Summary: An unreinforced concrete canal lining carries almost no load, which is why it does not fail the way a wall fails. It is a set of panels, and almost everything that goes wrong with it happens in the gaps between them: the panels are held in compression far below their strength while the joints are asked to absorb every movement the concrete produces and every movement the ground imposes, and a joint can only absorb about one millimetre of that before its sealant is spent. The arithmetic in this article runs in the direction an inspection does not: from a rotation that has been measured, back to the opening it implies, back to the void that had to open under the panel for the rotation to happen, and finally to the temperature difference that produces the same rotation on a sunny afternoon with nothing wrong at all. The conclusion is uncomfortable but useful. On this structure a single tilt reading is dominated by the weather, and the reading that means something is the difference between two panels rather than the value of one.

 

1. The Structure That Is Mostly Joints

A canal lining is not a retaining structure, and the first thing to get right about it is how little it does. It is a cover: a layer of concrete, placed on a prepared subgrade, whose job is to keep the water in the channel from reaching the soil underneath. In the ordinary operating condition the water sits on top of it at a depth of a metre or two and presses down more or less evenly. A panel loaded evenly on a supported base bends hardly at all. There is no span, no thrust, no overturning moment, and the compressive stress in the concrete is a small fraction of what the concrete can take.

That is the reason the failure modes on a canal are not the ones an engineer trained on walls expects. The panel does not crush and it does not shear off. What happens is that the support under it stops being even, or the ground pushes back up when the channel is drawn down, or the concrete tries to change length and is not free to. In every one of those cases the panel responds by rotating rather than by deflecting, because rotation is the only freedom a short thick plate on a continuous base has left.

The panels are not continuous with each other. Unreinforced lining is cast in bays separated by contraction joints, and the joints exist precisely so that the concrete cracks where someone chose rather than where it wants to. A joint is a groove cut partway through the thickness, and it does two things at once. It gives the shrinkage and the thermal movement a place to accumulate, and it gives water a path through the cover if the groove is not sealed properly, or is sealed with something that has since been stretched past what it can recover from.

The spacing of those joints is not a free design choice. A widely used rule, attributed to Reclamation practice, puts the contraction joint spacing at thirty six times the lining thickness, and the recommendations in ACI 224.3R land in the same territory once their imperial figures are converted: a two inch lining at seven and a half to ten feet, a four and a half inch lining at twelve to fifteen feet, which works out to somewhere between thirty two and sixty times the thickness. Thirty six sits inside that band, and it is used as the basis for everything below.

What that rule does is fix a ratio rather than a dimension. Whatever thickness is chosen, the panel length follows it, and the panel therefore always has the same proportions. The table below shows what the rule produces across the range of thicknesses actually built. The last column is the one that matters for instrumentation: it is the number of separate panels a single kilometre of canal contains.

Lining thickness	Contraction joint spacing	Length to thickness ratio	Transverse joints in one kilometre
60 millimetres	2.16 metres	36	463
75 millimetres	2.70 metres	36	370
100 millimetres	3.60 metres	36	278
125 millimetres	4.50 metres	36	222
150 millimetres	5.40 metres	36	185

A kilometre of a modest channel therefore contains a few hundred panels and, once the longitudinal joints at the wall and the base are counted, well over a kilometre and a half of joint. The joint is not a detail on this structure. Along with the panel surface it is one of the two things the structure consists of, and it is the only one of the two that is designed to move.

The rule changes when the lining is reinforced, and the change is worth knowing because it marks the boundary of this article. Reclamation guidance puts the maximum joint spacing for reinforced lining at twenty five feet regardless of thickness, because the steel carries the shrinkage rather than the joint absorbing it. A reinforced lining therefore has a fixed panel length and a length to thickness ratio that varies, and the neat proportionality used below does not apply to it. Unreinforced lining is the case analysed here, and it is also the common case on irrigation canals, where the cost of steel in a cover that carries almost no load is hard to justify.

