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GEOMECNICA APLICADA EN MINERA
1CONCEPTOS GEOMECNICOS FUNDAMENTALES
DETERMINACION DE LOSMODULOS ELASTICOS.
Lambe & Whitman (1969)SOIL MECHANICS
J. Wiley & Sons
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GEOMECNICA APLICADA EN MINERA
2CONCEPTOS GEOMECNICOS FUNDAMENTALES
RELACIONES ENTRE LOSMODULOS ELASTICOS.
Hunt (1984)
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GEOMECNICA APLICADA EN MINERA
3CONCEPTOS GEOMECNICOS FUNDAMENTALES
MODULOS DINAMICOS
Hunt (1984)
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GEOMECNICA APLICADA EN MINERA
4CONCEPTOS GEOMECNICOS FUNDAMENTALES
Goodman (1989)Lambe & Whitman (1969)
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GEOMECNICA APLICADA EN MINERA
5CONCEPTOS GEOMECNICOS FUNDAMENTALES
Calculo de las Propiedades de la Roca Intacta:
(1) Realizar ensayos de compresinm uniaxial (5 a 10) para
determinar UCS y los mdulos elsticos E y .
(2) Realizar ensayos triaxiales para un mnimo de 5 presiones de
confinamiento, y de modo que se alcance ewl 40% al 50% de
UCS. Se recomienda repetir a lo menos una vez cada ensayo
(o sea 2 ensayos x cada presin de confinamiento).
(3) Utilizar estos resultados para determinar los parmetros del
criterio de Hoek-Bown. Se recomienda emplear el software
ROCDATA y usar el mtodo simplex. Deber verificarse que
los resultados son razonables (e.g. mi < 36).
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GEOMECNICA APLICADA EN MINERA
6CONCEPTOS GEOMECNICOS FUNDAMENTALES
ESTRUCTURASY SUS
PROPIEDADES
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GEOMECNICA APLICADA EN MINERA
7CONCEPTOS GEOMECNICOS FUNDAMENTALES
PARAMETROS GEOMETRICOS
MANTEO
DIRECCION DE MANTEO
TRAZA O EXTENSINESPACIAMIENTO
GAP
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GEOMECNICA APLICADA EN MINERA
8CONCEPTOS GEOMECNICOS FUNDAMENTALES
Mquina de corte directo fija en laboratorio (tomada
de Franklin & Dusseault (1989)).
Mquina de corte directo porttil (tipo Hoek, tomada de
Franklin & Dusseault (1989)).
Ensayo de corte directo in situ sobre planos de
estratificacin, en un talud de reservorio en Grecia
(tomada de Franklin & Dusseault 1989)). Esquema del montaje tpico de un ensayo de corte
directo in situ (tomada de Franklin & Dusseault (1989)).
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GEOMECNICA APLICADA EN MINERA
9CONCEPTOS GEOMECNICOS FUNDAMENTALES
Montaje para la ejecucin
de ensayos de cortedirecto sobre estructurascon un rea expuesta deunos 400 cm2.
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GEOMECNICA APLICADA EN MINERA
10CONCEPTOS GEOMECNICOS FUNDAMENTALES
Estructura despus del ensayo.Estructura antes del ensayo.
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GEOMECNICA APLICADA EN MINERA
11CONCEPTOS GEOMECNICOS FUNDAMENTALES
RESIS
TENCIA
RESID
UAL
RESISTE
NCIA
PEAK
cpeak
peak
res
n
CONDICION PEAK
CONDICION RESIDUAL
Curva carga-deformacin
para un valor dado del es-fuerzo normal efectivo.
u
cres
RESIS
TENCIA
RESID
UAL
RESISTE
NCIA
PEAK
cpeak
peak
res
n
CONDICION PEAK
CONDICION RESIDUAL
Curva carga-deformacin
para un valor dado del es-fuerzo normal efectivo.
