El criterio de Hoek-Brown para roca intacta
Dr. Alejo O. Sfriso Universidad de Buenos Aires SRK Consulting (Argentina) AOSA
materias.fi.uba.ar/6408 latam.srk.com www.aosa.com.ar
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El criterio de Hoek-Brown Criterio de Hoek-Brown roca intacta
𝜏
Criterio de fluencia al corte en tensiones principales 𝜎' = 𝜎) − 𝜎"#
𝜎) 𝑠−𝑚 𝜎"#
+
Parámetros: 𝜎"# , 𝑚, 𝑠, 𝑎 Genera una superficie de fluencia similar a Mohr-Coulomb con generatriz curva
2
𝑐/
𝜎𝜎"
Criterio de Hoek-Brown roca intacta
Significado de los parámetros para roca intacta (𝜎"# , 𝑚# , 𝑠, 𝑎) Compresión simple (𝜎) = 0): 𝜎' = −𝝈𝒄𝒊 0 + −𝜎"# = 0 − 𝜎"# 𝑠 − 𝑚# →𝒔=𝟏 𝜎"# Tracción triaxial (𝜎' = 𝜎) = 𝑐/ ) 𝑐/ + 𝝈𝒄𝒊 𝑐/ = 𝑐/ − 𝜎"# 1 − 𝑚# → 𝒎𝒊 = 𝜎"# 𝒄𝒑 Compresión triaxial: 𝑎 ajusta la curvatura en el plano 𝜏 − 𝜎 𝒂 = 𝟎. 𝟓 para roca intacta 𝜎' = 𝜎) − 𝜎"# 3
𝜎) 1− 𝑐/
𝜏
Roca intacta
' >
𝑐/
𝜎-
𝝈𝒄𝒊
Criterio de Hoek-Brown roca intacta
Resistencia a compresión simple 𝝈𝒄𝒊
4
Debe medirse en ensayos de compresión simple o triaxiales Term
σci [MPa] > 250
Field estimate of strength
Examples
Can only be chipped with a geological hammer
Fresh basalt, chert, diabase, gneiss, granite,Quartzite
R6
Extrem. strong
R5
Very strong
100 250
Requires many blows of a geological hammer to fracture it
Amphibolite, sandstone, basalt, gabbro, gneiss, granodiorite, limestone, marble, rhyolite, tuff
R4
Strong
50 100
Requires more than one blow of a geological hammer to fracture it
Limestone, marble, phyllite, sandstone, schist, shale
R3
Med. strong
25 50
Cannot be scraped or peeled with a pocket knife Can be fractured with a single blow from a geological hammer
Claystone, coal, concrete, schist, shale, siltstone
R2
Weak
5.00 25.0
Can be peeled with a pocket knife with difficulty Shallow indentation made by firm blow with point of a geological hammer
Chalk, rocksalt, potash
R1
Very weak
1.00 5.00
Crumbles under firm blows with point of a geological hammer Can be peeled by a pocket knife
Highly weathered or altered rock
R0
Extrem. weak
0.25 1.00
Indented by thumbnail
Stiff fault gouge
Criterio de Hoek-Brown roca intacta
Parámetro 𝒎𝒊
5
Tracción isotrópica 𝜎"# 𝑚# = 𝑐/ Tracción simple 𝜎"# 𝜎? 𝑚# = − 𝜎? 𝜎"# El vértice es (casi) tracción simple 𝜎? 𝑐/ = 𝜎? 1− 𝜎"#
>
𝜎? ≅ 0.99
Calibración de 𝒎𝒊 Principal Stresses (IGR)
Principal Stresses (IBR)
160
160
140
140
220
200
180
120
120 160
100
140
80
Major principal stress (MPa)
100
Major principal stress (MPa)
Major principal stress (MPa)
Criterio de Hoek-Brown roca intacta
Principal Stresses (ILA)
80
60
60
40
40
120
100
80
60
40 20
20
Serie S1 vs S3 Env. mejor ajuste
Env. mejor ajuste
Env. ajuste restringido
Env. ajuste restringido
20
0
20 Minor principal stress (MPa)
40
Env. mejor ajuste Env. ajuste restringido
0
0
6
Series S1 vs S3 (IGR)
Serie S1 vs S3 (IBR)
0 0
20 Minor principal stress (MPa)
40
0
20
40
Minor principal stress (MPa)
60
Criterio de Hoek-Brown roca intacta
Críticas “académicas” al criterio de Hoek-Brown • Un mismo criterio para falla al corte y a tracción • Plano de ruptura oblicuo en el ensayo de tracción simple (indetectable en la práctica, error 0.5%|1.0%) 𝜏 • Fuerte curvatura deviatórica cerca de vértice 𝜋 𝜃= 6
Mohr-Coulomb Hoek-Brown lejos de 𝑐/ cerca de 𝑐/ 𝜋 𝜃=− 6
7
𝜎𝑐/ 𝜎?
ength s3 ¼ "7.75 MPa. In other has no provision for predicting 8, and highlighted by the “Ten-
fracture criterion
Hoek-Brown complementado con falla por tracción simple
t the Griffith failure criterion, could be generalized in terms of e strength sc =jst j as follows (a Appendix):
Criterio de Hoek-Brown roca intacta
occurs when s3 ¼ st; occurs when
Hoek (2014) propuso un “tension cut-off” • Mecanismos de corte y tracción independientes • Resuelve el problema de la “falla oblicua”
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi " # 2 " 4 s23 þ Ast s3 þ 2ABs2t
2
possible to arrive at a preliminary relationship between the Fairhurst tension cutoff (defined by sc =jst j) and the HoekeBrown parameter mi plotted in Fig. 10. While more work remains to be done on this topic, particularly more tests of the type carried out by Ramsey and Chester (2004) and Bobich (2005), the authors suggest that Fig. 10 provides a useful practical tool for estimating a tensile cutoff for the HoekeBrown criterion. Examination of Table 1 shows that, for low mi values, the Hoeke Brown criterion over-estimates the tensile strength compared with the Fairhurst criterion. However, for mi > 25 the HoekeBrown criterion under-estimates the tensile strength by an amount that is generally small enough to be ignored for most engineering applications. Hoek (1965) assembled a significant quantity of laboratory triaxial test data for a variety of rock types and concrete and these results (peak strength values) are plotted in a dimensionless form in Fig. 11. It can be seen that individual data sets plot on parabolic curves and that a family of such curves, covering all of the shear data collected, can be generated for different values of the Hoeke Brown constant mi. The constant mi is an indicator of the brittleness of the rock with weaker and more ductile rocks having low mi values while stronger and more brittle rocks have high mi values. A few data points for s3 < 0 are included in Fig. 11 and these are dealt with adequately by the tension cutoff discussed above.
(7)
Hoek (2002) Fairhust (1964)
𝜎𝜎?
8
𝜏
(Hoek 2014)
and triaxial compression tests by Ramsey Fig. 9. Combined plot of HoekeBrown and Fairhurst failure criteria with tension cutoff.
