Summary: Everything published about a buried culvert is written in one of three units, and none of them is a degree. The load on the barrel is a force per unit length, and the method published by Marston and Spangler derives it from two ratios that describe how the pipe was placed rather than what the soil is; in the projecting condition it reaches about 1.9 times the weight of the soil directly above at a cover of roughly three pipe widths, and the standard remedy for an overloaded culvert is to make the ground above it more compressible. A flexible pipe is graded on a share of its own diameter and a rigid one on a crack width. A gravity culvert is graded on a slope, chosen so that the water can carry its sediment, and on a one metre pipe that slope is small enough that the sensor’s own zero drift over a seasonal swing is worth more than the whole of it.
1. Two Loads, and the One That Is Not the Weight of the Soil
A culvert carries two vertical loads. The upper one is traffic, and it is the better documented of the two, because a highway authority has to publish a distribution method and a table of minimum cover for every pipe and every axle. The lower one is the soil the pipe was buried in, and the intuitive answer, that the pipe carries the weight of the soil directly above it, is wrong by a wide margin.
Anson Marston measured it. In his early experiments on rigid conduits installed above the natural ground and then covered by an embankment, the actual loads were 90 to 95 percent greater than the weight of the soil directly above the structure. The excess was not a measurement error and it is not rare. It is the ordinary behaviour of a stiff object buried in a fill, and the method that reproduces it has been in the standard civil engineering literature since the 1920s.
The mechanism is relative settlement. When a fill is placed over a pipe, the column of soil directly above the pipe and the columns beside it do not settle by the same amount, because the pipe is stiffer than the soil it replaced. Whichever column settles more drags the other down, or holds it up, through friction along the vertical planes between them, and that friction is a shear force applied to the pipe. The direction it points in decides whether the pipe carries more than its share of the fill or less.
That is the first of the three units. The load on a buried culvert is a force per unit length, and its size is decided by how the pipe was placed. The second unit, a share of the pipe’s own diameter, is used to grade a flexible pipe and is decided by the pipe. The third, a slope, is used to decide whether the culvert will stay open, and it is decided by the water. A tilt sensor reports an angle, which is none of the three, so the useful question at the start of a scheme is which of them the scheme is actually going to be judged against.
The number a design office writes down first is the prism load, the unit weight of the fill multiplied by the height of cover and by the outside width of the pipe. It is a lower bound in the projecting condition and an upper bound in a narrow trench, and neither bound is a number a designer should use without saying which installation was assumed.
2. Why the Stiffer Pipe Takes the Extra Load
Marston and Spangler grouped installations into four families, and the grouping is not about the soil. It is about where the pipe sits relative to the original ground and the order in which material was placed around it.
A trench conduit is a pipe in a narrow trench backfilled over it. The fill inside the trench settles more than the ground beside it, friction along the trench walls acts upward on the fill column, and the pipe carries less than the weight of the soil above it. A positive projecting conduit is a pipe placed at or above the original ground surface and then covered by an embankment. The side prisms are deeper and settle more, friction acts downward, and the pipe carries more. A negative projecting conduit is the same pipe in a shallow trench that leaves the crown below the surrounding ground, which reverses the comparison and reduces the load. The fourth family, an induced trench or imperfect ditch, is a deliberate version of that geometry and is treated in a section of its own.
The grouping is a statement about relative stiffness. If the pipe is stiffer than the soil it replaced, the arching transfers load to the pipe. If it is less stiff, the soil takes the load back. In the design literature the two cases are carried by the sign of a single number, the settlement ratio, defined as the difference between the settlement of the soil at the sides of the pipe and the settlement of the top of the pipe, divided by the consolidation of the embankment below the critical plane. A positive value means the side prisms are settling into the ground more than the pipe is, which is the projecting condition and the heavier load. A negative value means the opposite.
