A Comprehensive Asset Management Plan for the Bridges of Ontario for 2023–2025 ^†

Abstract

Bridges, like any other infrastructure, deteriorate over time, and the more they degrade, the more expensive it becomes to perform maintenance activities on them. Therefore, it is important to predict their deterioration and plan intervention programs from economic and functionality points of view. While deterministic models are used to predict the deterioration of a structure, they do not consider any maintenance activities carried out beforehand. In this paper, we adjusted the deterioration model to overcome those limitations and planned an intervention program for the bridges of Ontario for 2023–2025. To achieve this, we cleaned the dataset; formulated the models; ran simulations with multiple deterministic and stochastic models to find the best one; adjusted the model equation to account for various levels of previous maintenance works; formulated the intervention action requirement for the next three years by developing an algorithm to reflect previous maintenance trends and their effects on the condition ratings; prepared an equalized work requirement for each year; and prioritized the action requirements based on a proposed risk matrix. Finally, an exhaustive plan with an action requirement for all the bridges was prepared for 2023–2025. The proposed plan will help decision makers to take proper action to maintain the serviceability of the bridges.

1. Introduction

Engineering asset management (AM) can be defined as operating and maintaining a set of physical non-financial assets over their technical lifetime to ensure a proper return for the value for money of those assets and to provide the expected level of service (LOS) for the stakeholders [1]. An AM portfolio includes diverse assets like equipment, vehicles, buildings, roads, and bridges, focusing on planning, maintenance, valuation, and disposal [2].

Bridges are crucial for Canada’s connectivity, with Ontario’s Ministry of Transportation managing about 3000 key bridges out of 51,717 in Canada. Proper maintenance ensures they support the national economy and provide consistent service throughout their lifecycle [3]. However, just like any other civil infrastructure, bridges deteriorate over time due to factors like traffic, weather, chemicals, and wear. Unchecked deterioration leads to costly replacements. Regular maintenance and early damage detection reduce costs and disruptions. Continuous evaluation improves operation and maintenance by assessing conditions, identifying causes, planning rehabilitation, and budgeting effectively [4]. A comprehensive bridge management system (BMS) aids in making maintenance and repair decisions through inspection, performance evaluation, deterioration prediction, cost analysis, and strategy formulation [5]. Ontario’s BMS mandates biennial inspections, ensuring safety and identifying repair needs. Since 2007, Ontario has invested over $7.5 billion in bridge maintenance, increasing annual funding significantly [6,7,8]. The Ontario Structure Inspection Manual (OSIM) inspection process, supported by the Ministry’s BMS, involves entering data to calculate the Bridge Condition Index (BCI), ranging from 0 to 100. The BCI measures overall bridge condition, deterioration severity, and repair needs. It also helps predict future deterioration and allocate maintenance funding [9].

Over the years, many deterioration models have been developed and two important types are (i) deterministic models and (ii) stochastic models [4,10]. Deterministic models use mathematical correlations, often through regression, to predict the condition ratings of structures like bridges. Despite their structured approach, they fail to account for the unpredictable nature of deterioration. Jeong et al. used non-linear regression with the Inspection Reliability Index (IRI) to estimate bridge lifecycles. The model predicted an average service life of 70.8 years, helping to estimate the remaining useful life [11]. Bu et al. developed a backward prediction model (BPM) to recreate historical bridge condition ratings, improving prediction accuracy for performance modeling [12]. Bennetts et al. analyzed Highway England’s bridge data using decision science tools and Python scripts, identifying age, deck type, and structure type as key factors affecting condition scores [13].

Stochastic models use random variables to simulate deterioration, with state-based (e.g., Markov chain) and time-based models predicting condition indicators. Ranjith et al. utilized Markov chain models to predict timber bridge conditions in Victoria, Australia, showing high accuracy [14]. Yosri et al. developed a GA–Markov chain model for bridge deterioration, validating it with repaired and unrepaired bridge data, aiding predictive BMS rules and resource prioritization [4]. Tran et al. combined ordinal regression and Markov models for stormwater pipe functionality predictions [15].

