US 12,607,119 B2 · In-situ stress measurement method

Abstract

A cylindrical side-wall core is acquired from an inner circumferential surface of a well at a predetermined depth from a ground surface. First, second and third measurement cross sections spaced apart in a longitudinal direction of the core are set. In each cross section, the length of the maximum diameter of the cross section where the amount of distortion relative to the diameter of a standard circle is largest and the length of the minimum diameter where the amount of distortion relative to the diameter of the standard circle is smallest are measured. Six independent components among stress tensors for defining three-dimensional stress elements are obtained using an equation representing a difference between maximum and minimum stresses acting on the side-wall core along each cross section and another equation representing the angle between the well excavation direction and the action direction of the maximum stress on each cross section.

An in-situ stress measurement method for measuring three-dimensional stress elements acting on a ground configuring an earth's crust, comprising:

excavating the ground in a first excavation direction to form a well, the first excavation direction of the well being one of vertical direction or a direction inclined with respect to the vertical direction;
acquiring at least one cylindrical side-wall core by hollowing out the ground in the well at a predetermined depth from the earth's surface, from an inner circumferential surface of the well in a second excavation direction different from the first excavation direction of the well;
determining where a standard orientation of the ground from which the at least one cylindrical side-wall core has been acquired is directed;
setting at least first, second and third measurement cross sections in the side-wall core, wherein the first, second and third measurement cross sections are separated from each other in a longitudinal direction of the side-wall core;
measuring, in each of the shape of the first, second and third measurement cross sections, the length of the maximum diameter (Dmax_1, Dmax_2, Dmax_3) of each measurement cross section where the amount of distortion relative to the diameter of a standard circle is largest and the length of the minimum diameter (Dmin_1, Dmin_2, Dmin_3) where the amount of distortion relative to the diameter of the standard circle is smallest;
and
obtaining six independent components (σxx, σyy, σzz, τxy, τyz, τzx) among stress tensors for defining the three-dimensional stress elements from first to sixth equations below,
wherein the first equation (1) represents a difference (Δσ_1) between a maximum stress (σmax_1) and the minimum stress (σmin_1) acting on the side-wall core along the first measurement cross section,
σ
max
⁢
_
⁢
1
-
σ
min
⁢
_
⁢
1
=
(
σ
z
1
-
σ
θ
1
)
2
+
4
⁢
τ
θ
⁢
z
1
2
=
E
1
+
μ
·
D
max_
⁢
1
-
D
min_
⁢
1
D
min
⁢
_
⁢
1
(
1
)
the second equation (2) represents an angle (ωmax_1) formed by the first excavation direction of the well and the action direction of the maximum stress (σmax_1) on the first measurement cross section,
ω
max
⁢
_
⁢
1
=
1
2
⁢
tan
-
1
⁢
(
2
⁢
τ
θ
⁢
z
⁢
_
⁢
1
σ
z
⁢
_
⁢
1
-
σ
θ_
⁢
1
)
+
π
2
⁢
σ
θ_
⁢
1
=
(
σ
xx
+
σ
y
⁢
y
)
2
⁢
(
1
+
R
2
r
1
2
)
-
(
σ
xx
-
σ
yy
)
2
⁢
(
1
+
3
⁢
R
4
r
1
4
)
⁢
cos
⁢
2
⁢
θ
SWC
⁢
_
⁢
1
-
τ
x
⁢
y
⁢
(
1
+
3
⁢
R
4
r
1
4
)
⁢
sin
⁢
2
⁢
θ
swc
⁢
_
⁢
1
⁢
σ
z
⁢
_
⁢
1
=
σ
zz
-
2
⁢
μ
⁢
(
σ
xx
-
σ
y
⁢
y
)
⁢
R
2
r
1
2
⁢
cos
⁢
2
⁢
θ
SWC
⁢
_
⁢
1
-
4
⁢
μ
⁢
τ
xy
⁢
R
2
r
1
2
⁢
sin
⁢
2
⁢
θ
SWC
⁢
_
⁢
1
⁢
τ
θ
⁢
z
⁢
_
⁢
1
=
(
-
τ
zx
⁢
sin
⁢
θ
SWC
⁢
_
⁢
1
+
τ
yz
⁢
cos
⁢
θ
SWC
⁢
_
⁢
1
)
⁢
(
1
+
R
2
r
1
2
)
(
2
)
the third equation (3) represents a difference (Δσ_2) between the maximum stress (σmax_2) and the minimum stress (σmin_2) acting on the side-wall core along the second measurement cross section,
σ
max
⁢
_
⁢
2
-
σ
min
⁢
_
⁢
2
=
(
σ
z
⁢
_
⁢
2
-
σ
θ_
⁢
2
)
2
+
4
⁢
τ
θ
⁢
z
⁢
_
⁢
2
2
=
E
1
+
μ
·
D
max_
⁢
2
-
D
min_
⁢
2
D
min
⁢
_
⁢
2
(
3
)
