laboratorio 1 y tablas

Malla

2 1/2" 0.0 0.0 0.0 0.02" 495.3 0.0 0.0 0.0

1 1/2" 384.9 0.0 0.0 0.01" 255.6 58.3 0.0 0.0

3/4" 102.4 95.7 0.0 0.01/2" 0.0 86.2 98.3 0.01/4" 0.0 22.8 96.5 0.0

8 0.0 11.2 78.7 0.010 0.0 6.3 32.1 208.414 0.0 5.1 10.4 91.420 0.0 7.0 8.5 18.328 0.0 0.2 4.3 8.735 0.0 9.7 10.1 9.348 0.0 10.3 10.0 9.865 0.0 2.8 3.3 6.5

Fondo 0.0 14.6 22.9 31.51238.2 330.2 375.1 383.9

Masa inicial 1240.7 336.3 377.5 394.7

Análisis inicial

Chancado Primario

Chancado Secundari

oChancado Terciario

AJUSTE DE SCHUMANN

𝐹𝑢 = ൬𝑋𝐾൰𝑀 𝐹𝑢% = 100 ∗൬𝑋𝐾൰𝑀

Fu = Fracción Retenida Pasante por el tamaño X. K = Tamaño teórico por donde pasa el 100% del material. M = Constante de la distribución. (M ≠m)

X = log (abertura malla media en micrones) Y = log (Fu %) 𝑦= 𝑚𝑥+ 𝑏

𝑚 = ∑𝑥∑𝑦− 𝑛∑𝑥𝑦(∑𝑥)2 − 𝑛∑𝑥2 𝑏= ∑𝑥𝑦∑𝑥− ∑𝑦∑𝑥2(∑𝑥)2 − 𝑛∑𝑥2

Siendo n el número de tamices ocupados.

Por ejemplo, si se tiene lo siguiente (después de completar la tabla de tamizaje)

X Y XY X^2Malla log abertura media de malla log % retenido pasante

8 3.452 2.000 6.904 11.91510 3.301 1.245 4.109 10.89614 3.150 1.104 3.478 9.92520 3.000 1.012 3.035 8.99928 2.848 0.937 2.668 8.10935 2.697 0.812 2.190 7.27448 2.548 0.711 1.810 6.49265 2.397 0.608 1.457 5.748Σ 23.393 8.428 25.651 69.359

Se utilizan las fórmulas, para obtener los parámetros "m" y "b", a través de mínimos cuadradosPara determinar la ecuación de la recta que relaciona la abertura media (X) con el % de la muestra que pasa por esa abertura (Y) (todo en log)No se considera el fondo como parte de los tamices para determinar "n"

Siguiendo con el ejemplo, se obtienen los valores de los parámetros:m =b =

Finalmente, con estos valores se puede determinar el valor de K (tamaño teórico por donde pasa todo el material), si Y=log(100), por lo tanto K=10^xAltenativamente se puede determinar la abertura para cual pasa un cierto porcentaje de la muestra (80%, 50%, a%) con Y=log(a%)=mx+ndespejando x de la ecuacion y luego da=10^xdependiendo del valor de a%

n=8Nótese que son los logaritmos de base 10 de los parámetros señalados

Para determinar la ecuación de la recta que relaciona la abertura media (X) con el % de la muestra que pasa por esa abertura (Y) (todo en log)

1.056117231-2.03480001

Finalmente, con estos valores se puede determinar el valor de K (tamaño teórico por donde pasa todo el material), si Y=log(100), por lo tanto K=10^xAltenativamente se puede determinar la abertura para cual pasa un cierto porcentaje de la muestra (80%, 50%, a%) con Y=log(a%)=mx+n

Por ejemplo, si se tiene lo siguiente (después de completar la tabla de tamizaje)

AJUSTE ROSIN RAMMLER

Malla

X Y

X*Y X^2n=7

8 3.452 -- -- 11.91510 3.301 -0.714 -2.357 10.89614 3.150 -0.867 -2.731 9.92520 3.000 -0.965 -2.895 8.99928 2.848 -1.044 -2.972 8.10935 2.697 -1.174 -3.165 7.27448 2.548 -1.278 -3.256 6.49265 2.397 -1.383 -3.316 5.748

SUMA 19.941 -7.424 -20.693 57.444

Se utilizan las fórmulas, para obtener los parámetros "m" y "b", a través de mínimos cuadradosNo se considera el fondo como parte de los tamices para determinar "n"

Siguiendo con el ejemplo, se obtienen los valores de los parámetros:m = 0.72020573b = -3.11231802

Finalmente, con estos valores se puede determinar el valor de X0=10^(-b/m)Y d80=X0*(Ln5)^(1/m)

X0 = 20961.82679d80 = 40587.7213

log abertura media de malla

Log de Ln de (100/porcentaje retenido

acumulado(%))

No se considera la malla 8 ya que no tiene valores para Y

Se utilizan las fórmulas, para obtener los parámetros "m" y "b", a través de mínimos cuadradosNo se considera el fondo como parte de los tamices para determinar "n"

MALLA AB. MALLA (MICRAS) AB MEDIA MALLA ( MICRAS)2 1/2" 63500.0 63500.0

2" 50800.0 56796.11 1/2" 38100.0 43994.1

1" 25400.0 31108.53/4" 19050.0 21997.01/2" 12700.0 15554.31/4" 6350.0 8980.3

8 2380.0 3887.510 1680.0 1999.614 1190.0 1413.920 840.0 999.828 590.0 704.035 420.0 497.848 297.0 353.265 210.0 249.7

Fondo

SHUMANNMALLA LOG AB MEDIA (X) LOG RET PAS (Y)2 1/2" 4.803 2.000

2" 4.706 1.7781 1/2" 4.581 1.461

1" 4.405 0.918SUMA 18.494 6.157

Masa inicial 1240.7 Interpolacion Masa Real 1238.2 60148.1986640025Error gr 2.5Error % 0.2

n 4m 2.7b -11.1k 62019.0

F80 57147.8F50 48103.1

RAMBLER MALLA LOG AB MEDIA (X) LOG DE LN DE (100/ % RET ACUMULADO) (Y)

