FIELD OF THE INVENTION

The present invention relates to a method for determining the structural integrity of an infrastructural element, comprising the step of:measuring deformations, such as displacements or rotations, during a predetermined time period with deformation measurement means arranged at or near a main structural body of the infrastructural element, in particular supports of the main structural body.

BACKGROUND OF THE INVENTION

In the Netherlands infrastructure has always been important with regard to its status as transport country with Rotterdam as Europe's largest port. There has been a large infrastructural expansion in-between the sixties and eighties. Public authorities face a major replacement task given that most of the existing bridges are designed to serve for 50 years. This, combined with a large historical increase in traffic frequency and loads combined with new insights regarding structural behaviour, makes that the performance of some existing bridges can be questionable. Still, there isn't an indication of structural failing in the near future, so it is clear that the actual capacity of existing bridges is not directly related to a service life of 50 years the bridges were designed for.

Till now, for far most of the existing bridges qualitative and non-continuous methods are used to determine degradation. These methods are not able to give an accurate assessment of the real structural performance of a structure. Therefore, it can be favourable to apply a “structural health monitoring” (SHM) system on civil structures to conclude whether or not an intervention is mandatory (Cremona 2014). This makes that decisions regarding operating conditions can be made based on quantitative data. In addition to the re-evaluation of older existing bridges, SHM can be used to measure the load response of new bridge techniques and/or materials.

Patent literature discloses several such “smart” methods, in particular methods to investigate the bridge's structural integrity based on local deflection measurements.

For instance, Chinese Utility Model CN 2040 074 99 U discloses an automatic bridge monitoring system for measuring local structural deflection based on wireless sensors.

Chinese Utility Model CN 2014 38141 U furthermore discloses a dynamic bridge deflection test device that provides long-term monitoring of the deflection of the bridge deck by using magneto-telescopic deflection sensors arranged below the bridge deck.

A problem, however, with such methods is that a lot of local phenomena are to be measured and a complex system of sensors, data transmission networks, analysis systems, et cetera, is thus required to provide the desired monitoring system. Such complex systems are of course prone to malfunctioning and are expensive to install and maintain.

Thus, there is a need for a cheaper, more “global” monitoring method for infrastructural elements, such as bridges, that does not require the installation of complex systems incorporating a multitude of local sensors and associated data systems.

SUMMARY OF THE INVENTION

Thereto, according to the invention the method is characterized by:determining the load configuration of the main structural body over the course of the predetermined time period, such as the load configuration concerning the loading perpendicular to a longitudinal direction of the main structural body,calculating the bending stiffness (EI) of the main structural body over the course of the predetermined time period, from the load configuration and deformations measured by the deformation measurement means, andcomparing the bending stiffness (EI) at the end of the predetermined time period to the bending stiffness (EI) at the start of the predetermined time period to establish a difference in bending stiffness (EI) over the course of the predetermined time period.

The inventors have shown the insight that due to deterioration of the infrastructural element, material properties and/or geometrical properties of the main structural body, such as the bridge deck in case of a bridge, will change.

These changes will result in a change of the bending stiffness (EI) of the main structural body, such as the bridge deck. This change in bending stiffness can then be used as a “global” indicator of the amount of occurred damage.

The bending stiffness can be found as a relation between the deformations measured at certain positions at or near the main structural body and the load configuration on the main structural body.

The above method according to the invention requires only relatively few deformation measurement means (sensors) at relatively few locations. Consequently, associated data transmission systems, analysis systems, et cetera, can be much simpler in design, therefore being less prone to malfunctioning and therefore being cheaper to install and maintain.

Although the above method is highly suitable for use with bridges, the infrastructural element can also be a quay wall, a dike, a water supply duct, a sewer system duct, an electricity line, a road, a lock or a foundation, or any other infrastructural element.

However, advantageously the infrastructural element is a bridge, the main structural body is a bridge deck and the supports are bridge supports.

In case the load configuration is not known, the load configuration can be derived from reaction forces measured by force measurement means (although, to be factually correct, displacement measurement means will mostly be used to determine such forces) arranged at the supports.

Preferably, the bridge supports comprise bridge bearings and the force measurement means are arranged at the bridge bearings, wherein the force measurement means establish the force at the bridge bearing from the elastic deformation and the spring constant of the bridge bearing. The function of the bridge bearings is to transfer forces from the superstructure to the substructure. There are several different bearing types that are being used nowadays or in the past to accommodate different loading and movement requirements. Since (reinforced) elastomeric bearing pads have by far the largest market share for common concrete road bridges, these are preferably to be used. Also, unreinforced elastomeric bearings, pot bearings, spherical bearings and the like can be used.