u
cres
RESISTENCIA
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GEOMECNICA APLICADA EN MINERA
12CONCEPTOS GEOMECNICOS FUNDAMENTALES
MTODO DE BARTON-BANDIS:
MAX = tan( b + JRClog(JCS/))
MAX = tan( equiv )
MAX RESISTENCIA AL CORTE ESFUERZO NORMAL EFECTIVOb ANGULO BASICO DE FRICCION (b r)
JRC COEFICIENTE DE RUGOSIDADJCS RESISTENCIA EN COMPRESION UNIAXIAL
DE LA PARED DE LA ESTRUCTURA
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GEOMECNICA APLICADA EN MINERA
13CONCEPTOS GEOMECNICOS FUNDAMENTALES
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14CONCEPTOS GEOMECNICOS FUNDAMENTALES
MTODO DE BARTON-BANDIS:
equiv 70
0.01 /JCS 0.30
ESTRUCTURAS SIN RELLENO
ESTRUCTURAS SIN DESPLAZAMIENTO PREVIO
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GEOMECNICA APLICADA EN MINERA
15CONCEPTOS GEOMECNICOS FUNDAMENTALES
EFECTO DE ESCALA EN LA RESISTENCIA AL CORTE DELAS ESTRUCTURAS.
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GEOMECNICA APLICADA EN MINERA
16CONCEPTOS GEOMECNICOS FUNDAMENTALES
EL AUMENTO DE LA EXTENSIN DE LA ESTRUCTURA PRODUCE TRES EFECTOS
PRINCIPALES: REDUCE LA RUGOSIDAD, REDUCE LA DILATANCIA, E INCREMENTA ELDESPLAZAMIENTO NECESARIO PARA MOVILIZAR LA RESISTENCIA PEAK.
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GEOMECNICA APLICADA EN MINERA
17CONCEPTOS GEOMECNICOS FUNDAMENTALES
EFECTO DE ESCALA EN EL PARMETRO JRC
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GEOMECNICA APLICADA EN MINERA
18CONCEPTOS GEOMECNICOS FUNDAMENTALES
EFECTO DE ESCALA EN EL PARMETRO JCS
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GEOMECNICA APLICADA EN MINERA
19CONCEPTOS GEOMECNICOS FUNDAMENTALES
0.1 1 10 100 1000 10000 100000
EXTENSION DE LA DISCONTINUIDAD, L (m)
15
20
25
30
35
40
45
50
55
ANGULOD
E
FRICCION
(grados)
LA SALBANDA ARCILLOSASE HACE MUY IMPORTANTELA SALBANDA ARCILLOSASE HACE MUY IMPORTANTE
Efecto de escala en el valor peak del ngulo de friccin de estructuras de distinta extensin,conforme con lo valores reseados por Pusch (1997).
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GEOMECNICA APLICADA EN MINERA
20CONCEPTOS GEOMECNICOS FUNDAMENTALES
PROPIEDADES TIPICAS
JointsJoints c = 75 a 150 kPac = 75 a 150 kPa = 30= 30oo a 35a 35
Joints en Roca ArgilizadaJoints en Roca Argilizada c = 25 a 100 kPac = 25 a 100 kPa = 22= 22oo a 30a 30
Fallas con Salbanda ArcillosaFallas con Salbanda Arcillosa c = 0 a 50 kPac = 0 a 50 kPa = 18= 18oo a 25a 25
Zonas de FallaZonas de Falla con Salbandacon Salbanda c = 25 a 75 kPac = 25 a 75 kPa = 20= 20oo
a 30a 30y Rocay Roca BrechizadaBrechizada
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GEOMECNICA APLICADA EN MINERA
21CONCEPTOS GEOMECNICOS FUNDAMENTALES
CARACTERIZACIN& PROPIEDADES
DEL MACIZO ROCOSO
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GEOMECNICA APLICADA EN MINERA
22CONCEPTOS GEOMECNICOS FUNDAMENTALES
EL PROBLEMA ES DEFINIR UNA CALIFICACINDE LA COMPETENCIA DEL MACIZO ROCOSO QUEPERMITA EL ESCALAMIENTO:
Prop. Macizo Rocoso = Fact. Escala Prop. R. I.
