dilatational-wave-induced pore-water pressure in soil

Dilatational-wave-induced Pore-water Pressure in Soil

by W.A. Charlie, G.E. Veyera and D.O. Doehring

ABSTRACT--This paper examines peak and residual pore- water pressures in water-saturated soil induced by a dilatational stress wave. Our new laboratory testing device applies submillisecond, high pressure dilatational stress-wave Ioadings to water-saturated soil. The soil's initial effective stress, density, back pressure and saturation can be controlled with our device. Experimental results show that it is possible to induce residual excess pore-water pressure and liquefaction in water-saturated Monterey No. 0/30 sand. Liquefaction is induced with compressive strains exceeding 0.1 percent for loose samples consolidated at 172 kPa and 1 percent for dense samples consolidated at 690 kPa. Below a threshold compressive strain of about 0.005 percent, no significant residual excess pore-water pressures are developed.

List of Symbols B.,~ = bulk modulus of the mixture (kPa)

na

n w =

C = DR =

e = PPR =

PVC = R 2 _

S = Uex I/",=

Vp, = ep, =

Q. =

Q,V, = a t =

O R =

O'T =

Aup, = Aap, =

modulus of elasticity of the solids (kPa) bulk modulus of water (percent) pore-water pressure parameter relative density (percent) void ratio pore pressure ratio polyvinyl chloride coefficient of determination standard error of estimate residual excess pore-water pressure (kPa) compression wave velocity (m/s) peak particle velocity (m/s ) peak compressive strain (percent) total mass density (kg/m 3) acoustic impedance (kg/m 2-s) stress intensity of incident stress (kPa) stress intensity of reflected stress (kPa) stress intensity of transmitted stress (kPa) initial effective stress (kPa) peak change in pore-water pressure (kPa) peak change in compressive stress (kPa)

W.A. Charlie is Associate Professor of Civil Engineering, Colorado State University, Fort Collins, CO 80523. G.E. Veyera is Assistant Professor of Civil and Environmental Engineering, University of Rhode Island, Kings- ton, RI 02881. D.O. Doehring is Professor of Earth Resources, Colorado State University, Fort Collins, CO 80523. Original manuscript submitted: October 27, 1988. Final manuscript received: May 8, 1989.

Introduction Evaluating potential strength degradation of engineer-

ing materials from transient and cyclic loadings has received a considerable amount of study. For multi- phase particulate media, such as water-saturated sands, the shear strength is a function of several factors including the coefficient of friction of the soil grains and the normal stresses at the grain to grain contacts. Under gravity loading, increases in pore-water pressure will lead to a decrease in normal stresses at the grain to grain contacts and hence a reduction in the soil's shear strength. Pore-water pressure increases in granular soils have the potential to allow gravity to cause failure of earth slopes and settlement and uplift of surface and buried structures.

It is well documented that earthquake-induced distortional waves in water-saturated sands can lead to increases in pore-water pressure and loss of shear strength termed liquefaction. '.2 Limited documentation suggests that identical effects have also been triggered by explosion- induced dilatational stress waves2 -6 Increases in pore- water pressure in granular media also result in a reduction of the stress-wave propagation velocity of distortional and Rayleigh waves.

The classical methods for testing soils to determine the potential pore-water pressure increases under earthquake loadings have utilized cyclic triaxial, torsional shear, and simple shear apparatus3 .2.8 These tests are designed to measure pore-water pressure increase in soils subjected to cyclic shear strains induced by distortional waves which are generally assumed important for earthquake loading of soils.

The U.S. Army Waterways Experiment Station, the U.S. Air Force Weapons Laboratory, and others have developed testing equipment to rapidly apply compressive loads under plane strain conditions. 9.~~ However, because of boundary conditions and other factors, water-saturated soils have not been successfully evaluated.

This paper describes our new laboratory testing device developed to apply static and transient dilatational stress- wave loading to saturated soil3." The soil's initial effective stress, density, pore-water pressure and saturation can be controlled. Current testing utilizes saturated specimens that are consolidated and then subjected to submiUisecond dilatational stress-wave loadings. Pore-water pressure measurements are taken during and after the passage of the stress wave.

