MCEER/NCEER Bulletin Articles: Research
Seismic Vulnerability of Existing Bridge Abutments
by K.L. Fishman and R. Richards, Jr.
This article describes research conducted to date on the development of analytical procedures to assess the seismic performance of existing retaining structures and bridge abutments. It is part of a series of geotechnical studies being conducted under NCEER's Highway Project. Comments and questions should be directed to Professor Rowland Richards, University at Buffalo at (716) 645 2114 ext. 2417.
The objective of the research described in this article is to develop improved analytical procedures for assessing the seismic performance of existing retaining structures and bridge abutments. The current approach for analysis and design is based on the theoretical and experimental work of Richards and Elms (1979) and has been well documented in the AASHTO (1992) code provisions and commentary. The basis of this approach is a limit analysis using a sliding block mechanism for free standing walls or bridge abutments to estimate seismically induced permanent deformation. At present, only the possibility of a sliding mode of failure is considered in the code.
Earthquake damage reports and laboratory tests indicate that wall failure by rotation is fairly common. Bridge abutments may have restrained displacement at the deck level, so the possibility exists for a rotational and/or translational outward movement of the toe. Furthermore, the possibility exists for seismic loss of bearing capacity within the foundation soil in which case, beyond a threshold acceleration level, a mixed sliding and/or rotation mode of deformation can result. Therefore, the main focus of this research is to:
 Extend the current analytic method used to predict the seismic resistance of bridge abutments considering the possibility of seismic loss of bearing capacity
 Observe the seismic response of model bridge abutments in shake table tests
 Compare predictions of seismic resistance to observations, and
 Identify bridge abutments typical of those found in the eastern U.S. which may be considered free standing, and assess their seismic vulnerability
Research Approach
The seismic vulnerability of free standing bridge abutments on spread footings relates to their seismic resistance or that threshold acceleration level (k_{h}), beyond which permanent deformation will occur. A thorough seismic analysis must investigate the possibility of both a sliding mode of failure as well as seismic reduction of bearing capacity.Theory
Figure 1 shows the forces acting on a gravity wall bridge abutment during seismic loading. Loads from the bridge deck are considered to act at the top of the abutment. Depending on the connection detail, horizontal loads from the inertia of the bridge deck may be transferred to the abutment. Body forces acting on the wall are present as well as lateral earth pressure behind the wall. The inertial loading applied to the foundation soil beneath the abutment footing is also considered.Lateral earth pressures which develop behind rigid retaining walls which yield during earthquake loading may be evaluated using a rigid plastic model to describe soil behavior. This approach has been followed by Okabe (1926) and Mononobe and Matsuo (1929) who performed a modified Coulomb analysis in which the inertial load on the failed soil wedge was included in the analysis. The application of the Mononobe Okabe equation to seismic analysis of retaining walls is well established and details will not be repeated here. However, a relatively new approach to the problem of seismic reduction of bearing capacity is applied to the retaining wall problem and shall be described in what follows.
Seismic reduction in bearing capacity has been studied by Richards et al., (1990) and (1993), and Shi (1993). Seismic bearing capacity factors are developed considering shear tractions transferred to the soil surface as well as the effect of inertial loading on the soil in the failed region below the footing. For simplicity, a "Coulombtype" of failure mechanism is considered within the foundation consisting of an active wedge directly beneath the abutment and a passive wedge which provides lateral restraint with the angle of friction between them of f/2. Bearing capacity is evaluated via a limit equilibrium analysis whereby the critical orientations of the failure planes are determined, which minimize the resistance. Shi (1993) compares the Coulomb mechanism with d = f/2 to results from the method of characteristics to verify its accuracy. Shear transfer between the footing and foundation soil is conveniently described by a friction factor:
(1)
where S is the shear traction, k_{h}, is the coefficient of horizontal acceleration, and F_{v} is the normal force applied to the foundation.
