Load Testing of Bridges – Global State-of-Practice
Alok Bhowmick
Managing Director
B&S Engineering Consultants Pvt. Ltd.
Noida
Load testing of bridges is a practice, as old as bridge engineering. Since early days, there was a tradition for performing a load test prior to opening of a bridge, with the objective to convince the travelling public about the safety of the bridge. In India, it is a common practice to carry out load test of new bridges before opening the bridge to traffic. Fig. 1 shows some of the photographs of load testing in India, carried out on newly constructed bridges. Over the years however, the utility of load testing has shifted from a public demonstration during opening of new bridges to its use as effective tool for in-situ evaluation of the structural behaviour and assessment of existing old bridges. Load Testing is emerging as a highly specialised and very broad topic in Bridge Engineering. It can serve several objectives, such as:
– Field-validated analytical model of bridge
– Evaluation of effect of material deterioration and degradation on structural behaviour
– Evaluation of rehabilitation or repair actions
– Analysis of historical bridges
– Determination of additional load carrying mechanisms or load paths
– Evaluation of performance of new materials
– Estimation of remaining fatigue life
– Verification of behaviour of new bridges
– Measurement of dynamic properties
– Verification of aspects of performance
The practice of load testing varies widely across countries. Even within a country there are multiple practices and guidelines available.
The current body of knowledge on load testing is reflected by the available codes and guidelines that are in use. The provisions in available codes and guidelines differ across countries and are largely guided by the local demands and the construction industry practice. While the codes and guidelines reflect present practice based on past knowledge, there are new insights that have been successfully applied in some of the projects, which reflects the state-of-the-art. None of the existing national/international guidelines covers load testing methods of all bridge types. In many countries (including in India), efforts are geared towards improvement of the current guidelines for load testing.
At present, research on load testing is mainly focussing on applying new measurement techniques and using concepts of structural reliability and life cycle assessment together with proof load testing. More research is needed for proof load testing of concrete bridges which are critical in shear, punching shear, tension or torsion (since current practice is only to identify load limits considering ductile mode of failure). For steel and composite structures, more research is needed in fatigue assessment and assessment of fracture critical bridges to identify the critical structural response and the stop criteria in case of proof load testing.
History Of Bridge Load Testing
Load tests are as old as humanity itself. They served to confirm that the structures were capable of withstanding the traffic loads and helped to instil trust of the public and authorities in the load bearing capacity of the structure. In ancient times, it is reported that the engineer who designed the bridge had to stand under the bridge during the load testing before opening the bridge to public. If the bridge would collapse, the engineer who designed the bridge will get buried with his mistake [1]. Performing the load test and measuring deflections demonstrated to the public that the bridge was safe. Till 1650, there was hardly any documentation about load testing. Master builders used to pass on their life long experience and teachings to the next generation and that’s how the society progressed. It was only around 1650 that the documentation of load tests and experiments began, which resulted in improved understanding of the behaviour of structures.
The Romans were the first European civilisation to erect a large number of bridges as part of the infrastructure required for their economic and military success. At the end of 18th century, masonry arch bridges and timber bridges were the most commonly built types of bridges, and their designs were based exclusively on empirical knowledge. The construction practice changed to steel in 19th century when large quantities of steel of predefined quality became available. Load testing as a part of commissioning of new bridge was a long tradition.
In order to generate heavy loads for load testing, several means and methods are adopted. Depending upon the location, function of the bridge and availability of materials, different types of ballasts, water tanks, sand bags, steam rollers or heavy trucks, tram cars, steel rods were used in the past for producing the calculated load. Fig. 2, 3, 4 and 5 shows some of the load tests carried out in early part of 20th century. In those early load tests, full design loads were used—the bridge was considered to pass if (a) it did not collapse and (b) it fulfilled deflection or vibration criteria specified by the authorities.
In early days, lack of rules for the execution and evaluation of load tests resulted in numerous collapses during load testing. One example is the steel framework bridge over the Morawa River near Ljubitschewo in Serbia [1]. Fig. 6 shows the collapsed bridge over Morawa River. Gravel from the river bed of the Morawa was used as ballast load in load testing. On the 2nd day of testing, the bridge suddenly collapsed caused by a buckling of the under dimensioned upper chord.
