Lane's Weighted Creep Theory
Lecture-2
Lane's Weighted Creep Theory
This approach assigns
different weightages to vertical and horizontal creeps. Lane demonstrated that
vertical creep is three times more effective than horizontal creep in
minimizing uplift pressure. Vertical creep was assigned a weightage of unity,
while horizontal creep was assigned a weightage of 1/3.
The weighted creep length-
N
= Sum of all the horizontal contacts and the flat sloping contacts making an
angle less than 45o with the horizontal
V
= Sum of all vertical contacts and the steep sloping contacts making an angle
greater than 45o with the horizontal.
According to Lane's
weighted creep theory, structure will be safe if HL/Lw is less than the
safe hydraulic gradient 1/C1 for that soil, where, HL is the
seepage head, and C1 is Lane’s creep coefficient
The thickness of the
floor at any point:
Table: Lane's creep coefficient for different
types of soils
Example:
A hydraulic structure on
a river as shown in Figure below:
·
Check the floor thickness at points X, Y
and Z to counteract the uplift pressure (Gf = 2.4).
·
Check safety against piping if the soil
type is coarse sand (C1 = 5).
·
All dimensions are in meter.
Solution:
Lw = 1/3 N + V
N = 1.5 + 5.9 + 2 + 2 + [(5.1)2
+ (12.3)2]0.5 +10 + 16 + 1.5 = 52.215 m
V
= 1 + (5.2+5.2) + 0.5 + [(0.5)2 + (0.5)2]0.5 +
(3.2+3.2) + 1.5 + (4.6+4.6) +1.5 = 31.207 m
Lw = 1/3 * 52.215 +
31.207 = 48.612 m
HL = Difference between U/S
Level and D/S = 7.1 m
i = HL/Lw = 0.1461 < 1/5 (0.2), The
structure is safe against piping.
Now,
Nx = 1.5 + 5.9 + 2 + 2 =
11.4
Vx = 1 + (5.2+5.2) + 0.5
+ [(0.5)2 + (0.5)2]0.5 = 12.61
Lx = 1/3 * 11.4 + 12.61 =
16.41
NY = 1.5 + 5.9 + 2 + 2 + [(5.1)2
+ (12.3)2]0.5 = 24.72
VY = 1 + (5.2+5.2) + 0.5
+ [(0.5)2 + (0.5)2]0.5 + (3.2+3.2) = 12.61
LY = 1/3 * 24.72 + 12.61
= 20.84
Nz = 1.5 + 5.9 + 2 + 2 + [(5.1)2
+ (12.3)2]0.5 +10 + 16 = 50.715
Vz = 1 + (5.2+5.2) + 0.5
+ [(0.5)2 + (0.5)2]0.5 + (3.2+3.2) + 1.5 = 20.507
Lz = 1/3 * 50.715 + 20.507
= 37.412
Using Equation,
h = HL – HL/Lw (l)
hx = HL – HL/Lw (Lx) =
7.1 – 7.1/48.612 (16.41) = 4.703
hY = HL – HL/Lw (LY) = 7.1
– 7.1/48.612 (20.84) = 4.056
hz = HL – HL/Lw (Lz) = 7.1
– 7.1/48.612 (37.412) = 1.636
For checking floor
thickness at points X, Y and Z
t = h/(Gf -1)
tx = 4.703/(2.4-1) = 3.36 > 2 (Not sufficient at this point X)
tY = 4.056/(2.4-1) = 2.90 <
3 (1.5+1.5 = 3) (Sufficient at this point Y)
tz = 1.636/(2.4-1) = 1.17 < 1.5 (Sufficient at this point Z)