EJERCICIO DE CALCULO DE RESISTENCIA DE PILARES

Vista previa del material en texto

Metodo Area Tributaria
	r	sp/sz
	0.2	1.3
	0.3	1.4
	0.4	1.7
	0.5	2.0
	0.6	2.5
	0.7	3.3
	0.8	5.0
	0.9	10.0
sp/sz	0.2	0.30000000000000004	0.4	0.5	0.6	0.7	0.79999999999999993	0.89999999999999991	1.25	1.4285714285714286	1.6666666666666667	2	2.5	3.333333333333333	4.9999999999999982	9.9999999999999911	R
sp/sz
Resistencia Pilares Metodos
	1. Ensayo laboratorio (roca intacta)
	UCS	150	Mpa
	Ws	100	mm
	Hs	50	mm
	Volumen	196350	mm3
	Volumen probeta	0.00020	m3
	Ws/Hs	2
	2. Parámetros del macizo rocoso
	GSI	80
	mi	25
	D	0.5
	mb	9.65
	s	0.069
	a	0.50
				Resistencia a la compresión Global macizo
	UCS (macizo) H&B	39.6	MPa	141	Mpa
	Sigma t(macizo) H&B	-1.08	MPa
	Modulo macizo	52	Gpa
	3. Calculo Luz Máxima
	Resistencia tracción 		1.08	Mpa
	Modulo de Young (techo)		52	Gpa
	densidad		2.7	ton/m3
	peso especifico		26.46	KN/m3
	Peso especifico		0.02646	Mpa/m
	L (flexion)		9.0	m
	deformación maxima		0.000106784	m
	Esfuerzos inducidos
			4. Profundidad (Esfuerzos In Situ)
			Profundidad	400	m
			gamma	0.02646	Mpa/m
			Esfuerzo vertical	10.6	Mpa
			ESFUERZOS INDUCIDOS
			Configuraciones Pilares cuadrados
			Wp	Hp	Wo	sigma p / sigma z	Esfuerzo inducido
			m	m	m	adim	Mpa
			7	10	9	5.22	55.3
			8	10	9	4.52	47.8
			9	10	9	4.00	42.3
			10	10	9	3.61	38.2
			11	10	9	3.31	35.0
			12	10	9	3.06	32.4
			13	10	9	2.86	30.3
			14	10	9	2.70	28.6
			15	10	9	2.56	27.1
			16	10	9	2.44	25.8
			17	10	9	2.34	24.8
			18	10	9	2.25	23.8
			19	10	9	2.17	23.0
			20	10	9	2.10	22.3
			21	10	9	2.04	21.6
			22	10	9	1.99	21.0
			23	10	9	1.94	20.5
			24	10	9	1.89	20.0
			25	10	9	1.85	19.6
			26	10	9	1.81	19.2
	5. Resistencia de pilares mineros
			Lunder y Pakalnis (Roca Dura)
			Wp	Hp	W/H	Cpav	k	Sp	Sp/UCS	FS	Recuperación
			m	m	adim	adim	adim	Mpa	adim	adim	%
			7	10	0.7	0.0120	0.222	52	0.35	0.95	81%
			8	10	0.8	0.0252	0.326	56	0.37	1.17	78%
			9	10	0.9	0.0429	0.433	60	0.40	1.41	75%
			10	10	1	0.0635	0.538	63	0.42	1.66	72%
			11	10	1.1	0.0857	0.641	67	0.45	1.91	70%
			12	10	1.2	0.1085	0.739	70	0.47	2.17	67%
			13	10	1.3	0.1311	0.833	73	0.49	2.42	65%
			14	10	1.4	0.1529	0.923	77	0.51	2.68	63%
			15	10	1.5	0.1737	1.009	79	0.53	2.93	61%
			16	10	1.6	0.1932	1.090	82	0.55	3.18	59%
			17	10	1.7	0.2115	1.166	85	0.57	3.43	57%
			18	10	1.8	0.2284	1.239	87	0.58	3.67	56%
			19	10	1.9	0.2441	1.307	90	0.60	3.90	54%
			20	10	2	0.2587	1.372	92	0.61	4.13	52%
			21	10	2.1	0.2721	1.433	94	0.63	4.35	51%
			22	10	2.2	0.2844	1.491	96	0.64	4.57	50%
			23	10	2.3	0.2959	1.545	98	0.65	4.78	48%
			24	10	2.4	0.3064	1.596	100	0.66	4.98	47%
			25	10	2.5	0.3162	1.644	101	0.68	5.18	46%
			26	10	2.6	0.3252	1.690	103	0.69	5.36	45%
