Constructive Cost Models for Evaluating Bridge Design and Impact
Protection Techniques
Paige C. Selby, Intern
Structural Engineering Testing Hall
Civil and Environmental Engineering Department
University of California, Irvine
pselby@smes.org
Constructive Cost Models for Physical Systems
Constructive cost modeling methods provide an analytic approach for understanding the
development of software-intensive systems as well as sophisticated physical systems. One type
of physical system that affects most people every day is a bridge in terms of both efficient
transportation and personal safety. Researchers are focusing increasingly on bridge construction
and monitoring techniques due to the collapse and loss of life in the Minneapolis Interstate
Highway 35W bridge tragedy in August 2007. This article describes research that investigates a
constructive cost model for evaluating bridge design and quantifying the degree of improvement
resulting from emerging technology for impact protection structures. This research was
performed during an internship at the Structural Engineering Testing Hall (SETH) Laboratory in
the Civil and Environmental Engineering Department at the University of California, Irvine.
Constructive Cost Model for Concrete Bridge Maintenance Costs
This research defines an initial version of a constructive cost model for concrete bridge
maintenance costs that is analogous to the COCOMO model for software systems [Boe81]. The
initial model version is as follows:
E = A * L B *  Fi
where E is the bridge maintenance cost in person-months, A is a linear calibration constant, L is
the length of the bridge’s span in meters, B is an exponential calibration constant, and Fi are
multiplicative “cost driver” factors. The initial cost driver factors Fi, multiplicative values, and
definitions are as follows:
F1 = Live load on bridge including degree, duration, and frequency.
 Nominal (1.0) = Within design specification
 Minor stress (1.1) = Violation of design specification by less than 10%
 Major stress (1.2) = Violation of design specification by over 10%
F2 = Age of concrete. Note that concrete’s rate of getting stronger decreases over time.
 Nominal (1.0) = 0 to 5 years
 Minor aging (1.025) = 6 to 15 years
 Major aging (1.05) = 16 to 50 years
F3 = Quality of concrete mix and maturation of initial concrete cure. Note that a 28-day curing
process creates the strongest concrete.
 Nominal (1.0) = Standard concrete mix and 28-day curing process
1

Low (1.25) = Non-standard concrete mix or shorter than 28-day curing process, such as
concrete used pre-maturely at 14 days.
F4 = Geographic location including thermal cycles, degree, and frequency.
 Nominal (1.0) = Warm or moderate climate with minimal thermal cycles
 Minor stress (1.1) = Cool climate but no snow, ice, or freezing
 Major stress (1.2) = Cold climate with snow, ice, and/or freezing
F5 = Impact protection structures
 Nominal (1.0) = None
 Minor protection (0.9) = Honeycombed bumper structures
 Major protection (0.8) = Honeycombed bumper structures plus impact laminate and/or
composite wrap
The model calibration constants A and B are under development, and B is greater than 1.0
indicating the super-linear relationship between bridge length and maintenance cost. The
following sections describe improvements in bridge maintenance costs due to emerging
technologies for impact protection structures.
Horizontal Impact Problem for Bridge Construction
Bridges are designed to carry loads from the top, and most vehicles can fit under bridges easily.
Climate changes affect the clearance between bridges and the vehicles traveling underneath
them. For example, when snow or ice accumulates on top of a relatively tall truck, it may not be
able to fit underneath a bridge. The snow or ice will hit the bridge at a relatively high speed and
cause a horizontal impact to the bridge. The bridge is not structurally designed to receive such a
horizontal impact. Although such horizontal impacts may seem minor, their cumulative effect
on bridge maintenance costs can be substantial.
Honeycombed Bumper Structures for Protecting Bridges
This research investigates the use of honeycombed bumper structures to improve the
effectiveness and efficiency of bridge construction techniques and resulting maintenance costs in
cold climates [Med03]. These bumper structures are intended to dissipate the impact force of a
horizontal vehicle on a bridge because the honeycombed materials crush easily so a bridge is
protected. This protective approach is intended to achieve the following benefits:
 Enable an effective solution to prevent or minimize initial and subsequent damage to
bridges, and therefore, lower bridge maintenance costs
 Provide an efficient approach to design new and retrofit existing bridges
 Facilitate incremental installations of the bumper structures to accelerate benefits
One specific type of honeycombed bumper structure uses resilient materials similar to aluminum
foil. This specific solution has the following additional benefits:
 High strength to weight ratio
 Inexpensive raw materials
 Automated and scalable manufacturing process
2
Research Experiments Underway
Initial values were estimated for the multiplicative cost driver factor F5 that quantifies the effect
of impact protection structures. Research experiments underway at the UC Irvine SETH Lab
strive to measure actual improvement values in order to improve model accuracy. These
experiments quantify the benefits of using honeycomb bumper structures, impact laminate, and
composite wrap to protect bridges. These experiments involve the construction of actual
concrete bridge pillars, the application of strain gauges to the pillars, the crushing of pillars due
to impacts, and the electronic acquisition of detailed experimental data using LabView software
tools. The experimental data include measurements of damage to the bridges and damage to the
impact protection structures in terms of compression. These experiments and the improvements
in cost model accuracy help enable return-on-investment calculations for bridge design and
maintenance.
Future Research
Future research includes the design of “smart bridges” that use electronic sensors, controllers,
and actuators to monitor, control, and affect changes in bridge properties to minimize wear,
extend lifetime, decrease maintenance costs, and improve safety.
References
[Boe81] Barry W. Boehm, Software Engineering Economics, Prentice-Hall, Englewood Cliffs,
NJ, 1981.
[Med03] Medhat A. Haroun, Ayman S. Mosallam, Maria Q. Feng, and Hussein M. Elsanadedy,
“Experimental Investigation of Seismic Repair and Retrofit of Bridge Columns by Composite
Jackets,” Journal of Reinforced Plastics and Composites, Vol. 22, No. 14, 1243-1268, 2003.
3