8. Comparison of Load Testing Results to AxisVM Prediction
The four load tests on the bridge specimen resulted in more than 1,300 recorded measurements of deflections. Each scale reading was taken with an accuracy of 0.254 mm (0.010 in.) with a tolerance of 0.127 mm (0.005 in.). Readings from each pair of scales were averaged to calculate the deflection at that location along the specimen. All deflection values are reported to three decimal places. Using these calculated values, the response of the bridge to the load tests was established and illustrated using plots of the specimen's deflection. A negative value indicates a downward movement and a positive value indicates an upward movement. The results of load tests 2, 3 and 4 are presented, discussed and are compared to corresponding AxisVM model results. The AxisVM models that were created are representative of load tests 2, 3 and 4, will be referred to as AxisVM model 2, 3 and 4, respectively. Additional plots are given in Appendices D, E and F of Babcock (2005).
8.1 Comparison Methods
The most direct method of comparing the analytical results to the behavior of the physical specimen is through a simple visual comparison of the deformed shapes of the stringers and pile caps under each loading that was investigated. Plots of the deflected shapes of each stringer at each load level of each load test and plots of the pile cap displacements were created for each load level of each load test. In addition to the visual comparison, the Average Sum of Squared Errors (ASSE) [Rosenkrantz, 1997] was calculated for the deflections directly underneath the applied loads for each load increment of the three load tests. The following equation was used for this calculation
| ASSE = |  | (8.1) |
| n |
- ΔLTi = Observed deflection of location i from the load test
- ΔVMi = Predicted deflection of location i from the AxisVM model
- n = number of measurements taken underneath the applied load, usually n=4 for the number of stringers in the bridge chord
The calculated ASSE and deformed shape plots are presented in the subsequent sections.
8.2 Comparison of AxisVM Model 2 to Load Test 2
Load test 2 consisted of applying three 4448 N (1000 lb) increments of load at mid-span of span BD as illustrated in Figure 8.1.
Figure 8.2 illustrates the pile cap displacements for this load test at 13344 N (3000 lb). This figure shows that the AxisVM model predicts the pile cap displacement very closely.
Figures 8.3, 8.4, 8.5 and 8.6 illustrate both the observed and predicted deflected shapes of stringers 5, 6, 7 and 8, respectively, for the 13344 N (3000 lb) load level of load test 2.
The predicted deflection for stringer 5 is nearly identical to that observed in the load test, as shown in Figure 8.3. The AxisVM model over estimates the deflection of stringers 7 and 8 near pile cap D by more than 1 mm and under estimates the mid-span deflection for those same stringers by the same margin. However, Figures 8.2, 8.3, 8.4, 8.5 and 8.6 illustrate that the AxisVM model predicted the deflections reasonably well and in all cases the predictions display very similar behavior to those observed in this load test. Plots of the deformed shape of both the stringers and pile caps at the two lower load levels are provided in Appendix F of Babcock (2005) and show similar comparisons.
Table 8.1 lists the calculated ASSE value for the mid-span deflections of stringers 5, 6, 7 and 8 for all three load levels of this load test comparison.
| Load Level | ASSE |
|---|---|
| 4448 N | 5.43% |
| 8896 N | 4.55% |
| 13344 N | 5.17% |
The above table shows that the ASSE value for all three load levels is approximately 5 percent. This measure indicates that the AxisVM model predicted the mid-span deflection directly under the load to within approximately 5 percent of the observed deflection from the physical load testing of the specimen under all three load level increments.
8.3 Comparison of AxisVM Model 3 to Load Test 3
Load test 3 consisted of applying three 4448 N (1000 lb) increments of load at mid-span of span DE as illustrated in Figure 8.7.
Figure 8.8 illustrates the pile cap displacements for this load test at 13344 N (3000 lb). This figure shows that the AxisVM model predicts the pile cap displacement within 1.27 mm (0.05 in.).
Figures 8.9, 8.10, 8.11 and 8.12 illustrate both the observed and predicted deflected shapes of stringers 5, 6, 7 and 8, respectively, for the 13344 N (3000 lb) load level of Load Test 3.
The predicted maximum deflection for stringer 5 is approximately 0.76 mm (0.03 in.) less than what was observed in the load test as seen in Figure 10.9. The AxisVM model over estimates the deflection of stringer 7. Figures 8.8, 8.9, 8.10, 8.11 and 8.12 illustrate that the AxisVM model predicted the deflections reasonably well and in all cases the predictions display very similar behavior to those observed in this load test. Plots of the deformed shape of both the stringers and pile caps at the two lower load levels are provided in Appendix F of Babcock (2005), and show similar comparisons.
Table 8.2 lists the calculated ASSE value for the mid-span deflection of stringers 5, 6, 7 and 8 for all three load levels of this load test comparison.
| Load Level | ASSE |
|---|---|
| 4448 N | 8.59% |
| 8896 N | 7.18% |
| 13344 N | 5.72% |
The above table shows that the maximum ASSE value for all three load levels is slightly less than 9 percent. This measure indicates that the AxisVM model predicted the mid-span deflection directly under the load within 9 percent or less of what was observed from the physical load testing of the specimen under all three load level increments. Also the AxisVM model over estimated many of the stringer deflections.
8.4 Comparison of AxisVM Model 4 to Load Test 4
Load test e4 consisted of applying three 2224 N (500 lb) increments of load directly above pile cap B as shown in Figure 8.13.
Figure 8.14 illustrates the displaced shape of the pile caps under the maximum 6672 N (1500 lb) load for load test 4. AxisVM predicted nearly identical pile cap displacements for this load level.
Figures 8.15, 8.16, 8.17 and 8.18 illustrate both the observed and predicted deflected shapes of stringers 5, 6, 7 and 8, respectively, for the 6672 N (1500 lb) load level of load test 4.
The predicted deflections for all four stringers are very similar to the observed deflections observed from the specimen. Plots of the deformed shape of both the stringers and pile caps at the two lower load levels are provided in Appendix F of Babcock (2005), and show similar comparisons. The AxisVM predicted deflected shapes for the lower levels also match extremely well with the observed data.
Table 8.3 lists the calculated ASSE value for the mid-span deflection for all three load levels of this load test comparison.
| Load Level | ASSE |
|---|---|
| 2224 N | 11.43% |
| 4448 N | 10.01% |
| 6672 N | 1.04% |
The ASSE values for first two load levels are higher than expected. The 6672 N (1500 lb) load level has an extremely low ASSE value, which correlates well with the visual comparison. The noticeable variation in the ASSE values between the load levels is a result of the linear spring approximation used in the analytical computer modeling. The linear stiffness values used when modeling the sand was estimated using the load vs. deformation plots obtained from the pile group tests as described in chapter 5. These plots showed that the piles do not behave exactly linearly; the plots are slightly curvilinear. Therefore, soil stiffness varies at different load levels, with the stiffness being larger at lower load levels. Using the idealized, lower, soil stiffness caused the analytical model to deflect slightly more than what was observed in the physical testing under the lower load levels, causing the larger ASSE value for the 2224 N (500 lb) and 4448 N (1000 lb) load levels. This trend was also seen in the comparisons of load tests 2 and 3 but the variations were not as drastic. Also it is important to notice that the soil stiffness using in the analytical modeling was evaluated using load test results from load test 4 under the 6672 N (1,500 lb) load level. This load case produced the smallest ASSE value, which was expected.