Environmental Engineering Reference
In-Depth Information
Y
′2
-2
SY
′
+
P
= 0
(16)
Table 2. Basic data (for Mohr-coulomb linear or
hoek-Brown non-linear criteria)
where:
Data
Value
1
2
AB AB
AB
+
constant
ε
±1
sign +
active/
- pasive
10 10
11
u
u
S
=−
u
slope of the earth surface
on the wall backfilling (º)
α
P
AB
AB
=
00
11
u
µ
earth-wall friction (º)
µ = tanδ
Dilatancy (º)
ψ
u
internal friction angle
of the material
Mohr-
coulomb
linear
criterion
φ
dA
du
0
A
0
=
=
σ
;
u
u
β
strength modulus (kn/m
2
)
H
*
Real wall height (m)
h: adimens.
height.
h
*
/l
dA
du
==
A
σατ α
sin
−
cos
1
u
u
u
GSI
Geological strength index
γ
*
specific earth mass (kn/m
3
)
γ: adimens.
weight. =
γ
*
/γ = 1
dB
du
τ σ
α
0
u
u
B
=
=
;
0
u
m
0
hoek & Brown parameter <25
cos
a
hoek & Brown constant
14 or 28
σ
c
Unconfined strength of
the material (kn/m
2
)
dB
du
1
)
+
)
(
(
B
==+
σµατ αµ
1
tan
tan
−
1
u
u
u
d
du
σ
τ
d
du
τ
u
+
being:
σ
=
=
1
σ
=
k
ku
()
u
u
b
C
P
tan
φ
k
The two solutions of which define the failure
line in the case of active (+) and passive (-) pres-
sure, respectively:
)
u
u
(
+
k
11
+ −
n
−
u
tan
ψ
H
cos
ψ
cos
ψ
being:
2
YSSP
2
′
=± −
( )
⋅
( )
i
2
i
3
k
C
=
5
calcUlaTion PRoceDURe
2
k
p
= (3-
i
) (
i
-2)
5.1
Starting data for the calculation and
adimensionalisation
The intrinsic physical units referred to in Table 2
are taken to be able to work adimensionally. These
units depend on the geotechnical characteristics of
the earth.
The intrinsic longitude is defined, l = β/γ.
To treat as a group the three criteria, it can be
put forward:
( )
⋅
( )
i
1
i
2
k
H
=
2
where
i
= 1,2,3 to coulomb, Parabolic, or
hoek & Brown's criterion, respectively.
The obtention of every magnitude necessary
for the design of a wall can be programmed in a
spreadsheet, in columns, in the following manner:
1. u
2. τ (u)
3. σ(u)
4. τ′(u)
5. σ′(u)
6. a
0
7. a
1
8. B
0
9. B
1
10. c
1
11. a
0u
12. a
1u
13. B
0u
14. B
1u
15. s
16. P
18. X
17. Y′
21. Y
23. n
26.m
19. ∆X
20. ∆Y
22. ∆n
24. λ
25. ∆m
27. B = m/n
28. x
29. y
30. t
31. e
