THE UNIVERSITY OF MICHIGAN INDUSTRY PROGRAM OF THE COLLEGE OF ENGINEERING EFFECT OF VIBRATION AMPLITUDE ON WAVE VELOCITIES IN GRANULAR MATERIALS J R Hall, Jr. F, E. Richart, Jr. May, 1963 iP-618

ACKNOWLEDGMENT The studies presented in this paper represent a portion of work made possible through National Science Foundation research grant NSF-G19021. The support provided for this research is gratefully acknowledged. This investigation was conducted as a part of the research program of the Department of Civil Engineering and the Engineering and Industrial Experiment Station of the University of Florida, Gainesville, Florida. -ii

TABLE OF CONTENTS Page ACKNOWLEDGMENT e................................ 0 0..... 0...... ii LIST OF FIGURES..................... 4.......e.0e0 iv INTRODUCTION..............................00..............*.*.* 1 THEORIES USED IN THE EXPERIMENTAL DETERMINATION OF WAVE VELOCITY. 3 LABORATORY TESTS OF VELOCITY IN GRANULAR MATERIALS............. 5 Materials.. oooooCeo................................ ee..... 5 Equipment. O0...................................................0 0 5 Summary of Tests.................o................. 7 Results of Velocity.. eoee*eoe ooo eeo......................... 10 DISCUSSION OF THE RESULTS................................. 21 Group I...................................................... 21 Group II a a.............aa.................................aa. 21 Group III............................. oo *eO............... o 22 24 CONCLUSIONS.................................................... 24 REFERENCES o o.......... o o c. o o.......................................... o. o o e 4 - 26

LIST OF FIGURES Figure Page 1 Grain Size Curves for the Materials Used in the Present Research,......................................... 6 2 Vibration Mechanisms Used in the Present Research..... 8 3 Fixed-free Vibration Eqiuipment...................... 9 4 Variation of Velocity with Amplitude in Torsional Oscillation for Ottawa Sand Dry and saturated with Water.................................................OO o oO Oo o 11 5 Variation of Velocity with Amplitude in Longitudinal Oscillation for Ottawa Sand Dry and Saturated with Water................................................. 12 6 Variation of Velocity with Amplitude in Longitudinal Oscillation for Ottawa Sand Saturated with Dilute Glycerin o0 *eo........................ 13 7 Variation of Velocity with Amplitude in Longitudinal Oscillation for Glass Beads No. 2847 in the Dry and Water Saturated Condition,........................... 15 8 Variation of Velocity with Amplitude in Torsional Oscillation for Glass Beads No. 1725 in the Dry and Water Saturated Condition............................. 16 9 Variation of Velocity with Amplitude in Torsional Oscillation for Novaculite Noo 1250 Consolidated to 2030 lb/ft2 and 4100 lb/ft2.......................... 17 10 Variation of Velocity with Amplitude in Torsional Oscillation for Novaculite No. 1250 Consolidated to 7270 lb/ft2 and rebounded to 4130 lb/ft2 and 2050 lb/ft2............. 0... 18 iv

INTRODUCTION The dynamic properties of a soil can be determined from measurements of the propagation of stress waves through the soil. In order to estimate these properties as they occur in the field it is necessary to know the relative importance of the variables which may exist, Some studies have been made to determine the effects of confining pressure, relative density, or per cent saturation on the velocities of wave propagation and damping in soils, for example, the papers by K. Iida1'2, G. Shumway3, and B. O. Hardin and F. E. Richart4 However, there are several other variables which may have a significant influence on test results, S. D, Wilson and E. Ao Sibley5 have shown comparisons between values of the constrained modulus of elasticity as determined from seismic tests, laboratory vibration tests, and static confined compression tests, The amplitudes of deformation differ by orders of magnitude in these three testing methods. The smallest deformations are associated with the seismic tests while relatively large deformations are necessary to insure accuracy of measurement in the confined compression tests, The results obtained by Wilson and Sibley show that the seismic determination gives the highest value of constrained modulus while the confined compression tests give the lowest values, The primary object of this investigation was to determine the relative importance of the effect of amplitude of vibration on the wave velocity. The resonant column method was used to determine the velocity of the shear and longitudinal waves in a column of soil 11 inches long which was fixed at one end and free at the other, All test results are -1

-2related to the amplitude at the free end of the specimen. This amplitude varied from about 2x10-6 to 1x10-3 inch.double amplitude in longitudinal oscillation and from about lxlO to 2.5xlO 3 radians double amplitude in torsional oscillation.