In this paper, our objectives are to: (i) Categorize Ontario’s provincial bridges by BCI and analyze historical maintenance impacts to understand their conditions and functionalities. (ii) Identify the best deterioration model and adjust it to reflect previous maintenance to predict bridge conditions from 2023 to 2025. (iii) Prioritize and plan bridge maintenance from 2023 to 2025 using a risk-based matrix and balanced workload distribution.

2. Methodology

2.1. Data Collection and Preparation

As mentioned before, Ontario’s provincial bridges and culverts are inspected biennially using OSIM, resulting in a Bridge Condition Index (BCI) score from 0 to 100, with data available online at data.ontario.ca [16]. The dataset includes 5053 Ontario bridges and culverts, detailing ID, name, location, category, construction year, repairs, BCI scores, and many other datapoints. The dataset was filtered to include only 2993 bridges.

2.2. Categorizing the Conditions

To obtain an overview about the condition of the whole bridge network, the BCI range of 0–100 is divided into the following five the categories shown in Table 1. The condition categories of bridges in 2023 are shown in Table 2.

Table 1. Condition category as per BCI.

Condition	BCI (From–To)
Excellent	85	100
Good	70	<85
Fair	60	<70
Poor	30	<60
Very Poor	0	<30

Table 2. Condition categories of bridges in 2023.

Bridge Condition	2023 No of Bridges	2023 % of Bridges
Excellent	881	29%
Good	661	22%
Fair	405	14%
Poor	967	32%
Very Poor	79	3%
Grand Total	2993	100%

2.3. Model Formulations

As discussed in the introduction, deterministic and stochastic models are widely used for the purpose of deterioration modeling. In this paper, both of them were used to compare which one fits the best with our dataset.

2.3.1. Deterministic Models

In this paper, the following models were used: linear deterioration model (1), convex deterioration model (2), Concave Deterioration Model (3), convex–concave deterioration pattern (4), concave–convex deterioration pattern (5).

$$R_{Linear}=R_{max}\left(1-{\displaystyle \frac{t}{T}}\right)$$

(1)

$$R_{convex}=R_{max}\left(1-{\left({\displaystyle \frac{t}{T}}\right)}^2\right)$$

(2)

$$R_{concave}=R_{max}{\left({\displaystyle \frac{t}{T}}-1\right)}^2$$

(3)

$$R_{convex-concave}=R_{max}\left[1-{{\displaystyle \frac{t}{T}}}^{\left(\beta \left(1-{\displaystyle \frac{t}{T}}\right)\right)}\right]$$

(4)

$$R_{concave-convex}=R_{max}\left[1-2{\displaystyle \frac{t}{T}}{+{\displaystyle \frac{t}{T}}}^{\left(\beta \left(1-{\displaystyle \frac{t}{T}}\right)\right)}\right]$$

(5)

$R_{[Model name]}$ = the condition rating or BCI for the corresponding model to be calculated.

$R_{max}$ = the maximum condition rating or BCI available. In our case, $R_{max}$ = 100.

$t$ = age of the structure. In this paper, $t$ = 2022—the year of construction of the structure.

$T$ = the service life of the structure. For highway bridges in Ontario, $T$ = 88 years [17].

$\beta$ can be any real number. However, a too high or too low value of $\beta$ will provide an impractical value of $R$.