In 1903s and 1940s, EMPA, Zurich published several reports on systematic proof load tests of bridge structures. In 1950s, intense development and improvements of calculation methods occurred primarily due to the increased use of computer technology. Professionals became confident that it is possible to analytically calculate the load carrying capacity of bridges with sufficient accuracy and therefore load testing for validating a new bridge became less and less important. Some countries, such as France [2], Italy [3, 4], and Switzerland [5], however still require load tests prior to opening a new bridge. In India also it is a practice to load test newly constructed bridges. In some countries, load tests are used for long-span or special bridges or bridges in which novel concepts are applied [6–8].
At the beginning of the 21st century in the United States and Europe, numerous bridges built during periods of rapid expansion of road and railroad networks during the 1st half of 20th century reached the end of their originally designed service lives.
Consequently, increasing time and effort are required to assess and rate these existing stock of bridges to ensure the safety of the traveling public [9]. It is clear that asset management of stock of bridges is essential and sustainable development demands that old bridges are discarded, as a last resort, only when professionals are absolutely sure that the bridge cannot take the current design loads.
While advanced calculation methods to estimate the ultimate capacity of existing structures are widely available [10–15], timely and accurate data from existing structures needed as inputs for such models, are not always forthcoming. Furthermore, ongoing time-related deterioration of in-service bridges increases the difficulty of evaluation. Load testing provides a useful alternative for such cases where current calculation methods cannot provide satisfactory answers to performance questions on existing bridges [16, 17].
Type Of Load Tests Performed Universally
In current worldwide practice, load tests fall into two distinct categories:
a. Diagnostic Load Tests: conducted with small fractions of the design live loads and
b. Proof Load Tests: carried out with factored live loads, corresponding to those specified by applicable design codes.
Other than the above, parameter specific load tests are also carried out sometimes as a part of research, with the intent of determining the contribution of a specific bridge element to the behaviour of the structure.
Diagnostic Load Testing: Diagnostic Load Testing is used to validate an analytical model. What is aimed at is comparison of the difference between the original analytical model and the structural response measured during the test. These tests are typically carried out with known loads, which is a fraction of the design loads. Diagnostic load tests can be performed on newly opened bridges to verify the behaviour of the structure to adjust predictions of an analytical model and also on older bridges. This information is useful, if preserved, as it can be referred to later on, when a load test is carried out on the same structure after ages. The effect of material deterioration on the distribution of live load force effects can then be analyzed based on the reduction in stiffness between the newly opened bridge and the bridge after decades of service life. In a diagnostic load test, the load effects (i.e., strain–stress, rotation, crack widths or deflections) are measured in bridge members in response to applied loads. The measured load effects can be interpreted to determine the member forces. With all measurements zeroed before the beginning of the load test, the distribution of the live load effects is measured directly.
Interpretation of results from a diagonal load test is a complex task, which requires experience, skill and knowledge. Non-structural members can enhance the behaviour and stiffness of a member at service load levels which may cease to contribute at higher load levels and towards the ultimate capacity. The applied load should therefore be sufficiently high to properly model the behaviour of the bridge at the rating load level. In the final analysis, the contribution of mechanisms [18] that may not be reliable at the load levels representative of the ultimate limit state, cannot be accounted for. These contributions should be subtracted from the final total capacity.
Proof Load Testing: Proof load tests are typically carried out on existing bridges, in service to directly demonstrate that a given bridge can carry the required load. Proof load testing is recommended when there are large uncertainties about the structure, and engineers have reason to believe that significant reserve capacity is available, but it cannot be quantified exclusively via analytical approaches. In a proof load test, a target load is applied, and observations are made to determine if the bridge carries these loads without damage. Since magnitude of applied loads are high, they should be applied in increments and according to a loading protocol determined prior to the test, and the bridge should be closely monitored during the testing to observe warnings of possible distress or nonlinear behaviour. Proof load testing requires careful preparation and involvement of experienced personnel to analyze the response of the bridge and make decisions about the safety of continued loading on the structure. Caution is required to avoid damage to the structure, or injury to personnel or the public. For this reason, the bridge needs to be equipped with adequate sensors in appropriate locations. The measurements have to be analysed during the proof load test to verify that the stop criteria are not exceeded. In proof load tests, stop criteria are of the utmost importance because they indicate when certain thresholds for damage are about to be exceeded, thus resulting in an immediate ending of the proof load test. If the stop criteria are exceeded before reaching the required maximum load, the bridge will not be approved for the studied live load model or particular live load configuration.
