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A computer program for the analysis of sieve and hydrometer data
Computers & Geosciences Vol. 12. No. I, pp. 81-87, 1986 Printed in Great Brilain.
0098--3004/86 $3.00 + .00 © 1986 Pergamon Press Ltd.
SHORT NOTE A COMPUTER PROGRAM FOR THE ANALYSIS OF SIEVE AND HYDROMETER DATA ROBERT A. STEWART a n d BRIAN GEDLINSKE Department of Earth Sciences, Iowa State University, Ames, IA 50011, U.S.A.
(Received 27 March 1985; accepted 14 September 1985) phi value also is extracted. Swan, Clague, and Luternauer (1978) emphasize that to obtain the requisite percentiles for these statistics, Gaussian interpolations and extrapolations should be used. We therefore have followed their procedure, using their equation 12 (Swan, Clague, and Luternauer, 1978, p. 868), and the algorithm mentioned (Abramowitz and Stegun, 1965, p, 931-933). Where extrapolations beyond the finest percentile obtained in the analysis are necessary, the Gaussian function is used to extrapolate to 99.99% at 14 phi, again following the convention of Swan, Clague, and Luternauer (1978, p. 868). As pointed out by Swan, Clague, and Luternauer (1978), this technique, although arbitrary, does add consistency to the analysis of large numbers of fine-grained samples. The percentiles used to calculate the grain-size statistics of Folk and Ward (1957) then are listed along with the statistics themselves. The program has several advantages. It is fast and inexpensive both in terms of computing and plotting time in that it uses an interactive terminal and line plotter instead of a "hard" plotter. The statistical interpolations and extrapolations used are consistent with the assumptions implicit in plotting grain size distributions on probability paper (e.g., Folk, 1974; Swan, Clague, and Luternauer, 1978). We have learned that for use with Pleistocene tills, the distribution of grainsize classes is a useful way of examining the incorporation of glaciers of substratal materials, such as fluvial sands or older tills, into younger tills and other related glacigenic sediments.
We routinely use a combination of sieving (for sand) and ASTM 152H (Bouyoucos) hydrometer analysis (for silt and clay) to study Pleistocene tills and other sediments. We have developed a computer program to reduce rapidly these raw data, compute various grain-size statistics, and print a cumulative curve and histogram of class weight percent vs. phi class interval. The program is written in FORTRAN and is used with an interactive terminal and online printer coupled to a Digital Equipment Corp. VAX computer. The program (Appendix 1), sample input, and sample output (Appendix 2) are listed here. For sieve data, the program uses the raw weight of sediment on each sieve, the sieve mesh size in millimeters, and the total sample weight. Hydrometer input data include: elapsed time (in minutes), uncorrected hydrometer reading, hydrometer correction, and temperature. A combined maximum of 30 sieve and hydrometer readings can be used. The actual data reduction to this point is similar to the ASTM (1964) method, except that Wadelrs modification of Stokes' Law settling times (Wadell, 1936) also is incorporated into the program to better accommodate the heterogeneous shapes of particles finer than 63 microns. The program calculates grain diameters for silt and clay particles based on the effective depth of settling, elapsed time, temperature of the suspension, and particle density (taken as 2.65, although this value may be changed with a minor adjustment to an array). Output to this point for sieve data consists of phi size, size class weight percent, and percent of the sample finer and coarser than sand size; and for the hydrometer data, the particle diameter in millimeters and phi units (for Stokes' and Wadell's settling), and the percent finer and percent coarser than a given size. Additionally, the percentages of sand (2 mm to 0.063 mm), silt (0.063 to 0.002 mm) and clay (finer than 0.002 ram) also are calculated. The program provides two graphs on the line printer, first,a histogram of class weight percent vs. phi class interval, and secondly, a plot of cumulative weight percent vs. phi class interval. On the latter graph, the data arc plotted according to a probability scale using an algorithm for the approximation of the inverse norreal function outlined in Abramowitz and Stcgun (1965, p. 931-933). The final function of the program is to calculate the Folk and Ward (1957) graphic grainsize statistical parameters: mean, inclusive graphic standard deviation, skewness and kurtosis; the median
REFERENCES
Abramowitz, M., and Stegun, I. A., 1965, Handbook of mathematical functions:U.S. National Bureau of Standards, U.S. Government Printing Office, Washington, D.C., 1046 p. American Society for Testingand Materials, 1964, Procedures for testing soils (4th ed.): Philadelphia, Pennsylvania, 535 p. Folk, R. L., 1974, Petrology of sedimentary rocks: Hemphill Publ. Co., Austin, Texas, 182 p. Folk, R. L., and Ward, W. C., 1957, Brazos River bar--a study in the significanceof grain size parameters: Jour. Sed. Pet. v. 27, no. l, p. 327-354. Swan, D., Clague, J. J., and Lutemauer, J. L., 1978, Grain size statistics I: Evaluation of the Folk and Ward graphic measures: Jour. Sed. Pet. v. 48, no. 3, p. 863-878. Wadell, H., 1936, Some practical sedimentation formulas: Geol. F~ren. Forh/indl., v. 58, p. 397-407. 81
Sho~ Notes
82
APPENDIX 1 C T H I S PROGRAN CALCULATE3 FOLK AND WARD S T A T I S T I C S USING C
GRAIN SIZE
ANALYSIS DATA FRON HYDROHETER AND SIEVE RESULTS,
CHARACTER NAHE*20 REAL SNUNPEDEPTH(61), K V A L U E ( 1 5 ) , T E N P ( 3 0 ) , HYDR(30) REAL C O R R ( 3 0 ) , D I A N ( 3 0 ) , KUSED(30), PHI(30), WADPHI(30) REAL P F I N E R ( 3 0 ) , P C O A R S ( 3 0 ) t CORHYD(30), WDIAM(30) REAL W T ( 3 0 ) , WTF'ERC(30), X ( 3 0 ) , Y(30), XPHI(I01), INGAUS REAL TOTWT, RNTr RNHYDR, SAND, S I L T , CLAYt NEANe R REAL STDDEU, SKEW, KURT, HEDIAN, HOLD, X P , E D U S E D ( 3 0 ) e K E E P INTEOER N, l , J, INT, INTPI, INHR, INHRPI, M, 111 T I N E ( 3 0 ) C E
THE EFFECTIVE DEPTH TABLE VALUES BASED ON THE ACTUAL HYDROMETER READING OF HYDROHETER t 1 5 2 H . THESE VALUES ARE F'LACED IN THE EFFECTIVE DEF'TH A R R A Y - E D E P T H ( 6 1 ) ,
÷ ÷ ÷ + ÷ t: C C C
THE THE ARE THE
+ ÷
DATA EDEPTH/16,SP 1 6 . 1 , 1~.2, 15.0p 14.8, 14.7, 1].7, 13.5, 13.3, 13.2, 12.2, 12.0J 11.9, 11.7, 10.7, 10.6, 10.4, 10.2, 9.1, S.9, 8.8, 8.6, 8.4, 7.3, 7.1p 7.0, 6.8, 6.6,
16.0, 14.5, 13.0, 11.5P 10.1~ 8.3, 6.5/
15.8, 15.6, 15.5, 15.3, 14.3, 14.2, 14.0, 13.8, 12.9, 12.7, 12.5, 12.4, 11.4, 11.2, 11.1r 10.9, 9.9, 9.7, 9.6r 9.4, 9.2, 8.1, 7.9, 7.8, 7.6, 7.4,
TABLE VALUES OF ' K ' FOR USE IN THE FORMULA WHICH COHPUTES DIAMETER OF PARTICLES IN HYDROMETER ANALYSIS. THESE VALUES BASED ON A S P E C I F I C GRAVITY OF 2 . 6 5 AND ARE DEPENDENT ON TENPERATURE.
