Calculo de Reservas y Relacion de Descapote

8/19/2019 Calculo de Reservas y Relacion de Descapote

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CALCULO DE RESERVAS Y RELACION DE DESCAPOTE

EVER ORTEGA RODRÍGUEZ CÓD. 1180640

TATIANA SABOGAL JACOME CÓD. 1180692

JUAN CAMILO TARAZONA CÓD. 1180699

EMIL EDUARDO ORTIZ CÓD. 118069

!E"IN E. RODRIGUEZ CÓD. 1180688

MAYRA ALEJANDRA ARENAS CÓD. 1180648

MINERÍA CIELO ABIERTO

UNIVERSIDAD #RANCISCO DE PAULA SANTANDER #ACULTAD DE INGENIERIA

INGENIERIA DE MINASSAN JOSE DE C$CUTA

2016

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TABLA DE CONTENIDO.

PAG.

INTRODUCCIÓN 4

OBJETIVOS %

1 CALCULO DE RESERVAS Y RELACIÓN DE DESCAPOTE 61 CALCULO DE RESERVAS 6

1 TIPO DE RESERVAS &2 RELACIÓN DE DESCAPOTE 8 M'TODO DE LOS PER#ILES 94 CORTE GEOLÓGICO 10

2 MAPAS ESTRUCTURALES 111 APLICACIÓN DE LOS MAPAS ESTRUCTURALES 122 M'TODOS DE CONTORNO 1

1 CONTORNEO DE LOS PLANOS DE #ALLAS 1% RE(UERIMIENTOS PARA UNA INTERPRETACIÓN

ESTRUCTURAL RAZONABLE 164 ISOLÍNEAS 16

1 ISOPACAS 1&2 ISOCOROS 18 ISOBATAS 194 ISOTENORES 20

CALCULO DE )REA POR M'TODOS CL)SICOS 201 M'TODO DE LOS TRI)NGULOS 202 M'TODO DE LOS POLÍGONOS 2%

4 CONCLUSIONES 9% RE#ERENCIAS BIBLIOGR)#ICAS 40

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INTRODUCCION.

D*+,* -/* /-+ +35+ 7+ 5 3*7: - *;3+3,< +* =*,* ,*/37 >* - +3, ,* 5+ /3?3,,*+ + 3+ ,* 5 -3+73 ,* 5 -3,,< +: >* @ *+ 5** =73/3=5 ,* 73//3 ,* ,3*7**+ *735*+ >* +* + ,: ,:.

L+ 7*/7++ 3*75*+ *+ ,3+733,+ * *5 ++*5 ,* ,3*7**+ 7+ ,**+* /7 ,*=*,* 5 *5*//3 ,* , ,*/, =7 *;7*75+. P7 ,**737 +3- 3*75 * F ,, +* 3** >* 7*53F7 *+,3+ ,* /5/5+ ,* 7*+*7?+ >*=7* 37/3 +3/3**< =7 //*7 *5 *+, ,*5 3*75 + ,3+73/3. E5/5/5 ,* 7*+*7?+ /+3+* * ,3?3,37 5 F *+,37 * 7*+ ,* /3*7 ,3+/3 ,, =737 ,* =+ ,* 37/3 573* *3,+ * /=< / 5 *737 +**+5*/* -/3 ,,* - 3*75 +* 7*53F /5/5+ ,* ?5@**+ ,* /*7, 5+7*+*7?+ *;3+**+< =73*7 5+ 7*+*7?+ *,3,+< 5* 5+ 7*+*7?+ 3,3/,+ =7 @535+ 7*+*7?+ 3*73,+ / *+ 37/3 ,*55, ,* ,,* +* */*7 *5 3*75 +*

=*,* 55*7 =533/7 =7*/ 3*7 * ,**73, F ,,* +* =7 +=*+*/3/** 7*5* 5 *;=5/3 ,* ,3/- 3*75.

E *5 +33** 7H +* *3F7 * / 7*53F7 /5/5+ ,* 7*+*7?+ *,3*,3*7**+ ,+ +* *;=53/7 ,*55* 5+ =7/*,33*+ ,* ,3/-+ ,+ =755*7 5 H*3? 35 >* *+ +*7 / 3*75 *+ @35 * F ,,* 57 +*+* >* +* */*7 ,3/-+ 3*75*+ =7 5+ /7/*7:+3/+ *53/+ *+,3+ =7*?3** 7*53F,+.

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OBJETIVOS

GENERAL

D7 //*7 5+ ,3*7**+ ,+ ,* /5/5 ,* 7*+*7?+ *,3* *H*7/3/3+ =7/3/+ >* =7* 5 *+,3* 5 37/3 */*+73 =7 *+5*/*7 5 /3,, ,*3*75 >* =*,* -*7 * /33* ,,.

