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

Broms Method for Cohesionless Soils

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Soldier Rev B

Figure 6-11: Earth pressure, shear, and moment diagrams for Broms method in cohesionless soils (from Brown et al. 2010).

6.5.2
Broms Method for Cohesionless Soils
For a short pile/shaft in cohesionless soil, the maximum soil resistance per unit length of the pile/shaft by the Broms method is the passive earth pressures applied for three times the width of the pile. Passive earth pressure is assessed using Rankine theory. The earth pressure, shear, and moment diagrams fora pile/shaft in cohesionless soil according to the Broms method are shown in Figure 6-11.
Figure 6-11: Earth pressure, shear, and moment diagrams for Broms method in cohesionless soils
(from Brown et al. 2010).
Therefore, at a depth, z, below the ground surface the soil resistance per unit length of shaft, p
z
, is
𝑝𝑝
𝑘𝑘
= Equation 6-13) Where B
b

is the width of the pile/shaft, γ’z is the vertical effective stress (effective unit weight multiplied by depth, and K
p
is the Rankine passive earth pressure coefficient, given as
𝐾𝐾
𝑝𝑝
= tan +
∅′
2
� Equation 6-14) In which φ’ is the effective friction angle of the cohesionless soil.

82 The pressure distribution in Figure 6-11 represents a simplification with a concentrated force at the bottom of the pile on the left-hand side. In actuality, the passive earth pressure will cross the vertical axis at the point of rotation. Fora pile of minimum length, L
min
, the depth z is replaced by L
min
. The requirements of overall moment equilibrium at the base of the shaft are applied (using the simplified approximate pressure distribution) to determine the maximum force at the pile head for L
min
: Equation 6-15) Equation 6-15 can also be solved to determine L
min
for an applied force, P
t
The point of zero shear and the point of maximum moment occurs at depth, f, which can be determined by
𝑓𝑓 = Equation 6-16) The maximum moment, M
max
, is determined from the sum of the moments about depth f
𝑀𝑀
𝑚𝑚𝑚𝑚𝑥𝑥
= 𝑀𝑀
𝑡𝑡
+ 𝑃𝑃
𝑡𝑡
(𝑓𝑓) − �
𝐵𝐵
𝑏𝑏
𝛾𝛾′𝑓𝑓
3
𝐾𝐾
𝑝𝑝
2
� Equation 6-17) An example of the Broms method for cohesionless soils is included in Appendix Bib

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