Dry-Stone Wall Stability

What is modelled

One metre of a dry-stone wall with a trapezoid section. A horizontal gust of uniform pressure pushes on the windward face. The wall can fail by turning about its leeward toe (overturning), by sliding along the ground, or by cracking open at its base when the load line leaves the middle third of the thickness.

Equations

• Weight per metre W = ρ g (tb + tt) h / 2, centroid height yc = h (tb + 2 tt) / (3 (tb + tt)).
• Overturning FS = W tb / (p h²), sliding FS = μ W / (p h).
• Ground pressure σ = (W / tb) (1 ± 6e / tb) for eccentricity e up to t_b/6, then a triangle over 3(t_b/2 − e).
• Tipping angle atan(tb / (2 yc)).

Checks run in the page

• Summed stone courses against the trapezoid weight and centroid.
• Gust that overturns by moment integration against the closed form.
• Ground pressure integrated to give back weight and moment.
• Tipping angle and energy barrier from scanning rotation about the toe.

Honest simplifications

A rigid monolith with a straight taper and a flat gust load: no individual stones, no infill or interlocking, no ground settlement, no gust turbulence and no seismic shaking beyond the quasi-static value shown. The real wall is much more forgiving than a monolith because it can shed stones. This is a teaching model, not a structural assessment of the heritage site.

• Press Thin garden wall and watch it topple in the moderate gust.
• Press Slippery footing: the safety factor against sliding falls below one before overturning matters.
• Widen the base and read how the ground pressure becomes a trapezoid inside the middle third.