RQD
FFRMR (Bieniawski)
Factor de EscalaRMR (Laubscher)QGSI
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GEOMECNICA APLICADA EN MINERA
23CONCEPTOS GEOMECNICOS FUNDAMENTALES
Ejemplo 04
Modo de Clculo del RQD(Deere (1989))
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GEOMECNICA APLICADA EN MINERA
24CONCEPTOS GEOMECNICOS FUNDAMENTALES
Indice RMRBieniawski (1989)
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GEOMECNICA APLICADA EN MINERA
25CONCEPTOS GEOMECNICOS FUNDAMENTALES
Indice RMRLaubscher (1996)
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GEOMECNICA APLICADA EN MINERA
26CONCEPTOS GEOMECNICOS FUNDAMENTALES
GEOLOGICAL STRENGTH INDEX
The strength of a jointed rock mass depends on the properties of theintact rock pieces and also upon the freedom of these pieces to slide
and rotate under different stress conditions. This freedom is controlledby the geometrical shape of the intact rock pieces as well as thecondition of the surfaces separating the pieces. Angular rock pieceswith clean, rough discontinuity surfaces will result in a much strongerrock mass than one which contains rounded particles surrounded by
weathered and altered material.
The Geological Strength Index (GSI), introduced by Hoek (1994) andHoek et al. (1995) provides a system for estimating the reduction inrock mass strength for different geological conditions.
This system is presented in Table 3, for blocky rock masses, and Table4 for schistose metamorphic rocks.
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27CONCEPTOS GEOMECNICOS FUNDAMENTALES
Table 3:Characterisation of a blocky rock masseson the basis of particle interlocking anddiscontinuity condition.After Hoek, Marinos and Benissi (1998).
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GEOMECNICA APLICADA EN MINERA
28CONCEPTOS GEOMECNICOS FUNDAMENTALES
Table 4:Characterisation of a schistose metamorphicrock masses on the basis of foliation anddiscontinuity condition.(After M. Truzman, 1999).
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GEOMECNICA APLICADA EN MINERA
29CONCEPTOS GEOMECNICOS FUNDAMENTALES
AL CALIFICAR LA COMPETENAL CALIFICAR LA COMPETEN--
CIA DEL MACIZO ROCOSO ESCIA DEL MACIZO ROCOSO ESPRECISO CONSIDERAR UNPRECISO CONSIDERAR UN RANRAN--GOGO DE VALORES, YA QUEDE VALORES, YA QUE DIFIDIFI--CILMENTECILMENTE ESTAESTA CORRESPONCORRESPON--DERADERA A UN SOLO VALOR.A UN SOLO VALOR.
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GEOMECNICA APLICADA EN MINERA
30CONCEPTOS GEOMECNICOS FUNDAMENTALES
GENERALIZED HOEK-BROWN CRITERION
, are the maximum and minimum efective stresses atfailure
is the value of the Hoek-Brown parameter m for therock mass
, are constants which depend upon the rock mass cha-
racteristics
is the uniaxial compressive strength of the intact rockpieces
a
ci
bci sm
++=
''' 331
'1
'3
ci
bm
a s
(1)
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GEOMECNICA APLICADA EN MINERA
31CONCEPTOS GEOMECNICOS FUNDAMENTALES
Eq. (1) can be used to generate a series of triaxial test values,simulating full-scale field tests, and a curve fitting process can be usedto derive an equivalent Mohr envelope given by:
, are material constants
is the normal effective stress
is the tensile strength of the rock mass
'
n
tm
A B
B
ci
tmn
ciA
=
'(2)
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GEOMECNICA APLICADA EN MINERA
32CONCEPTOS GEOMECNICOS FUNDAMENTALES
In order to use the Hoek-Brown criterion for estimating the strength ofjointed rock masses, three properties of the rock mass have to beestimated:
(1) The uniaxial compressive strength of the intact rockpieces
(2) The value of the Hoek-Brown constant for these intactrock pieces
(3) The value of the Geological Strength Index GSI for therock mass
ci
im
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GEOMECNICA APLICADA EN MINERA
33CONCEPTOS GEOMECNICOS FUNDAMENTALES
The Hoek-Brown failure criterion, which assumes isotropic rock androck mass behaviour, should only be applied to those rock masses inwhich there are a sufficient number of closely spaced discontinuities,with similar surface characteristics, that isotropic behaviour involving
failure on multiple discontinuities can be assumed. When the structurebeing analysed is large and the block size small in comparison, therock mass can be treated as a Hoek-Brown material.
