Method for determining three-dimensional tortuosity of loose and broken rock-soil mass
A method for determining a three-dimensional tortuosity of a loose and broken rock-soil mass, includes the following steps: a particle grading curve of the loose and broken rock-soil mass is obtained by utilizing a particle size analysis, and followed by calculating an equivalent particle size and an average particle size; a porosity of the loose and broken rock-soil mass is obtained by utilizing a moisture content test, a density test, and a specific gravity test; the three-dimensional tortuosity of the loose and broken rock-soil mass is obtained by utilizing the equivalent particle size, the average particle size and the porosity of the loose and broken rock-soil mass. The method has the advantages of simple logic, accuracy and reliability, simple and fast parameter determination, and has high practical value and promotion value in the field of environmental protection and ecological restoration technology.
1. A method for determining a three-dimensional tortuosity of a loose and broken rock-soil mass, comprising steps:
obtaining a particle grading curve of the loose and broken rock-soil mass by utilizing a particle size analysis, and obtaining an equivalent particle size d 20 and an average particle size d 50 ; wherein the obtaining an equivalent particle size d 20 and an average particle size d 50 comprises: selecting horizontal coordinate values corresponding to a point of 20% and a point of 50% on a vertical axis of the particle grading curve of the loose and broken rock-soil mass to record as the equivalent particle size d 20 and the average particle size d 50 , respectively;
obtaining a porosity ϕ of the loose and broken rock-soil mass by utilizing a moisture content test, a density test, and a specific gravity test; and
obtaining the three-dimensional tortuosity τ of the loose and broken rock-soil mass by utilizing the equivalent particle size d 20 , the average particle size d 50 and the porosity ϕ of the loose and broken rock-soil mass; wherein the three-dimensional tortuosity τ is expressed as follows:
τ
=
A
×
(
1
-
B
C
)
D
×
E
A
=
7.42
×
1
0
-
7
ρ
w
g
(
1
-
ϕ
)
3
(
3
ln
(
4
3
2
1
0
6
d
5
0
1
-
ϕ
1
-
0.342
ϕ
)
-
ln
(
ϕ
)
)
B
=
4
3
2
1
0
6
d
5
0
1
-
ϕ
1
-
0.342
ϕ
C
=
2
-
ln
(
ϕ
)
ln
(
4
3
2
1
0
6
d
50
1
-
ϕ
1
-
0.342
ϕ
)
D
=
d
2
0
μ
w
(
1
-
0.342
ϕ
)
E
=
2
ln
(
4
3
2
1
0
6
d
50
1
-
ϕ
1
-
0.342
ϕ
)
-
ln
ϕ
;
wherein ρ w represents a density of water, g represents a gravitational acceleration, μ w represents a viscosity of water, and In represents a logarithmic function with a base of 10.
2. The method for determining the three-dimensional tortuosity of the loose and broken rock-soil mass as claimed in claim 1 , wherein the particle grading curve is obtained by combining a sieve analysis method with a densitometer method or a pipette method.
3. The method for determining the three-dimensional tortuosity of the loose and broken rock-soil mass as claimed in claim 1 , wherein the porosity ϕ of the loose and broken rock-soil mass is expressed as follows:
ϕ
=
1
-
ρ
G
S
ρ
W
4
°
C
.
(
1
+
ω
)
;
wherein ρ W 4° C. represents a density of pure distilled water at 4° C.; ρ represents a density of the loose and broken rock-soil mass; ω represents a mass water content of the loose and broken rock-soil mass; G s represents a specific gravity of the loose and broken rock-soil mass.
4. The method for determining the three-dimensional tortuosity of the loose and broken rock-soil mass as claimed in claim 3 , wherein the mass water content ω of the loose and broken rock-soil mass is obtained by utilizing a measurement of a drying method.
5. The method for determining the three-dimensional tortuosity of the loose and broken rock-soil mass as claimed in claim 3 , wherein the specific gravity G s of the loose and broken rock-soil mass is obtained by utilizing a measurement of a combination of a pycnometer method and a siphon tube method.