In an embodiment of the aforementioned method, the bending stiffness (EI) of the bridge deck over the predetermined time period is calculated based on a moving load passing over the bridge deck, such as a train or a car, comprising the steps of:determining the type of load,determining the position of the load,determining the speed of the load,calculating influence lines,establishing kinematic relations between the load configuration of the bridge deck caused by the load and the forces measured by the force measurement means, andcalculating the bending stiffness (EI) of the bridge based on the load configuration resulting from the load and the deformations measured by the deformation measurement means.

The above method advantageously allows to determine the load history of the main structural body, such as the bridge deck, from the reaction force history of this bridge deck as well as a method to determine the bending stiffness when this load history is known. When the load is a vehicle having axles, the axle loads usually have a static and a dynamic component. In most situations the static axle load is by far the largest part of the total axle load. Over the length of for instance the bridge deck this component will be constant. The magnitude of this static component will range from 2 kN up to 115 kN for regular road traffic. Since overloading of trucks is a regular occurrence this range can be expanded up to around 250 kN. Often there is also a noise component. The noise component is the part of the measured axle load that can't be explained by the two previously mentioned components. Noise can be caused by lots of factors, but the most important ones are axle dynamics with other causes than the expansion joint, sensor noise and weather influences.

For a one-dimensional main structural element, e.g. a bridge, the axle loads are preferably to be modelled as point loads which are constant over the span of the bridge. This means that both the dynamic component and noise are excluded from the model. The point load will move over the length of the bridge deck with a constant speed v.

For three-dimensional models, the axle load can be assumed to be equally distributed over the wheels. Again the load will be constant over the length of the bridge deck, meaning that the dynamic component and noise are excluded from the model and the load will move over the length of the bridge deck with a constant speed (v).

Different models can be used to model the main structural body, in casu the bridge deck, such as:Simply supported one dimensional beamInfinitely stiff plate on spring supportsIsotropic plate on stiff supportsOrthotropic plate on stiff supportsOrthotropic plate on spring supports

Many other models are conceivable though.

Two dimensional models are preferably considered with only two supports per side, three supports per side, and seven supports per side. The system with two supports per side is the most simple system for a bridge deck possible. It is expanded to three supports per side because this is the most simple system that is statically indeterminate along the width of the bridge deck. A system with seven supports per side is modelled because of the increased complexity and resemblance to existing bridge decks.

Preferably, the bridge deck is modelled as a simply supported beam. From the given model the support reactions at e.g. a support A and support B can be determined as a function of time. To do this, first the influence lines for the support reactions are determined. These influence lines are given by the magnitude of the support reaction at the concerning support resulting from a unit load located at a location x along the main structural body. From these influence lines, which are a function of x, the influence lines are determined as a function of time. Multiplying the results with the point load of a single axle Pngives the support reactions as a function of t for the passing of a single axle. The summation of N of these equation results in the total support reaction at A and B as a function of time. The magnitude of the axle load is equal to the change in support reaction A upon entering the bridge or the change in support reaction B upon leaving the bridge (ΔRi,Aand ΔRi,B). This change is also equal to the change in the total reaction force (Ri,A+B). By measuring these changes for each individual axle or axle group it is theoretically possible to determine the magnitude of the axle loads or axle group loads.

By looking for a two corresponding changes in support reaction at support A and support B (ΔRi,Aand ΔRi,B), or two corresponding changes in the sum of support reactions (Ri,A+B) it is be possible to identify the time moment at which an axle enters ti,eand leaves ti,lthe bridge. From these two time moments the axle speed can be determined:

vi=Lti,l-ti,e.
As we now have a time moment of entering the bridge and a speed the x-location can be calculated at any time moment:
xi=vi·(t−ti,e)

It should be noted that this method to determine the x-location of an axle will only work under the assumption that there are no axles overtaking each other while on the bridge.

Alternatively, the bridge deck can be modelled as an infinitely stiff plate on spring supports, i.e. a two-dimensional model. A very simple two dimensional model for a bridge deck is an infinitely stiff plate on spring supports. The previously described axle can be modelled on the bridge deck.

