Geotechnical Engineering Circular No. 9 Design, Analysis, and Testing of Laterally Loaded Deep Foundations that Support Transportation Facilities



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hif18031
Soldier Rev B
Loading Condition
Coefficient k
s
or k
c
(pci)
Average Undrained Shear
Strength, C
a
(ton/ft
2
)
0.5 - 1
Coefficient k
s
or k
c
(pci)
Average Undrained Shear
Strength, C
a
(ton/ft
2
)
1 - 2
Coefficient k
s
or k
c
(pci)
Average Undrained Shear
Strength, C
a
(ton/ft
2
)
2 - 4
Static
500 1,000 2,000 Cyclic
200 400 800 6. Calculate y
50
as:
𝑦𝑦
50
= 𝜀𝜀
50
𝐷𝐷 Equation A)
ε
50
can be obtained from the results of lab tests or from Table Ab Table A Re
presentative values of ε50 for stiff clays (Reese et alb
ε
50
(-)
Average Undrained Shear Strength,
C
a
(ton/ft
2
)
0.5 - 1
ε
50
(-)
Average Undrained Shear Strength,
C
a
(ton/ft
2
)
1 - 2
ε
50
(-)
Average Undrained Shear Strength,
C
a
(ton/ft
2
)
2 - 4
0.007 0.005 0.004 7. Construct the first portion of the nonlinear part of the p-y curve using the following 2
nd
- degree equation
𝑝𝑝 = Equation A) Where p
c
is the smaller value calculated from Equations A and A.


223 8. Obtain factor A
s
to be used into construct the nonlinear part of the p-y curve. Obtain A
s
from Figure A for the selected normalized depth z/D (note that in Figure A, the variable x coincides with depth
z
).
9. If the curves defined by Equations A and A intersect in the deformation range 0 ≤ y ≤ As

y
50
, the straight line defined by Equation A is maintained. If these curves do not intersect, Equation A controls the p-y curve and the 2
nd
- degree equation is extended toy, while the linear portion is discarded.
10. Establish the second portion of the nonlinear part of the p-y curve as follows
𝑝𝑝 = 𝑝𝑝
𝑐𝑐
�0.5 �
𝑦𝑦
𝑦𝑦
50

0.5
− 0.055 �
𝑦𝑦 − 𝐴𝐴
𝑠𝑠
𝑦𝑦
50
𝐴𝐴
𝑠𝑠
𝑦𝑦
50

1.25
� Equation A) The equation above defines the portion of the p-y curve in the range A
s
y
50
≤ y ≤ 6 A
s
y
50
11. Establish the next straight line portion of the p-y curve as
𝑝𝑝 = 0.5𝑝𝑝
𝑐𝑐
�6𝐴𝐴
𝑠𝑠
− 0.411𝑝𝑝
𝑐𝑐

0.0625
𝑦𝑦
50
𝑝𝑝
𝑐𝑐
(𝑦𝑦 − 6𝐴𝐴
𝑠𝑠
𝑦𝑦
50
) Equation A) The equation above defines the portion of the p-y curve in the range 6A
s
y
50
≤ y ≤ 18 A
s
y
50
12. Establish the final straight line portion of the p-y curve.
𝑝𝑝 = 0.5𝑝𝑝
𝑐𝑐
�6𝐴𝐴
𝑠𝑠
− 0.411𝑝𝑝
𝑐𝑐
− Equation A) The equation above defines the portion of the p-y curve in the range 18 A
s
y
50
≤ y. Cyclic Loading For cyclic loading, follow the steps indicated below to construct the p-y curve.
1. Follow Steps 1 - 6 for the p-y curve for static loading.
2. Obtain factor A
c
to be used into construct the nonlinear part of the p-y curve. Obtain A
c
from Figure A for the selected normalized depth z/D (note that in Figure A, the variable x coincides with depth
z
).
3. Calculate
𝑦𝑦
𝑝𝑝
= Equation A)
4. Construct the parabolic portion of the p-y curve as follows
𝑝𝑝 = 𝐴𝐴
𝑐𝑐
𝑝𝑝
𝑐𝑐
�1 − �
𝑦𝑦 − 0.45𝑦𝑦
𝑝𝑝
0.45𝑦𝑦
𝑝𝑝

2.5
� Equation A) The equation above defines the portion of the p-y curve between the point of intersection of the initial straight line and the curve defined by Equation A and y 0.6 y
p
. If there is no intersection. Equation A controls.


224 5. Establish the next straight line portion of the p-y curve as follows
𝑝𝑝 = 0.936𝐴𝐴
𝑐𝑐
𝑝𝑝
𝑐𝑐

0.085
𝑦𝑦
50
𝑝𝑝
𝑐𝑐
�𝑦𝑦 − 0.6𝑦𝑦
𝑝𝑝
� Equation A) The equation above defines the portion of the p-y curve in the range 0.6y
p
≤ y ≤ 1.8y
p
6. Establish the final straight line portion of the p-y curve as follows
𝑝𝑝 = Equation A) The equation above defines the portion of the p-y curve in the range 1.8y
p
< y.

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