Parameter-Specific Load Testing: Parameter-specific load testing refers to collecting sensor measurements from a structure with the intent of determining the contribution of a specific bridge element to the behaviour of the structure. The end goal may not be to conduct a bridge load rating, but rather to simply provide insight into the performance of a specific element or component as well as its impact to the behaviour of the structural system.
When Not To Consider A Load Test - Load testing of bridges is not recommended when the developed analytical (FEM) model and analysis results in sufficient rating, or when the safety cannot be guaranteed during the load test; for example, when there is a risk of a brittle failure during a proof load test.
Current National/International Codes & Guidelines On Load Testing - Different national/international codes (and guidelines) addresses load testing from a different objectives. The current body of knowledge and practices worldwide is given below based on literature review.
Indian Railway Standard (IRS) Code (Applicable For Railway Bridges Only)
Railways have issued a guideline for load testing of bridges recently vide circular from Ministry of Railways No. 2019/9/CE-III/BR/RDSO Misc. dated 27.01.2021 Objective of the load test is stated as follows:
– Validating the design of a typical and innovative type of bridge superstructure, about which Indian Railways doesn’t have prior experience
– Evaluating the safe load carrying capacity of existing bridges
– Investigating the adequacy (or otherwise) of the bridge superstructure in case of doubt
– Monitoring the condition of distressed bridges
– Assessing the results of major structural repairs or strengthening
– Validating the mathematical models
– Complying with the contractual conditions It is made clear in this guideline that the primary objective of performing load test is to understand bridge’s response to static and dynamic loadings. The levels of loading necessary should be such that they are sufficient to obtain measurable responses from the structure without causing any permanent structural damage.
Indian Roads Congress (IRC) Codes (Applicable For Highway Bridges)
There are 2 guidelines published by IRC which has reference to load testing of Bridges:
– IRC:SP:51 2014 titled “Guidelines for Load Testing of Bridges”
– IRC:SP:37 2010 titled “Guidelines for Evaluation of Load Carrying Capacity of Bridges”
IRC:SP:51-2015[19]: First published in 1999 and revised in 2014, this is a publication which deals with load testing of Superstructure for Highway Bridges (Fig. 7). The Guideline deals with Proof Load Test. The nomenclature used for proof load test in this guideline differs from the nomenclature used in several countries (e,g. USA and Europe), but is aligned with the British guideline. In line with the British guideline, the code defines proof loading as the load tests to validate the design method and design assumptions for newly constructed bridges, with loading levels matching the Serviceability Limit State (SLS). The guideline covers testing of superstructures, excluding arches. Testing for shear capacity is not considered. Load test as per this guideline is not intended to assess ultimate load carrying capacity of bridge superstructure. The acceptance/rejection of bridge as per this guideline is only on the basis of live load deflection and recovery after unloading. Criteria based on load test is as follows:
– Measured deflections shall be equal to or less than theoretical deflections.
– % Recovery of Deflection @ 24 hours shall be not less than 75% (RCC & Composite) and 85% (PSC & Steel) Superstructures
IRC:SP:37-2010[20]: First published in 1991 and revised in 2010, this guideline covers load testing of existing bridges for rating and posting purposes (Fig. 8). Load rating is the measure of a bridge’s ability to carry a given live load. A Load Rating reflects the current condition of each bridge and provides a valuable tool that is used in identifying the need for load posting or bridge strengthening and in making overweight-vehicle permit decisions. Load Test for rating is done when it is not possible to determine the rated capacity of a bridge due to lack of essential details. For rating of masonry arches load testing is recommended. Load Test for posting is done when details required for verifying the strength of all elements of existing structure by analytical methods is not possible due to lack of reliable data. For rating/posting purposes, use of mobile test vehicles are preferred in load testing. Test loads shall be applied in stages following the given values 0.5W, 0.75W, 0.90W, 1.0W, where ‘W’ is the gross laden weight of the test vehicle. For each stage, the correspondingly loaded test vehicle shall be brought to the intended position, deflection measured immediately on loading and after 5 minutes, test vehicle removed and deflection recovery noted 5 minutes after removal of load. The acceptance/rejection of bridges as per this guideline is on the basis of deflection and recovery after unloading. Criteria based on load test is given for girder bridges as well as arch bridges.