The analytic solution gives a bearing capacity formula in terms of seismic bearing capacity factors N_{qE}, N_{cE}, and N_{gE} as
(2)
similar to its counterpart for the static case. For a surface footing on sand only, N_{gE} provides bearing capacity. Figure 2 presents the ratio of N_{gE}/N_{gS}, where N_{gS} is the static case bearing capacity factor. The seismic bearing capacity factor is a function of the friction angle of the foundation soil, f, seismic acceleration coefficient, k_{h} , and f (Shi 1993).
Analysis
Since seismic bearing capacity factors are dependent on ground acceleration, determination of the threshold acceleration requires an iterative procedure easily programmed for digital computation (Fishman et al., 1995(a) and (b)). Referring to figure 1:1. Assume a trial value for k_{h} , and determine P_{AE} from the MO equations.
2. Compute the vertical force result, F_{v} , as
(3)
3. Compute the result of the shear traction to be transferred to the foundation soil as
(4)
4. Compute the factor f using equation (1).
5. Sliding will occur when S= F_{v} tan d_{f} and therefore
(5)
where d_{f} is the interface friction angle between the abutment footing and the foundation soil.
6. Given the friction angle of the foundation soil, f_{f}, and f from step 4, find the seismic bearing capacity factor from figure 2.
7. Compute the seismic bearing capacity P_{LE} using equation (2).
8. Compute the ratio of the limit load to the actual load as
(6)
9. If FS_{B/C}, determined in step 8 is nearly equal to one and FS_{slide} from step 5 is greater than one, stop the iteration procedure. The assumed value for k_{h} is the threshold acceleration for bearing capacity failure, k_{h}^{b}.
10. If FS_{slide} determined in step 5 is nearly equal to one, and FS_{B/C} is greater than one, stop the iteration procedure. The assumed value for k_{h} is the threshold acceleration for sliding failure, k_{h}^{S}.
11. If neither of the conditions in step 9 or 10 is met, select a new trial value for k_{h} and return to step 1.
Description of Experiments
Smallscale bridge abutments were constructed in a seismic soilstructure interaction test chamber which was placed on the shaking table at the University at Buffalo. Complete details of the test chamber are provided by Fishman et al., (1995(a), (b) and (c)), and Divito (1994).Ottawa sand (ASTM C109) was used to study the response of dry soil in the test chamber. Engineering properties of this Ottawa sand are consistent and well established. Pluviation as described by Richards et al., (1990) was used to place the soil in the chamber. This placement method deposits a near homogeneous sand in a very dense state. In future testing, other densities may be obtained by varying the distance that sand is dropped from the hopper.
Model bridge abutments, shown schematically in figure 3, were constructed having a height of 46 cm and a footing width between 15 and 20 cm. The foundation soil beneath the wall footing was 46 cm deep so that development of a failure region, associated with a seismic loss of bearing capacity, was not inhibited. The top of the model provided support for two (W8x10) girders representative of a bridge deck load. Although a prototype abutment may not be properly modeled in a lg test when elastic response is being considered, the limit state scaling laws apply; i.e., model dimensions are scaled in direct proportion to those of the prototype, whereas forces considered on the prototype are proportional to the dimensional scaling factor squared. Deformations are independent of scale.
Three different models were tested. For Model I, the bridge deck rested on a roller support atop the bridge abutment such that no shear transfer was allowed between the deck and abutment. The abutment was designed such that a sliding mode of failure was expected. Model II used the same bridge deck/abutment connection detail, but failure from seismic loss in bearing capacity was anticipated. For Model III, a pinned connection between the bridge deck and abutment was used. Table 1 summarizes the parameters for each model including the wall weight, W_{W} , deck load, F_{deck}, length of footing, B_{f}, backfill/wall interface friction angle, d_{W} footing/ foundation soil interface friction angle d_{f}, the foundation soil friction angle, f_{f}, unit weight of the backfill soil, g_{W}, and unit weight of the foundation soil, g_{f}.
