Code_Aster
®
Version
8.1
Titrate:
SSNV184 - Triaxial compression test 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
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-62/06/005/A
Organization (S):
EDF-R & D/AM, CS-SI
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
Document: V6.04.184
SSNV184 - Triaxial compression test 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.
Code_Aster
®
Version
8.1
Titrate:
SSNV184 - Triaxial compression test 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
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-62/06/005/A
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 mesh ........................................................................................................... 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 mesh ........................................................................................................... 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 mesh ........................................................................................................... 9
7.3
Functionalities tested .................................................................................................................... 9
8
Results of modeling C ............................................................................................................ 10
8.1
Values tested .............................................................................................................................. 10
9
Summary of the results ......................................................................................................................... 11
Code_Aster
®
Version
8.1
Titrate:
SSNV184 - Triaxial compression test 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
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-62/06/005/A
1
Problem of reference
1.1 Geometry
One considers here a cube of dimension 1m
× 1m × 1m.
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
end
C
S
)
(
2
= 225 MPa
2
rup
C
S
)
(
2
= 482.5675 MPa
2
end
C
m
)
(
= 13.5 MPa
rup
C
m
)
(
= 83.75 MPa
= 3 MPa
rup
= 15°
LMBO
= 30°
= 3.3
X
Z
y
With
B
D
·
·
·
C
1 m
1 m
1 m
·
Code_Aster
®
Version
8.1
Titrate:
SSNV184 - Triaxial compression test 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
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-62/06/005/A
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
zz
yy
xx
=
=
. For
that, the corresponding confining pressure is imposed on the front faces (
1
=
X
),
side straight line (
1
=
y
) and higher (
1
=
Z
), while displacements are taken null on
the faces postpones (
0
0
=
=
X
X
U
), side left (
0
0
=
=
y
y
U
) and lower (
0
0
=
=
Z
Z
U
).
2) Once the homogeneous state obtained, displacements are maintained locked on the faces
rear, 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 (
)
(T
U
Z
)
in order to obtain a deformation
zz
equalize with 25% starting from the beginning of the second phase
(with t=2). The increment of deformation is taken constant:
4
5
.
2
-
-
=
E
zz
for
modelings A and B, and
4
33
.
3
-
-
=
E
zz
for modeling C.
2
Reference solution
2.1
Calculation of solution
The value of the major main stress can be calculated at the frangible joint (
rup
) and with
residual resistance (
LMBO
) starting from the form of the diverter of stress:
rup
C
LMBO
rup
C
rup
C
rup
C
D
B
D
B
LMBO
LMBO
C
LMBO
C
LMBO
rup
C
rup
C
rup
S
B
S
m
m
B
m
S
m
S
)
(
and
)
1
(
2
)
(
)
1
(
4
)
)
((
)
(
with
1
)
(
)
(
)
(
)
(
2
2
2
2
2
3
3
3
3
2
3
1
3
2
3
1
-
=
-
-
+
-
-
=
-
-
-
=
-
-
=
-
-
-
2.2
Results of reference
Stresses
)
(
3
xx
,
)
(
1
yy
and
)
(
3
zz
at point D.
Displacements
)
(
3
xx
and
)
(
1
zz
at point D.
Code_Aster
®
Version
8.1
Titrate:
SSNV184 - Triaxial compression test 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
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-62/06/005/A
3 Modeling
With
3.1
Characteristics of modeling
Modeling 3D
Cutting: 1m in height, 1m in width
Loading of phase 1:
MPa
5
-
0
0
0
=
=
=
zz
yy
xx
(confining pressure)
Boundary conditions:
0
0
0
0
=
=
=
=
=
=
Z
Z
y
y
X
X
U
U
U
3.2
Characteristics of the mesh
A number of nodes: 20
A number of meshs and types: 6 QUAD8 and 1 HEXA20
3.3 Functionalities
tested
Controls
DEFI_MATERIAU HOEK_BROWN
STAT_NON_LINE COMP_INCR
RELATION
“HOEK_BROWN”
Code_Aster
®
Version
8.1
Titrate:
SSNV184 - Triaxial compression test 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
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-62/06/005/A
4
Results of modeling A
4.1 Values
tested
Rupture:
%
0.90
:
-
ref.
relative
Variation
43
:
command
of
number
29.7520
:
Value
30.0219
:
reference
of
Value
)
(
Code_Aster
Code_Aster
=
-
=
-
rup
rup
ref.
3
1
3
1
Residual resistance:
)
(
:
65
:
command
of
number
15.7215
:
Value
15.7215
reference
of
Value
=
-
=
-
rup
rup
ref.