International Codes / Guidelines On Load Testing Of Bridges[22,23]
United States: The Manual for Bridge Rating through Load Testing (NCHRP 1998) [21], uses the concept of load testing and bridge rating. The manual is valid for all types of bridges except long span bridges, shear critical concrete beam bridges, bridges with extremely low capacity (analytically), bridges with frozen joints (that could cause a sudden release of energy), steel bridges with fracture critical members and bridges on poor soil and foundation conditions. The concepts from manual are also repeated in the Manual for Bridge Evaluation (MBE), (AASHTO, 2018 with interim revision in 2019). The transport research board subsequently issued in 2019 an e-Circular [24], which provided significant updates to reflect the current state of the practice on bridge load testing, and covers the preparation, execution, and analysis of load tests, including diagnostic and proof tests.
United Kingdom: The guideline for load testing from the United Kingdom (ICE, National Steering Committee for the Load Testing of Bridges 1998) describes following type of load tests:
a. Supplementary Load Tests: Load test to supplement the analytical methods of assessment based on calculation and the use of codes of practice (called diagnostic load test in Europe and USA).
b. Proof Loading: Load tests to validate the design method and design assumptions for newly constructed bridges, with loading levels to the SLS (called diagnostic load test in Europe and USA).
c. Proving Load Testing: called as proof load test in Europe and USA. d. Dynamic Load Testing: Load testing using ambient or forced vibrations to measure the structural stiffness.
The guideline is limited to supplementary load testing as an integral part of the overall assessment procedure for existing bridges. This guideline was originally developed to assess existing bridges [18]. The results of such a load test can be used to improve the existing FEM based on the field measurements. The updated analytical model is then used for the assessment.
Germany: The guidelines for load testing of concrete structures (Deutscher Ausschuss für Stahlbeton, 2000), mostly aimed at buildings, are available to ensure a safe execution of load test on bridges as well. The scope of the guidelines is plain and reinforced concrete structures, and the guideline only considers the ductile failure mode of flexure. Guideline cannot be used for shear critical bridges. Testing for shear is not allowed. The guideline prescribes 5 stop criteria to be checked during proof load tests. These are:
a. Limiting strain in concrete (εc < εc,lim – εc0), where εc is the strain measured during proof loading, εc,lim equals 0.6‰ in general and can be 0.8‰ when the concrete compressive strength is more than M25 and εc0 is the analytically determined short term strain in the concrete caused by the permanent loads that act on the structure before the application of proof load.
b. Limiting strain in reinforcing steel (εs2 < 0.7(fym/Es ) – εs02), where es2 refers to measured strain in the steel, es02 is the analytically determined strain (assuming that the concrete cross section is cracked) in the concrete caused by the permanent loads that act on the structure before the application of proof load. The value of f ym is the average yield strength of the tension steel.
c. Width of new crack that can occur during load testing, as well as the increase in crack width that can occur during the load test.
d. Limitation on measured deflection – the stop criteria is exceeded when a clear increase of the non-linear part of the deformation is observed or when more than 10% permanent deformation is found after removing the load.
e. Added limitation for strains in shear spans in case of beams with shear reinforcements. Maximum strain in concrete limited to 60% of the limit in a) above and for steel reinforcement, it is limited to 50% of the maximum strain given in b) above.