Exper imenta l Mechan ics �9 437

T h e o r y

The objective of our research is to systematically evaluate the undrained pore-water pressure response of saturated granular soil under dilatational stress-wave loading. Test equipment was developed to study the effect of variations in the soil 's initial effective stress, initial relative density, and the intensity of the applied compressive stress-wave loading,

The peak compressive strain, e~k, in a mixture of solids suspended in water can be calculated from the peak compressive stress increase, Aa~k, caused by the passage of a transient compression stress wave by the following equation.

Aa~k (1)

where B.~. is the bulk modulus of the mixture and is given by

1 e 1 1 1 - - - - + (2 )

B,,~ l + e B~ l + e B,

where e is the void ratio, B, is the bulk modulus of water and B, is the modulus of elasticity of the solid particles? 2 For plane strain, the peak compressive strain, E~k, and the peak shear strain, %k, are numericaly equal. '3 ' ' ' The peak radial particle velocity, Vpk, can also be calculated by the following equations which are based on elastic stress wave, propagation theory.

v , , = ~,, vo (3)

v,~ = A o , . / ( o , V , ) (4)

where V,~ is the peak particle velocity in the wave propagation direction, V, is the dilatational wave propagation velocity of the material, and O, is the total mass density of the material. The product, (o,V,) is called the acoustic

impedance.'5 The wave velocity through a mixture can be experimentally determined or calculated by the following equation. ~ 2

vo = (B , . , : / e , ) o.' (5)

As shown by eqs (1) and (3), the peak stress, peak strain and peak particle velocity are proportional.

When a stress wave strikes an interface between two dissimilar materials, part of the stress wave is transmitted across the interface and part is reflected. The magnitude of the stress reflected, a , , and the stress transmitted, ar, depends on the acoustic impedance of the materials on both sides of the interface and the incident stress, at. For incident dilatational stress waves traveling perpendicular to a boundary,

= [(o, vo)2- (o , vo),l (6) ~, ( o , v , ) , + ( e , vo),

and

or 2(0, V=)2 -- = (7)

a, (~ ,vo) .+ (~ .voh

where the subscript 1 denotes the incident wave medium and the subscript 2 denotes the transmitting medium.'5

Water at 20 ~ C has an acoustic impedance of 1,480,000 kg-m/m3-s. For soil, 0, and I,', will vary with saturation, void ratio, and density of the solids. Table 1 shows that the acoustic impedance of the saturated soil we tested ranges from 2,900,000 to 3,200,000 kg-m/m3-s. Utilizing an average acoustic impedance of 3,050,000 kg-m/m3-s, eqs (6) and (7) yield reflected and transmitted stress at a water soil interface of about 20 percent and 120 percent of the incident stress intensity, respectively.

If plastic strain occurs in the soil skeleton (particle to particle slippage or crushing) as a result of the peak strain induced by the stress wave, a pressure increase in the elastic pore fluid will occur. The increase in pore-water

/--'-- GAS PRESSURE

~oPP~, ~,~ --~ / ~ PoR~s / /--- ~Ro~cT~

~-~ - ~ ,.\\\, ~\, X- ,\\\\\\\\\\\\" a -~ ~ I

O-RING SEAL ACCUMULATOR RESERVOIR

OPEN TO ATMOSPHERE

Fig. 1 - - C r o s s section of the cannon

TO COMPRESSED GAS SUPPLY

438 ~ December 1989

pressure will be directly related to the plastic strain, the initial particle to particle stress and drainage conditions.

Experimental Apparatus Simulation of the type of loading produced by an

explosion or impact requires a dilatational stress wave of sufficient intensity and having a submillisecond time to peak stress. Measurement of pore-water pressure in such an environment requires special instrumentation and recording equipment.

