AFWL-TR-65-161 FWL-TR161 co EXPERIMENTAL STUDY OF STATIC AND DYNAMIC FRICTION BETWEEN SOIL AND TYPICAL CONSTRUCTION MATERIALS G. A. Leonards Purdue University School of Civil Engineering Lafayette, India .. E C LEA R 1!4 c, ! .:. - . . FOR D- TECHNICAL REPORT NO. AFWL-TR-65-161 December 1965 AIR FORCE WEAPONS LABORATORY Research and Technology Division Air Force Systems Command Kirtland Air Force Base . New Mexico -' I" S .I 4~., -11"
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AFWL-TR-65-161 FWL-TR161
co
EXPERIMENTAL STUDY OF STATICAND DYNAMIC FRICTION BETWEEN
SOIL AND TYPICALCONSTRUCTION MATERIALS
G. A. LeonardsPurdue University
School of Civil EngineeringLafayette, India .. EC LEA R 1!4 c, ! .:. - . .
FOR D-
TECHNICAL REPORT NO. AFWL-TR-65-161
December 1965
AIR FORCE WEAPONS LABORATORYResearch and Technology Division
Air Force Systems CommandKirtland Air Force Base .
New Mexico -'
I" S .I
4~.,
-11"
ApwL-TR-65-161
R , -
I Research and Teerhology r-..- vision... ..... .... ..... iAR OIC . L r ATOIY
- j AIR FORCE WIAC AFTATR.... ....... .. Air For-re Systems 0,.,.and
-,D~ w .... Kirtlazi Air Force Base$ v. Mexico
When U. S. Government drawings, specifications, or other data are used forany purpose other than a definitely related Government procurement operation,tb. Government thereby incurs no responsibility nor any obligation whatsoever,ad the fact that the Government may have formulated, furnished, or in any
* way supplied the said drawings, specifications, or other deta, is not to beregarded by implication or otherwise, as in any manner licensing the holderor any other person or corporation, or conveying any rights or permission to
* manufacture, use, or sell any patented invention that may in any way berelated thereto.
This report is made available for study with the understanding thatproprietary interests in and relating thereto will not be impaired. Incase of apparent conflict or any othcr questions between the Government'srights and those of others, notify the Judge Advocate, Air Force SystemsCoimand, Andrews Air Force Base, Washington, D. C. 20331.
Distribution of this document is unlimited.
I4vi
AFWL-TR-65-161
EXPERIMENTAL STUDY OF STATIC AN'D D' NAHIC
FRICTION BETWEEN SOIL AND TYPICAL CONSTRUCTION MATERIALS
G. A. LeonardsPurdue University
School of Ciril EngineeringLafayette, Indiana
Distribution of this documentis unlimited.
V!
FOREWORD
This report was prepared by the School of Engineering, PurdueUniversity, Lafayette, Indiana, under contract AF 29(601)-5204. Theresearch was performed under Program Element 7.60.06.01.D, Project
Vi 5710, Subtask 13.144, and was funded by the Defense Atomic SupportAgency (DASA).
Inclusive dates of research were 1 April 1962 to I April 1965.The report was submitted 24 November 1965 by the Air Force WeaponsLaboratory project officer lLt John E. Seknicka (WLDC).
JO E. SEKNICKAILt, USAFProject Officer
AYROBERT E. CRAWFORD JOHN W. KODIS(f Major, USAF Colonel, USAF
Deputy Chief, Civil Engineering Chief, Development DivisionBranch
ii
ABSTRACT
A report is made of research carried out at Purdue University to determine, onthe basis of laboratory measurements, the coefficient of friction between two
8sands of different gradation (one vith angular and the other with rcundedparticles) in contact with Portland cement mortar, steel, teflon, and graphite.In the static tests, loads were applie. at a uniform rate until sLip occurredin approximately 5 minutes. Dynamic loa4. were applied by means of a shocktube, which produced a gcep-like forcing function; slip usually occurred inapproximately 2 milliseconds or less. It was foind that the coefficients offriction depend on the relative size, shape and surface roughness of the sandgrains with respect to that of the surface in question; when the sliding surfaceis "rough" in comparison with the sand particles, the coefficient of frictionapproaches the coefficient of internal friction of the sand. Both graphite andteflon serve as friction reducers, compared to the plain surfaces, irrespectiveof the rate at which slip is initiated. For plain steel or cement mortar, thedynamic coefficient of friczion was greater than the static coefficient offriction by about 25 percent, unless the static coefficient was such thatsand/sand slip was approached. The angle of shearing resistance of the sandthus provides an upper limit to the coefficient of wall friction at all ratesof loading.
iii
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iv
TABLE OF CONTENTS
Section Page
I INTRODUCTION. . . . . . . . . . . . ....... 1
II EXERIMENTAL CONCEPT ........ ........ 2
General Considerations . ...... . . . . 2Dynamic Friction Force .... 4Inertia Force. ................. 6Dynamic Nomal Force ............. 6
2. Brtmind, W. F., 1965, "Static and Dynamic Coefficients of Friction
Between Sand and Selected Construction Materials," M.S.C.E. thesis,
Purdue University, Lafayette, Indiana.
