Bridge Rehabilitation Feasibility 

This article is an abbreviated version of the paper presented by D. C. Marett, P. Eng., Chief Structural Engineer, Regional Municipality of Ottawa-Carleton, and W. Remisz, Structural Evaluation Engineer, Regional Municipality of Ottawa-Carleton, which was presented at Bridge Evaluation & Rehabilitation Seminars on 14 March 1988 in Ottawa and 16 March 1988 in Montreal. The seminars were organized by the Canadian Society for Civil Engineering and the Technical University of Nova Scotia. For a full text refer to the proceedings.

General

In the last few decades, much emphasis has been placed on bridge rehabilitation. Often it is not clear what is meant by various terms, and such words as renovation, reconstruction, retrofit, restoration have been used interchangeably.

For our purposes, the definition used herein is similar to that of the American Heritage Dictionary, namely, "restore to privileges, reputation, or proper condition..." Upgrading or global structural strengthening is not part of the standard rehabilitation process, although individual components may be replaced or strengthened.

The technical definition is "a modification, alteration, retrofitting or improvement to a structural system or sub-system in order to correct defects or deficiencies to ensure a reasonable service life". It realises the post construction activities that are necessary to restore a structure to a level of strength and condition previously held by the existing structure.

It assumes an initial satisfactory level of service that has been eroded by some mechanism be it material deterioration, initial fault or accident damage. Any upgrading is in order to restore the structure to a satisfactory service level. Rehabilitation is a construction action taken at some point in time during a structure's service life. Whether it is feasible to undertake that action either in itself or in combination with past or future anticipated events is another matter.

The dictionary definition of feasibility is "practicable, manageable, serviceable or plausible". In the engineering sense, an action today would depend on the financial sensitivity of the action "rehabilitation" when taken in the context of other events, both past and predicted in the structure’s life cycle.

At the present state of our technology, it may be assumed that just about anything can be rehabilitated, but at what cost?

Philosophy

Perhaps the best way to trace a decision making process is through an example. For this purpose, I have taken a relatively new bridge, which has undergone few construction activities. Before describing this structure, it is imperative to realise that if one makes a decision today in isolation, without looking at future costs and without looking at the existing structure's history, this is tantamount to a "hunch" decision.

The Structure

Carling Avenue Grade Separation

Background

This grade separation was built by the City of Ottawa (contract 62-92, Carling Avenue, Stage IVB, Phase 2) in 1963 as a Connecting Link Agreement.

Structure

The structure is a three span continuous steel girder system of spans of 65', 87' and 65' bearing to bearing. It has a grade of +1.3% and a skew of ten degrees. In section, 6 rows of 36 WF 170 girders at 7'- 9" centres form the primary system which act composite with a 8" deck slab through 5" channel shear connectors. The girders are cover plated at the piers on both flanges (11" x 1" x 32' sym.). The structure has a width of 92' and contains four traffic lanes, two 6 ft sidewalks and a 4 ft median.

Initial Construction

Construction of this bridge was completed by public tender and the low bid of $310,750.20 was by W. D. Laflamme Ltd. This bid was received by the City of Ottawa on 22 Jan 63 and was awarded by City Council on 18 Mar 63. Allowances of $31,075.00 (10%) for both engineering and contingencies resulted in a gross allocation of $372,900.20 at this time. This was subsequently increased to $525,000.00 later in the year.

The original construction schedule called for utility relocation in May and early June, pile driving in June, substructure work in July, structural steel in August, deck slab concreting in September, and railing, etc. in October 1963. Project completion was delayed about a month from the above schedule. By 31 October 1963 the deck steel and concrete had been placed and the structure substantially finished.

Structure Chronology

At the time of the construction of this facility, finger plates were used on many structures. The use of an open type joint in combination with the bearing type utilised and bearing seat geometry resulted in what would be realised as a major initial defect.