ESPECI#ICOS• A53F7 / +* 7*53F *5 /5/5 ,* 7*+*7?+ *,3* 75+ /?*/35*+

• A=53/7 5+ //*=+ ,* I+5:*+ 7*53F7 *H*7/3/3+ =7/3/+ =7 7

**,33*

• D*337 /7+ *+7/75*+ =737 ,* =+ ,* 37/3

• C/*7 5+ ,+ ,* 735/3 =5: =7 =53/75+ 5 /5/5 ,*

7*+*7?+

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1. CALCULO DE RESERVAS Y RELACION DE DESCAPOTE

1.1. CALCULO DE RESERVAS

L+ 3*75*+ +* */*7 ,3+=*7++< ,* *7 ,*+35 *F/5,+ / 7+*735*+ * *5 ++*5. E 5 /3?3,, 3*7< 5 =73*7 >* ,** 7*53F7+* *+ +/7 *3,*33/7 ?5@**+ /+3,*75*+ ,* 3*77 >* =7*+** 5+ 5**+ ,* /*3, ,*3*75 /33*.

A5+ /33*+ *+ + /*7/ ,* 5 +=*73/3* >* 7+< 7 /*7=+<

?*+ +. A+: 3+< =*,* */77+* ,3+3+ 3?*5*+ ,* //*7/3 ?5*< * ,3+3+ F+ ,*5 3+< 5+ /5*+ +*7 7*5*+ =7 */3 ,*,**73,+ =7*/3+.

Recurso +* *3*,* =7 3*75 >* +* +* *;3+* * 5 /7*F *77*+7* ,*

3*7*/3 *53/ 3* ,/*, +* HF +* =75* >* *;3+.

E5 /5/5 ,* 7*+*7?+ +/ *7*7 *5 =*/35 */3/ >* =*,* **7 5+7*/7++ 3*7+ ,, 73* ,3+*K+ 3*7+ >* ++* *5 =5 3*7 =737 ,*5/5 *+ /5/5, *5 5H ,* /H ,*5 =7*/.

E5 *5H* ?5* ,* 7*+*7?+ ,* 3*75 >* +* */*7 * *5 7* H3?*+3/3 +* /5/5 =737 ,* 5 37/3 *53/ ,*5 7*< =7 *,3 ,*+*7?/3*+ ,37*/+< =*< 573*+< 73/-*7+< 7H+ ,* *;/?/3 =7 *,3 ,* 5+ 7*+5,+ *3,+ * 5 +* ,* *,3/3*+ -*/-+ * =7+=*//3.

U ?*F 3,*33/, *5 /33*< +* =7/*,* ,**737 *5 ?5* ,* 3*75 >*+* =,7: **7 ,*5 3+.

1.1.1. TIPOS DE RESERVAS

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Reservas Minerales: R*/7+ 3*75 >* 7?+ ,* + //33* *?5/3 +* 55* 5 //5+3 ,* >* =*,* +*7 *;=55* / 5 */5: /,3/3*+ */3/+ /5*+.

Reservas eol!"icas: C+3* *5 /H ,*5 /33*< *+ ,*/37< , *5*735 =7*+** H + /,3/33*+ ,**73,+.

• Pro#a$as o %e$i$as: V5* ,* 3*75 >* +* /5/5 +, / +* 5+

7*+5,+ *3,+ ,* 5+ 7H+ ,* *+7* +,H*+. L+ =+ ,*37/3 ,3+ -+ %00< *5 ,*5 7 *+ *>3?5* 35*/3 ,*-+ 2%0 /,+ =737 ,* = ,* 37/3

• Pro#a#les o in$ica$as: V5* ,* 3*75 >* +* /5/5 * +* 37/3

*+ *;-+3? >* * *5 /+ ,* 5+ 7*+*7?+ =7,+. T 5 **7:< /*5 ?5* ,* 3*75 5 5* - +3, 3*73,+ =737 ,* *+,3+ =7*5337*+<

=7 5 >* +* 3,3/ >* *;3+* 73*+ ,* ,3+/33,,.

L+ =+ ,* 37/3 ,3+ *7* %00 1%00 *5 ,*5 7< *+ *>3?5* 35*/3 ,* -+ %00 /,+ =737 ,* = ,* 37/3.