The Gas Gun and Projectile Explosive loadings are simulated in our laboratory by

utilizing a projectile fired from a gas gun (Fig. 1). The gas gun subjects the projectile to a constant pressure and hence, constant acceleration, as it moves down the gas gun barrel. An interval counter is used to determine the actual projectile velocity as it leaves the gun barrel. We use a stainless-steel projectile having a mass of 2.88 kg, a length of 10.15 cm and a diameter of 6.80 cm.

The Fluid Shock Tube, Sample Container, and Momentum Trap

The stress wave is imparted to the fluid in the shock tube via a stainless-steel piston which is impacted by the projectile. The piston is separated from the stainless-steel

shock tube by rubber '0 ' rings to insure that the stress wave is transferred from the piston to the fluid and not to the stainless-steel tube. The projectile-induced stress wave is transferred from the piston to the soil sample in 0.8 ms by fluid contained in a rigid stainless-steel tube. As shown in Fig. 2, our fluid shock tube is 122-cm long with an inner and outer diameter of 8.90 and 11.44 cm, respectively. The fluid shock tube's length is greater than ten times the diameter to ensure a plane stress wave. Deaired water is used as the transmitting fluid.

Calculations based on water-hammer velocity in pipes predict a stress-wave velocity of about 1,450 m/s for our fluid shock tube? ~ Experimental calibration of the fluid shock tube produced similar velocities. Since 1,450 m/s i s

TABLE 1--STRESS-WAVE PROPAGATION PARAMETERS FOR WATER-SATURATED MONTEREY NO. 0/30 SAND

DR (percent) Void Ratio (e) ~, (kg/m 3) V,,j,(m/s) o,V,,~=

0 0.803 1915 1519 2,910,000 20 0.755 1940 1532 2,970,000 40 0.707 1967 1546 3,040,000 60 0.659 1995 1563 3,120,000 80 0.611 2024 1582 3,200.000

The compressive stress wave velocity in fresh water at 20~ is 1480 m/s. V,,~, is calculated from eqs (23) and (5).

TO INTERFACE PRESSURE VESSELS

tt HIGH PRESSURE ~LU(3 VALV~ ~ /

HIGH PRESSURE, ONE-WAY ooicK Drsco EcT VALVE \ r

~i'l~"~\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\~\" ,\~ \\, \\\\r ~\\\\- \~ ~

L.-.L.J \ - =ME~E o w , ~ xl.x , , \ ALONI FOIL

-- TEFLON SEAL 'V

ALTERNATE (NOT TO SCALE) PRESSURE LINE

SAMPLE 4 CONFINING PRESSURE TUBE ~- ~

CONTAINER

ALIGNMENT --BOLT HOLES

MOMENTUM TRAP q

/

Fig. 2--Cross section of the fluid shock tube, sample container and momentum trap

Experimental Mechanics �9 439

very close to the theoretical velocity of 1,480 m/s for water in a rigid pipe, both our shock tube and sample container can be considered rigid (i.e., no lateral strain).

Figure 2 shows a cross sectional view of the rigid-wall soil-sample container. It is 15.25-cm long and has an inside and outside diameter of 8.90 and 11.44 cm, respectively and has a 2.54-cm thick stainless-steel end plate. The sample container is bolted to the end of the fluid shock tube and a flexible latex rubber membrane is used to separate the confining tube and sample container so that the sample's initial effective stress can be varied. After saturation and consolidation, all valves are closed to ensure undrained conditions.

We utilize a momentum trap to minimize stress-wave reflections at the end of the sample. Solid PVC for the trap was chosen because it has an acoustic impedance close to water. The 2-m length was chosen to ensure that the full length of the stress wave was trapped. The PVC

Fig. 3--Photomicrograph of Monterey No. 0/30 sand

momentum trap reduces the intensity of reflections from the end of the sample container by about 80 percent.