During the passage of time, concrete in the north west abutment disintegrated to such an extent that major repairs would become necessary. The disintegration was attributed to a poor air-void system.

This ultimately caused other problems, which were rehabilitated as the deficiencies occurred. The details of this work are itemised on Figure 1 -"Structure Chronology and Cost Chart" and in Appendix 'A' entitled "Deficiency Occurrence and Retrofit".

Reference to this material will generally indicate the accumulation of substructure deficiencies as a consequence of inadequate joints. Table No 1 entitled "Single Application (Rehab Costs) details the major contract cost breakdown for this work.

Reference to the Structure Chronology is also important with respect to the study of past deficiency and rehabilitation history and the projection of future construction actions that may take place.

Figure 1 is divided vertically by three sections. The middle row is chronologically divided into a past history data file, future data file, and a projected life range. Symbolically, the major structure actions and works are depicted by year in terms of the three sub-systems considered.

Structure No. 609

Carling Avenue Grade Separation

SINGLE APPLICATION (REHAB COST)

CONSTRUCTION COSTS

Table No 1 – Single Application (Rehabilitation Costs)

a. Protection Sub-system,
b. Superstructure Sub-system, and
c. Sub-structure Sub-system

Also included because of their importance for durability and articulation parameters respectively are joints and bearings.

The future data file indicates projected future construction activities that will probably be necessary to maintain structure serviceability. This Life Cycle Case, as indicated, is one of a few scenarios which can be examined to determine the feasibility of a certain program and decision pertinent to this structure.

Also in this figure, on the upper area, is a histogram of past construction costs. In the bottom area is a histogram of engineering costs as well as a record of historic average annual daily traffic (AADT) information. It is to be noted this information may be manipulated to yield present worth data by direct relationship to construction cost indices.

The manipulation of future cost data is more cumbersome. This is handled on the basis of present day estimates projected to the future dates by means of interest formulas and effective interest rate data. Hence, the projected costs are transformed back to present worth and annual cost. The details of this are presented in a later section.

Technical Feasibility

It has been seen that this structure, like all others, is not a perfect structure even at its origins. Some components have degraded faster than others.

What has taken place is a controlled component replacement or retrofitting to maintain its service life.

The previous Table No 1 entitled "Single Application Rehabilitation Costs" detailed the cost in terms of the sub-systems and implementation costs. In general, it can be seen that for these rehabs the cost was less than 20% of the Bench Mark replacement costs. What has happened however, is that more of this money is being used for implementation or non- structural items. For the rehabs detailed, the costs range from 15% to 55% of the project costs, exclusive of user costs.

It is also noted that these rehabs involved a relatively small part of the structure. As the structure ages, relatively larger works and costs can be expected. A standard failure rate versus time graph categorises a three stage life cycle with a break-in period at early life, a middle normal operating period and a later degrading or deteriorating period in which the increase in failure tends to be exponential. In the immediate period before this stage is the time when rehabilitation decisions are critical.

Program Models

In order to facilitate a comparison of engineering decisions and their impact on expected cash flows, different economical models have been developed.

There are two basic approaches to the problem of evaluating rehabilitation and replacement options.

One, widely accepted, is to disregard present worth of the existing structure and any costs incurred to date.

This problem is then reduced to two alternatives; Models 'A' and 'B'.

1. This model replaces the structure today and starts a new operating cycle which will end after a design life of N years (say 50), or
   
2. This model includes rehabilitating the existing structure today and then replaces it after N1 years.

In both alternatives, one must include all future single (F_k), constant (C), or gradient (G_m) costs associated with regular upkeep of the structure. In Model 'A', the cycle will end after N years, whereas in Model 'B' the cycle will end after (N1+N) years. In other words, Model 'B' is immediately followed by and includes the cash flow of Model 'A'. In any cases, utilising these models one may consider the salvage value of the existing structure (B), and/or the salvage value of the replacement structure (S) at the end of the cycle.

