Determining rock properties
Techniques for determining rock properties include exerting a compressive load with a test apparatus across a rock sample that includes a specified length-to-diameter ratio; measuring, with a strain gauge, a strain on the rock sample during the compressive loading; determining, based at least in part on the compressive load, a mechanical property of the rock sample; and determining, based at least in part on the measured strain and the compressive load, an elastic property of the rock sample.
1. A method for determining rock properties, comprising:
exerting a compressive load with a Brazilian test apparatus across a rock sample that comprises a specified length-to-diameter ratio;
measuring, with the Brazilian test apparatus, a tensile strength of the rock sample based on the compressive load;
measuring, with at least one strain gauge that is coupled to an axial surface of the rock sample, a strain on the rock sample during the compressive loading, the measuring comprising:
measuring an incremental axial strain on the rock sample during a compressive load increment with a first strain gauge, and
measuring an incremental radial strain on the rock sample during the compressive load increment with a second strain gauge;
determining, based at least in part on the compressive load, a mechanical property of the rock sample; and
determining, based at least in part on the measured strain and the compressive load, an elastic property of the rock sample, the determining comprising:
determining a first coefficient based at least in part on the diameter of the rock sample, the length of the rock sample, and an effective length of the first and second strain gauges,
determining a second coefficient based at least in part on the diameter of the rock sample, the length of the rock sample, and the effective length of the first and second strain gauges, and
determining the elastic property of the rock sample based at least in part on the measured incremental axial and radial strains on the rock sample, the first and second coefficients, and the compressive loading increment.
2. The method of claim 1 , wherein the specified length-to-diameter ratio is between 0.2 and 0.75.
3. The method of claim 1 , wherein determining, based at least in part on the measured strain and the compressive load, the elastic property of the rock sample comprises determining a Young's modulus of the rock sample based on at least one of:
E
=
Δ
P
Δ
ɛ
x
(
-
F
+
vG
)
,
(
i
)
where E is stress dependent Young's modulus of the rock sample, ΔP is the compressive loading increment, Δϵ x is the incremental radial strain, υ is Poisson's ratio of the rock sample, F is a first coefficient, and G is a second coefficient; or
E
=
P
ɛ
x
(
-
F
+
vG
)
,
(
ii
)
where E is Young's modulus of the rock sample, P is a particular compressive load, ϵ x is a radial strain at the particular compressive load, υ is Poisson's ratio of the rock sample, F is the first coefficient, and G is the second coefficient.
4. The method of claim 1 , wherein determining, based at least in part on the measured strain and the compressive load, the elastic property of the rock sample comprises determining Poisson's ratio of the rock sample based on at least one of:
υ
=
(
Δ
ɛ
x
Δɛ
y
)
G
+
F
(
Δ
ɛ
x
Δɛ
y
)
F
+
G
,
(
i
)
where υ is stress dependent Poisson's ratio of the rock sample, Δϵ x is the incremental radial strain, Δϵ y is the incremental axial strain, F is a first coefficient, and G is a second coefficient; or
υ
=
(
ɛ
x
ɛ
y
)
G
+
F
(
ɛ
x
ɛ
y
)
F
+
G
,
(
ii
)
where υ is Poisson's ratio of the rock sample, ϵ x is a radial strain at a particular compressive load on the rock sample, Δϵ y is an axial strain at the particular compressive load on the rock sample, F is the first coefficient, and G is the second coefficient.
5. The method of claim 1 , wherein the mechanical property comprises at least one of a tensile strength or a brittleness of the rock sample.
