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Budelmann, Holst & Proske: Proceedings of the 9th International Probabilistic Workshop, Braunschweig 2011

1

Assessment of Engineering Structures based on Influ-

ence Line Measurements & Model Correction Approach

Roman Wendner, Alfred Strauss,

Alexander Krawtschuk, Thomas Zimmermann, Konrad Bergmeister

Institute for Structural Engineering, University of Natural Resources and Life Sciences,

Vienna

Abstract: In structural bridge engineering, maintenance strategies and thus

budgetary demands are highly influenced by construction type and quality of

design. Nowadays bridge owners and planners tend to include life-cycle cost

analyses in their decision processes regarding the overall design trying to opti-

mize structural reliability and durability within financial constraints. However,

efforts to reduce maintenance costs over the expected lifetime by adopting well

established design principles lead to unknown risks concerning for instance

boundary conditions. Smart permanent and short term monitoring concepts can

reduce the associated risk of new design concepts by observing the perfor-

mance of structural components during prescribed time periods. The objectives

of this paper are the discussion of concepts for (a) the effective incorporation

of monitoring data in model updating procedures by means of the influence

line and the model correct factor concept, (b) the investigation of the function-

ality of monitoring systems including error tracking, and (c) the inverse identi-

fication and evaluation of sensor properties and monitoring values. The

proposed methodology will be applied to an integrative monitoring system ap-

plied on an existing three-span joint less bridge structure.

1 Introduction

In recent years major advances have been accomplished in the design, modeling, analysis,

monitoring, maintenance and rehabilitation of civil engineering systems. These develop-

ments are considered to be at the heart of civil engineering, which is currently undergoing

a transition towards a life-cycle and performance oriented design philosophy. In addition,

monitoring is a key element in a life-cycle design and assessment philosophy. The general

term “monitoring” represents all types of direct acquisition, observation and supervision of

an activity or a process. One of the main tasks of monitoring is the corrective intervention

Wendner et al.: Assessment of Eng. Structures based on Influence Line Measurements & Model Correction Approach

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if all or some of the processes which are observed don’t develop as assumed, e.g. violating

predefined thresholds. Monitoring may include (a) the production quality control of mate-

rials, structural components, and structures, and (b) the identification and observation of

degradation processes in local structural details [1] or global structures by observing me-

chanical or energy related quantities. The latter monitoring target concerns prognosis pro-

cedures that must include beyond a monitoring or advanced sensing technology, data

interrogation procedures for damage detection, novel model validation and uncertainty

quantification techniques, and reliability-based decision-making algorithms [1]. However,

there is a large interest [2, 3] in the investigation and development of monitoring systems

in order to increase their ability in performance forecast matters related i.e. with the identi-

fication of defects and degradation processes. Promising statistical and analytical models

have been already developed for the optimization of monitoring periods and sensor loca-

tions [4, 5, 6] and for monitoring based prediction models. These models are partly based

on monitored extreme data probability distribution functions (PDFs) and Bayesian theorem

in order to enable a direct incorporation of monitoring information into structural perfor-

mance assessment and lifetime prediction [7]. In general, monitoring campaigns and asso-

ciated performance and lifetime assessment models are based only on a few physical

quantities. Nevertheless, maintenance processes should guarantee the compliance of a se-

ries of design code specifications during the whole lifetime of a structure. The safety and

integrity of the structural system is ensured by preventing the performance indicators from

crossing their thresholds [8]. In consequence, a comprehensive life-cycle performance as-

sessment requires a transformation of code specifications in limit state formulations with

its associated random variables in order to allow (a) the code specific definition of perfor-

mance on a reliability level and (b) the incorporation of monitored quantities in perfor-

mance indicators. The aims of this paper are the analysis of the functionality, any potential

sources of failure and failure modes and effects analysis of a monitoring system installed

on an integral bridge and to systematically determine and analyze any potential failure

causes, failure effects, and worst case scenarios of concatenated failure events in order to

derive measures for the installed monitoring system.

