree-of-freedom system with viscous damping. In the latter approach, the soil is assumed to be represented by a sys­tem of masses, springs, and dashpots. The inputs to the approach are the mass m , spring constant k , and the coefficient of viscous damp­ing c . These are not the only ways to model the stress-strain-time behavior of soil, but they are two common methods that have been used in the past.

2. Various laboratory techniques have been developed to aid in the evaluation of the spring constant and the damping coefficient of given materials. Presently, there are some discrepancies between the values of damping obtained in the laboratory and the values of damping that are used in actual design and analysis of systems. A broad objec­tive of this study was to identify some of these discrepancies and, hopefully, to suggest means to eliminate them.

Objective

3. The objectives of this report are to review the laboratory procedures for determining damping, to state what assumptions are in­volved in each procedure, and to assess the validity of such assumptions.

1

Scope of Work

U. This investigation was limited to a review of laboratory techniques currently being used to determine the damping capacity of soil samples. This report will take some of the models developed in Report 1 and discuss how the input parameters to these models are de­termined in the laboratory using representative soil samples. Part II is a simple discussion of the solution of the equation of motion for a single-degree-of-freedom system with viscous damping. Part III dis­cusses the various laboratory techniques for determining damping.Part IV is a discussion of the discrepancies that exist between the theoretical work and the actual laboratory procedures, and Part V states the conclusions and recommendations for this investigation.

2

PART II: THEORY

Single-Degree-of-Freedom System

5. In order for a medium such as the earth’s crust to be modeled mathematically, several simplifying assumptions must be made. One such assumption is that the soil behaves as a viscoelastic material. Again, the model can be simplified by restricting it to a single degree of freedom. This is the simplest mathematical material model with an energy-absorbing characteristic and is shown schematically in fig. 1. This is the rheological model discussed in paragraph 39 of Report 1.

Fig. 1. Schematic of a Kelvin-Voigt material

6. The equation of motion for this system, with no forcing function, is

k.2 12

z

mz + cz + kz = 0 (1)*

If z = exp (ßt) , then equation 1 becomes

(2)

The solution for equation 2 is

(3)

* Equation 1 can be obtained from equation b2 of Report 1, with minor manipulation.

3

and

(3 = ( - c - V c2 - Ukm )k2 2m ' /2The overdamped case exists when c > Ukm , and no oscillation will

occur. The critically damped case is represented by c = ^km ; this is the minimum damping required for no oscillation.

cc = 2 ' (5)

wherecc = critical damping

In the literature, the damping ratio D is frequently used. D is defined by

D =-2-Cc

(6)2The underdamped case occurs when c < Ukm , and the system oscillates

(see fig. 2).

Fig. 2. Underdamped free vibration

This decay yields

ô 2nD (reference 2) (7)

1+

where6 = logarithmic decrement

From equation 7? tor small values of D

6 ̂ 2ttD (8)

7. The preceding discussion deals with free vibrations, i.e. no forcing function. Now, consider the same with a harmonic force Q of amplitude Qq . For this case, equation 1 becomes

mz + cz + kz = Qq sin u)t (9)

whereoo = circular frequency of the exciting force t = time8. Simple mathematical manipulation of equation 9 yields

M = ---- ----- (reference 2) (10)max I-----p2D VI - D

whereM = magnification factor of displacement at resonant fre- max quency of the system

9. Along these same lines, damping may be computed if the phase angle f t is known, f t is the angle in degrees between the exciting force and the displacement vector. The relation is

tan f t =1 - (® > n )2

(11)

whereU)n = natural circular frequency10. Now consider the same system being excited by forces produced

by unbalanced rotating masses (fig. 3). For this system, the equation of motion becomes

5

wherem = 2m, e 1

Mathematical manipulation of equation 12 yields

A

,_(mee ) / m max 2DVi- Dwhere

(reference 2) (13)

A = displacement amplitude m = total mass including m^ e = eccentricity

□ = the quantity at resonance maxThe quantity in brackets is not equal to the magnification factor M but is related to it by

A (iu)11. Damping can be obtained in another way. Here the geometri­

cal shape of the resonance curve is used. Fig. h is an amplitude versus frequency curve for the single-degree-of-freedom system excited by a harmonic force.