Another approach would be to consider the present value of the structure (PW) and its age or past life (PL) and to forecast future costs (FC) up to the end of future life (FL). This should be the time when the original structure reaches its design life. It is noted that, in this model, one is evaluating the cash flow necessary to provide service for a shorter period of time, even though the overall life cycle is considered the same.

Two alternatives have been developed for this approach; Models 'C' and 'D'.

3. This model is for the operation of the structure to the end of life expectancy (M) and then the structure is replaced.
4. This model is to rehabilitate the structure at any time (N2) in the future and then to have the structure in service for an extended future life (FL) until the structure reaches its life expectancy (M1).

A BRICOM (from BRIidge COst Management) computer program was written in QuickBasic which simulates a spread sheet philosophy in manipulating all data pertaining to models 'A', 'B', 'C' and 'D'. These models provide Equivalent Annual Cash Flows (EUACs) necessary to replace, rehabilitate, or operate the structure.

The present value of all past costs (PC), including the original construction cost, are calculated using Highway Construction Price Indices (Statistics Canada), whereas the present worth of all future costs are calculated by relevant economic formulae using effective interest rates (I_eff). This takes into account bank interest, any expected inflation rate and the availability of funding.

Once the present worth of all past costs are calculated, one calculates the value of past EUAC, which yields the comparative value of the past service cost. In the early life of the structure this value will be high, since it includes unammortized original construction costs. One then divides the sum of all past and future costs (expressed in terms of today’s dollars) by the life expectancy of the original or rehabilitated structure. The Average Annual Life Cycle Costs are calculated and referred to as Models E and F respectively.

Notations, formula and the mathematical models used are as follows:

NOTATIONS

A = replacement structure first cost;
B = salvage value of present structure;
C = annual maintenance cost (for cleaning deck, drainage, inspections);
CI_i = construction price index - Stats Canada, in year i;
CI_t = construction price index at the year of assessment (today);
D = initial major repair cost - rehab model;
F = single future expenditures (eg., deck overlay, abutment underpinning, painting);
FC = present worth of all future costs of the existing structure;
FL = existing structure future life, ie time left to the end of cycle;
FR = future rehabilitation cost - operating model;
f = inflation rate;
G = annual increase in maintenance cost due to progressive deterioration (eg., deck patching);
g = time to beginning of increasing maintenance costs due to progressive deterioration;
h = duration of increasing maintenance costs due to progressive deterioration;
i = bank interest rate;
I_eff = effective interest rate;
M1 = life expectancy of existing structure;
M2 = extended life expectancy of existing structure - if rehabilitated (M2 > M1);
N = life of replacement bridge;
N1 = time to required replacement - rehab model;
N2 = time to major rehab - operating model;
n = time of single future expenditure;
PC_i = single past cost of the existing structure, (any rehabilitation, repairs, etc.);
PC₁ = original construction cost of the existing structure;
PL = age of existing structure, past life;
PW = present worth of all past costs of the existing structure;
q = rate of increase in funding; and
S = salvage value of replacement structure.

The Mathematical Models and their Cash Flow Diagrams are as follows:

EUAC_past is evaluated from the following formulae:

Present worth of past costs of the structure:

PW = PC_i CI_t / CI_i

Average rate of return (effective interest rate) for the existing structure:

Ip = ((PW - PC₁) / PC₁ +1)^1/PL - 1

. EUAC _past = PW / (F/A, I_p, PL)

= PW (A / F, I_p, PL)

Replacement Model 'A' - Ignoring Present Value of the Existing Structure:

EUAC^A_Replace = (A / P) I_eff N) [(A-S)+G_m (P / G) I_eff, h_m+1) (P/F) I_eff, g_m-1) +

+F_k (P / F, I_eff, n_k)] + (S - B) I_eff + C

where:

A/P = capital recovery factor

= I_eff (1 + I_eff) ^N / ((1+I_eff)^N-1)