6. The method of claim 1 , wherein the strain gauge comprises a linear variable differential transformer (LVDT).
7. A rock property test system, comprising:
a load cell configured to exert a compressive load across a rock sample, the load cell comprising a Brazilian test apparatus;
at least one strain gauge configured to attach to an axial surface of the rock sample and positioned to measure a strain on the rock sample during the compressive loading, the at least one strain gauge comprising a first strain gauge configured to measure an incremental axial strain on the rock sample during the incremental compressive load and a second strain gauge configured to measure an incremental radial strain on the rock sample during the incremental compressive load; and
a control system communicably coupled to the load cell and the at least one strain gauge and configured to perform operations comprising:
controlling the load cell to exert an incremental compressive load on the rock sample;
determining a tensile strength of the rock sample based on the compressive load;
receiving a measured incremental axial strain on the rock sample and a measured incremental radial strain on the rock sample, based on the incremental compressive load, from the at least one strain gauge;
determining a first coefficient based at least in part on the diameter of the rock sample, the length of the rock sample, and an effective length of the first and second strain gauges;
determining a second coefficient based at least in part on the diameter of the rock sample, the length of the rock sample, and the effective length of the first and second strain gauges;
determining, based at least in part on the incremental compressive load, a mechanical property of the rock sample; and
determining, based at least in part on the measured incremental axial and radial strains on the rock sample, the first and second coefficients, and the incremental compressive load, an elastic property of the rock sample.
8. The rock property test system of claim 7 , wherein the rock sample comprises a length-to-diameter ratio between 0.2 and 0.75.
9. The rock property test system of claim 7 , wherein the operation of determining, based at least in part on the measured strain and the compressive load, the elastic property of the rock sample comprises determining a Young's modulus of the rock sample based on at least one of:
E
=
Δ
P
Δɛ
x
(
-
F
+
vG
)
,
(
i
)
where E is stress dependent Young's modulus of the rock sample, ΔP is the compressive loading increment, Δϵ x is the incremental radial strain, υ is Poisson's ratio of the rock sample, F is a first coefficient, and G is a second coefficient; or
E
=
P
ɛ
x
(
-
F
+
vG
)
,
(
ii
)
where E is Young's modulus of the rock sample, P is a particular compressive load, ϵ x is a radial strain at the particular compressive load, υ is Poisson's ratio of the rock sample, F is the first coefficient, and G is the second coefficient.
10. The rock property test system of claim 7 , wherein the operation of determining, based at least in part on the measured strain and the compressive load, the elastic property of the rock sample comprises determining Poisson's ratio of the rock sample based on at least one of:
υ
=
(
Δ
ɛ
x
Δɛ
y
)
G
+
F
(
Δ
ɛ
x
Δɛ
y
)
F
+
G
,
(
i
)
where υ is stress dependent Poisson's ratio of the rock sample, Δϵ x is the incremental radial strain, Δϵ y is the incremental axial strain, F is a first coefficient, and G is a second coefficient; or
υ
=
(
ɛ
x
ɛ
y
)
G
+
F
(
ɛ
x
ɛ
y
)
F
+
G
,
(
ii
)
where υ is Poisson's ratio of the rock sample, ϵ x is a radial strain at a particular compressive load on the rock sample, Δϵ y is an axial strain at the particular compressive load on the rock sample, F is the first coefficient, and G is the second coefficient.
11. The rock property test system of claim 7 , wherein the mechanical property comprises at least one of a tensile strength or a brittleness of the rock sample.
12. A method, comprising:
performing a Brazilian test on a rock sample, the Brazilian test comprising:
exerting an incremental compressive load across a rock sample; and
determining, based at least in part on the incremental compressive load, a-tensile strength of the rock sample;
measuring, with a strain gauge, a strain on the rock sample during the incremental compressive load, the strain comprising an axial strain and a radial strain; and
determining, based at least in part on the measured axial and radial strains on the rock sample and the incremental compressive load, an elastic property of the rock sample.
13. The method of claim 12 , wherein the rock sample comprises a disc having a length-to-diameter ratio between 0.2 and 0.75.
14. The method of claim 12 , wherein determining the elastic property of the rock sample based at least in part on the axial and radial strains on the rock sample and the incremental compressive load comprises:
determining the elastic property of the rock sample based at least in part on the axial and radial strains on the rock sample, the incremental compressive load, and two predetermined constants.
15. The method of claim 14 , wherein the two predetermined constants are based at least in part on a diameter of the rock sample, a length of the rock sample, and an effective length of the strain gauge.
