Code_Aster ®
Version
8.3
Titrate:
WTNV128 - Triaxial Essai not drained with the model of Hoek-Brown
Date:
04/05/06
Author (S):
C. CHAVANT, V. GERVAIS Key
:
V7.31.128-A Page:
1/8

Organization (S): EDF-R & D/AMA, CS-SI
Handbook of Validation
V7.31 booklet: Thermo hydro-mechanical in porous environment of voluminal structures
Document: V7.31.128
WTNV128 - Triaxial Essai not drained with the model
of Hoek-Brown modified in effective constraints

Summary

This test makes it possible to validate the elastoplastic law of behavior of Hoek-Brown modified in constraints
effective, that is to say HOEK_BROWN_EFF with hydraulic coupling. It is about a triaxial compression test in condition not
drained. The aspect not drained is modelled by a null voluminal deformation of the skeleton and the coupling
hydraulics is taken into account. The sample is completely saturated, the skeleton and the fluid being supposed
incompressible.
For reasons of symmetry, one is interested only in the eighth of a sample subjected to a triaxial compression test.
The level of containment applied is 5 MPa.
It is about a test of nonregression.

Modeling A is a modeling of the 3d_HM type with integration at the points of Gauss.
Modeling B is a modeling of the 3d_HMS type with integration at the points of Gauss or the nodes
(see Doc. [R7.01.10]).
Handbook of Validation
V7.31 booklet: Thermo hydro-mechanical in porous environment of voluminal structures
HT-62/06/005/A

Code_Aster ®
Version
8.3
Titrate:
WTNV128 - Triaxial Essai not drained with the model of Hoek-Brown
Date:
04/05/06
Author (S):
C. CHAVANT, V. GERVAIS Key
:
V7.31.128-A Page:
2/8

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 Modeling A ....................................................................................................................................... 5
2.1 Characteristics of modeling ................................................................................................. 5
2.2 Characteristics of the grid ........................................................................................................... 5
2.3 Functionalities tested .................................................................................................................... 5
3 Results of modeling A .............................................................................................................. 6
3.1 Values tested ................................................................................................................................ 6
4 Modeling B ....................................................................................................................................... 7
4.1 Characteristics of modeling ................................................................................................. 7
4.2 Characteristics of the grid ........................................................................................................... 7
4.3 Functionalities tested .................................................................................................................... 7
5 Results of modeling B .............................................................................................................. 8
5.1 Values tested ................................................................................................................................ 8
6 Summary of the results ........................................................................................................................... 8

Handbook of Validation
V7.31 booklet: Thermo hydro-mechanical in porous environment of voluminal structures
HT-62/06/005/A

Code_Aster ®
Version
8.3
Titrate:
WTNV128 - Triaxial Essai not drained with the model of Hoek-Brown
Date:
04/05/06
Author (S):
C. CHAVANT, V. GERVAIS Key
:
V7.31.128-A Page:
3/8

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
V7.31 booklet: Thermo hydro-mechanical in porous environment of voluminal structures
HT-62/06/005/A

Code_Aster ®
Version
8.3
Titrate:
WTNV128 - Triaxial Essai not drained with the model of Hoek-Brown
Date:
04/05/06
Author (S):
C. CHAVANT, V. GERVAIS Key
:
V7.31.128-A Page:
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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), the water pressures are taken null everywhere and
displacements are taken null on the faces postpones (U
= 0), side left
X x=0
(U
= 0) and the lower (U
= 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. Hydraulic flows are null on all the faces. One
displacement is forced on the higher face (U (T)) in order to obtain a deformation
Z
equalize with ­ 25% starting from the beginning of the second phase, by increments of deformation
zz
constant
= 2
- .5E - 4. On the front faces and side straight line, one imposes conditions
zz
with the limits in total constraint: N
0
= = 5
- MPa.