2 Principles of Fiber Optical Sensor Systems

2.1 General

Fiber optical sensing is a comparably new sensing technology with two main areas of ap-

plication, temperature and strain measurement [9]. The basic element of fiber optical sys-

tems is the optical fiber itself, which is a usually cylindrical guidance system for light. An

optical fiber is a cylinder of transparent dielectric material surrounded by another dielectric

material with a lower refractive index, which is called cladding, as well as a third protec-

tive layer. A beam of light entering such a fiber from one end face is trapped inside en-

sured by the Snell’s law in optics, see equation (1), as long as the reflection angle θ is

larger than the critical angle of reflection θc defined by the ratio between the refractive in-

dices n of the outer layer and the core of the optical fiber [9].

Budelmann, Holst & Proske: Proceedings of the 9th International Probabilistic Workshop, Braunschweig 2011

3

1

2

sin n

n

c

(1)

According to WHEELER et al. [9] the main advantages of fiber optic systems are immunity

to electromagnetic and radio-frequency interference, high accuracy, small size, high capac-

ity, data purity, and multiplexing capability. The last aspect means that signals from vari-

ous sensors can be carried simultaneously, reducing cabling significantly.

2.2 Fiber Optic Sensing Technologies

Most physical properties can be detected with fiber optical systems ranging from light in-

tensity over displacement, pressure, temperature, strain, flow, magnetic field to chemical

composition [10]. Fiber optical sensors can be divided into intrinsic and extrinsic sensors

[9]. In case of intrinsic sensors the fiber itself performs the measurement, whereas in ex-

trinsic sensors an additional device attached to the fiber performs the actual measurement.

Furthermore phase-modulated and intensity-modulated sensors can be differentiated. The

most popular and promising sensing technologies depending on the type of application

comprise according to INAUDI [11] Microbending sensors, Fibre Bragg grating sensors,

Interferometric sensors, Low Coherence sensors and Brillouin sensors. Further information

regarding fiber optical sensing technologies can be found in [12]. The main focus in this

paper is placed on Fiber Bragg grating sensors (FBGs), which are typical wave-length-shift

based sensors that can be applied in temperature, strain and displacement measurement, see

also [13]. FBGs allow a localized measurement of a chosen physical property in the grating

area of typically only a few centimeters length. This grating reflects light at a specific

wavelength defined by the spacing of the grating and the materials refractive index n. If

the optical fiber is subjected to strain (mechanical or temperature related) the spacing of

the grating and thus the wavelength of reflected light changes.

2.3 Strain-FBG: Calibration and Data Transformation

As already mentioned, Fiber Bragg Grating (FBGs) sensors use the fact, that strains acting

on an optical fiber influence the optical characteristics of the grating imposed on an optical

fiber [11]. The grating specific reflected wavelength changes with acting mechanical

strains which results in a shift in the reflected wavelength that is directly proportional to

the acting strain variation . Consequently FBGs allow for a localized measurement of

the physical properties strain and temperature depending on the size of the grating and its

influence length that is determined by the construction of the sensor. Every sensor reflects

light at a unique and predefined wavelength depending on the imposed grating, which al-

lows the direct spatial allocation of the measured property within a serial system (frequen-

cy multiplexing). The wavelength shift (t) is calculated as difference between currently

reflected wavelength (t)and a reference wavelength (T0)at a known temperature T0 ,

see equation (2).

)()()( 00 Ttt

(2)

Wendner et al.: Assessment of Eng. Structures based on Influence Line Measurements & Model Correction Approach

4

Taking into account the actual temperature T(t) at time t and the respective effects on the

measurement, total strains can be obtained by equation (3), where sε represents the strain

sensitivity of the sensor, which typically amounts to values about 1.2 pm/. The tempera-

ture influence on the wavelength shift is specified by a thermal response factor s

with

values around 10 pm/°K. Reference wavelength (T0) and reference temperature T0 are

ordinarily specified in a calibration sheet or can be determined at site at the start of the

measurement campaign in case only relative values are of interest.

s

sTtTTt

s

stTt

tT

T))(()()(

)()(

)( 000

(3)

In case of temperature sensors the optical fiber is loosely installed in a sensor casing in

order to exclude any kind of mechanical strain in the grating area. Consequently the spac-

ing of the grating is solely influenced by the temperature of the fiber and thus the tempera-

ture field in the vicinity of the sensor. A change in the spacing caused by a temperature

variation T leads to a wavelength shift T, which however is not linearly dependent on

the temperature variation. Instead a polynomial equation of second order is used to decent-

ly capture the relationship. The empirical transformation equation thus yields to

32

2

1)()()( atatatT (4)

with the coefficients a1 to a3 specified in the calibration chart together with the reference

wavelength at a given temperature, usually 20°C.