| Installation condition | Settlement ratio in design | What the relative settlement does to the load | Load against the prism load |
| Trench conduit | Positive, but the trench walls take the shear | The fill inside the trench settles more than the ground beside it, so wall friction acts upward on the fill column and carries part of it | Less than the prism load |
| Positive projecting conduit | Plus 0.5 to plus 0.8 for a rigid pipe on ordinary soil | The side prisms are deeper and settle more, so friction acts downward and adds the weight of the neighbouring soil to the pipe | More than the prism load |
| Negative projecting conduit | Between minus 0.3 and zero for a flexible pipe | The pipe crown sits below the surrounding ground, so the interior prism settles first and the shear reverses | Less than the prism load |
| Induced trench, also called imperfect ditch | Engineered rather than assumed | A soft column is built directly over the pipe so that it settles more than its neighbours and hands its weight back to them | Deliberately the lowest of the four |
The published ranges of the settlement ratio put the two pipe materials on opposite sides of zero. For rigid culverts on foundations of ordinary soil the settlement ratio is generally chosen between plus 0.5 and plus 0.8. For flexible pipes the product of the settlement ratio and the projection ratio is typically taken between minus 0.3 and zero. The consequence is worth stating plainly, because it reverses an instinct: the stiffer the conduit, the larger the share of the fill it is asked to carry. A concrete pipe under a given embankment takes an extra load that a corrugated steel or polyethylene pipe in the same place sheds back into the ground.
The second consequence is about the record rather than the pipe. The number that decides the load was chosen at design time from a chart, on the basis of an assumed relative stiffness, and it was then realised on site by the sequence in which the fill was placed and compacted around the pipe. Neither of those is a property of the site that a survey can establish afterwards. The load a buried pipe is carrying is, in the most literal sense, a record of how it was built.
3. The Load That Grows Faster Than the Fill
For a positive projecting conduit in the condition the literature calls complete, the load on the pipe is the embankment load coefficient multiplied by the unit weight of the fill and by the square of the outside width of the pipe. The coefficient itself is an exponential of the depth to width ratio:
Cc = ( e to the power of two K mu times H over Bc, minus one ) divided by two K mu
where H is the height of cover, Bc is the outside width or diameter of the pipe, K is the Rankine lateral pressure coefficient and mu is the coefficient of friction of the embankment material. The standard practice documents publish the product K mu rather than the two factors separately. The value Marston first assigned, and the value used for the conservative envelope, is 0.1924 for a cohesionless granular fill.
Put numbers into it and the shape of the problem appears. The cover is expressed in pipe widths, because the ratio of H to Bc is what the coefficient depends on.
| Cover, in pipe widths over the pipe | Load coefficient, and the load as a multiple of the soil above | What happens to the load as the cover rises one step |
| 1 | 1.220, so 1.22 times the soil above | Reference row |
| 2 | 3.012, so 1.51 times the soil above | The load rises 2.47 times while the soil above only doubles |
| 3 | 5.645, so 1.88 times the soil above | The load rises 1.87 times while the soil above rises by half |
| 4 | 9.514, so 2.38 times the soil above | The load rises 1.69 times while the soil above rises by a third |
| 5 | 15.198, so 3.04 times the soil above | The load rises 1.60 times while the soil above rises by a quarter |
| 10 | 119.281, so 11.93 times the soil above | The load rises 7.85 times while the soil above only doubles |
At a cover of about three pipe widths the load is 1.88 times the weight of the soil directly above the pipe, which is where the 90 to 95 percent figure measured by Marston sits when the same formula is evaluated with the published coefficient. The increase does not stop there, and it does not grow in proportion to the fill. Doubling the cover from two pipe widths to four multiplies the load by 3.16 while the weight of the soil above only doubles. Doubling it again, from five pipe widths to ten, multiplies the load by 7.85. Asymptotically each additional pipe width of cover multiplies the load by about 1.47, which is an increase of 47 percent per pipe width, and the multiplier does not fall away.
The coefficient is also the reason two design offices can disagree about the same culvert without either having made a mistake. The published band of K mu runs from 0.11 for saturated clay to 0.1924 for cohesionless granular fill, and at a cover of three pipe widths that band spans 1.42 to 1.88 times the weight of the soil above the pipe, a range of about a third across a single coefficient that is selected from a table rather than measured on site.