For the infinitely stiff plate some additional assumptions have to be made, such as: no dynamic effects/smooth bridge joint, time on bridge is very short, ratio

EIk
is very large, no changing lanes while on the bridge deck, the load on both tires of an axle is equal and the axle track is set to a constant value.

The other models, such as an isotropic plate on spring supports, will not be further discussed here.

Finally, the bending stiffness (EI) can then be determined. The models that are preferably to be used are the:Simply supported one dimensional beam, and theOrthotropic plate on spring supports

These models will be further explained with reference to drawings in the detailed description.

For the same model for the simply supported beam as described earlier, the equivalent bending stiffness will be calculated as a function of the loading determined in the same section, and the measured rotations at the support. To do this first the influence line for rotations at a single support is determined. This influence line can be established by applying well-known engineering formulas (in Dutch known as “vergeet-me-nietjes”), then:

For⁢⁢0>x>LIφ,supportA=0For⁢⁢0<x<LIφ,supportA=-x⁡(L-x)⁢(2⁢L-x)6⁢EIL=-x3+3⁢Lx2-2⁢L2⁢x6⁢EIL

Multiplying the influence line with the magnitude of the load n, Pn, and changing x to xngives the rotation at the support due to load n. Summing up all these rotations for load n=1 to n=N gives us the total rotation.

For⁢⁢0>x>LφA,n=0For⁢⁢0<x<LφA,n=Pn·(-xn3+L2⁢xn)6⁢EILφA,n=∑n=1N⁢(φA,n)=∑n=1N⁢(Pn·(-xn3+L2⁢xn)6⁢EIL)=1EI⁢∑n=1N⁢(Pn·(-xn3+L2⁢xn)6⁢EIL)
Now the bending stiffness can be determined as:

EI=1φ⁢⁢A⁢∑n=1N⁢(Pn·(-xn3+L2⁢xn)6⁢⁢L)

The output variables calculated before with the measured support rotations can be used to determine the bending stiffness of the simply supported beam as a function of time.

The same method can be applied for the orthotropic plate on spring supports, with the only difference that for each individual lane a separate influence line has to be determined. These influence lines are preferably to be determined by using computer software, such as Scia Engineer (instead of hand calculations). This model will be explained in detail with reference to drawings in the detailed description.

The influence lines for the rotations at the support can be found by performing a fourth order polynomial fit for the obtained data points. A fourth order polynomial has been chosen because this gave a near-perfect fit for the data points. A higher order polynomial would of course give a better fit but this would make the equations harder to handle. This results in the following equations:
Iφ,Lane 1 & 4=9.0071·10−11·x4−2.8203·10−9·x3−1.9723·10−8·x2+8.0688·10−7·x−2.7327·10−7
Iφ,Lane 2 & 3=−5.7965·10−11·x4+4.8628·10−9·x3−1.5914·10−7·x2+1.7249·10−6·x−6.8949·10−7

Now to find a value for the bending stiffness (EI) the same procedure as for the simply supported beam model is followed. However, this time there is no EI in the equation. To solve this problem the following ratio is added:

EItheoreticalEIeq.
In this ratio EI is the theoretical bending stiffness of the bridge deck used in e.g. the Scia model, while EIeqis the bending stiffness to be obtained using the method:

Iφ,Lane⁢⁢1&⁢4=⁢⁢EItheoreticalEIeq⁢(9.0071·10-11·x4-2.8203·10-9·x3-1.9723·10-8·x2+8.0688·10-7·x-2.7327·10-7)Iφ,Lane⁢⁢2&⁢3=EItheoreticalEIeq⁢(-5.7965·10-11·x4+4.8628·10-9·x3-1.5914·10-7·x2+1.7249·10-6·x-6.8949·10-7)

Again the output values as calculated earlier, together with the measured support rotation at the indicated support, can be used to extract values for the EIeq. These values should be looked at individually per lane.

In practice it would be difficult to find the exact influence lines from a theoretical model due to the model parameters being largely unknown. It would be easier to obtain these lines by means of calibration. This would be done by having a vehicle of known, large weight with a known axle configuration and speed pass over the bridge deck and measuring the support rotations. Now the resulting rotations should be a superposition of a multiple influence lines for the considered lane.

If necessary, the aforementioned method may further comprise the step of further inspecting the infrastructural element when the difference in bending stiffness (EI) has exceeded a predetermined value, such as for fatigue, cracks or geometrical damage.

