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Actuarial Life Expectancy Projections for Bridges.
March 1997
By Heinrich O. Bonstedt, Executive Director
Prestressed Concrete Association of Pennsylvania
1042 North Thirty Eighth Street
Allentown, Pennsylvania 18104-3420
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INTRODUCTION
DATA SOURCE
LIMITATIONS OF ANALYSIS
GENERAL
THE EVALUATION PROCESS
ESTIMATES
CONCLUSIONS
ACKNOWLEDGMENTS
APPENDIX A
APPENDIX B
APPENDIX C
INTRODUCTION
One can hardly read a newspaper or listen to a newscast without learning what has
been determined by the latest poll or to find what latest trend has been discovered
by a new study.
Modern marketing executives depend upon deep and continuous flows of information
in order to draw conclusions and make decisions. In the past twenty years, new information
technologies and systems have been developed that allow for the effective management
and analysis of such information flows.
Marketing decision models are frequently used to determine the characteristics,
study the trends, performance and satisfaction contained in the marketing data flow
and to make long range forecasts and projections.
This is, for example, of great importance in the marketing of life insurance products.
While the general population, born in a specific year, may have a life expectancy
of 70 years, there will be certain sub-segments who can expect to live longer, e.g.
women, while other sub-segments, such as divorced males, will have a shorter life
expectancy. Such global life expectancy projections consider that some members of
the sub-segment will die in their teens while others will live beyond 100. Life
expectancy numbers, which are the basis for rate making in insurance, may be specifically
wrong but will be generally right.
When viewing deficiency rates for bridges and the age of bridges when their conditions
reach poor and intolerable ratings that require a high priority for replacement,
it is interesting to note that this is very similar to what actuaries see when studying
mortality rates of populations.
Maintenance and environmental factors could be used for creating further sub-segments
for evaluation: for example in the area of life insurance by people who never exercise
or smoke or in the world of bridges by those that are subject to the use of deicing
salts and poor maintenance practices. But the lack of such sub-segmentation does
not invalidate the overall trend that might be measured in otherwise defined segments.
Today, there is an increasing interest in the highway engineering community to consider
life-cycle costs in the design of highway structures.
Indeed, the 1991 Intermodal Surface Transportation Efficiency Act mandates that
planning processes consider life-cycle costs.
The objective of this paper is to show that when engineering data is entered into
such a marketing decision model, one of the ingredients for a reasonable scenario
that will allow life-cycle cost analysis can be established: the ultimate relative
life expectancy of various design material alternatives.
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DATA SOURCE
Good and reliable market and trend projections rely on appropriate information selection
to ensure that sample size and design as well as useful information items (i.e.
base data) are utilized.
For analysis of highway bridges, the Federal Highway Administration compiles a significant
amount of data on all of the nation's bridges in the National Bridge Inventory
data base which is prepared according to a standard Recording and Coding Guide.
"By having a complete and thorough inventory, an accurate report can be made
to Congress" and it provides the data necessary to "produce Defense Bridge
and Federal Emergency Management Agency (FEMA) reports".
The data is the result of the more than 90 items that are organized on a Structure
Inventory and Appraisal sheet which is prepared for each bridge according to rules
contained in a coding guide.
This raw data is the basis for this study, but, for the purpose of this analysis,
some limits were applied:
•Only bridges constructed after 1950 were considered. The reason for placing this
limitation on the data is that not all material alternatives to be compared were
available prior to that time.
•Only structures where the distance between the backwalls of the abutments was over
20 feet were selected. The reason for this to eliminate culverts.
The result is a universe of 327,829 bridges.
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• Only deficiencies as the result of condition ratings of 4 or less for deck, superstructure
and substructure or an appraisal rating of 2 or less for structural condition were
considered. The reason for these levels were established because of the urgency
for remedial action that is called for. (Appendix A - Definitions of Deficiency
Ratings) Deficiencies resulting from waterway adequacy or approach roadway alignment
were excluded.
This results in 45,587 bridges that are rated as deficient. (Table 1)
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Table 1: Summary of 1994 National Bridge Inventory |
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Inventory
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Rated as Structurally Deficient
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units |
|
units |
% |
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Concrete |
|
|
|
|
|
Reinforced |
91,886 |
6,027 |
6.6 |
|
|
Prestressed |
88,393 |
3,219 |
3.6 |
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Structural Steel
|
118,424 |
22,928 |
19.4 |
|
Timber |
27,817 |
13,199 |
47.4 |
|
Other |
1,309 |
214 |
16.3 |
|
|
---------- |
---------- |
-------- |
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Total |
372,829 |
45,587 |
13.9 |
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Over the timeframe considered by this study, there has been a shift in the use of
construction materials - especially since the introduction of prestressed concrete
in the 1950’s.