2.4 Possible Sources of Errors

Errors in monitoring data basically can be random or systematic and can concern both ab-

solute and relative values depending on the source of the error. Typical systematic errors in

data are caused e.g. by a wrongly assumed sensor location or incorrect sensor calibration.

Recent experience with different monitoring systems has shown that the most severe errors

in monitoring data are already caused during installation [4]. Sources for this range from

bad application of individual sensors over an incorrect documentation of the respective

locations to unwanted effects during construction works (e.g. compression of a concrete

strain sensor during concrete pouring). Unfortunately these effects can hardly be excluded

based on theoretical considerations and available monitoring data and need be investigated

experimentally [14]. Systematic errors in monitoring data can furthermore originate from

an uncertain behavior of the sensor itself. A fiber optic concrete strain sensor for instance,

loosely fixed to a rebar, may record the average concrete strain, steel strain or something in

between depending on the load level [15]. Additionally some uncertainty in the strain read-

ings may be introduced by the accuracy of the temperature compensation, especially if no

closely located temperature sensor is available. Furthermore the fiber optic temperature

sensor itself may to a certain extent be influenced by the mechanical strain state, consider-

ing e.g. its location in a cracked section. As a consequence the layout of the monitoring

system should account for some redundancy in order to (a) avoid a complete loss of e.g.

reference temperature information, and (b) allow a cross-verification of strain or tempera-

Budelmann, Holst & Proske: Proceedings of the 9th International Probabilistic Workshop, Braunschweig 2011

5

ture measurements by means of physical models or statistical tools such as correlation

analysis.

3 Influence Line and Model Correction Factor Methods

3.1 Influence Lines

Influence lines serve for the explicit determination of a structure specific mechanical quan-

tity at a defined location, such as an internal moment, shear force or deformation, due to a

defined load magnitude and position. In other words, influence lines allow the easy deter-

mination of mechanical quantities for individual loads and load combinations without the

use of complex equilibrium and compatibility conditions as used in classical mechanics for

statically determined and undetermined systems [17]. In particular, the mechanical quanti-

ties due to specific loads or load combinations can be obtained from the load associated

deflection of the influence lines by the following energy based general approach:

W*= Wa*+ Wi* = Zi

i + P(x)

w(x) –

Z

dx (5)

with Wa,i*= external or internal work, Zi = actual internal force in the entire system due to

the force P = 1, i = virtual mutual deformation of the inserted degree of freedom of the

associated mechanical quantity of interest, w(x) = virtual deflection of the influence lines

on the location and in the direction of P due to i = -1, and = virtual deformation of the

entire system due to i = -1. Further details regarding this procedure are documented in

[8]. For instance, Figs. 1(a) and 1(b) portray numerically simulated influence lines for a

jointless bridgesystem.

3.2 Model Correction Factors

In general, an initial model layout for the description of e.g. engineering structures will not

capture the real behavior due to aleatory and epistemic uncertainties and weak knowledge.

These uncertainties can be reduced by engineering knowledge and their experience as well

as by computationally intensive model updating procedures using recorded model re-

sponse. In addition, uncertainties can also be taken into account by model correction fac-

tors according to EN1990 Appendix D “Basis of structural design – Design assisted by

testing” [18]. The model correction factor based evaluation requires the development of a

design model for the theoretical monitored quantity mt of the member or structural detail

considered and represented by the model function

mt = gmt(X) (6)

The model function has to cover all relevant basic variables X that affect the design model

at the monitoring locations. The basic parameters should be measured or tested. Conse-

quently, there is interest in a comparison between theoretically computed and monitored

values. Therefore, the actual measured or tested properties have to be substituted into the

Wendner et al.: Assessment of Eng. Structures based on Influence Line Measurements & Model Correction Approach

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design model so as to obtain theoretical values mti to form the basis for a comparison with

the recorded values mei from a monitoring system. If the design model is exact and com-

plete, then all of the points will lie on the line = /4. In practice the points will show

some scatter. However the cause of any systematic deviation from that line should be in-

vestigated to check whether this indicates errors in the monitoring system or in the design

model.

