System and method for measuring stress in a rock mass
View Patent ↗Systems and methods for measuring stress in a rock mass using sleeve fracturing are provided. A system for measuring stress in the rock mass includes an expandable sleeve insertable into a borehole formed in the rock mass and operable to apply a radially outward force against a wall of the borehole by expansion of the sleeve. A positive displacement pump is operatively connected to the sleeve and is operable to deliver a liquid to the sleeve at a constant flow rate to cause expansion of the sleeve. A pressure sensor is operable to measure a pressure of the liquid. A pressure recorder is operatively connected to the pressure sensor for recording the pressure of the liquid.
1 . A method for determining a stress tensor defining a state of stress in a segment of rock mass, the method comprising:
conducting six sleeve fracturing tests in the segment of rock mass, the six sleeve fracturing tests including three different borehole orientations;
determining tangential stresses (σ θ1 -σ θ6 ) respectively associated with the six sleeve fracturing tests; and
determining the stress tensor using the tangential stresses (σ θ1 -σ θ6 ),
wherein:
the six sleeve fracturing tests each have a trend (T i -T n ) of the borehole orientation, a plunge (P i -P n ) of the borehole orientation, a polar angle (θ 1 -θ 6 ) of a location of a fracture about a borehole;
the stress tensor includes: three normal stresses (σ′ x , σ′ y , σ′ z ) in three orthogonal directions and three shear stresses (τ′ xy , τ′ xz , τ′ yz ) associated with the three orthogonal directions; and
determining the stress tensor includes solving the following equation:
[
σ
θ
1
σ
θ2
σ
θ3
σ
θ4
σ
θ5
σ
θ6
]
=
[
(
1
-
cos
2
θ
1
)
cos
2
T
i
+
(
1
+
cos
2
θ
1
)
sin
2
T
i
sin
2
P
i
+
2
sin
2
θ
1
sin
2
T
i
sin
P
i
(
1
-
cos
2
θ
2
)
cos
2
T
j
+
(
1
+
cos
2
θ
2
)
sin
2
T
j
sin
2
P
j
+
2
sin
2
θ
2
sin
2
T
j
sin
P
j
(
1
-
cos
2
θ
3
)
cos
2
T
k
+
(
1
+
cos
2
θ
3
)
sin
2
T
k
sin
2
P
k
+
2
sin
2
θ
3
sin
2
T
k
sin
P
k
(
1
-
cos
2
θ
4
)
cos
2
T
l
+
(
1
+
cos
2
θ
4
)
sin
2
T
l
sin
2
P
l
+
2
sin
2
θ
4
sin
2
T
l
sin
P
l
(
1
-
cos
2
θ
5
)
cos
2
T
m
+
(
1
+
cos
2
θ
5
)
sin
2
T
m
sin
2
P
m
+
2
sin
2
θ
5
sin
2
T
m
sin
P
m
(
1
-
cos
2
θ
6
)
cos
2
T
n
+
(
1
+
cos
2
θ
6
)
sin
2
T
n
sin
2
P
n
+
2
sin
2
θ
6
sin
2
T
n
sin
P
n
(
1
-
cos
2
θ
1
)
sin
2
T
i
+
(
1
+
cos
2
θ
1
)
cos
2
T
i
sin
2
P
i
-
2
sin
