7. UNSTRENGTHENED ARCHES - COMPARISON OF TEST AND PREDICTED RESULTS

7.1 General

Predicted and experimental load versus displacement characteristics have been compared for each of the full-scale single span arch tests and for each different arch assessment program. Where the method of analysis is independent of displacement, which is the case for Archie, Archie-M and RING, horizontal lines at constant load are plotted alongside other results. For multi-span arch comparisons only those results calculated with ELFEN have been presented since similar mechanism analysis is considered too subjective for inclusion here.

All graphs of displacement are of results measured or calculated at the position of the applied load. Additional data that was often recorded during tests, displacements and strains, has been considered in the verification of ELFEN but is not included here.

Peak load measured during the full-scale tests has been defined as the failure load and values are separately summarised in tables for each arch together with normalising factors with the test data. Despite many of the tests having different widths all loads have been converted to load per unit width measured across the bridge (kN/m).

Appendix A shows typical output produced by the mechanism programs Archie, Archie-M and RING. Appendix B includes colour contour diagrams of ELFEN results, vertical displacement, principal compressive stress and Von Mises equivalent (effective) stress for each of the arches investigated at the failure load. The mode of failure is also included.

7.2 TRL Unstrengthened Arches

7.2.1 Mortar Bonded Brick Rings

Figure 7.1 compares the load versus displacement results obtained by all methods of analysis with those obtained from the test. Failure loads are summarised in Table 7.1 and contours of ELFEN results are given in Figure B.1 in Appendix B.

Predictions made with both Archie and ELFEN are almost exact, considered to be somewhat fortuitous, with both failure load predictions within 2% of test results. The best RING prediction was very conservative at just 52% failure load.

The prediction of stiffness by ELFEN was reasonable throughout the load range with displacements within 15% of test results at all stages. Clearly, the conventional arch analysis programs can provide no information on displacement and stiffness.

Figure 7.1 5m Span TRL Laboratory Arch – Comparison of Predicted and Test
Results - Mortar Bonded Brick Rings
Load versus vertical displacement under the line load

It is not clear why the full-scale test exhibited a plateau at around 100 kN/m after which further load could be carried and why the test was stopped at failure and not continued in displacement control. Perhaps the bridge exhibited very little ductility and the researchers anticipated imminent collapse.

Table 7.1 Summary of Test and Predicted Failure Loads

7.2.2 Separated Brick Rings

Figure 7.2 compares the load versus displacement results obtained by all methods of analysis with those obtained from the test. Again failure loads are tabulated appearing in Table 7.2 and contours of ELFEN results are given in Figure B.2 in Appendix B.

Again predictions made with ELFEN are almost exact and within 2% of test results. In this case the best of the conventional analysis programs is Archie-M. Using the highest recommended passive pressure factor the predicted failure is 92% failure load. Interestingly the same analysis with at rest soil pressures yields a predicted failure load of 69% the test result. As displacements cannot be calculated by conventional mechanism analysis the most appropriate soil pressure model has to be judged by the assessment engineer.

As with the mortar bonded case, the prediction of stiffness by ELFEN was reasonable throughout the load range with displacements within 17% of test results at all stages, but with the largest difference occurring during the loading stage between deflections of 2mm and 10mm.

It is suspected that the tested arch during most of the loading was in fact softer than would have been expected had the arch not been damaged before the test and subsequently repaired. It is believed that the repaired arch remained defective for the following reasons.

1. Some distortion had been introduced into the arch profile where the load ¼ point was 10mm high, the crown 55mm low and the ¾ point on average 40mm high compared with the intended shape. Hence the segmental arch had become a slightly lopsided ellipse with the span to crown rise ratio increased by 5%.
    
2. There is some doubt how effective the repair of any damaged masonry in the barrel would have been and so failure of the repaired arch may have been inadvertently preconditioned.

It is unlikely that these factors have significantly affected the failure load but, as has been investigated separately with ELFEN, are the cause of the loading stage stiffness differential.

Figure 7.2 5m Span TRL Laboratory Arch – Comparison of Predicted and Test Results
Separated Brick Rings
Load versus vertical displacement under the line load

Table 7.2 Summary of Test and Predicted Failure Loads

7.3 Bolton Arches

7.3.1 5m Single Span Brick Arches

The load versus displacement results obtained by all methods of analysis with those obtained from the tests for the ring separated and mortar bonded arches are shown in Figures 7.3 and 7.4 respectively. As before failure loads are tabulated with the ring separated failure loads summarised in Table 7.3 and the mortar bonded arch results given in Table 7.4. Contours of ELFEN results are given in Figures B.3 and B.4 in Appendix B.

Predictions made with ELFEN are closest to both test results with the calculated failure loads 14% greater and 12% lower than the test results for the separated and bonded cases respectively. These predictions are matched closely by RING using classic passive soil behaviour in the separated case but ring gives a very conservative result of 46% the failure load for the mortar bonded case.

There is little correlation between the results obtained with Archie and Archie-M and the Test Results. This appears to be entirely due to the limitation of not being able to represent discrete arch ring behaviour. Clearly, this limitation has to be accounted for in any arch bridge strength assessment.

