r - The Hong Kong Polytechnic University

469.1m,f m =55%,f I =45%
-50
Σ 3 -Σ 1 (MPa)
-40
-30
Argilite
Matrix
1.0
E 1 (×10 -2 )
0.5
0.0
-20
-10
0
-0.5
-1.0
E 3 (×10 -2 )
Figure 9 Comparison of macroscopic responses of argillite and those of clay matrix alone during a triaxial
compression test with 10MPa confining pressure – influence of mineral inclusions
-1.5
-2.0
466.8m,f m =51%,f I =49%
451.5m,f m =49%,f I =51%
-40
Σ 3 -Σ 1 (MPa)
-50
Σ 3 -Σ 1 (MPa)
-30
-40
-30
-20
-20
1.0
E 1 (×10 -2 )
0.5
-10
0.0 -0.5
0
(a: Pc=0)
E 3 (×10 -2 )
-1.0
-1.5
1.0
E 1 (×10 -2 )
0.5
-10
0.0 -0.5 -1.0
0
(b: Pc=5MPa)
E 3 (×10 -2 )
-1.5
-2.0
451.4m,f m =47%,f I =53%
482.2m,f m =60%,f I =40%
-60
Σ 3 -Σ 1 (MPa)
-50 Σ 3 -Σ 1 (MPa)
-50
-40
-40
-30
-30
-20
-20
E 1 (×10 -2 )
1.0 0.5
-10
0.0
0
-0.5
-1.0
E 3 (×10 -2 )
-1.5
-2.0
E 1 (×10 -2 )
0.5
0.0
-10
0
-0.5
-1.0
E 3 (×10 -2 )
-1.5
-2.0
(c: Pc=10MPa)
(d: Pc=20MPa )
Figure 10 Simulation of triaxial compression tests under different confining pressures and on argillite
samples with different mineral compositions
CONCLUSIONS
In this short review paper, we have presented the general framework for multi-scale modelling of heterogeneous
geomaterials using rigorous homogenization procedures. Physical mechanisms involved at different material
scales can be directly involved in the formulation of the models. Influences of mineral compositions and
microstructure evolution can be properly taken into account. Such models appear very promising for the
physics-based modelling of geomaterials. It remains a number of challenges for future works such as influences
of microstructure morphology, intra phase heterogeneities, multi-physical and chemical coupling, linking
different materials scales from nano to macro scales.
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