For practical purposes, Seed and Whitman (1970) proposed to separate the total (static + dynamic) active lateral force, P_AE, into two components: the initial active static component, P_A, and the dynamic increment due to the base motion, ΔP_AE, where P_AE = P_A +ΔP_AE as illustrated in Figure 2.2.
The static thrust calculated from the Coulomb theory is applied at H/3 from the base of the wall, resulting in a triangular distribution of pressure.
As Seed and Whitman (1970) stated, most of the investigators agree that the increase in lateral pressure due to the shaking, Δp_AE(z), is greater near the top of the wall and the resultant increment in force acts at a height varying from H/2 to 2H/3 above the base of the wall.
Seed and Whitman (1970) in particular recommended that the resultant dynamic thrust be applied at 0.6H above the base of the wall (i.e., inverted triangular pressure distribution).
It is worth to mention that in this approach dry cohesionless backfill material is assumed.
The state of practice in British Columbia (DeVall et al., 2010) is to apply the ΔP_AE at height 2H/3 above the base of the wall, resulting in an inverted triangular distribution of pressure.
On this basis, the total thrust will act at a height h = [P_A*(H/3)+ΔP_AE*(2H/3)] / P_AE above the base of the wall.
The value of h depends on the relative magnitudes of P_A and ΔP_AE, and it often ends up near the mid-height
of the wall.
This method as presented in Figure 2.2 hereinafter will be referred to as ”the modified M-O method”.
https://open.library.ubc.ca/soa/cIRcle/collections/ubctheses/24/items/1.0300247
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