3
1
3
1
Code_Aster
Localization Number
of command Forced
(MPa) Code_Aster
Not D
12
xx
- 5.00
40
xx
- 5.00
12
yy
- 5.00
40
yy
- 5.00
12
zz
- 18.5
16
zz
- 22.4982
30
zz
- 29.0442
43
zz
- 34.7520
45
zz
- 31.3756
50
zz
- 24.4274
55
zz
- 21.6325
65
zz
- 20.7215
Localization Number
of command Code_Aster Deformation
Not D
12
xx
0.9 E-3
16
xx
1.22296 E-3
30
xx
2.82301 E-3
43
xx
4.59944 E-3
45
xx
5.39287 E-3
50
xx
7.41788 E-3
55
xx
9.07385 E-3
65
xx
11.9257 E-3
12
zz
- 3rd-3
65
zz
- 16.25 E-3
Code_Aster
®
Version
8.1
Titrate:
SSNV184 - Triaxial compression test 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
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-62/06/005/A
5 Modeling
B
5.1
Characteristics of modeling
Modeling 3D
Cutting: 1m in height, 1m in width
Loading of phase 1:
MPa
12
-
0
0
0
=
=
=
zz
yy
xx
(confining pressure)
Boundary conditions:
0
0
0
0
=
=
=
=
=
=
Z
Z
y
y
X
X
U
U
U
5.2
Characteristics of the mesh
A number of nodes: 20
A number of meshs and types: 6 QUAD8 and 1 HEXA20
5.3 Functionalities
tested
Controls
DEFI_MATERIAU HOEK_BROWN
STAT_NON_LINE COMP_INCR
RELATION
“HOEK_BROWN”
Code_Aster
®
Version
8.1
Titrate:
SSNV184 - Triaxial compression test 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
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-62/06/005/A
6
Results of modeling B
6.1 Values
tested
Rupture:
%
0.32
:
-
ref.
Variation
51)
:
command
of
(number
38.4447
:
Value
38.5690
:
reference
of
Value
Code_Aster
Code_Aster
=
-
=
-
rup
rup
ref.
3
1
3
1
Residual resistance:
80)
:
command
of
(number
30.8023
:
Value
30.8023
:
reference
of
Value
=
-
=
-
rup
rup
ref.
3
1
3
1
Code_Aster
Localization Number
of command Forced
(MPa) Code_Aster
Not D
16
xx
- 12.00
50
xx
- 12.00
16
yy
- 12.00
50
yy
- 12.00
16
zz
- 30
20
zz
- 33.2264
40
zz
- 44.5889
51
zz
- 50.4447
55
zz
- 48.0512
60
zz
- 45.5579
70
zz
- 43.0472
80
zz
- 42.8023
Localization Number
of command Code_Aster Deformation
Not D
16
xx
1.2 E-3
20
xx
1.56091 E-3
40
xx
3.78317 E-3
51
xx
5.22869 E-3
55
xx
6.32002 E-3
60
xx
7.74068 E-3
70
xx
10.5716 E-3
80
xx
13.3372 E-3
16
zz
- 4th-3
80
zz
- 2nd-2
Code_Aster
®
Version
8.1
Titrate:
SSNV184 - Triaxial compression test 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
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-62/06/005/A
7 Modeling
C
7.1
Characteristics of modeling
Modeling 3D
Cutting: 1m in height, 1m in width
Loading of phase 1:
MPa
25
-
0
0
0
=
=
=
zz
yy
xx
(confining pressure)
Boundary conditions:
0
0
0
0
=
=
=
=
=
=
Z
Z
y
y
X
X
U
U
U
7.2
Characteristics of the mesh
A number of nodes: 20
A number of meshs and types: 6 QUAD8 and 1 HEXA20
7.3 Functionalities
tested
Controls
DEFI_MATERIAU HOEK_BROWN
STAT_NON_LINE COMP_INCR
RELATION
“HOEK_BROWN”
Code_Aster
®
Version
8.1
Titrate:
SSNV184 - Triaxial compression test 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
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-62/06/005/A
8
Results of modeling C
8.1 Values
tested
Rupture:
%
0.89
:
-
ref.
Variation
46)
:
command
of
(number
50.3064
:
Value
50.7574
reference
of
Value
:
Code_Aster
Code_Aster
=
-
=
-
rup
rup
ref.
3
1
3
1
Residual resistance:
81)
:
command
of
(number
55.1249
:
Value
55.1249
:
reference
of
Value
=
-
=
-
rup
rup
ref.
3
1
3
1
Code_Aster
Localization Number
of command Forced
(MPa) Code_Aster
Not D
18
xx
- 25.00
81
xx
- 25.00
18
yy
- 25.00
81
yy
- 25.00
18
zz
- 50.8398
24
zz
- 56.4340
36
zz
- 66.9436
46
zz
- 75.3064
54
zz
- 77.6467
66
zz
- 79.7633
81
zz
- 80.1249
Localization Number
of command Code_Aster Deformation
Not D
18
xx
1.85408 E-3
24
xx
2.63445 E-3
36
xx
4.35497 E-3
46
xx
5.98034 E-3
54
xx
7.90516 E-3
66
xx
11.3535 E-3
81
xx
16.7102 E-3
18
zz
- 6th-3
36
zz
- 12th-3
81
zz
- 27 E-3
Code_Aster
®
Version
8.1
Titrate:
SSNV184 - Triaxial compression test 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
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-62/06/005/A
9
Summary of the results
The results obtained show an agreement of the stress
1
with the rupture and residual resistance
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.
Code_Aster
®
Version
8.1
Titrate:
SSNV184 - Triaxial compression test 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
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-62/06/005/A
Intentionally white left page.