Where the block size is of the same order as that of the structure being
analysed or when one of the discontinuity sets is significantly weakerthan the others, the Hoek-Brown criterion should not be used.
In these cases, the stability of the structure should be analysed byconsidering failure mechanisms involving the sliding or rotation of
blocks and wedges defined by intersecting structural features. Figure2 summarises these statements in a graphical form.
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GEOMECNICA APLICADA EN MINERA
34CONCEPTOS GEOMECNICOS FUNDAMENTALES
Intact RockSpecimensUSE EQ. 3
One Joint Set
DO NOT USEHB CRITERION
Many JointsUSE EQ. 1
WITH CAUTION
Heavily Jointed Rock MassUSE EQ. 1
Two Joint Sets
DO NOT USEHB CRITERION
Figure 2:Idealised diagram showing thetransition from intact to a heavily
jointed rock mass with increasingsample size.
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35CONCEPTOS GEOMECNICOS FUNDAMENTALES
Once the Geological Strength Index has been estimated, theparameters that describe the rock mass strength characteristics, arecalculated as follows:
= 2814
100
exp a
GSI
mm ib
= 96
100
expo0 a
GSI
s
200
65.0o0.5
GSI
a =
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GEOMECNICA APLICADA EN MINERA
36CONCEPTOS GEOMECNICOS FUNDAMENTALES
For better quality rock masses (GSI > 25), the value of GSI can beestimated directly from the 1976 version of Bieniawskis RMR, with the
groundwater rating set to 10 (dry) and the adjustment for joint orientationset to 0 (very favourable). If the 1989 version of Bieniawskis classificationis used, then GSI = RMR89 - 5 where RMR89 has the groundwater rating setto 15 and the adjustment for joint orientation set to zero.
For very poor quality rock masses the value of RMR is very difficult toestimate and the balance between the ratings no longer gives a reliablebasis for estimating rock mass strength. Consequently, Bieniawskis RMRclassification should not be used for estimating the GSI values for poor
quality rock masses (RMR < 25) and the GSI charts should be useddirectly.
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GEOMECNICA APLICADA EN MINERA
37CONCEPTOS GEOMECNICOS FUNDAMENTALES
DEFORMATION MODULUSSerafim and Pereira (1983) proposed a relationship between the in situmodulus of deformation and Bieniawskis RMR. This relationship is basedupon back analysis of dam foundation deformations and it has been found
to work well for better quality rocks. However, for many of the poor qualityrocks it appears to predict deformation modulus values that are too high.
Based upon practical observations and back analysis of excavationbehaviour in poor quality rock masses, the following modification to
Serafim and Pereiras equation is proposed for:
= 40
10
10100
GSI
ci
mE
(12)
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38CONCEPTOS GEOMECNICOS FUNDAMENTALES
Figure 5: Deformation modulus versus Geological Strength Index GSI.
Geological Strength Index GSI
0 10 20 30 40 50 60 70 80 90 100
DeformationmodulusE-GPa
0
20
40
60
80
100
120
140
160
180 ci = 100 MPa
ci = 50 MPa
ci = 30MPa
ci = 15 MPa
ci = 10 MPa
ci = 5 MPa
ci = 1MPa
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39CONCEPTOS GEOMECNICOS FUNDAMENTALES
Note that GSI has been substituted for RMR in this equation and that themodulus E
mis reduced progressively as the value of falls below 100.
This reduction is based upon the reasoning that the deformation of betterquality rock masses is controlled by the discontinuities while, for poorerquality rock masses, the deformation of the intact rock pieces contributesto the overall deformation process.
Based upon measured deformations, eq. 12 appears to work reasonablywell in those cases where it has been applied. However, as more fieldevidence is gathered it may be necessary to modify this relationship.
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40CONCEPTOS GEOMECNICOS FUNDAMENTALES
MODULO DE DEFORMABILIDAD:
E = ESEISMIC (Deere et al. (1967)).
