Workshop 05: Component Reliability Analysis 2

This workshop was assigned on GitHub, and can be accessed via this link (you can still use it to do the assignment, but future submissions will not be reviewed).

The solution is provided here in the following three sub-pages, and is a subset of what was included in the repository:

• Report: the Markdown report with 6 questions about the analysis

• Analysis (Deterministic): the Jupyter notebook where the FEM calculations were made

• Analysis (Reliability): the Jupyter notebook where MCS and/or FORM calculations were made

• Feedback: the general feedback provided to all students (in addition to individual feedback in each group repository)

Contents of README.md

This workshop focuses on the component reliability analysis of the structural capacity of a submerged tunnel element subjected to various hydraulic loads. It provides nearly-completed Python code that needs to be filled in to complete the analysis; the code can also be easily adapted to solve other component reliability problems you may deal with in the future. The answers you will provide in Report.md illustrate the type of information expected when describing any component reliability analysis (e.g., your final report, as well as in your future career as an engineer).

You should be able to complete the entire assignment during the in-class session; if not, make sure you at least have all the code implemented, so that outside of class you only have to review how the reliability algorithms work and interpret the results.

The repository contains a variety of files and file types. To complete this assignment, you should do the following:

1. Look through the repository and observe the files and file types provided.

2. Read (briefly) the questions in Report.md to get an idea of what you will have to answer at the end of this workshop.

3. Read the rest of this README.md file to understand the context of the tunnel problem.

4. Complete the Tasks in notebook Analysis_deterministic.ipynb to get familiar with the model for calculating stress in the tunnel element.

5. Complete the Tasks in notebook Analysis_reliability.ipynb to set up and complete the component reliability analysis.

6. Answer the questions in Report.md.

You should be able to complete this assignment using a Python environment with the packages installed that are listed in requirements.txt.

Submission and Grading

Due date: make your last commit before 4am on Tuesday, May 28, 2024. Contact Robert if you can’t make the deadline.

The instructions are the same as for WS02; Unit Website.

If your group has changed from WS02, email Robert an updated list of your group members.

Problem Introduction: Crossing the Straight

The joint consortium of Colomes & Agarwal Inc. and Frank & Co designed a floating and submerged tunnel in the Strait of Gibraltar. This project would be a ‘permanent’ link between Spain and Morocco, eliminating the need for ferries.

The consortium, however, still needs to perform a risk analysis. An important meeting with their client is coming up soon and the client needs preliminary assessment of the risks associated with the tunnel. Specifically, the probability of failure of the special concrete they intend to use for tunnel components due to the complex loads caused by fluid-structure interaction.

The firm Lanzafame Consulting was hired to perform the calculations. For the preliminary analysis, using a static scenario instead of dynamic would be sufficient, as running simulations for dynamics would cost too much time. In a later phase the static calculations can easily be updated to a dynamic model.

As such, the project goal is as follows:

Perform a component reliability analysis for a tunnel element such that the probability of failure due to exceedance of the compressive strength is calculated, which must be less than 1%. Water velocity is used to compute compressive stress, and is a function of three random variables: wave conditions (wind and swell waves) and current. The compressive strength of the tunnel material also can be a random variable. The consortium has already built a FEM model that can be used to perform the stress calculations.

Tunnel Characteristics and Metocean Conditions

Tunnel characteristics:

• The tunnel is curved and modelled as an Euler-Bernoulli Beam.

• The tunnel is located at 30 meters below M.S.L.

• A ‘special’ concrete has a compressive strength of 75 MPa.

• Steel is an alternative material that has a compressive strength of 250 MPa.

It is assumed that the water velocity at the project location is a result of the following 3 processes:

1. Swell waves

2. Wind sea waves

3. Current

The deterministic analysis has been set up as follows:

• compute water velocity from wind waves, swell waves and current

• compute forces on the tunnel using Morrison’s equation (makes the dynamic problem static)

  • note that the force due to the swell waves includes the current water velocity

• from each component of force, compute stresses in the tunnel elements with the finite element method (FEM)

• total stress is the superposition of the components from the hydraulic loads

• check whether the compressive capacity of the tunnel element is exceeded

Random Variables

The random variables to use in the analysis are summarized here:

Symbol	Code	Description	Units	Distribution	Parameter(s)
\(H^{1/3}\)	X1	Significant wave height, swell waves	m	Exponential	2.0309
\(H^{1/3}\)	X2	Significant wave height, wind sea waves	m	Exponential	2.0663
\(u\)	X3	Velocity of current	m/s	Normal	2, 0.2
\(\sigma_c\)	X4	Compressive strength of concrete	MPa	Normal	75, 5
\(\sigma_s\)	X4	Compressive strength of steel	MPa	Normal	250, 20

Distributions and parameters are for OpenTURNs.

Component Reliability Algorithm

Note that a summary of FORM (and its results) and a comparison of FORM and MCS have been added to the workbook, and could be useful to choose your component reliability analyses used in class.