Code_Aster ®
Version
8.1
Titrate:
SSNV184 - Triaxial Essai with the model of Hoek-Brown modified Date
:

15/02/06
Author (S):
C. CHAVANT, V. GERVAIS Key
:
V6.04.184-A Page:
1/12

Organization (S): EDF-R & D/AM, CS-SI
Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
Document: V6.04.184
SSNV184 - Triaxial Essai with the model of Hoek-
Brown modified

Summary

This test makes it possible to validate the elastoplastic law of behavior of Hoek-Brown modified in mechanics of
rocks. It is about a triaxial compression test for which calculations are carried out in pure mechanics. Three levels of
containment are applied: 5 MPa, 12 MPa and 25 MPa. For reasons of symmetry, one is interested only in
eighth of a sample subjected to a triaxial compression test.
It is about a test of not-regression.
Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-62/06/005/A

Code_Aster ®
Version
8.1
Titrate:
SSNV184 - Triaxial Essai with the model of Hoek-Brown modified Date
:

15/02/06
Author (S):
C. CHAVANT, V. GERVAIS Key
:
V6.04.184-A Page:
2/12

Contents

1 Problem of reference .......................................................................................................................... 3
1.1 Geometry ........................................................................................................................................ 3
1.2 Properties of the material .................................................................................................................... 3
1.3 Initial conditions, with the limits and loading ................................................................................ 4
2 Reference solution ............................................................................................................................. 4
2.1 Calculation of solution ............................................................................................................................ 4
2.2 Results of reference ..................................................................................................................... 4
3 Modeling A ....................................................................................................................................... 5
3.1 Characteristics of modeling ................................................................................................. 5
3.2 Characteristics of the grid ........................................................................................................... 5
3.3 Functionalities tested .................................................................................................................... 5
4 Results of modeling A .............................................................................................................. 6
4.1 Values tested ................................................................................................................................ 6
5 Modeling B ....................................................................................................................................... 7
5.1 Characteristics of modeling ................................................................................................. 7
5.2 Characteristics of the grid ........................................................................................................... 7
5.3 Functionalities tested .................................................................................................................... 7
6 Results of modeling B .............................................................................................................. 8
6.1 Values tested ................................................................................................................................ 8
7 Modeling C ....................................................................................................................................... 9
7.1 Characteristics of modeling ................................................................................................. 9
7.2 Characteristics of the grid ........................................................................................................... 9
7.3 Functionalities tested .................................................................................................................... 9
8 Results of modeling C ............................................................................................................ 10
8.1 Values tested .............................................................................................................................. 10
9 Summary of the results ......................................................................................................................... 11

Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-62/06/005/A

Code_Aster ®
Version
8.1
Titrate:
SSNV184 - Triaxial Essai with the model of Hoek-Brown modified Date
:

15/02/06
Author (S):
C. CHAVANT, V. GERVAIS Key
:
V6.04.184-A Page:
3/12

1
Problem of reference

1.1 Geometry

One considers here a cube of dimension 1m × 1m × 1m.

Z

1 m

· D

· C

1 m

With
B

·
·

y

X
1 m

Co-ordinates of the points (in m):

WITH B C D
X 0 0.0.5 1
y 0 1.0.5 1
Z 0 0.0.5 1

1.2
Properties of material

Parameters of the elastic law of behavior:
E = 4500 MPa
= 0.3

Parameters of the law of Hoek-Brown modified:
rup
= 0.005
LMBO
= 0.017
2 end
(S) = 225 MPa2
C
2 rup
(S) = 482.5675 MPa2
C
end
(m) = 13.5 MPa
C
rup
(m) = 83.75 MPa
C
= 3 MPa
rup
= 15°
LMBO
= 30°
= 3.3
Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-62/06/005/A

Code_Aster ®
Version
8.1
Titrate:
SSNV184 - Triaxial Essai with the model of Hoek-Brown modified Date
:

15/02/06
Author (S):
C. CHAVANT, V. GERVAIS Key
:
V6.04.184-A Page:
4/12

1.3 Conditions
initial,
with the limits and loading

The test breaks up into two phases:


1) Initially, one brings the sample in a homogeneous state 0
0
0
= =. For
xx
yy
zz
that, the corresponding confining pressure is imposed on the front faces (X = 1),
side straight line (y = 1) and higher (Z = 1), while displacements are taken null on
the faces postpones (U
= 0), side left (U
= 0) and the lower (U
= 0).
X x=0
y y=0
Z z=0
2) Once the homogeneous state obtained, displacements are maintained blocked on the faces
back, side left and lower and the confining pressure are always imposed on
front faces and side straight line. A displacement is imposed on the higher face (U (T))
Z
in order to obtain a deformation equalizes with ­ 25% starting from the beginning of the second phase
zz
(with t=2). The increment of deformation is taken constant:
= 2
- .5E - 4 for
zz
modelings A and B, and = 3
- .33E - 4 for modeling C.
zz