DATA K V A L U E / O . O 1 4 3 G , 0 . 0 1 4 1 7 t 0.01399, 0.01382~ 0.01365, 0.048, 0.01332, 0.01317, 0.01301, 0.01286, 0.01272, 0.012~8P 0.01244J 0.012301 0.01217/
C THE DATA FRON THE HYDROHETER EXPERINENT I S READ IN FROH A DATA FILE. THE NAME OF THE ANALYST ( N A H E ) , THE SANPLE NUHBER ( S N U N ) , THE TOTAL WEIGHT OF THE SANPLE (TOTWT), THE NUNSER OF READINGS C: ( H ) , THE TIHE ( T I I t E ) , THE HYDROMETER READINO (HYDR)e THE C CORRECTION (CORR)t AND THE TEMPERATURE (TEHP) ARE READ FRON THE F I L E . C ~
10 C C C C
DETERNININO THE VALUE OF ' K " DIAMETER. (KUSED)
20 C C C
READ ~ NANE READ Z, SNUM PRINT S , ' N A N E OF ANALYST . . . . ",NAME PRINT I , ' S R H P L E NUHBER . . . . . ,SNUN READ $ , TOTWT PRINT ~ , ' T O T A L MEIGHT OF SAMPLE . . . . . ~TOTWT READ ~, N PRINT $ p ' T H E NUHBER OF HYDRONETER READINGS . . . . . DO 10 I ~ I , N READ $f T I N E ( I ) p HYDR(I)r CORN(I), TENP(I) CONTINUE
DO 20 I - l e N INT-TENP(IJ INTPlmINT÷I-15 RNT-INT INT=INT-15 I F (RNT . L T . T E N P ( I ) ) IF (RNT .EO. T E N P ( I ) ) CONTINUE
,N
TO BE USED IN CALCULATING GRAIN
KUSED(I)~(KVALUE(INT)÷KVALUE(INTP1))/2oO KUSED(I)=KVALUE(INT)
DETERMIHINO THE VALUE OF " L ' (THE EFFECTIVE DEPTH) TO BE USED IN CALCULATINO GRAIN DIAMETER. THE EFFECTIVE DEPTH USED (EDUSED) I S DETERNZNED FRON THE TABLE VALUES OF THE EFFECTIVE DEPTH ( E D E P T H ) . DO 30 I = l , N INHR-HYDR(I)+I.0 RNHR~IHHR INHRPI=INHR+I I F (RNHR . L T . H Y D R I I ) ÷ I . 0 )
EDUSED(I)=(EDEPTH(INHR)÷EDEPTH
Short Notes
30
(INHRP1))/2.0 IF (RNHR . E O . CONTINUE
HYDR(I)+I.O)
CALCULATION OF THE ORAIN D)AMETER
40 C C C C C
DO 50 I = l , N WDIAM(I)=KUSED(I)ZSQRT(EDUSED(1)/TIME(I)~.64) CONTINUE
PHI.In(I/DIAH)/Ir,(2).
DO 70 l ~ l , N PHI(1)=LOO(1/DIAM(1))/0.69314718 CONTINUE
I, ETERMINING THE PHI SIZES USING WADELLS MODIFICATION. WADPHI~ln(1/WDIAM)/ln2
80 C C
(DIAM)~KUSED$(EDUSED/TIME)*$.5
DO 40 I = I , N DIAM(I)~KUSED(I)*SORT(EDUSED(I)/TINE(I)) CONTINUE
DETERMININO THE PHI SIZES.
70 C C C
EDUSED(I)-EDEPTH(INHR)
CALCULATION OF GRAIN DIAMETER USIN6 WADELL'S M O D I F I C A T I O N . DIAMET~R=WDIAM=KUSED$((EDUSED/TIME)~°64)~.5
50 L C C
83
DO SO I ~ I , N WADFHI(I)=LOG(1/WDIAM(I))/O.6931471B CONTINUE
CALCULATINB THE CORRECTED HYDROMETER READING. DO 75 I ~ I , N CORHYD(1)-HYDR(1)-CORR(I) IF (HYDR(I) .LT. CORk(It) CORHYD(1)-O 75 CONTINUE C CALCULATINO PERCENT FINER ( P F I N E R ) AND PERCENT COARSER ( P C O A R S ) o DO 9 0 I ~ I , N PFINER(I)-CORHYD(I)Z(IOO.O/TOTWT) PCOARS(1)~.IOO.O-PFINER(I) 90 CONTINUE PRINT $ ~ ' ' PRINT ' ( ' ' O ' ' P 2 O X ~ A ) ' , ' H Y D R O M E T E R RESULTS' PRINT ' ( ' ' O ' ' P A 4 ~ 3 X r A 1 2 p 3 X t A 1 1 ~ 3 X ~ A S ~ 3 X ~ A S ~ 3 X ~ A 6 ) ' ~ ' T I M E ' p ÷ 'HYD. R~ADIHO','MYD. CORRN.'r'TEMP.'~'K FCTo'~'L FCT.' DO 100 I - l e N PRINT ' ( . . . . ,15,2X,FS.2,10X,F4.2,10X,FS.2,3X,F7.612X,FS.2)', ÷ TIME(1), HYDR(1), CORR(1), TEMP(1), KUSED(I)~ EDUSED(I) 100 CONTINUE PRINT ' ( ' ' O ' ' , A S p 3 X p A S , S X ~ A S p 3 X ~ A B ~ 3 X ~ A g ~ 3 x r A g ) ' t ' PHI 'p + 'DIAM.'r 'W P H I ' ~ 'W D I A M . ' p 'PCT. FNR.'p 'PCT. CSR.' DO 110 I ~ l , N PRINT ' ( ' ' '',FS.2~3XrF7.5,3X~FS.2,3XtF7.Sp3X~F6.2pSXpF7o2)'p + P H I ( 1 ) r DIAM(I)~ WADPHI(1)r WDIAM(I), P F I N E R ( I ) t PCOARS(I) 110 CONTINUE C C SIEVE DATA FOR PARTICLES LESS THAN 2am. C "J';THE NUMBER OF S I E V E S I Z E S C READ ~wJ PRINT S p ' ' PRINT ~ , ' T H E NUMBER OF SIEVES . . . . . ~J DO 115 I ~ N f l ~ N + J READ *pDIAM(1)~ WT(1) WTPERC(1)=(WT(I)/TOTWT)$100.O WADPNI(I)'LOO(I/OIAM(1))/0.69314710 IF ( I .GT. M+l) THEN PFINER(I)~PFINER(I-1)-WTPERC~I) ELSE PFINER(I)-IO0.O END I F PCOARS(I)=IOO.O-PFINER(I) 115 CONTINUE F'F:INT'(''O''~A11~3X~AS~3X~AS~3X,AS,3XpA9~3X~A9)'~'DIAM. (BB)'t + 'WT. O M S . ' , ' PHI ' , 'WT° P C T ° ' , 'PCT. FNR°', 'PCT° C S R ° ' PRINT $~ ( ' - ' ~ I - 1 p 6 4 ) " PO 120 I = N + I e N + J , PRINT ' ( . . . . ,F7.4~7X,FS.2~6X,FS.2~3X~F7.2~4X,F7.2~SX~F7°2)'~ -,~ OIAM(I), WT(I), W A D P H I ( 1 ) , WTPERC(I)~ P F I N E R ( I ) , PCOARS(I) 120 CONTINUE
