Resistencia de macizos rocosos con discontinuidades
Dr. Alejo O. Sfriso Universidad de Buenos Aires SRK Consulting (Argentina) AOSA
materias.fi.uba.ar/6408 latam.srk.com www.aosa.com.ar
[email protected] [email protected] [email protected]
Resistencia al corte de discontinuidades
Parámetros de resistencia de discontinuidades
2
(Hoek 2006)
1
Resistencia al corte de discontinuidades
Efecto de escala en la resistencia de pico y en la rigidez de discontinuidades
(Alejano 2005)
3
Resistencia al corte de discontinuidades
Modelo de Barton-Bandis 𝜙* + 𝑠 = 𝜎$ % 𝑡𝑎𝑛
𝐽𝑅𝐶$ ⋅ 𝑙𝑜𝑔
𝜙* = 𝜙4 − 20 + 20
𝐽𝐶𝑆$ 𝜎$
𝑟 𝑅
𝐽𝑅𝐶$ = 𝐽𝑅𝐶9
𝐿$ 𝐿9
;9.9= ?@AB
𝐽𝐶𝑆$ = 𝐽𝐶𝑆9
𝐿$ 𝐿9
;9.9C ?@AB
4
2
Resistencia al corte de discontinuidades
Modelo de Barton-Bandis 𝜙* + 𝑠 = 𝜎$ % 𝑡𝑎𝑛
𝐽𝑅𝐶$ ⋅ 𝑙𝑜𝑔
𝜙* = 𝜙4 − 20 + 20
𝐽𝐶𝑆$ 𝜎$
𝑟 𝑅
𝐽𝑅𝐶$ = 𝐽𝑅𝐶9
𝐿$ 𝐿9
;9.9= ?@AB
𝐽𝐶𝑆$ = 𝐽𝐶𝑆9
𝐿$ 𝐿9
;9.9C ?@AB
5
Resistencia al corte de discontinuidades
Resistencia de discontinuidades con puentes de roca Falla alineada (Jennings)
Lj
𝐿E 𝑘= 𝐿E + 𝐿* 𝑠 = 𝑘 ⋅ 𝑠E + 1 − 𝑘 ⋅ 𝑠G 2𝑐* (1 − 𝑘) + 𝜎C 1 + cot 𝛽 𝑘 tan(𝜙E ) + 1 − 𝑘 tan 𝜙* sin (2𝛽) 𝜎H = 1 − tan 𝛽 𝑘 tan 𝜙E + (1 − 𝑘) tan 𝜙*
Falla escalonada (Cording-Jamil)
𝑑 𝜎 + 𝜎$ tan 𝜙 + 𝑖 𝐿E U 𝑑 2𝜎U ⋅ 𝐿E + 𝜎C 1 + tan 𝜙 + 𝑖 cot(𝛽 − 𝑖) sin 2(𝛽 − 𝑖) 𝜎H = 1 − tan 𝜙 + 𝑖 tan 𝛽 − 𝑖 𝑠=
Lr Lj
tan i=d/Lj Lj d Lj
6
3
Resistencia al corte de discontinuidades
Criterios de Jennings y CordingJamil: validación experimental
7
Ensayos de compresión biaxial ARTICLE IN PRESS Prudencio, M. Van 30x15x5cm Sint Jan / International Journal of Rock Mechanics & Mining Sciences 44 (2007) 890–902 893 • BloquesM.mortero 3. Test results and experimental observations high stress concentration. The initial spreading of these • Fracturas: láminas 0.1mm fissures, or wing cracks, is practically perpendicular to the In agreement with Griffith’s criterion, when a sample direction of the joint. The propagation of the cracks is removidas a las 24 hrs containing non-persistent joints is loaded in compression, influenced by the geometry of the neighboring joints, as new fissures are created at the tip of the joints subjected to defined by Fig. 1. Similar failure modes can be defined, Configuraciones depending on the way in which the new cracks spread until the model collapses.
3.1. Failure modes
S1
S2
S7
S8
S3
S4
S5
S9
S 10
S 11
Fig. 3. Joint geometries tested.
S6
We observed three failure modes in the test program: failure through a plane, stepped failure, and rotation of new blocks (Fig. 5). Some samples failed by a combination of rotation with stepped failure, a mode that can be considered included in the previous three modes. Failure through a plane results when the failure surface propagates along a joint set and the intervening rock bridges, developing a single plane with the same dip as the joints. Failure starts at the joint tipsy Jan and 2007) propagates (Prudencio through the rock bridge until it reaches another colineal joint tip. Stepped failure occurs by sliding on a joint segment and stepping between adjacent parallel joints (Fig. 6). Failure of the intact material starts at the joint tip and propagates quasi perpendicularly to the joint until it is connected with another wing crack coming from the joint tip of a parallel system. The resulting failure surface has an average slope angle cf ¼ c1+Dc, where c1 is the dip of the joint system and Dc ¼ tan"1 (d/Lj). Rotation of new blocks takes place when the joints are relatively close and aE 901, so that all the joint tips are nearly along the same line. The wing cracks of parallel joints coalesce and the model fractures into a series of blocks that can rotate. Failure usually spreads in a ductile way. At large strains, the blocks tend to slide into a multiple stepping mechanism, which can be described as an interaction between rotation and stepped failure. However, the strength of the model is controlled by the rotation mode, and is much smaller than the strength for stepped failure.
Resistencia al corte de discontinuidades
Criterios de Jennings y CordingJamil: validación experimental
Fig. 4. Loading frame and sample set up (plan view).
PROB 41 July 6 β = 15 3=0 Fig. 5. Observed failure modes: (a) through a plane, series 3, s2 =sc ¼ 0:00; (b) stepped, series 2, s2/sc ¼ 0.00; (c) rotation of new blocks series 5, s2/sc ¼ 0.00; (d) interaction between rotation and stepped, series 8, s2/sc ¼ 0.01.
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a) Por un plano Serie 3, s2/sc=0.00
b) Escalonada Serie 2, s2/sc=0.00
c) Rotación de bloques Serie 5, s2/sc=0.00
(Prudencio y Jan 2007) d) Interacción escalonada-rotación Serie 8, s2/sc=0.01
e) Por material intacto Serie 6, s2/sc=0.18
4
ARTICLE IN PRESS 900
M. Prudencio, M. Van Sint Jan / International Journal of Rock Mechanics & Mining Scien
80
σ1
70
P
60
Criterios de Jennings CordingARTICLEyIN PRESS M. Prudencio,Jamil: M. Van Sint Jan / Internationalexperimental Journal of Rock Mechanics & Mining Sciences 44 (2007) 890–902 validación 50
S
θ−β
0
80 P
60
θ−β
40 30
S&P
P
β
2 transición
θ
S
S&P
20 P+S 10 0
escalonada 3
S MS R+S
R
σ2
Lr
Failure Mode
1
Sliding on a single plane
2
Transition zone between sliding on a single plane and stepping fa if σ2/σc>0.04 planar failure if σ2/σc