Two qualifications belong in the same paragraph, because the formula is easy to quote and easy to misuse. The complete condition holds only while the plane of equal settlement, the height at which the two prisms stop settling differently, lies above the finished surface; below that height the coefficient takes a second term. And the load that a real pipe sees is limited by the strength of the fill around it, because a fill cannot transfer more shear than the soil can carry. Both qualifications matter most at high covers, which is exactly where the formula produces its largest numbers.
4. The Remedy That Makes the Ground Above the Pipe Softer
If a culvert is being overstressed by a fill that is already designed, the obvious remedy is to make the pipe stronger. The published remedy is the opposite. The induced trench method, also called the imperfect ditch or imperfect trench method, is a construction sequence whose entire purpose is to reduce the load on the pipe by making the ground directly above it more compressible than the ground beside it.
The sequence is specific. The conduit is installed as a positive projecting conduit, at or above the original ground surface, and the fill is thoroughly compacted at its sides and up to some elevation above its crown. Then a trench of the same width as the pipe is excavated directly over it and down to the crown. That trench is refilled with loose, highly compressible soil, and normal embankment construction continues above it.
The effect is to reverse the shear. The prism directly above the pipe now settles more than the adjacent masses instead of less, friction along the vertical planes acts upward on it, and part of its weight is transferred sideways into the soil beside the pipe rather than downward into the pipe. Marston is recorded as suggesting that layers of straw, hay or cornstalks could be worked into the refill to guarantee the compressibility. The documented outcomes include pipe culverts under high fills built according to a California highway department method and described as supporting those fills successfully, and a sewer protected from a proposed increase in the height of fill above it by the same sequence.
One objection was raised at the time and is worth repeating, because it is the natural first reaction: engineering a soft column above the pipe looks as though it must produce a sag in the road. The published answer is that the method is economically justified only for relatively high fills, and that at those heights the plane of equal settlement lies below the finished grade, so the interior and exterior prisms converge again before the surface is reached and the finished grade stays true. A railway project using the method is recorded as reporting no differential settlement of the embankment surface during the first 17 months after completion.
For a monitoring plan the important sentence is the one about where the scheme’s premise lives. The induced trench method works by controlling the relative settlement of two soil prisms, one directly above the pipe and one beside it. The quantity that decides whether the method succeeded is a settlement in the fill, not a movement of the structure. An instrument mounted on the pipe records the deflection that the load produces. It cannot show whether the soft column was built to the specification the design assumed.
5. Where the Shear Stops: The Plane of Equal Settlement
The shear transfer between the two prisms cannot continue upward for ever, because friction can only act while the two are settling differently. At some height above the pipe they settle by the same amount, the relative movement goes to zero, and the shear stops. Marston called that height the plane of equal settlement, and it is found by solving an equation in which the height appears both inside an exponential and outside it:
e to the power of two K mu times He over Bc, minus two K mu times He over Bc, equals two K mu times r times p, plus one
where He is the height of the plane of equal settlement, r is the settlement ratio and p is the projection ratio, the height of the pipe above the existing ground expressed as a fraction of the pipe height. The equation has to be solved numerically, which is why the original method was published as a set of curves rather than as a formula. If the answer puts the plane above the finished surface, the condition is called complete and the coefficient takes the simple exponential form used earlier. If the plane falls inside the fill, the condition is incomplete and the coefficient picks up a second term for the part of the fill above it.
The projection ratio is where the method meets the site, and its published numbers are worth separating. Design practice ordinarily takes it as 0.5 or 1.0. A pipe bedding estimator’s own manual states that ordinary preparation of the bedding by a contractor produces a projection ratio between 0.7 and 0.9. A designer who solves for 0.5 and a site that delivers 0.9 have not solved the same problem, and the difference is not an error by either party. It is the gap between a design assumption and a construction outcome.
Two published refinements of the method belong here. Marston initially assigned the conservative value of 0.1924 to K mu for every case, then refined the curves to 0.13 for the ditch condition and 0.19 for the projecting condition, after finding that the load formulas were relatively insensitive to both the settlement ratio and the projection ratio. And the load coefficient for a projecting conduit in the incomplete condition is not simply capped at the value it reached at the plane of equal settlement: the second term continues to grow linearly with the height of cover above the plane, which is why the complete condition, with its entirely exponential form, is the one that produces the largest numbers.