2" 4.754 -0.0381 1/2" 4.643 -0.467

1" 4.493 -1.0643/4" 4.342 -6.000

SUMA 18.233 -7.569

n 4m 13.643b -64.082

X0 49765.518d80 51531.979

MASA (GR) MASA CORREGIDA (GR) % RET. PARC % RET ACUM % RET PAS0.0 0.0 0.0 0.0 100.0

495.3 496.3 40.0 40.0 60.0384.9 385.7 31.1 71.1 28.9255.6 256.1 20.6 91.7 8.3102.4 102.6 8.3 100.0 0.0

0.0 0.0 0.0 0.0 0.00.0 0.0 0.0 0.0 0.00.0 0.0 0.0 0.0 0.00.0 0.0 0.0 0.0 0.00.0 0.0 0.0 0.0 0.00.0 0.0 0.0 0.0 0.00.0 0.0 0.0 0.0 0.00.0 0.0 0.0 0.0 0.00.0 0.0 0.0 0.0 0.00.0 0.0 0.0 0.0 0.00.0 0.0 0.0 0.0 0.0

SHUMANNXY X^2

9.606 23.0678.368 22.1456.693 20.9854.041 19.403

28.708 85.599

RAMBLER XY X^2

-0.181 22.604-2.168 21.561

4 . 3 5 0 4 . 4 0 0 4 . 4 5 0 4 . 5 0 0 4 . 5 5 0 4 . 6 0 0 4 . 6 5 0 4 . 7 0 0 4 . 7 5 0 4 . 8 0 0 4 . 8 5 00.000

0.500

1.000

1.500

2.000

2.500

f(x) = 2.72791077601558 x − 11.0735803889939R² = 0.995345180339639

Chart Title

-4.780 20.186-26.054 18.856-33.183 83.207

d80=X0*(Ln5)^(1/m)

2 1/2"2"

1 1/2"1"

3/4"1/2"1/4"########################

Fondo

Masa inicial

masa realperd

% error

4 . 3 5 0 4 . 4 0 0 4 . 4 5 0 4 . 5 0 0 4 . 5 5 0 4 . 6 0 0 4 . 6 5 0 4 . 7 0 0 4 . 7 5 0 4 . 8 0 0 4 . 8 5 00.000

0.500

1.000

1.500

2.000

2.500

f(x) = 2.72791077601558 x − 11.0735803889939R² = 0.995345180339639

Chart Title

MALLA AB. MALLA (MICRAS) AB MEDIA MALLA ( MICRAS)

1 1/2" 38100.0 38100.01" 25400.0 31108.5

3/4" 19050.0 21997.01/2" 12700.0 15554.31/4" 6350.0 8980.3

8 2380.0 2808.410 1680.0 1982.414 1190.0 1404.220 840.0 991.228 590.0 696.235 420.0 495.648 297.0 350.565 210.0 247.8

Fondo

SHUMANNMALLA LOG AB MEDIA (X) LOG RET PAS (Y)

1 1/2" 4.581 2.0001" 4.493 1.916

3/4" 4.342 1.7271/2" 4.192 1.4351/4" 3.953 1.309

8 3.448 1.22910 3.297 1.17814 3.147 1.13120 2.996 1.05628 2.843 1.05435 2.695 0.92448 2.545 0.72265 2.394 0.646

SUMA 44.927 16.326

Masa inicial 336.3Masa Real 330.2Error gr 6.1Error % 1.8

n 13m 0.524b -0.555k 75190.869

F80 49114.560

MASA (GR) MASA CORREGIDA (GR) % RET. PARC % RET ACUM % RET PAS

0.0 0.0 0.0 0.0 100.058.3 59.4 17.7 17.7 82.395.7 97.5 29.0 46.6 53.486.2 87.8 26.1 72.7 27.322.8 23.2 6.9 79.6 20.411.2 11.4 3.4 83.0 17.06.3 6.4 1.9 84.9 15.15.1 5.2 1.5 86.5 13.57.0 7.1 2.1 88.6 11.40.2 0.2 0.1 88.7 11.39.7 9.9 2.9 91.6 8.4

10.3 10.5 3.1 94.7 5.32.8 2.9 0.8 95.6 4.4

14.6 14.9 4.4 100.0 0.0

SHUMANNXY X^2

9.162 20.9858.607 20.1867.500 18.8566.017 17.5725.173 15.6284.240 11.8923.883 10.8713.558 9.9063.165 8.9772.997 8.0812.490 7.2641.837 6.4751.546 5.732

60.173 162.425

Interpoacion lineal30180.3197802778

2 . 0 0 0 2 . 5 0 0 3 . 0 0 0 3 . 5 0 0 4 . 0 0 0 4 . 5 0 0 5 . 0 0 00.000

0.500

1.000

1.500

2.000

2.500

f(x) = 0.523965795295865 x − 0.5549437262762R² = 0.928417368719275

Chart Title

2 . 0 0 0 2 . 5 0 0 3 . 0 0 0 3 . 5 0 0 4 . 0 0 0 4 . 5 0 0 5 . 0 0 00.000

0.500

1.000

1.500

2.000

2.500

f(x) = 0.523965795295865 x − 0.5549437262762R² = 0.928417368719275

Chart Title

MALLA AB. MALLA (MICRAS) AB MEDIA MALLA ( MICRAS)3/4" 19050.0 19050.01/2" 12700.0 15554.31/4" 6350.0 8980.3

8 2380.0 2808.410 1680.0 1982.414 1190.0 1404.220 840.0 991.228 590.0 696.235 420.0 495.648 297.0 350.565 210.0 247.8

Fondo


3/4" 4.27989498001164 21/2" 4.1918493504838 1.8680190216341/4" 3.95328872312397 1.68184866257168

8 3.44845896436264 1.4327466437971810 3.29719128903199 1.2678377404393914 3.14742896869866 1.1974404167305320 2.99616129336801 1.1300034526890828 2.84273401894827 1.0914339268672335 2.69513129770403 0.98456150638244248 2.54463845662334 0.84415422716902265 2.39410130204004 0.785688418189165

SUMA 35.7908786443964 14.2837340164697


n 11m 0.615751902851513b -0.70496069214045k 24713.7832549253

F80 17201.027741159

MASA (GR) MASA CORREGIDA (GR) % RET. PARC % RET ACUM0.0 0.0 0.0 0.0

98.3 98.9 26.2 26.296.5 97.1 25.7 51.978.7 79.2 21.0 72.932.1 32.3 8.6 81.510.4 10.5 2.8 84.28.5 8.6 2.3 86.54.3 4.3 1.1 87.7

