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

80
Figure 6-10: Earth pressure, shear, and moment diagrams for Broms method in cohesive soils
(from Brown et al. 2010).
The point of zero shear, and therefore the maximum moment, occurs at the depth, f. To satisfy horizontal force equilibrium, the resultant of the earth pressures below that point, over the depth, g, must be zero, so the earth pressures are equally divided over the depth, g. The resulting moment due to the earth pressures acting over the depth, g, must be equal to the maximum moment, which is the moment due to the applied shear, moment, and earth pressures above the point of zero shear. Note that only horizontal forces and moments are considered, and that no vertical loads are considered. Also, the earth pressures are considered as fully mobilized on opposite sides of the pile, regardless of the magnitude of the actual deflections along the pile length. Based on the diagrams, the location of maximum moment and zero shear is defined by the distance, f, given by
𝑓𝑓 Equation 6-8) The maximum moment is given by
𝑀𝑀
𝑚𝑚𝑚𝑚𝑥𝑥
= 𝑀𝑀
𝑡𝑡
+ 𝑃𝑃
𝑡𝑡
(1.5𝐵𝐵
𝑏𝑏
+ 0.5𝑓𝑓) Equation 6-9) The maximum moment can also be calculated by applying moment equilibrium at the point of zero shear, or
𝑀𝑀
𝑚𝑚𝑚𝑚𝑥𝑥
= Equation 6-10) The depth, g, can be determined from

81
𝑔𝑔 = �
𝑀𝑀
𝑚𝑚𝑚𝑚𝑥𝑥
2.25𝑆𝑆
𝑢𝑢
𝐵𝐵
𝑏𝑏
�
1 Equation 6-11) And the minimum pile length can be determined as
𝐿𝐿 ≥ 1.5𝐵𝐵
𝑏𝑏
+ 𝑓𝑓 + 𝑔𝑔 Equation 6-12)

Download 6.03 Mb.

Share with your friends: