Method for estimating elastic constants of anisotropic material
The present disclosure provides a method for estimating the elastic constants of an anisotropic material such as anisotropic rocks such as gneiss and shale even when using a general loader, the method enabling anisotropic elastic constants to be estimated even with only a single core sample, thereby significantly reducing time and costs.
1 . A method for estimating elastic constants, comprising:
collecting a core sample from an anisotropic material;
applying a load to respective ends of the core sample;
measuring a strain value on a surface of the core sample to which the load is applied;
calculating a strain in the same position as a position in which the strain was measured by performing a computer numerical simulation test under the same load condition applied to a core sample while changing an input elastic constant value; and
determining an elastic constant value when an error between the measured strain and the calculated strain is the lowest, as an elastic constant value of the core sample,
wherein at least one of the load applied to respective ends of the core sample is a concentrated load applied only to a portion of a surface of an end.
2 . A method for estimating elastic constants, comprising:
collecting a core sample from an anisotropic material;
applying a load to respective ends of the core sample;
measuring a strain value on a surface of the core sample to which the load is applied;
calculating a strain in the same position as a position in which the strain was measured by performing a computer numerical simulation test under the same load condition applied to a core sample while changing an input elastic constant value; and
determining a value of an elastic constant obtained when the error between the measured strain and the calculated strain falls within an allowable range, as an elastic constant value of the core sample,
wherein at least one of the load applied to respective ends of the core sample is a concentrated load applied only to a portion of a surface of an end.
3 . The method for estimating the elastic constants of an anisotropic material of claim 1 , wherein only a single sample is used as the core sample.
4 . The method for estimating the elastic constants of an anisotropic material of claim 1 , wherein the core sample has a columnar shape.
5 . The method for estimating the elastic constants of an anisotropic material of claim 1 , wherein a soft loading plate is provided so as to come into contact with only a portion of an end surface to which the load is applied.
6 . The method for estimating the elastic constants of an anisotropic material of claim 5 , wherein a Young's modulus of the soft loading plate is 1/10 or less as compared to a Young's modulus of the core sample.
7 . The method for estimating the elastic constants of an anisotropic material of claim 1 , wherein in the measuring a strain value, a strain measurement sensor is attached to the surface of the core sample to measure a strain value at each attachment point,
when attaching the strain measurement sensor, one or more strain measurement sensors are attached to a first position a certain distance away from an end surface of the core sample in an axial direction, and
one or more additional strain measurement sensors are attached to a second position further away from the end surface of the core sample in the axial direction than the first position.
8 . The method for estimating the elastic constants of an anisotropic material of claim 5 , wherein in the measuring a strain value, a strain measurement sensor is attached to the surface of the core sample to measure a strain value at each attachment point,
one or more strain measurement sensors are attached to a position A included in a region parallel to an axial direction with respect to a region in which the soft loading plate is in contact with an end surface of the core sample, and
one or more additional strain measurement sensors are attached to a position B not included in a region parallel to the axial direction with respect to the region in which the soft loading plate is in contact with the end surface of the core sample.
9 . The method for estimating the elastic constants of an anisotropic material of claim 8 , wherein two or more strain measurement sensors in which one or more of an attachment position and an attachment direction is different from each other are attached to the position A.
10 . The method for estimating the elastic constants of an anisotropic material of claim 5 , wherein in the measuring a strain value, a strain measurement sensor is attached to the surface of the core sample to measure a strain value at each attachment point,
the core sample comprises a position A included in a region parallel to an axial direction with respect to a region in which the soft loading plate is in contact with the end surface, and a position B not included in a region parallel to the axial direction with respect to the region in which the soft loading plate is in contact with the end surface, and
three or more strain measurement sensors in which one or more of an attachment position and an attachment direction is different from each other are attached to at least one position selected from the position A and the position B, and one or more strain measurement sensors are attached to a remaining position.
11 . The method for estimating the elastic constants of an anisotropic material of claim 1 , wherein the number of strain measurement sensors attached to the surface of the core sample is 5 or more.
12 . The method for estimating the elastic constants of an anisotropic material of claim 8 , wherein in the position A, one or more strain measurement sensors are attached to a first position a certain distance away from the end surface of the core sample in the axial direction, and
in the position A, one or more strain measurement sensors are attached to a second position further away from the end surface of the core sample in the axial direction (X-direction) than the first position.
13 . The method for estimating the elastic constants of an anisotropic material of claim 1 , further comprising:
after the measuring a strain value, prior to the calculating a strain,
performing an indirect tensile test on a partial sample additionally collected from the core sample.
14 . The method for estimating the elastic constants of an anisotropic material of claim 1 , wherein as a relative error rate defined by the following relational expression 1, a Young's modulus satisfies 20% or less, and a shear modulus satisfies 10% or less, and
an error for a Poisson's ratio defined by the following relational expression 2 satisfies 0.1 or less,
1
n
∑
n
i
-
1
(
X
i
-
X
true
X
true
)
2
×
100
(
%
)
[
Relational
Expression
1
]
1
n
∑
i
=
1
n
(
X
i
-
X
true
)
2
[
Relational
Expression
2
]
(in the relational expressions 1 and 2, X i represents a value of an optimal elastic constant estimated in the i-th test, X true represents a value of an elastic constant for an actual core sample, and n represents the total number of tests).
15 . The method for estimating the elastic constants of an anisotropic material of claim 13 , wherein as a relative error rate defined by the following relational expression 1, a Young's modulus satisfies 8% or less, and a shear modulus satisfies 8% or less, and
an error for a Poisson's ratio defined by the following relational expression 2 satisfies 0.05 or less,
1
n
∑
n
i
=
1
(
X
i
-
X
true
X
true
)
2
×
100
(
%
)
[
Relational
Expression
1
]
1
n
∑
n
i
=
1
(
X
i
-
X
true
)
2
[
Relational
Expression
2
]
(in the relational expressions 1 and 2, X i represents a value of an optimal elastic constant estimated in the i-th test, X true represents a value of an elastic constant for an actual core sample, and n represents the total number of tests).