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

234 where c
a
is the average undrained shear strength, θ is the angle of the slope measured from the horizontal, and H = depth from ground surface to where the soil resistance is calculated. For sand, the following equations presented by Reese et al. (2005) can be used to modify p
u
of soil near surface except that the horizontal surface needs to be adjusted as a slope. The soil resistance at the front of the pile is Equation A)
𝑝𝑝
𝑢𝑢
= 𝛾𝛾𝑘𝑘 tan ∅ sin tan (𝛽𝛽−∅) cos 𝛼𝛼
(4𝐷𝐷
1 3
− 3𝐷𝐷
1 2
+ 1) +tan tan (𝛽𝛽−∅)
(𝐷𝐷𝐷𝐷
2
+ 𝑘𝑘 tan 𝛽𝛽 tan 𝛼𝛼𝐷𝐷
2 2
) + 𝐾𝐾
0
𝑘𝑘 tan tan ∅ sin 𝛽𝛽 tan 𝛼𝛼)(4𝐷𝐷
1 3
− 3𝐷𝐷
1 2
+ 1) − 𝐾𝐾
𝐴𝐴
𝐷𝐷� Where
D
1
=
tan 𝛽𝛽 tan tan 𝛽𝛽 tan 𝜃𝜃 + Equation A)
𝐷𝐷
2
= 1 − Equation A)
𝐾𝐾
𝐴𝐴
= cos cos 𝜃𝜃 − cos − cos
2
∅
cos 𝜃𝜃 + cos − cos
2
∅
(Equation A) The soil resistance at the back of the pile is Equation A)
𝑝𝑝
𝑢𝑢
= 𝛾𝛾𝑘𝑘 �
𝐾𝐾
0
𝑘𝑘 tan ∅ sin tan − ∅) cos 𝛼𝛼
(4𝐷𝐷
3 3
− 3𝐷𝐷
2 2
+ 1) +tan tan − ∅)
(𝐷𝐷𝐷𝐷
4
+ 𝑘𝑘 tan 𝛽𝛽 tan 𝛼𝛼𝐷𝐷
4 2
)
+ 𝐾𝐾
0
𝑘𝑘 tan tan ∅ sin 𝛽𝛽 − tan 𝛼𝛼)(4𝐷𝐷
3 3
− 3𝐷𝐷
3 2
+ 1) − 𝐾𝐾
𝐴𝐴
𝐷𝐷� Where tan 𝛽𝛽 tan 𝜃𝜃
1 − tan 𝛽𝛽 tan Equation A)
𝐷𝐷
4
= 1 + Equation A)

235

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