10.1 10.2 2.7 90.310.0 10.1 2.7 93.03.3 3.3 0.9 93.9

22.9 23.0 6.1 100.0

SHUMANNXY X^2

8.55978996002328 18.31750103992887.83045432252785 17.57160097715146.64883335174574 15.62849172837914.94076800746286 11.8918692288934.18030355368276 10.87147039646843.76885865590827 9.906309113003483.38567260631922 8.976982495876653.10265635333977 8.081136702485782.65352253036594 7.263732711863782.14806730977545 6.47518487492641.88101766498446 5.73172104442984

49.0999443161356 120.716000313407


2 2 . 5 3 3 . 5 4 4 . 50

0.5

1

1.5

2

2.5

f(x) = 0.615751902851511 x − 0.70496069214044R² = 0.990418206461902

Chart Title

% RET PAS100.073.848.127.118.515.813.512.39.77.06.10.0

2 2 . 5 3 3 . 5 4 4 . 50

0.5

1

1.5

2

2.5

f(x) = 0.615751902851511 x − 0.70496069214044R² = 0.990418206461902

Chart Title

MALLA AB. MALLA (MICRAS) AB MEDIA MALLA ( MICRAS)8 2380.0 2808.4

10 1680.0 1982.414 1190.0 1404.220 840.0 991.228 590.0 696.235 420.0 495.648 297.0 350.565 210.0 247.8

Fondo


8 3.37657695705651 210 3.22530928172586 1.6600590086844414 3.07554696139253 1.3405778836805120 2.92427928606188 1.2340077814965528 2.77085201164214 1.1724179961284435 2.6232492903979 1.0952097844947148 2.47275644931721 0.99556548449940565 2.32221929473392 0.914092441672196

SUMA 22.790789532328 10.4119303806563


n 8m 0.93b -1.34k 4006.22

F80 3148.77

RAMBLER MALLA LOG AB MEDIA (X) LOG DE LN DE (100/ % RET ACUMULADO) (Y)

10 3.29719128903199 -0.21401367203516314 3.147 -0.60683468976112120 2.996 -0.72580449060204628 2.843 -0.79308312312642635 2.695 -0.87623533349477248 2.545 -0.98199732035112865 2.394 -1.06744908415651

SUMA 19.917 -5.265

n 7

m 0.821b -3.088

X0 5774.670d80 10309.968

MASA (GR) MASA CORREGIDA (GR) % RET. PARC0.0 0.0 0.0

208.4 214.3 54.391.4 94.0 23.818.3 18.8 4.88.7 8.9 2.39.3 9.6 2.49.8 10.1 2.66.5 6.7 1.7

31.5 32.4 8.2

SHUMANNXY X^2

6.75315391411302 11.4012719469255.35420372892255 10.4026199627874.12301023666361 9.458989111730823.60858339426954 8.551409342890593.24859676305795 7.677620870421322.8730082900126 6.88143683957309

2.46179097251352 6.114524457639872.12272310522161 5.392702452834530.5450704047744 65.8805749848022


RAMBLER XY X^2

-0.706 10.871-1.910 9.906-2.175 8.977-2.255 8.081-2.362 7.264-2.499 6.475-2.556 5.732

-14.461 57.307

2 . 2 2 . 4 2 . 6 2 . 8 3 3 . 2 3 . 4 3 . 60

0.5

1

1.5

2

2.5

f(x) = 0.926544408763691 x − 1.33809352897904R² = 0.884102871348566

Chart Title

% RET ACUM % RET PAS0.0 100.0

54.3 45.778.1 21.982.9 17.185.1 14.987.5 12.590.1 9.991.8 8.2

100.0 0.0

2 . 2 2 . 4 2 . 6 2 . 8 3 3 . 2 3 . 4 3 . 60

0.5

1

1.5

2

2.5

f(x) = 0.926544408763691 x − 1.33809352897904R² = 0.884102871348566

Chart Title

% RET. PARC AB MEDIA MALLA ( MICRAS) LOG % RET. PARC2" 40.00 56796.13 1.60207752830557

1 1/2" 31.09 43994.09 1.49255711141771" 20.64 31108.52 1.31477004980948

3/4" 8.27 21997.05 0.917509156962926

% RET. ACUM AB. MEDIA MALLA ( MICRAS) LOG % RET. ACUM2" 40.00 56796.13 1.60207752830557

1 1/2" 71.09 43994.09 1.851790564550041" 91.73 31108.52 1.96251106467055

3/4" 100.00 21997.05 1.9999995657053

% RET. PASANTE AB. MEDIA MALLA ( MICRAS) LOG % RET. PASANTE2 1/2" 100.00 63500 2

2" 60.00 56796.13 1.778139558671811 1/2" 28.91 43994.09 1.46109222696699

1" 8.27 31108.52 0.917509156962926

30000 40000 50000 60000 700000.00

20.00

40.00

60.00

80.00

100.00

120.00

f(x) = 4.06736885807803E-15 x^3.4086684147018R² = 0.996408892539504

% RET. PASANTE V/S AB. MEDIA MALLA

% RET. PASANTE V/S AB. MEDIA MALLA Power (% RET. PASANTE V/S AB. MEDIA MALLA )

F80 60696.8395979671

X Y XY X^2Malla log abertura media log % retenido pasante2 1/2" 4.803 2.000 9.606 23.067

2" 4.754 1.778 8.454 22.6041 1/2" 4.643 1.461 6.784 21.561

1" 4.493 0.918 4.122 20.186Suma 18.693 6.157 28.966 87.417

n 4m 3.40866841470038b -14.390686440875k 64347.3429571224F80 60269.856586466

30000 40000 50000 60000 700000.00

20.00

40.00

60.00

80.00

100.00

120.00

f(x) = 4.06736885807803E-15 x^3.4086684147018R² = 0.996408892539504



LOG AB. MEDIA MALLA 4.754318718787954.643394343979774.492879346147784.34236434831579



4.3 4.35 4.4 4.45 4.5 4.55 4.6 4.65 4.7 4.75 4.81.5

1.6

1.7

1.8

1.9

2

2.1

LOG % RET.ACUM V/S LOG AB MEDIA MALLA

LOG AB. MEDIA MALLA

LOG

% R

ET. A

CUM

4.3 4.35 4.4 4.45 4.5 4.55 4.6 4.65 4.7 4.75 4.80.80.9

11.11.21.31.41.51.61.7

LOG % RET. PARC. V/S LOG AB. MEDIA MALLA

LOG. AB. MEDIA MALLA

LOG

% R

ET. P

ARC.