2. Thirty Six Times the Thickness, and the Budget It Sets

The rule is usually presented as a crack control measure, and it is, but it is worth reading as a budget instead. Every panel shrinks as it cures and changes length with temperature, and the joint at its end has to absorb the difference between the panel and its neighbour. The published estimate for that movement is simple: the joint opening equals a friction restraint factor, multiplied by the panel length, multiplied by the thermal coefficient and the temperature change. The restraint factor is about 0.8 for a granular base and 0.65 for a stabilised one, because a panel dragged by friction does not deliver its whole movement to the joint.

Put the rule and the movement estimate together and the result is a constant. Since the panel length is thirty six times the thickness, the joint opening at a given temperature change is also proportional to the thickness. A hundred millimetre lining with a forty kelvin swing opens its joints by less than a millimetre. A hundred and fifty millimetre lining opens them by a little over one. Those are the design numbers, and they are the whole allowance the joint has.

Lining thickness	Joint spacing	Opening at a 40 kelvin swing, granular base	Same, using the general thermal coefficient
75 millimetres	2.70 metres	0.57 millimetres	0.86 millimetres
100 millimetres	3.60 metres	0.76 millimetres	1.15 millimetres
150 millimetres	5.40 metres	1.14 millimetres	1.73 millimetres

The two columns differ because two coefficients are in circulation: the one used in the joint movement formula is specific to the coarse aggregate and is lower than the general figure for concrete. The gap between them, about half as much again, is small next to what comes later, but it is worth knowing that the budget itself is not a single agreed number.

A joint opening of about a millimetre is what the sealant is there to handle, and the sealant is rated for it. The standard classification for elastomeric joint sealants, ASTM C920, rates a product by the movement it can take as a share of the joint width at installation. A class 25 sealant is rated to move by a quarter of that width in each direction, so a joint thirteen millimetres wide is good for plus or minus three and a quarter millimetres. That is the largest movement anywhere in the design, and everything the structure does beyond it has to come from somewhere else.

3. What a Fraction of a Degree Does to a Joint

A panel that rotates about one edge does not simply drop at the other. Its far edge swings through an arc, and the joint at that edge opens by the panel length multiplied by the tangent of the rotation. On a three and a half metre panel the geometry is unforgiving, because the movement is amplified by the full length of the panel while the sealant allowance was set by a joint a few millimetres wide.

Panel rotation	Joint opening on a 3.6 m panel	Times a 10 mm joint allowance	Times a 13 mm joint allowance
0.005 degrees	0.31 millimetres	0.1	0.1
0.01 degrees	0.63 millimetres	0.3	0.2
0.02 degrees	1.26 millimetres	0.5	0.4
0.05 degrees	3.14 millimetres	1.3	1.0
0.10 degrees	6.28 millimetres	2.5	1.9
0.20 degrees	12.57 millimetres	5.0	3.9

The figure worth carrying away is the fourth row. A rotation of five hundredths of a degree, which is ten times the specified accuracy of an ordinary MEMS tiltmeter and would look like nothing at all on site, opens the joint by three millimetres. That is already past what a class 25 sealant installed in a ten millimetre joint can take. At a tenth of a degree the joint has opened six millimetres, which is two and a half times the allowance, and at that point the sealant has either torn away from one wall or is being stretched beyond the range in which it recovers.

Two qualifications belong here, and both of them make the situation worse rather than better. The first is that many irrigation canals do not seal their contraction joints at all. The groove is cut, sometimes filled with a poured bitumen or a mortar, and left. In that case there is no sealant allowance to exceed, because there was never a sealant, and the joint is a straight path from the water to the subgrade as soon as it opens at all. The second is that the rotation does not have to be sudden. A panel that loses a few centimetres of support a month reaches the same joint opening in a year, and not one reading in that year will look unusual on its own.

Why it matters hydraulically is a separate article of evidence, and it comes from laboratory work rather than from inspection records. A study of cracked concrete lining channels tested crack widths from a tenth of a millimetre to three, with lining thicknesses of sixty to eighty millimetres and heads of two hundred to six hundred millimetres. Below half a millimetre the flow through the crack followed a viscous relation and was insensitive to head and thickness. Above that it stopped behaving that way, and the permeability rose steeply with width: from half a millimetre to eight tenths of a millimetre it went up by a factor of about two and a third. The same study found that when crack area reached one percent of the lining area, the cracks carried up to sixty five percent of the total seepage. A separate numerical study of rigid liners found a single crack increasing seepage by two and a third to four and a half times the uncracked value, with the worst case at the centre of the bed.