This steady shift in market shares would not have occurred if the only thing that
the new material, prestressed concrete, had to offer was a low initial cost.
While engineering standards and specifications aim to create solutions of equal
performance across all materials, the actual results indicate that concrete bridges
seem to out-perform their competitive materials.
It is reasonable to expect that, as a given population ages, the percentage of structures
rated as deficient will increase. This assumption is generally confirmed by the
trends across all materials and holds true for all of the road systems studied (Appendix
B) as well as for the elements that are considered for the sources of deficiencies:
substructures, superstructures, decks and the appraisal ratings (Appendix C).
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LIMITATIONS OF ANALYSIS
Within the sample, conditions affecting life expectancy, such as location, maintenance,
uniformity of rating guideline applications, etc., may vary substantially, but overall
trends and relative relationships should hold true for the universe.
The impact of maintenance, or the lack thereof, was not considered in the computations
and a continuation of past practices was assumed for the future.
The resulting projections, which may in specific cases be wrong, are meant to show
directions that will be generally true.
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GENERAL
The purpose of this project is to further evaluate the National Bridge Inventory
data with the following goals:
•To determine the deficiency trend rates by type of bridge construction material
and by type of road system for these bridges.
•To evaluate differences in the types of deficiencies noted by type of bridge material
and by type of road system for these bridges.
•To compare the various alternatives and to establish a basis on which a comparison
of relative service life expectancy could be made.
For bridges constructed after 1950 in five categories of road systems (Interstate
Highways, US Highways, State Routes, County Roads, and All Roads), four categories
of bridge materials (Prestressed Concrete, Reinforced Concrete, Structural Steel,
and Timber) and four reasons for deficiencies (deck, superstructure, substructure
and appraisal rating) were extracted from the National Bridge Inventory.
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THE EVALUATION PROCESS
All data is input to data files and evaluated using SORITEC, a well known statistical
program, to establish trends. In each case, the resulting trend formula was parabolic,
following the general algorithm:
Y = a + bx + cx2
Where,
Y = the percentage of bridges rated deficient
x = the number of years since the bridge was constructed
In total 18 estimators were calculated, one for every category of road type against
each bridge type, except for timber bridges on the Interstate Highway and US Numbered
Route systems, where there were insufficient data to allow computation of an estimator.
The fit of the data was very close and resulted in the standard errors listed in
Table 2.
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Table 2: Standard Errors |
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Highway System Type |
Prestressed Concrete
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Reinforced Concrete
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Structural Steel
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Timber |
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Interstate |
3.240 |
4.621 |
2.017 |
N/A |
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US Numbered
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2.638 |
3.990 |
2.062 |
N/A |
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State Highways
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2.151 |
2.849 |
1.729 |
15579 |
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County Roads
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2.472 |
1.841 |
6.437 |
11390 |
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All Road Systems |
4.940 |
5.038 |
5.008 |
12358 |
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Note that standard error, in this case must be expressed in the same terms as Y.
So, it becomes the percentage variation around the central estimate of the percentage
of bridges becoming deficient in any "x" year. |
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ESTIMATES
Service Life Expectancy was defined as the time required for all structures to reach
a 95 percent probability of being rated as structurally deficient, given a continuation
of the maintenance and rehabilitation practices of the past which have generated
the basic data.
To estimate the number of years required for all structures of a specific type to
reach this 95 percent probability of being rated as deficient, the estimator formulas
established by SORITEC were used to produce the estimated years of service life
expectancy shown in Table 3.
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Table 3: Estimated Years of Service Life Expectancy, by Category |
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Road System
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Bridge Type
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Interstate Highways |
US Highways
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State Routes
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County Roads
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Concrete |
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Prestressed |
83 |
75 |
69 |
73 |
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Reinforced |
102 |
93 |
78 |
66 |
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Structural Steel
|
67 |
68 |
63 |
55 |
|
Timber |
N/A |
N/A |
53 |
50 |
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CONCLUSIONS
While it is certainly true that to an engineer every bridge is different in thousands
of ways, from design and construction technique to climate, weather conditions,
and traffic, an exhaustive engineering study of each variable would require an enormous
amount of time and would only raise more questions without ever being able to provide
an answer. The marketing approach, on the other hand, seeks to examine only basic
criteria shared in, to varying degrees, by all the systems under investigation.
An analogy would be the comparison of a photograph to a simple line sketch: unlike
the photo, a sketch uses only the absolute minimum of detail, yet, is sufficiently
capable of illustrating the subject.