4.45 4.5 4.55 4.6 4.65 4.7 4.75 4.8 4.850.8

11.21.41.61.8

22.2

f(x) = 3.4086684147018 x − 14.3906864408819R² = 0.996408892539504

LOG % RET. PASANTE V/S LOG AB. MEDIA MALLA

LOG AB. MEDIA MALLA

LOG

% R

ET. P

ASAN

TE

30000 40000 50000 60000 700000.00

20.00

40.00

60.00

80.00

100.00

120.00

f(x) = 4.06736885807803E-15 x^3.4086684147018R² = 0.996408892539504



4.45 4.5 4.55 4.6 4.65 4.7 4.75 4.8 4.850.8

11.21.41.61.8

22.2

f(x) = 3.4086684147018 x − 14.3906864408819R² = 0.996408892539504


LOG AB. MEDIA MALLA

LOG

% R

ET. P

ASAN

TE

30000 40000 50000 60000 700000.00

20.00

40.00

60.00

80.00

100.00

120.00

f(x) = 4.06736885807803E-15 x^3.4086684147018R² = 0.996408892539504



4.400 4.500 4.600 4.700 4.800 4.9000.800

1.000

1.200

1.400

1.600

1.800

2.000

2.200

f(x) = 3.40866841470179 x − 14.3906864408818R² = 0.996408892539504

Grafico Schumann

Grafico SchumannLinear (Grafico Schumann)

LOG ABERTURA MEDIA MALLA

LOG

% R

ETEN

IDO

PAS

ANTE

MEDIANA MEDIA

4.3 4.35 4.4 4.45 4.5 4.55 4.6 4.65 4.7 4.75 4.81.5

1.6

1.7

1.8

1.9

2

2.1

LOG % RET.ACUM V/S LOG AB MEDIA MALLA

LOG AB. MEDIA MALLA

LOG

% R

ET. A

CUM

4.3 4.35 4.4 4.45 4.5 4.55 4.6 4.65 4.7 4.75 4.80.80.9

11.11.21.31.41.51.61.7


LOG. AB. MEDIA MALLA

LOG

% R

ET. P

ARC.

4.45 4.5 4.55 4.6 4.65 4.7 4.75 4.8 4.850.8

11.21.41.61.8

22.2

f(x) = 3.4086684147018 x − 14.3906864408819R² = 0.996408892539504


LOG AB. MEDIA MALLA

LOG

% R

ET. P

ASAN

TE

56796.13 43994.09 31108.52 21997.050.00

5.00

10.00

15.00

20.00

25.00

30.00

35.00

40.00

45.00

% RET PARC.

% RET PARC.

4.45 4.5 4.55 4.6 4.65 4.7 4.75 4.8 4.850.8

11.21.41.61.8

22.2

f(x) = 3.4086684147018 x − 14.3906864408819R² = 0.996408892539504


LOG AB. MEDIA MALLA

LOG

% R

ET. P

ASAN

TE

25.925.0

MALLA % RET. PARC AB MEDIA MALLA ( MICRAS)1" 17.7 31108.5

3/4" 29.0 21997.01/2" 26.1 15554.31/4" 6.9 8980.3

8 3.4 2808.410 1.9 1982.414 1.5 1404.220 2.1 991.228 0.1 696.235 2.9 495.648 3.1 350.565 0.8 247.8

Fondo 4.4

MALLA % RET. ACUM AB MEDIA MALLA ( MICRAS)1" 17.7 31108.5

3/4" 46.6 21997.01/2" 72.7 15554.31/4" 79.6 8980.3

8 83.0 2808.410 84.9 1982.414 86.5 1404.220 88.6 991.228 88.7 696.235 91.6 495.648 94.7 350.565 95.6 247.8

Fondo 100.0

MALLA % RET. PAS AB MEDIA MALLA ( MICRAS)1 1/2" 100 38100

1" 82.3440339188371 31108.51973334643/4" 53.3615990308904 21997.04525612471/2" 27.2562083585706 15554.25986667321/4" 20.351302241066 8980.25612106915

8 16.9594185342217 2808.410 15.0514839491218 1982.414 13.5069654754694 1404.220 11.3870381586917 991.228 11.3264688067838 696.2

35 8.38885523924897 495.648 5.26953361599034 350.4665 4.42156268927926 247.8

Fondo 0

X Y XYMalla log abertura media de malla log % retenido pasante1 1/2" 4.58092497567562 2 9.16184995135124

1" 4.49287934614778 1.91563213866073 8.606704070605673/4" 4.34236434831579 1.72722883514925 7.500256915135131/2" 4.1918493504838 1.43546544051255 6.017254874454471/4" 3.95328872312397 1.30859220412705 5.1732428037434

8 3.44845896436264 1.22941095807943 4.2395732392746510 3.29719128903199 1.17757931980656 3.882704275410414 3.14742896869866 1.13055778978537 3.5583503383583920 2.99616129336801 1.05641077600089 3.1651770769507228 2.84273401894827 1.05409453327371 2.9965103889245635 2.69513129770403 0.923702700137675 2.4895000569147748 2.54463845662334 0.721772179355828 1.8366492445096865 2.39410130204004 0.645575786857665 1.54557383188146

SUMA 44.927 16.326 60.173

n 13m 0.523965795295861b -0.554943726276194k 75190.8688378056F80 49114.5599325248

X Y XYMalla media de malla log % retenido pasante1 1/2" 38100 2 76200

1" 31108.5197333464 1.91563213866073 59592.48018735973/4" 21997.0452561247 1.72722883514925 37993.93085446181/2" 15554.2598666732 1.43546544051255 22327.60249136071/4" 8980.25612106915 1.30859220412705 11751.4931510953

8 2808.4 1.22941095807943 3452.6777346702610 1982.4 1.17757931980656 2334.4332435845214 1404.2 1.13055778978537 1587.5292484166120 991.2 1.05641077600089 1047.1143611720828 696.2 1.05409453327371 733.86061406515435 495.6 0.923702700137675 457.78705818823248 350.46 0.721772179355828 252.95227797704365 247.8 0.645575786857665 159.973679983329