2
Reference solution

2.1
Calculation of solution

The value of the major principal constraint can be calculated at the frangible joint (rup
) and with
residual resistance (LMBO
) starting from the form of the diverter of constraint:

rup
2 rup
rup
-
= (S) - (m)
1
3
C
3
C
LMBO


2 LMBO
LMBO
LMBO
-
= (S) - (m) - B
1
3
-

1
3
C
3
C


data base




3

rup
rup 2
2
2 rup
- (m) - ((m)) + 4 1
(-) (S)
data base
C
C
C
LMBO
2 rup

with
=
B
and

= - (S)
3
2
C
2 1
(-)

2.2
Results of reference

Constraints (), () and () at point D.
xx
3
yy
1
zz
3
Displacements () and () at point D.
xx
3
zz
1

Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-62/06/005/A

Code_Aster ®
Version
8.1
Titrate:
SSNV184 - Triaxial Essai with the model of Hoek-Brown modified Date
:

15/02/06
Author (S):
C. CHAVANT, V. GERVAIS Key
:
V6.04.184-A Page:
5/12

3 Modeling
With

3.1
Characteristics of modeling

Modeling 3D
Cutting: 1m in height, 1m in width
Loading of phase 1: 0
0
0
= = = - MPa

5
(confining pressure)
xx
yy
zz
Boundary conditions: U
= U
= U
= 0
X x=0
y y=0
Z z=0

3.2
Characteristics of the grid

A number of nodes: 20
A number of meshs and types: 6 QUAD8 and 1 HEXA20

3.3 Functionalities
tested

Commands



DEFI_MATERIAU HOEK_BROWN


STAT_NON_LINE COMP_INCR
RELATION
“HOEK_BROWN”

Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-62/06/005/A

Code_Aster ®
Version
8.1
Titrate:
SSNV184 - Triaxial Essai with the model of Hoek-Brown modified Date
:

15/02/06
Author (S):
C. CHAVANT, V. GERVAIS Key
:
V6.04.184-A Page:
6/12

4
Results of modeling A

4.1 Values
tested

Rupture:
rup
Value
:
reference

of

-
= 30.0219
1
3 ref.
rup
Value



Code_Aster: -
= 29.7520 (
of

number
43
:

command
)
1
3

relative

Variation
ref.


-
Code_Aster
%

0.90
:


Residual resistance:
rup
Value

reference

of


:
-
= 15.7215
1
3 ref.

rup
Value



Code_Aster
: -
= 15.7215 (
of

number
65
:

command
)
1
3

Localization Number
of Contrainte command
(MPa) Code_Aster
Not D
12

- 5.00
xx
40

- 5.00
xx
12

- 5.00
yy
40

- 5.00
yy
12

- 18.5
zz
16

- 22.4982
zz
30

- 29.0442
zz
43

- 34.7520
zz
45

- 31.3756
zz
50

- 24.4274
zz
55

- 21.6325
zz
65

- 20.7215
zz

Localization Number
of command Déformation Code_Aster
Not D
12

0.9 E-3
xx
16

1.22296 E-3
xx
30

2.82301 E-3
xx
43

4.59944 E-3
xx
45

5.39287 E-3
xx
50

7.41788 E-3
xx
55

9.07385 E-3
xx
65

11.9257 E-3
xx
12

- 3rd-3
zz
65

- 16.25 E-3
zz
Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-62/06/005/A

Code_Aster ®
Version
8.1
Titrate:
SSNV184 - Triaxial Essai with the model of Hoek-Brown modified Date
:

15/02/06
Author (S):
C. CHAVANT, V. GERVAIS Key
:
V6.04.184-A Page:
7/12

5 Modeling
B

5.1
Characteristics of modeling

Modeling 3D
Cutting: 1m in height, 1m in width
Loading of phase 1: 0
0
0
= = = - MPa

12
(confining pressure)
xx
yy
zz
Boundary conditions: U
= U
= U
= 0
X x=0
y y=0
Z z=0

5.2
Characteristics of the grid

A number of nodes: 20
A number of meshs and types: 6 QUAD8 and 1 HEXA20

5.3 Functionalities
tested

Commands



DEFI_MATERIAU HOEK_BROWN


STAT_NON_LINE COMP_INCR
RELATION
“HOEK_BROWN”

Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-62/06/005/A

Code_Aster ®
Version
8.1
Titrate:
SSNV184 - Triaxial Essai with the model of Hoek-Brown modified Date
:

15/02/06
Author (S):
C. CHAVANT, V. GERVAIS Key
:
V6.04.184-A Page:
8/12

6
Results of modeling B

6.1 Values
tested

Rupture:
rup
Value
:
reference

of

-
= 38.5690
1
3 ref.
rup
Value



Code_Aster: -

=
of

(number

38.4447
51)
:

command
1
3

ref.