So the millimetre scale is not a comfort. Half a millimetre is the point where a joint stops being a sealed groove and starts being a leak, and the rotation that produces three millimetres is a twentieth of a degree.

4. What Has to Open Under the Panel First

A void does not have a single cause, and the cause decides whether monitoring it is useful. The first source is construction. A subgrade trimmed to line and grade by machine is never as uniform as the drawing assumes, and a panel cast over a hollow of a few centimetres starts its life partly unsupported. The second is internal erosion: water that has found a way through the cover, at a joint or a crack, moves through the subgrade and carries fines with it, and the void grows from the joint inward. That is the mechanism that links this section to the previous one, because the water that does the washing is the water the joint let through. The third is volume change in the subgrade itself, whether from a falling water table, from the collapse of a compacted fill under first wetting, or from the thaw of a frost bulb that heaved the panel the previous winter.

Only two of those three are gradual, and the distinction matters for what a sensor can offer. A construction void is present from the day the panel is cast and never changes, so it is a baseline problem rather than a monitoring problem: it biases the initial reading and it makes that panel more sensitive than its neighbours from the start. Erosion and subgrade collapse are progressive and they are what a continuous record can catch. They are also the two that a walkover inspection is least likely to find in time, because the surface of the panel stays intact while the support leaves.

The rotation in the previous section is not something a panel can do while it is fully supported. It has to lose its bearing at one edge, and the length of the void controls the rotation. A panel supported along one edge and unsupported along the other behaves as a cantilever under its own weight, and the standard result gives the rotation at the free end as the distributed load times the cube of the void length, divided by six times the flexural rigidity.

Inverting that expression is the useful move, because it converts an angle into a length of missing support. The result depends only on the panel thickness, the density of concrete and the rotation being looked for, and the table below solves it for a hundred millimetre lining on the thirty six times rule.

Panel rotation	Void length needed	As a share of the panel length	Drop at the unsupported edge
0.005 degrees	0.77 metres	0.21	0.05 millimetres
0.01 degrees	0.97 metres	0.27	0.13 millimetres
0.02 degrees	1.22 metres	0.34	0.32 millimetres
0.05 degrees	1.66 metres	0.46	1.08 millimetres
0.10 degrees	2.09 metres	0.58	2.73 millimetres

Read the first row against the sensor specification and the whole problem becomes visible. A tiltmeter with an accuracy of five thousandths of a degree, which is a good instrument, does not begin to read clearly until about three quarters of a metre of the panel has lost its bearing. At that point the void is already a fifth of the panel. The instrument is not at fault; the geometry is. A short thick plate on a continuous base is stiff, and it takes a large loss of support to produce even a small rotation.

The last row is where the two previous sections meet. A void of two metres, more than half the panel, produces a rotation of a tenth of a degree, and that rotation opens the joint by six millimetres. The threshold at which the instrument starts to read clearly is the same threshold at which the joint has already lost its seal. There is no comfortable interval between detection and consequence on this structure, which is the opposite of what a monitoring specification usually assumes.

There is an upper bound as well, and it is worth knowing because it sets the range a sensor needs. When the void extends under the whole panel the panel stops behaving as a cantilever and starts behaving as a simply supported slab resting on its two neighbours, and the rotation stops growing with the void. For a fully unsupported panel the rotation is fixed by the panel weight and its proportions. Because the thirty six times rule makes the length cube and the rigidity grow at the same rate, the rotation of a fully unsupported panel turns out to depend on the thickness alone, and it increases with it. Thicker panels rotate more, not less, which is not what intuition suggests.