2.3.2. Stochastic Model

A stochastic process can be regarded as a Markov process when the probability of a future state is dependent only on the current state and not on how it was obtained [18]. The transition probability matrix (P), with the order (n × n) where n is the number of condition states, represents the probability of transitioning from one state to another. The future condition vector (P_T) at any time (T) can be determined as follows if the initial condition vector (P_o) of the bridge element is known [19]: P_T = P_o × P, where for the transition matrix used in this paper

$$P=\left[\begin{array}{cccccc}0.839& 0.159& 0.002& 0& 0& 0\\ 0& 0.958& 0.04& 0.002& 0& 0\\ 0& 0& 0.89& 0.101& 0.008& 0\\ 0& 0& 0& 0.792& 0.178& 0.03\\ 0& 0& 0& 0& 0.625& 0.375\\ 0& 0& 0& 0& 0& 1\end{array}\right]$$

2.4. Root Mean Square Error (RMSE) Calculation

The RMSE was calculated using the following formula

$$RMSE=\sqrt{{\displaystyle \frac{\sum _{i=1}^N{(X_{pi}-X_{oi} )}^2}{N}}}$$

where N = the total number of observations = 2993, $X_{pi}$ = the predicted value for the ith observation, and $X_{oi}$ = the observed value for the ith observation.

2.5. Finding Out the Optimum Values of $\beta$ and Selecting the Best Model Based on RMSE

Simulations were run for 2993 bridges using 51 values of β ranging from 1 to 13.5 for the convex–concave model and from 0.6 to 1.1 for concave–convex model—as the independent variable—and RMSE as the dependent variable, and the resulting diagram can be seen in Figure 1a,b. The β value for which the RMSE was lowest was 8.5 for the convex–concave and 0.94 for the concave–convex model.

Figure 1. (a) The simulation of RMSE values for a range of β values for the convex–concave model, (b) the simulation of RMSE values for a range of β values for the concave–convex model, and (c) the RMSE values for the five models.

Later, the RMSE was calculated for one stochastic model and five deterministic models. The values are shown in Figure 1c. $R_{convex-concave}$ was found to have the lowest RMSE. Therefore, it was selected for further analysis.

2.6. Formulation of the Initial Intervention Requirement for 2023

Before starting the formulation of the plan, we need to find out the trend and timeline of previous intervention activities and their effects on the BCI.

2.6.1. Analysis of Previous Repair Works and Their Effect on the BCI

The ministry of transportation has conducted intervention works on many bridges from time to time. From our dataset, we tried to find out the answers to two questions:

Q1: what was the BCI of the bridges when they carried out the maintenance works?

Q2: what was the improvement in BCI after the maintenance works?

For example, the bridge named “Highway 24 underpass at Highway 403” underwent repairs in 2014. Before the repairs, its BCI was 72.3 in 2012. After the repairs in 2014, its BCI increased to 81.2, an 8.9 index score improvement.

2.6.2. Analysis of the Repair Threshold and Improvement in BCI

From our analysis, as shown in Table 3, we found that there were varying degrees of intervention activities depending on the condition level of a bridge, resulting in a varying degree of BCI improvement. The intervention threshold and its effect on BCI was calculated.

Table 3. Intervention initiation threshold and corresponding improvement in BCI.

Repair Initiation Threshold (BCI)	Repair Initiation Threshold (Numerical)	Improvement in BCI	Average Improvement in BCI (Numerical)
~a	~70	a + ka	Current BCI + 7.77
~b	~65	b + kb	Current BCI + 25
~c	~60	kc	100 (absolute BCI)

Where, a > b > c and k_a < k_b < k_c. It is to be noted that, for threshold BCI values ~a and ~b, incremental average BCI values k_a and k_b were added to the current BCI values; whereas, for the BCI values of ~c, instead of adding any incremental value, the BCI was upgraded to a value of k_c.

After analyzing the dataset for intervention activities and the corresponding improvements in BCI, the information is summarized in Table 4.

Table 4. Intervention requirement matrix.

Current BCI	Current BCI (Numerical)	Action	Resulting BCI	Resulting BCI (Numerical)
≥a	≥70	No action	-	-
b≤ and <a	65≤ and <70	Repair	a + ka	Current BCI + 7.77
c≤ and <b	60≤ and <65	Major repair	b + kb	Current BCI + 25
<c	<60	Rehabilitation	kc	100

2.6.3. Determination of Intervention Needs for 2023

Based on the BCI of the bridges in 2022, the intervention requirements for 2993 bridges (if any) in 2023 were determined as per Table 5.

