Aqueduct Pier Stability

What is modelled

One stone pier is a tall block whose weight, plus the load of the arches, deck and water above it, presses on its base. Wind and ground shaking add a sideways force that tilts the resultant away from the centre. Masonry carries almost no tension, so engineers keep the resultant inside the middle third of the base; beyond it a crack opens under the base, and at the edge the pier overturns.

Equations

• Weight W = ρ g t ∫b(z) dz for a pier whose width b tapers linearly.
• Wind pressure q = ½ ρair Cd U2; seismic force kh × weight at each centre of gravity.
• Eccentricity e = M / N; stress σ = N/(b t) (1 ± 6e/b) inside the middle third, 2N / (3 t (b/2 − e)) beyond it.
• Overturning factor (b/2)/e; sliding factor μ N / V.

Checks run in the page

• Pier weight and centroid against the trapezoid formula.
• The wind moment by integration against the closed form.
• The stress block integrates to the force and the moment.
• The two stress formulas meet at the edge of the middle third.

Honest simplifications

The pier is a rigid solid block with a uniform granite density; the wind acts as a static pressure on the pier and one deck block with a single drag coefficient; the earthquake is a static horizontal coefficient, not a dynamic analysis; the arches are replaced by a lump load; and a friction coefficient of 0.6 is assumed between stone courses.

• Press Storm and watch the resultant dot leave the centre of the base.
• Press Earthquake and see how the coefficient moves it faster than wind.
• Press Slender tall pier: a thin base brings the dot out of the green band at much lower load.