• Posi#les o in&eri$as: M+ 3*75 5/53F, * *;*+3*+ *;=57,+ =7 5

>* 5+ *+33?+ /33?+ +* + ,*5** * *5 //33* ,*/7/*7 *53/ ,*5 ,*=+3 >* *;3+* *,3,+ 3 *+7+ *++ + *+/++ ,+ ,* *;=57/3 / ,* ,*+7755 =7 *;3+*3 /*7*F /*7/ ,* + 5/53F/3 *;*+3. L+ =+ ,* 37/3,3+ *7* 5+ 1%00 4%00 < *5 ,*5 7< *+ *>3?5* 35*/3 ,*-+ 1%00 /=7*,3, *7* 5+ &%0 5 22%0< /,+ =737 ,* = ,* 37/3

• Reservas 'i(o)*)icas: L+ =+ ,* 37/3 + ,3+*+ + 4%00 *7* +:.

• Reservas es(ecula)ivas: N - =+ ,* 37/3 + +** ,3+*+.

P ,* I7/3 P 7*5 >* *;3+* * /= =*,* +*7 573*< =*77/3< 57*+ 3*7+< */.

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L+ 7*+*7?+ +*7 /+3,*7,+ */3/+ /, *5 ?57 >* +* *+=*7 **7 =7 + ?* +=*7 5+ /++ * 5+ >* +* *+3 3/7737 =7 +/75+ ,*5 ++*5

=7/*+75+.E5 =7=+3 **75 ,*5 /5/5 ,* 7*+*7?+ *+ *7*7 *5 =*/35 */3/ >*

=*,* **7 5+ 7*/7++ 3*7+ ,, 73* ,3+*K 3*7< ,**73 5 /3,,</53,, 5 /3353,, ,* 5 *;=5/3 ,* /33*

E+* /5/5 ,** 7*53F7+* ,7* , 5 ?3, =7,/3? ,* 5 3< ,*+,* 5+*=+ ,* =7+=*//3 -+ *5 3* ,* 5+ 7*+*7?+ /*3,+ * *5 ,*=+3. E+3 3=7* //*7 5 =*/353,, ,*5 /33* =7 ,**737 *5 5:3* ,* 5+*;=57/3*+ ,*+7755+ *53/+ 5 ,3+73/3 ,* 5+ ?57*+ ,*7 ,*5 /*7= *53= ,* 73* *5@73/ >* ,**7 +*7 +*3,+ *++< K 3= ,* *>3=

>* +* ,**7 3+57 * 5 ?3, /3? ,* 5 3< *5 , ,* *;=5/3< 57*>*733*+ ,*5 /=35 3/33*< **7: */*+73< ,* 7< *735*+*/.

1.+. RELACION DE DESCAPOTE

E 3*7: /3*5 3*7< *+ 5 *= * 5 /5 +* 7**?* 5 /= ?**5< *5 +*5 *5*+7353*75 7/ >* 7*=7*+* **3/3 */3/ =7 5 *=7*+ 3*7>* /7* /33*< =7 ,*H7 ,*+/3*7 *5 3*75 ,* 3*7+ */3/.O=*7/3 >* +* 7*53F ,7* 5 +* ,* =7*=7/3. E5 *735 ,*5 ,*+/=* ,** +*7 ,3+=*+ ,*/,** =7 + =+*737 7*353F/3 * =7/*++ ,* 7*+7/3

7*/=*7/3 3*5.E5 /7 ,**73* * 3*7: /3*5 3*7 *+ *5 ,*3, 73< ,*33,

/ *5 7*+5, *7* 5 /3,, ,* *+735 77/, 5 ,*5 3*75 *;7:,< E+* =7*7 3** + //3*+ */3/+ ,*5*+ *+ *5 >* 73* 5 =7,3,, *;*+3 >* 5/F 5 3. (* *5 73 +* 5 +=* *5*?,+ ++ =7 *;7*7 3,, ,* 3*75< 5 >* =*,* 55*7 =7,/37 =*7,3,+ =7 *5/773< 73+ H+ 3=53/ /+*+ /- *7*+ * **75 **3/3+.

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E+ 5 7*5/3 *7* *5 @*7 ,* *5,+ 7*?3,+ / ,*+*/- *5 @*7 ,**5,+ ,* 3*75 7*?3,+ ,* 3 /3*5 3*7.