6

Fig. k . Amplitude versus frequency curve

For this case, -when A = 0.707A and if D is small.5 max *

mwhere

Af = f2 f1

Hysteresis Curve

(15)

12. Another method of calculating damping (see fig. 5) is to plot a shear stress-strain curve through one complete cycle of loading

r

7

and unloading. In this plot, damping is defined by

where

(reference 3) (l6)

A = area of the loop hA, = area of crosshatched triangle13. This has heen a brief discussion of the calculations that

can be made from laboratory data to arrive at values of damping. The damping value is an equivalent viscous damping, since the soil is assumed to be Kelvin-Voigt material.

8

PART III: LABORATORY TESTING

lb. Laboratory methods for determining damping can be basically divided into three categories:

a. Resonant column testing•b. Cyclic triaxial testing.£. Uniaxial-triaxial stress-strain testing.

This chapter -will discuss briefly the manner in -which the damping values are obtained, what assumptions are made, and the validity of the assumptions.

Resonant Column Testing

15. The resonant column test is used to determine the viscoelas­tic properties of soil specimens. The specimen, encased in a rubber membrane, is placed in a compression chamber in which confining pressure can be regulated to simulate overburden pressure. The specimen is then subjected to sinusoidal vibration in either a torsional or longitudinal mode. The resonant frequency of the sample and the amplitude of motion are determined. From these measurements, the elastic moduli and damp­ing characteristics can be computed.

16. About six different resonant column apparatus, identified as follows, have been developed in the United States:

a. U. S. Army Engineer Waterways Experiment Station (WES) apparatus.

b. U. S. Army Cold Regions Research and Engineering Labo­ratory (CRREL) apparatus.

£. Shannon and Wilson apparatus.d. Hardin oscillator._e. Drnevich oscillator.f . Hall oscillator.

The Shannon and Wilson apparatus does not determine damping and is not discussed further.

9

WES and CREEL apparatus17. These devices are basically the same, both having been de­

veloped at CREEL. The apparatus at WES has more electronic equipment, which adds to its automation. These devices are both excited at the base and can be excited in either the longitudinal or torsional mode.The base acceleration is held constant, and the ratio of the accelera­tion at the top to the acceleration at the base is monitored. Thus, by varying the frequency, one obtains amplitude ratio versus frequency data. The following equation is used to determine the damping ratio D :

D = sin | (17)

whereft = the lag angle or phase angle between stress and strain

Reference b also gives the relation

tan £2 2ttRmax

(18)

whereR = the ratio of acceleration measured at the top of the max specimen to the acceleration measured at the base of

resonance

18. The following assumptions are made:a. Small damping (tan < O.l) .b. Material follows the Kelvin-Voigt model.

Hardin oscillator519. The Hardin oscillator is very popular since it can operate

inside a slightly modified standard triaxial cell. The top of the spec­imen is excited in a torsional mode only and the bottom of the specimen is held fixed. The frequency is varied until resonance is determined. Then, by varying the current (which varies the force), the desired am­plitude is maintained. Because resonance is dependent on strain am­plitude, it is an iteration procedure to determine the resonant fre­quency at a given strain amplitude. Two methods can be used for

10

determ ining damping: a f r e e - v ib r a t in g method and a s t e a d y - s ta te method.