This investigation of underlying trends through approximation does establish general
vectors and velocities, which indicate that concrete out performs any of the competing
materials in bridge construction.
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Datasource
Table 3 shows that bridges on road systems with higher traffic loads (Interstate
Highways) tend to have longer life expectancies than bridges on road systems normally
associated with lower traffic volumes (State Routes or County Roads). This may be
the result of closer maintenance attention.
The data presented for evaluation is minimal to allow the comparisons of all the
individual road system and material categories that were to be attempted. Especially,
since years when no deficiencies were reported can not be considered in the computations.
Thus, the information generated for the "All Roads" category will be more
reliable than the individual road system categories, simply because there is more
data to use.
Table 4 shows the comparable order of service life expectancy for all the materials
studied for all the road systems and it shows that concrete bridges, given the experiences
of the past, will generally last twenty five percent longer than steel bridges and
fifty percent longer than timber bridges.
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Table 4: Service Life Expectancy for All Roads |
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|
Upper Estimate** |
Central Estimate
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Lower Estimate** |
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Concrete |
|
|
Prestressed |
78 |
73 |
68 |
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Reinforced |
77 |
72 |
67 |
|
Structural Steel
|
63 |
58 |
53 |
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Timber |
62 |
50 |
38 |
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Note: **The Upper and Lower Estimate is one standard error out from the Central
Estimate. |
The broad trends identified for each of the categories have high coefficients of
correlation, indicating that the relationships seem to make sense and thus are worthy
of attention.
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It is also worthy of note, that the relative performance between the competing bridge
construction materials always have the same relationships and general performance
trends for each of the four elements for deficiency: Sub Structure, Super Structure,
Deck and Appraisal Rating, that were considered in this study (Appendix C).
If an insurance actuary had to establish insurance rates for bridges, these performance
results certainly would result in much lower premiums for a concrete bridge than
one constructed of timber or steel.
If an accountant had to develop the depreciation cost for a life cycle costing model,
the reduction of the asset value, based on wear and tear in use, would certainly
have to consider these relative performances in service life expectancy.
To have parity on the basis of life expectancy, the initial costs for a bridge would
have to be factored by the following:
Prestressed Concrete 1.00
Reinforced Concrete 1.01
Structural Steel 1.26
Timber 1.44
The debate will go on while improvements in design and construction and materials
will continue. And, although these conclusions will be specifically wrong in many
instances, there are too many indications that the projected relative performance
between these materials will be generally right!
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Acknowledgments
The author would like to acknowledge the contributions of Reid Castrodale, Program
Manager Bridges, Portland Cement Association, for providing the data extracts of
the specific fields used from the 1994 National Bridge Inventory, and of Kip Cassino,
Research Director, Knight Ridder, for refining the data analysis and for making
independent checks of the projection methods and results.
Appendix A
Definitions of Deficiency Ratings from Federal Highway Administration Report FHWA-ED-89-044
(December 1988) "Recording and Coding Guide For The Structure Inventory And
Appraisal of The Nation’s Bridges"
Condition Rations for use in evaluating: Substructure, Superstructure and Deck
9 Excellent Condition
8 Very Good Condition - no problems noted
7 Good Condition - some minor problems
6 Satisfactory Condition - structural elements show some minor deterioration
5 Fair Condition - all primary structural elements are sound but may have minor
section loss, deterioration, spalling or scour
4 Poor Condition - advanced section loss, deterioration, spalling or scour
3 Serious Condition - loss of section, deterioration, spalling or scour have seriously
affected primary structural components. Local failures are possible. Fatigue cracks
in steel or shear cracks in concrete may be present
2 Critical Condition - advanced deterioration of primary structural elements. Fatigue
cracks in steel or shear cracks in concrete may be present or scour may have removed
substructure support. Unless closely monitored it may be necessary to close bridge
until corrective action is taken.
1 "Imminent" Failure Condition - major deterioration or section loss present
in critical structural components or obvious vertical or horizontal movement affecting
structure stability. Bridge is closed to traffic but corrective action may put back
in light service.
0 Failed Condition - out of service - beyond corrective action.
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Appraisal Ratings for use in Structural Evaluation
9 Superior to present desirable data
8 Equal to present desirable data
7 Better than present minimum criteria
6 Equal to present minimum criteria
5 Somewhat better than minimum adequacy to tolerate being left in place as is
4 Meets minimum tolerable limits to be left in place as is
3 Basically intolerable requiring high priority of corrective action
2 Basically intolerable requiring high priority of replacement
1 This value of rating code not used
0 Bridge closed
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Appendix B
Rates of Deficiency of Considered Road Systems
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Appendix C
Rates of Deficiency of Considered Elements
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