6. The Acceptance Test That Is a Gauge, Not a Measurement
A buried flexible pipe is not accepted by reading an instrument. It is accepted by pulling a rigid gauge through it. The mandrel is a ring of a fixed diameter, chosen as a stated percentage below the pipe’s nominal diameter, and the test is simply whether it passes. A state specification that is typical of the practice reads: if no resistance is met at 5.0 percent, the inspection is complete; if resistance occurred at 5.0 percent, the run is re-tested with the mandrel set to the 10.0 percent limit, and if the deflection of the entire run cannot be verified with the mandrel, the engineer is notified immediately.
The test produces a verdict rather than a curve, and the payment schedule behind it turns the verdict into money. A published deduction schedule pays 100 percent of the unit bid price for a deflection between 0.0 and 5.0 percent, 50 percent between 5.1 and 9.9 percent, and requires removal and replacement at 10 percent or above, with a structural analysis permitted as the route to leaving a pipe in the ground. The standards on the other side of the process put the same bands to work as actions rather than as payments: a deflection exceeding 5 percent of the inside diameter requires an evaluation by a Professional Engineer, and a deflection exceeding 7.5 percent requires remediation or replacement.
There is a physical alternative for runs that a person can enter, and it is the one that produces a number. The smallest interior diameter is measured through the centre point of the pipe, at the most deflected portion of the run and at intervals no greater than ten feet, and the loss is expressed as a percentage of the nominal diameter. Where preset monitoring points were established before backfilling, the percentage is taken against the measured diameter recorded at installation instead.
| Test or published boundary | The published value | The quantity the answer comes back in |
| Mandrel, construction acceptance | No resistance at 5.0 percent ends the inspection; resistance sends the run to a 10.0 percent mandrel | A pass or a fail on one date |
| Payment deduction schedule | Full price to 5.0 percent, half price to 9.9 percent, replacement at 10 percent or above | A share of the contract price |
| AASHTO construction specification | Evaluation by a Professional Engineer above 5 percent, remediation or replacement above 7.5 percent | An action, and the ratio between the two bands is 1.5 |
| Physical diameter measurement | Smallest interior diameter through the centre point, at intervals no greater than ten feet | A diameter loss, which is the only one of the four that trends |
| Rigid concrete pipe rating table | Cracking open more than 0.12 inch, which is 3.05 millimetres; invert scaling deeper than 0.25 inch, which is 6.35 millimetres | A crack width or a loss of section, not a diameter |
The pattern across that table is that the published tests answer different questions. The mandrel answers whether the pipe is inside a band today, and it cannot answer how fast it got there. The payment schedule answers what the contractor is owed. The action bands answer what has to be done next. The physical measurement answers how much diameter has been lost, and it is the only one of the four that a reader can turn into a rate. And the rigid pipe table answers a different question again, because a concrete pipe is not graded on a diameter at all.
7. Two Limits for One Pipe: a Crack Width and a Share of the Diameter
The two pipe materials are graded in units that cannot be compared directly, and the published numbers make the difference concrete. A rigid pipe is graded on a crack width in millimetres. A flexible pipe is graded on a deflection expressed as a share of its own inside diameter, which means that the absolute allowance scales with the pipe.
| Stated pipe size | AASHTO nominal inside diameter | Diameter loss at the 5 percent band | Diameter loss at the 10 percent band |
| 15 inches | 14.78 inches | 24.5 millimetres | 43.2 millimetres |
| 24 inches | 23.64 inches | 39.2 millimetres | 69.2 millimetres |
| 36 inches | 35.46 inches | 58.8 millimetres | 103.8 millimetres |
| 48 inches | 47.28 inches | 78.3 millimetres | 138.4 millimetres |
| 60 inches | 59.10 inches | 97.9 millimetres | 173.0 millimetres |
The table carries three separate findings. First, the allowance is a share of the pipe, so the same criterion is a 24.5 millimetre loss on a 375 millimetre pipe and a 173 millimetre loss on a 1.5 metre pipe, a factor of seven across a single product line. A statement that a culvert may deflect by five percent says almost nothing until the diameter is named, in the same way that a statement that a tank has tilted by one tenth of a degree means nothing without the arc it was measured over.