R= m ³deestéril

m ³demineral ó

Tonestéril

Tonmineral

BESR R*5/3 E/3/ ,* ,*+/=*

BESR=

Costobocamina

tonmineral B .T −

tonmineralB.T

tonmineral CA

Costo descapote de1 ton deestéril

C,

BESR R.D +* =*,* *;=57 C3*5 3*7

BESR R.D *+ 3,3*7** *;=57 C.A B.T

BESR R.D +* ,** *;=57 C.A

1.,. M-TODOS DE LOS PERILES

E5 , ,* *+3/3 *,3* /7*+ =*735*+ +* =*,* +7 +3 *5 /33** *;=57, * 7*, 7*57 >* =*73* 5 /+7//3 ,* /7*+ *53/+. L+

/7*+ *53/+ ,* /33*< +*@ + 73*/3< =*,* +*7 -73F5*+<?*73/5*+ =*735*+ =75*5+. L ,3+/3 ** 5+ /7*+ =73/57*+ *+ /+* /77*+=,* 5 ,3+/3 *7* 5+ 5:*+ ,* *;=57/3 * *5 /+ ,* =*735*+ ?*73/5*+ 5 57 *7* 3?*5*+ ,* 3 * *5 /+ ,* /7*+ -73F5*+.

E5 7* ,* 5 +*//3 ,*5 /*7= 3*753F, 3*7/*=, =7 /, =*735 +* =*,*/5/57 =7 ?73+ ,+ =5:*7< 7*5 ,* S3=+< */..

L +/*+3 ,* /5/5 *+ 5 +33**.

Q C+7//3 5+ =*735*+ =7 +,* >* - /7, *5 ,*=+3.

Q C5/57 *5 ?5* ,* /, ,* *++ 5>* 7?+ ,*5 =7*,3 5 *,3/3 ,*57* /=, =7 *5 ,*=+3 * 5+ =*735*+ 5:3*+ ,*5 5>*< 53=53/, =7 5+*=7/3 *;3+** *7* 5+ =*735*+ 1 2 2.

Q S* ,**73 *5 ?5* ,* 5+ ,+ /3*77*+ *;7*+ ,*5 ,*=+3.

2

S3*,

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#/ +=*73/3* ,*5 =*735 + =7;3 5 /3*77*.

D/ ,3+/3 ,*5 =*735 + =7;3 5 /3*77* 5 5:3* ,* *+* /3*77*.

Q S* /5/5 *5 ?5* 5 ,*5 ,*=+3 *+

Q C5/5 ,* 7*+*7?+ ,* /, 5>* =7 + 7*+=*/3? ,*+3,,

Q

Q C33//3 ,* 5+ 7*+*7?+ 5*+ Q =7.

E5 ?5* ,*5 5>* /=7*,3, *7* =*735*+ +* =*,* **7

53=53/, *5 7* ,* /, +*//3 =7 5 3, ,* 5 ,3+/3 5 =*735 /3 /,5, /, =*735 **7 5>* V A2Q,12A2Q,22.

-55, *5 7* *,3 ,* ,+ =*735*+ /+*/3?+ 53=53/, + =7 5 ,3+/3*7* ,3/-+ =*735*+. E *+* /+< 5+ ?5@**+ ,* 5+ *;7*+ +* /5/5 V1 A1Q,12

75=73+3,5 +* 7*+ +*//3*+ =7 /5/57 *5 ?5* /=7*,3, *7*5+ ,+ *;7*+< ,,5* 7 =*+ 5 ,*5 /*7

V A142AQ,1,26. E+* =7/*+ +* 7*=*37: =7 A< A4 A6 +3+/*+3?**< +3*, */*+73 /77*//3 =7 5+ *;7*+.

U ?*F /5/5,+ 5+ ?5@**+ ,* /, 5>*< +* -55 5+ ,*+3,,*+=7**+ *,3+ 5+ 5**+ *,3+ /+3,*7, ,+ 5+ ?57*+ *3,+ * 5++,*+ ,* /, 5>* =7 =,*7 /5/57 *5 *5H* ,* 3*753F/3 ,* /, 5>*<+3*, *5 *5H* 5 ,* *5 * *5 /33*< 5 + ,* 5+ *5H*+ =7/35*+.

1./. CORTE EOLOICO

E+ 5 3*7=7*/3 73/< * =5 ?*73/5< ,* 5 *+7/7 *53/ ,*5++*5. P7 /+7375 -/* 5 +37 +7* =*735 =73/< 5+ ,+ *53/+>* +* +*7? +7* *5 = 5 57 ,* 5 +*//3 /+3,*7,.

S* /+7* *5 =*735 =73/ ,* 5 +*//3 ?*73/5 >* +* ,* 3*7+. P7 *55<+* 353F7 5 37/3 =73/ =7*+** * *5 =.

A /3/3< +* 7+5,7 5 =*735 =73/ 5+ =+ ,* // *7*7/3*+ *53/+ ,*+ /7/*7:+3/+ *53/+ 7*+*K5*+. ,3+/7,/3+<55+< */.. D3/-+ =+ *+ * *5 = < =7 < * *5 /7* -7 ,* *+7 +7* *5 =*735 =73/.