SUMA 124716.341 16.326 217891.835

n 13m 2.99592835664483E-05b 0.968431572080038k 34432.3463420609

F80 31197.6223609913

X Y XYMalla log ab media de malla % retenido pasante1 1/2" 4.58092497567562 100 458.092497567562

1" 4.49287934614778 82.3440339188371 369.9618092724353/4" 4.34236434831579 53.3615990308904 231.7155052008611/2" 4.1918493504838 27.2562083585706 114.2539193045251/4" 3.95328872312397 20.351302241066 80.4545736504939

8 3.44845896436264 16.9594185342217 58.483858874714710 3.29719128903199 15.0514839491218 49.627621764049114 3.14742896869866 13.5069654754694 42.512214416705120 2.99616129336801 11.3870381586917 34.117402977176628 2.84273401894827 11.3264688067838 32.198138191600735 2.69513129770403 8.38885523924897 22.609066307208348 2.54463845662334 5.26953361599034 13.409057887718565 2.39410130204004 4.42156268927926 10.5856689914551

SUMA 44.927 369.624 1518.021

n 13m 33.6058653266893b -87.7070277574996k 2.66938603977133

F80 2.66650231658593

LOG % RET. PARC. LOG AB MEDIA MALLA 1.24689148583224 4.492879346147781.46213486885007 4.342364348315791.41673019689794 4.19184935048380.83915777807368 3.953288723123970.53044095374341 3.448458964362640.28056348052681 3.297191289031990.18879310717116 3.147428968698660.32632097108748 2.99616129336801

-1.21774707326279 2.842734018948270.46799466533947 2.69513129770403

0.4940601557784 2.54463845662334-0.07161903758456 2.39410130204004

LOG % RET. PARC. LOG AB MEDIA MALLA 1.24689148583224 4.492879346147781.66874365190969 4.342364348315791.86179593414011 4.19184935048381.90117867956298 3.953288723123971.91929038152672 3.448458964362641.92915579666541 3.297191289031991.93698113417736 3.147428968698661.94749725286252 2.996161293368011.94779400345958 2.842734018948271.96194831006171 2.695131297704031.97648967546104 2.544638456623341.98035992561061 2.39410130204004

LOG % RET. PAS. LOG AB MEDIA MALLA 2 4.58092497567562

1.91563213866073 4.492879346147781.72722883514925 4.342364348315791.43546544051255 4.19184935048381.30859220412705 3.953288723123971.22941095807943 3.448458964362641.17757931980656 3.297191289031991.13055778978537 3.147428968698661.05641077600089 2.996161293368011.05409453327371 2.84273401894827

2.3 2.8 3.3 3.8 4.3 4.8-1.5

-1

-0.5

0

0.5

1

1.5

LOG % RET. PARC. V/S LOG AB MEDIA MALLA


LOG AB. MEDIA MALLA

LOG

% R

ET. P

ARC.

2.3 2.8 3.3 3.8 4.3 4.81.21.31.41.51.61.71.81.9

22.1

LOG % RET. ACUM V/S AB MEDIA MALLA


Axis Title

Axis Title

2.3 2.8 3.3 3.8 4.3 4.80.50.70.91.11.31.51.71.92.1

f(x) = 0.523965795295865 x − 0.5549437262762R² = 0.928417368719275

LOG % RET. PAS V/S LOG AB MEDIA MALLA

LOG % RET. PAS V/S LOG AB MEDIA MALLALinear (LOG % RET. PAS V/S LOG AB MEDIA MALLA)

LOG AB MEDIA MALLA

LOG

% R

ET. P

AS

0.92370270013768 2.695131297704030.72177217935583 2.544638456623340.64557578685767 2.39410130204004

X^2

20.984873632768720.185964819041318.856128133524

17.571600977151415.628491728379111.891869228893

10.87147039646849.906309113003488.976982495876658.081136702485787.263732711863786.4751848749264

5.73172104442983162.425

X^2

145161000096774000048387000024193500080645000

7887110.563929909.761971777.64982477.44484694.44245619.36

122822.211661404.84

3241485816.252

2.3 2.8 3.3 3.8 4.3 4.80.50.70.91.11.31.51.71.92.1

f(x) = 0.523965795295865 x − 0.5549437262762R² = 0.928417368719275



LOG AB MEDIA MALLA

LOG

% R

ET. P

AS

0 10000 20000 30000 400000.50.70.91.11.31.51.71.92.1

f(x) = 2.99592835664483E-05 x + 0.968431572080039R² = 0.866908884730139

LOG % RET PAS V/S AB MEDIA MALLA

LOG % RET PAS V/S AB MEDIA MALLA Linear (LOG % RET PAS V/S AB MEDIA MALLA )

Axis Title

Axis Title

X^2

20.984873632768720.185964819041318.856128133524

17.571600977151415.628491728379111.891869228893

10.87147039646849.906309113003488.976982495876658.081136702485787.263732711863796.4751848749264

5.73172104442984162.425 2.2 2.7 3.2 3.7 4.2 4.7

0

20

40

60

80

100

120

f(x) = 33.6058653266895 x − 87.7070277575004R² = 0.712584318422878

LOG AB MEDIA MALLA V/S % RET PAS

LOG AB MEDIA MALLA V/S % RET PASLinear (LOG AB MEDIA MALLA V/S % RET PAS)

2.3 2.8 3.3 3.8 4.3 4.8-1.5

-1

-0.5

0

0.5

1

1.5



LOG AB. MEDIA MALLA

LOG

% R

ET. P

ARC.

2.3 2.8 3.3 3.8 4.3 4.81.21.31.41.51.61.71.81.9

22.1



Axis Title

Axis Title

2.3 2.8 3.3 3.8 4.3 4.80.50.70.91.11.31.51.71.92.1

f(x) = 0.523965795295865 x − 0.5549437262762R² = 0.928417368719275



LOG AB MEDIA MALLA

LOG

% R

ET. P

AS

240 5240 10240 15240 20240 25240 30240 352400

20

40

60

80

100

120

f(x) = 3.62844526762581E-08 x² + 0.00107959556439333 x + 9.02813252240476R² = 0.983787153967071

f(x) = 9.29889988713504 exp( 6.89837997368853E-05 x )R² = 0.866908884730139

f(x) = 0.00231235759070098 x + 6.24889940577388R² = 0.96358340288437

% RET. PAS V/S AB. MEDIA MALLA

% RET. PAS V/S AB. MEDIA MALLA Polynomial (% RET. PAS V/S AB. MEDIA MALLA )Exponential (% RET. PAS V/S AB. MEDIA MALLA )Linear (% RET. PAS V/S AB. MEDIA MALLA )

AB MEDIA MALLA

% R

ET. P

AS

31108.5

21997.0

15554.3

8980.3

2808.4

1982.4

1404.2991.2

696.2495.6

350.5247.8

0.0

5.0

10.0

15.0

20.0

25.0

30.0

35.0

% RET. PARC.