Transducers, Data Recorders, and Computers

The pore-water pressure transducers used (Endevco Model 8511A-5KM1) have a natural frequency exceeding 500 kHz and a pressure range of 0 to 35,000 kPa. They are explosive air-blast transducers modified by the manu- facturer by placing a stainless-steel plate, in which a star pattern of small holes has been laser drilled, over the pressure sensing element. This plate is used instead of a porous stone to enable measurement of high-frequency pore-water pressure. Silicon oil, placed by the manufac- turer between the pressure sensor and the stainless-steel plate, ensures fluid contact between the sensor and the water in the sample and sensor saturation. These pressure ~transducers have proven to be very durable, accurate, and sensitive both during the transient passage of the stress wave and for measuring long term residual pore-water pressure. The transducers are located in the confining pressure tube to measure the incident compressive loading and in the sample container to measure the sample's pore- water pressure response (Fig. 2). As predicted by eq (7), the soil sample's peak pore-water pressure recorded during the tests is greater than the measured incident fluid pressure.

Voltage output from these transducers is amplified and the conditioned output is recorded by high-speed dual- time base digital waveform recorders. The dual-time base is particularly advantageous in recording transient and relatively long-term responses. The digital waveform recorders operate at a sampling rate of 50 kHz to record the transient pulse. After passage of the stress wave, the recorders automatically reduce the sampling rate to 200 Hz to record the long-term residual pore-water pressure.

A key component of the laboratory instrumentation and recording system is the computer. The computer is essential for controling the electronic instrumentation and analyzing the data. Recorded information is transferred from the waveform devices to the computer and stored on disks for detailed analysis at a later time. The computer and peripherals used in this study consist of a desktop computer, graphics plotter, disk storage device and line printer.

v

22B0

20BB

l B B 8

168B

14B8

128B

1080

8 8 0

6 8 0

400

2BB

B

~ ' ' ' ' ' ~ . ~ ' I~ '."3~'~'.' " ' ' ' ' ' ' ' ' ' ' ' ' ~ '

I~ ~ TEST IO No. : RD48-CP75-BP58-1}4~-L

r , i ,11, i , | , 1 , i , i , i ,1 , i , I , I , i , i ,1 , I , i , I , I , I ,

8

, i , l , l , [ , ) , l , l , l ' l ' l ' l ' ] ' t ' l ' l ' l ' l ' t ' l I]RTR FILE NRMES: I48X11 lind 54BXt l (LON)

INITIRL EFFECTIVE STRESS: 172 KPm INITIRL RELRTIVE gENSITY: 47.1

POREHRTER PRESSUE ~1 " I0 " .686

INCOMING

, .... ....... ,I ( - - - (ONE ]] IV. " . ~ 51EC)---> .~21 ( - - - (ONE DIV. " �9 125 SEC)--- : ' 5 . B 2 1

TIME (Seconds)

Fig. 4--Typical pressure- time histories for the shock tube's water and the sample's pore-water

440 �9 December 1989

Sample Preparation and Soil Properties

Testing Conditions and Procedure Samples of Monterey No. 0/30 sand are prepared at

five initial relative densities (0, 20, 40, 60 and 80 percent) and tested at four initial effective stresses (86, 172, 345 and 690 kPa). Each specimen is placed in the sample container using an undercompaction procedure to obtain the required density. '7 Full saturation is obtained by flushing the sample with carbon dioxide, followed by flushing with distilled, deaired water and, finally, a back pressure of 345 kPa is applied to the pore-water. Satura- tion is checked utilizing Skempton's 's pore-water pressure parameter C and the stress-wave propagation velocity as calculated from eq (5). After full saturation is reached, the samples are subjected to a transient, compressive stress-wave loading to examine the effect of loading intensity on the undrained pore-water pressure response. All samples are tested in dynamic uniaxial compression with no drainage allowed. Samples are subjected to single compressive shock loadings inducing peak transient pore- water pressures of 0.1 to 8.5 MPa.

The pore-water pressures in the sample and in the confining pressure tube are recorded throughout each test to determine the peak and residual pore-water pressures. Liquefaction is determined by calculating the pore-water pressure ratio (PPR) as shown in eq (8).