Fig. 1: Numerically generated influence lines for the three span abutment free bridge

S33.24 along lane 1 for (a) the stresses associated with sensor d7u and (b) the

stresses associated with sensor d90o

Nevertheless, an estimation of the mean value correction factor b presents the appropriate-

ness of the developed model. The probabilistic model of the monitored quantity m can be

represented in the format:

m = b mt (7)

where b = “Least Squares” best fit to the slope, given by

b = mei mti / (

mti mti) (8)

In addition, the mean value of the theoretical design model, calculated using the mean val-

ues Xm of the basic variables, can be obtained from:

mm = b mt (Xm) = b gmt (Xm)

(9)

The mean value mm associated uncertainties are captured by its coefficient of variation,

which can be determined by error terms. In addition to this consideration in the scattering

quantities, there is the requirement for a compatibility analysis, in order to check the as-

sumptions made in the design model, see STRAUSS ET AL. [8].

3.3 Performance Indicators

It is obvious to assign performance indicators to the recorded quantities of the installed

sensors of a monitoring system. In particular, the sensor associated performance indicators,

7

such as the model correction factor b and the characteristic model quantity mk, provide the

basis for (a) the assessment of the ability of the numerical or analytical model to capture

the realistic performance, (b) the description of the time variable performance, and (c) the

assessment of the performance characteristic with respect to given code specific limit

states. For the determination of the quantity mk see e.g. [8, 18].

4 Case Study on the Abutment free Bridge system S33.24

The joint less Marktwasser Bridge S33.24 is a foreshore bridge leading to a recently erect-

ed Danube crossing which is part of an important highway connection to and from Vienna.

The structure actually consists of two structurally separated bridge objects, the wider one

of which allows for five lanes of highway traffic. The S33.24 is a three-span continuous

plate structures with span lengths of 19.50 m, 28.05 m and 19.50 m orthogonal to the

abutment (20.93 m, 29.75 m, 20.93 m parallel to the main axis) as is shown in Fig. 2. The

top view of the so called “Marktwasser Bridge”, see Fig. 2(a), shows a crossing angle of

74° between center-line of the deck slab and abutment-axis. Further design aspects of this

non-prestressed construction are monolithical connections between bridge deck, pillars and

abutments as well as haunches going from a constant construction height of 1.00 m to

1.60 m in the vicinity of the pillars to account for the high restraint moment. The deck

width ranges from 19.40 m to 22.70 m excluding two cantilevers of 2.50 m length each.

The entire structure is founded on four lines of drilling piles with length of 12.00 m and

19.50 m respectively. Further information about the geometry of the structure is given in

[20].

4.1 Monitoring System

As the design and the performance of jointless structures depend not only on dead load and

the traffic loads but especially on constraint loads resulting from temperature, earth pres-

sure and creep/shrinkage processes an integrative monitoring concept had to be developed

covering the superstructure, its interaction with the reinforced earth dam behind the abut-

ment and the dilatation area above the approach slabs. In total 5 different sensor systems

consisting of strain gages, temperature sensors and extensometers were permanently in-

stalled [16]. More details are reported in KAMPEL AND KEHRER [19].

