⚡ electrical engineering

Cost-effective Comparison of Alternatives to Retrofit Seismic Damage in Schools

This paper evaluates the cost-effectiveness of two seismic retrofit techniques for Mexican schools by employing a probabilistic Monte Carlo approach to calculate life-cycle costs, ultimately demonstrating that the optimal repair strategy depends on the specific type and extent of seismic damage.

Original authors: David De León-Escobedo, Francisco Bañuelos

Published 2026-10-14

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CC BY 4.0

Original authors: David De León-Escobedo, Francisco Bañuelos

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Earthquakes do not merely shake the ground; they test the integrity of the buildings that shelter us, and among the most vulnerable are schools. When a school is damaged by a tremor, the immediate question is how to fix it so it can safely house children for decades to come. The challenge lies in choosing the right repair method. Some fixes are cheap but weak, while others are robust but prohibitively expensive. Engineers must weigh the cost of the repair against the risk of future failure, considering not just the price of materials and labor, but also the potential cost of human life and the disruption to education if the building fails again. This balancing act requires looking beyond the immediate bill to the entire lifespan of the structure, asking how much safety is worth over the next fifty years.

In a recent study, researchers from the Autonomous University of Mexico State tackled this complex decision-making process by analyzing two actual schools in Mexico that had suffered damage during the 2017 earthquake. The team focused on two specific locations: a one-story school in Tetela del Volcán and a two-story school in Tehuacán. Both buildings, constructed with reinforced concrete frames and brick walls, had sustained cracks and structural weaknesses that threatened their future safety. The researchers wanted to determine which repair strategy offered the best value, not just in terms of the initial construction cost, but by calculating the total expected cost over the life of the building. This total cost includes the price of the retrofit itself, plus the projected costs of any future damage, including the tragic financial valuation of potential injuries or loss of life, and the cost of moving students to temporary facilities if the school were to close again.

To reach their conclusion, the team simulated the behavior of these schools under the threat of future earthquakes. They did not simply guess which repair would work; they used computer models to run thousands of scenarios, accounting for the uncertainty of how strong a future quake might be and how the building materials would actually perform. They tested two distinct repair methods. The first involved attaching steel angles to the corners of the damaged columns and beams to reinforce them. The second method, known as jacketing, involved wrapping the damaged members in new concrete and steel to make the entire cross-section larger and stronger. For each method, the researchers adjusted the size of the added materials until the calculated risk of the building failing dropped to a very low, acceptable level.

The results revealed a clear winner that defied the intuition that "bigger is always better." For both schools, the method using steel angles proved to be the more cost-effective solution. While the jacketing method did make the structural members physically larger, it required significantly more material and labor, driving up the initial price tag without providing a proportional increase in safety. In contrast, the steel angles provided a highly efficient confinement for the damaged sections, drastically reducing the probability of failure with a much lower initial investment. When the researchers added the potential future costs of failure to the initial repair bills, the difference became even more stark. The total expected life-cycle cost for the steel angle retrofit was substantially lower than that of the jacketing method for both schools.

The study highlights that the best repair strategy depends heavily on the specific type and extent of the damage. For the localized cracks and moderate damage observed in these two schools, a targeted, localized repair was sufficient and far more economical than a massive, global overhaul. The researchers found that the most expensive part of the equation was not the construction itself, but the potential cost of human tragedy. Because the schools are filled with children, the financial weight of a potential fatality is enormous, making it critical to choose a repair that minimizes the chance of collapse. By selecting the steel angle retrofit, the schools achieved a safety level where the risk of failure dropped from a high, unacceptable level to a very low one, all while saving money over the long term.

This approach offers a practical roadmap for school administrators and engineers facing similar dilemmas. It suggests that when a school is damaged, the goal should not simply be to make the building as strong as possible, but to make it strong enough to be safe for its entire remaining life at the lowest reasonable cost. The study concludes that for moderate damage, localized fixes are often superior to global ones, and that a careful calculation of future risks is essential for making the right choice. By monitoring these structures and applying the right repair at the right time, communities can ensure that their schools remain safe havens for generations to come.

