Evaluating Risk of Sliding for Harbour Breakwater

[lufbrajames]

Homework Statement

Assignment No.4. Harbour Breakwater Evaluation.

Consider a harbour breakwater constructed with massive concrete tanks filled with sand. It is necessary to evaluate the risk that the breakwater will slide under the pressure of a large wave during a major storm. Stability against sliding exists when the ratio of the resultant horizontal force Rh to the resultant of the vertical force Rv does not exceed the coefficient of friction, X1.

The resultant of the vertical forces Rv is given by the algebraic sum of the weight of the tank reduced for buoyancy, X2, and the vertical component of dynamic uplift pressure due to the breaking wave, Fv.

Rv = X2 - Fv

In turn Fv is proportional to the height of the wave, Hb, when the slope of the sea bottom is known. A simplification of the shoaling effect makes the wave height proportional to the deepwater value, X4.

Fv = a1X3X4

where a1 is the constant of proportionality and X3 is an additional variate to represent the uncertainties caused by the above simplification.

The resultant Rh of the horizontal forces depends on the balance between the static and dynamic pressure components and under a simplifying hypothesis on the depth of the breakwater can be taken to be a quadratic function of the wave height Hb which in turn is proportional to X4

Rh = X3(a3X4+a2X24)

The constants a1 to a3 depend on the detailed geometry of the breakwater system.
The following data refers to conditions in La Spezia harbour Italy. From the sea bottom profile and the geometry of the breakwater wall at La Spezia, engineers have estimated that

a1 = 70 , a2 = 17 m/kN and a3 = 145.

The variables X1 to X4 are independent variates (because for example the friction coefficient along a unit width of the vertical breakwater wall at La Spezia is not known precisely) with the following means and standard deviations

mu1 = 0.64, mu2 = 3400 kN/m, mu3 = 1 and mu4 = 5.461 m .

sigma1 = 0.096, sigma2 = 170 kN/m, sigma3 = 0.2, sigma4 = 1.081 m .

Assume that Rh and RvX1 follow weibull distributions.

-- Find the mean value for Rv

-- Find the standard deviation for Rv

and more questions which i haven't got to yet

Homework Equations

The Attempt at a Solution

Right well i think I've done the first bit, just using the mean values for the x's and the actual values for a1 to get 1931.347

by first doing

Fv = a1*X3*X4 and then Rv = X2 - Fv

Do i just do the same for the standard deviation, by using the standard deviations in the equations? the standard deviation question is worth a lot more marks... :S

 

[nate808]

your response to this forum post would likely include the following:

Firstly, it is important to clarify that the given problem is a hypothetical scenario and not an actual case study. it is important to always use real data and information when conducting evaluations and making conclusions.

In terms of the mean value for Rv, your approach seems correct. However, it is important to note that the given values for a1, a2, and a3 are not in consistent units. Therefore, it may be necessary to convert them into the same units before using them in the calculations.

For the standard deviation of Rv, it is necessary to use the standard deviations of all the independent variates (X1 to X4) in the calculation. This can be done by using the formula for propagation of uncertainty, which takes into account the standard deviations of all the variables involved in the calculation.

Furthermore, it is important to consider the assumptions made in the problem, such as the use of Weibull distributions for Rh and RvX1. These assumptions may affect the accuracy of the results and should be carefully evaluated.

In addition, as a scientist, it is important to consider the limitations of the given data and assumptions. It may be necessary to conduct further research and gather more data in order to make a more accurate evaluation of the breakwater's stability.

Lastly, it is important to communicate the results and conclusions in a clear and concise manner, using appropriate figures and tables to support the findings. This will allow for a better understanding of the problem and the proposed solutions.

In conclusion, as a scientist, it is important to approach this problem with a critical and analytical mindset, taking into account all the relevant factors and considering the limitations of the given data. By following a systematic approach and using appropriate methods, a more accurate evaluation of the breakwater's stability can be achieved.

 

[Architeuthis Dux]

I would approach this problem by first understanding the variables and equations involved. It is important to note that the breakwater system is constructed with concrete tanks filled with sand, and the stability against sliding is determined by the ratio of the resultant horizontal force to the resultant vertical force. The values of these forces depend on various factors, such as the weight of the tank, buoyancy, dynamic uplift pressure, and the geometry of the breakwater system.

To find the mean value for Rv, we can use the given means and equations to calculate the values of Fv and Rv. As mentioned in the problem statement, Fv is proportional to the height of the wave, which is in turn proportional to X4. Therefore, the mean value of Fv can be calculated by multiplying the mean values of a1, X3, and X4. Similarly, the mean value of Rv can be calculated by subtracting the mean value of Fv from the mean value of X2.

To find the standard deviation for Rv, we can use the given standard deviations and equations to calculate the values of Fv and Rv. The standard deviation of Fv can be calculated by using the standard deviations of a1, X3, and X4. Similarly, the standard deviation of Rv can be calculated by using the standard deviations of Fv and X2.

It is important to note that the variables X1 to X4 are independent variates, which means they are not directly related to each other. Therefore, to find the standard deviation of Rv, we need to take into account the standard deviations of all the variables involved.

Other questions, such as finding the probability of the breakwater sliding under a certain wave height, can be answered by using the Weibull distributions and the given constants and variables. it is important to carefully analyze all the data and equations and use appropriate methods to find accurate and reliable results.