F.S. y Recuperación v/s Ancho Pilar
Factor de Seguridad	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22	23	24	25	26	0.94913532737816064	1.1730650889390666	1.4107926308104133	1.6579621378620402	1.9110510688411224	2.1672457606761171	2.4242911228410593	2.6803724964465676	2.9340300687987266	3.1840961338398337	3.4296470266642474	3.6699645176903668	3.904503646019152	4.1328652957007872	4.354772545610194	4.570050199560904	4.7786070893133914	4.9804208329408217	5.175524775459782	5.3639968637803843	Recuperación	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22	23	24	25	26	0.80859375	0.7785467128027681	0.75	0.7229916897506925	0.69750000000000001	0.67346938775510212	0.65082644628099162	0.62948960302457468	0.609375	0.59040000000000004	0.5724852071005917	0.55555555555555558	0.5395408163265305	0.52437574316290125	0.51	0.4963579604578563	0.4833984375	0.47107438016528924	0.45934256055363309	0.448163265306	12238	Ancho Pilar [m]
Factor de Seguridad [#]
Recuperación [%]
Hoja1
		0.3789291416
		3.1622776602	1.1982791594
			12.5100344237
		23
		300
		6900	6.9	Mpa
	Wp	10
	Wo	4.2
		2.0164
		13.91316	0.90
		0.153256705
		0.4044468692
	H	Wp	Wo	Resistencia pilar	Si	Sinducido		radio
	4	2	4	5.5946574744	9.0	62.1	0.09	0.67
	4	3	4	6.852028049	5.4	37.5666666667	0.18	0.57
	4	4	4	7.9120404772	4.0	27.6	0.29	0.50
	4	5	4	8.8459301739	3.2	22.356	0.40	0.44
	4	6	4	9.6902309967	2.8	19.1666666667	0.51	0.40
	4	7	4	10.4666457329	2.5	17.0387755102	0.61	0.36
	4	8	4	11.1893149489	2.3	15.525	0.72	0.33
	4	9	4	11.8680607158	2.1	14.3962962963	0.82	0.31
	4	10	4	12.5100344237	2.0	13.524	0.93	0.29
	4	11	4	13.1206347945	1.9	12.8305785124	1.02	0.27
	4	12	4	13.704056098	1.8	12.2666666667	1.12	0.25
	4	13	4	14.263633817	1.7	11.799408284	1.21	0.24
	4	14	4	14.802072348	1.7	11.406122449	1.30	0.22
	4	15	4	15.3216005013	1.6	11.0706666667	1.38	0.21
	4	16	4	15.8240809544	1.6	10.78125	1.47	0.20
	4	17	4	16.3110893008	1.5	10.5290657439	1.55	0.19
	4	18	4	16.7839724233	1.5	10.3074074074	1.63	0.18
	4	19	4	17.2438924386	1.5	10.1110803324	1.71	0.17
	4	20	4	17.6918603477	1.4	9.936	1.78	0.17
	4	21	4	18.1287621941	1.4	9.7789115646	1.85	0.16
	4	22	4	18.5553796733	1.4	9.6371900826	1.93	0.15
	4	23	4	18.9724065671	1.4	9.5086956522	2.00	0.15
4
2
32
L
Et
g
h
=
4232LEt
2
ú
ú
û
ù
ê
ê
ë
é
+
=
p
o
p
z
p
W
W
W
s
s
2










p
op
zp
W
WW

22
2
2
()
()
vp
v
p
wowpwp
wowp
wp
ss
s
s
+=
+
=
2222()()vpvpwowpwpwowpwp
0.44(0.680.52)
pc
S
sk
=+
0.44(0.680.52)pcS
(
)
(
)
(
)
tancos11
pavpav
aCC
k
éù
=-+
ëû
tancos11pavpavaCC
1.4
/
0.46log(0.75)
wh
pav
w
C
h
éù
=+
êú
ëû
1.4/0.46log(0.75)whpavwCh
roca
s
roca

p
p
S
S
F
s
=
.
.
p
p
S
SF

..
a
ci
c
s
s
s
=
a
cic
s
ci
t
b
s
m
s
s
-
=
citbsm
t
L
T
2
2
g
s
=
t
L
T
2
2


roca
s
p
s
p
s
p
s
p
S