Strona 2_redak - Instytut Agrofizyki im. Bohdana Dobrzańskiego ...

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A
-1 5
-1 0
-5
1 0
5
-5
5
1 0
1 5
2 0
2 5
3 0
3 5
40
-1 0
B
-2 0
-1 5
-1 0
-5
1 0
5
-5
5
1 0
1 5
2 0
2 5
3 0
3 5
-1 0
C
-3 0 -2 5
-1 5
-1 0
-5
1 0
5
-5
5
1 0
1 5
2 0
2 5
Fig. 7.10. Displacement distribution across shear band ε 1 = 0.17 [64]
7.2.7. Correction of change in sample cross-section area
-1 0
Increase in moisture content of grain results in an increase in susceptibility of
grains to deformation. Grain bedding of higher moisture content requires larger
displacement to attain critical state than dry grain. As a result, the surface area of
cross-section of the sample perpendicular to σ 1 increases as well. This in turn leads
to an increase in measurement error of the angle of internal friction because σ 1 is
calculated as a ratio of vertical force and undeformed cross-section area of the
sample [101]. Correction was introduced to account for change in the sample cross
section area. Assuming that volume of the sample remains constant during the test:
V = H (1 − ε ) 1
S1
= HS = const.
(7.5)
mean surface area S 1 of cross-section of deformed sample may be expressed as a
function of strain ε 1 :
S
(7.6)
Mean surface area obtained in this way was used to determine the corrected value
of higher principal stress σ 1k :
that was used for the determination of the angle of internal friction.
1
=
S
1−
ε
1
S(
σ1
− σ3)
σ
1k
= σ3
+
= σ3
+ ( σ1
− σ3)(1−
ε1)
,
S
1
(7.7)