Table 1: Abutment Model Parameters
Model
W_{w} (N)
F_{deck} (N)
B_{f} (mm)
f_{W}
d_{W}
d_{f}
f_{f}
g_{W}
g_{r}
I
276
818
143
30
20
20
38
15.4
17.0
II
1172
356
152
36
22
30
38
16.7
17.0
III
1221
356
203
36
22
30
28
16.7
17.0
Interface friction angles for Model I and Models II and III are different. In Model I, the interface friction was developed between smooth steel and sand. Models II and III were designed to reduce the risk of sliding failure so interface shear strengths were increased by attaching coarse sand paper to the backside of the wall and the underside of the footing. Interface shear strengths were determined by pull tests with the model inside the test box.
Given the soil parameters and wall geometry for each model as presented in table 1, static loading from active earth pressure P_{As}, and static safety factors against sliding and bearing capacity failure were computed and are shown in table 2. Table 3 summarizes the threshold acceleration levels computed for each model. These were determined using the analytic method already described. The computed dynamic active earth pressure, necessary to develop sliding failure, P^{s}_{AE}, or bearing capacity failure, Pb_{AE} is also shown in table 3. The smallest of these values governs the seismic response of the wall. The observed threshold acceleration of each test is also shown in table 3.
Table 2: Static Factors of Safety
Model
P_{As} (N)
FS _{slide}
FS_{BC}
I^{1}
347
1.4
1.4
II
374
2.77
3.7
III
374
2.86
3.54
^{1} In Series I, H = 406 mm initially. H is 457 mm for models II and III.
Table 3: Threshold Levels of Acceleration
Model
P^{SAs/PbAE (N)}
K^{Sh}
K^{bh}
k^{obsh}
I^{1}
365/?
0.2
0.5
0.25
II
743/587
0.30
0.22
0.20
III
1619/1023
0.60
0.43
0.46
^{1} In Series I, H = 356 mm when k_{h} =0.2 g.
H is 457 mm for models II and III.Preliminary Results
Model Testing
Model bridge abutments were subjected to a series of sine ramped pulses of acceleration, sine train acceleration records, and time histories of acceleration from records of naturally occurring earthquakes. Colored lines were placed in a horizontal and vertical grid pattern beneath the footing and behind the bridge abutment in order to observe soil deformation. Figures 4 (a) and (b) are photographs of Model II before and after testing. Model II featured a free connection to the bridge deck at the top of the abutment. Figure 4(b) shows the bridge abutment after being subjected to acceleration pulses with a maximum amplitude of 0.5g. Failure surfaces which developed within the backfill and foundation soil are vividly portrayed. Significant tilting of the bridge abutment is also observed corresponding to a loss of bearing capacity.Figures 5(a)  (e) show the response of the Model II bridge abutment subjected to an input sine train acceleration record. Figures 5(a) and (b) display the time history of acceleration of the input (solid line) compared to the acceleration response observed at the bottom of the abutment (dashed line, 5(a)) and within the foundation soil (dashed line, 5(b)). Due to the sensitivity of accelerometer output to changes in alignment and the excessive rotations which occurred during deformation, the measured acceleration for the abutment and foundation soil did not return to zero at the end of the sine train. The error that rotation and corresponding misalignment of the accelerometers introduces on measured acceleration may explain the erroneous observation of increased seismic resistance with increasing cycles of input. Prior to excessive abutment tilting, a threshold acceleration level for the wall of 0.2 g is clearly evident. Furthermore, evidence of a threshold acceleration within the foundation soil is indicative of a seismic loss of bearing capacity.
The observed permanent deformation presented in figures 5(c), (d) and (e) includes horizontal displacement, vertical displacement, and wall rotation. Note that permanent displacement only occurs when the input acceleration exceeds the seismic resistance of the bridge abutment (threshold acceleration). The occurrence of significant vertical displacements and eventual tilting of the bridge abutment confirms that the mode of failure is seismic loss of bearing capacity. Results presented in table 3 show that the predicted and observed response of the Model II bridge abutment are in good qualitative and quantitative agreement.
