One Line Pile Group
6
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One Line Pile Group
Transcript of One Line Pile Group
Why E-footing shows that “one small shift of the pile coordinate will make the system unstable” in one line pile group.E-Footing uses a standard equation:
( )( )∑ ∑ ∑
∑ ∑
∑ ∑ ∑∑∑
−
−=
−−
=
±±=
222
2
222
2
nnnn
nnxxnyy
nnnn
nnyynxx
nnn
yxyx
yxeyeNB
AndyxyxyxexeN
A
Where
BxAynNP
)()(
For the calculation of pile stress. In a one-line pile group system, the dominator of A and B will tend to zero because either nx or ny is zero for all n .To prove this let’s us create a simple pile group as follow
200 200
500 450
225 x 225 stump with 300kN axial force
125 x 125 pile with 12 tones capacity
Failure pile with 0 contributions
kNnN
nosn
kNN
10033003
300
=
=
=∴
=pilefailureis1pile Since
x)the tosymetric is group pile (
..
x
centre stump about moments take group pile the of centroid the determine
Themm
ny
y
mmm
nx
To
030
083303383
3450500200
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=
−=−=
+−−=
=
∑
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The same centroid calculation is shown also in E-Footing software.
mmeme
xx
yy
008330
== .
0.116m
eyy
= 0.083m
0.416m 0.533m
0
0416001160053300
0000
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2
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).(*).(*).(*
.
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( )
ndefined
B
ndefined
A
PofstressPile
u000
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u000
00*47.00*083.047.0*0300
3
2
=
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For one-line pile group, the A and B are undefined and the above equation breaks down. However there is a catch: read on.
Modified formula of E-footing to cater case like “one line pile group” For piles that are exactly aligned along a line where the equivalent load point is falling on, the above equation is still applicable with some modification. The idea is that we get the limit of the term A and B as both their numerator and dominator approaches 0 using L' Hospital's Rule (Calculus: An Intuitive and Physical Approach (Second Edition), Morris Kline ). The derivation is shown below:
( )( )
axes xx aboutgroup pile the of area ofmoment secondIWhere
)(
)(
,
)()(
know, we As
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xeqFrom
eqyxyx
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And
eqyxyxyxexeN
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QQqqxWhere
BxAynNP
2
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0
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01
2
1
0
axesyy about group pile the of area of moment secondI Where
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,
yy =
•=
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INe
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nNP ±±=
belowasmodifyisgrouppilelineoneforformulafinal theconclusionAs