P P R - u,, (8)

where u,z is the residual-excess pore-water pressure above the initial pore-water pressure in the sample and tr" is the initial effective stress imposed on the soil particles. The residual-excess pore-water pressure is measured after passage of the stress wave. A PPR of unity indicates liquefaction while a PPR of zero indicates no increase in the residual-excess pore-water pressure.

Descr ipt ion of Soil

Monterey No. 0/30 material is a clean beach sand. The photomicrograph given in Fig. 3 shows that the soil grains are subangular to subrounded. The dominant mineral constituent is quartz. Basic physical and index properties for the Monterey No. 0/30 sand were evaluated according to accepted standard laboratory testing procedures set forth by the American Society for Testing and Materials. '9

TABLE 2 - -PHYSICAL PROPERTIES OF MONTEREY NO. 0 /30 SAND

USCS Class i f i ca t ion

Speci f ic Gravi ty

Part ic le Size Data Oso O,o Olo

Percent Passing #20 sieve Percent Passing #100 sieve

c. c,

Relat ive Densi ty Test Data: Dry-mass dens i ty

Max imum Min imum

SP

2.65

0.45 mm 0.38 mm 0.29 mm 100 percent 0.05 percent 1.65 1.00

1700 kg / m 3 1470 kg / m 3

A summary of the results is given in Table 2 and details of the tests are given in earlier papers. ",~~

Experimental Results and Analysis Our test results include the relationship between the

pore-water pressure ratio, PPR, and the peak compressive strain, epk, for confining pressures of 86, 172, 345 and 690 kPa and for five relative densities ranging from 3.8 to 87.9 percent. Typical pressure-time histories recorded by the pore-water pressure transducers located in the shock tube and sample are shown in Fig. 4. The results are for a sample from the '40-percent' relative density series (actual density of 47.1 percent) at an initial effective stress of 172 kPa. They are typical of .pressure-time histories observed in this investigation. The sample was subjected to a transient compressive stress wave inducing a peak increase in pore-water pressure, Aup,, of 1692 kPa above the initial pore-water pressure. As a result, the residual sample pore-water pressure increased by 105 kPa (PPR of 0.61).

TABLE 3 - - P E A K PORE-WATER PRESSURE, PEAK COMPRESSIVE STRAIN AND PORE-PRESSURE RATIO FOR MONTEREY NO. 0 /30 SAND (FIRST IMPACTS)

Test ID ~o DR Upk* Epkt PPR* (kPa) (percent) (kPa) (percent)

DR = '0-percent' Series 86 10.0 272 0.0061 0.33

172 4.6 461 0.0103 0.77 172 4.6 5711 0.1283 0.66 345 7.5 1222 0.0273 0.56 345 3.8 6585 0.1481 1.08

690 7.5 81 0.0018 0.02 690 5.8 2912 0.0653 1.01


172 27.9 534 0.0114 0.10 172 23.8 3817 0.0833 1.01 345 29.6 661 0.0143 0.23 345 27.5 5400 0.1172 0.99 690 28.8 380 0.0082 0.18 690 22.1 5768 0.1262 1.03


172 47.1 1692 0.0355 0.61 172 44.2 4524 0.0955 0.50 345 45.9 543 0.0114 0.06 345 46.7 4693 0.0987 0.83 690 46.7 742 0.0152 0.35 690 46.7 3845 0.0808 0.79


172 67.1 380 0.0077 0.16 172 61.1 4156 0.0850 0.83 345 66.3 290 0.0059 0.12 345 64.2 6022 0.1226 0.66 690 65.8 480 0.0097 0.18 690 62.5 5994 0.1224 0.62


172 87.9 950 0.0184 0.53 172 81.3 6867 0.1353 1.15 345 85.4 697 0.0136 0.36 345 83.3 8198 0.1607 0.33 690 86.3 715 0.0139 0.33 690 83.8 5966 0.1169 0.63

*Measured tCalculated

Experimental Mechanics �9 441

First impact results for 35 tests are summarized in Table 3 and plotted on Fig. 5. These experiments indicate that the residual pore-water pressure increases with increasing peak compressive strains and decreases with increasing initial density and initial effective stresses. The results of a multivariate regression analysis of the data given in Table 3 produced the following equation.

u,, = (16) (epk)~176 "~ (9)

where relative density, D,, and peak compression strain, e,~, are both in percent and the initial effective stress, ~o, is in kPa. The standard error of estimate of u,=, S, is 0.19 and the coefficient of determination, R 2, is 66 percent.