3. Leonards, G. A., 1963, "Labc-atory Experiments on the Response of
Soils to Shock Loadings," Technical Documentary Report No. AFSWC-
TDR-62-90.
4. Kennedy, D. J. L., 1961, "A Study of the Failure of Liners for Oil
Wells Associated with Compaction of Producing Strata," Ph.D. thesis,
Graduate College University of Illinois, Urbana, Illinois.
5. Suklje, L. and Brodnik, J., 1963, "Deformation Conditions of the
Mobilization of the Friction between Concrete and Soil," Acta
Geotechnica 4-6, Ljubljana, Yugoslavia.
6. Potyondy, J. G., 1961, "Skip Friction Between Various Soils and
Construction Materials," Geotechnique, Vol. XI, Number 4, Institution
of Civil Engineers, London.
55
A PENDIX A
DETERMINATION OF THE FORCING FUNCTION
The shock tube used to produce the forcing function had a 4.5-f" -t
rarefaction chamber and a 4.0-foot compression chamber with an ir ±de
diameter of 2.75 inches. Details of the relatively inexpensive shock
tube that was constructed may be found in Reference 3.
T wo methods were used to evaluate the forcing func-ion. First,
piezoelectric gages were placed on a rigid piston r-~itioned in the
downstream end of the shock tube. The average recorded pressure times
the area of Che piston was taken as the magnitude of the forcing function,
which is shown plotted in Figure 2. By placing piezoelectric gages in
the sidewalls of the shock tube, the shock wave velocity and the over-
pressure were measured directly, which permitted comparing of the
theoretical reflected pressure on the piston with that actually
recorded (1). The theoretical pressure acting on the fixed piston was
about 7-10 percent greater than the pressure actually recorded by the
gages. Part of this difference can be atrributed to leakage around
the piston face.
The forcing function, F(t), having been determined, as described
above, a moveable piston was placed in the downstream end of the shock
tube. By measuring the velocity of this system with the LVDT, a set of
time-displacement curves was obtained, which are compared with those
obtained by double integration of F(t) = m dv/dt in Figure 28. It is
evident that excellent agreement was obtained.
56
0
'iw
_ _ _ _ _0 >
ww
___ 0- z
Jz 0
w_j Uo0q
coo: 4 _ _ _
-w.j wf
~WWO
6s 0 0 c;
WsOWu) IN3PI3OVISIO
57
APPENDIX B
USE OF LINEAR VARIABIE DIFFERENTIALTRANSFOR4ER FOR VELOCITY MEASUREMENTS
A Schaevitz No. IOOOSL LVDT, consisting of a hollow cylindical
nonconductive coil form about 5/8 inch in diameter was used. Three
independent equally spaced coils are wound on the coil form. The
center coil is the primary winding and the two flanking coils are
secondaries. The transformer is provided with a cylindrical shield,
fitting tightly around the coils, for both physical protection and
electrostatic shielding from random electrical radiations. Inside the
hollow coil form is a coaxial steel core about 1/4 inch in diameter.
If direct current is fed to the primary coil, the core is converted
into a magnet, setting up a flux field around it. If the core is moved,
the flux field moves through the secondary coils, inducing a direct
current voltage whose magnitude is proportional to the speed of the
core, and whose phase is determined by the direction of motion of the
core. If the secondary coils are connected in "series adding," the
output voltages are amplified. The circuit needed to use the 1000SL
LVDT as a velometer is shown in Figure 29.
To calibrate the LVEJT, the core was connected to a piston in the
shock tube and displaced a known distance (about 0.2 inches) from the
end plate by means of a micrometer. A shock wave was generated in
the tube and the output from the LVDT was recorded through the oscillo-
scope. A typical record is shown in Figure 30. The area under this
curve equals the known initial displacement, whence a calibration factor
of 258 inches/second-volt was obtained when the primary coil current
58
S -
SCHAEVITZ 1000 SL LVDT
PRI SEC I SEC II
YB YR R BLU GR BLK
TERMINALBLOCK
It N
SKL MODEL302 FILTER
OUT -
.5K POT. AW INPUT
Eu 3 VOLTS TEKTRONIX16:15 MA MODEL 502
SCOPE
FIG. 29 CIRCUIT DIAGRAM FOR LVDT USED AS
A VELOCITY TRANSDUCER
59
" - Tw-
FTG. 30. TYPICAL TRACE FOR VELCNETER CALIBRATION
60
was 15 milliamps. The procedure was repeated with a variety cf dummy
loads added to the piston. In this manner the LVDT coil was moved over
the range in velocities that developed in the dynamic friction tests
without significant variation in the calibration factor.
