Journal of Scientific & Industrial Research SAHU et al: RATING OF BRIDGES UNDER UNCERTAIN STRUCTURAL PARAMETERS Vol. 67, September 2008, pp. 703-707
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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 *Author for correspondence E-mail:
[email protected],
[email protected]
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)
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J SCI IND RES VOL 67 SEPTEMBER 2008
Fig. 1—Vehicle path as modeled on RCC slab bridge
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.
Field Study using Strain Gauges
FEM modeling (Geometry, Material, BC)
Estimate Strain at Known Points
Linear Elastic Analysis
Assess Strain at Known Points
Statistical Analysis
Modify FEM Model based on Field Values
…(2)
Percent error =
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).
Comparison Acceptable
No
Yes
Scale error = Σ(|Em - Ec|max,gauge / Σ(|Em|)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.
C om p u te R a tin g Compute F a c to r Rating Factor
Correlation coefficient = ) (Ec . ) / Σ(Em .
Σ Em . where, model,
Assess for New Live Load
)2 . (Ec .
)2
…(4)
Fig. 2—Schematic of integrated load test methodology
= estimated value of response by analytical = estimated value of response by
= average of the measurement during field study, 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 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.
SAHU et al: RATING OF BRIDGES UNDER UNCERTAIN STRUCTURAL PARAMETERS
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.
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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