Summary of Results
Table 3 provides a summary of the observed threshold accelerations, k_{h}^{obs} for the three models, and provides a comparison with thresholds predicted for sliding and bearing capacity, k_{h}^{s} and k_{h}^{b}. In all cases, the observed threshold acceleration is close to the lowest, and therefore most critical, as predicted by the analysis of sliding and seismic reduction of bearing capacity modes. The comparison between predicted and observed threshold accelerations is considered good and implies a range of error between predicted and observed values of 6 0.05g. Further details of the shake table testing and results are presented by Fishman et al. (1995 (a) and (b)), and Divito (1994).Survey of Existing Bridge Abutments
As part of its bridge inspection program, New York State maintains a comprehensive data base describing its existing bridge inventory (NYDOT, 1991). The data base may be obtained in a compressed format on diskettes and is accessible through a number of commercially available database management programs. The data base contains over 170 fields of information for each bridge including the age of the structure, number of spans, type of bridge abutment, height of bridge abutment, foundation type, and details of the bearing between the bridge deck and the top of the bridge abutment. In the first part of the survey, this data base was queried to study the demographics of the bridge abutment population in the State and to identify those for which the methodology under investigation may apply.Based on information obtained from the initial survey, fifty bridge abutments were identified for detailed analysis in part two of the survey. Construction drawings and subsurface soils data were obtained for the selected bridge abutments. Using this information, wall geometry, bridge deck loads and shear strength parameters of the wall backfill and foundation soils were determined. Each bridge abutment was analyzed to determine both static factors of safety as well as the seismic resistance. The following is a summary of results from the survey of New York State bridge abutments. A detailed discussion is presented by Younkins (1995).
Of the 39,346 bridge abutments listed in the New York State inventory, 15,716 are noted as being founded on spread footings placed on cut or fill material. Therefore, the analysis addressed by this research may be applicable to as much as 40% of all bridge abutments in New York State. Editor's note: The state bridge inventory may not adequately reflect that many of these abutments could have piles under the footings. As a result, the conclusions regarding the number of abutments for which this analysis is applicable may have been overestimated.
There is no clear distinction between the construction practices of the New York State Department of Transportation (NYSDOT) and those of other agencies within the state. NYDOT is the owner of 43% of the bridge abutments on spread footings. Historically, the practice of using spread footings has not changed when comparing those constructed prior to 1960 to those after 1960. However, since 1960, there is a clear trend favoring cantilever wall designs over gravity wall designs. Fortyfive percent of all the bridge abutments on spread footings are the gravity type design, and 39% are the cantilever type. More than half (63%) of all the bridge abutments founded on spread footing are for single span bridges. Of particular interest is the fact that nearly half (44%) of the bridge abutments on spread footings are taller than 20 ft. The significance of this statement will become apparent from the results of the detailed analysis.
The demographics of bridge abutments constructed in westem New York were compared to those of the state population and deviations were found to be minor. Therefore, the inventory of bridge abutments in western New York was considered representative of the state. Fifty bridge abutments located in western New York were selected for detailed analysis. As a point of reference, static safety factors relative to a sliding failure, overturning and bearing capacity were computed for all abutments considered. The computed safety factors for sliding and overturning were all above 1.5 and 2.0, respectively, but were much higher for shorter walls. This was due to the fact that deck loads are uncorrelated to wall height. For shorter walls, the deck load overpowers the weight of the wall itself; thus, it has a much larger impact on computed safety factors when compared to taller, heavier walls. Relatively speaking, for shorter walls, the seismic resistance is strongly affected by the connection detail between the top of the abutment and the bridge deck. If the bridge deck is fixed to the top of the abutment, an inertial reaction is transferred to the abutment/soil system which tends to drive the system to failure during a seismic event. If a free connection exists between the bridge deck and the top of the wall, this inertia is not transferred to the abutment and seismic resistance is higher.
