SAHU et al: RATING OF BRIDGES UNDER UNCERTAIN STRUCTURAL PARAMETERS 703Journal of Scientific & Industrial Research

Vol. 67, September 2008, pp. 703-707

*Author for correspondence

E-mail: rkgcrri@gmail.com, rkgcrri@yahoo.co.in

Performance evaluation and rating of bridges under uncertain structural

parameters using integrated load test

G K Sahu, R K Garg* and Ram Kumar

Bridges and Structures Division, Central Road Research Institute, Mathura Road, New Delhi 110 020

Received 17 August 2007; revised 09 June 2008; accepted 11 June 2008

An integrated load-test technique has been developed to test load carrying capacity of bridges. The technique has been

illustrated with a case study implemented on one of the bridges at NH 24 near Hapur. This methodology can also be used for

performance evaluation, developing load ratings and for detecting possible degradation or damage in bridges.

Keywords: Bridges, Load test, Optimization, Performance evaluation, Rating of bridges, Uncertain structural parameters

Introduction

Structural deterioration may take place due to aging

of materials, varying environmental conditions, damage

due to impact of heavy vehicles etc., thus reducing load

carrying capacity of existing bridges1,2. Testing of a

bridge in field cannot be replaced for assessment of its

performance under passage of live loads. However, there

remains difference between response observed in field

and those modeled analytically3. Attempts are to be

made towards minimizing gap between field and

analytical responses. One approach would be to use field

(static) response data to calibrate an analytical model

that closely represents behavior observed in the field4.

In this paper, an integrated load test technique has

been described and illustrated for developing load rating

and detecting possible damages through structural

response tests conducted on a RCC Slab Bridge near

Hapur on NH 24 in UP (India).

Proposed Integrated Load Tests Approach

Load testing5,6 is to place vehicles of known weight

at a few predetermined positions on the deck. In

integrated load test technique, vehicle is allowed to

move slowly along a predetermined path (Fig. 1). As

wheels move, their position is noted and corresponding

induced strains (or deflections) as response of bridge is

recorded. Each position of wheels can be considered as

an individual load case. The corresponding induced strains

are marked as field response, which is compared with

strains obtained from analytical model for each position

of wheels. This provides a number of equations in terms

of response for various load cases as available from field

study. Analytical model, which may have several

parameters associated with uncertainty and treated as

variables, is prepared.

A few uncertain (stiffness in terms of modulus of

elasticity of material, cross-sectional area or depth of

beam, boundary conditions modeled as spring

coefficients) can be varied in analytical model to match

analytical response with that of experimental response.

Variation in some parameters within analytical model

helps realizing possible degradation in material like loss

in cross-section of beam. This exercise in mathematical

terms is reduced to optimize an error function of

responses by varying magnitude of involved parameters

(Fig. 2). Statistical values of analytical and experimental

responses can be computed for comparative study and to

achieve threshold by iterative process7. Absolute error is

computed as a sum of absolute values of strain differences

between measured and theoretical values at each of the

gauge locations under known truck position. It reflects

relative importance of model as

Absolute error = …(1)

704 J SCI IND RES VOL 67 SEPTEMBER 2008

Percent error provides qualitative measure of

accuracy in terms of root mean square (rms) values of

strain differences. Typically, percent error (< 10%)

indicates that analytical model is quite good. It is also

equal to the objective function required to be optimized.

Percent error = …(2)

Scale error is related to the ratio of maximum value

of each gauge and observed maximum strain during

loading cycle signifying closeness of wheel near gauge

(producing maximum strain under a load in closest

proximity to sensor).

Scale error =

Σ(|Em - E

c|max,gauge / Σ(|E

m|)max.gauge …(3)

Correlation coefficient is measure of closeness of

theoretical strain with measured values and may range

between -1 to +1. A value of 0.9 is considered sufficient

to achieve good analytical model.

Correlation coefficient =

Σ(Em . ) (E

c . ) /

Σ Em

. )2 . (Ec . )2 …(4)

where, = estimated value of response by analytical

model, = estimated value of response by

measurement during field study, = average of the

set of estimated value of response by analytical model,

and = average of the set of estimated value of

response by measurement during field study.

Field Study

using Strain

Gauges

FEM modeling

(Geometry,

Material, BC)

Estimate

Strain at

Known Points

Linear Elastic

Analysis

Modify

FEM Model

based on

Field Values

Comparison

Acceptable

Statistical

Analysis

Assess

Strain at

Known Points

Yes

No

Assess for

New Live Load

Compute

Rating Factor

C o m p u te R a tin g

F a c to r

Field Implementation

Whole process involves simulation of controlled live

load conditions in field by appropriately planned test

conditions, observation of response, comparison of test

results with theoretical model leading to its calibration using

optimization techniques and load rating of the structure.