Technical Summary: Cost-effective Comparison of Alternatives to Retrofit Seismic Damage in Schools

Problem Statement
Current strategies for retrofitting schools following seismic damage often fail to account for life-cycle costs, focusing instead on immediate repair without a comprehensive assessment of long-term structural safety and economic efficiency. While various methodologies exist for assessing structural performance under seismic hazards, specific proposals for school retrofits that explicitly integrate failure probabilities and life-cycle cost analyses are scarce. Existing guidelines, such as those by INIFED (2016), lack cost-benefit ratios, and other studies have proposed retrofitting techniques without accompanying economic analyses. This paper addresses the need for a risk-based formulation to assess the cost-effectiveness of alternative retrofit schemes by calculating both the failure probability and the expected life-cycle cost for schools in Mexico.

Methodology
The study proposes a probabilistic framework to evaluate retrofit alternatives for two actual schools in Mexico (Tetela del Volcán, Morelos, and Tehuacán, Puebla) that sustained seismic damage. The methodology involves the following key steps:

Structural Modeling and Damage Calibration: Preliminary models were calibrated using records from the September 19, 2017, earthquake to reproduce observed damages and identify critical structural members.
Failure Probability Calculation: The failure probability ( $F_p$ ) is defined as the event where the safety margin ( $LS$ ) is less than zero. This is calculated using Monte Carlo simulation techniques, treating seismic demands and structural capacities as lognormal random variables. The total probability theorem is applied to discretized Peak Ground Acceleration (PGA) scenarios.
Life-Cycle Cost (LCC) Assessment: The expected total cost ( $E(LC)$ $E (L C)$ ) combines the initial retrofit cost ( $C_i$ $C_{i}$ ) with the expected future costs of failure consequences ( $E(PCF)$ $E (P C F)$ ). These consequences include:
- Cost of school contents ( $C_{co}$ ).
- Cost of business interruption ( $C_{int}$ ).
- Cost of injuries ( $C_{inj}$ ).
- Cost of potential deaths ( $C_d$ ), calculated using a human capital approach based on lost income over a productive lifetime.
- A present value factor (PVF) is applied to future costs using an 8% interest rate over a 50-year school lifetime.
Iterative Retrofit Design: Two retrofit alternatives were tested for each school:
- Retrofit 1 (R1): Addition of steel structural angles to the corners of damaged members.
- Retrofit 2 (R2): Jacketing of damaged columns and beams with increased dimensions and reinforcement.
  The design process is iterative; dimensions are increased until the failure probability falls below the target value of $10^{-3}$ , as recommended by ISO 8930 (2021) and previous studies.

Key Results
The application of the proposed methodology to the two case studies yielded the following findings:

Initial Risk: Before retrofitting, the schools exhibited high failure probabilities due to observed damage: 0.39 for Tetela del Volcán and 0.23 for Tehuacán.
Retrofit Effectiveness:
- Tetela del Volcán: R1 reduced the failure probability to 0.0026, while R2 reduced it to 0.0086.
- Tehuacán: R1 reduced the failure probability to 0.0045, while R2 reduced it to 0.006.
Cost Analysis:
- Retrofit Costs: R1 was generally less expensive ($16,000 and $31,000 USD for Tehuacán and Tetela, respectively) compared to R2 ($13,000 and $24,000 USD).
- Life-Cycle Costs: The expected life-cycle cost for R1 was significantly lower than for R2 in both locations. For Tetela del Volcán, R1 cost $70,700 USD versus $146,300 USD for R2. For Tehuacán, R1 cost $56,400 USD versus $69,200 USD for R2.
Dominant Cost Factor: The cost of potential fatalities ( $C_d$ ) was the most significant component of the life-cycle cost, justifying the high priority placed on school safety.

Significance and Conclusions
The paper concludes that the selection of an appropriate retrofit scheme must be driven by the type, level, and extension of the damage, as well as the seismic hazard and the consequences of failure.

Optimal Strategy: For the localized and moderate damages observed in the case studies, a localized retrofit (R1: steel angles) proved more cost-effective and safer than a global section jacketing (R2). The confinement provided by the steel angles contributed more to safety than the increased section size of the jacketing.
Decision-Making Tool: The expected life-cycle cost is presented as an effective metric for decision-making, balancing initial investment against the probability of future catastrophic events and their associated costs.
Recommendations: The authors recommend permanent monitoring programs for schools to facilitate timely maintenance decisions. They also suggest extending this formulation to cover other structural types, retrofit alternatives, and failure modes to establish general guidelines for schools in seismic zones.

The study emphasizes that while extensive damage may require global interventions (e.g., steel braces or shear walls), localized damages are best addressed with targeted, cost-effective solutions that minimize life-cycle costs while meeting reliability targets.

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