Peak compressive strains were calculated utilizing eq (1) and assuming that the peak change in the sample's pore- water pressure, Au,~, was equal to the peak change in the sample's total stress. For small strains in water-saturated soil, this is a good approximation provided that the drained constrained modulus of the soil skeleton is considerably less than B,,= given in eq (2).

Summary and Conclusions A new laboratory testing device was developed at

Colorado State University. It is capable of applying transient dilatationai stress-wave loading to water-saturated soil under undrained, uniaxial conditions. The new testing device and instrumentation improves the under- standing of the undrained behavior of saturated sands subject to transient stress-wave loadings.

Experimental results show that it is possible to induce liquefaction of saturated Monterey No. 0/30 sand by applying transient dilatational stress-wave loading. Residual pore-water pressure increases can be induced even in dense samples with high initial effective stresses. For

10 rY [2_ 0_

0 I.-- < 1 rY

Ld Od

U3 0'3 Ld ac 10 -1 . [2_

LLI n" 0 13-

1 0 -2

PLOT OF PPR vs PEAK STRAIN F i rs t I m p a c t s

i [ l I l I I I I

PPR = 1 UQUEF/~CTION t : ~ , ~ ! ~ . . . . . . . . . . . . . . _ . ; ~ o ~ - , , - - - - - - - - ~ . 7

J ' i " - I | i_ i - - - ~ . . . . . . . ~ . . . . . . . . . . .

/ / Io ',

/ L EQUA~O~ 9 FOR Or-- 1~ ~D ES- aS kPo I I

L EQUATIOI ~hl_,, g FOR D r == 8 0 ~ '4ND~N ES == 6 g 0 k P a O I t

I I I I

' I I I I I I I I 1 [ I [ I I I I l l I I I [ I I I I

0 -2 1 0 -2 1 0 -1 PEAK STRAIN (~ )

Fig. 5 - - P o r e - w a t e r p ressure ra t io as a f unc t i on of dens i t y and e f f ec t i ve s t ress fo r the f i rs t impac ts

dense samples, consolidated at an effective stress of 690 kPa, compressive strains on the order of 1.0 percent are required to liquefy the samples. Loose samples consolidated at 86 kPa require compressive strains in excess of 0.05 percent to induce liquefaction. The data suggest that below a threshold compressive strain of about 0.005 percent, significant residual excess pore-water pressures do not develop.

Acknowledgments

This research effort was funded by the Air Force Office of Scientific Research under Grant No. AFOSR-80-0260. This support is gratefully appreciated. Mr. Matt Muzzy conducted the basic physical and index properties for the Monterey No. 0/30 sand. The authors would like to express their thanks to Carol A. Smoot for typing this paper.

References

1. Seed, H.B., "'Landslides During Earthquakes Due to Soil Lique- faction, "" Fourth Terzaghi Lecture, J. Soil Mech. and Foundations Eng. Div., ASCE, 94 (SMS), 1053-1122 (Sept. 1968).

2. National Research Council, "'Liquefaction of Soils during Earth- quakes," Committee on Earthquake Engineering, National Academy Press, Wash., D.C. (1985).

3. Charlie, W.A., "'The Dial Pack Event, "" Proc. of the International Workshop on Blast-lnduced Liquefaction, U.S. Air Force Office of Scientific Research, Maidenhead, UK, 149-165 (Sept. 1978).