Fig. 1—Vehicle path as modeled on RCC slab bridge

Fig. 2—Schematic of integrated load test methodology

SAHU et al: RATING OF BRIDGES UNDER UNCERTAIN STRUCTURAL PARAMETERS 705

Typical load test comprises of known truck loading, strain

transducers, data acquisition system, power supply,

automatic remote load position indicator, a laptop as a

system control, testing software and analysis software.

Choice of sensors includes strain gauges, LVDTs,

accelerometers, and other full-bridge type sensors. An

indicator based on photo light system is fixed at truck

body to sense another marker placed on wheel. Thus at

every turn of completed wheel movement, photo sensor

records the event by way of recognizing marker of wheel.

Simultaneously, data acquisition mode is activated

manually to record marker at that instant while strain

recording has been a continuous process. Thus marked

position in time domain can also be retrieved as load

(truck) position in analytical model.

Load Test Simulation

Live load conditions of field are simulated by

appropriate placement of sensor locations (coordinate

wise) on analytical model. Strain gages, LVDTs, tilt

meters can be applied to analytical model at same

locations as in the field and are identified with the same

strain transducer to assure that data comparison between

analytical and experimental values has been performed

accurately. Truck path simulation is carried out by

knowing truck loading at various time steps and

corresponding location in the field. Association of load

test data with those of modeled truck paths is achieved

in analytical model. Key data points that correspond to

each analysis load case (for various truck positions) are

retrieved for data comparison. Typical data acquisition

software4 allows control over sampling rates, test durations,

and automatic transducer circuit balancing. Recorded

measurements can be displayed during test and then shown

as a function of load position when test is completed. Data

is stored in ASCII file format for ease of processing.

Structural Analysis and Correlation

Analytical model is generally based on Finite Element

Methods employing suitable elements. A linear elastic

3-D frame analysis is carried out. Modeling of boundary

conditions (BCs) involves careful choice of end restraints

of translational as well as torsional nature in terms of

appropriate spring coefficients. For example, at pier end,

rotational stiffness can be obtained as beam stiffness

given by 4EI/L. An initial value may be considered as

10% of stiffness as EI/(2.5 L), where E, I and L are

modulus of elasticity, second moment of inertia and length

of structural member, respectively.

Truck loading and truck path as used during field study

are specified to simplify analysis of bridge system.

Computation of responses (strain, displacement) at

different locations of sensor is carried out. In an iterative

manner, statistical analysis and error analysis of results

is carried out for analytical as well as measured responses

using Eqs (1) - (4), followed by optimization by

minimizing error between measured and computed

responses. Analytical model is calibrated when

correlation coefficient is achieved above a threshold

value. Response envelopes are generated for series of

load cases (truck paths) and a combined envelope is

obtained for multi lane load conditions. Further,

calculation of load rating factor and identification of

corresponding critical elements helps appropriate rating

analysis and may also be used to rehabilitate or

strengthen weak structural elements.

Rating of Bridges

Basic principle8 involved in design and evaluation of

a bridge is that resistance (strength) of a bridge

component should be more than demand (load effect).

Rating factor5 is a measure of available reserve capacity

in a bridge with respect to applied live load (SF or BM).

When rating factor (RF) equals or exceeds unity, bridge

is capable of carrying rating vehicle. If RF is <1, bridge

may be overstressed while carrying rating vehicle.

Further, for computing RF, dead loads and live loads

are to be considered. In the evaluation of RF, thermal,

wind and hydraulic loads may be neglected because the

likelihood of occurrence of extreme values of these loads

is small. RF is defined as

Rating Factor (RF) =

(Capacity of Section - Factored Dead Load)

(Factored Live Load with Impact) …(5)

An accurate analytical model evaluates how bridge

will respond when standard design loads, rating vehicle

or permit loads (of unusual condition) are applied to the

structure. Since load testing is generally not performed

with all vehicles of interest, an analysis is carried out to

determine a load-rating factor for each of the truck types.

Load rating is accomplished by applying desired rating

loads in calibrated analytical model and computing

stresses on (primary) members.

It is assumed that measured as well as computed

responses are linear with respect to applied load.

Integrated approach is an excellent method for estimating

706 J SCI IND RES VOL 67 SEPTEMBER 2008

service load stress values. Therefore, operating rating

values are computed using conventional assumptions

regarding the member capacity. Based on calibrated

analytical model, study of responses in future helps in

evaluating current load carrying capacity and presence

of possible degradation or damages in various

components of bridge.