Second, the band is narrower than its name suggests. The nominal inside diameter of a flexible pipe is defined by the material specification as the stated pipe size, and the same specification permits the manufactured inside diameter to be 1.5 percent less than that figure. The mandrel is then set 5 percent below the nominal. Measured against the size the pipe was ordered as, the 5 percent band is therefore a 6.4 percent loss, and the figure is identical at every diameter from 375 millimetres to 1.5 metres, because both deductions are percentages of the same quantity. A pipe sitting at the edge of its acceptance band has given up 6.4 percent of the diameter it was ordered as, not the 5 percent the band is named after.
Third, the construction band and the service band are not the same criterion, and the tighter one is the service band. A full scale field study of high density polyethylene, PVC and metal pipes under highway truck loading found the 5 percent limit adequate during the construction phase and suggested a vertical deflection limit of 2 percent for polyethylene pipe in service, on the basis of the truck load response and the repeated loading effect. Two percent is 40 percent of the construction limit, or read the other way, the construction limit is 2.5 times the service limit. A pipe accepted on the day the fill was finished has been accepted against a criterion two and a half times looser than the one its designers used for its service life.
8. What Decides a Gravity Culvert Is the Slope the Water Needs
Almost none of the preceding applies to the question that decides whether a gravity culvert still works. A culvert that carries a stream under a road has one job, which is to pass the flow without silting up, and the published criterion for that is a velocity rather than a stress or a diameter. The self-cleansing velocity is the minimum average velocity at which the flow will carry its own solids onward instead of depositing them, and each national document that uses the approach publishes it as a single number.
The published values differ by jurisdiction and by sewer type, and the spread is part of the story. The American Society of Civil Engineers’ guidance gives 0.6 metres per second for sanitary sewers and 0.9 for storm sewers, at full or half full flow. British Standard 8005 gives 0.75 metres per second for storm sewers and 1.0 for combined sewers, at full flow. The European standard EN 752-4 gives 0.7 metres per second once a day for pipes below 300 millimetres. The German ATV A 110 rule gives a value that depends on diameter, rising from 0.48 metres per second at 150 millimetres to 2.03 at 3,000 millimetres. And because solids are abrasive, the same literature publishes a ceiling as well: 2.4 metres per second is treated as the maximum allowable velocity in storm and sanitary sewers.
A velocity has to be produced by a slope, so the criterion becomes an angle through the Manning equation. For a circular pipe flowing full the hydraulic radius is one quarter of the diameter, and with a roughness coefficient of 0.013, which is the value given for concrete in the same design literature, the minimum slope for each published velocity follows directly. The values below are for the 0.6 metres per second criterion.
| Pipe diameter | Minimum slope, as a percentage | The same slope as a ratio and as an angle | Fall over a 30 metre barrel |
| 100 millimetres | 0.832 percent | 1 in 120, which is 0.477 degrees | 250 millimetres |
| 200 millimetres | 0.330 percent | 1 in 303, which is 0.189 degrees | 99 millimetres |
| 300 millimetres | 0.192 percent | 1 in 520, which is 0.110 degrees | 58 millimetres |
| 500 millimetres | 0.097 percent | 1 in 1,027, which is 0.056 degrees | 29 millimetres |
| 800 millimetres | 0.052 percent | 1 in 1,922, which is 0.030 degrees | 16 millimetres |
| 1000 millimetres | 0.039 percent | 1 in 2,589, which is 0.022 degrees | 12 millimetres |
| 2000 millimetres | 0.015 percent | 1 in 6,522, which is 0.009 degrees | 4.6 millimetres |
The computed values reproduce a published design table exactly at every diameter that table lists, which is the check that makes the ladder usable: 0.192 percent at 300 millimetres, 0.097 at 500, 0.076 at 600, 0.052 at 800, 0.039 at 1,000 and 0.030 at 1,200. The same design literature also publishes maximum slopes for a velocity of 2.4 metres per second, and the minimum and the maximum together define the band a designer has to work inside.