the fourth equation (4) represents an angle (ωmax_2) formed by the first excavation direction of the well and the action direction of the maximum stress (σmax_2) on the second measurement cross section,
ω
max
⁢
_
⁢
2
=
1
2
⁢
tan
-
1
⁢
(
2
⁢
τ
θ
⁢
z
⁢
_
⁢
2
σ
z
⁢
_
⁢
2
-
σ
θ_
⁢
2
)
+
π
2
⁢
σ
θ_
⁢
2
=
(
σ
xx
+
σ
y
⁢
y
)
2
⁢
(
1
+
R
2
r
2
2
)
-
(
σ
xx
-
σ
yy
)
2
⁢
(
1
+
3
⁢
R
4
r
2
4
)
⁢
cos
⁢
2
⁢
θ
SWC
⁢
_
⁢
2
-
τ
x
⁢
y
⁢
(
1
+
3
⁢
R
4
r
2
4
)
⁢
sin
⁢
2
⁢
θ
swc
⁢
_
⁢
2
⁢
σ
z
⁢
_
⁢
2
=
σ
zz
-
2
⁢
μ
⁢
(
σ
xx
-
σ
y
⁢
y
)
⁢
R
2
r
2
2
⁢
cos
⁢
2
⁢
θ
SWC
⁢
_
⁢
2
-
4
⁢
μ
⁢
τ
xy
⁢
R
2
r
2
2
⁢
sin
⁢
2
⁢
θ
SWC
⁢
_
⁢
2
⁢
τ
θ
⁢
z
⁢
_
⁢
2
=
(
-
τ
zx
⁢
sin
⁢
θ
SWC
⁢
_
⁢
2
+
τ
yz
⁢
cos
⁢
θ
SWC
⁢
_
⁢
2
)
⁢
(
1
+
R
2
r
2
2
)
(
4
)
the fifth equation (5) represents a difference (Δσ_3) between the maximum stress (σmax_3) and the minimum stress (σmin_3) acting on the side-wall core along the third measurement cross section,
σ
max
⁢
_
⁢
3
-
σ
min
⁢
_
⁢
3
=
(
σ
z
⁢
_
⁢
3
-
σ
θ_
⁢
3
)
2
+
4
⁢
τ
θ
⁢
z
⁢
_
⁢
3
2
=
E
1
+
μ
·
D
max_
⁢
3
-
D
min_
⁢
3
D
min
⁢
_
⁢
3
(
5
)
and the sixth equation (6) represents an angle (@max_3) formed by the first excavation direction of the well and the action direction of the maximum stress (σmax_3) on the third measurement cross section,
ω
max
⁢
_
⁢
3
=
1
2
⁢
tan
-
1
⁢
(
2
⁢
τ
θ
⁢
z
⁢
_
⁢
3
σ
z
⁢
_
⁢
3
-
σ
θ_
⁢
3
)
+
π
2
⁢
σ
θ_
⁢
3
=
(
σ
xx
+
σ
y
⁢
y
)
2
⁢
(
1
+
R
2
r
3
2
)
-
(
σ
xx
-
σ
yy
)
2
⁢
(
1
+
3
⁢
R
4
r
3
4
)
⁢
cos
⁢
2
⁢
θ
SWC
⁢
_
⁢
3
-
τ
x
⁢
y
⁢
(
1
+
3
⁢
R
4
r
3
4
)
⁢
sin
⁢
2
⁢
θ
swc
⁢
_
⁢
3
⁢
σ
z
⁢
_
⁢
3
=
σ
zz
-
2
⁢
μ
⁢
(
σ
xx
-
σ
y
⁢
y
)
⁢
R
2
r
3
2
⁢
cos
⁢
2
⁢
θ
SWC
⁢
_
⁢
3
-
4
⁢
μ
⁢
τ
xy
⁢
R
2
r
3
2
⁢
sin
⁢
2
⁢
θ
SWC
⁢
_
⁢
3
⁢
τ
θ
⁢
z
⁢
_
⁢
3
=
(
-
τ
zx
⁢
sin
⁢
θ
SWC
⁢
_
⁢
3
+
τ
yz
⁢
cos
⁢
θ
SWC
⁢
_
⁢
3
)
⁢
(
1
+
R
2
r
3
2
)
(
6
)
where, degrees of variables below are regarded as being already known, and the first to third measurement cross sections are set such that pairs of values of (r, θSWC) do not become the same,
R:
a radius of the well, E:
Young's modulus of the ground, μ:
Poisson's ratio of the ground,
Dmax_1:
the length of the maximum diameter of the first measurement cross section where the amount of distortion relative to the diameter of the standard circle is largest,
Dmin_1:
the length of the minimum diameter of the first measurement cross section where the amount of distortion relative to the diameter of the standard circle is smallest,
Dmax_2:
the length of the maximum diameter of the second measurement cross section where the amount of distortion relative to the diameter of the standard circle is largest,
Dmin_2:
the length of the minimum diameter of the second measurement cross section where the amount of distortion relative to the diameter of the standard circle is smallest,
Dmax_3:
the length of the maximum diameter of the third measurement cross section where the amount of distortion relative to the diameter of the standard circle is largest,
Dmin_3:
the length of the minimum diameter of the third measurement cross section where the amount of distortion relative to the diameter of the standard circle is smallest,
r1:
a distance from a center of the well to the first measurement cross section,
r2:
a distance from the center of the well to the second measurement cross section,
r3:
a distance from the center of the well to the third measurement cross section,
θswc_1, θswc_2, θswc_3:
an angle formed by the standard orientation and the second excavation direction of the side-wall core,
ωmax_1:
the angle formed by the first excavation direction of the well and the action direction of the maximum stress on the first measurement cross section,
ωmax_2:
the angle formed by the first excavation direction of the well and the action direction of the maximum stress on the second measurement cross section, and
ωmax_3:
the angle formed by the first excavation direction of the well and the action direction of the maximum stress on the third measurement cross section.

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In-situ stress measurement method

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In-situ stress measurement method

Life of this patent

Abstract

Claims3