Case Study: Load Test at Bridge at Hapur

Test Planning

A reinforced concrete slab bridge near Hapur on

NH 24 route is a four-lane slab type bridge (span length,

6 m; total carriage way width, 24 m; slab thickness,

575 mm). The testing was carried out on one of the

carriageway. Sensors (re-mountable strain based

transducers) were installed on bottom side of slab bridge.

Spacing between sensors was decided based on lane

width of bridge. For load test of bridge, a two-axle truck

(axle weights, 6.77 & 22.25 tonnes) having gross vehicle

weight of 29.02 tonnes was used. Measured axle spacing

of vehicle was 4.23 m. Test vehicle was driven twice

over pre-defined path (Fig. 1) at crawl speed.

Results and Discussions

The position of sensors was located on analytical model

(Fig. 3). Response data of strains was collected during

field study. An analytical FEM model using beam and

plate elements was prepared. Sensor identification

number is 9040 under two tests of truck movement

(hapurt7 & hapurt8); A-1 represents results from

corresponding analytical model. Close values in tests

(hapurt7 & hapurt8) show acceptable repeatability of

obtaining response in the field (Fig. 4).

Correlation properties [Eqs (1-4)] were computed for

each iteration during optimization process and finally

obtained values are as follows: absolute error, 467.1;

percent error, 9.2%; scale error, 11.6%; and correlation

coefficient, 0.987. A correlation coefficient (0.987, an

excellent correlation) suggests that variables within

given constraints have well performed, therefore,

practical values of variables might have been achieved

(Table 1). Modulus of elasticity of slab material and

cross-section of edge beam (depth) has not been varied

during optimization process. However, influence of

(marginal) end restraints is clearly visible from optimized

Fig. 3—Location of gauges as in FEM model of

RCC slab bridgeFig. 4—Strain plots of experimental and analytical results:

a) Before optimization; b) After optimization

Str

ain

(mic

ro-s

trai

n)

Load position, m

Str

ain

(mic

ro-s

trai

n)

Load position, m

SAHU et al: RATING OF BRIDGES UNDER UNCERTAIN STRUCTURAL PARAMETERS 707

Table 1—Variables optimized during calibration of analytical model

Group Id/ Parameter, unit Lower limit Upper limit Value after Remarks

Name optimization

2/ Slab-1 E, MPa 2.7400E4 3.2500E4 2.7400E4 Not varied

1/ Edge Beam Depth of member, cm 2.2000E1 2.8000E1 2.2000E1 Not varied

3/ R-Spring Stiffness, N/m2 0.0000E0 2.2060E5 4.0048E4 Possible end restraints

4/ L-Spring Stiffness, N/m2 0.0000E0 2.2060E5 2.2059E5 Possible end restraints

values. This agrees with observed visual condition of the

bridge. As bridge is new and changes in cross-sectional

properties (from time of construction) are not expected

which otherwise reflects upon degradation of structural

member. This feature of methodology helps assessing

performance evaluation and possible degradation in

structural members (or bridge). These inferences are

essentially based on computations using numerical

techniques although they have basis of matching field

behaviour, and should be corroborated with visual inspection

as well as other NDT techniques. The results indicate

presence of uncertainty of boundary conditions, which have

been taken into account in calibrated analytical model in

present study. It might be further useful to take into account

uncertainties in structural parameters, live loads and

environmental loads using other techniques like reliability

methods9.

During computational process, every structural

component (member) has been assessed for RF as per

Eq. (5) using several truck paths. RF of different

components has been found to vary between 1.5 and 4.6,

depending upon their relative position with load path. From

such an iterative approach, lowest value of RF (1.5)

obtained for members in present study may be generalized

as RF (1.5) of bridge. This technique in present form is

more suitable to road bridges. However, with necessary

modifications in analysis procedure, it can be applied to

railway bridges. The load transfer mechanism in railway

bridges is quite complex due to presence of several non-

load bearing components such as rails, sleepers, ballasts

and rubber pads between axle and bridge. Although, in

present study, results have been discussed for

superstructure, appropriate modeling of substructure and

foundation should be carried out particularly, when

foundation is flexible.

Conclusions

Methodology of using field measurements to modify an

analytical model termed as integrated technique has been

successfully implemented. It is also possible to

simulate influence of uncertainty in elastic parameters

(modulus of elasticity and boundary conditions).

RF 1.5 has been assessed based on data obtained in

field study for Hapur Bridge. Methodology is useful

for assessment of load carrying capacity of existing

bridges and obtaining its rating for a set of desired

(unusual) live-loads.

Acknowledgements

The support provided by DST sponsoring an R&D

project on Bridge Management System is gratefully

acknowledged. Authors thank Director, CRRI, New

Delhi to permit publishing this paper and Mr A Garg

of NHAI at Hapur, for providing details of the bridge

used during tests.

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