Civil Group 3
Official White Paper
As Prepared for the Probability and Statistics Engineering Course
Prepared By:
Robert Ruppel
Cole Thorton
Andre Cozier
Yunior Gomez Nieto
Daniel Avalos-Medina
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Table of Contents
Introduction …...................................................................................3
Case 1: Risky Business in the Construction World........................4-8
Case 2: Using Artificial Neural Networks to Calculate Significance
of Parameters................................................................................9-13
Case 3: Review of a Performance Analysis of Predicting People`s
Presence in a Building................................................................14-17
Case 4: Using Limit Equilibrium Methods to Recalculate the Factor
of Safety for Slope Failures........................................................18-23
Case 5: Review of Correlative Analysis of Steel
Characteristics.............................................................................24-28
Conclusion.......................................................................................28
References........................................................................................29
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Introduction
As a valued client, the full understanding, implementation and transparency of projects past,
present, and future are key elements to which our team is committed to serving you. Among the
several values such as honesty, reliability, and loyalty that our team upholds, we put safety above
all. With safety as our corner stone, our team can then put full effort into completing our client’s
demands with full confidence that hazard is mitigated. The development of infrastructure in dense
and populated areas follow strict guidelines as to uphold the safety of citizens. Our team makes
safety in all aspects of the construction and civil engineering discipline a top priority to ensure
longevity in our partnerships. Motivated by our successes in past projects, we are excited to present
the following cases which demonstrate our team’s emphasis on safety and reliability by
implementing a variety of statistical methods.
This safety starts at the foundations of these large projects to which we analyze the slope failure
of soils using descriptive statistical methods to yield higher factors of safety. From then, the
implementation of Gauss, Lognormal and Shift Lognorm probability density functions help our
team choose materials that hold up against their appropriate loads while modeling data of yield
strength and partial safety factor elements. Soon after, water utilities must be placed. By using and
analyzing water quality data, we estimate potential hazards in the water resources that may be
below quality standards. The Monte Carlo method as well as the Artificial Neural Network gives
our team the ability to identify factors that influence chlorine decay in water, subsequently leading
to health and hazard alleviation for occupants of the building. This safety protocol extends to our
construction workers and other building trades as our team hires and contracts a variety of building
trades to complete the project. The use of statistical methods such as risk matrices and risk analyses
allow our team to prevent fatal and non-fatal work-related injuries among our hired building trades
such as carpenters, electricians, and equipment operators on site. To maximize efficiency among
these many moving trades, the use of inferential statistics and probability models are applied to
infer occupancy of roads, equipment and rooms. By avoiding redundancy in tasks and maximizing
the use of time to complete projects, costs of operation go down, saving both the company and the
client money.
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Risky Business in the Construction World
By: Andre Cozier
This case study reviews the article Comparative Injury and Fatality Risk Analysis of Building
Trades by Selim Baradan1 and Mumtaz A. Usmen.
Study Objective
The construction industry has many assumptions about the life-jeopardizing risk of building
trades. This study uses data from the Bureau of Labor Statistics on injury and fatalities among all
industries under the construction of buildings to develop a coherent understanding of what
specific trades are at most risk. There will be 16 trades scrutinized in this article relating to the
construction of buildings.
Study Outcome
Out of the article’s focus on 16 trades, the workers with the highest fatality rates are roofers with
a score of 55.30 with iron workers in second highest risk with a score of 52.70. The least risky
building related trades that have a non-zero risk score are equipment operators, however, the
trades with no risk score (no measured occupational related deaths in a given year) are carpet,
floor, and tile installers and finishers, cement masons, concrete and terrazzo finishers, glaziers,
plasterers and stucco masons, tile setters, and marble setters. These scores will be further
understood in the following ‘Data Used for the Research’ section below.
Data Used for the Research
The article is largely based on data collected in a 2003 published article by the Bureau of Labor
Statistics to provide information on risk in construction related jobs. Unfortunately, this data has
had negligible changes in the decade preceding the study with an average of 1,126 fatalities in
the construction industry per year. The data used by the BLS (Bureau of Labor Statistics) in this
study includes annual incidence and fatality rates. The incidence rate is a standard measurement
calculated by the number of injuries or illnesses from 100 workers in a specific field. These 100
workers are assumed to be full time workers based off a 40-hour work week for 50 weeks in a
year. The data from these 100 workers per each field are then used as a microcosm for the
entirety of their respective industry in the United States. The fatality rate is then defined as the
number of occupational deaths per 100,000 workers in a year and is used to represent the deaths
in the respective industry per year. Among data relating to the risk of fatalities by the 16 trades
listed (iron workers, roofers, carpet, floor, tile installers, drywall installers, insulation workers,
carpenters, brick masons, plumbers, electricians, plasterers and stucco masons, tile setters, and
marble setters, glaziers, painters and paperhangers, sheet metal workers, cement masons,
concrete finishers, and construction equipment operators), the study analyzes the cost of time lost
after a non-fatal injury, median wages among each of the 16 trades, and the median amount of
days away from work to develop a final risk assessment score.