E = 2RMR 100 (RMR > 50, Bieniawski (1978)
E = 10((RMR 10)/40) (Serafim & Pereira (1983))
EMIN = 10log(Q)
EMEAN = 25log(Q) (Barton (1983))
EMAX = 40log(Q)
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41CONCEPTOS GEOMECNICOS FUNDAMENTALES
1.0
0.8
0.6
0.4
0.2
0.01.00.80.60.40.20.0
VFIELD/ VLAB , RQD
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42CONCEPTOS GEOMECNICOS FUNDAMENTALES
STRESS RELAXATIONWhen the rock mass adjacent to a tunnel wall or a slope is excavated, arelaxation of the confining stresses occurs and the remaining materialis allowed to expand in volume or to dilate.
This has a profound influence on the strength of the rock mass since,in jointed rocks, this strength is strongly dependent upon theinterlocking between the intact rock particles that make up the rockmass.
As far as the authors are aware, there is very little research evidencerelating the amount of dilation to the strength of a rock mass. One setof observations that gives an indication of the loss of strengthassociated with dilation is derived from the support required to
stabilize tunnels. Sakurai (1983) suggested that tunnels in which thestrain, defined as the ratio of tunnel closure to tunnel diameter,exceeds 1% are likely to suffer significant instability unless adequatelysupported.
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43CONCEPTOS GEOMECNICOS FUNDAMENTALES
This suggestion was confirmed in observations by Chern et al. (1998)who recorded the behavior of a number of tunnels excavated inTaiwan.
They found that all of those tunnels that exhibited strains of greaterthan 1 to 2% required significant support. Tunnels exhibiting strainsas high as 10% were successfully stabilized but the amount of effortrequired to achieve this stability increased in proportion to the amountof strain.
While it is not possible to derive a direct relationship between rockmass strength and dilation from these observations, it is possible toconclude that the strength loss is significant.
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44CONCEPTOS GEOMECNICOS FUNDAMENTALES
An unconfined surface that has deformed more than 1 or 2% (basedupon Sakurais definition of strain) has probably reached residualstrength in which all of the effective cohesive strength of the rockmass has been lost.
While there are no similar observations for rock slopes, it is reasonableto assume that a similar loss of strength occurs as a result of dilation.
Hence, a 100 m high slope which has suffered a total crest displace-
ment of more than 1 m (i.e. more than 1% strain) may start to exhibitsignificant signs of instability as a result of loss of strength of the rockmass.
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45CONCEPTOS GEOMECNICOS FUNDAMENTALES
BLAST DAMAGE
Blast damage results in a loss of rock mass strength due to thecreation of new fractures and the wedging open of existing fractures by
the penetration of explosive gasses.
In the case of very large open pit mine blasts, this damage can extendas much as 100 m behind the final row of blast holes.
In contrast to the strength loss due to stress relaxation or dilation,discussed in the previous section, it is possible to arrive at anapproximate quantification of the strength loss due to blast damage.
This is because the blast is designed to achieve a specific purpose
which is generally to produce a fractured rock mass that can beexcavated by means of a given piece of equipment.
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46CONCEPTOS GEOMECNICOS FUNDAMENTALES
Figure 6 presents a plot of 23 case histories of excavation by digging,ripping and blasting published by Abdullatif and Cruden (1983). Thesecase histories are summarised in Table 5. The values of GSI areestimated from the data contained in the paper by Abdullatif and
Cruden while the rock mass strength values were calculated assumingan average slope height of 15 m.
These examples shows that rock masses can be dug, obviously withincreasing difficulty, up to GSI values of about 40 and rock mass
strength values of about 1 MPa.
Ripping can be used up to GSI values of about 60 and rock massstrength values of about 10 MPa, with two exceptions where heavyequipment was used to rip strong rock masses.
Blasting was used for GSI values of more than 60 and rock massstrengths of more than about 15 MPa.