In the f i r s t method, the e x c i t a t io n i s removed and a decay curve i s r e ­

corded . Damping can then be computed u sin g

D a [ M 1 + s > - v ] (19)

where

6^ = system (ap p ara tu s and s o i l ) lo g arith m ic decrement

= ap p aratu s lo g arith m ic decrement

S = system energy r a t i o (th e system energy r a t i o i s a fu n c tio n o f mode sh ap e, specimen d im ensions, specimen s t i f f n e s s , and ap p aratu s c o n sta n ts )

The second method o f computing damping i s b ased on the system m ag n ifica ­

t io n f a c t o r s . U sing t h i s method, damping i s c a lc u la te d u sin g

D [ ( y r ) /9 r - a y ]

s/ r^ J [j o/J - kyiU-r^Jf2 ) ]

which reduces to

( 20 )

| f r t Cr ) / 9 r - 2 n y ]

(W2Rf2J o - R k J

where

= ap p aratu s to rq u e /cu rre n t c o n sta n t , FL amp"1

= cu rren t flow in g through the c o i l s o f the v ib r a t io n d e v ic e , amp

9 = am plitude o f v ib r a t io n a t th e system reso n an t frequ en cy ,ra d ia n s

kp = ap p aratu s damping co n stan t (d im en sio n le ss)

f = system reso n an t frequ en cy , Hz

R = resonance f a c t o r determ ined from curves g iven in re fe re n ce 6 ( dimens io n le s s )

J = mass p o la r moment o f in e r t i a o f th e specim en about i t s a x i s , FLT2

J = mass p o la r moment o f in e r t i a o f the r i g i d mass (v ib r a t io n ° h e a d ), FLT2

k = ap p aratu s r o t a t io n a l sp r in g c o n sta n t , FLT2

11

Drnevich and Hall oscillators20. The Drnevich and Hall apparatus are similar, both having

1 7 8fixed-free boundary conditions and being excited at the top. 5 ’ The primary difference in these two apparatus is that Drnevich's apparatus has more power and is capable of accepting a wider range of specimen size and geometry. With these apparatus, damping can be calculated by record­ing a decay curve and computing the logarithmic decrement. Apparatus damping is assumed to be small and is neglected. Damping can also be computed using a method based on magnification factors. For this method, the current through the driving coils at resonance is divided by the accelerometer output at resonance multiplied by a constant. The follow­ing assumptions are made:

a. Small damping, e.g., 6 = (2ttD ) / V i - D2 « 2 ttDb. Material behaves as a Kelvin—Voigt model.

Sources of error21. The resonant column test is a fairly simple means of comput­

ing the damping of soils in the laboratory; however, there are several sources of error. These apply generally to all the different apparatus. Some of these are as follows:

a. It is assumed that 100 percent coupling exists between— the driving apparatus and the soil specimen and between

the accelerometer and the soil specimen.b. The boundary conditions are never exactly fixed or free

as assumed.c. The additional damping provided by the radial drainage~ filter paper and the rubber membrane used in the test is

neglected.d. The viscosity of the confining medium is neglected. The

confining medium may be air, glycerin, water, or other fluid or gas. The effect of the specimen being sur­rounded by the confining medium is neglected.

Cyclic Triaxial Testing

22. The cyclic triaxial device is essentially a modified standard triaxial cell.^ The loading ram (vertical load) is connected to an air- driven piston. The axial strain is measured using an LVDT and the axial

12

stress is measured with a load cell. Presently, the device is limited to fairly low frequencies. In running a cyclic triaxial test, it is possible to obtain a stress-strain curve for a complete cycle of loading and unloading, which yields a hysteresis loop; from this loop, damping can be determined.10 Using this method, the load should be measured in­side the cell; or if the load is measured outside of the cell, piston friction must be minimized and neglected. A special triaxial cell top with a rolling membrane has been developed that helps to minimize the piston friction.