84
Short Notes DO 137 I = l p N + J X(I)mNADPHI(I) Y(I)mPFINER(I) CONTINUE DO 140 I a l t N + J - 1 11=I+1 DO 150 H = I l t N ÷ J IF ( X ( I ) , L T . HOLD=:X(I)
137
X(H))
THEN
X(1)=X(M) X(N)=HOLD KEEP=Y(I) Y(I)=Y(N) Y(N)=KEEP END I F CONTINUE CONTINUE PRINT ' ( ' ' O ' ' t A B ~ 4 X ~ A 1 3 ) ' t ' P H I SIZE', DO 160 I ~ I , N ÷ J PRINT ' ( ' " "'~FS°2tTXpF7.2)',X(I)PY(I) CONTINUE
150 140
'PERCENT
FINER'
160 C C 6RANULOMETRIC COMPOSITION DO 165 I = l w N ÷ J I1=I+1 IF ( X ( I ) .NE. X(I1)) THEN IF (X(II) . L E . 4 .AND. X ( I ) . G E . 4 ) THEN SAHD=IOO.O-(Y(I)÷(Y(I1)-Y(I))~(4-X(I))/(X(I1)-X(I))) ELSE I F ( X ( I I ) . L E . 9 .AND. X ( I ) .GE. 9 ) THEN CLAY-Y(I)÷(Y(I1)-Y(I))$(9-X(I))/(X(II)-X(I)) END I F END IF 165 CONTINUE SILT=IOO.O-SAND-CLAY PRINT ~ t ' ' PRINT ~t 'ORANULOHETRIC COMPOSITION' PRINT ~ t 'PERCENT SAND . . . . . '~SAND PRINT St 'PERCENT S I L T . . . . . . PSILT PRINT St 'PERCENT CLAY . . . . . . tCLAY DO 170 I = I , N + J I1=1÷1 IF (Y(I) .HE. Y~I1)) THEN DO 180 N = O t l O 0 R'N I F (N . G E . Y ( I ) .hND. H .LE. Y(ZI)) THEN XPHI(N)~X(I)÷(X(II)-X(I))~((INOAUS(R)-INOAUS(Y(I)))/ + (INGAUS(Y(I1))-INGAUS(Y(I)))) ELSE IF (N . L T . Y ( I ) ) THEN XPHI(N)=14.0+(X(I)-I4.0)~((INGAUS(R)-INOAU8(O))/ + (INGAUS(Y(1))-INGAUS(O))) END I F 180 CONTINUE END I F 170 CONTINUE PRINT ' ( ' ' O ' ' ~ 2 X t A 4 P 3 X I A 4 ~ 3 X ~ A 4 t 3 X t A 4 ~ 3 X ~ A 4 t 3 X I A 4 t 3 X t A 4 ) ' t +
+
+
÷
+
'5~','16X't'25X't'50g','75X','S4~'~'95X' PRINT Sr ( ' - ' p I = l e 4 8 ) PRINT ' ( . . . . tF6.2tlXtF6.2tlXJF6.2P1XtF6.2tlXpF6.2PIXe F6.2p1XpF6.2)'pXPHI(5)pXPHI(16)PXPHI(25)tXPHI(50)tXPHI(75)t XPNI(S4)PXPHI(95) MEDIAN-XPHI(50) HEAN=(XPHI(16)+XPHI(50)fXPHI(84))/3.0 STDDEV=ABS((XPHI(B4)°XPHI(16))/4.0+(XPHI(95)-XPHI(5))/6.6) SKEW=-I$((XPHI(16)+XPHI(S4)-2~XPHI(50))/(25(XPHI(84)-XPHI(16))) ÷(XPHI(5)+XPHI(95)-2~XPHI(50))/(25(XPHI(95)-XPHI(5)))) KURT=(XPHI(?5)-XPHI(5))/(2.441(XPHI(75)-XPHI(25))) PRINT " ( ' ' O ' ' t A 6 t 3 X ~ A 6 P 3 X p A 6 p 3 X , A S , 3 X t A 8 ) ' P ' N E D I A N ' , '~EAN', "STDDEU'~ 'SKEWNESS', 'KURTOSIS' PRINT ~w . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . F RZNT " ( . . . . ~F6.3t3XtFb°3t3X~F6.4t3XtFS.5~3X~FS.5)'~ H E D I A N t HEANe STDDEVt SKENt KURT CALL PLOT ( X t Y, N + J ) STOP END REAL FUNCTION I N O A U S ( O ) REAL C O t C 1 , C 2 , D 1 , D 2 , D 3 , Y , T , O X , Q C0~2.515517 C1=0.802853 C2-0.010328 D1-1.432788
Short Notes D2~0,189269 D3=O.OO130G OX-O/lO0.O IF (QX . E O . O) GX=O.O001 I F (QX , E G . 1) OX:~O.9999 IF (GX , L E . 0 . 5 ) THEN T=SGRT(LOG(IlGX~2)) ELSE T-GORT(LOG(1/(1-QX)*~2)) END I F Y-T-(CO+CI~T÷C2~T~2)/(I÷DI~T÷D2ZT$&2÷D3$T$~3) I F (OX . L E . 0 . 5 ) THEN INOAUS~Y ELSE INGAUS'-Y END I F RETURN END T H I S SUBROUTINE PLOTS A HISTOGRAM OF THE PERCENTAGE OF SEDIHENT CONTAINED IN HALF PHI I N T E R V A L S . I T ALSO PLOT8 THE CUNULATIVE PERCENTAOEG FOR HALF PHI I N T E R V A L S . SUBROUTINE P L O T ( X X P Y Y ~ N ) REAL X X ( N ) , Y Y ( N ) , R A N G E , P E R ( 2 S ) e S U N w P H I ( 2 6 ) INTEGER NJ NUN, I , J~ COUNTt L I N E ( I O 0 ) CHARACTER I N T R V L ( 2 5 ) I I G t GRIDZ115 DATA I N T R V L / ' 1 1 AND FINER I ' ,'10.5 TO 11 I', |'p + ' 1 0 TO 1 0 . 5 ','9.5 TO 10 ",'9 TO 9 . 5 + ' 8 . 5 TO 9 ','O TO B . 5 ','7.5 TO B I'e ÷ ' 7 TO 7 . 