Probabilistic modeling and extreme-value analysis of traffic-induced bending moments in reinforced concrete culverts using Monte Carlo simulation and statistical tail fitting.
This project demonstrates how structural engineering problems can be solved using computational modeling, statistical inference, and scientific programming in Python.
The repository combines civil infrastructure reliability analysis with data-driven statistical modeling techniques.
Infrastructure such as culverts and bridges is subjected to highly variable traffic loads. While most vehicles produce moderate loads, rare heavy axle loads control structural safety.
This project models random axle loads from traffic data and estimates the mean maximum bending moment over a multi-year period using extreme-value theory.
The workflow includes:
- Modeling axle load distributions
- Generating bending-moment samples via Monte Carlo simulation
- Constructing a load spectrum using a normal probability plot
- Fitting the upper tail of the distribution
- Projecting extreme load effects over a long reference period
The analysis estimates the mean maximum bending moment over 5 years, assuming an average daily truck traffic (ADTT) of 5000.
The final estimate obtained from the dataset is approximately:
Mean maximum bending moment over 5 years ≈ 16.18 kip-ft
StatisticalProjection_LoadEffects/
├── main.ipynb # Main notebook containing Task (a) and Task (b)
├── moment_samples.npz # Provided bending moment samples for statistical projection
├── ProblemStatement.pdf # Original problem statement and background
└── README.md # Project documentation
Three probability models are tested for axle loads:
- Lognormal distribution
- Truncated lognormal distribution
- Weibull distribution
The Weibull distribution is estimated by solving for its shape and scale parameters using numerical root finding so that the generated samples match the observed mean and standard deviation.
Random axle loads are generated according to the selected probability model.
Loads are converted to bending moments using linear scaling.
The resulting bending moments are combined into a simulated load spectrum.
The simulated bending moments are used to build:
- histogram of load effects
- empirical cumulative distribution function (CDF)
The distribution is visualized using a normal probability plot.
The upper 5% of the data is extracted and fitted using linear regression in normal probability space.
This provides estimates of the event-level mean and standard deviation of extreme load effects.
Using extreme-value theory (Gumbel approximation), the maximum load effect over a multi-year period is estimated.
Number of events:N = ADTT × 365 × years