Uniaxial-Triaxial Stress-Strain Testing

23. For this procedure two types of laboratory tests are con­ducted. First uniaxial strain tests are run.11 In this test, the soil is subjected to an axial stress while the radial strain isheld at zero. The radial stress required to maintain a conditionof zero radial strain is also measured. From these data, load-unload curves of a versus e (e = axial strain) and a versus a aremade. This is a static test. The second type of test is the triaxial shear test.11 In the triaxial shear test, a constant hydrostatic pres­sure is first imposed on the specimen; then a controlled axial stress or controlled axial strain is applied until the specimen fails in shear.The response of the specimen is measured. The final product is a plot of principal stress difference versus vertical strain. Using only the stress information at failure, an envelope is plotted of maximum prin­cipal stress difference versus pressure. This information is obtained from several tests on several specimens for several states of stress (see reference 11). Because most of the computer codes now in use can accept only incremental elastic-plastic loading and unloading data, it is neces­sary to develop a compatible constitutive equation from the laboratory data.11 Using this method, damping is indirectly determined. Energy is dissipated by following the load-unload curve or the hysteretic path.The major disadvantages of this method appear to be the following:

a. The radial stress required to maintain the radial strain at zero is difficult to measure.

13

b. Considerable experience and judgment are needed to select representative data and develop a compatible model, since data come from static and dynamic tests.

Other Methods

2h. Another laboratory method of computing damping has been de-12veloped at the University of California. In this method, a cylindrical

specimen of soil is subjected to a seating load. At a given time, theload is increased in a nearly instantaneous manner. A decay curve isrecorded and the soil damping computed using equation 7.

25. Hardin has recently developed an electromagnetic, hollow-13cylinder, torsional shear device. This device yields a hysteresis

loop from -which damping can be computed as previously discussed (see paragraph 12). The device can be used to determine damping at various— c:

strain levels from 10 in./in.* to near failure.

* Multiply inches by 25.U to obtain millimeters.

PART IV: MECHANICS THEORY USED TO ASSESS SOIL DAMPING

26. The following discussion briefly relates the theories used to evaluate energy dissipation or damping of soil material in laboratory test devices to continuum mechanics theory as expressed in Report 1. These relations (where defined) are given below, with reference to the appropriate laboratory test method.

Resonant Column Tests

27. Soil damping in the resonant column test Is evaluated by as­suming that the soil is a viscoelastic material and that the boundary conditions encompassing the laboratory soil specimen are ideal. If these assumptions are valid, lateral specimen displacement is neglected, and the constitutive equation for the soil specimen is taken' (equation 39* Report l) as

a. .ij = (U -L + V i) 6ij + + 2 ll d. . Kv 1J (22)

Then the effective stiffness (see equation l) of the soil (equation U3a, Report l) is

k Mah (23)

the damping coefficient (equation ^3b, Report l) is

(210

and the notation is defined in Report 1. In this case, the constitutive equation for evaluating resonant column tests is time-dependent.

Cyclic Triaxial Tests

28. Principal stresses and one average principal strain are mea­sured on a cylindrical specimen subjected to cyclic deviator stresses.

15

The test method is independent of time, so appropriate constitutive re­lations would also he time-independent. The current test method, how­ever, does not include sufficient measurements or assumptions to define a constitutive relation for the test specimen.

Uniaxial-Triaxial Tests

29. Laboratory tests to define the behavioral characteristics of soil to very high transient stress levels include uniaxial (one­dimensional) compression tests and triaxial compression tests on soil specimens. In the uniaxial test, radial deformation of the specimen is not allowed, and axial stress, axial deformation, and radial stressare measured. In the associated triaxial test, axial stress, axial de­formation, radial stress, and radial deformation of the specimen are measured.

30. Although loads can be applied to the laboratory specimens quite rapidly in the uniaxial-triaxial tests, the appropriate constitu­tive relations are independent of time and are evolved from the measured hysteresis characteristics of the test specimen. One popular constitu­tive formulation (equation 60, Report l) for these tests is

1 + vE

VE do, , 6. . kk ij 6ij (25)

The notation used in equation 25 depends on the loading conditions sus­tained by the soil specimen and is defined in Report 1.