Table 5. Action requirement for 2023.

2023 Actions	No. of Bridge	%
Repair (R)	177	6%
Major repair (MR)	228	8%
Rehabilitation (RH)	1046	35%
Do Nothing (N)	1542	52%

2.7. Major Limitation of the Deterministic Model

Although these models are widely used, they have some limitations such as predicting for a group of infrastructures without considering the current conditions and estimating the condition for only the “no maintenance” state [5].

In our case, although we are planning intervention activities for 2023, while calculating the BCI for 2024 and 2025, the existing deterministic model does not take into account the improvement in BCI for 2023. Therefore, to overcome the two limitations stated above, we adjusted the formula for the deterioration model to reflect the most current state of intervention.

2.8. The Adjusted Formula for the Deterministic Model to Overcome the Limitations

The concave–convex deterioration model equation can be written to reflect the condition before the intervention works:

$$R_{(concave-convex)1}=R_{\left(\mathrm{m}\mathrm{a}\mathrm{x}\right)1}\left[1-2{\displaystyle \frac{t1}{T}}{+{\displaystyle \frac{t1}{T}}}^{\left(\beta \left(1-{\displaystyle \frac{t1}{T}}\right)\right)}\right]$$

(6)

where

$R_{(concave-convex)1}$ = the BCI before any maintenance works.

$R_{\left(\mathrm{m}\mathrm{a}\mathrm{x}\right)1}$ = the maximum condition rating or BCI available for the main structure. In our case, $R_{\left(\mathrm{m}\mathrm{a}\mathrm{x}\right)1}$ = 100.

$t_1$ = the age of the structure. In this paper, $t_1$ = 2022—the year of construction of the structure.

$T$ = the service life of the structure. For highway bridges in Ontario, $T$ = 88 years [17].

$\beta$ = the optimum value found from Section 2.5.

After the repair or major repair works are completed in year n, the BCI increases by k in the year n + 1, where

$$k=\left\{\begin{array}{c}0, if{R}_{\left(concave-convex\right)1}>a\\ k_a, if b\le R_{(concave-convex)1}<\mathrm{a}\\ k_b, if{c \le R}_{\left(concave-convex\right)1}<b\end{array}\right.$$

After rehabilitation works are completed in year n, the BCI increases to k in the year n + 1 where

$$k=k_c, if{R}_{(concave-convex)1}<c$$

To reflect the BCI increment after the maintenance works, the model equation can be adjusted to

$$R_{(concave-convex)2}=k\left[1-2{\displaystyle \frac{t2}{T}}{+{\displaystyle \frac{t2}{T}}}^{\left(\beta \left(1-{\displaystyle \frac{t2}{T}}\right)\right)}\right]$$

(7)

where:

$R_{(concave-convex)2}$ = the BCI calculated after any intervention works.

$k$ = the maximum condition rating or BCI available for the increment.

$t_2$ = the age of the structure. In this paper, $t_2$ = plan year—the year of intervention works.

Combining Equations (6) and (7) we obtain the adjusted formula.

The adjusted rating for nth year is

$$\begin{gathered} R_{(concave-convex)nA}=R_{(concave-convex)1}+R_{(concave-convex)2} \\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}=R_{\left(\mathrm{m}\mathrm{a}\mathrm{x}\right)1}\left[1-2{\displaystyle \frac{t1}{T}}{+{\displaystyle \frac{t1}{T}}}^{\left(\beta \left(1-{\displaystyle \frac{t1}{T}}\right)\right)}\right]+k\left[1-2{\displaystyle \frac{t2}{T}}{+{\displaystyle \frac{t2}{T}}}^{\left(\beta \left(1-{\displaystyle \frac{t2}{T}}\right)\right)}\right] \end{gathered}$$

(8)