5 "~'6,5 TO 7 ' , '6 TO 6 . 5 I'! + "5.5 TO 6 ','5 TO 5,5 ' , '4.5 TO 5 |'9 ÷ ' 4 TO 4 . 5 ','3.5 TO 4 ','3 TO 3 . 5 |'e I'p + ' 2 . 5 TO 3 ','2 TO 2 . 5 ','1.5 TO 2 |'p + ' 1 TO 1 , 5 ','0.5 TO I ','0 TO 0 . 5 ,/ + '-0.5 TO 0 ','-1 TO - 0 . 5 DATA L I N E / l O O n ' '/ DATA GRID / ' I ......... I ......... I ......... I ÷......... I ......... i ......... I ......... I ......... I ......... I +......... I'/ PHI(O)uO.O RANGE t 1 1 . 0 NUH= 1 DO WHILE (RANGE . G T . X X ( 1 ) ) PHI(NUH)=-IO((14.0-RANGE)8-YY(1)/(14.0-XX(I))) PER(NUN)-PHI(NUH)-PHZ(NUH-1) NUN - NUN÷I RANGE - R A N G E - O . 5 END DO DO 5 I = N U H , 2 5 DO 10 J = l r N Jl = J + 1 IF (RANGE . L T . X X ( J ) .AND. RANGE . B E , X X ( J 1 ) ) THEN PHI(I)aYY(J)-((XX(J)-RANOE)8(YY(J)-YY(J1))/(XX(J)-XX(JI))) PER(I)LPHI(I)-PHI(I-1) END IF 10 CONTINUE RANGE = RANGE-Oo5 CONTINUE 5 PRINT ' ( ' ' O ' ' t I O X ~ A ) ' p ' P L O T OF PERCENT I N I N T E R V A L ' PRINT ' ( ' ' ''tAplOXeA)'p'PHI INTERVAL's'PERCENT IN INTERVAL' PRINT ' ( ' ' '',A)'~GRID DO 20 I ~ 1 , 2 5 DO 25 COUNT - 1 , H I N T ( P E R ( I ) ) LINE(COUNT)-'~' 25 CONTINUE PRINT ' ( ' ' '',AFIOOAI)'rINTRVL(I)PLINE PRINT " ( . . . . t A ) ' p G R I D DO 30 C O U N T - 1 , N I N T ( P E R ( I ) ) LINE(COUNT)-' ' CONTINUE 30 20 CONTINUE PRINT ' ( ' ' O ' ' p l S X ~ A ) ' P ' C U N U L A T I V E PLOT ~IX ' PRINT ' ( ' ' ''PAeTXpA)'p'INTERVRL'F'PERCENT' PRINT ' ( ' ' ''~A)'~ORID SUN-O DO 35 I w l , 2 5 SUit=SUH÷NIHT(PER(1)) DO 40 COUNT~I~SUN LINE(COUNT)-'~'
85
Short Notes
86 40
CONTINUE PRINT '('' '',A~IOOA1)',INTRVL(1),LINE PRINT '('' '',A)'fORID DO 5 0 C O U N T ~ I , S U N LINE(COUNT)=' ' CONTINUE CONTINUE RETURN END
50 35
APPENDIX 2
Example data and output for a Till Sample NAME OF ANALYST. . . . STEWART SAMPLE NUMBER. . . . 2,000000 TOTAL WEIGHT OF SAMPLE . . . . 50,00000 I'HE NUMBER O F H Y D R O M E T E R READINGS. . . .
HYDROMETER TIME 1 4 15 60 240 720
1440
H Y D . READING 30.00 24.00 20.00 17.00 14.00 12.00 11.00
PHI 4.51 5 45 6 37 7 34 8 31 9 09 9 58
DIAM. 0.04393 0.02291 0.01211 0.00617 0.00314 0.00183
HYD. CORRN. 6.00 6.00 6,00 6.00 6.00 6,00 6.00
W PHI 4,83 5,77 6,69 7,66 8.64 9,41 9,90
0.00131
RESULTS TEMP. 24,00 24.00 24.00 24.00 24.00 24.00 24.00
W DIAM. 0.03514 0.01833 0,00969 0.00494 0.00251 0.00147 0.00104
IHE NUMBER OF SIEVES. . . .
DIAM.
(mm)
WT,
2.0000 1.0000 0,5000 0.2500 0.1250 0.0630 PHI SIZE 9 90 9.41 8 64 7,66 6 69 5.77 4 83 3.99 3 O0
FNR.
48.00
36,00 28.00 22,00 16.00 12.00 10.00
PHI
WT.
-1,00 0.00 1,00 2.00 3,00 3,99
PCT,
PCT.
0,00 0,00 0,00 21.80 14,20 7,00
78.20
100.00 0 O0 100.00 -1 O0 I00.00 GRANULOMETRIC COMPOSITION PERCENT SAND. . . . . 43.12284 PERCENT SILT . . . . . 42.75094 PERCENT CLAY. . . . . 14.12622 5%
].0.51 MEDIAN
4,644
16%
8,64 MEAr~
5.069
25%
7.16
50%
4,64
STDDEV
3.0120
PCT. CSR. 52.00 64,00 72.00 78,00 84.00 88.00 90,00
75X 2,25
SKEWNESS
0°26129
95X
84Z
1,93
FNR.
100,00 100~00 100,00 78.20 64,00 57,00
PERCENTFINER 10.00 12.00 16,00 22,00 28.00 36.00 48.00 57.00 64.00
2.00 ] O0
L FCT. 11.40 12.40 13.00 13.50 14,00 14.30 14.50
6
GMS.
0,00 0.00 0.00 10.90 7,10 3.50
PCT.
K FCT, ,013010 .013010 .013010 .013010 ,013010 .013010 .013010
1,71
KURTOSIS
0.73501
PCT,
CSR.
0,00 0,00 0.00 21.80 36,00 43,00
Sho~ Notes PLOT PHI
OF
PERCENT
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11
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TO
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TO TO
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It
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+
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0098--3004/86 $3.00 + .00 © 1986 Pergamon Press Ltd.
