Made weaker on purpose

Every other structural idea in this collection makes something bigger. A deeper beam, a stiffer wall, a stronger connection, more material further out. Base isolation makes something smaller, on purpose, and the thing it makes smaller is the stiffness of the whole building’s connection to the ground.

The reason it works is not about the structure at all. It is about the shape of the curve the demand is read off.

Which free body produced the number #

A response spectrum is a plot of the peak response of a single oscillator against its period, for a given ground motion. Its characteristic shape has three regions: a rising branch at very short periods, a plateau where the acceleration is roughly constant, and a falling branch beyond a corner period where the acceleration falls roughly as $1/T$.

A conventional low-rise building sits on the plateau — its period is a few tenths of a second, and it is asked for the full plateau acceleration, which for a design event is of the order of one $g$. That is the whole of the seismic design problem: a horizontal force comparable with the building’s own weight, applied at every floor, and distributed up the height by the mode shape rather than uniformly.

Now put the building on bearings. If the bearings’ lateral stiffness is small compared with the frame’s, the combined structure has a first period set almost entirely by them:

$$T_1 \approx 2\pi\sqrt{\frac{m_{total}}{k_b}}$$

and it can be made two or three seconds without difficulty. That is well down the falling branch, so the spectral acceleration falls in proportion — from about 1.05 $g$ to 0.10 in the case drawn here, a factor of ten.

There is nothing subtle about the mechanism. What is worth noticing is how little it costs: the bearings carry the building’s weight, which they were going to have to do anyway, and their lateral stiffness is a design variable rather than a strength.

The price, which is written in displacement #

Spectral displacement and spectral acceleration are not independent. For an oscillator,

$$S_d = \frac{S_a}{\omega^2} = \frac{S_a T^2}{4\pi^2}$$

so a tenfold reduction in acceleration at a fivefold increase in period is a two-and-a-half-fold increase in displacement. The building that swayed 65 millimetres now moves 165, and all of that movement happens across the isolation plane rather than being spread up the height.

That number is the design. A base-isolated building needs a moat: a gap all the way round it, wide enough for the design displacement plus a margin, spanned by cover plates that slide. Every service crossing the plane — water, drainage, gas, power, lifts, stairs — needs a flexible connection able to take the same movement, and every one of them is a detail somebody has to draw.

It is also the detail most likely to be lost. A gap is an absence, and absences are what later works fill in. A planter, a bicycle rack, a new duct, a paving slab bridging the moat — any of them turns an isolated building back into a fixed-base one with a discontinuity in it, and none of them looks like a structural alteration. The commissioning and maintenance regime for an isolated building exists mostly to prevent that.

The mode with no shape in it #

Something else changes at the same time, and it is arguably worth more than the base-shear reduction.

Solve the two-degree-of-freedom problem — the superstructure’s mass on the frame’s stiffness, on the base slab’s mass on the bearings’ stiffness — and the first mode is almost entirely deformation of the bearings. The mode shape above the plane is nearly a straight vertical line, and the effective modal mass in it exceeds 99 per cent.

So every floor accelerates by nearly the same amount. The storey shears are nearly uniform up the height, there is no whip at the top, and the inter-storey drift — which is what breaks cladding, jams doors and destroys partitions — is very small.

That is the property that decides where isolation gets used. A hospital, a data centre, a museum, an emergency operations centre and a semiconductor fabrication plant are all buildings whose contents matter more than their frames, and no amount of strength in a frame protects contents: a strong frame still accelerates — which is the same complaint a vibrating floor answers — and an accelerating floor throws everything on it around. Isolation is the only structural measure that reduces floor acceleration, and that is a different objective from not falling down.

What the bearings actually are #

The arithmetic above treats the bearings as a linear spring, and real ones are chosen to be something more useful than that.

A laminated rubber bearing is alternating layers of rubber and steel shim. The shims prevent the rubber from bulging sideways, which makes the bearing enormously stiff vertically — it has to carry the column load — while leaving it soft in shear, because shear deformation of a rubber layer is not restrained by the shims at all. The ratio between the two stiffnesses is several hundred, and it is achieved by geometry rather than by material.

A lead-rubber bearing adds a lead plug down the middle. Lead yields at a low stress and recrystallises at room temperature, so it dissipates energy in a hysteresis loop and does so repeatedly without degrading. That raises the effective damping from rubber’s five per cent to fifteen or thirty.

A friction pendulum replaces the spring entirely: a slider on a spherical dish, whose restoring force comes from gravity and whose period is set by the dish’s radius alone. $T = 2\pi\sqrt{R/g}$, with no mass in it — so the period is the same whatever the building weighs, which removes one of the harder uncertainties in the design and makes the period something chosen rather than inherited.

Damping matters more here than in most structures because the demand is read off a curve rather than computed. Codes reduce the spectral ordinates by $\eta = \sqrt{10/(5+\zeta\%)}$, so twenty per cent damping is worth a further factor of 0.63 on both the acceleration and the displacement. That reduction on the displacement is often what makes the moat buildable.

The energy account, which is the honest description #

There is a second way of looking at the whole idea, and it is the one that makes the relationship between isolation, damping and ductility clearest.

An earthquake delivers energy to a structure. That energy has to go somewhere, and there are exactly four places: kinetic energy in the moving mass, recoverable strain energy in the elastic deformation, energy dissipated by damping, and energy dissipated by damage — which is to say, by the structure yielding.

A conventional ductile design balances the account by putting a large fraction into the last term. That is what a ductility demand is: a licence to break some of the structure in a controlled way so that the input energy has a home. The building survives and is often not repairable, which is an entirely legitimate design outcome and the one nearly every code is written around.