L 37/3 7*53? 5+ //+ * =7,3,, +* *,7 *,3* *5*=5* ,* 5:*+ ,* /= ;3537*+< 5 / +* ,*+/7337 + ,*5*.

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+. MAPAS ESTRUCTRALES

S =+ >* /+3+* * 7F7 *5 /=73* :+3/ ,* 5+ *+7/7+*53/+ * *5 ++*5< = *+7/75 *+ 5 =7*//3 * *5 =5 +* ,* /*7= 3*75 ,* 3*7+.

E5 = *+7/75 *+ /7, =7 5+ /7+ /7?+ *+7/75*+ 5+7F+ ,* 5+ 55+.

L+ /7+ *+7/75*+ + 37 +7* 5 73*/3 ,*5 *+7 =*,7< 5 3/53/3 3, ,*5 *+7 * 7*5/3 5 =5 -73F5 F3*<5 75: ,* 5 *+7/7 * /+ ,* -*7 =53**+< *5 ,*+=5F3* ,* 5+ 55+< */.

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U * /75 *+7/75 =*73* *+5*/*7 5+ *H7*+ ,3+*K+ ,* =*77/3< =7 *H*=5< *+5*/*7 5+ =7,3,,*+ -+ ,,* =*777< 73F,< =7 =7*<*/77 *5 H*3?< =7 7< =*777 * *;/*+

W L+ **+ ,* 37/3 =7 5 /+7//3 ,* *+* 3= ,* =< + * =73*73+/3 5+ ,+ +:+3/+ 5+ 7*3+7+ ,* =F+.

+.1. APLICACIONES DE LOS MAPAS ESTRUCTURALES

1. A=77 /3*7 3= ,* 37/3 =7 >* H / 7+ =+ =,*7 *?57 5+F+ ,* *+,3.

2. E;*,*7 5 37/3 //3, 7?+ ,* 5+ 7*+ ,,* ,3/- 37/3 +* =/ 5.

. P,*7 ,**737 5+ 7*5/3*+ *7* 5+ =+ ,* +*7?/3.

W E 7*+ ,* 533, /75 ,* 55+ ?*73/5*+< *+ 3=7* /7*7 5 533,, =7 7*5*H7 5 3*7=7*/3 *53/ +3=5* / +* =+35*

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. W C5>3*7 /3 7,3/5 * 5 ,37*//3 ,* 5+ /7+ =*,* +*737 553*< /, 5+ 55+ - +3, 7*//3,+ =7 *5 =F /75.

W U 3/7** * *5 ?57 ,* F3* /=K, =7 /3 7= * 5,37*//3 *+ *7* *?3,*/3 ,* 553* 3+-= 1960 .

W U /3 3?*7+3 * 5 ,37*//3 ,*5 F3* +3*7* *5 /7/* ,*5 *H* ,* =53**.

W L+ *+7/7+ =*,* **7 **7 /=3353,, ,* /7 7?+ ,* 55.

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W L+ *+7/7+ 5+ +* =5 * *5 *H* / F3*+ +?*+ * =* ,* 5*+7/7< **7, *+=/33*+ 7,*+ ,* 5+ 5:*+ ,* /7 7?+ ,* 5 /7*+,* 5 *+7/7 /=7, 5 *+=/33* * 5+ 5/+.

W U =*,3** 7= /3 -/3 5 /7*+ / *+/+ 5 =53* ,* 5 =*,3**< 3,3/ >* 5 +=*73/3* +3, */, =7 5 *7+3 3,3/ 5 =7*+*/3 ,* ,3+/7,/3.

+.+. M-TODOS DE CONTORNEO

W C7* */3/ +* +* >* 5 =*,3** *5 5 ,* F3* ,* 5 +

=*73/3* >* *+ +3*, /7*, *+ 37* *7* =+ ,* /75.

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W C7* =75*5 / *+* ,< 5+ 5:*+ ,* /7 + ,3H,+ =75*5+ /*7/** =75*5+ 5+ 7+

W I5 *+=/33* +* =*,3** 5 ,* F3* 37* +7* 7***7 5 *+ +7* 5/ 3,3?3,5 ,* *+7/7.

W C7* 3*7=7*3? *5 *5 3** =5* /=/3,, =7 **77 = >*7*5*H* 5 *H7 3*7=7*/3 ,*5 7* ,* *+,3< 3*7+ -7 *5 /75 ,3+=35*.

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+.+.1. CONTORNEO DE PLANOS DE ALLAS

WD*53* 5 =+3/3 ,* 5+ 7F+ ,* 5 55 * *5 5>* 5*?, * *5 5>*,*=733,

.WR*=7*+* 5 +*=7/3 ?*73/5 ,* 5 55 * *5 -73F* =73/57 +*7 =*,.