% RET. PARC.

F100 (poli) 36800.61F80 (poli) 31438.02F100 (exp) 33933.87F80 (exp) 30746.1F(100) LIN 46876

2.3 2.8 3.3 3.8 4.3 4.80.50.70.91.11.31.51.71.92.1

f(x) = 0.523965795295865 x − 0.5549437262762R² = 0.928417368719275



LOG AB MEDIA MALLA

LOG

% R

ET. P

AS

240 5240 10240 15240 20240 25240 30240 352400

20

40

60

80

100

120

f(x) = 3.62844526762581E-08 x² + 0.00107959556439333 x + 9.02813252240476R² = 0.983787153967071

f(x) = 9.29889988713504 exp( 6.89837997368853E-05 x )R² = 0.866908884730139

f(x) = 0.00231235759070098 x + 6.24889940577388R² = 0.96358340288437



AB MEDIA MALLA

% R

ET. P

AS

0 10000 20000 30000 400000.50.70.91.11.31.51.71.92.1

f(x) = 2.99592835664483E-05 x + 0.968431572080039R² = 0.866908884730139


LOG % RET PAS V/S AB MEDIA MALLA Linear (LOG % RET PAS V/S AB MEDIA MALLA )

Axis Title

Axis Title

2.2 2.7 3.2 3.7 4.2 4.70

20

40

60

80

100

120

f(x) = 33.6058653266895 x − 87.7070277575004R² = 0.712584318422878

LOG AB MEDIA MALLA V/S % RET PAS

LOG AB MEDIA MALLA V/S % RET PASLinear (LOG AB MEDIA MALLA V/S % RET PAS)

MEDIANA 3.0MEDIA 8.0

240 5240 10240 15240 20240 25240 30240 352400

20

40

60

80

100

120

f(x) = 3.62844526762581E-08 x² + 0.00107959556439333 x + 9.02813252240476R² = 0.983787153967071

f(x) = 9.29889988713504 exp( 6.89837997368853E-05 x )R² = 0.866908884730139

f(x) = 0.00231235759070098 x + 6.24889940577388R² = 0.96358340288437



AB MEDIA MALLA

% R

ET. P

AS

31108.5

21997.0

15554.3

8980.3

2808.4

1982.4

1404.2991.2

696.2495.6

350.5247.8

0.0

5.0

10.0

15.0

20.0

25.0

30.0

35.0

% RET. PARC.

% RET. PARC.

240 5240 10240 15240 20240 25240 30240 352400

20

40

60

80

100

120

f(x) = 3.62844526762581E-08 x² + 0.00107959556439333 x + 9.02813252240476R² = 0.983787153967071

f(x) = 9.29889988713504 exp( 6.89837997368853E-05 x )R² = 0.866908884730139

f(x) = 0.00231235759070098 x + 6.24889940577388R² = 0.96358340288437



AB MEDIA MALLA

% R

ET. P

AS

MALLA % RET. PARC AB MEDIA MALLA ( MICRAS)1/2" 26.2 15554.31/4" 25.7 8980.3

8 21.0 2808.410 8.6 1982.414 2.8 1404.220 2.3 991.228 1.1 696.235 2.7 495.648 2.7 350.565 0.9 247.8

MALLA % RET. ACUM AB MEDIA MALLA ( MICRAS)1/2" 26.2 15554.31/4" 51.9 8980.3

8 72.9 2808.410 81.5 1982.414 84.2 1404.220 86.5 991.228 87.7 696.235 90.3 495.648 93.0 350.565 93.9 247.8

MALLA % RET. PAS AB MEDIA MALLA ( MICRAS)3/4" 100 190501/2" 73.7936550253266 15554.25986667321/4" 48.0671820847774 8980.25612106915

8 27.0861103705679 2808.410 18.5283924286857 1982.414 15.7557984537457 1404.220 13.4897360703812 991.228 12.3433750999733 696.235 9.65075979738735 495.648 6.98480405225273 350.4665 6.1050386563583 247.8

SCHUMANNX Y XY

Malla log abertura media de malla log % retenido pasante3/4" 4.27989498001164 2 8.559789960021/2" 4.1918493504838 1.868019021634 7.830454322531/4" 3.95328872312397 1.68184866257168 6.64883335175

8 3.44845896436264 1.43274664379718 4.9407680074610 3.29719128903199 1.26783774043939 4.1803035536814 3.14742896869866 1.19744041673053 3.7688586559120 2.99616129336801 1.13000345268908 3.3856726063228 2.84273401894827 1.09143392686723 3.1026563533435 2.69513129770403 0.984561506382442 2.6535225303748 2.54463845662334 0.844154227169022 2.1480673097865 2.39410130204004 0.785688418189165 1.88101766498

SUMA 35.791 14.284 49.100

n 11m 0.615751902851513b -0.70496069214045k 24713.7832549253F80 17201.027741159

LOG % RET. PARC. LOG AB MEDIA MALLA 1.41840645368141 4.19184935048381.41038024919307 3.953288723123971.32182766820834 3.44845896436264

0.932357968254149 3.297191289031990.442886275148058 3.147428968698660.35527186156357 2.99616129336801

0.059321391428864 2.842734018948270.43017430963192 2.69513129770403

0.425852935849277 2.54463845662334-0.05563312427284 2.39410130204004

LOG % RET. ACUM. LOG AB MEDIA MALLA 1.41840645368141 4.19184935048381.71544188839187 3.953288723123971.86281026651873 3.448458964362641.91100628575293 3.297191289031991.92554001846768 3.147428968698661.93706763698567 2.996161293368011.94278474471729 2.842734018948271.95592450468666 2.695131297704031.96855390529739 2.544638456623341.97264228748054 2.39410130204004


1.868019021634 4.19184935048381.68184866257168 3.953288723123971.43274664379718 3.448458964362641.26783774043939 3.297191289031991.19744041673053 3.147428968698661.13000345268908 2.996161293368011.09143392686723 2.84273401894827

0.984561506382442 2.695131297704030.844154227169022 2.544638456623340.785688418189165 2.39410130204004

2 2.5 3 3.5 4 4.5-0.10.10.30.50.70.91.11.31.5



LOG AB MEDIA MALLA

LOG

% R

ET. P

ARC.

