performance evaluation and rating of bridges under
TRANSCRIPT
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: [email protected], [email protected]
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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