Footfall wear on monuments

How can visitors who each touch a stone step once wear the step away?

Stand on a cathedral stair worn into a shallow dish, or watch a queue file past a bronze whose toes have been rubbed featureless, and there is something genuinely hard to accept. No single visitor did anything. A shoe on marble leaves no mark you can find with a hand lens. The tread is harder than the sole, and the visitor is gone in a second.

Yet the dish is real, and deep enough to hold rainwater. So either something other than the visitors is doing the damage, or a great many effects too small to detect are adding up to one impossible to miss. Which is it, and if it is the second, what exactly is being added up?

Take the arithmetic first, because the intuition that fails here is a numerical one rather than a physical one.

Suppose a step loses one centimetre of marble over three centuries, taking two million visitors a year. That is six hundred million footfalls for ten millimetres, so each removes about seventeen picometres — roughly a tenth of the width of one atom. Nobody's shoe removes a tenth of an atom, of course; what it means is that perhaps one footfall in ten does anything at all, and what it does is dislodge a few grains. That is the whole difficulty: our sense of "negligible" is calibrated to single events and cannot represent a quantity that is negligible and repeated a billion times.

So what physical process is the arithmetic describing? Grit. Almost all of it is abrasion by particles the visitor carried in — quartz sand and street dust, harder than limestone or marble, pressed under body weight and dragged a few centimetres as the foot rolls. The shoe is the vehicle; the sand is the tool. Which is why entrance matting is one of the most effective interventions available, out of all proportion to how trivial it looks.

Now the question that decides whether the wear is even. Do visitors spread out? They do not, and that matters more than the total. People walk where other people walked — the inside of the turn, the handrail side, the shortest line between doors. Half a million annual visitors do not distribute across a two-metre tread; they concentrate onto a band perhaps thirty centimetres wide. The local flux, which is what governs wear, can be five or ten times the average, and the hollow appears exactly along the desire line.

Then a second effect, which turns steady accumulation into something that speeds up. Once a hollow exists it collects the grit that made it, holds water after rain, and channels the next visitor into the same line, since a dish is easier to walk in than a crown. Weathered stone often carries a hardened skin as well — on limestones, a case-hardened crust of recrystallised calcite — and once breached, the softer material beneath erodes faster. So the curve steepens: the first millimetre takes longer than the fifth.

Now the property that makes all this consequential rather than merely interesting. Stone does not repair. Turf, soil and vegetation have a rate of renewal, so for them there is a genuine sustainable footfall at which loss and regrowth balance. Marble has no such rate. Every grain removed is gone permanently, so wear only increases and has no equilibrium to settle at. No visitor number is "safe" in the sense of causing no loss — only slower.

That makes the accumulation different in kind from most tourism impacts. Litter, noise and crowding are flow problems: stop the flow and the problem stops. Stone wear is a stock problem, governed not by today's rate but by the sum of every rate there has ever been — which is why a monument can survive a thousand years of pilgrims and then be visibly damaged in three decades, once annual visitor numbers rise by an order of magnitude.

One honest caveat. Attributing wear to footfall is harder than it looks, since acid rain, freeze-thaw, salt crystallisation and cleaning all remove stone from the same surfaces. Conservators separate them by pattern rather than by measuring the wear itself — abrasion follows the walking line and the handrail, chemical weathering follows rainwater and shelter. Where the two coincide, the split is genuinely uncertain.

The most useful correction is to the idea of a carrying capacity. It is a reasonable concept for a meadow or a coral reef, where damage and recovery both have rates and can be balanced. Applied to stone it quietly assumes a recovery term that does not exist. The honest version of the question is not "how many visitors can this step take?" but "over what period are we willing to spend it, and on whom?" — which is a decision about distribution across generations, not a technical threshold.

That reframing explains why effective interventions look the way they do. None try to find a safe number. They either reduce wear per visit — entrance matting to remove grit, softer flooring, timed entry to stop shuffling queues grinding in one spot — or they redistribute the flux, by rerouting the path, widening the walking line, or fitting a sacrificial surface meant to be consumed and renewed. That last is the clearest admission of the mechanism: it does not stop the accumulation, it moves it onto something replaceable.

Worth naming the trap in the other direction too. Because no visit is detectable, each visit really is harmless in isolation — so no case for restricting any particular visitor can rest on the damage that visitor does. It has to rest on the total, which is nobody's doing in particular.

• How conservators separate abrasion from chemical weathering on the same surface.
• Sacrificial surfaces and replica treads — what is preserved and what is quietly given up.

Every term the collection defines is gathered in the glossary.