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