Read as angles, the criterion moves across a factor of 54 from the smallest pipe to the largest, from 0.477 degrees at 100 millimetres to 0.009 degrees at 2 metres. Read as a length, the consequence is more arresting still. A 30 metre barrel laid at the self-cleansing slope for its size falls 250 millimetres from end to end at 100 millimetres diameter and 58 millimetres at 300 millimetres, but only 12 millimetres at one metre diameter. On a one metre culvert the entire drainage fall over thirty metres is about a centimetre, so a settlement of six millimetres at one end has used half of it, not because the pipe has been overstressed but because the water no longer has a gradient to run down.
It is worth putting those numbers beside a criterion from a different industry, because the comparison is not the one a reader expects. The tightest settlement criterion published for a flat bottomed storage tank is a planar tilt of 1 in 1000, which is 0.057 degrees. The self-cleansing slope of a 300 millimetre concrete pipe at 0.6 metres per second is 1 in 520, or 0.110 degrees, which is 1.92 times that tank criterion. The same criterion on a one metre pipe is 1 in 2,589, or 0.022 degrees, which is 0.39 times it. One family of criteria, taken from a single design table, straddles a number taken from a completely different standard.
The instrument terms land differently at the two ends of that ladder, and the difference is worth stating in full because it decides whether a tilt channel is useful at all. The published datasheet of the wireless tiltmeter most often specified for this class of work gives a resolution of 0.001 degree, an accuracy of 0.005 degree, and a zero point temperature drift of 0.001 degree per degree Celsius. On a 300 millimetre culvert, whose criterion is 0.110 degrees, the resolution is 0.9 percent of the criterion, the accuracy is 4.5 percent, and the drift over a 40 degree Celsius swing is 0.040 degrees, which is 36 percent of it. On a one metre culvert, whose criterion is 0.022 degrees, the same three terms are 4.5 percent, 22.6 percent and 181 percent. On the large culvert the instrument’s own zero stability across a seasonal temperature swing is worth nearly twice the slope the water needs, and the default alarm angle of 3 degrees is 136 times that criterion.
9. The Row of the Inspection Form That Has Words Instead of Numbers
A culvert already in service is assessed on published scales, and the scales are more quantitative than a reader might expect. The federal rating guideline grades the barrel from 9 down to 0 on alignment, settlement, joints, structural condition and scour. Concrete barrel tables place cracking open more than 0.12 inch, invert scaling deeper than 0.25 inch and invert scaling deeper than 0.5 inch at three separate rating levels. Joint tables place minor openings, differential movement with separation and significant infiltration, and significant openings with dislocated joints exposing fill material at three more. Settlement tables place minor settlement or misalignment, considerable settlement or misalignment, and severe movement or differential settlement with loss of fill at three more again. Blockage is rated as a share of the cross sectional area of the opening, and sediment as a depth relative to the rise of the pipe.
Then there is the row for the headwall and the wingwall, and that row is written differently. The published scale reads: little or no cracking, rotation or displacement; then minor rotation and displacement with a gap in the barrel seam; then significant displacement at cracks, or wall rotation causing a gap at the wall to barrel interface greater than 4 inches, which is 102 millimetres; then partially or totally collapsed. A state bridge inspection manual adds, in the same section, that wingwalls should be inspected to ensure that they are in proper vertical alignment, and that they may be tilted due to settlement, slides or scour.
Rotation is named on that row and no angle is given for it. Every other item on the same form has a number attached to at least its more severe levels, and the one item an angle channel is best suited to is written in words. This is the reverse of the situation in the rest of this series, where a standard publishes a number and the instrument has to be good enough to reach it. Here the instrument can produce a number that the standard does not ask for, and the honest use of it is to supply, from the site’s own record, the magnitude that the published scale leaves open.
What an angle channel contributes on a buried structure follows from that, and it is narrower than a product page would suggest. It makes the rotation of the headwall and wingwall continuous where an inspection makes it periodic. It separates a rotation that is still developing from one that finished before the first visit. And during construction it watches the load being applied, because the deflection of a flexible pipe builds as the fill goes up, the published limit applies during the fill rather than after it, and a headwall reading taken while the embankment is being placed is a reading about the load rather than about the pipe.