2.2 2.7 3.2 3.7 4.21.31.41.51.61.71.81.9

22.1

LOG % RET. ACUM. V/S LOG AB MEDIA MALLA


LOG AB MEDIA MALLA

LOG

% R

ET. A

CUM

.

2 2.5 3 3.5 4 4.50

0.5

1

1.5

2

2.5

f(x) = 0.615751902851511 x − 0.704960692140441R² = 0.990418206461902

LOG % RET PAS V/S LOG AB MEDIA MALLA


Linear (LOG % RET PAS V/S AB MEDIA MALLA )

LOG AB MEDIA MALLA

LOG

% R

ET. P

AS.

SCHUMANN

X^2

18.317501039928817.571600977151415.628491728379111.891869228893

10.87147039646849.906309113003488.976982495876658.081136702485787.263732711863786.4751848749264

5.73172104442984120.716

2 2.5 3 3.5 4 4.5-0.10.10.30.50.70.91.11.31.5



LOG AB MEDIA MALLA

LOG

% R

ET. P

ARC.

2.2 2.7 3.2 3.7 4.21.31.41.51.61.71.81.9

22.1



LOG AB MEDIA MALLA

LOG

% R

ET. A

CUM

.

2 2.5 3 3.5 4 4.50

0.5

1

1.5

2

2.5

f(x) = 0.615751902851511 x − 0.704960692140441R² = 0.990418206461902

LOG % RET PAS V/S LOG AB MEDIA MALLA


Linear (LOG % RET PAS V/S AB MEDIA MALLA )

LOG AB MEDIA MALLA

LOG

% R

ET. P

AS.

15554.3

8980.3

2808.4

1982.4

1404.2991.2

696.2495.6

350.5247.8

0.0

5.0

10.0

15.0

20.0

25.0

30.0

% RET PARC V/S AB MEDIA MALLA

% RET PARC

AB MEDIA MALLA %

RET

PAR

C


15554.3

8980.3

2808.4

1982.4

1404.2991.2

696.2495.6

350.5247.8

0.0

5.0

10.0

15.0

20.0

25.0

30.0


% RET PARC

AB MEDIA MALLA

% R

ET P

ARC

MALLA % RET. PARC AB MEDIA MALLA ( MICRAS)10 54.2849700442824 1982.414 23.8082834071373 1404.220 4.7668663714509 991.228 2.26621516019797 696.235 2.42250586090128 495.648 2.55274811148737 350.4665 1.69314925761917 247.8

MALLA % RET. ACUM AB MEDIA MALLA ( MICRAS)10 54.3 1982.414 78.1 1404.220 82.9 991.228 85.1 696.235 87.5 495.648 90.1 350.565 91.8 247.8

MALLA % RET. PAS AB MEDIA MALLA ( MICRAS)8 100 2808.4

10 45.7150299557176 1982.414 21.9067465485804 1404.220 17.1398801771295 991.228 14.8736650169315 696.235 12.4511591560302 495.648 9.89841104454285 350.565 8.20526178692369 247.8

SCHUMANNX Y

Malla log abertura media de malla log % retenido pasante8 3.448 2.000

10 3.297 1.66014 3.147 1.34120 2.996 1.23428 2.843 1.17235 2.695 1.09548 2.545 0.99665 2.394 0.914

SUMA 23.366 10.412

n 8m 0.93b -1.40k 4727.34

F80 3715.55


MallaX Y

log abertura media de malla

10 3.297 -0.21414 3.147 -0.60720 2.996 -0.72628 2.843 -0.79335 2.695 -0.87648 2.545 -0.98265 2.394 -1.067

SUMA 19.917 -5.265

n 7m 0.82101490115474b -3.08826984655335X0 5774.66980632382d80 10309.9684149802

X Y XYAbertura media de malla log % retenido pasante

2808.400 2.000 5616.8001982.400 1.660 3290.9011404.200 1.341 1882.439

Log de Ln de (100/porcentaje retenido acumulado(%))

991.200 1.234 1223.149696.200 1.172 816.237495.600 1.095 542.786350.460 0.996 348.906247.800 0.914 226.512

8976.260 10.412 13947.730

m 0.00040b 0.849n 8K 2853

F80 2613

LOG % RET. PARC. LOG AB MEDIA MALLA 1.73467960251008 3.297191289031991.37672808361643 3.147428968698660.67823297761302 2.996161293368010.35530114050121 2.842734018948270.38426483643653 2.695131297704030.40700796357509 2.544638456623340.22869524452545 2.39410130204004

LOG % RET. ACUM. LOG AB MEDIA MALLA 1.73467960251008 3.297191289031991.89261351639486 3.147428968698661.91834555698996 2.996161293368011.93006393574297 2.842734018948271.94225040035207 2.695131297704031.95473244989696 2.544638456623341.96281778762261 2.39410130204004


1.66005900868444 3.297191289031991.34057788368051 3.147428968698661.23400778149655 2.996161293368011.17241799612844 2.842734018948271.09520978449471 2.695131297704030.99556548449941 2.54463845662334

0.9140924416722 2.39410130204004

2 2.2 2.4 2.6 2.8 3 3.2 3.40

0.20.40.60.8

11.21.41.61.8

2


LOG % RET. PARC. V/S LOG AB. MEDIA

LOG AB MEDIA MALLA

LOG

% R

ET. P

ARC

2.2 2.4 2.6 2.8 3 3.2 3.41.6

1.651.7

1.751.8

1.851.9

1.952



LOG AB MEDIA MALLA LO

G %

RET

. ACU

M

2.2 2.4 2.6 2.8 3 3.2 3.40.8

1

1.2

1.4

1.6

1.8

2

2.2

f(x) = 0.926544408763691 x − 1.40469540093924R² = 0.884102871348567

LOG % RET. PAS. V/S AB MEDIA MALLA

LOG % RET. PAS. V/S AB MEDIA MALLA Linear (LOG % RET. PAS. V/S AB MEDIA MALLA )