THEORIES USED IN THE EXPERIMENTAL DETERMINATION OF WAVE VELOCITY The wave velocity through a column of soil was determined from the resonant frequency of the column when excited into longitudinal or torsional oscillation. The resonant frequency is that frequency which produced the maximum amplitude of oscillation at the upper, free end of the specimen. For this type of test equipment, the resonant frequency, f, for the first mode of vibration is associated with a wave length which is four times the length of the specimen. Thus, by designating the specimen length as L' and the wave length as L, the wave velocity may be calculated from the relationship v = fL = 4fL' (1) From the computed values of shear or longitudinal wave velocities, the shear modulus and longitudinal modulus of elasticity may be evaluated from vL = p (2) and VS = (3) In Equations (2) and (3), p = y/g is the mass density of the material, E is the dynamic longitudinal modulus of elasticity, G is the dynamic shear modulus, vL is the longitudinal wave velocity, and vS is the shear wave velocity. The specimens used in this research were fixed at the base and the driver and pickup were fastened to the top free end. Therefore -3

-4a correction was applied to correct for the added mass at the end of the specimen. The solution governing the natural frequency of such a system under torsional vibrations is given by cL' tan cL' = I (4) vG uG -lo ( I where Io is the mass polar moment of inertia of the mass attached to the free end, I is the Mass polar moment of inertia of the specimen of length L', and Xo is the circular frequency (2if). Equation (4) must be solved graphically or by trial and error. It is convenient to put Equation (4) into the form B tan = I (5) Io Thus, v 2tfL' (6) P

LABORATORY TESTS OF VELOCITY IN GRANULAR MATERIALS Materials Four different materials were used in this investigation. Each is described below and the grain size curve for each is shown in Figure 1. Ottawa sand, Standard Ottawa sand passing the No. 20 sieve and retained on the No. 30 sieve was used for most of the investigation. This material has a minimum void ratio of 0.50 and a maximum void ratio of 0~77. It has a specific gravity of 2.67. Glass beads No, 2847. Glass beads, all of which lie between the No. 16 and No. 20 sieve, were obtained from the Prismo Safety Corporation, Huntingdon, Pennsylvania. These beads appear to be perfect spheres when examined under a microscope. They have a specific gravity of 2.50, a minimum void ratio of 0~57 and a maximum void ratio of 0.75. Glass beads No, 1725, This material was also obtained from the Prismo Safety Corporation. Ninety-five per cent pass the No. 200 sieve and 96 per cent are retained on the No, 400 sieve. They have a high specific gravity of 4.31 resulting from the requirement of a high index of refraction for their commercial use. The minimum void ratio for this material is 0.57 and the maximum void ratio is 0.76. Novaculite No, 1250, This is a very find quartz powder obtained from the American Graded Sand Co,, 189-203 East Seventh Street, Paterson 4, New Jersey, This material was considered to be a silt as shown by the grain size curve in Figure 1o Equipment Two pieces of equipment were specially designed and built to vibrate the specimen at relatively large amplitudes in the longitudinal and -5

I00 90 GLASS BEADS ~~~NO. 2847 ~~~~NO. 1250 p-0 OTTAWA H- SAND'1 70.. (O I GLASS NO. LLJ BEADS1725 60 m 50 Z 40 I.L I — Z 30..... U.J LLI 20...... 0 I 0-~~~~lI[ II.......111I, I t,~I!I J I.... 1.) 0.5 0.2 0.1 0.05 0.02 0.01 0.005 0.002 0.001 GRAIN DIAMETER IN mm. Fig. 1. Grain Size Curves for the Materials Used in the Present Research.