SHORT NOTE A COMPUTER PROGRAM FOR THE ANALYSIS OF SIEVE AND HYDROMETER DATA ROBERT A. STEWART a n d BRIAN GEDLINSKE Department of Earth Sciences, Iowa State University, Ames, IA 50011, U.S.A.
(Received 27 March 1985; accepted 14 September 1985) phi value also is extracted. Swan, Clague, and Luternauer (1978) emphasize that to obtain the requisite percentiles for these statistics, Gaussian interpolations and extrapolations should be used. We therefore have followed their procedure, using their equation 12 (Swan, Clague, and Luternauer, 1978, p. 868), and the algorithm mentioned (Abramowitz and Stegun, 1965, p, 931-933). Where extrapolations beyond the finest percentile obtained in the analysis are necessary, the Gaussian function is used to extrapolate to 99.99% at 14 phi, again following the convention of Swan, Clague, and Luternauer (1978, p. 868). As pointed out by Swan, Clague, and Luternauer (1978), this technique, although arbitrary, does add consistency to the analysis of large numbers of fine-grained samples. The percentiles used to calculate the grain-size statistics of Folk and Ward (1957) then are listed along with the statistics themselves. The program has several advantages. It is fast and inexpensive both in terms of computing and plotting time in that it uses an interactive terminal and line plotter instead of a "hard" plotter. The statistical interpolations and extrapolations used are consistent with the assumptions implicit in plotting grain size distributions on probability paper (e.g., Folk, 1974; Swan, Clague, and Luternauer, 1978). We have learned that for use with Pleistocene tills, the distribution of grainsize classes is a useful way of examining the incorporation of glaciers of substratal materials, such as fluvial sands or older tills, into younger tills and other related glacigenic sediments.
We routinely use a combination of sieving (for sand) and ASTM 152H (Bouyoucos) hydrometer analysis (for silt and clay) to study Pleistocene tills and other sediments. We have developed a computer program to reduce rapidly these raw data, compute various grain-size statistics, and print a cumulative curve and histogram of class weight percent vs. phi class interval. The program is written in FORTRAN and is used with an interactive terminal and online printer coupled to a Digital Equipment Corp. VAX computer. The program (Appendix 1), sample input, and sample output (Appendix 2) are listed here. For sieve data, the program uses the raw weight of sediment on each sieve, the sieve mesh size in millimeters, and the total sample weight. Hydrometer input data include: elapsed time (in minutes), uncorrected hydrometer reading, hydrometer correction, and temperature. A combined maximum of 30 sieve and hydrometer readings can be used. The actual data reduction to this point is similar to the ASTM (1964) method, except that Wadelrs modification of Stokes' Law settling times (Wadell, 1936) also is incorporated into the program to better accommodate the heterogeneous shapes of particles finer than 63 microns. The program calculates grain diameters for silt and clay particles based on the effective depth of settling, elapsed time, temperature of the suspension, and particle density (taken as 2.65, although this value may be changed with a minor adjustment to an array). Output to this point for sieve data consists of phi size, size class weight percent, and percent of the sample finer and coarser than sand size; and for the hydrometer data, the particle diameter in millimeters and phi units (for Stokes' and Wadell's settling), and the percent finer and percent coarser than a given size. Additionally, the percentages of sand (2 mm to 0.063 mm), silt (0.063 to 0.002 mm) and clay (finer than 0.002 ram) also are calculated. The program provides two graphs on the line printer, first,a histogram of class weight percent vs. phi class interval, and secondly, a plot of cumulative weight percent vs. phi class interval. On the latter graph, the data arc plotted according to a probability scale using an algorithm for the approximation of the inverse norreal function outlined in Abramowitz and Stcgun (1965, p. 931-933). The final function of the program is to calculate the Folk and Ward (1957) graphic grainsize statistical parameters: mean, inclusive graphic standard deviation, skewness and kurtosis; the median
REFERENCES
Abramowitz, M., and Stegun, I. A., 1965, Handbook of mathematical functions:U.S. National Bureau of Standards, U.S. Government Printing Office, Washington, D.C., 1046 p. American Society for Testingand Materials, 1964, Procedures for testing soils (4th ed.): Philadelphia, Pennsylvania, 535 p. Folk, R. L., 1974, Petrology of sedimentary rocks: Hemphill Publ. Co., Austin, Texas, 182 p. Folk, R. L., and Ward, W. C., 1957, Brazos River bar--a study in the significanceof grain size parameters: Jour. Sed. Pet. v. 27, no. l, p. 327-354. Swan, D., Clague, J. J., and Lutemauer, J. L., 1978, Grain size statistics I: Evaluation of the Folk and Ward graphic measures: Jour. Sed. Pet. v. 48, no. 3, p. 863-878. Wadell, H., 1936, Some practical sedimentation formulas: Geol. F~ren. Forh/indl., v. 58, p. 397-407. 81
Sho~ Notes
82
APPENDIX 1 C T H I S PROGRAN CALCULATE3 FOLK AND WARD S T A T I S T I C S USING C
GRAIN SIZE
ANALYSIS DATA FRON HYDROHETER AND SIEVE RESULTS,
CHARACTER NAHE*20 REAL SNUNPEDEPTH(61), K V A L U E ( 1 5 ) , T E N P ( 3 0 ) , HYDR(30) REAL C O R R ( 3 0 ) , D I A N ( 3 0 ) , KUSED(30), PHI(30), WADPHI(30) REAL P F I N E R ( 3 0 ) , P C O A R S ( 3 0 ) t CORHYD(30), WDIAM(30) REAL W T ( 3 0 ) , WTF'ERC(30), X ( 3 0 ) , Y(30), XPHI(I01), INGAUS REAL TOTWT, RNTr RNHYDR, SAND, S I L T , CLAYt NEANe R REAL STDDEU, SKEW, KURT, HEDIAN, HOLD, X P , E D U S E D ( 3 0 ) e K E E P INTEOER N, l , J, INT, INTPI, INHR, INHRPI, M, 111 T I N E ( 3 0 ) C E
THE EFFECTIVE DEPTH TABLE VALUES BASED ON THE ACTUAL HYDROMETER READING OF HYDROHETER t 1 5 2 H . THESE VALUES ARE F'LACED IN THE EFFECTIVE DEF'TH A R R A Y - E D E P T H ( 6 1 ) ,
÷ ÷ ÷ + ÷ t: C C C
THE THE ARE THE
+ ÷
DATA EDEPTH/16,SP 1 6 . 1 , 1~.2, 15.0p 14.8, 14.7, 1].7, 13.5, 13.3, 13.2, 12.2, 12.0J 11.9, 11.7, 10.7, 10.6, 10.4, 10.2, 9.1, S.9, 8.8, 8.6, 8.4, 7.3, 7.1p 7.0, 6.8, 6.6,
16.0, 14.5, 13.0, 11.5P 10.1~ 8.3, 6.5/
15.8, 15.6, 15.5, 15.3, 14.3, 14.2, 14.0, 13.8, 12.9, 12.7, 12.5, 12.4, 11.4, 11.2, 11.1r 10.9, 9.9, 9.7, 9.6r 9.4, 9.2, 8.1, 7.9, 7.8, 7.6, 7.4,
TABLE VALUES OF ' K ' FOR USE IN THE FORMULA WHICH COHPUTES DIAMETER OF PARTICLES IN HYDROMETER ANALYSIS. THESE VALUES BASED ON A S P E C I F I C GRAVITY OF 2 . 6 5 AND ARE DEPENDENT ON TENPERATURE.