2
θ
1
sin
2
T
i
sin
P
i
(
1
-
cos
2
θ
2
)
sin
2
T
j
+
(
1
+
cos
2
θ
2
)
cos
2
T
j
sin
2
P
j
-
2
sin
2
θ
2
sin
2
T
j
sin
P
j
(
1
-
cos
2
θ
3
)
sin
2
T
k
+
(
1
+
cos
2
θ
3
)
cos
2
T
k
sin
2
P
k
-
2
sin
2
θ
3
sin
2
T
k
sin
P
k
(
1
-
cos
2
θ
4
)
sin
2
T
l
+
(
1
+
cos
2
θ
4
)
cos
2
T
l
sin
2
P
l
-
2
sin
2
θ
4
sin
2
T
l
sin
P
l
(
1
-
cos
2
θ
5
)
sin
2
T
m
+
(
1
+
cos
2
θ
5
)
cos
2
T
m
sin
2
P
m
-
2
sin
2
θ
5
sin
2
T
m
sin
P
m
(
1
-
cos
2
θ
6
)
sin
2
T
n
+
(
1
+
cos
2
θ
6
)
cos
2
T
n
sin
2
P
n
-
2
sin
2
θ
6
sin
2
T
n
sin
P
n
(
1
+
cos
2
θ
1
)
cos
2
P
i
-
(
1
+
cos
2
θ
1
)
sin
2
T
i
sin
2
P
i
-
4
sin
2
θ
1
(
1
+
cos
2
θ
2
)
cos
2
P
j
-
(
1
+
cos
2
θ
2
)
sin
2
T
j
sin
2
P
j
-
4
sin
2
θ
2
(
1
+
cos
2
θ
3
)
cos
2
P
k
-
(
1
+
cos
2
θ
3
)
sin
2
T
k
sin
2
P
k
-
4
sin
2
θ
3
(
1
+
cos
2
θ
4
)
cos
2
P
l
-
(
1
+
cos
2
θ
4
)
sin
2
T
l
sin
2
P
l
-
4
sin
2
θ
4
(
1
+
cos
2
θ
5
)
cos
2
P
m
-
(
1
+
cos
2
θ
5
)
sin
2
T
m
sin
2
P
m
-
4
sin
2
θ
5
(
1
+
cos
2
θ
6
)
cos
2
P
n
-
(
1
+
cos
2
θ
6
)
sin
2
T
n
sin
2
P
n
-
4
sin
2
θ
6
(
cos
2
T
i
sin
P
i
-
sin
2
T
i
sin
P
i
)
+
(
1
-
cos
2
θ
1
)
sin
2
T
i
-
(
cos
2
T
j
sin
P
j
-
sin
2
T
j
sin
P
j
)
+
(
1
-
cos
2
θ
2
)
sin
2
T
j
-
(
cos
2
T
k
sin
P
k
-
sin
2
T
k
sin
P
k
)
+
(
1
-
cos
2
θ
3
)
sin
2
T
k
-
(
cos
2
T
l
sin
P
l
-
sin
2
T
l
sin
P
l
)
+
(
1
-
cos
2
θ
4
)
sin
2
T
l
-
(
cos
2
T
m
sin
P
m
-
sin
2
T
m
sin
P
m
)
+
(
1
-
cos
2
θ
5
)
sin
2
T
m
-
(
cos
2
T
n
sin
P
n
-
sin
2
T
n
sin
P
n
)
+
(
1
-
cos
2
θ
6
)
sin
2
T
n
-
4
sin
2
θ
1
cos
T
i
cos
P
i
-
2
(
sin
T
i
cos
P
i
sin
P
i
)
(
1
+
cos
2
θ
1
)
2
(
1
+
cos
2
θ
1
)
4
sin
2
θ
2
cos
T
j
cos
P
j
-
2
(
sin
T
j
cos
P
j
sin
P
j
)
(
1
+
cos
2
θ
2
)
2
(
1
+
cos
2
θ
2
)
4
sin
2
θ
3
cos
T
k
cos
P
k
-
2
(
sin
T
k
cos
P
k
sin
P
k
)
(
1
+
cos
2
θ
3
)
2
(
1
+
cos
2
θ
3
)
4
sin
2
θ
4
cos
T
l
cos
P
l
-
2
(
sin
T
l
cos
P
l
sin
P
l
)
(
1
+
cos
2
θ
4
)
2
(
1
+
cos
2
θ
4
)
4
sin
2
θ
5
cos
T
m
cos
P
m
-
2
(
sin
T
m
cos
P
m
sin
P
m
)
(
1
+
cos
2
θ
5
)
2
(
1
+
cos
2
θ
5
)
4
sin
2
θ
6
cos
T
n
cos
P
n
-
2
(
sin
T
n
cos
P
n
sin
P
n
)
(
1
+
cos
2
θ
6
)
2
(
1
+
cos
2
θ
6
)
cos
T
i
cos
P
i
sin
P
i
-
4
sin
2
θ
1
sin
T
i
cos
P
i
cos
T
j
cos
P
j
sin
P
j
-
4
sin
2
θ
2
sin
T
j
cos
P
j
cos
T
k
cos
P
k
sin
P
k
-
4
sin
2
θ
3
sin
T
k
cos
P
k
cos
T
l
cos
P
l
sin
P
l
-
4
sin
2
θ
4
sin
T
l
cos
P
l
cos
T
m
cos
P
m
sin
P
m
-
4
sin
2
θ
5
sin
T
m
cos
P
m
cos
T
n
cos
P
n
sin
P
n
-
4
sin
2
θ
6
sin
T
n
cos
P
n
]
[
σ
x
′
σ
y
′
σ
z
′
τ
xy
′
τ
xz
′
τ
yz
′
]
.