1
GESTIONE AMMINISTRATIVA CONTRATTI NUMERICAL METHODS
IN GEOTECHNICAL ENGINEERING
Marco Barla Dipartimento di Ingegneria Strutturale, Edile e Geotecnica
APPLICATIONS 2-3 Pont Ventoux–F2 tunnel Geotechnical characterisation of the site
OUTLINE
• Geotechnical characterisation of the site
Elementi di meccanica e ingegneria delle rocce by Barla, Celid, 2010
Need to brush up topics from
2
A number of laboratory tests were carried out on samples of micaschists, obtained from boreholes 2S13i and 2S14i:
• Unconfined compression tests (Table 1) • Triaxial compression tests (Table 2 and 3) • Brasilian tensile strength tests (Table 4) • Tests ROC240 and ROC225 are given in
graphical form.
DATA AVAILBLE
The aim of applications 2 to 3 is to determine the intact rock and rock mass geotechnical parameters on the basis of laboratory test results and geomechanical classification.
The intact rock strength characteristics (both Hoek & Brown and Mohr-Coulomb peak and residual parameters) will be determined on the basis of the test results of the laboratory investigations undertaken.
The rock mass parameters will also be determined.
SCOPE
3
a) Determine the intact rock peak and residual strength parameters by using the Hoek & Brown failure criterion, on the basis of the data given in Tables 1, 2, 3, 4 and 5.
b) Determine the intact rock peak and residual strength parameters by using the Mohr-Coulomb failure criterion by linearization of the Hoek & Brown failure criterion. Reference should be made to the recommendations given by Hoek & Brown (1997) for appropriate choice of the minimum principal stress range (i.e. 8 values of σ3 between 0 and 0.5 times the intact rock unconfined compressive strength).
c) Determine the rock mass peak strength, residual strength and deformability parameters making reference to the rock mass classification in section 011 (Data sheet 3).
WHAT TO DO?
Intact rock
4
50
331 1
,'''
⎟⎟⎠
⎞⎜⎜⎝
⎛++=
ciici m σσ
σσσ
σci = unconfined compression strength of the intact rock
mi = Hoek–Brown constant for the intact rock
σ'1
σ'3
A
B
C
Unconfined compression
Triaxial compression
Unconfined traction σci
σti
HOEK & BROWN CRITERION
It is possible to plot the laboratory data on a Oxy reference system defined as below:
One can write:
( )2'3'1
'3
σσ
σ
−=
=
y
x
2cici xmy σσ +=
intercept slope
σci, mi are parameters to be determined from laboratory tests (MX and TX) in the range 0 < σ3 < 0,5 σci
y
x
DETERMINING mi AND σci
5
Unconfined peak compressive strength σc,p = 135 MPa Unconfined residual compressive strength σc,r = 10 MPa Hoek-Brown peak constant mi,p = 8.1 Hoek-Brown residual constant mi,r = 56.1
PICCO
RESIDUO
0
50
100
150
200
250
300
350
-25 -15 -5 5 15 25 35 45
σ'3 (MPa)
σ' 1
(MP
a)
INTACT ROCK
by direct interpolation of experimental data by linearization of the Hoek-Brown criterion in the range 0<σ3<0.5σci
DETERMINING MOHR-COULOMB PARAMETERS
6
LINEARIZATION PROCESS • Selection of eight equally spaced
pairs of values σ1’-σ3’ in the range 0<σ3’<0,5 σci
• Linear interpolation (y=ax+b) among those values determining c’ e φ’
'
''
2'
'
sin1cos2
245tan
sin1sin1
φφ
φφφ
φ
−==
⎟⎠
⎞⎜⎝
⎛ +°=−
+==
cCb
Na
o
σ’3
σ’1
5,0'3'
3'1 1⎟⎟
⎠
⎞⎜⎜⎝
⎛++=
cic m σσ
σσσ
'3
'1 sin1
sin1σ
φφ
σσ−
++= ci
0 < σ’3 < 0.5 σci
Rock mass
7
GSI = RMR -5
Where the RMR index is computed by assuming: P5 (no water) = 15 P6 (orientation) = 0
Two ways
GRAPHICAL FORM FROM RMR
GSI INDEX
RMR > 50 (Bieniawski, 1978) 1002 −⋅= RMREd
Deformability modulus for the rock mass may be determined by field tests or estimated on the basis of the rock mass quality:
4010
10−
=RMR
dE
4010
10100
−
⋅σ
=GSI
cidE
QlogEd 1025⋅=
∀ values of RMR (Serafim & Pereira, 1983)
σci < 100 MPa (Hoek & Brown, 1997)
∀ values of Q (Grimstad & Barton, 1993)
R.M. DEFORMATION MODULUS
8
σ'1
σ'3
HOEK & BROWN CRITERION FOR THE ROCK MASS
α
⎟⎟⎠
⎞⎜⎜⎝
⎛+
σ
σσ+σ=σ sm
ci
'
bci'' 331
σci = intact rock unconfined compressive strength
s, mb = Hoek–Brown constants for the rock mass
α = exponent (often = 0.5)
Intact rock
Rock mass
[ ] sci''
cm σ==σσ=σ 031α = 0,5
[ ] ( )smm bbci''
tm 421
0 213 +−σ==σσ=σ
= rock mass unconfined compressive strength
= rock mass tensile strength
Following Hoek & Brown (1997):
DETERMINING mb, s AND α
⎟⎠
⎞⎜⎝
⎛=28100-exp GSImm ib
GSI > 25
GSI < 25
0200
650
=
⎟⎠
⎞⎜⎝
⎛−=α
s
GSI.
509100
.
-exp
=
⎟⎠
⎞⎜⎝
⎛=
α
GSIs
9
α
⎟⎟⎠
⎞⎜⎜⎝
⎛+
σ
σσ+σ=σ b
ci
'
bci'' sm 331
σci and mi are derived from the laboratory tests
σ’3
σ’1
α
⎟⎟⎠
⎞⎜⎜⎝
⎛+
σ
σσ+σ=σ sm
ci
'
bci'' 331
'3
'1 sin1
sin1σ
φφ
σσ−
++= ci
HOEK & BROWN MOHR-COULOMB
0 < σ’3 < 0.25 σci New linearization range!
LINEARIZATION PROCESS
⎟⎠
⎞⎜⎝
⎛=28100-exp GSImm ib
509100
.
-exp
=
⎟⎠
⎞⎜⎝
⎛=
α
GSIs
0
25
50
75
100
125
150
175
200
225
250
-10 10 30 50 70 90
σ'3 (MPa)
σ' 1
(MPa
)
Intact rock unconfined compressive strength σci = 135 MPa Intact rock Hoek-Brown constant mi = 8.1 Geological Strength Index GSI = 70 Hoek-Brown constant mb = 2.8 Hoek-Brown constant s = 0.04 Rock mass unconfined compressive strength σcm = 36.7 MPa Deformation modulus Ed = 35 GPa
MOHR-COULOMB HOEK-BROWN
ROCK MASS