+.,. RE0UERIMIENTOS PARA UNA INTERPRETACINESTRUCTURAL RA2ONA3LE

1. C77*5/3*+ /77*/+ ,* 7*3+7+ +:+3/.

2. U * **,33* ,*5 *+/*73 */3/ >* - +3, 7H,.

. U /57 **,33* ,* 5+ =73/3=3+ +3/+ ,* *5:< 3/5*, 5 **7:,* 3*7+*//3 ,* 7/3*+ 55+.

4. V53,/3 73,3*+35 ,* 5 3*7=7*/3.

%. U+ ,* , 5 , ,3+=35*.

6. U **,33* ,* 5 *;/3, ,* 5 ,.

&. U+ ,* /3/+ ,* =* /77*/+ *;/+.

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8. C+7//3 * 3*7/3 ,* ,+ 5+ =+ 7*>*73,+. 9. /+7//3 ,* +*//3*+*+7/75*+.

10. M=* ,* @53=5*+ -73F*+.

11. B* ,/*/3 ,* , *5 7H.

+./. ISOLINEAS

I+5X*+ + /7?+ >* * ,+ 5+ =+ ,* 35 ?57. L+ 3+53*+ +=53** +,+ * 3*3*7: =7 35+77 5+ ,3+73/3*+ ,* ?57*+.

E5 , +* + * 5 7*5 ,* 5+ ,3+73/3*+ 7,5*+< =5 /+7//3*+ ,*5+ I+5:*+< +* 7*/77* 5 3*7=5/3 3 ,* -557 5+ ?57*+ 3*7*,3+ *7* =+ ,* ?57 //3,. L *+3/3 ,* 7*/7++ =7 *5 , ,* 5+ 3+53*+ =7*+=* >* 5+ ?57*+ ,* 5 ?735* ,* 3*7+ ?7: 7,5 /3** *7* 5+

3*7+*//3*+ ,* *;=57/3.

L+ 3+53*+< + >*55+ 5:*+ /7?+ >* * =5 = * ,+ 5+ =+ ,* 35 ?57 373. S* *=5* =7 35+77 73/** 5+ =7=3*,,*+ :+3/+ >:3/+ >*55+ =7/*++ **+ >* =*,+ +*7 *;=7*+, =7 ?57*+373+.

A5+ ,* 5+ =7=3*,,*+ ,* 5+ /*7=+ 3*75*+ =*,* 7*=7*+*7+* =7 *,3 ,*I+5X*+. E /H< 5+ 5:*+ /73* +=*73/3* 3373 >* ?3** +*7 5*;=7*+3 73/ ,* ?57*+ >* *,*/* 5+ =73/3=3+ ,* **7: 5:3/ ,* 5**7: ,* +53,+.

E 5 *?5/3 ,* /33*+ 5+ ++ + /*+ ,* 5+ I+5X*+ + *5 /= ,**+=*+7*+< *7*+ /7*+ =7*,3+.

+./.1. Iso(acas

L ?73/3 ,*5 *+=*+7 7*5 ,* 5+ /*7=+ *53/+ +* 7*=7*+* 73/** =7 *,3 ,*5 = 3+=/< ,* 5:*+ 3+=/+. C, 5:* /7? 3+=/ * =+ ,*35 *+=*+7 7*5 ,* 5+ *+7+.

L:* >* * 5+ =+ ,* 35 *+=*+7 ,* *+7 *+=*+7 7*5.

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* *+=*+7 =7**

*7 *+=*+7 7*5

B A5 ,* F3*

ISOPACA C7 ,* */- C7 ,* =3+Q/+B *Q/+B

I= C.T. C.P. Q /+B *7

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P7 7*53F7 *5 /5/5 ,* ?5* ,* 3*75 *7* ,+ 5:*+ 3+=/+

Ip1∗ Ip 2(¿)

Ip1+ Ip2+√ ¿

V =( A

3 )¿

+./.+. Isocoros

L:* >* * 5+ =+ ,* 35 *+=*+7 ,* *+7 *+=*+7 =7**.

