Ji Lu Investigation - End Piers
Ji Lu Investigation - End Piers |
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| The P11 and P13 end
piers (Figure 1) were damaged during the Taiwan Earthquake. The crack pattern
observed and surveyed in the P11 and P13 support columns were nearly
identical. Both showed a shear mechanism in the transfer beam and
tension cracking on the outsides of the piers.
Evidence of the shear mechanism in the P11/P13 piers can be seen by the tell tale diagonal shear cracking damage pattern observed. The foundation level tension cracking (Figure 2) was also seen in both the P11/P13 column supports. The cracks were only seen in the outsides of the outer columns. They were orientated mostly horizontal and slightly worse on P13 support. In analysis of the transfer beam, the nominal shear capacity as found from section analysis, shows the section failing in shear at 16.9 MN. From collapse load analysis incrementing the bridge load and given the shear capacity, the section yields in shear far before reaching its bending capacity. This matches well observation found in the field (Figure 1). The frame is shear critical for the geometry and loading pattern. |
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Figure 1 - P11/P13 end pier |
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Figure 3 - Foundation damage of P11 |
| However, in careful observation of the end
pier columns at the foundation level, the crack pattern is opposite from
that predicted by basic frame flexural theory.
In Figure 4, a schematic plot of the moment diagram is shown for the end pier at the north side of the main span (P11). The yellow diagram is shown for the yellow applied lateral load in conjunction with the red vertical load. The blue diagram is show for the case where the load is in the opposite direction and again, in conjunction with the red vertical load. Both diagrams are plotted on the compression side. The crack pattern suggested from this diagram at the foundation level would be minor tension cracking on either the inside of each column only; or, major cracking on the inside of each column with some minor cracking on the outsides. If only one direction of lateral load was prominent, then cracking of the two columns would appear on the same side - the beginning of a flexure mechanism. None of these scenarios were observed. |
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Figure 4 - Moment Diagram of vertical deck load with lateral load |
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| From elastic finite element
analysis of the frame, a diagonal shear strut is formed when coupling the
bridge load with nominal lateral earthquake loading. This principle
compression matches the crack pattern and upon load reversal correlates
well with collapse analysis and visual observation.
However there is, again, a discrepancy in the cracks at the foundation level. The largest compression stresses, marked in green, are on the outside. This matches flexural theory but does not match investigative observation. |
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Figure 5 - FE model of the end pier |
| Modeling the end pier as a series
on struts and ties where the crack angle was measured from observation we
see results that still miss the overall behavior of the frame.
The nonlinear strut and tie model predicted a force displacement load that saw yielding at 17 MN and strain hardening of 4%. The diagonal compression struts never yielded while the vertical ties and the horizontal steel saw behavior in the nonlinear range. The longitudinal anchorage of the smaller depth beam was modeled long enough in length to bring the steel out of the nonlinear range. Then it was connected to the end section with rigid links to maintain equilibrium. The model matched the crack pattern seen in the field again at the beam
level but falls short at the foundation. The model predicted
diagonal cracking along the lines of the struts and contrary to previous
models predicts an inward movement of
the top corner node. However, the inward movement was not enough to
counter the large rotations at the edge of the strut and tie model.
These rotation coupled with inward translations netted in a moment diagram
for the column with less compression in the outside base section
fiber. But, nonetheless, compression. Tension cracking is
still predicted on the inside column faces. |
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Figure 6 - Strut and Tie model force displacement
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| Each of the columns in the P11 and
P13 bents are on independent foundation systems. The
foundation support for the columns are 6 meter diameter pile
extensions.
Upon close observation and consideration of the actual bridge bent boundary conditions, it is clear that the 2 meter by 4.5 meter columns are restrained in the vertical and torsional directions. The columns are also fixed rotationally about the weak axis as the 6 meter bending dimension of the pile extension is paired against the column's 2 meter depth. Lastly, there is sufficient fixity against rotation about the column's strong bending axis. The fixity is evident in the tension cracking observed at the base of the column. The transverse stiffness of each individual column at the ground level, however, is unclear. Laterally at the bottom of the bent column, there is flexibility. The flexibility is from the pile extension bearing on soil but exact values are highly uncertain. Running a suite of analysis in which the lateral spring stiffness is varied from very stiff to nearly free results in curves showing how the base moment and foundation displacement varies with spring stiffness (Figure 7). The frame was modeled elastic with cracked section properties and loading was assumed to be just before shear yield of the transfer girder. |
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Figure 7 - Lateral soil spring model |
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Figure 8 - Response parameters verses soil/pile extension stiffness |
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Given that vertical load is near yield and all other models predict diagonal cracking, the inclusion of a lateral restraining spring with rotational rigidity predicts cracking on the outside with lateral stiffnesses and < 2,500 MN/m. This now provides good agreement with field investigation. |
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