16

PART V: CONCLUSIONS AND EE C OMMEND AT IONS

Conclusions

31. In general, the phenomenon of energy dissipation by the earthTs crust is not well understood, and more research in this area is needed. This review of laboratory methods of determining damping has led to the following conclusions:

a. Laboratory soil samples are assumed to act as a Kelvin- Voigt material, which is the simplest mathematical material model with an energy-absorbing characteristic.

b. Most measurements of energy absorption are converted to an equivalent viscous damping. This assumes that damp­ing is related to velocity, which may or may not be the case.

_c. The damping measured in the laboratory is only internal damping and does not include other energy losses, i.e., geometric damping.

d. The most up-to-date, two-dimensional finite difference” ground motion codes do not use damping as a direct input;

instead, damping is indirectly input using loading and unloading curves. In this way, the energy is absorbed by the hysteretic nature of the medium.

Eec ommendat ions

32. For cyclic loading triaxial tests, additional laboratory mea­surements should be made to help define a behavioral constitutive relation.

33. It is recommended that this study be extended to include the conceptual development of laboratory techniques that will measure the damping capacity of soil materials. Such techniques should be compatible with continuum mechanics theory and should generate quantitative damping values applicable to current dynamic analysis methods.

17

LITERATURE CITED

1. Rohani* B. * ’’Damping Capacity of Soil During Dynamic Loading; Re­view of Mathematical Material Models*” Miscellaneous Paper S-72—11* Report 1* Apr 1972 * U. S. Army Engineer Waterways Experiment Sta­tion* CE* Vicksburg* Miss.

2. Richart* F. E.* Jr.* Hall* J. R.* Jr.* and Woods * R. D.* Vibra- tions of Soils and Foundations* Prentice-Hall* Englewood Cliffs,N. J.* 1970.

3. Hardin* B. 0. and Drnevich* V. P.* ’’Shear Modulus and Damping in Soils*” Technical Report UKY 32-71-CE5* Soil Mechanics Series No. U* 1970* University of Kentucky* Lexington* Ky.

b. Stevens* H. W.* ’’Measurement of the Complex Moduli and Damping of Soils Under Dynamic Loads*” Technical Report 173* 1966* U. S. Army Cold Regions Research and Engineering Laboratory* Hanover* N. H.

5. Hardin* B. 0. and Music* J.* ’’Apparatus for Vibration During the Triaxial Test*” Symposium on Instrumentation and Apparatus for Soil and Rock* Special Technical Publication STP No. 392* 1965? American Society for Testing and Materials* Philadelphia* Pa.

6. Hardin* B. 0.* ’’Suggested Methods of Test for Shear Modulus and Damping of Soils by the Resonant Column*” Special Procedures for Testing Soil and Rock for Engineering Purposes; Suggested Methods* Standards and Tentative Methods* Definitions* and Nomenclature (by Reference Only)* Special Technical Publication STP No. ^79? pp 516-529? 1970* American Society for Testing and Materials* Philadelphia* Pa.

7. Drnevich* V. P.* Effects of Strain History on the Dynamic Proper­ties of Sand* Ph. D. Dissertation* University of Michigan* Ann Arbor * Mich.* 1967•

8. Hall* J. R.* Jr.* and Richart* F. E.* Jr.* ’’Dissipation of Elastic Wave Energy in Granular Soils*” Journal* Soil Mechanics and Founda­tions Division* American Society of Civil Engineers* Vol 893No. SM6* Nov 1963* PP 27-56.

9. Lee* K. L.* Triaxial Compressive Strength of Saturated Sand Under Seismic Loading Conditions* Ph. D. Dissertation* University of California, Berkeley* Calif.* 1965.

10. Hardin* B* 0.* ’’The Nature of Damping in Sands*” Journal* Soil Mechanics and Foundations Division* American Society of Civil Engi­neers* Vol 91 > No. SMI* Jan 1965, PP 63-97.

11. Jackson* J. G.* Jr.* "Analysis of Laboratory Test Data to Derive Soil Constitutive Properties*” Miscellaneous Paper S-69-16* Apr 1969 ̂U. S. Army Engineer Waterways Experiment Station* CE* Vicksburg* Miss.