Subject to

$$\left\{\begin{array}{c}for no previous intervention works,k= 0 and R_{(concave-convex)1}\ne 0\\ for repair works in the previous years, k = k_a= 7.7 and R_{(concave-convex)1}\ne 0\\ for major repair works in the previous years, k =k_b =25, and R_{(concave-convex)1}\ne 0\\ for rehabilitation works in the previous years, k = k_c=100 and R_{(concave-convex)1}=0\end{array}\right.$$

2.9. Intervention Action Requirement for 2023–2025

Using Equation (8), the BCI values for 2993 bridges were calculated for 2024 and 2025. Later, the action requirement was created based on the intervention requirement matrix.

The conditions of the 2993 bridges for 2023, 2024, and 2025 are shown in Table 6.

Table 6. Conditions of bridges in 2023–2025.

Bridge Condition	2023 No of Bridges	2024 No of Bridges	2025 No of Bridges	2023 % of Bridges	2024 % of Bridges	2025 % of Bridges
Excellent	881	2125	1967	29%	71%	66%
Good	661	835	985	22%	28%	33%
Fair	405	33	41	14%	1%	1%
Poor	967	0	0	32%	0%	0%
Very Poor	79	0	0	3%	0%	0%
Grand Total	2993	2993	2993	100%	100%	100%

Based on the calculated BCI values, the action requirements for 2023, 2024, and 2025 are shown in Table 7.

Table 7. Action requirements for 2023–2025.

Actions	No. of Bridge in 2023	No. of Bridge in 2024	No. of Bridge in 2025	% of Bridge in 2023	% of Bridge in 2024	% of Bridge in 2025
Repair (R)	177	33	74	5.9%	1.1%	2.5%
Major repair (MR)	228	0	0	7.6%	0.0%	0.0%
Rehabilitation (RH)	1046	0	0	34.9%	0.0%	0.0%
Do Nothing (N)	1542	2960	2919	51.5%	98.9%	97.5%

As per this action plan, shown in Table 7, a significant number of bridges went through rehabilitation and major repairs. As a result, most of the bridges in 2024 and 2025 were in excellent or in good condition, no longer needing any repairs. However, it is not economically feasible to rehabilitate all the bridges in a single year. That is why risk-based prioritization was performed to allocate the rehabilitating and major repair activities among 2023, 2024, and 2025.

2.10. Risk-Based Prioritization

The risk scale for any element is measured based on two components: the condition scale and the consequence scale. The condition scale for 2023 was calculated based on the current BCI and is shown in Table 8. The consequence scale, shown in Table 9, was calculated based on the area of the bridge. The reasoning is that the larger the area, the higher the repair cost. Therefore, the larger the area, the earlier it needs to be repaired to avoid any additional cost due to further deterioration.

Table 8. Condition scale index.

Condition	Abbreviation	BCI Lower Value	BCI Upper Value
Very Poor	VP	0	30
Poor	P	30	60
Fair	F	60	70
Good	G	70	85
Excellent	E	85	100

Table 9. Consequence scale.

Consequence	Abbreviation	Lower Limit of Area (m2)	Upper Limit of Area (m2)
Very High	VH		35,000
High	H	15,000	35,000
Medium	M	5000	15,000
Low	L	2000	5000
Very Low	VL	2000

After combining the condition scale and consequence scale, the risk matrix is shown in Table 10:

Table 10. Risk Matrix.

		VP	P	F	G	E		Where,
	VL	M	M	M	VL	VL		Very High	VH
Consequence	L	H	M	M	VL	VL		High	H
	M	VH	H	M	L	VL		Medium	M
	H	VH	H	H	L	L		Low	L
	VH	VH	VH	VH	H	L		Very Low	VL

Based on the matrices and scales developed in this section, the risk matrix for the bridges for three years was measured and is shown in Table 11.

Table 11. Risk level of bridges.