16. A method for determining rock properties, comprising:
exerting a compressive load with a test apparatus across a rock sample that comprises a specified length-to-diameter ratio;
measuring, with at least one strain gauge, a strain on the rock sample during the compressive loading, the at least one strain gauge coupled to an axial surface of the rock sample, the measuring comprising:
measuring an incremental axial strain on the rock sample during a compressive load increment with a first strain gauge; and
measuring an incremental radial strain on the rock sample during the compressive load increment with a second strain gauge;
determining, based at least in part on the compressive load, a mechanical property of the rock sample; and
determining, based at least in part on the measured strain and the compressive load, an elastic property of the rock sample, the determining comprising:
determining a first coefficient based at least in part on the diameter of the rock sample, the length of the rock sample, and an effective length of the first and second strain gauges;
determining a second coefficient based at least in part on the diameter of the rock sample, the length of the rock sample, and the effective length of the first and second strain gauges; and
determining the elastic property of the rock sample based at least in part on the measured incremental axial and radial strains on the rock sample, the first and second coefficients, and the compressive loading increment.
17. The method of claim 16 , wherein the specified length-to-diameter ratio is between 0.2 and 0.75.
18. The method of claim 16 , wherein the test apparatus comprises a Brazilian test apparatus.
19. The method of claim 16 , wherein the strain gauge is coupled to an axial surface of the rock sample.
20. The method of claim 16 , wherein the mechanical property comprises at least one of a tensile strength or a brittleness of the rock sample.
21. The method of claim 16 , wherein the strain gauge comprises a linear variable differential transformer (LVDT).
22. A method for determining rock properties, comprising:
exerting a compressive load with a test apparatus across a rock sample that comprises a specified length-to-diameter ratio;
measuring, with at least one strain gauge, a strain on the rock sample during the compressive loading, the at least one strain gauge coupled to an axial surface of the rock sample, the measuring comprising:
measuring an incremental axial strain on the rock sample during a compressive load increment with a first strain gauge; and
measuring an incremental radial strain on the rock sample during the compressive load increment with a second strain gauge;
determining, based at least in part on the compressive load, a mechanical property of the rock sample; and
determining, based at least in part on the measured strain and the compressive load, an elastic property of the rock sample, the determining comprising:
determining a Young's modulus of the rock sample based on at least one of:
E
=
Δ
P
Δ
ɛ
x
(
-
F
+
v
G
)
,
(
i
)
where E is stress dependent Young's modulus of the rock sample, ΔP is the compressive load increment, Δϵ x is the incremental radial strain, υ is Poisson's ratio of the rock sample, F is a first coefficient, and G is a second coefficient; or
E
=
P
ɛ
x
(
-
F
+
v
G
)
,
(
ii
)
where E is Young's modulus of the rock sample, P is a particular compressive load, ϵ x is a radial strain at the particular compressive load, υ is Poisson's ratio of the rock sample, F is the first coefficient, and G is the second coefficient.
23. A method for determining rock properties, comprising:
exerting a compressive load with a test apparatus across a rock sample that comprises a specified length-to-diameter ratio;
measuring, with at least one strain gauge, a strain on the rock sample during the compressive loading, the at least one strain gauge coupled to an axial surface of the rock sample, the measuring comprising:
measuring an incremental axial strain on the rock sample during a compressive load increment with a first strain gauge; and
measuring an incremental radial strain on the rock sample during the compressive load increment with a second strain gauge;
determining, based at least in part on the compressive load, a mechanical property of the rock sample; and
determining, based at least in part on the measured strain and the compressive load, an elastic property of the rock sample, the determining comprising:
determining Poisson's ratio of the rock sample based on at least one of:
υ
=
(
Δ
ɛ
x
Δ
ɛ
y
)
G
+
F
(
Δ
ɛ
x
Δ
ɛ
y
)
F
+
G
,
(
i
)
where υ is stress dependent Poisson's ratio of the rock sample, Δϵ x is the incremental radial strain, Δϵ y is the incremental axial strain, F is a first coefficient, and G is a second coefficient; or
υ
=
(
ɛ
x
ɛ
y
)
G
+
F
(
ɛ
x
ɛ
y
)
F
+
G
,
(
ii
)
where υ is Poisson's ratio of the rock sample, ϵ x is a radial strain at a particular compressive load on the rock sample, Δϵ y is an axial strain at the particular compressive load on the rock sample, F is the first coefficient, and G is the second coefficient.