LOG AB MEDIA MALLA

LOG

% R

ET. P

AS

SCHUMANN

XY X^2

6.897 11.8925.474 10.8714.219 9.9063.697 8.9773.333 8.0812.952 7.2642.533 6.4752.188 5.732

31.294 69.198


X*Y X^2

-0.706 10.871-1.910 9.906-2.175 8.977-2.255 8.081-2.362 7.264-2.499 6.475-2.556 5.732

-14.461 57.307

X^2

7887110.5603929909.7601971777.640

2.2 2.4 2.6 2.8 3 3.2 3.40.8

1

1.2

1.4

1.6

1.8

2

2.2

f(x) = 0.926544408763691 x − 1.40469540093924R² = 0.884102871348567



LOG AB MEDIA MALLA

LOG

% R

ET. P

AS

2.200 2.700 3.200-1.200

-1.000

-0.800

-0.600

-0.400

-0.200

0.000

f(x) = 0.821014901154716 x − 3.08826984655328R² = 0.890095621860625

AJUSTE DE ROSIN RAMMLER

AJUSTE DE ROSIN RAMMLER Linear (AJUSTE DE ROSIN RAMMLER )


LOG

DE LN

DE

(100

/PO

RCEN

TAJE

RET

E-N

IDO

ACU

MUL

ADO

(%))

0.000 1000.000 2000.000 3000.0000.000

0.500

1.000

1.500

2.000

2.500

f(x) = 0.000403480791793345 x + 0.848772736064165R² = 0.987594839325311

AB MEDIA MALLA V/S LOG % RET. PAS

AB MEDIA MALLA V/S LOG % RET. PAS Linear (AB MEDIA MALLA V/S LOG % RET. PAS )Linear (AB MEDIA MALLA V/S LOG % RET. PAS )Linear (AB MEDIA MALLA V/S LOG % RET. PAS )

982477.440484694.440245619.360122822.21261404.840

15685816.252

0.000 1000.000 2000.000 3000.0000.000

0.500

1.000

1.500

2.000

2.500

f(x) = 0.000403480791793345 x + 0.848772736064165R² = 0.987594839325311



2 2.2 2.4 2.6 2.8 3 3.2 3.40

0.20.40.60.8

11.21.41.61.8

2


LOG % RET. PARC. V/S LOG AB. MEDIA

LOG AB MEDIA MALLA

LOG

% R

ET. P

ARC

2.2 2.4 2.6 2.8 3 3.2 3.41.6

1.651.7

1.751.8

1.851.9

1.952



LOG AB MEDIA MALLA

LOG

% R

ET. A

CUM

2.2 2.4 2.6 2.8 3 3.2 3.40.8

1

1.2

1.4

1.6

1.8

2

2.2

f(x) = 0.926544408763691 x − 1.40469540093924R² = 0.884102871348567



LOG AB MEDIA MALLA

LOG

% R

ET. P

AS

1982.4 1404.2 991.2 696.2 495.6 350.46 247.80

10

20

30

40

50

60


% RET. PARC

AB MEDIA MALLA

% R

ET P

ARC

suma

2.2 2.4 2.6 2.8 3 3.2 3.40.8

1

1.2

1.4

1.6

1.8

2

2.2

f(x) = 0.926544408763691 x − 1.40469540093924R² = 0.884102871348567



LOG AB MEDIA MALLA

LOG

% R

ET. P

AS

2.200 2.700 3.200-1.200

-1.000

-0.800

-0.600

-0.400

-0.200

0.000

f(x) = 0.821014901154716 x − 3.08826984655328R² = 0.890095621860625

AJUSTE DE ROSIN RAMMLER

AJUSTE DE ROSIN RAMMLER Linear (AJUSTE DE ROSIN RAMMLER )


LOG

DE LN

DE

(100

/PO

RCEN

TAJE

RET

E-N

IDO

ACU

MUL

ADO

(%))

0.000 1000.000 2000.000 3000.0000.000

0.500

1.000

1.500

2.000

2.500

f(x) = 0.000403480791793345 x + 0.848772736064165R² = 0.987594839325311



0.000 1000.000 2000.000 3000.0000.000

0.500

1.000

1.500

2.000

2.500

f(x) = 0.000403480791793345 x + 0.848772736064165R² = 0.987594839325311




2.2 2.4 2.6 2.8 3 3.2 3.41.6

1.651.7

1.751.8

1.851.9

1.952



LOG AB MEDIA MALLA

LOG

% R

ET. A

CUM

2.2 2.4 2.6 2.8 3 3.2 3.40.8

1

1.2

1.4

1.6

1.8

2

2.2

f(x) = 0.926544408763691 x − 1.40469540093924R² = 0.884102871348567



LOG AB MEDIA MALLA

LOG

% R

ET. P

AS

0.0 500.0 1000.0 1500.0 2000.0 2500.0 3000.00

20

40

60

80

100

120

f(x) = 7.05948038826802 exp( 0.000929048856492791 x )R² = 0.987594839325311

% RET. PAS V/S AB MEDIA MALLA

% RET. PAS V/S AB MEDIA MALLA Exponential (% RET. PAS V/S AB MEDIA MALLA )

AB MEDIA MALLA

% R

ET P

AS

1982.4 1404.2 991.2 696.2 495.6 350.46 247.80

10

20

30

40

50

60


% RET. PARC

AB MEDIA MALLA

% R

ET P

ARC

F80 24277.232363k 26508.667876

2.2 2.4 2.6 2.8 3 3.2 3.40.8

1

1.2

1.4

1.6

1.8

2

2.2

f(x) = 0.926544408763691 x − 1.40469540093924R² = 0.884102871348567



LOG AB MEDIA MALLA

LOG

% R

ET. P

AS

0.0 500.0 1000.0 1500.0 2000.0 2500.0 3000.00

20

40

60

80

100

120

f(x) = 7.05948038826802 exp( 0.000929048856492791 x )R² = 0.987594839325311

% RET. PAS V/S AB MEDIA MALLA

% RET. PAS V/S AB MEDIA MALLA Exponential (% RET. PAS V/S AB MEDIA MALLA )

AB MEDIA MALLA

% R

ET P

AS

laboratorio 1 y tablas

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