French Guideline: In France, all new bridges (including pedestrian bridges) must be subjected to a diagnostic load test prior to opening (Cochet et al. 2004). Simplified procedures for rigid frame bridges, slab bridges, and girder bridges are provided. For bridges of span less than 10 m, simplified load tests can be carried out, for which it is not required to measure load effects. When it is necessary to measure load effects, following effects can be measured:
– Deflection
– Settlements (of supports)
– Horizontal displacements at the supports, abutments or pylon heads
– Flexural rotations (at top or bottom of supports)
– Strains (on steel members)
– Curvatures
– Tension Forces (in Hangars)
When large number of similar bridges are being delivered, at least 10% of these and at least one, has to be load tested. For other bridges, results of the tested bridges can be extrapolated. For repaired bridges, a load test can be used to compare the behaviour of the bridge to its original state.
Work Of Technical Committee On Load Testing By International Association For Bridge Management And Safety (IABMAS)
IABMAS is a premier international organization for the advancement of the state-of-the-art in the fields of bridge maintenance, safety and management. The IABMAS Bridge Load Testing Committee, in which the author is a member, is an international committee of participants from academia, industry and bridge owners, which provides a forum for the exchange of ideas on bridge load testing. It is clear that different codes and guidelines addresses load testing from a different perspective. The available codes/guidelines do not adequately cover all bridge types. For this reason, efforts are currently geared globally to improve the present guideline/code on load testing. These efforts include the following:
– Unifying existing guidelines so that these cover all bridge types
– Unifying all bridges codes so that these covers both diagnostic and proof load testin
– Including guidelines for existing bridges
– Including guidelines that can fail in brittle manner, such as shearcritical concrete bridges and fracture critical steel bridges
– Organize dedicated international sessions and exchange information on the use of load testing in different countries
Recent Advances In Measurement Techniques For Load Testing
Digital Image & Video Based Measurements - Image and video based measurement techniques have significant advantages over traditional physical sensors since they are applied remotely without physical contact with the structure, they require no cabling and they allow for measuring displacement where no ground reference is available. There are two techniques that analyse digital images:
– Based on Digital Image Correlation (DIC)
– Based on Eulerean Virtual Visual Sensors (VVS) It is expected that the video-based techniques will be continued to be advanced and developed to the point where they become a common measurement technique.
Acoustic Emission Measurement
Acoustic Emission (AE) technology is also used for real-time examination of bridge components under stress. AE waves are stress waves that are generated by rapid release of strain energy due to micro structural changes in a material and can travel through the structure. These waves are raised from localized source(s) within a material and have the ability to locate the source initiation. Varying load conditions that exist in bridge components such as steel and concrete can cause these elements to emit energy in the form of elastic waves due to various material-relevant damage mechanisms. These waves can be captured by means of AE sensors placed on the surface of bridge component. Analysis of the signals received from the sensors provides information about the source of emission.
Fibre Optics Application
The most regularly practices SHM applications, where load testing is included, are based on electric strain sensors, accelerometers, inclinometers, global navigation satellite system-based sensors, acoustic emission, wave propagation and so forth. Nevertheless, all of them present genuine challenges when deployed in real-world application. In order to improve the accuracy and efficiency of measurements acquired during those practices, Optical Fibre Sensors (OFS) have been used for the past two decades. Because of the OFS inherent distinctive advantages (such as small size, lightweight, immunity to electromagnetic interference (EMI) and corrosion, and embedding capability), a significant number of innovative sensing systems have been exploited in the civil engineering for SHM used in projects (including buildings, bridges, tunnels, etc.)
OFS can be categorised into different classes: Interferometric sensors, grating based sensors and distributed sensors. The Interferometric sensors and grating based sensors are point sensors, which are extensively used in civil engineering applications. The distributed sensors are of recent origin and is based on the interaction between the emitted light and the properties of the optical physical medium, defined as scattering.
Deflection Measurement By Radar Techniques
Vibration testing of bridges and large structures is generally performed by using piezoelectric or force-balanced accelerometers since these sensors are very accurate and relatively inexpensive. Although accelerometers have been and still are extensively and successfully used, their drawbacks are well-known: (1) the sensors must be installed at selected locations that are representative of the structure motion and access may be difficult and often dangerous; (2) the installation and wiring are the most time-consuming tasks during the tests; (3) the use in permanent monitoring systems is prone to the typical failures of any system provided with cables and electrical circuits; and (4) accelerometers do not provide a direct measurement of displacement, something that could positively affect the development of the Structural Health Monitoring (SHM) in operational conditions.