12. deGraft-Johnson* J. W. S.* "The Damping Capacity of Compacted

18

Kaolinite Under Low Stresses," Proceedings, International Sympo­sium on Wave Propagation and Dynamic Properties of Earth Materials, Albuquerque, N. Mex., 1967.

13. Hardin, B. 0., "Constitutive Relations for Airfield Subgrade and Base Course Materials," Technical Report UKY 32-71-CE5, Soil Me­chanics Series No. b, 1971, College of Engineering, University of Kentucky, Lexington, Ky.

19

U n c l a s s i f i e dS e c u r ity C l a s s i f ic a t io n

DOCUMENT CONTROL DATA - R & D

1. O R I G I N A T I N G A C T I V I T Y (Corporate author)

U. S . Army E n g in e e r W aterw ays E x p e rim e n t S t a t i o n V ic k s b u rg , M i s s i s s i p p i

2 4 . R E P O R T S E C U R I T Y C L A S S I F I C A T I O NU n c l a s s i f i e d

2 b . G R O U P

3 . R E P O R T T I T L E

DAMPING CAPACITY OF SOIL DUPING DYNAMIC LOADING; R e p o r t 2 , REVIEW OF LABORATORY METHODS OF DETERMINING DAMPING

4 . D E S C R I P T I V E N O T E S (T ype o f report and in c lu s iv e d a te s)R e p o r t 2 o f a s e r i e s5 . A U T H O R ( S ) (F ir st name, m iddle in itia l, la s t nam e)

W illia m F . M arcuson I I I6 . R E P O R T D A T E

May 19737 a. T O T A L N O . O F P A G E S 7b. N O . O F R E F S

22 138a. C O N T R A C T O R G R A N T N O .

b, p r o j e c t n o . ^+A06ll02B52E T ask 0 1 , Work U n i t 012

C.

d.

9 a . O R I G I N A T O R ’ S R E P O R T N U M B E R ( S )

M is c e l la n e o u s P ap e r S -7 2 -1 1 , R e p o r t 2

9b. O T H E R R E P O R T N C ( S ) (Any other numbers that may be a s s ig n e d th is report)

1 0 . D I S T R I B U T I O N S T A T E M E N T

A p proved f o r p u b l i c r e l e a s e ; d i s t r i b u t i o n u n l im i t e d .1 1 . S U P P L E M E N T A R Y N O T E S 1 2 . S P O N S O R I N G M I L I T A R Y A C T I V I T Y

O f f i c e , C h ie f o f E n g in e e r s , U. S . Army W ash in g to n , D. C.

1 3 . A B S T R A C T

I n p r e d i c t i n g th e r e s p o n s e o f s o i l s s u b je c te d t o dynam ic l o a d s , t h e p e r t i n e n t s o i l p r o p e r t i e s m ust be known. T h is r e p o r t d i s c u s s e s th e v a r io u s l a b o r a t o r y m ethods f o r d e te r m in in g th e dam ping v a lu e f o r a s o i l , r e s o n a n t colum n t e s t i n g , c y c l i c t r i a x i a l t e s t i n g , and u n i a x i a l - t r i a x i a l s t r e s s - s t r a i n t e s t i n g . The p ro c e d u re s f o r c a l c u l a t i n g th e dam ping v a lu e s a r e g iv e n .

DD FORM 1473 R K P L A C U D O F O R M 1 4 7 « . 1 J A N « 4 . W H IC H IS O B S O L E T E F O R A RM Y U S B . U n c l a s s i f i e d Security C lassifica tio n

U n c la s s i f ie dSecurity C la ss if ic a t io n

1 4 L I N I K A L 1 N K B L I N I K C

R O L E W T R O L E W T R O L E W T

Damping Dynamic loads L ab o ra to ry ..te s ts S o i l dynamics S o i l p r o p e r t ie s

U n c la s s i f ie dSecurity Classification