Figure 6 presents the results of the seismic vulnerability study applied to western New York bridge abutments. All bridge abutments over 20 ft. high had a computed seismic resistance less than 0.2g with many less than 0.15g. These levels of acceleration are considered possible even with the moderate level of seismic hazard in parts of New York. Considering that there are 7,000 bridge abutments in New York over 20 ft. high and founded on spread footings, a significant portion of the bridge abutment inventory is vulnerable to seismically induced, permanent deformation.
In addition, two of the cases studied, representing abutments over 25 ft. high, had computed seismic resistances of less than 0. l g with one as low as 0.06 g. There are nearly 1,400 bridge abutments in New York State which could fit into this category. The likelihood of these structures suffering excessive permanent seismic induced deformation in the future is very high. A more thorough investigation of bridge abutments on spread footing having heights in excess of 25 feet is warranted, and strongly recommended.
Conclusions
The research presented in this article is part of a broader, six year research effort on Seismic Vulnerability of Existing Highway Construction sponsored by the Federal Highway Administration. The analysis described herein applies to bridge abutments which may be treated independent from the bridge superstructure and subject to a sliding and/or tilting mode of failure. The analytic method has been verified based on results from shaking table tests with small model bridge abutments. A survey of existing construction in New York State indicates that the analysis may be applicable to a significant portion of the inventory. The methodology will be useful from the standpoint of seismic risk assessment as applied to existing construction and levels of seismic hazard typical of the eastern United States.References
AASHTO, (I 992) Guide Specifications for Seismic Design of Highway Bridges.Divito, R., (1994), "An Investigation of the Seismic Reduction of Bearing Capacity for Gravity Retaining Wall Bridge Abutments, " Master's Thesis, submitted, University at Buffalo, New York.
Fishman, K.L., Richards, R. and Divito, R.C., (1995), "Critical Acceleration Levels for Free Standing Bridge Abutments, " Proceedings, Third International Conference on Recent Advances in Geotechnical Earthquake Engineering and Soil Dynamics, University of Missouri, Rolla, Vol. 1, pp. 163169.
Fishman, K.L., Richards, R. and Divito, R.C., (1995) "Seismic Reduction of Bearing Capacity and Threshold Acceleration Levels for Gravity Wall Bridge Abutments," Journal of Geotechnical Engineering, ASCE, accepted and under revision.
Fishman, K.L., Mander; J.B. and Richards, R., (1995), "Laboratory Study of Seismic Free Field Response of Sand, " Soil Dynamics and Earthquake Engineering, Elsevier; Vol. 14, No. I, pp. 3345.
Mononobe, N. and Matsuo, H., (1929), "On the Determination of Earth Pressures During Earthquakes, " Proceedings, World Engineering Congress, Vol. 9, pp. 179187.
NYDOT (1991), "Bridge Inventory Manual, " Bridge Inventory and Inspection System, Albany, New York.
Okabe, S., (1926), "General Theory of Earth Pressure," Journal of Japanese Society of Civil Engineering, Vol. 12, No. 1.
Richards, R., Elms, D.G., and Budhu, M., (1990), "Dynamic Fluidization of Soils, " Journal of Geotechnical Engineering, ASCE, Vol. 116, No. 5, pp. 740759.
Richards, R., Elms, D.G., and Budhu, M., (1993), "Seismic Bearing Capacity and Settlements of Foundations, " Journal of Geotechnical Engineering, ASCE, Vol. 119, No. 4, pp. 662674.
Shi, X., (I 993), "Plastic Analysis for Seismic Stress Fields, " Ph.D. Thesis, University at Buffalo, New York.
Younkins, J., (1994), "Seismic Vulnerability of Bridge Abutments in New York State, " Masterís Project, submitted, University at Buffalo, New York.
NCEER Bulletin, July 1995, Vol. 9, No. 3
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