DATA K V A L U E / O . O 1 4 3 G , 0 . 0 1 4 1 7 t 0.01399, 0.01382~ 0.01365, 0.048, 0.01332, 0.01317, 0.01301, 0.01286, 0.01272, 0.012~8P 0.01244J 0.012301 0.01217/
C THE DATA FRON THE HYDROHETER EXPERINENT I S READ IN FROH A DATA FILE. THE NAME OF THE ANALYST ( N A H E ) , THE SANPLE NUHBER ( S N U N ) , THE TOTAL WEIGHT OF THE SANPLE (TOTWT), THE NUNSER OF READINGS C: ( H ) , THE TIHE ( T I I t E ) , THE HYDROMETER READINO (HYDR)e THE C CORRECTION (CORR)t AND THE TEMPERATURE (TEHP) ARE READ FRON THE F I L E . C ~
10 C C C C
DETERNININO THE VALUE OF ' K " DIAMETER. (KUSED)
20 C C C
READ ~ NANE READ Z, SNUM PRINT S , ' N A N E OF ANALYST . . . . ",NAME PRINT I , ' S R H P L E NUHBER . . . . . ,SNUN READ $ , TOTWT PRINT ~ , ' T O T A L MEIGHT OF SAMPLE . . . . . ~TOTWT READ ~, N PRINT $ p ' T H E NUHBER OF HYDRONETER READINGS . . . . . DO 10 I ~ I , N READ $f T I N E ( I ) p HYDR(I)r CORN(I), TENP(I) CONTINUE
DO 20 I - l e N INT-TENP(IJ INTPlmINT÷I-15 RNT-INT INT=INT-15 I F (RNT . L T . T E N P ( I ) ) IF (RNT .EO. T E N P ( I ) ) CONTINUE
,N
TO BE USED IN CALCULATING GRAIN
KUSED(I)~(KVALUE(INT)÷KVALUE(INTP1))/2oO KUSED(I)=KVALUE(INT)
DETERMIHINO THE VALUE OF " L ' (THE EFFECTIVE DEPTH) TO BE USED IN CALCULATINO GRAIN DIAMETER. THE EFFECTIVE DEPTH USED (EDUSED) I S DETERNZNED FRON THE TABLE VALUES OF THE EFFECTIVE DEPTH ( E D E P T H ) . DO 30 I = l , N INHR-HYDR(I)+I.0 RNHR~IHHR INHRPI=INHR+I I F (RNHR . L T . H Y D R I I ) ÷ I . 0 )
EDUSED(I)=(EDEPTH(INHR)÷EDEPTH
Short Notes
30
(INHRP1))/2.0 IF (RNHR . E O . CONTINUE
HYDR(I)+I.O)
CALCULATION OF THE ORAIN D)AMETER
40 C C C C C
DO 50 I = l , N WDIAM(I)=KUSED(I)ZSQRT(EDUSED(1)/TIME(I)~.64) CONTINUE
PHI.In(I/DIAH)/Ir,(2).
DO 70 l ~ l , N PHI(1)=LOO(1/DIAM(1))/0.69314718 CONTINUE
I, ETERMINING THE PHI SIZES USING WADELLS MODIFICATION. WADPHI~ln(1/WDIAM)/ln2
80 C C
(DIAM)~KUSED$(EDUSED/TIME)*$.5
DO 40 I = I , N DIAM(I)~KUSED(I)*SORT(EDUSED(I)/TINE(I)) CONTINUE
DETERMININO THE PHI SIZES.
70 C C C
EDUSED(I)-EDEPTH(INHR)
CALCULATION OF GRAIN DIAMETER USIN6 WADELL'S M O D I F I C A T I O N . DIAMET~R=WDIAM=KUSED$((EDUSED/TIME)~°64)~.5
50 L C C
83
DO SO I ~ I , N WADFHI(I)=LOG(1/WDIAM(I))/O.6931471B CONTINUE
CALCULATINB THE CORRECTED HYDROMETER READING. DO 75 I ~ I , N CORHYD(1)-HYDR(1)-CORR(I) IF (HYDR(I) .LT. CORk(It) CORHYD(1)-O 75 CONTINUE C CALCULATINO PERCENT FINER ( P F I N E R ) AND PERCENT COARSER ( P C O A R S ) o DO 9 0 I ~ I , N PFINER(I)-CORHYD(I)Z(IOO.O/TOTWT) PCOARS(1)~.IOO.O-PFINER(I) 90 CONTINUE PRINT $ ~ ' ' PRINT ' ( ' ' O ' ' P 2 O X ~ A ) ' , ' H Y D R O M E T E R RESULTS' PRINT ' ( ' ' O ' ' P A 4 ~ 3 X r A 1 2 p 3 X t A 1 1 ~ 3 X ~ A S ~ 3 X ~ A S ~ 3 X ~ A 6 ) ' ~ ' T I M E ' p ÷ 'HYD. R~ADIHO','MYD. CORRN.'r'TEMP.'~'K FCTo'~'L FCT.' DO 100 I - l e N PRINT ' ( . . . . ,15,2X,FS.2,10X,F4.2,10X,FS.2,3X,F7.612X,FS.2)', ÷ TIME(1), HYDR(1), CORR(1), TEMP(1), KUSED(I)~ EDUSED(I) 100 CONTINUE PRINT ' ( ' ' O ' ' , A S p 3 X p A S , S X ~ A S p 3 X ~ A B ~ 3 X ~ A g ~ 3 x r A g ) ' t ' PHI 'p + 'DIAM.'r 'W P H I ' ~ 'W D I A M . ' p 'PCT. FNR.'p 'PCT. CSR.' DO 110 I ~ l , N PRINT ' ( ' ' '',FS.2~3XrF7.5,3X~FS.2,3XtF7.Sp3X~F6.2pSXpF7o2)'p + P H I ( 1 ) r DIAM(I)~ WADPHI(1)r WDIAM(I), P F I N E R ( I ) t PCOARS(I) 110 CONTINUE C C SIEVE DATA FOR PARTICLES LESS THAN 2am. C "J';THE NUMBER OF S I E V E S I Z E S C READ ~wJ PRINT S p ' ' PRINT ~ , ' T H E NUMBER OF SIEVES . . . . . ~J DO 115 I ~ N f l ~ N + J READ *pDIAM(1)~ WT(1) WTPERC(1)=(WT(I)/TOTWT)$100.O WADPNI(I)'LOO(I/OIAM(1))/0.69314710 IF ( I .GT. M+l) THEN PFINER(I)~PFINER(I-1)-WTPERC~I) ELSE PFINER(I)-IO0.O END I F PCOARS(I)=IOO.O-PFINER(I) 115 CONTINUE F'F:INT'(''O''~A11~3X~AS~3X~AS~3X,AS,3XpA9~3X~A9)'~'DIAM. (BB)'t + 'WT. O M S . ' , ' PHI ' , 'WT° P C T ° ' , 'PCT. FNR°', 'PCT° C S R ° ' PRINT $~ ( ' - ' ~ I - 1 p 6 4 ) " PO 120 I = N + I e N + J , PRINT ' ( . . . . ,F7.4~7X,FS.2~6X,FS.2~3X~F7.2~4X,F7.2~SX~F7°2)'~ -,~ OIAM(I), WT(I), W A D P H I ( 1 ) , WTPERC(I)~ P F I N E R ( I ) , PCOARS(I) 120 CONTINUE