Risk Level	2023 Bridge Risk Level	2024 Bridge Risk Level	2025 Bridge Risk Level	2023 % Risk Level	2024 % Risk Level	2025 % Risk Level
Very High (VH)	1	0	0	0.03%	0.00%	0.00%
High (H)	25	0	0	0.84%	0.00%	0.00%
Medium (M)	57	0	1	1.91%	0.00%	0.03%
Low (L)	1028	19	14	34.38%	0.64%	0.47%
Very Low (VL)	1879	2971	2975	62.84%	99.36%	99.50%

2.11. Generating an Equalized Work Volume for Three Years

Since bridges vary greatly by length and width, any plan based on “number of bridges” can be misleading as it does not enumerate the “volume of work”. Therefore, “number of bridges” was converted to “bridge deck area (m²)”. After combining all the activities from Section 2.1, Section 2.2, Section 2.3, Section 2.4, Section 2.5, Section 2.6, Section 2.7, Section 2.8, Section 2.9, Section 2.10, an equalized maintenance area plan was created where each year was allocated an equal area for each maintenance category based on the risk level.

2.12. Final Plan for 2023–2025

Finally, a holistic plan for the management of 2993 bridges was created for 2023–2025. Subject to the constraints of maintenance area per year discussed before, action plan for all the 2993 bridges was created by scheduling the number of bridges equivalent to the total maintenance area quota for each category and each year.

3. Result

3.1. Action Requirement Based on Risk–Based Prioritization

After combining the condition-based actions and the risk-based prioritization, an action requirement for 2023–2025 is shown in Table 12.

Table 12. Relationship of Risk Level and Condition-Based Actions in Number of Bridges and in Bridge Area.

Risk Level	Condition-Based Action	No. of Bridge in 2023	No. of Bridge in 2024	No. of Bridge in 2025	Area in 2023 (m2)	Area in 2024 (m2)	Area in 2025 (m2)
Very High (VH)
	Rehabilitation (RH)	3	0	0	57,987	0	0
High (H)
	Rehabilitation (RH)	23	0	0	195,356	0	0
	Do Nothing (N)	1	1	1	44,967	44,967	44,967
Medium (M)
	Repair (R)	177	28	38	165,965	31,498	38,414
	Major repair (MR)	228	0	0	265,431	0	0
	Rehabilitation (RH)	1020	0	0	781,147	0	0
	Do Nothing (N)	0	5	3	0	5599	2042
Low (L)
	Do Nothing (N)	11	15	15	78,379	195,282	193,172
Very Low (VL)
	Repair (R)	0	5	36	0	4857	37,403
	Do Nothing (N)	1527	2936	2897	1,559,448	2,866,477	2,832,683

However, as the lengths and widths of bridges vary, it is more appropriate to translate the number of bridges into bridge area (m²) to arrive at the whole picture for the volume of activity.

3.2. Generating an Equalized Maintenance Work Volume for Three Years

As shown in Table 12, maintenance actions are required for large bridge areas in 2023, which is not economically feasible. On the other hand, much less activity is found for 2024 and 2025. To make the maintenance process more feasible, the maintenance requirement is equally divided among the three years following risk-based prioritization. For example, the total rehabilitation requirement for 2023 is 1,034,490 m². If this activity is divided among the three years, each year will be allocated 344,830 m². For 2023 there is a very high-risk area of 57,987 m² and a high-risk area of 195,356 m²—in total, 253,343 m². To make up the allocation of 344,830 m², a 91,487 m² area is taken from the medium risk category and the rest of the area is equally divided and allotted to 2024 and 2025. A similar strategy was followed for other risk levels and condition-based actions. The yearly area-based plan for actions is shown in Table 13:

Table 13. Final (Area-Based) Maintenance Plan.