Recent progresses in radar techniques and systems have favoured the development of a microwave interferometer, potentially suitable to the non-contact vibration monitoring of large structures. The main characteristic of this new radar system entirely designed and developed by Italian researchers is the possibility of simultaneously measuring the static or dynamic deflections of several points of a structure, with sub-millimetric accuracy.
Practical Recommendations For Load Testing
Detailed planning and preparation is key to a successful load test. The first step in the design of a load test is identification of test objectives. Once the test objectives are determined and goals of the load test are clearly spelt out, the required measurement types and locations, as well as appropriate sensors, sampling rates, and post-processing schemes to obtain the desired measurements must be identified. Load testing agency should have the experience, knowledge and wisdom to perform the load test and to interpret the results of load test correctly. From a practical point of view, a good starting point is to carry out a technical inspection of site, prior to load test. This is important in order to identify the possible site restrictions and limitations. A detailed planning of the on-site activities is necessary to help with finishing the load test within the available time. Prior to load test, the testing agency needs to think through possible failures of equipment and personnel. A plan B for each scenario should be developed, and the necessary backup equipment and sensors should be made available at site.
Communication and safety on site are of utmost importance, to protect the structure, personnel involved at site and the travelling public. For the structural safety an adequate sensor plan and a thorough preparatory calculations exploring the expected structural behaviour is important. For the safety of the personnel involved with the load test, the local safety regulations should be closely followed and a safety engineer should be dedicated to the safety of the personnel and the execution. Finally the safety of the travelling public surrounding the bridge during load testing is an important consideration. A full closure of the surrounding roads for public may become necessary.
Summary And Conclusions
– Load testing is a topic, which is internationally of interest. Indian codes on load test is currently under revision and it is hoped that the revised guideline will be at par with the international practice.
– Historically, load testing was adopted prior to opening of any bridge to show the travelling public that the bridge is safe and to earn trust of the public. Now a days, load testing is used more and more for assessment of existing bridges.
– Before conducting a load test, the best practices is first to identify the objective and goals. The Client must be clear with the objective of conducting the load test and how the load test is to be carried out. Depending upon the objective, it needs to be decided whether a a diagnostic test or a proof load test will be required.
– It’s important to prepare well for any load testing. It’s important to see the bridge before testing. It’s important to instrument the bridge well so that one can study the behaviour of the bridge well. For proof load testing, cyclic loading is recommended.
– In general loading tests today have the importance they deserve, namely as an accepted alternative method to prove the load bearing capacity of structures. Loading tests allow an economic and functional further use of existing and damaged concrete structures and helps to limit necessary renovation or strengthening to an extent required.
References
Bolle, G., G. Schacht, and S. Marx. Loading Tests of Existing Concrete Structures - Historical Development and Present Practise. FIB Symposium, Prague, Czech Republic, 2011, p. 14.
Cochet, D., et al. Load Tests on Highway Bridges and Pedestrian Bridges (in French). Setra– Service d’Etudes Techniques des Routes et Autoroutes, Bagneux-Cedex, France, 2004.
Veneziano, D., D. Galeota, and M. M. Giammatteo. Analysis of Bridge ProofLoad Data I: Model and Statistical Procedures. Structural Safety, Vol. 2, No. 2, 1984, pp. 91–104. https://doi.org/10.1016/0167-4730(84)90013-4.
Veneziano, D., D. Galeota, and M. M. Giammatteo. Analysis of Bridge ProofLoad Data II. Numerical Results. Structural Safety, Vol. 2, No. 3, 1985, pp. 177–198. https://doi.org/10.1016/0167-4730(85)90025-6.
Brühwiler, E., T. Vogel, T. Lang, and P. Lüchinger. Swiss Standards for Existing Structures. Structural Engineering International, Vol. 22, No. 2, 2012, pp. 275–280. https://doi.org/10.2749/101686612X13291382991209.
Taylor, P., T. Hosteng, X. Wang, and B. Phares. Evaluation and Testing of a Lightweight Fine Aggregate Concrete Bridge Deck in Buchanan County, Iowa. InTrans Project 12-434; IHRB Project TR-648. Iowa State University, 2016, p. 51.