84
Short Notes DO 137 I = l p N + J X(I)mNADPHI(I) Y(I)mPFINER(I) CONTINUE DO 140 I a l t N + J - 1 11=I+1 DO 150 H = I l t N ÷ J IF ( X ( I ) , L T . HOLD=:X(I)
137
X(H))
THEN
X(1)=X(M) X(N)=HOLD KEEP=Y(I) Y(I)=Y(N) Y(N)=KEEP END I F CONTINUE CONTINUE PRINT ' ( ' ' O ' ' t A B ~ 4 X ~ A 1 3 ) ' t ' P H I SIZE', DO 160 I ~ I , N ÷ J PRINT ' ( ' " "'~FS°2tTXpF7.2)',X(I)PY(I) CONTINUE
150 140
'PERCENT
FINER'
160 C C 6RANULOMETRIC COMPOSITION DO 165 I = l w N ÷ J I1=I+1 IF ( X ( I ) .NE. X(I1)) THEN IF (X(II) . L E . 4 .AND. X ( I ) . G E . 4 ) THEN SAHD=IOO.O-(Y(I)÷(Y(I1)-Y(I))~(4-X(I))/(X(I1)-X(I))) ELSE I F ( X ( I I ) . L E . 9 .AND. X ( I ) .GE. 9 ) THEN CLAY-Y(I)÷(Y(I1)-Y(I))$(9-X(I))/(X(II)-X(I)) END I F END IF 165 CONTINUE SILT=IOO.O-SAND-CLAY PRINT ~ t ' ' PRINT ~t 'ORANULOHETRIC COMPOSITION' PRINT ~ t 'PERCENT SAND . . . . . '~SAND PRINT St 'PERCENT S I L T . . . . . . PSILT PRINT St 'PERCENT CLAY . . . . . . tCLAY DO 170 I = I , N + J I1=1÷1 IF (Y(I) .HE. Y~I1)) THEN DO 180 N = O t l O 0 R'N I F (N . G E . Y ( I ) .hND. H .LE. Y(ZI)) THEN XPHI(N)~X(I)÷(X(II)-X(I))~((INOAUS(R)-INOAUS(Y(I)))/ + (INGAUS(Y(I1))-INGAUS(Y(I)))) ELSE IF (N . L T . Y ( I ) ) THEN XPHI(N)=14.0+(X(I)-I4.0)~((INGAUS(R)-INOAU8(O))/ + (INGAUS(Y(1))-INGAUS(O))) END I F 180 CONTINUE END I F 170 CONTINUE PRINT ' ( ' ' O ' ' ~ 2 X t A 4 P 3 X I A 4 ~ 3 X ~ A 4 t 3 X t A 4 ~ 3 X ~ A 4 t 3 X I A 4 t 3 X t A 4 ) ' t +
+
+
÷
+
'5~','16X't'25X't'50g','75X','S4~'~'95X' PRINT Sr ( ' - ' p I = l e 4 8 ) PRINT ' ( . . . . tF6.2tlXtF6.2tlXJF6.2P1XtF6.2tlXpF6.2PIXe F6.2p1XpF6.2)'pXPHI(5)pXPHI(16)PXPHI(25)tXPHI(50)tXPHI(75)t XPNI(S4)PXPHI(95) MEDIAN-XPHI(50) HEAN=(XPHI(16)+XPHI(50)fXPHI(84))/3.0 STDDEV=ABS((XPHI(B4)°XPHI(16))/4.0+(XPHI(95)-XPHI(5))/6.6) SKEW=-I$((XPHI(16)+XPHI(S4)-2~XPHI(50))/(25(XPHI(84)-XPHI(16))) ÷(XPHI(5)+XPHI(95)-2~XPHI(50))/(25(XPHI(95)-XPHI(5)))) KURT=(XPHI(?5)-XPHI(5))/(2.441(XPHI(75)-XPHI(25))) PRINT " ( ' ' O ' ' t A 6 t 3 X ~ A 6 P 3 X p A 6 p 3 X , A S , 3 X t A 8 ) ' P ' N E D I A N ' , '~EAN', "STDDEU'~ 'SKEWNESS', 'KURTOSIS' PRINT ~w . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . F RZNT " ( . . . . ~F6.3t3XtFb°3t3X~F6.4t3XtFS.5~3X~FS.5)'~ H E D I A N t HEANe STDDEVt SKENt KURT CALL PLOT ( X t Y, N + J ) STOP END REAL FUNCTION I N O A U S ( O ) REAL C O t C 1 , C 2 , D 1 , D 2 , D 3 , Y , T , O X , Q C0~2.515517 C1=0.802853 C2-0.010328 D1-1.432788
Short Notes D2~0,189269 D3=O.OO130G OX-O/lO0.O IF (QX . E O . O) GX=O.O001 I F (QX , E G . 1) OX:~O.9999 IF (GX , L E . 0 . 5 ) THEN T=SGRT(LOG(IlGX~2)) ELSE T-GORT(LOG(1/(1-QX)*~2)) END I F Y-T-(CO+CI~T÷C2~T~2)/(I÷DI~T÷D2ZT$&2÷D3$T$~3) I F (OX . L E . 0 . 5 ) THEN INOAUS~Y ELSE INGAUS'-Y END I F RETURN END T H I S SUBROUTINE PLOTS A HISTOGRAM OF THE PERCENTAGE OF SEDIHENT CONTAINED IN HALF PHI I N T E R V A L S . I T ALSO PLOT8 THE CUNULATIVE PERCENTAOEG FOR HALF PHI I N T E R V A L S . SUBROUTINE P L O T ( X X P Y Y ~ N ) REAL X X ( N ) , Y Y ( N ) , R A N G E , P E R ( 2 S ) e S U N w P H I ( 2 6 ) INTEGER NJ NUN, I , J~ COUNTt L I N E ( I O 0 ) CHARACTER I N T R V L ( 2 5 ) I I G t GRIDZ115 DATA I N T R V L / ' 1 1 AND FINER I ' ,'10.5 TO 11 I', |'p + ' 1 0 TO 1 0 . 5 ','9.5 TO 10 ",'9 TO 9 . 