Variation

-
Code_Aster
%

0.32
:


Residual resistance:
rup
Value
:
reference

of

-
= 30.8023
1
3 ref.

rup
Value



Code_Aster: -
=
of

(number

30.8023
80)
:

command
1
3

Localization Number
of Contrainte command
(MPa) Code_Aster
Not D
16

- 12.00
xx
50

- 12.00
xx
16

- 12.00
yy
50

- 12.00
yy
16

- 30
zz
20

- 33.2264
zz
40

- 44.5889
zz
51

- 50.4447
zz
55

- 48.0512
zz
60

- 45.5579
zz
70

- 43.0472
zz
80

- 42.8023
zz

Localization Number
of command Déformation Code_Aster
Not D
16

1.2 E-3
xx
20

1.56091 E-3
xx
40

3.78317 E-3
xx
51

5.22869 E-3
xx
55

6.32002 E-3
xx
60

7.74068 E-3
xx
70

10.5716 E-3
xx
80

13.3372 E-3
xx
16

- 4th-3
zz
80

- 2nd-2
zz
Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-62/06/005/A

Code_Aster ®
Version
8.1
Titrate:
SSNV184 - Triaxial Essai with the model of Hoek-Brown modified Date
:

15/02/06
Author (S):
C. CHAVANT, V. GERVAIS Key
:
V6.04.184-A Page:
9/12

7 Modeling
C

7.1
Characteristics of modeling

Modeling 3D
Cutting: 1m in height, 1m in width
Loading of phase 1: 0
0
0
= = = -
MPa

25
(confining pressure)
xx
yy
zz
Boundary conditions: U
= U
= U
= 0
X x=0
y y=0
Z z=0

7.2
Characteristics of the grid

A number of nodes: 20
A number of meshs and types: 6 QUAD8 and 1 HEXA20

7.3 Functionalities
tested

Commands



DEFI_MATERIAU HOEK_BROWN


STAT_NON_LINE COMP_INCR
RELATION
“HOEK_BROWN”

Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-62/06/005/A

Code_Aster ®
Version
8.1
Titrate:
SSNV184 - Triaxial Essai with the model of Hoek-Brown modified Date
:

15/02/06
Author (S):
C. CHAVANT, V. GERVAIS Key
:
V6.04.184-A Page:
10/12

8
Results of modeling C

8.1 Values
tested

Rupture:
rup
Value

reference

of


:
-
= 50.7574
1
3 ref.
rup
Value



Code_Aster: -
=
of

(number

50.3064
46)
:

command
1
3

ref.

Variation

-
Code_Aster
%

0.89
:


Residual resistance:
rup
Value
:
reference

of

-
= 55.1249
1
3 ref.

rup
Value



Code_Aster: -
=
of

(number

55.1249
81)
:

command
1
3

Localization Number
of Contrainte command
(MPa) Code_Aster
Not D
18

- 25.00
xx
81

- 25.00
xx
18

- 25.00
yy
81

- 25.00
yy
18

- 50.8398
zz
24

- 56.4340
zz
36

- 66.9436
zz
46

- 75.3064
zz
54

- 77.6467
zz
66

- 79.7633
zz
81

- 80.1249
zz

Localization Number
of command Déformation Code_Aster
Not D
18

1.85408 E-3
xx
24

2.63445 E-3
xx
36

4.35497 E-3
xx
46

5.98034 E-3
xx
54

7.90516 E-3
xx
66

11.3535 E-3
xx
81

16.7102 E-3
xx
18

- 6th-3
zz
36

- 12th-3
zz
81

- 27 E-3
zz

Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-62/06/005/A

Code_Aster ®
Version
8.1
Titrate:
SSNV184 - Triaxial Essai with the model of Hoek-Brown modified Date
:

15/02/06
Author (S):
C. CHAVANT, V. GERVAIS Key
:
V6.04.184-A Page:
11/12

9
Summary of the results

The results obtained show an agreement of stress the rupture and to residual resistance
1
between the computed values and those obtained with Code_Aster.
This case test is a test of not-regression developed to validate the modified model of Hoek-Brown.

Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-62/06/005/A

Code_Aster ®
Version
8.1
Titrate:
SSNV184 - Triaxial Essai with the model of Hoek-Brown modified Date
:

15/02/06
Author (S):
C. CHAVANT, V. GERVAIS Key
:
V6.04.184-A Page:
12/12

Intentionally white left page.
Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-62/06/005/A