Risk Level	Condition Based Action	Area in 2023 (m2)	Area in 2024 (m2)	Area in 2025 (m2)
Very High (VH)
	Rehabilitation (RH)	57,987	0	0
High (H)
	Rehabilitation (RH)	195,356	0	0
	Do Nothing (N)	0	0	0
Medium (M)
	Repair (R)	78,626	78,626	78,626
	Major repair (MR)	88,477	88,477	88,477
	Rehabilitation (RH)	91,487	344,830	344,830
	Do Nothing (N)	0	0	0
Low (L)
	Do Nothing (N)	0	0	0
Very Low (VL)
	Repair (R)	0	0	0
	Do Nothing (N)	0	0	0
	Total Action Taken (m2)	511,933	511,933	511,933

In the above table, we can observe that each year has the same maintenance area (511,933 m²) to be taken care of. Moreover, each maintenance category for each year has been allocated an equal area. For example, the total rehabilitation work for each of 2023, 2024, and 2025 is 344,830 m².

3.3. Final Plan

Subject to the equalized area maintenance plan generated above for each year, the action plan for all the 2993 bridges was created depending on their risk levels. Table 14 is an excerpt of that final plan. Bridges with a higher risk index were scheduled to be repaired in 2023, the rest were scheduled for 2024 and 2025, based on a descending order of risk level while meeting the year quota for each type of intervention activity. The whole plan is provided in the supplementary document.

Table 14. Final Maintenance Plan (by Number of Bridges).

ID (SITE N°)	STRUCTURE NAME	2023 Actions	2024 Actions	2025 Actions
01X-0032/B0	Highway 24 Underpass at Highway 403	Rehabilitation (RH)	Do Nothing (N)	Do Nothing (N)
01X-0085/B0	GURNEY CREEK WHITEMAN BRIDGE	Do Nothing (N)	Do Nothing (N)	Do Nothing (N)
01X-0139/B0	BRANT COUNTY RD.# 27 (Oak Park Road) Underpass Interchange	Repair (R)	Do Nothing (N)	Do Nothing (N)
01X-0140/B0	CNR SUBWAY	Do Nothing (N)	Do Nothing (N)	Repair (R)
…
34X-0160/B0	BEAVER DAMS RD. U/P	Do Nothing (N)	Major Repair (MR)	Do Nothing (N)
…
2993 bridges

4. Conclusions and Discussion

In our paper, we analyzed the present conditions of the 2993 bridges of Ontario and created an action plan for 2023–2025. To find out the deterioration rate, five models were tested and the concave–convex model was found to have the lowest RMSE. Next, we analyzed the maintenance trend and found four possible interventions based on the current BCI: if the BCI ≥ 70, no action is required; if it is 65 ≤ BCI < 70, repairs are required that will result in a 7.77 point increase in BCI; if 60 ≤ BCI < 65, major repairs are required, resulting in a 25 point increase in BCI; if the BCI < 60, rehabilitation is suggested, leading to the restoration of the BCI value to 100. After calculating the BCI of the bridges for 2023 using the concave–convex model and applying the above algorithm, the intervention requirement for 2023 was generated. It was found that around 35% of the bridges need rehabilitating in 2023. Since one of the main limitations of the deterministic model is that it does not take into account the previous maintenance work, the model equation was adjusted based on four BCI conditions to reflect any earlier repair activities. Later, condition ratings and corresponding repair requirements for 2024 and 2025 were calculated using the adjusted equation. As the 2023 requirement showed that too many bridges need interventions, which is not financially feasible, a risk-based approach was taken to select which bridges are to be prioritized. However, “number of bridges” was converted to “bridge deck area (m²)” to reflect the actual volume of intervention work. Then, a risk matrix was created where both condition and consequence scales comprised five classes. The consequence scale was based on the area of the bridge, assuming that the larger the area, the higher the delayed intervention cost will be. Similarly, the failure of a larger area bridge will have a greater economic, social, and environmental impact. Based on the risk matrix, an equal maintenance work area for each category of action for each year was created. Subject to that equalized work area, bridges with higher risk index were scheduled to be repaired in 2023, and the rest were scheduled for 2024 and 2025 based on a descending order of risk level. Finally, a balanced intervention plan for 2023–2025 was created for each of the 2993 bridges.