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E 5+ =+ ,,* /, ,* *++ /7?+ +* /7F =,*+ -557 5 ,3*7*/3,* 3?*5 >* - *7* *++< 57, / *55 55 ,* =+ =7,/ ,* *+ 7*+.E++ =+ 3,3/ 5 ,3*7*/3 ,* 3?*5 >* - *7* *5 */- *5 =3+ ,* *+ 3,,* 5+ /7/*+ +*K5,+

S* =*,* /5/57

ISOCORA C7 ,* */- C7 ,* =3+ *I/ C.T. C.P. *7/+B

C 5 55 ,* =+< 7*+5* ,* 5 7*+ ,* 5+ 3++ * *5 /7* ,* 5+/7+ ,* */- =3+< 5+ /5*+ 7*=7*+* 5 ,3+/3 ?*73/5 *7* *++< =,*+,*53*7 *5 = ,* /7?+ I+/7+ ,* ,3/- /*7= * ++*5

+./.,. Iso#a)as

C, 5:* /7? 3+ * =+ ,* 35 =7,3,, ,* 5 +=*73/3* *53/.

E+ 353F, =7 /5/57 5 7*5/3 ,* ,*+/=*.

ISOBATA C =73/ C7 *+7/75 ,* */-

P7 7*53F7 *5 /5/5 ,* ?5* ,* 3*75 *7* ,+ 5:*+ 3++

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Ib1∗ Ib 2(¿)

Ib1+ Ib2+√ ¿

V =( A

3 )¿

+././. Iso)enores

L:* >* * 5+ =+ ,* 35 *7. S* /5/5 3*7=5, =+ ,* =*77/3< / *7*+ //3,+.

T*7 /3,, 7*53? *5 =7/*H* ,* /*3, ,*5 *5 * + /33*.

T*7 7 T

C5/5 ,* V5* R*+*7?+ ,* T*7*+

V 1= Ah1

3 × Ib1+ Ib2×√ Ib1× Ib2

d=m

V ;m=d ×V

T́ 1=T 1+T 2+…+Tn

n

R1=m× T́ 1 Rt = R1+ R2+…+ Rn

.

,. CALCULO DE 4REA POR M-TODOS CL4SICOS.

,.1. M-TODO DE LOS TRI4NULOS.

E5 , /+3+* * ,3?3,37 +*//3 5>* ,*5 ,*=+3 3*75 * *+,3<

* +3+* >* /+3+* * 5 /7*/3 ,*5 ;3 @*7 ,* 735+ *,3* 5/*;3 ,* +,* /*75 -/3 +,*+ *;*7+.

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Imagen. Método de los Triángulos.Fuente. Autores del trabajo.

E5e%(lo.

E 5>* ,* *+,3 +* - 7*53F, 9 =*77/3*+ *3*, 5 +33**37/3 //*7/3 ,* 7 -55,.

Per&oraci!n Es(esor.

6%7

Tenor.

6"r.8)on.71 6


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1 )7* ,* *+,3 / + 7*+=*/3? =*77/3.

2 G**7/3 ,* 735+ =7 *,3 ,* =7*//3*+ ,*+,* = /*7.

C5/5 ,* 7*.

A=( H ∗ L)

2

pág. 22


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Tabla. Calculo Áreas del Método Triangular Fuente. Autores del trabajo.

Figura b (m) a (m) Área (m2)

1


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V ?5*

M1 &4.0% . M% 6&9.99

M2 69.409 . M6 &9.418 .

M %&1.8%9 . M& 69.449 .

M4 60.18 . M8 &06.9%9 .

• S* /5/5 *5 =7*,3 ,* *7*+ ,* /, 7*< +* 53=53/ =7 5+ ++ **+ 5 /3,, ,* 7*+*7?+ * ,3/- =5:

4rea Nu%ero Tenor Pro%e$io 6"r8)on.7 Reservas6"r.7

1 4


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,.+. M-TODO DELOS POL9ONOS.

S* *=5* =73/3=5** * /*7=+ 57*+. L+ +,*+ +* ,373*

75** 90[ / 7*+=*/ 5 + 57 *?57.

E+* , /+3+* * -557 7* ,* 35 35*/3 * 57*+ 3*7+ >* =*, 7*=7*+*7+* * = *,3* =+. L +* ,*5 =5: +*7 *5 7* ,*35*/3 /77*+=,3** 5+ 57*+.

E5 *+=*+7< *7< 7?*,, *+=*/:3/ + 5+ *3,+ =7 /, 57.

E;3+* ,+ ,+ =7 ,**737 *5 ?5* ,*5 3*75 ,* 3*7+ =5:+ 3+*/7*+ =*7=*,3/57*+< 3+*/7*+ 57*+.

a7 3isec)or (er(en$icular.S* /+7* 7F, 5:*+ =*7=*,3/57*+ 5 +**. U3*, *5

+,* =*7373/ / *5 /*7.

Imagen. Polgono bisector !er!endicular.Fuente. Autores del trabajo.

