BUITEMS

BUITEMS
Quality & Excellence in Education
Rational Design of Retaining Walls
4 s
y = m
g
4 s
= m
g
4
y = m
g
( F(z) - m )( F(z) m -1)
2
( F ) - 1)( - 1)
F 2
( z)
( - )( - )
4 s F(z) m F(z) m 1
dF( z)
= m
dF(z)
=
(z m 2 F 3 ( z)
g F 2 z m 2 F 3 ( z)
m - F(
z)
m
( ( z) -1)( m 2 -1)
F 2 2
2
( m - ) Π( ( ) -1)
- F(
z)
+ m dF ( z)
= m
F 3 ( z)
( + )
( ( ) - 1)( - 1)
2
4 s F ( z)
m - F(
z)
( m + 1)
+
g
2F ( 2 ( z) -1)( m 2 - 1) F 3 ( z)
s m Ø 1
m 2 1 1
dF( z)
-
dF(z) + ...
1 º F 2 z F(
z)
m ( F 2 ( z ) - 1)
F 2 ( z)
( F ( z)
- 1) F ( z)
ß
œ
m dF ( z)
1
ø
... +
dF ( z ) ; (1.13)
2 3
The integrals in (1.13), taken closed. We obtain:
4 s m Ø 1 F 2 ( z)
( m 2 + 1)
1 1 1+
F(z) ø
y = m Π- ln + - +
œ
( - )
ln
(1.14)
2
2
2
g m 1 μ
2 F ( z)
Ł1-
F ( z)
ł m Ł F(
z)
2 Ł1-
F ( z)
łłœß
We introduce the notation:
Ø
2
1 F
2 ( z)
( m + 1)
1 1 1+
F(
z)
œ œ ø
W( F(z))
= Π- ln + - + ln
; (1.15)
2
2
μ
2 F ( z)
Ł1-
F ( z)
ł m Ł F(
z)
2 Ł1-
F ( z)
łłß
And finally:
4 s m
y = m W( ( ))
m F z
(1.16)
g
2 -
( 1)
Figure 1.3. The effective retaining wall
To visual demonstration of solutions we consider some examples.
Пример 1
Data:
Angle of internal friction j = 40 0 Total depth z max =18m
103