-7torsional modes. Each was constructed so that one end of the specimen was free and the other was fixed as shown in Figures 2 and 3. Both pieces of equipment are basically the same except for the driver and the pickup as shown in Figure 2, The frames were made from a piece of 4 inch steel pipe with lead attached for added mass to give a total weight of about 30 lbs. for each apparatus. This is necessary in order to reduce the movement of the "fixed" end to a negligible amount. Power to the driving coil was supplied through an amplifier connected to an oscillator in the MB Electronics Type P11 power supply. Pickups were calibrated with an MB Electronics Model C31 calibrator and also with an MB Electronics Type 115 vibration pickup. A Tektronix Model 502 dual beam oscilloscope was used for the measurement of output from the pickups and also for monitoring the input to the driver. A more detailed description of the equipment and testing procedures was given by J. R. Hall6, Summary of Tests Three groups of tests were run and are summarized as follows: Group Io These tests used specimens of Ottawa sand to obtain data on the effect of amplitude on wave velocity, The test variables included the confining pressure, pore fluid (air, water, and dilute glycerin), and the relative density of the material, Group II.o After tests of Group I were completed, tests were run on samples of each of the two sizes of glass beads in the dense condition both dry and saturated.

(a) Torsional Vibration Apparatus. (b) Longitudinal Vibration Apparatus. BRASS ROD BRASS RODS KF~RAMER~~~ A = = ESOFT STEE FRAME galI IIg I ERMANENT MAGNET PICKUP COIL PERMANENT PERMANENT MAGNET MAGNET BRASS ROD COIL COIL SPECIMEN TOP VIEW SIDE VIEW Fig. 2. Vibration Mechanisms Used in the Present Research.

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-10Group IIIo A torsional vibration test was run to determine the variation of velocity with amplitude for a specimen of Novaculite No. 1250 in the dry condition. Results of Velocity Group I. Figures 4 through 6 are representative of the results for velocity in torsional and longitudinal oscillation as calculated from the tests of Group I on Ottawa sand. In these tests the variation of velocity with amplitude of vibration was determined for various confining pressures, density, and pore fluids (air, water, and dilute glycerin). The confining pressures chosen for each test were approximately 5, 10, 25, and 50 lb/in2 and the results at each pressure are plotted in the same figure. Tests were run using the sand in both the loose and dense conditions corresponding to void ratios of approximately 0o65 and 0o51, respectively. For saturation with dilute glycerin, the mixture was 3 parts water to 1 part glycerin. Pure glycerin was not used because its viscosity is so high that an unreasonable length of time is required to saturate the specimen0 Figure 4 shows the variation of velocity with amplitude for dense Ottawa sand, dry and saturated with water, in torsional oscillation0 Figure 5 shows the variation of velocity with amplitude for loose Ottawa sand, dry and saturated with water, in longitudinal oscillation0 The results for the specimen in the loose and dense conditions are essentially the same except for the change in velocity due to a change in void ratio, therefore curves for torsional oscillation of loose Ottawa sand and

-111300.... TEST'NO. 10 TEST NO. 14 e =O.52 DRY —... e =0.52 SATURATED 1200 I 100'r-: _07160 Lb/Ft 2 () 4L 900 to | o 362290 Lb/Ft2 o X i 0-' — ~O+.........-00 800 <- 11 95 Lb/ Ft2 it 700 ~ -J 1-455 Lb/ Ft2 mI 600 -— 0 — 119576 Lb/Ft2 400 L 0 1.0 2.0 x 10-3 DOUBLE AMPLITUDE, RADIANS Fig. 4. Variation of Velocity with Amplitude in Torsional Oscillation for Ottawa Sand Dry and Saturatuaed with Water.

-121700 TEST NO. 16 7240 Lb/Ft2 e 0.66 ~O —, —-- ~0 DRY ---- - 1600... TEST NO. 15 1500 -.. e_ = 0. 66 7200 Lb/ Ft2 SATURATED 1400.... (j 3600 Lb/Ft2'~~"~-J4 L 1 300 5750 Lb/Ft2 01 200 I Hi 7iI0_1455 L b/tFt 700.0 756 Lb/Ft2 700,, I I 0 0.5 1.0 x 10-3 DOUBLE AMPLITUDE,INCHES Fig. 5. Variation of Velocity with Amplitude in Longitudinal Oscillation for Ottawa Sand Dry and Saturated with Water,

-131 700 C TEST NO. 19 e =0.64 1600 * ___ SATU RATED 7360 Lb/Ft2 1 500 0 w - 1 400 z 1 40 0 1 3730 Lb/Ft2 o 1300 w_._ 1200 -J i Z i 0 00 0 0.5 X10.3 DOUBLE AMPLITUDEINCHES Saturated with Dilute Glycerin.