#7 3isec)or an"ular.S* /+7* 3*7+*/, 5+ 3+*/73/*+ ,* 5+ 5+ >* +* 7 5 37

5+ ,3+3+ =+ ,* =*77/3.

pág. 25


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Imagen. Polgono bisector angular.Fuente. Autores del trabajo.

APLICACIN.

a7 Pol"ono 3isec)or Per(en$icular.

E 5>* ,* *+,3 +* - 7*53F, & =*77/3*+ *3*, 5 +33**37/3 //*7/3 ,* 7 -55,.

Per&oraci!n Es(esor.6%7

Tenor.6"r.8)on.7

1 6


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+7 S* 7F 3+*/7*+ =*7=*,3/57*+.

,7 S* **7 *5 =5: /*75 3*, 5+ *;7*+ ,* 5+ ?*/7*+ /7*,+.

pág. 27


28/39

/7 S* *;7=5 5+ ?*/7*+< 5+ /5*+ * **75 5+ 7*+ ,* 35*/3 ,* 5+ =*77/3*+.

;7 S* /7* 37+ //3,+ =7 *5 /5/5 ,* 7*.

pág. 28


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E5 7* +* ,**73 =7 5 +33** 75

A=( H ∗ L )+( H 1∗ L1 )+…( Hn∗ln)

2

pág. 29


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)7* T5 4&.&8 2.

V = A∗e

V1 4.88% . V% 20.468 .

V2 1.&% . V6 2%.62 .

V 41.968 . V& 2&.99 .

V4 1&.92 .

V. 209.%89


31/39

V ?5*

M1 846.98 . M% 9%.02

M2 612.48% . M6 494.%2 . M 809.982 M& %40.20& .

M4 4%.8%6 .

• S* /5/5 *5 =7*,3 ,* *7*+ ,* /, 7*< +* 53=53/ =7 5+ ++ **+ 5 /3,, ,* 7*+*7?+ * ,3/- =5:

4rea Nu%ero Tenor6"r8)on.7

Reservas6"r.7

1


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1 )7* ,* *+,3.

2 S* *5F 5+ +,*+< *5 3*7 -/3 /, ,* 5+ *;*7+< 5+ *;*7+*7* +:.

pág. 32


33/39

S* **7 5+ 3+*/73/*+ >* * ,**737 *5 =5: /*75.

4 S* /7* *5 =5: /*75 =737 ,* 5+ =+ ,,+ * 5 /7*/3 ,* 5+ 3+*/73/*+< 5+ ,*+ =5:+ + **7, =737 ,* 5 *;7=5/3 ,* 55:* 3+*/73F /*75.

pág. 33


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% S* /7* 5+ 37+ //3,+ =7 *5 /5/5 ,*5 7*.

E5 7* +* ,**73 =7 5 +33** 75

pág. 34


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A=( H ∗ L )+( H 1∗ L1 )+…( Hn∗ln)

2

)7* 5 1 2.

pág. 35


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V = A∗e

V1 .64 . V% 1.804 .

V2 21.&2% . V6 1.4%% .

V 16.&& . V& 14.62% .

V4 20.8 .

V. 14.09

=7 D*33/3 ,* 5 /3,, ,* 7*+*7?+

• C5/5 ,* R*+*7?+ 5*+ ,* 3*75

D*+3,, ,*5 7 19. 7/.

M , ; V.

M+

, ,*+3,,

V ?5*

M1 649.1 . M% 266.42

M2 419.29 . M6 2%9.68 .

M 2.66 . M& 282.26 .

M4 401.44 .

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• S* /5/5 *5 =7*,3 ,* *7*+ ,* /, 7*< +* 53=53/ =7 5+ ++ **+ 5 /3,, ,* 7*+*7?+ * ,3/- =5:

4rea Nu%ero Tenor

6"r8)on.7

Reservas

6"r.71


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S* /=53*7 5+ H*3?+ =7=*++ +* +/353F / ,+ 5+ *+,3*+

/ +* 7*53F /5/5 ,* 7*+*7?+.

S* *+,37 5+ ,3*7**+ 3=+ ,* I+5X*+ ++ /3*+.

S* ,3 //*7 5+ ,+ ,* 735/3 =5: *,3* *H*=5+

=7/3/+ =7 >* 5+ *+,3*+ +* 35373F7 / 5+ *+.

REERENCIAS 3I3LIORAICAS.

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R. OYARZUN ESTIMACION DE RESERVAS.http://es.slideshae.net/!h"nRi#had$ill#"/estima#in%de%ese&as

• CALCULO DE RESERVAS POR METODOS CONVENCIONALES.

'''.bdigital.unal.edu.#"/()*+/,/(-%*Capi*.pd0
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