Figure 7.3 5m Span Bolton Arch – Comparison of Predicted and Test Results
Separated Brick Rings
Load versus vertical displacement under the line load

Table 7.3 Summary of Test and Predicted Failure Loads

Although good correlation of predicted and test failure loads for both 5m arches has been achieved with ELFEN comparisons of stiffness in the loading stage is not so good. In the mortar bonded case the test stiffness was approximately double the predicted stiffness. The reason for this disparity is believed to be attributed to the tensile strength of the mortar used in the tests. The mortar, presumably intended to be of designation (iv) did in fact possess compressive characteristics of designation (i), see section 6.3.5, and very likely had some tensile strength.

Figure 7.4 5m Span Bolton Arch – Comparison of Predicted and Test Results
Mortar Bonded Brick Rings
Load versus vertical displacement under the line load

The interface model used to represent mortar joints in ELFEN currently does not include tensile strength nor the accompanying fracture energy to define softening. This type of model, necessary for modern masonry construction, is generally not appropriate for traditional construction of the past two or three centuries; relatively soft bricks and weak mortar.

Table 7.4 Summary of Test and Predicted Failure Loads

7.3.2 3m Single Span Arches and Multi-span Brick Arches

Figure 7.5 3m Single Span Bolton Arch – Comparison of Predicted and Test
Results Mortar Bonded Brick Rings
Load versus vertical displacement under the line load

The load versus displacement results obtained by all methods of analysis with those obtained from the tests for the mortar bonded single and multiple arch bridge test are shown in Figures 7.5 and 7.7 respectively. Failure loads have been tabulated together in Table 7.5. Contours of ELFEN results are given in Figures B.5 and B.6 in Appendix B.

Multi-span results have not been obtained with the convention arch analysis programs since there use here is too subjective for valid comparisons with ELFEN simulations.

Table 7.5 shows that in both single and multi-span cases ELFEN predictions of failure load are 90% of the test results. Stiffness correlation is also reasonable. As to be expected, the influence of multi-span behaviour including piers, with a height to thickness ratio of 3.5, has been to reduce the single span test result by approximately 40%. This trend is reflected by the ELFEN simulations.

Also noteworthy is the test failure mechanism which as shown in Figure 7.6 was matched very closely by the ELFEN analysis. During the test a mechanism involving four hinges in the loaded span and fifth hinge at the base of the first pier, away from the loaded side of the arch,  developed. A very similar pattern emerged in the ELFEN simulation after the failure load had been reached and as the modelled bridge softened, see second inset in Figure 7.6.

Hinge positions recorded during Bolton Test

ELFEN Simulation showing evolving hinge positions, shows contoured vertical displacements

Figure 7.6 3m Multi-span Arch - Predicted Failure Mechanism

Figure 7.7 3m Multi-Span Bolton Arch – Comparison of Predicted and Test Results
Mortar Bonded Brick Rings
Load versus vertical displacement under the line load

The ELFEN model of the multi-span test described in Section 6.3.4 differed slightly from the actual test in terms of the boundary provided by the spandrel walls. Although the walls in the test were separated from the three arch barrels they were built on and connected to the outer  edges of the piers and abutments. Hence their behaviour would have been to provide some strutting across the spans which may have contributed to an elevated test failure load compared with the completely separated spandrel wall equivalent. It was this idealised equivalent spandrel wall that has been modelled. Inclusion of spandrel strutting may have improved the correlation of ELFEN predictions with the test results.

Table 7.5 Summary of Test and Predicted Failure Loads

7.4 TRRL Arches

7.4.1 9.5m Single Span Stone Arch

The load versus displacement results obtained by all methods of analysis with those obtained from the test are shown in Figures 7.8. An additional set of ELFEN predicted results where the influence of mortar softening has been represented are shown in Figure 7.9. All failure loads are summarised in Table 7.6. Contours of ELFEN results where mortar softening has been included are given in Figures B.7 in Appendix B.

Predictions made with ELFEN shown in Figure 7.8 are closest the test results with a calculated failure within 5% test result. Predictions by RING using classic passive soil behaviour are also good and within 10% the test value. The results obtained with both forms of Archie are reasonable and conservative.

The correlation of stiffness between ELFEN and the test was markedly poor in the second half of the loading stage between a load of 160 kN/m to 250 kN/m. It is believed the reduced stiffness exhibited in the test is attributed to the mortar behaviour. To explore this possibility, and to illustrate the flexibility of numerical simulation, a separate ELFEN analysis was undertaken with modified masonry parameters. Essentially a lower characteristic strength for the masonry was used but with additional strain hardening until the original masonry strength was reached. The results are shown in Figure 7.9 and illustrate improved stiffness correlation.

Figure 7.8 Strathmarshie Bridge – Comparison of Predicted and Test Results
9.5m Span Random Rubble Barrel
Load versus vertical displacement under the line load

Figure 7.9 Strathmarshie Bridge – Comparison of Predicted and Test Results
9.5m Span Random Rubble Barrel – Mortar Softening
Load versus vertical displacement under the line load

Table 7.6 Summary of Test and Predicted Failure Loads