Due to the different nature of the relevant load cases the instrumentation of the deck slab

had to ensure that both a constant and linear strain distribution across the cross section can

be detected. Similarly by a proper placement of the temperature sensors constant tempera-

ture and temperature gradient were to be measured [20]. Based on those requirements the

contractor designing the monitoring system opted for a fiber optic sensor (FOS) system

consisting of 12 strain and eight temperature sensors, which were placed in the southern

span’s deck slab, as shown in Fig. 2(b). For redundancy as well as installation reasons two

independent FOS strands were placed in the top and the bottom reinforcement layer of the

southern span’s deck slab, see Fig. 2(c). All temperature and strain sensors are equally dis-

tributed between upper and lower reinforcement layers. The location of the temperature

8

sensors allows capturing differences in the environmental conditions due to solar radiation,

wind and the development of cold air pockets below the deck. Strain sensors d2u, d3u and

their counterparts d2o up to d7o provide information about the strain contribution from dead

load, creep/shrinkage and temperature gradient. The placement of sensors d7u, d9u and d9o

was governed by the goal to determine the zero-crossing of the moment distribution

whereas d10o and d10u are mainly affected by a constraint moment near the pillar. The index

o in the sensor names indicates upper position and u lower position respectively.

Fig. 2: Monitoring installation plan of the bridge system S33.24; (a) top view indicating

the traffic lanes and instrumented area; (b) longitudinal cut including sensor

placement; (c) serial system topology of fiber optical monitoring system [8]

4.2 Mechanical Model

During design of the monitoring system a 3D finite element (FE) model was set up in

SOFISTIK in order to (a) optimize the sensor location with respect to the expected struc-

tural response and (b) allow for a meaningful data interpretation. The abutments, columns

and deck slab were discretized using shell elements. The four rows of drilling piles were

modeled by means of beam elements resulting in a total of 569,035 elements and 18,945

nodes. Geometry and material properties were taken out of the initial statics and available

plans. Material properties are listed in Tab. 1. In the initial model all piles are placed on

stiff vertical springs with an initial spring stiffness cp of 3,000,000 kN/m. Horizontally nei-

ther the abutment nor the deck slab are supported. The piles are bedded considering a line-

ar increase in the horizontal stiffness modulus from 0 to 40,000 kN/m² at a depth of 5.0 m

below the top end of the pile. In the lower area a constant stiffness modulus of the bedding

of 60,000 kN/m² is considered.

9

4.3 Proof Loading Procedure (PLP)

Proof load tests have been performed on Friday, Feb. 19th 2010 between 10:50 a.m. and

14:45 pm with ambient temperatures between 0° to 2°C. The results of these proof load-

ings serve for the calibration of the static linear model and the verification of the assumed

structural behavior. The concept for the proof loading procedure was developed with the

following goals in mind. Firstly defined load situations with significant structural response

were to ensure a proper model calibration mainly with respect to the boundary conditions.

As a consequence three 40 to trucks with known axle loads were positioned in 16 static

scenarios. The trucks were positioned independently as well as in the most unfavorable

configurations on lanes 1 to 3, see Fig. 2(a) and Tab. 2.

Tab. 1: Code based material properties of the bridge system S33.24

Characteristics Unit Value

Concrete

C30/37

Elastic modulus, E MPa 31939

Poisson’s ratio,

- 0.20

Shear modulus, G MPa 13308

Specific Weight,

kN/m3 25

Coefficient of thermal expansion, α 1/K 1.00E-05

Concrete

C25/30

Elastic modulus, E MPa 30472

Poisson’s ratio,

- 0.20

Shear modulus, G MPa 12696

Specific Weight,

kN/m3 25

Coefficient of thermal expansion, α 1/K 1.00E-05

Reinforcment

BST 550

Elastic modulus, E MPa 210000

Poisson’s ratio,

- 0.30

Shear modulus, G MPa 80769

Specific Weight,

kN/m3 78.5

Coefficient of thermal expansion, α 1/K 1.20E-05

Tab. 2: Static proof loading positions (coordinates of model point) of truck N°1 along

lane 1 of the bridge system S33.24

Position of Truck N°1 X [m] Y [m] Z [m] Position [m]

P1 5.05 1.56 0.06 4.83

P2 11.86 1.60 0.11 11.83

P3 18.38 1.67 0.16 17.84

P4 26.84 1.58 0.22 26.83

P5 35.89 1.59 0.34 35.84

P6 44.61 1.59 0.38 44.83

P7 54.22 1.66 0.44 53.84

P8 61.18 1.64 0.52 60.83

P9 67.97* 1.64* 0.58* 67.83*

* estimated position

4.4 Numerical Representation of PLP

The recorded strains during the PLP are influenced not only by the well-defined proof

loads but also by dead-load and constraint loads due to constant temperature, temperature

10

gradient and possibly the effects of earth pressure against the abutments as well as partial

settlements. In order to account for these contributions all the mentioned load situations are

analyzed in the FE model and subjected to a sensitivity analysis.