Isolation changes two terms at once. It reduces the energy that gets in at all — a structure whose period is far from the ground’s receives less — and it moves the dissipation from the frame into a device that is designed to do it and can do it repeatedly. The building’s own material stays elastic, which is why an isolated hospital is operational the day after and a ductile one is not.

That is also the sharpest way to say what the extra cost buys. Isolation is more expensive than conventional design in every case, and what it buys is not safety — a well-designed ductile building is safe — but continuity of function. Whether that is worth paying for is a question about the building’s purpose, and it is why the technique is concentrated in a narrow band of building types rather than spreading.

Where the argument reverses #

The whole case rests on the spectrum having a falling branch where the isolated period lands. On soft ground it does not.

A deep deposit of soft clay filters the incoming motion and amplifies the components near its own period, which can be one to two seconds. The spectrum then has its plateau extended out to a corner period well past two seconds — and shifting a building from half a second to two and a half moves it along the plateau or up onto it, not down.

Mexico City in 1985 is the standing case, and the mechanism there was the fixed-base version of the same thing: buildings of six to fifteen storeys, with periods around two seconds, on a lake bed whose own period was two seconds, in an earthquake whose epicentre was three hundred kilometres away. The ground amplified a narrow band and handed it to exactly the buildings that could receive it.

So isolation is a site decision before it is a structural one. The question is not whether the building’s period can be raised; it is what the ground’s spectrum does at the raised period. On rock the answer is nearly always favourable; on soft ground it can be the opposite, and the same design is then actively harmful.

The buildings it is on, and the one it started with #

The idea is old and the practice is not, which is the usual pattern when a technique needs a material rather than a theory.

Proposals to stand buildings on rollers, on sand layers, on talc, or on a course of loose ball bearings go back to the nineteenth century, and Frank Lloyd Wright’s floating foundation for the Imperial Hotel in Tokyo is sometimes claimed as an early case — inaccurately, since what it did was accommodate settlement in soft ground rather than shift a period. None of them was buildable in a form that could be relied on for a century, because a bearing that has to carry a building’s weight, stay soft in shear, not creep, not perish, and still work after fifty years is a materials problem.

Laminated rubber bearings solved it, and they solved it first for a different purpose: they were developed for bridges, to accommodate thermal movement and rotation at a support. The seismic application is that bearing used at a much larger shear strain, and the first buildings on them date from the late 1960s in New Zealand, where William Robinson’s lead-rubber bearing added the damping that made the displacements manageable.

What has spread since is narrow and deliberate. Isolation is on a few thousand buildings worldwide — heavily concentrated in Japan, which has more than the rest of the world combined, and used almost exclusively on hospitals, emergency facilities, data centres, museums and a handful of residential towers where the marketing value of it is real. It is also used on a great many bridges, where the moat problem does not exist because a bridge deck is already detailed to move.

The technique did not fail to spread; it found its band. A structure whose contents are worth more than its frame is worth isolating, and one whose contents are not is not.

Where the model stops #

The bearings are not linear and the spectrum assumes they are. A lead-rubber bearing’s force–displacement relation is bilinear, and the whole calculation above uses an effective stiffness and an equivalent viscous damping taken at the design displacement — which is a linearisation whose validity depends on the answer it produces. The design is therefore iterative, and a serious one ends with a non-linear time-history analysis rather than with a spectrum.

Uplift is a real limit. A rubber bearing has very little tensile capacity, and a slender isolated building overturning about its base can put its windward bearings into tension. That constrains the aspect ratio far more tightly than a fixed-base building’s, and it is why isolation is overwhelmingly used on low- and medium-rise structures. The check is an overturning calculation with the bearings standing in for the toe.

And the displacement is a second-order problem. The building’s whole weight is displaced sideways by a quarter of a metre, so there is a $P$-$\Delta$ moment on the isolation plane that has to be carried by the bearings themselves — the load making itself worse, at the one plane in the building least able to argue.

What the superstructure above it is designed for #

One detail deserves separating, because it is where isolation’s economics actually live and it is not the bearings.

If the base shear falls by a factor of ten, the frame above could in principle be designed for a tenth of the force. Codes do not allow that, and for a good reason: an isolated structure has to remain elastic, because the whole argument depends on the superstructure moving as a rigid body. A superstructure that yields has a longer effective period, a different mode shape and a ductility demand nobody computed, and the isolation system was designed against none of it.

So the reduction taken on the superstructure is modest — typically a factor of two rather than ten — and the rest of the benefit is banked as elastic behaviour rather than as material saved. That is the reason isolation rarely pays for itself in steel or concrete tonnage, and the reason the case for it is nearly always made on performance rather than on cost.

It also produces a design that looks odd on paper. An isolated building’s frame is stiff, regular and relatively strong for the force it is designed for, with none of the detailing for plastic hinge rotation that dominates a conventional seismic frame. The ductility has been moved out of the structure and into a component, which is the same relocation an eccentrically braced frame performs on a smaller scale and in a different place.

The generalisation #

The idea underneath this is more general than earthquakes and it is worth stating without them.

A structure’s demand is often a function of its own dynamic properties, and those properties are a design variable. Where that is true, the response to an excessive demand is not necessarily to resist it — it may be to move the structure to a part of the curve where the demand is smaller.

A machine on a floor is isolated by the same argument: soften the mounting until the machine’s period is well above the forcing period, and the transmitted force falls. A tuned mass damper is the same argument again, moving the response rather than the structure. Ductility is a third version — accepting damage in exchange for a lower demand — and base isolation is the version that gets the reduction without the damage.

What all four share is a shape: a curve of demand against a structural property, with the structure free to choose where on it to sit. Design in that setting is a choice of position rather than a provision of capacity, and it is the closest this subject comes to getting something for nothing.