Hernandez, E. S., and J. J. Myers. In-Situ Field Test and Service Response of Missouri Bridge A7957. Proc., European Bridge Conference, Edinburgh, U.K., 2015, p.
8. Au, A., C. Lam, J. Au, and B. Tharmabala. Eliminating Deck Joints Using Debonded Link Slabs: Research and Field Tests in Ontario. Journal of Bridge Engineering, Vol. 18, No. 8, 2013, pp.768– 778. https://doi.org/10.1061/ (ASCE)BE.1943-5592.0000417.
Frangopol, D. M. and S. Kim. Chapter 10: Bridge Health Monitoring. In Bridge Engineering Handbook, Vol. 5: Construction and Maintenance (W. F. Chen and L. Duan, eds.) CRC Press/ Taylor & Francis Group, Boca Raton, Fla., 2014, p. 247–268.
Hendriks, M. A. N., A. de Boer, and B. Belletti. Guidelines for Nonlinear Finite Element Analysis of Concrete Structures. Report RTD:1016-1:2017. Rijkswaterstaat Centre for Infrastructure, 2017.
Ferreira, D., J. Bairán, and A. Marí. Efficient 1D Model for Blind Assessment of Existing Bridges: Simulation of a Full-Scale Loading Test and Comparison with Higher Order Continuum Models. Structure and Infrastructure Engineering, Vol. 11, No. 10, 2015, pp. 1383–1397. https://doi.org/10.108 0/15732479.2014.964734.
Puurula, A. M., O. Enochsson, G. Sas, T. Blanksvärd, U. Ohlsson, L. Bernspång, B. Täljsten, and L. Elfgren. Loading to Failure and 3D Nonlinear FE Modelling of a Strengthened RC Bridge. Structure and Infrastructure Engineering, Vol. 10, No. 12, 2014, pp. 1606–1619. https://doi.org/10.108 0/15732479.2013.836546.
Ghodoosi, F., A. Bagchi, and T. Zayed. System-Level Deterioration Model for Reinforced Concrete Bridge Decks. Journal of Bridge Engineering, Vol. 20, No. 5, 2014, p. 10.
Belletti, B., et al., Developing Standardized Guidelines for Safety Assessment of Shear-Critical RC Beams Based on Nonlinear Finite Element Modeling. Proc., 3rd FIB International Congress, Washington, D.C., 2010, p. 13.
Fanning, P. J., L. Sobczak, T. E. Boothby, and V. Salomoni. Load Testing and Model Simulations for a Stone Arch Bridge. Bridge Structures (Abingdon), Vol. 1, No. 4, 2005, pp. 367–378. https://doi.org/10.1080/ 15732480500453532.
Schacht, G., G. Bolle, and S. Marx. Belastungsversuche—Internationaler Stand des Wissens. Bautechnik, Vol. 93, No. 2, 2016, pp. 85–97. https://doi. org/10.1002/bate.201500097.
Fu, G., F. P. Pezze III, and S. Alampalli. Diagnostic Load Testing for Bridge Load Rating. Transportation Research Record 1594, 1997, pp. 125–133. https:// doi.org/10.3141/1594-13.
“Bridge Load Testing: State-of-the-Practice”; Sreenivas Alampalli, Dan M. Frangopol, Jesse Grimson, Marvin W. Halling, David E. Kosnik, Eva O. L. Lantsoght, David Yang, and Y. Edward Zhou; ASCE Journal of Bridge Engineering, 2021
IRC:SP:51 – 2015 : Guidelines for Load Testing of Bridges (First Revision), Indian Roads Congress
IRC:SP:37 – 2010 : Guidelines for Evaluation of Load Carrying Capacity of Bridges, Indian Roads Congress
Manual for Bridge Rating through Load Testing, NCHRP Report No. 234, November 1998
Eva O. L. Lansought : Load Testing of Bridges : Current Practice and Diagnostic Load Testing,; CRC Press, Volume 12
Eva O. L. Lansought : Load Testing of Bridges : Proof Load Testing and the Future of Load Testing; CRC Press, Volume 13
Transportation Research Board (TRB) Circular Number E-C257 (November 2019) titled “Primer on Bridge Load Testing”.