24. A rock property test system, comprising:
a load cell configured to exert a compressive load across a rock sample;
at least one strain gauge positioned to measure a strain on the rock sample during the compressive loading, the strain gauge configured to attach to an axial surface of the rock sample and comprising a first strain gauge configured to measure an incremental axial strain on the rock sample during the incremental compressive load, and a second strain gauge configured to measure an incremental radial strain on the rock sample during the incremental compressive load; and
a control system communicably coupled to the load cell and the at least one strain gauge and configured to perform operations comprising:
controlling the load cell to exert an incremental compressive load on the rock sample;
receiving a measured strain on the rock sample, based on the incremental compressive load, from the at least one strain gauge;
determining, based at least in part on the incremental compressive load, a mechanical property of the rock sample; and
determining, based at least in part on the measured strain and the incremental compressive load, an elastic property of the rock sample, the determining comprising:
determining a first coefficient based at least in part on the diameter of the rock sample, the length of the rock sample, and an effective length of the first and second strain gauges;
determining a second coefficient based at least in part on the diameter of the rock sample, the length of the rock sample, and the effective length of the first and second strain gauges; and
determining the elastic property of the rock sample based at least in part on the measured incremental axial and radial strains on the rock sample, the first and second coefficients, and the incremental compressive load.
25. A method for determining rock properties, comprising:
exerting a compressive load with a Brazilian test apparatus across a rock sample that comprises a specified length-to-diameter ratio;
measuring, with the Brazilian test apparatus, a tensile strength of the rock sample based on the compressive load;
measuring, with a strain gauge that is coupled to an axial surface of the rock sample, a strain on the rock sample during the compressive loading, the measuring comprising:
measuring an incremental axial strain on the rock sample during a compressive load increment with a first strain gauge, and
measuring an incremental radial strain on the rock sample during the compressive load increment with a second strain gauge;
determining, based at least in part on the compressive load, a mechanical property of the rock sample; and
determining, based at least in part on the measured strains and the compressive load increment, a Young's modulus of the rock sample according to at least one of:
E
=
Δ
P
Δ
ɛ
x
(
-
F
+
v
G
)
,
(
i
)
where E is stress dependent Young's modulus of the rock sample, ΔP is the compressive load increment, Δϵ x is the incremental radial strain, υ is Poisson's ratio of the rock sample, F is a first coefficient, and G is a second coefficient, or
E
=
P
ɛ
x
(
-
F
+
v
G
)
,
(
ii
)
where E is Young's modulus of the rock sample, P is a particular compressive load, ϵ x is a radial strain at the particular compressive load, υ is Poisson's ratio of the rock sample, F is the first coefficient, and G is the second coefficient.
26. A method for determining rock properties, comprising:
exerting a compressive load with a Brazilian test apparatus across a rock sample that comprises a specified length-to-diameter ratio;
measuring, with the Brazilian test apparatus, a tensile strength of the rock sample based on the compressive load;
measuring, with a strain gauge that is coupled to an axial surface of the rock sample, a strain on the rock sample during the compressive loading, the measuring comprising:
measuring an incremental axial strain on the rock sample during a compressive load increment with a first strain gauge, and
measuring an incremental radial strain on the rock sample during the compressive load increment with a second strain gauge;
determining, based at least in part on the compressive load, a mechanical property of the rock sample; and
determining, based at least in part on the measured strains and the compressive load increment, a Poisson's ratio of the rock sample according to at least one of:
υ
=
(
Δ
ɛ
x
Δ
ɛ
y
)
G
+
F
(
Δ
ɛ
x
Δ
ɛ
y
)
F
+
G
,
(
i
)
where υ is stress dependent Poisson's ratio of the rock sample, Δϵ x is the incremental radial strain, Δϵ y is the incremental axial strain, F is a first coefficient, and G is a second coefficient; or
υ
=
(
ɛ
x
ɛ
y
)
G
+
F
(
ɛ
x
ɛ
y
)
F
+
G
,
(
ii
)
where υ is Poisson's ratio of the rock sample, ϵ x is a radial strain at a particular compressive load on the rock sample, Δϵ y is an axial strain at the particular compressive load on the rock sample, F is the first coefficient, and G is the second coefficient.