Lining thickness	Joint spacing	Panel self weight	Rotation at the joint	Deflection at mid panel
60 millimetres	2.16 metres	1.44 kilopascals	0.077 degrees	0.91 millimetres
75 millimetres	2.70 metres	1.80 kilopascals	0.096 degrees	1.42 millimetres
100 millimetres	3.60 metres	2.40 kilopascals	0.128 degrees	2.52 millimetres
125 millimetres	4.50 metres	3.00 kilopascals	0.160 degrees	3.94 millimetres
150 millimetres	5.40 metres	3.60 kilopascals	0.192 degrees	5.67 millimetres

The practical consequence is a range requirement and not a resolution requirement. A panel that has lost all of its support, on any of the thicknesses in the table, rotates by a fifth of a degree at most. Anything larger than that on an otherwise sound canal is not panel bending. It is the subgrade moving, or the slope going, and those are different problems with different instruments.

5. The Weather Rotates the Panel More Than the Damage Does

Everything so far has treated the panel as a load path. It is also a plate exposed to the sun, and the two faces of it are not at the same temperature. The top face absorbs solar radiation and the bottom face sits on soil that stays close to a constant temperature. The result is a temperature gradient through the thickness, and a gradient through a plate means curvature. The edges lift, the centre stays down, and the rotation at the edge is the thermal strain divided by the thickness, multiplied by half the panel length.

That expression has the same variables as the structural one and produces numbers of the same size. A temperature difference of eight kelvin across a hundred millimetre slab, on a three and a half metre panel, rotates the edge by eight hundredths of a degree and lifts it by two and a half millimetres. There are published field measurements from instrumented concrete pavement slabs that agree with that order of magnitude: corner curling in the range of three and a half millimetres, edge curling under one, with the peak in the early afternoon and the reverse before dawn.

Temperature difference through the slab	Edge rotation	Edge lift	Share of the maximum structural rotation
5 kelvin	0.052 degrees	1.62 millimetres	0.40
8 kelvin	0.083 degrees	2.59 millimetres	0.64
10 kelvin	0.103 degrees	3.24 millimetres	0.81
12 kelvin	0.124 degrees	3.89 millimetres	0.97
15 kelvin	0.155 degrees	4.86 millimetres	1.21

The last column is the argument of this article. At a temperature difference of about twelve kelvin the weather produces the same rotation as a panel that has lost its entire support. Twelve kelvin across a hundred millimetres of concrete in sunlight is an ordinary afternoon, not an extreme. So on any sunny day, on any canal, the largest rotation in the record will be a weather signal, and it will be larger than the rotation the structure is capable of producing from damage.

The same field work adds two details that make the problem sharper. The lift at a corner is about four times the lift at an edge, because the corner is further from the centre of the panel than the middle of a side is, so the reading depends on where on the panel the instrument sits. And the number of cycles is not small: a slab cycled daily for thirty years sees about eleven thousand of them. The weather is not noise in the statistical sense of something rare and random. It is the largest and most regular signal on the structure, and it is there every day.

6. Why No Flow Measurement Will Ever Catch This

The natural response to a lining that leaks is to measure the water. That does not work, and the arithmetic shows why in one line. Take a trapezoidal channel with a two metre bed, side slopes of one and a half to one, and a metre of depth. The flow area is three and a half square metres. Now take a hundred millimetre panel and let it lose all of its support, so that it sags at mid panel by two and a half millimetres across its own length. Treating that sag as a triangular depression with the panel length as its base, the cross sectional area of the channel changes by a little over a tenth of one percent.

Now compare that with the number the flow calculation actually depends on. The roughness coefficient of a concrete lining is usually taken between 0.014 and 0.015, and the uncertainty in choosing between those two values changes the discharge by nearly seven percent. The geometric effect of the panel losing its support entirely is about fifty times smaller than the uncertainty in a coefficient that is copied from a table. No water level measurement, no gauging station, and no water balance will resolve it.

There is a second reason, and it is worse. The seepage does not scale with the area of damaged lining, it scales with the width of the openings. The laboratory work cited earlier found that cracks covering one percent of the lining area carried about two thirds of the total seepage, and that the same opening carried disproportionately more as it widened past half a millimetre. A water balance integrates all of that into a single number for a whole reach, which is the one form in which a local joint problem is least visible.