P/G = gradient present worth factor (n=h_m+1)

= 1 / I_eff (((1+I_eff)ⁿ-1) / (I_eff (1+I_eff)ⁿ)-n / (1+I_eff)ⁿ)

P/F = single payment present worth factor (n = g_m-1)

= 1 / (1+I_eff)ⁿ

where the effective interest rate is expressed in the following form:

I_eff = [(1+i) (1+q) / (1+f)] -1

Rehabilitation Model 'B'

The replacement EUAC^A must be calculated first, since it is used as an input parameter in this model.

EUAC^B_Rehab = (EUAC^A_Replace) (P / F, I_eff, N1) + I_eff [ D + C (P/A, I_eff, N1) +

+Gm (P / G, I_eff, h_m+1) (P / F, I_eff, g_m-1) + F_k (P / F,I_eff, n_k)]

where:

P/A = uniform series present worth factor

= 1/ (A/P)

This model can also be manipulated to reflect rehabilitation in some time in the future by setting D = 0 and assigning rehabilitation cost to one of the single future expenses F_k.

Operating Models 'C' and 'D' - Including Present Value of the Existing Structure.

Operate only - Model 'C'

Projected future cash flow can be expressed as:

EUAC^C_Operate = (A / P, I_eff, FL) [F_k (P / F, I_eff, n_k)+G_m (P / G, I_eff, h_m+1)

(P / F, I_eff, g_m-1)]+ C

Operate Existing Future Rehab - Model 'D'

The mathematical relationship for this model is:

EUAC^D_Rehab = (A / P, I_eff, FL) [F_k (P / F, I_eff, n_k) + G_m (P / G, I_eff, h_m+1)

(P / F, I_eff, g_m-1) + FR (P / F, I_eff, N2)] + C

Average Annual Life Cycle Costs

Operate only - Model 'E'

AALCC^E_operate = (PW + FC) / M1

Where:

FC = Fk (P / F, I_eff, n') + Gm (P / G, I_eff, h_m+1) (P / F, I_eff, g_m-1) +

+ C (P / A, I_eff, FL)

For Operate future rehab - Model 'F':

AALCC^F_rehab = (PW + FC) / M2

and where (FC) includes future rehabilitation cost and is a function of the extended future service life (M2).

FC = FR (P / F, I_eff, N2) +F_k (P / F, I_eff, n') + G_m (P / G, I_eff, h_m+1)

(P / F,I_eff, g_m-1) + C (P/A, I_eff, FL)

The Decision - Rehabilitate or Replace

In order to have a cost base for a decision to rehabilitate or replace, it is necessary to establish reasonable first construction costs for the structure in question. For the Carling Avenue Grade Separation, a detailed construction estimate was undertaken on the basis of incorporating current material (i.e., epoxy reinforcement) in a structure of similar dimensions to the existing structure. Functional obsolescence was not considered. Of course, any requirement for widening or capacity improvement should be considered but not with respect to the financial assessment of the existing structure.

The completed estimate is part of Table No 2 entitled "First Construction Costs" and is detailed in the 1988 Bench Mark Replacement Columns. It is interesting to note the figures indicated for the three sub-systems are comparable to the original cost estimate, which is also detailed in Table No 2.

Structure No. 609

Carling Avenue Grade Separation

SINGLE APPLICATION (FIRST COST)

CONSTRUCTION COSTS

Table No. 2 – First Construction Costs

A reduction of 4% in sub-structure cost of the 1988 estimate has been shifted to the Protection Sub-system. By use of the developed formula and construction price indices, the current estimate was pro-rated to 1963. This figure was $384,000. The difference of approximately $70,000 can be attributed to additional costs of current standards, the original structure wear surface (this was not included in the original estimate), and errors in methodology. It is interesting to note, however, the original $525,000 total which included engineering and contingencies. If one allows for 15% Engineering and 10% Contingency, the net result in 1963 would be $393,750.