61
SAM.Zk AJ" ~
itatic Tests
In the static test, the applied load minus the force needed to
overcome the restriction of the rubber membrane at each end of the
sample equaled the effective static friction force. By placing the
rod in a sleeve to isolate it from the surrourding sand, the restraining
force due to the membrane was measured and found to equal 9 pounds.
The confining pressures reported are nominal gage pressures. It
was found that the vacuum gage was not accurate, and a calibration,
using a mercury manometer, was performed (Figure 31). All computations
used corrected gage pressures.
Sample Calculation:
Referring to Figure 24, for 20-30 sand cn Teflon coated steel
(static test No. 15),
am = 5 psi gage
Applied force - 79 lbs. (Virgin Pull)
The lateral area of the square steel rod is:
A = 4 x 1 1/8 x 10 = 45 square inches.
Therefore, F - FNS A x am actual
91= 79 - 9 = -0 = 0. 33
S45x4.75 214
This result may also be found in Table V.
62
8 10 12
FG. 31VCUMGGECLBRTO
12- - --
663
4 /2 /_____
0 2 4 6 8 I0 12
VACUUM GAGE (psi)
FIG. 31 VACUUM GAGE CALIBRATION
63
Q -:- - _ - - ..
Dynamic Tests
For 60-SO sand on plain steel (dynamic test No. 2000 R)
1. Membrane pressure =crm = 5 psi gage
Therefore, N1s = 214 pounds
2. Forcing function (shock tube pressure = 40 psig).
From Fig. 2, F(t) = 185 pounds at 2 milliseconds (since
F(t) can be determined with an accuracy of +5 pounAs, no
attempt was made to correct for the restrictbe effect of
the membrane).
3. Mass of moving system
m= 1.43 x 10- 2 lbs. - sec2
in.
4. LVDT constant
in258 sec-volt at 15 milliamperes through primary coil
Sample Calculation:
Interpreting the LVDT trace shown in Figure 25,
sweep = 0.002 seconds/centimeter
sensitivity (top) = 0.02 vclts/centimeter
slope of trace after slip:
2.4 cm x 0.02 volts= 12 volts
0.002 sec. sec2 cm x cm
The acceleration is:
12 Volts x 258 in 3.1 x 103 in/sec2
sec sec-volt
64
= F(t) - maTherefore, = d
d Ns
= 195 - (143 x0- 2 ) (3.1 x 1o3)14
= 0.66
This result may also be found in Table Vill.
65
1TCT A"STp;TRflSecurity Classification
DOCUMENT CONTROL DATA -R&D(Security clessi.ication of title, body of abstrsct and indexing annotation must be entered when the overall report to classied)
I ORIGINATING ACTIVITy (Corporate author) 2. REPORT SECURITY CLASSIFICATION
Purdue University UNCLASSIFIEDSchool of Civil Engineering zb GROUP
Lafayette, Indiana3 REPORT TITLE
*. EXPERIMENTAL STUDY OF STATIC AND DYNAMIC FRICTION BETWEEN SOIL AND TYPICALCONSTRUCTION MATERIALS
4. DESCRIPTIVE NOTES (Type of report and Incluelve de.)
1 April 1962-1 April 19655. AUTHOR(S) (Lost name. ft.-at name. Initial)
Leonards, G. A.
6. REPORT DATE 70- TOTAL NO. OF PAGMS 7b. No. or mars
December 1965 76 6so CotiTRACT OR GRANT NO. AF 29(601)-5204 t s. OisiNATOM'S REPORT NUMBER(S)
b. PRoJECT NO. 5710 AFWL-TR-65-161
SSubtask No. 13.144 Sb. OTHIER RPORT NO(S) (Any other nmb.re that may be a.iodthis repoto
d.
1. A V A ,L ABILTY/ LMTATON NOTICE$Distribution of this document is unlimited.
11 SUPPLEMENTARY NOTES 12. SPONSOPING MILITARY ACTIVITY
AFWL (WLDC)Kirtland AFB. NM 87117
13. ABSTRACT
A report is made of research carried out at Purdue University to determine, on thebasis of laboratory measurements, the coefficient of friction between two sands ofdifferent gradation (one with angular and the other with rounded particles) incontact with Portland cement mortar, steel, teflon, and graphite. In the statictests, loads were applied at a uniform rate until slip occurred in approximately5 minutes. Dynamic loads were applied by means of a shock tube, which produced astep-like forcing function; slip usually occured in approximately 2 millisecondsor less. It was found that the coefficients of friction depend on the relativesize, shape and surface roughr.ess of the sand grains with respect to that of thesurface in question; when the sliding surface is "rough" in comparison with thesand particles, the coefficient of friction approaches the coefficient of internalfriction of the sand. Both graphite and teflon serve as friction reducers,compared to the plain surfaces, irrespective of the rate at which slip is initi-ated. For plain steel or cement mortar, the dynamic coefficient of friction wasgreater than the static coefficient of friction by about 25 percent, unless thestatic coefficient was such that sand/sand slip was approached, The angle ofshearing resistance of the sand thus provides an upper limit to the coefficientof wall friction at all rates of loading.
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