In total 17 load cases are evaluated as listed in Tab. 3. Partial settlement of the four indi-

vidual bridge axes is considered by a magnitude of 5 mm. Earth pressure against the abut-

ments is accounted for by a linear pressure distribution of up to 25 kN/m² (approximation

of active earth pressure). The proof loading scenarios are modeled utilizing the spatial dis-

tribution of all eight wheel loads and the respective model points.

Tab. 3: Load cases applied on the S33.24

Load case

N° Type Value Unit

1 Deadload var. kN/m

2 Temperature 10 °K

3 Temp. gradient 10 °K/m

11-14 Settlement of bridge axis 5 Mm

21 Earth pressure 25 kN/m²

101-109 Proof loading 407.6 kN

4.4.1 General interpretation of FOS- and LVDT- associated influence lines

During the proof loading procedure stress/strain as well as deformation contributions

caused by dead load, temperature loads, earth pressure and the time dependent processes

creep and shrinkage can be assumed to remain constant.

Consequently for the interpretation of the obtained influence line data only relative chang-

es in the monitoring data, which can be solely attributed to the proof loading vehicle, need

to be considered, or in other words the generated influence lines are generated only for

moving proof loading vehicles. In consequence, temperature, creep and shrinkage effects

could be neglected.

In general, a good agreement between the numerically generated influence lines for hori-

zontal strain (stress) at the location of the fiber optical sensors and the experimentally ob-

tained values can be observed, see Fig. 3(a). This figure portrays the simulated influence

lines for sensor d7u of the initial FE model (solid line) as well as the idealized models

(dashed, dash-dotted and dotted line) in the rotational stiffness to the base in comparison to

the extracted sensor readings during the experimental proof loading procedure (vertical

black bars). This agreement allows a first conclusion that the chosen 3D FE Model ade-

quately represents the real structural behavior.

Similarly the numerically generated influence lines for vertical deflections show a general-

ly good agreement with the respective influence values that were experimentally obtained

during the proof loading procedure.

In Fig. 3(b) the numerically generated deflection influence lines at the location of the

LVDT sensor w1 and the respective discrete experimental influence values are presented

for the model.

11

4.4.2 Interpretation of IL with respect to modeling and monitoring

The span by span comparison between simulated influence lines and experimental influ-

ence values shows deviations of 10 % to 45 % with respect to the FE model, see Figs. 3(a)

and (b). Apart from divergences between model and reality the reasons for the observed

deviations may be (a) an inaccurate determination of model points during the proof loading

procedure (truck positions), or (b) an insufficiently well calibrated monitoring systems.

Fig. 3: Influence lines (IL) extracted from the FE Model of the bridge system S33.24

with respect to the measured values of the nine proof loading positions: (a) IL of

stresses associated with the fiber optical sensor d7u; and (b) IL of vertical deflec-

tions associated with the LVDT sensor w1

4.5 Quantification of goodness of fit – model correction factor

A more analytical and statistical based procedure for the quantification of the agreement

between numerically generated influence lines and experimentally obtained influence is

provided by the model correction factor concept, as presented in equations (7) to (9) and

further in [18]. The model correction factor allows (a) the assessment of the model behav-

ior with respect to the real structural response, (b) the assessment of the time variable

structural performance due to degrading processes based on sensor data, and (c) a limit

state analysis with respect to code given requirements. The simulated and recorded sensor

characteristics for all nine load proof positions associated with the proof loading of the

bridge system S33.24 serve for the computation of the model correction factor b as docu-

mented in Tab. 4, which in case of a perfect model (total agreement between numerical and

measured quantities) yields b = 1.