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47CONCEPTOS GEOMECNICOS FUNDAMENTALES
Blasting8685
Blasting11785
Blasting6477
Blasting13577Blasting8477
Blasting5476
Blasting3571
Blasting1569
Blasting1768
Blasting3068
Ripping by D9L bulldozer4267Ripping by D9L bulldozer3367
Ripping by track loader2.458
Ripping by 977L track loader9.557
Ripping by track loader0.851
Digging by 977L track loader1.242
Digging by wheel loader0.540 Digging by hydraulic face shovel0.534
Digging by 977L track loader0.325
Digging by wheel loader0.225
Digging by hydraulic backhoe0.224
Digging by D9 bulldozer0.119
Digging by 977L track loader0.119
Excavation MethodRock Mass Strength, CM
( MPa )GSI
Table 5:Summary of methods used to excavate rock masses with a range of uniaxial compressive strength values,based on data published by Abdullatif and Cruden (1983).
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48CONCEPTOS GEOMECNICOS FUNDAMENTALES
Figure 6: Plot of rock mass strength versus GSI for different excavation methods, afterAbdullatif and Cruden (1983).
Geological Strength Index GSI
0 10 20 30 40 50 60 70 80 90 100
Rockmassstrength
ci-MPa
0.1
1
10
100
Excavation method
Dig
Rip
Blast
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49CONCEPTOS GEOMECNICOS FUNDAMENTALES
Figure 7 summarizes the conditions for a muckpile that can be dug
efficiently and the blast damaged rock mass that lies between thedigging limit and the in situ rock mass. The properties of this blastdamaged rock mass will control the stability of the slope that remainsafter digging of the muckpile has been completed.
Figure 7: Diagrammatic representation of the transition between the in siturock mass and blasted rock that is suitable for digging.
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50CONCEPTOS GEOMECNICOS FUNDAMENTALES
The thickness D of the blast damaged zone will depend upon the designof the blast. Based upon experience, the authors suggest that thefollowing approximate relationships can be used as a starting point in
judging the extent of the blast damaged zone resulting from open pitmine production blasting:
D = 0.3 to 0.5 H Carefully controlled poduction blast with a free face
D = 0.5 to 1.0 H Production blast with some control, e.g. one or more buffer rows,
and blasting to a free face
D = 1.0 to 1.2 H Production blast, confined but with some control, e.g. one or morebuffer rows
D = 1.0 to 1.5 H Production blast with control but blasting to a free face
D = 2.0 to 2.5 H Large production blast, confined and with litle or no control
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51CONCEPTOS GEOMECNICOS FUNDAMENTALES
EN LA PRACTICA SE ESTA UTILIZANDO CADA VEZ MAS EL MTODO DEHOEK & BROWN, CON LAS CONSIDERACIONES SIGUIENTES:
SE DETERMINAN LOS PARAMETROS mi Y ci EN BASE A UNACUIDADOSA INTERPRETACION DE LOS RESULTADOS DE ENSAYOS
TRIAXIALES SOBRE TESTIGOS DE ROCA INTACTA (USUALMENTEUTILIZANDO ROCKDATA).
SE DETERMINA EL RANGO DE VALORES PROBABLES PARA EL INDICEGSI (USUALMENTE 15 A 20 PUNTOS).
SE DETERMINA EL RANGO DE PRESIONES DE CONFINAMIENTO Y SI SETRATA DE UN MACIZO BIEN TRABADO O NO.
SE ESTIMA LA INCERTEZA ASOCIADA A CADA PARAMETRO Y SUPOSIBLE FUNCION DE DISTRIBUCION.
SE EVALUAN LAS PROPIEDADES DEL MACIZO ROCOSO UTILIZANDO LAMETODOLOGIA PROPUESTA POR HOEK (1998,99).
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52CONCEPTOS GEOMECNICOS FUNDAMENTALES
PROBLEMAS :
EL METODO NO SIEMPRE ES APLICABLE.
SE DEFINE UNA RESISTENCIA ISOTROPICA.
PARA MACIZOS MASIVOS Y COMPETENTES EL METODODEBE APLICARSE EN FORMA FLEXIBLE.
PARA MACIZOS DE MALA CALIDAD GEOTECNICA, POBRE-MENTE TRABADOS Y POCO CONFINADOS EL METODOPUEDE SOBREVALUAR LA RESISTENCIA.
EN EL CASO DE ROCAS ESQUISTOSAS O FOLIADAS EL
METODO DEBE APLICARSE MUY CUIDADOSAMENTE.