-14longitudinal oscillation of dense Ottawa sand are omitted. Figure 6 shows the variation of velocity with amplitude for specimens of loose Ottawa sand, saturated with dilute glycerin and excited into longitudinal oscillation. Group IIo Typical test results for the large size glass beads are shown in Figure 7~ These curves show the results of the variation of velocity with amplitude for samples in the dense condition, both dry and saturated, in longitudinal oscillation. Figure 8 shows results of the variation of velocity with amplitude in torsional oscillation for the small size glass beads in, the dense condition. The same specimens were used for both the dry and saturated tests of the glass beads. Group III o Figures 9 and 10 show the results for the variation of wave velocity with amplitude for a specimen of crushed quartz0 This specimen was formed by compaction of material which had been dried for several days at a temperature of 2200Co The behavior of the crushed quartz is quite different than that of the Ottawa sand or the glass beads because of the very small grain size0 The stress wave velocities depend upon the time of load application and stress history as well as upon the other variables0 During test No0 28, for which the initial void ratio was o083 under a pressureof 14 lb/in2, the specimen consolidated to a void ratio of o080 after having been subjected to a stress cycle with confining pressures as high as 50 lb/in2o After each pressure was applied to the specimen, measurements of the resonant frequency were made at different time intervals0 These time intervals are noted on Figures 9 and 10 and represent the total

-15TEST NO.23 -0o7240 Lb/Ft2 e o.58 1800 DRY...- SAT URATED 1700 7250 Lb/ Ft2 I 600 -— O 3720 Lb/F 2 3680 Lb/Ft2 LL 1 500 Oo 1400 -J 1 300 N''z 1477 Lb/Ft2 C1200.. 1200 1425 Lb/Ft2 o 1100 I7 5 Lb/Ft2 1000 749 Lb/Ft 2 900 I 0 0.5 x 10'3 0 0.5 x10'3 DOUBLE AMPLITUDE, INCHES Fig. 7. Variation of Velocity with Amplitude in Longitudinal Oscillation for Glass Beads No. ~2847 in the Dry and Water Saturated Condition.

1000 I TEST NO. 26 e = 0.58 DRY.... 7290 Lb/F 4t2- 0 " SATURATED 0 7290 Lb / Ft 2 I- 800 6 700 Lb/Ft 4 700 590 Lb/ __Ft - 600 02 DOUBLE AMPLITUDE,RADIANS Saturated469 LbFt ondition. 720 Lb/ Ft 2 < 500 - 742 Lb/Ft2 400 0 I x I(3 0 I x 10'3 DOUBLE AMPLITUDE,RADIANS Fig. 8. Variation of Velocity with Amplitude in Torsional Oscillation for Glass Beads No. 1725 in the Dry and Water Saturated Condition.

900 O TEST NO.28 C 80eo o. 83 800 U~ /1~-40HR. 7 00 7- 0 HR 7OO~3 I HR- "J 50 MIN. W 500 C CONSOLIDATED TO 4100 Lb/Ft 25 MIN. 600 I 5MIN. _<~ --- 26 HR. 0 —— "- 13 HR. DOUBLE AMPLITUDE,RADIANS Fig. 9. Variation of Velocity with Amplitude in Torsional Oscillation for Novaculite No. 1250 Consolidated to 2030 lb/ft2 and 4100 lb/ft2. 4100 lb/ft2.