What it does not produce is the other three units. The diameter loss that the mandrel gauges and that the tape measures is a convergence measurement. The crack width that places a concrete barrel on the rating scale is a crack measurement. The share of the opening that is blocked and the depth of sediment in the barrel are hydraulic measurements. A rotation channel substitutes for none of them, and a scheme that reads only rotation has chosen to watch the one row of the form whose scale is verbal.
The company’s published record in this family is drainage and buried infrastructure rather than the culvert itself. At the Zhanghuabang East drainage system in Baoshan District, Shanghai, a scheme serving about 288 hectares and combining a rainwater pump house, a sewage pump house and a storage tank on one constrained site, the pump house is 10.7 metres deep and the storage tank below it is 15.2 metres deep; twelve inclinometer casings were installed in advance, each 30 metres deep, and read once a day through the construction period with a Bluetooth single-operator inclinometer, model ZCT-CX03E-JC230, whose dual axis probe is published at 0.005 degree accuracy with a system repeatability of 1 millimetre over 30 metres. On a bored underground channel in Hangzhou, a 5.124 kilometre tunnel in double tube with four lanes and a design speed of 60 to 80 kilometres per hour, LoRa wireless tilt sensors, model ZCT800ML-215SR, were mounted on the structures to be watched, with a published accuracy of 0.005 degree and a gateway range of 3 to 5 kilometres. Neither deployment is a culvert, and no design role is claimed for either. What they establish is the class of structure this article has been about: buried, unpowered, and read by an instrument that sits inside the ground rather than on a gable.
Frequently Asked Questions
- How much settlement or deflection can a buried culvert tolerate? There is no single figure, because three different published criteria answer three different questions. A flexible pipe is limited to a share of its own inside diameter, so the allowance is 24.5 millimetres on a 375 millimetre pipe and 173 millimetres at 1.5 metres, and that band is measured against a nominal diameter which the material specification itself defines as 1.5 percent below the ordered size. A rigid concrete pipe is limited by crack width, with a published rating table placing cracking open more than 3.05 millimetres at one level. And a gravity culvert is limited by whether the water still has enough slope to carry its sediment, which on a one metre pipe over a thirty metre barrel is about 12 millimetres of fall in total. Quote all three, and name the diameter every time.
- Why do two identical pipes under the same embankment carry different loads? Because the load depends on how the pipe was placed, not only on the fill. The published method derives it from the relative settlement of the soil column directly above the pipe and the columns beside it, and the sign of that difference decides whether friction transfers load onto the pipe or away from it. A pipe in a narrow trench carries less than the weight of the soil above it. A pipe placed at ground level and then covered by an embankment carries more, reaching about 1.88 times that weight at a cover of three pipe widths with the conservative coefficient, and roughly 1.9 times where Marston measured it. The published range of the coefficient moves the answer by about a third in either direction, so two offices choosing different soil types from the same table will not agree.
- My culvert passed the mandrel test when it was built. Is it still within tolerance? That result is a statement about the day it was taken. The mandrel is a rigid gauge set 5 percent below the nominal diameter, so passing it means the run was inside that band at that time, and it says nothing about the rate at which the diameter is changing. The construction limit and the published service suggestion are also different numbers: a full scale field study of polyethylene, PVC and metal pipes under highway truck loading found the 5 percent limit adequate during construction and suggested 2 percent for polyethylene in service. Turning a verdict into a trend needs a measurement rather than a gauge, which in practice means reading the smallest interior diameter at fixed points at intervals, or reconstructing the shape of the barrel from its rotation profile where a chain of sensors spans it.
- Where should a tilt sensor be mounted on a culvert, and what does it tell you? The headwall and the wingwalls are the usual answer, both because they rotate visibly with embankment settlement and with scour at the outlet, and because rotation is the one item on the published assessment form whose scale is written in words rather than numbers. A sensor there makes a periodic judgement continuous and separates a rotation that is still developing from one that finished. If the question is the barrel rather than the ends, the measurements that answer it are a convergence reading and a crack width, and a rotation channel replaces neither. Only where a chain of sensors spans the barrel does the rotation profile reconstruct the shape of the pipe, and the conversion from there follows the same segmental summation that any deflection profile uses.
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