Handbook of Validation
V7.31 booklet: Thermo hydro-mechanical in porous environment of voluminal structures
HT-62/06/005/A

Code_Aster ®
Version
8.3
Titrate:
WTNV128 - Triaxial Essai not drained with the model of Hoek-Brown
Date:
04/05/06
Author (S):
C. CHAVANT, V. GERVAIS Key
:
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2 Modeling
With

2.1
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
Coefficient of Biot: 1
UN_SUR_K of water: 0 (coefficient of incompressibility of water)
Modeling: 3d_HM

2.2
Characteristics of the grid

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

2.3 Functionalities
tested

Commands



DEFI_MATERIAU HOEK_BROWN


STAT_NON_LINE COMP_INCR RELATION
“KIT_THM”
“RELATION_KIT” =
“HOEK_BROWN_EFF”, “LIQU_SATU”, “HYDR_UTIL”

Handbook of Validation
V7.31 booklet: Thermo hydro-mechanical in porous environment of voluminal structures
HT-62/06/005/A

Code_Aster ®
Version
8.3
Titrate:
WTNV128 - Triaxial Essai not drained with the model of Hoek-Brown
Date:
04/05/06
Author (S):
C. CHAVANT, V. GERVAIS Key
:
V7.31.128-A Page:
6/8

3
Results of modeling A

3.1 Values
tested

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

xx
- 0.239568
28

xx
- 0.257851
36

xx
- 1.10550
44

xx
- 4.29762
52

xx
- 7.28266
80

xx
- 15.7587
16

yy
- 0.239568
28

yy
- 0.257851
36

yy
- 1.10550
44

yy
- 4.29762
52

yy
- 7.28266
80

yy
- 15.7587
16

zz
- 16.0195
28

zz
- 20.4913
36

zz
- 24.7968
44

zz
- 28.9045
52

zz
- 33.7174
80

zz
- 54.1101
16
Pressure
water
5.23957
44
Pressure
water
0.702380
80
Pressure
water
- 10.7587

Handbook of Validation
V7.31 booklet: Thermo hydro-mechanical in porous environment of voluminal structures
HT-62/06/005/A

Code_Aster ®
Version
8.3
Titrate:
WTNV128 - Triaxial Essai not drained with the model of Hoek-Brown
Date:
04/05/06
Author (S):
C. CHAVANT, V. GERVAIS Key
:
V7.31.128-A Page:
7/8

4 Modeling
B

4.1
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
Coefficient of Biot: 1
UN_SUR_K of water: 0 (coefficient of incompressibility of water)
Modeling: 3d_HMS

4.2
Characteristics of the grid

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

4.3 Functionalities
tested

Commands



DEFI_MATERIAU HOEK_BROWN

STAT_NON_LINE COMP_INCR RELATION
“KIT_THM”
“RELATION_KIT” =
“HOEK_BROWN_EFF”, “LIQU_SATU”, “HYDR_UTIL”

Handbook of Validation
V7.31 booklet: Thermo hydro-mechanical in porous environment of voluminal structures
HT-62/06/005/A

Code_Aster ®
Version
8.3
Titrate:
WTNV128 - Triaxial Essai not drained with the model of Hoek-Brown
Date:
04/05/06
Author (S):
C. CHAVANT, V. GERVAIS Key
:
V7.31.128-A Page:
8/8

5
Results of modeling B

5.1 Values
tested

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

xx
- 0.239568
28

xx
- 0.257851
36

xx
- 1.10550
44

xx
- 4.29762
52

xx
- 7.28266
80

xx
- 15.7587
16

yy
- 0.239568
28

yy
- 0.257851
36

yy
- 1.10550
44

yy
- 4.29762
52

yy
- 7.28266
80

yy
- 15.7587
16

zz
- 16.0195
28

zz
- 20.4913
36

zz
- 24.7968
44

zz
- 28.9045
52

zz
- 33.7174
80

zz
- 54.1101
16
Pressure
water
5.23957

44
Pressure water
0.702380

80
Pressure water
- 10.7587

6
Summary of the results

This case test is a test of not-regression developed to validate the model of Hoek-Brown modified in
effective constraints, HOEK_BROWN_EFF, with hydraulic coupling.

One obtains the same results with two modelings 3d_HM or 3d_HMS.

Handbook of Validation
V7.31 booklet: Thermo hydro-mechanical in porous environment of voluminal structures
HT-62/06/005/A