27. A rock property test system, comprising:
a load cell configured to exert a compressive load across a rock sample, the load cell comprising a Brazilian test apparatus;
at least one strain gauge configured to attach to an axial surface of the rock sample and positioned to measure a strain on the rock sample during the compressive loading, the at least one strain gauge comprising a first strain gauge configured to measure an incremental axial strain on the rock sample during the incremental compressive load and a second strain gauge configured to measure an incremental radial strain on the rock sample during the incremental compressive load; and
a control system communicably coupled to the load cell and the at least one strain gauge and configured to perform operations comprising:
controlling the load cell to exert an incremental compressive load on the rock sample;
determining a tensile strength of the rock sample based on the compressive load;
receiving a measured incremental axial strain on the rock sample and a measured incremental radial strain on the rock sample, based on the incremental compressive load, from the at least one strain gauge;
determining a first coefficient based at least in part on the diameter of the rock sample, the length of the rock sample, and an effective length of the first and second strain gauges;
determining a second coefficient based at least in part on the diameter of the rock sample, the length of the rock sample, and the effective length of the first and second strain gauges;
determining, based at least in part on the incremental compressive load, a mechanical property of the rock sample; and
determining, based at least in part on the measured strains and the incremental compressive load, a Young's modulus of the rock sample according to at least one of:
E
=
Δ
P
Δ
ɛ
x
(
-
F
+
v
G
)
,
(
i
)
where E is stress dependent Young's modulus of the rock sample, ΔP is the compressive loading increment, Δϵ x is the incremental radial strain, υ is Poisson's ratio of the rock sample, F is a first coefficient, and G is a second coefficient; or
E
=
P
ɛ
x
(
-
F
+
v
G
)
,
(
ii
)
where E is Young's modulus of the rock sample, P is a particular compressive load, ϵ x is a radial strain at the particular compressive load, υ is Poisson's ratio of the rock sample, F is the first coefficient, and G is the second coefficient.
28. A rock property test system, comprising:
a load cell configured to exert a compressive load across a rock sample, the load cell comprising a Brazilian test apparatus;
at least one strain gauge configured to attach to an axial surface of the rock sample and positioned to measure a strain on the rock sample during the compressive loading, the at least one strain gauge comprising a first strain gauge configured to measure an incremental axial strain on the rock sample during the incremental compressive load and a second strain gauge configured to measure an incremental radial strain on the rock sample during the incremental compressive load; and
a control system communicably coupled to the load cell and the at least one strain gauge and configured to perform operations comprising:
controlling the load cell to exert an incremental compressive load on the rock sample;
determining a tensile strength of the rock sample based on the compressive load;
receiving a measured incremental axial strain on the rock sample and a measured incremental radial strain on the rock sample, based on the incremental compressive load, from the at least one strain gauge;
determining a first coefficient based at least in part on the diameter of the rock sample, the length of the rock sample, and an effective length of the first and second strain gauges;
determining a second coefficient based at least in part on the diameter of the rock sample, the length of the rock sample, and the effective length of the first and second strain gauges;
determining, based at least in part on the incremental compressive load, a mechanical property of the rock sample; and
determining, based at least in part on the measured strains and the incremental compressive load, Poisson's ratio of the rock sample according to at least one of:
υ
=
(
Δ
ɛ
x
Δ
ɛ
y
)
G
+
F
(
Δ
ɛ
x
Δ
ɛ
y
)
F
+
G
,
(
i
)
where υ is stress dependent Poisson's ratio of the rock sample, Δϵ x is the incremental radial strain, Δϵ y is the incremental axial strain, F is a first coefficient, and G is a second coefficient; or
υ
=
(
ɛ
x
ɛ
y
)
G
+
F
(
ɛ
x
ɛ
y
)
F
+
G
,
(
ii
)
where υ is Poisson's ratio of the rock sample, ϵ x is a radial strain at a particular compressive load on the rock sample, Δϵ y is an axial strain at the particular compressive load on the rock sample, F is the first coefficient, and G is the second coefficient.