The Replacement Model 'A' as run with a base value of $1,993,000 from Table No 2 resulted in an Equivalent Uniform Annual Cost of $147,577. This is indicated on Figure No 6 as EUAC Replacement Model 'A'.

A number of trial cases of the various costs and times of implementation were computed. Three rehabilitation cases are plotted on Figure No 6, using Equivalent Uniform Annual Costs as ordinates and a percentage of the Bench Mark Replacement Costs as abscissa.

Case 'A' plots show Model 'D', which as previously explained, is the operating model without future replacement costs. A major rehabilitation today is most important, with respect to the minimisation of an economically feasible rehabilitation. Appendix B attached details the input/output for the case closest to the intersection of the replacement and Model 'D',

Case 'A' curves (shown hatched). The existing structure cost history is as detailed on the printout. The abscissa of 70% BM cost is $1,397,000 and the Model 'D' annual cost is $144,821.

This model with a major rehabilitation in 1988, Case 'B', as per the Carling Avenue Chronolog, indicates an annual cost of $67,507. The projected life to approximately 2020 is to be noted.

In other words, if expenditure in the order of $1,250,000 were necessary today for rehabilitation, then the decision to rehabilitate would be the correct one.

It is to be noted, the longer in the life cycle that a major rehabilitation can be postponed the better (i.e., Case 'C', Model 'D').

Also note, major expenses are only warranted with a reasonable post-rehabilitation service life, in this case, taken as 20 years.

Conclusions

By examining the past history of a structure and the deficiencies inherent in the structural system, one can predict one or more future plans of action for further rehabilitation implementation.

A breakdown in terms of the protection, superstructure and sub-structure sub-systems is adequate to predict future works. The time of proposed implementation can be shown on a chronolog.

By choosing appropriate models of either operating costs (Computer Models C & D), Replacement (Computer Models A & B), and Average Annualised Costs (Computer Models E & F), one can generate data quickly for rehabilitation versus replacement decisions.

One can also use the data for financial performance measurements with respect to particular structural systems or sub-systems through the use of Average Annual Life Cycle Costs.

Specifically, for the Carling Avenue Grade Separation, the anticipated major rehabilitation (per the chronolog) Case B for 70% of the Bench Mark replacement cost ($1,397,000) would, in economic terms, be approximately 50% of the anticipated cash flow for replacement option.

In the case of an unscheduled deficiency and action being required today (Case A), the $1,397,000 expenditure would be approximately equivalent to the replacement option.

In general, in the later stage of the structure's life cycle, it is usually more economical to rehabilitate than to replace.

Bibliography

Weyers, R. E., Cady, P.D., and McClure, R. M., "Cost Effective Decision Models for Maintenance Rehabilitation and Replacement of Bridges", Proceedings, Second Bridge Engineering Conference, Transportation Research Record 950, Volume I, pages 28-33, Transportation Research Board,

Washington, 1984.

Grant, E. L., Ireson, W. G., "Principles of Engineering Economy", The Ronald Press Company, New York, New York, Fifth Edition, 1970.

Klaiber, F. W., Dunker, K. F., Wipf, T. J., and Sanders, W. W., "Methods of Strengthening Existing Highway Bridges", National Cooperative Highway Research Program, NCHRP Report 293, pages 39-47, Washington, September, 1987.

Appendix ‘A’

DEFICIENCY OCCURRENCE AND RETROFIT

PS

Since the publication of this paper, several similar computer programs or spreadsheets were developed and used. Currently we are using an Excel version, which can produce basic charts, and where data are input for any year within the Life Cycle. For new bridges we were using 50 year, for some rehabilitation projects 25 or 30 years. Shortly after our presentation, the Ontario Ministry of Transportation introduced its own Lotus version called SFAM, with some guidelines about the life spans to replacement of various components.

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