So the failure is in the category where instrumentation is not an optimisation but the only option. The channel runs full, the water arrives at the outlet, the accounts balance within their tolerance, and the subgrade under one panel is being washed out. What makes it worse is the feedback: seepage raises the water content of the subgrade, which in a freezing climate increases frost susceptibility, which lifts and cracks the lining further, which increases the seepage. The literature on cracked linings calls this a cycle rather than a sequence, and the reason it can persist for years is precisely that none of the standard measurements respond to it.

7. The Only Reading That Separates Them

If a single panel rotation is dominated by weather, the reading that carries information has to be built from more than one panel. Two properties separate the two causes, and both of them are structural rather than statistical.

The first is spatial. A temperature gradient is a property of the whole canal at a given hour. Every panel along a reach sees nearly the same sun, the same air temperature and the same soil temperature, so every panel curls in the same direction by nearly the same amount at nearly the same time. A void under one panel is a local condition. It affects one panel and, at most, its immediate neighbours through the load they share. So the temperature signal is common mode and the damage signal is differential, and taking the difference between two adjacent panels cancels the first and preserves the second.

The second is temporal. A temperature rotation follows the sun with a daily period and a phase lag of a couple of hours, and it reverses sign overnight. A panel that loses its bearing does so once, over hours or days, and does not reverse. So the shape of the record separates them as well: a sinusoid with a period of a day is weather, and a step that stays is structure. Neither test needs a reference point outside the canal, which is what makes the approach work on a structure that runs for tens of kilometres.

There is a way to do this that needs no temperature channel at all, and it is worth writing down because it changes what the deployment has to contain. At any given moment, take the readings from every instrument on the reach and compute the median. That median is an estimate of the common mode, because weather affects all of them and a void affects one. Subtracting it from each reading leaves a residual that is, to first order, the structural component of that panel. The method assumes only what the physics already says: that the weather is shared and the damage is not.

The assumption has limits that should be stated with it. The median needs enough instruments to be meaningful, so three or four points on a kilometre is not a network, it is a set of unrelated readings. It also fails where the damage is shared, which happens on soft ground where a whole reach settles together, and in that case the common mode contains the signal and the method cancels what it was meant to find. The practical answer is to instrument a short reach densely rather than a long reach sparsely, so that the reference is local and the anomaly is a minority.

Put together, those two properties define a different deployment from the one a single instrument suggests. A tiltmeter on a canal panel is not a measuring device on its own. It is half of a measurement, and the other half is the panel next to it. Two panels instrumented and read on the same clock give a differential that is largely free of weather; one panel instrumented gives a record that is mostly a temperature log with a small structural component buried in it.

There is a cost consequence that ought to be stated, because it decides whether the method is practical. Instrumenting one panel in twenty on a kilometre of canal means fourteen instruments, and instrumenting alternate panels means a hundred and forty. The pairing requirement pushes the count up by a factor that a single point budget does not anticipate. What makes it affordable is that the instrument per point is cheap, battery powered and needs no cabling, because the alternative on a canal is not a wired sensor. It is a person with a level, once a season.

8. What the Instrument Cannot Do

The boundary on this structure is wide, and it is better stated plainly than discovered later.

A tilt channel cannot measure the joint opening. It measures the rotation of the panel, and the opening follows from the rotation only if the panel length and the geometry are known and if the adjacent panel is not moving too. A joint meter, a demountable extensometer or a feeler gauge measures the opening directly, and where the opening itself is the quantity of interest those are the correct instruments.

It cannot measure seepage, and it cannot tell a leaking joint from a sealed one that happens to be open. It cannot locate the edge of a void, because the rotation it reads is an integral of the support loss over the whole panel rather than a map of it. It cannot see a crack that has not yet changed the panel attitude, which is most cracks for most of their lives.

It does not replace a walkover inspection or a drawdown examination, and on a canal those remain the only way to find the things this instrument is blind to: a crack at the surface, a spalled edge, a joint with the sealant gone, a panel that sounds hollow under a boot. What continuous monitoring changes is the interval between those examinations, not the need for them.