5 + ' 8 . 5 TO 9 ','O TO B . 5 ','7.5 TO B I'e ÷ ' 7 TO 7 . 5 "~'6,5 TO 7 ' , '6 TO 6 . 5 I'! + "5.5 TO 6 ','5 TO 5,5 ' , '4.5 TO 5 |'9 ÷ ' 4 TO 4 . 5 ','3.5 TO 4 ','3 TO 3 . 5 |'e I'p + ' 2 . 5 TO 3 ','2 TO 2 . 5 ','1.5 TO 2 |'p + ' 1 TO 1 , 5 ','0.5 TO I ','0 TO 0 . 5 ,/ + '-0.5 TO 0 ','-1 TO - 0 . 5 DATA L I N E / l O O n ' '/ DATA GRID / ' I ......... I ......... I ......... I ÷......... I ......... i ......... I ......... I ......... I ......... I +......... I'/ PHI(O)uO.O RANGE t 1 1 . 0 NUH= 1 DO WHILE (RANGE . G T . X X ( 1 ) ) PHI(NUH)=-IO((14.0-RANGE)8-YY(1)/(14.0-XX(I))) PER(NUN)-PHI(NUH)-PHZ(NUH-1) NUN - NUN÷I RANGE - R A N G E - O . 5 END DO DO 5 I = N U H , 2 5 DO 10 J = l r N Jl = J + 1 IF (RANGE . L T . X X ( J ) .AND. RANGE . B E , X X ( J 1 ) ) THEN PHI(I)aYY(J)-((XX(J)-RANOE)8(YY(J)-YY(J1))/(XX(J)-XX(JI))) PER(I)LPHI(I)-PHI(I-1) END IF 10 CONTINUE RANGE = RANGE-Oo5 CONTINUE 5 PRINT ' ( ' ' O ' ' t I O X ~ A ) ' p ' P L O T OF PERCENT I N I N T E R V A L ' PRINT ' ( ' ' ''tAplOXeA)'p'PHI INTERVAL's'PERCENT IN INTERVAL' PRINT ' ( ' ' '',A)'~GRID DO 20 I ~ 1 , 2 5 DO 25 COUNT - 1 , H I N T ( P E R ( I ) ) LINE(COUNT)-'~' 25 CONTINUE PRINT ' ( ' ' '',AFIOOAI)'rINTRVL(I)PLINE PRINT " ( . . . . t A ) ' p G R I D DO 30 C O U N T - 1 , N I N T ( P E R ( I ) ) LINE(COUNT)-' ' CONTINUE 30 20 CONTINUE PRINT ' ( ' ' O ' ' p l S X ~ A ) ' P ' C U N U L A T I V E PLOT ~IX ' PRINT ' ( ' ' ''PAeTXpA)'p'INTERVRL'F'PERCENT' PRINT ' ( ' ' ''~A)'~ORID SUN-O DO 35 I w l , 2 5 SUit=SUH÷NIHT(PER(1)) DO 40 COUNT~I~SUN LINE(COUNT)-'~'
85
Short Notes
86 40
CONTINUE PRINT '('' '',A~IOOA1)',INTRVL(1),LINE PRINT '('' '',A)'fORID DO 5 0 C O U N T ~ I , S U N LINE(COUNT)=' ' CONTINUE CONTINUE RETURN END
50 35
APPENDIX 2
Example data and output for a Till Sample NAME OF ANALYST. . . . STEWART SAMPLE NUMBER. . . . 2,000000 TOTAL WEIGHT OF SAMPLE . . . . 50,00000 I'HE NUMBER O F H Y D R O M E T E R READINGS. . . .
HYDROMETER TIME 1 4 15 60 240 720
1440
H Y D . READING 30.00 24.00 20.00 17.00 14.00 12.00 11.00
PHI 4.51 5 45 6 37 7 34 8 31 9 09 9 58
DIAM. 0.04393 0.02291 0.01211 0.00617 0.00314 0.00183
HYD. CORRN. 6.00 6.00 6,00 6.00 6.00 6,00 6.00
W PHI 4,83 5,77 6,69 7,66 8.64 9,41 9,90
0.00131
RESULTS TEMP. 24,00 24.00 24.00 24.00 24.00 24.00 24.00
W DIAM. 0.03514 0.01833 0,00969 0.00494 0.00251 0.00147 0.00104
IHE NUMBER OF SIEVES. . . .
DIAM.
(mm)
WT,
2.0000 1.0000 0,5000 0.2500 0.1250 0.0630 PHI SIZE 9 90 9.41 8 64 7,66 6 69 5.77 4 83 3.99 3 O0
FNR.
48.00
36,00 28.00 22,00 16.00 12.00 10.00
PHI
WT.
-1,00 0.00 1,00 2.00 3,00 3,99
PCT,
PCT.
0,00 0,00 0,00 21.80 14,20 7,00
78.20
100.00 0 O0 100.00 -1 O0 I00.00 GRANULOMETRIC COMPOSITION PERCENT SAND. . . . . 43.12284 PERCENT SILT . . . . . 42.75094 PERCENT CLAY. . . . . 14.12622 5%
].0.51 MEDIAN
4,644
16%
8,64 MEAr~
5.069
25%
7.16
50%
4,64
STDDEV
3.0120
PCT. CSR. 52.00 64,00 72.00 78,00 84.00 88.00 90,00
75X 2,25
SKEWNESS
0°26129
95X
84Z
1,93
FNR.
100,00 100~00 100,00 78.20 64,00 57,00
PERCENTFINER 10.00 12.00 16,00 22,00 28.00 36.00 48.00 57.00 64.00
2.00 ] O0
L FCT. 11.40 12.40 13.00 13.50 14,00 14.30 14.50
6
GMS.
0,00 0.00 0.00 10.90 7,10 3.50
PCT.
K FCT, ,013010 .013010 .013010 .013010 ,013010 .013010 .013010
1,71
KURTOSIS
0.73501
PCT,
CSR.
0,00 0,00 0.00 21.80 36,00 43,00
Sho~ Notes PLOT PHI
OF
PERCENT
]NT[EVML
11
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It
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IIIII I . . . . . . . . . 6
TO
4
TO
5
4.5 TO
3
TO
1
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2,5 2
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