As we know that masonry structure cannot resist tension, hence all the lateral force should be resisted by its weight component only. In this article we will derive expression for width/height ratio for a simple rectangular masonry structure.
γ=density of water
Sm=specific gravity of masonry material
SL=specific gravity of material giving lateral force (e.g. water, soil etc)
h=height of the structure
x=width of the structure
W=weight of structure=h*x*s* γ
μ= coefficient of friction
Case1: For overturning
Moment dut to lateral force=moment due to weight of the material
½* γ*sL*h2*h/3 =W*x/2
Or, ½* γ*h2*h/3*sL = γ *sm*h*x*x/2
For water sL=1;for stone masonry sm=22/9.81=2.14
Case2: For Sliding
Horizontal force=friction factor*weight of the structure
½* γ*sL*h2= μ (γ*sm*h*x)
Or, x/h=sL/(2*sm* μ)
For water and stone masonry and using μ=0.65
Thus from above derivation we see that the minimum base width/height ratio of the rectangular block to resist the lateral (triangular here) force with safety factor 1 is 0.4.
With safety factor of 1.5 the minimum width/height ratio becomes 1.5*0.4=0.6.