4..Charlie, W.A., Shinn, J. and Melzer, S., "'Blast Induced Soil Liquefaction, "" 2nd U.S. Nat. Conf. on Earthquake Eng., Stanford Univ., 997-1005 (Aug. 1979).

5. Charlie, W.A., Shinn, J., Melzer, L.S., Martin, J.P. and Blouin, S.E., "'Blast-lnduced Liquefaction Pehnomenon and Evaluation, '" Proc. Int. Symp. on Soils Under Cyclic and Transient Loading, Swansea, U.K., 533-542 (Jan. 1980).

6. Charlie, W.A., Veyera, G.E., Doehring, D.O. and Abt, S.R., "'Blast-lnduced Liquefaction Potential and Transient Porewater Pressure Response of Saturated Sands, "" Final Report prepared for the Air Force Office of Scientific Research Under Grant No. AFOSR-80-0260, Dept. of Ovil Eng., Colorado State Univ., Ft. Collins, CO (Oct. 1985).

7. Seed, H.B. and Peacock, W.H., "Test Procedures for Measuring Soil Liquefaction Characteristics, "" J. Soil Mech. and Foundations Div., ASCE, 97 (SM8), 1099-1119 (1971).

8. Ishibashi, L, Kawamura, M. and Bhatia, S.K., "'Effect of Initial Shear on Cyclic Behavior of Sand, "" J. Geotechnical Eng. Div., ASCE, 111 (12), 1395-1410 (Dec. 1985).

9. Jackson, J.G., Erghott, J.Q. and Rohani, B., "'Loading Rate Effects on Compressibility of Sand, "" J. Geotechnical Engineering Div., ASCE, 105 (GTS), 839-852 (1980).

10. Felice, C.W., Gqffney, E.S., Brown, J.A, and Olsen, J.M., "'Dynamic High Stress F_A'periments on Soil, '" Geotechnical Testing J., ASTM, 10 (4), 192-202 (Dec. 1987).

11. Vcyera, G.E., "'Transient Porewater Pressure Response and Lique- faction in a Saturated Sand, "" PhD Diss., Dept. of Civil Eng., Colorado State Univ., Fort Collins, CO (Fall 1985).

12. Richart, F.E., Hall, J.R. and Woods, R.D., Vibrations of Soils and Foundations, Prentice-Hall, Englewood Cliffs, NJ, 414 (1970).

13. Timoshenko, S.P. and Goodier, J.W., Theory of Elasticity, McGraw-Hill, New York, 567 (1970).

14. Dobry, R., Ladd, R.S., Yokel, R,Y., Chung, R.M. and Powell, D., "'Prediction of Porewater Pressure Buildup and Liquefaction of Sands During Earthquakes by Cyclic Strain Method, "' Nat. Bur. of Stand. Building Science Series No. 138, U.S. Dept. of Commerce, U.S. Govern- ment Printing Office, Wash., D.C., 150 (1982).

15. Rinehart, J.S., Stress Transients in Solids, Hyperdynamics, Inc., P.O. Box392, Santa Fe, NM, 230 (1975).

16. Streeter, V.L. and Wylie, E.B., Fluid Mechanics, 8th Ed., McGraw- Hill Book Co., New York, 586 (1985).

17. Ladd, R.S., "'Preparing Test Specimens Using Undercompaction, "" Geotechnical Testing J. ASTM, Philadelphia, 1 (1), 16-23 (March 1978).

18. Skempton, A.W., "The Pore-Pressure Coeff'wient A and B, "' Geotechnique, 4, 143-147 (1954).

19. American Society for Testing and Materials, Annual Book of ASTM Standard& Part 19, Philadelphia, 634 (1982).

20. Charlie, W.A., MuZZy, M.W., Tiedmann, D.A. and Doehring, D.O., "'cyclic Triaxial Behavior of Monterey Number 0 and Number 0/30 Sands, "" Geotechnical Testing J., ASTM, 7 (4), 211-215 (Dec. 1984).

442 �9 December 1989

dilatational-wave-induced pore-water pressure in soil

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