The model correction factor concept (see equation 8) facilitates the objectification of the

evaluation methods whose results are shown in Tab. 4. In agreement with the principles of

JCSS a spectrum of values ranging from 0.60 to 1.40 is acceptable due to aleatory and ep-

istemic uncertainties [21, 22]. This corresponds to the limits in between which correlation

is usually considered to be significant. The individual b-values can be summarized with

respect to (a) the goodness of fit of an individual model, (b) the capability of an entire

monitoring system to represent a certain structural characteristic, or (c) to evaluate single

sensors. In that context, an average quadratic deviation from the perfect fit (bsys = 1) is pro-

posed as system indicator, see equation (10).

12

n

i

isys b

n

b

1

2

1

1

1 (10)

From the representations in Tab. 4, it follows that based on the model correction factor

concept, the initial model may be interpreted as statistically most suitable with a system

indicators bsys= 0.73 followed by the flexible Model N°1 with bsys= 0.57.

Tab. 4: Model correction factors as indicator for the goodness of fit

Model

Sensor Initial N° 1

cm = 1 GNm/rad

N° 2

cm = 3 GNm/rad

N° 3

cm = 9 GNm/rad Mixed

d2u 0.0606 0.2114 0.3106 0.1455 ---

d3u 0.5819 0.1296 0.3971 0.2232 ---

d5u 2.1542 1.7308 1.2504 0.8577 ---

d7u 1.7426 1.3328 0.8782 0.4903 1.0036

d2o 0.6418 -0.2196 -0.3196 -0.1712 ---

d3o 0.1894 -0.0425 -0.0953 -0.0844 ---

d5o 0.8525 0.1333 -0.1481 -0.187 ---

d9o 1.7072

1.1770 0.6588 0.3052 ---

d10o (2.8754) (5.4864) (5.9021) (6.0325) 1.0751

w1 1.1310 0.6994 0.4375 0.2886 1.1310

w2 1.8591 1.3039 0.8760 0.5941 1.0264

w3 2.4504 1.8200 1.2207 0.7813 ---

b

sy

s 0.73 0.57 0.54 0.53

---

5 Conclusions

The objective of this article was the investigation of monitoring concepts based on influ-

ence lines for the evaluation of the real behavior of engineering structures. In particular,

the proposed influence line method and the model correction factor method have been used

for the evaluation of the modeling of the jointless bridge system S33.24 based on meas-

urement data. The concepts of influence lines and model correction factors have been theo-

retically presented and combined to an efficient procedure for the incorporation of

monitoring data during the processes of modeling and subsequently assessing a structure’s

real behavior. The presented methodology was successfully applied to a three-span joint-

less bridge structure utilizing monitoring data of a proof loading procedure obtained by a

fiber optic strain and LVDT based deflection monitoring system.

The presented approach combining the influence line concept with the model correction

factor concept does not only provide the basis for efficient and objective model updating

strategies but also is quintessential to the performance assessment of structures over time.

As investigations show, some sensors are associated with unfavorable data due to (a) an

unfortunate location of the sensor, or (b) an insufficiently accurate model with respect to

the monitored quantity. Consequently statistically based testing for outliers is mandatory

prior to any assessment procedure. In the presented analyses model correction factors have

been determined for individual sensors (bi) as well as the combined monitoring systems

13

(bsys,i) based on a proof loading procedure performed at a discrete point in the life time of

the investigated jointless bridge. These partially still biased model correction factors can be

considered a first estimation of a performance base line for an optimized future model. The

development of these b-factors over time allows the identification and even quantification

of expected and unforeseen processes with respect to code given requirements based on

changes between observed and simulated influence lines (utilizing the optimized model).

Influence line based model correction factors thus can be regarded as ideal performance

indicators, as suggested by OKASHA AND FRANGOPOL [23].

6 References

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Doebling, S.W.; Schultze, J.F.; Lieven, N.; Robertson, A.N.: "Damage prognosis:

current status and future needs", 2004

[2] Strauss, A.; Bergmeister, K.; Wendner, R.; Hoffmann, S.: "System- und Schadens-

identifikation von Betonstrukturen". Betonkalender 2009. K. Bergmeister, F.

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