One mechanism is deliberately left out of this article. Frost heave lifts and cracks canal linings in seasonal cold regions more than any other single cause, and it is the subject of a separate discussion in this series, because its signature is a seasonal cycle rather than a step and the way it defeats a tilt record is different from the way the daily thermal cycle defeats it. Mentioning it here without that treatment would blur two distinct arguments.

9. The Shape of a Deployment This Structure Implies

A canal is the opposite of a dam as an instrumentation problem. A dam has a few dozen points of interest concentrated in one place, each of them accessible, each of them worth an expensive instrument. A canal has hundreds of points per kilometre, scattered along a line in a field, with no power, no network and no reason for anyone to visit between inspections.

That shape rules out most of the usual answers. Wired instruments are not viable along tens of kilometres of channel. Solar powered nodes are viable but need maintenance of their own. What fits is a battery powered wireless instrument with a life measured in years, which is why this is one of the few structural applications where the power budget is the design driver rather than an afterthought.

The orientation of the instrument is decided by which void geometry is expected. A panel on the side slope loses its support most often along the slope, so it rotates about an axis parallel to the channel and its reading is the cross slope. A panel on the bed loses it at the upstream or downstream edge of the joint, so it rotates about an axis across the channel and its reading is the longitudinal slope. Those two rotations are different numbers about different axes, and a single axis instrument installed without deciding which one is being watched will read the other one as a partial projection and call it noise. On a reach where both are expected, the instrument has to have both axes, not because more data is better but because the two mechanisms are not the same mechanism.

Two of the requirements follow from the physics in the earlier sections and are worth specifying explicitly. The first is a shared clock. A differential between two panels is only a differential if the two readings were taken at the same moment, because the common mode that has to cancel is moving with the sun. Sampling two panels an hour apart does not cancel the weather, it aliases it. The second is that the sampling interval has to resolve the daily cycle if the phase test is to be used at all, which puts a floor of a few readings a day, and a preference for more.

A third follows from the shape of the record rather than from its content, and it is the one the structure argues for most strongly. The event this instrument is looking for is a step, and a step has no schedule. A device that reports on a fixed interval can miss a step entirely if it happens between two uploads, which on a multi year battery budget can be an upload interval of hours. A device that evaluates a threshold locally and transmits when it is crossed does not have that failure mode, and on a canal, where the step is the signal and the interval is long, that difference is the whole value of the installation.

A note on what is not claimed here. No canal lining deployment is presented as a case in this article, because there is none to present. The company publishes work on dams and bridges, tunnels, tailings facilities, storage racking and buried drainage, and the closest of those to a canal is buried drainage infrastructure, which shares the structure type without sharing the loading. The arithmetic above is a design argument, not a field record, and it should be read as one.

 

Frequently Asked Questions

1. Can a tilt sensor find a leak in a canal lining? No. It cannot see water. What it can do is record the rotation of a panel, and a rotation of a few hundredths of a degree is enough to open the joint at its edge past what the sealant can hold, which is how the leak starts. The instrument is upstream of the leak, not on it.
2. Why not just measure the joint opening directly? Where the opening is the quantity of interest, that is the right instrument, and a joint meter or a demountable extensometer does it properly. The reason to use a tiltmeter instead is scale: an extensometer spans one joint and has to be read or wired, while one tiltmeter per panel covers a whole panel and the pair of joints at its ends, on a battery, for years. The two are complements rather than substitutes.
3. How much void has to open under a panel before it rotates? About three quarters of a metre on a hundred millimetre lining before the rotation reaches five thousandths of a degree, which is a fifth of the panel. That is the geometry, not a limitation of the sensor: a short thick plate on a continuous base is stiff, and it takes a substantial loss of support to tilt it at all.
4. Is frost heave the main cause of canal lining failure? In seasonal cold regions it is the most common cause, and this article does not attempt to cover it. The argument here is about the daily thermal cycle and the loss of support, which act on every canal in every climate. Frost heave adds a seasonal signal on top of the daily one, and separating those two from each other and from structural movement is a larger problem than one article.

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