1000 TEST NO.28 6 j I I | eo: 0.83 OU 900 0 MIN. CONSOLIDATED TO 7270 Lb/Ft2 0 1 2 3==-13.4 HR 800 -O-22. 8 HR. V i-I o 25 MIN boude t Ro45B EBOIINDED TO 4150 Lb/Ft 2 -----— 22.8 HR. OQ~~~~~~~~~~~~~~~HR -1'12 -15 MiIN. L 700 REBOUNDED TO 2050 Lb/ Ft 2 W | 12, |I C- _. _ - t HR 60 2 | 2-5 MIN (O 500 O 1.0 2.0 50 4x 0DOUBLE AMPLITUDE, RADIANS Fig. 10. Variation of Velocity with Amplitude in Torsional oscillation for Novaculite No. 1250 Consolidated to 7270 lb/ft2 and rebounded to 4130 lb/ft2 and 2050 lb/ft2.

-19elapsed time after the pressure was applied to the specimen. The stress history of test No. 28 was as follows: 1. The specimen was compacted, placed under a vacuum, and measurements were made for void ratio, The initial void ratio was 0.83~ 2. The specimen was placed in the triaxial cell and a pressure of 2030 lb/ft2 was applied. Velocity measurements were made intermittently over a period of 38 hrso 3. The pressure was raised to 4100 lb/ft2. Velocity measurements were made intermittently over a period of 140 hours. 4. The pressure was rebounded to 2050 lb/ft2 and measurements of velocity were made intermittently over a period of 12 hours, 5. The specimen was placed under a vacuum and measurements were made for void ratio. At this time the void ratio was 0o810' 6. The specimen was replaced into the triaxial cell and the pressure was raised to 7270 lb/ft2o Measurements of velocity were made intermittently over a period of 13 hours. 7~ The pressure was reduced to 4130 lb/ft2 and measurements of velocity were made intermittently over a period of 30 hours0 8, Final measurements under a vacuum gave a value of void ratio equal to o080o During the time intervals between measurements the specimen was not vibrated, The first measurements after each time interval were made at low amplitudes iof vibration, The following measurements were

-20made at increasing amplitudes until the maximum obtainable with the equipment was reached. Since the high amplitude vibrations affect the low amplitude measurements, a second set of measurements were usually taken after the specimen had been vibrating at high amplitudes for a period of approximately five minutes, These two methods of measurement are indicated in the figures by arrows on each curve.

DISCUSSION OF THE RESULTS Group I Figure 4 shows the results for Ottawa sand in the dense condition under torsional oscillation~ The results for this material in the loose condition were essentially the same and are not shown. The curves for the dry specimen show that the variation of velocity with amplitude is greatest at low confining pressures and low amplitudes of oscillation. The amount of velocity variation over the amplitude range measured is about 13 per cent at the low confining pressure and about 3 per cent at the high confining pressure. The results shown in Figure 5 for the longitudinal oscillations of the specimen in the dry and loose condition are very similar to those in Figure 4 for the torsional oscillations. The curves are similar in shape and the amount of variation of velocity is approximately the same order of magnitude. The results for specimens in the dense condition for longitudinal oscillations are not shown because they were essentially the same as for the loose condition. When the specimen was saturated with water the amount of variation of velocity with amplitude was decreased somewhat and most of it took place at small amplitudes. There was little variation of velocity with amplitude at the higher amplitudes of oscillation. Figure 6 shows the results for Ottawa sand saturated with dilute glycerin0 These curves are practically the same as those for the same material saturated with water0 Group II Figure 7 shows the results for the large size glass beads in the dense condition under longitudinal oscillation0 For this material -21

-22the effect of amplitude of vibration on the stress wave velocity is much more pronounced than that for the Ottawa sand. The saturated condition of the specimen gives a much greater variation of velocity in the low amplitude range than for the dry condition. The difference between the behavior of this material and that of Ottawa sand is probably due to the difference in the grain characteristicso The particles in both cases are rounded but the surface of the glass beads is much smoother than that of the Ottawa sand. The small size glass beads also show a larger variation of velocity wi.th amplitude than, does the Ottawa sand. The curves for the small glass beads in the saturated condition shown on Figure 8 do not flatten out as was indicated for the other test conditions. This difference could be due to the small grain size as well as the difference in the specific gravity of the particles~ As mentioned before, the specific gravity of this material is 4031 as compared to 2050 for the large size glass beads. If the tests for the small glass beads could be carried out to higher amplitudes the results might be similar to those for the Ottawa sand and the larger size glass beads. Group III Figures 9 and 10 show the results for the silt-size crushed quartz. As mentioned before, the dynamic properties of this material are time dependent. Consequently, the results are shown in terms of the time elapsed after the particular confining pressure had been applied0 For this material there was also a variation of wave velocity with amplitude of vibration. However, the behavior is much different than for the

