Performance evaluation and rating of bridges under uncertain structural parameters using integrated load test

Transcription

1 Journal of Scientific & Industrial Research SAHU et al: RATING OF BRIDGES UNDER UNCERTAIN STRUCTURAL PARAMETERS 703 Vol. 67, September 2008, pp 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 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 bridges 1,2. 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 analytically 3. 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 field 4. 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 testing 5,6 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 process 7. 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 *Author for correspondence rkgcrri@gmail.com, rkgcrri@yahoo.co.in Absolute error = (1)

2 704 J SCI IND RES VOL 67 SEPTEMBER 2008 Field Study using Strain Gauges FEM modeling (Geometry, Material, BC) Estimate Strain at Known Points Linear Elastic Analysis 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. Assess Strain at Known Points Statistical Analysis Modify FEM Model based on Field Values 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( E m - 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(E m. ) (E c. ) / Comparison Acceptable Yes Assess for New Live Load Compute Rating Rating Factor Factor No Σ E m. ) 2. (E c. ) 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. Fig. 2 Schematic of integrated load test methodology 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.

3 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 software 4 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 principle 8 involved in design and evaluation of a bridge is that resistance (strength) of a bridge component should be more than demand (load effect). Rating factor 5 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

4 706 Strain (micro-strain) J SCI IND RES VOL 67 SEPTEMBER 2008 Strain (micro-strain) Load position, m Fig. 3 Location of gauges as in FEM model of RCC slab bridge 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 & tonnes) having gross vehicle weight of 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. Load position, m Fig. 4 Strain plots of experimental and analytical results: a) Before optimization; b) After optimization 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, 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

5 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 E E E4 Not varied 1/ Edge Beam Depth of member, cm E E E1 Not varied 3/ R-Spring Stiffness, N/m E E E4 Possible end restraints 4/ L-Spring Stiffness, N/m E E E5 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 methods 9. 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 nonload 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. References 1 OECD, Evaluation of Load Carrying Capacity of Bridges, Road Research Group Report (Organisation of Economic Cooperation and Development, Paris) 1979, Phares B M, Wipf T J, Klaiber F W & Abu-Hawash A, Bridge load rating using physical test, in Proc Mid- Continent Transportation Res Symp (Iowa State Univ, USA) Bakht B & Jaeger L G, Bridge testing a surprise every time, J Struct Engg, ASCE, 116 (1990) Win S T S, Operation Manual-Structural Testing System II (Bridge Diagnostic Inc, USA) 2005, IRC SP: 9, Guidelines for Rating of Bridges (Indian Roads Congress, New Delhi) IRC SP: 37, Guidelines for Evaluation of Load Carrying Capacity of Bridges (Indian Roads Congress, New Delhi) Goble G, Schultz J & Commander B, Load Prediction and Structural Response, Final Report, FHWA DTFH61-88-C (Univ. Colorado at Boulder, USA) AASHTO, Standard Specifications for Highway Bridges (AASHTO, USA) Bhattacharya B, Li D, Chajes M & Hastings J, Reliabilitybased load and resistance factor rating using in-service data, J Bridge Engg, ASCE, 10 (2005)