-23other materials tested. The other materials showed the maximum amount of velocity variation within the small amplitude ranges while this material shows almost no variation in the same range of amplitude. It can be seen in Figure 9 that as the material is allowed to remain under a given pressure the velocity continues to increase. However, some of this build-up can be destroyed by vibrations of larger amplitude, as shown by Figure 9o After the specimen had remained at a confining pressure of 4100 lb/ft2 for 140 hours the variation of velocity with amplitude was as shown by the top curve. After the specimen had been vibrated at high amplitudes the lower curve for 1.40 hours was obtained. Figure 10 shows the results when the specimen had been consolidated to 7270 lb/ft2, rebounded to 4130 lb/ft2, and then to 2050 lb/ft20 When the confining pressure was reduced. from a high to a low pressure the velocity decreased, but when it was allowed to remain at the lower pressure the velocity increased. This increase can also be destroyed by high amplitude vibrations as shown by the lower of the three curves of Figure 10o

CONCLUSIONS The conclusions obtained from this study necessarily apply to granular soils which have been subjected to several load repetitions and have reached a relatively stable condition, This corresponds to construction conditions where the soil. has been pre-vibrated or pre-compacted to eliminate the disastrous settlements which may accompany the first dynamic load application on loose granular soils, The tests on Ottawa sand and glass beads gave results which should be typical, for clean sands with rounded grains, The more important conclusions are listed below: 1. Both the shear and longitudinal wave velocities decrease as the amplitude of vibration is increased. This decrease may be as much as 10 to 15 per cent as the double amplitude is increased from 1x10-5 to 2,5x10-3 radians in the torsion tests or from 2x10-6 to 1x10-3 inch in the longitudinal tests. 2., Tests have shown. that the effects on wave velocities produced by changes of void ratio from the maximum to the minimum value is about 10 to 15 per cent. Thus void ratio changes and changes of amplitude infl.uence the wave velocities by comparable amounts, Tests on the Novaculite No, 1250, a very fine-grained crushed quartz, produced results which were somewhat different from those obtained from the larger grained materials, The primary difference is that the wave velocity values obtained from laboratory tests are dependent upon -24

-25stress history and upon the time the loading has been applied. The wave velocity increases slightly as a particular confining pressure continues to be applied to the specimen. However, it was also found that the higher amplitudes of vibration tended to destroy this time-dependent increase in velocity. Further investigation is required in order to evaluate the time-dependent increase in wave velocity and the vibrational energy required to destroy this gain.

REFERENCES 1. Iida, Ko "The Velocity of Elastic Waves in Sand," Tokyo Imperial University, Bulletin, Earthquake Research Institute, 16, (1938) 131-144o 20 Iida, Ko "Velocity of Elastic Waves in a Granular Substance," Bulletin, Earthquake Research Institute, 17, (1939) 783-807. 3~ Shumway, Go "Sound Speed and Absorption Studies of Marine Sediments by a Resonance Method - Parts I and II," Geophysics, XXV, Nos. 2 and 3, (April and June, 1960) 451-467 (April) and 659-682 June)o 4~ Hardin, B. 0. and Richart, Fo E,, Jr0 "Elastic Wave Velocities in Granular Soils," to be published in the Journal of the Soil Mechanics and Foundations Division., ASCE, Spring, 1963o 5~ Wilson, S. D. and Sibley, E. A. "Ground Displacements from Air-Blast Loading, " Journal of the Soil Mechanics and Foundations Division, ASCE, (December, 1962) 1-31o 6. Halls J. R,, Jr., Effect of Amplitude on Damping and Wave Propagation in Granular Materials, Ph_ Dissertation, University of Florida, August, 1962o -26