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Table 1: Risk of Construction Related Jobs
The risk assessment score begins with a chart that ranks the index of risk from 0.01 to 1.5 or
more in roughly 0.25 increments. The index is then correlated to a score from 1-7, 7 being the
riskiest. It is noted that the index numbers that signify risks for a certain trade or job found in the
North American Industry Classification System. The table below shows the Risk Score Criteria.
Table 2: Fatalities vs Nonfatal Injuries
The risk score is calculated by multiplying the risk score of the fatalities by its respective index
number and adding it to the risk score of nonfatal injuries.
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Statistical Analysis Review
Inferential statistics is mostly used in the collection of data by the BLS, for the data of 100
workers is a representation of a larger population in the United States. This can also be seen in
the 16 trades being represented. With respect to the methodology used, risk analysis is the
overarching tool used for developing the figures. Risk analysis in an overarching technique that
applies largely to fields where physical risk is inevitable. This method is typically used during
the design and development phases of a variety of system safety applications, including chemical
processing, manufacturing, automobile, cruise, and plane industries for assessing the risk
associated with different scenarios. Furthermore, risk analysis methodologies implement risk
control measures to mitigate the likelihood of damage if a certain risk value is unacceptable. A
risk matrix is then a technique under risk analysis which uses the extent of damages and the
likelihood of occurrence to describe a specific event. The occurrences are measured as fifths of
100 (0-20%, 21-40%, 41-60%, 61-80%, and 81-100%) and labelled in respective columns as
“impossible”, “unlikely”, “possible”, “likely”, and “highly likely”. The article further extended
the concepts of risk analysis and risk matrices to occupational safety in construction related
fields. This was done by the implementation of inferential statistical data from 16 building
trades.
Evolution of the Article’s Text
While the article is targeted towards occupants of building related trades, the study effectively
delivers the information in colloquial English as to inform any person interested in such topic.
Despite dealing with very specific statistical methodologies, the study synopsizes the data
extruded from the BLS to produce a legible article which almost anyone can understand.
Presenting the construction industry and its various subsequent trades in the introduction leads
the reader to understand what the article will be focusing on. The article then flows toward a
more analytical form of communication in the context of risk score criteria and risk ranking.
Following the explanation of methodologies and graphs, the summary and conclusion
accomplish its goal in highlighting the study’s takeaways. This section is the most
comprehensible as it reviews the content chronologically and focuses on the importance of
understanding risk analysis using quantitative techniques.
Evaluation of the Articles Graphics
The use of tables and graphs are prevalent in the study. The tables in the article include two
charts which inform the reader on the data being analyzed. The graphs are then dependent on the
two tables. These two graphs include one line graph that correlates nonfatal injuries with the cost
of lost time. This line graph is shown below.
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Table 3: Nonfatal Injury Rate vs Cost of Lost Time
The next graph is a bar graph that compares nonfatal injuries, fatalities, and the combination of
the fatal and nonfatal injures with building trades and their risk score. This bar graph is shown
below.
Table 4: Building Trades and Risk Scores
The graphs are important in demonstrating the findings of the study without much prior
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Contribution of the Research
The study mentions their sources toward the end of the article. Out of the 16 sources mentioned,
the Bureau of Labor Statistics and the Department of Health and Human Services seem to be the
most commonly used within the in-text citations. The article is consistent in giving credit to the
suppliers of the data, as well as formulating conclusions from said data on their own merit,
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Using Artificial Neural Networks to Calculate Significance of
Parameters
By: Daniel Avalos-Medina
This case study reviews the article Using artificial neural network models to assess water quality
in water distribution networks by G.A Cuesta Cordoba, L. Tuhovacak, and M. Taus
Study Objective
The purpose of this research was to use a model to simulate chlorine decay under a specific zone
of the Water Distribution System in the district of Brno-Kohoutovice, Czech Republic. The
Artificial Neural Network along with the Monte Carlo method were both developed to simulate
chlorine decay at selected nodes with good accuracy while determining its influencing factors.
Study Outcome
The key parameters to chlorine decay are initial chlorine, temperature and flow. These
parameters have the largest influence in predicting the chlorine decay at pressure zone 1.3.1
Kohoutovice. Temperature at different location at the zone should be ideally calibrated to
consider the reaction of chorine at different temperatures during different seasons of the year.
The larger the database containing historic data and parameters, the more capable Artificial
Neural Network is to be precise in conducting the results of the simulation.
Data Used for the Research
The data was collected by a water system that is operated by Brnenske vodarny a kanalizace,
(BVK) which is located in the city district of Brno-Kohoutovice in the country of Czech
Republic. The BVK provides water to a population consisting of 13,338 people. Data was
obtained from two tanks called Bosonohly and Kohoutovice, which provide water to the area
with each one consisting of two chambers. The data consists of the geometric dimensions of the
tanks and the maximum water level for each. Historical data of flow, pH, turbidity, and initial
chlorine was collected to create a data base for the Artificial Neural Network to make predictions
of the parameters of chlorine decay. Data collected included 667 values for parameters and was
obtained by BVK during September and October of 2011. Any data missing was fulfilled by the
Monte Carlo method to manage the level of uncertainty and provide more accurate results.
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Statistical Analysis Review
The researchers used two different types of methods to examine the influential factors causing
chlorine decay in the water. The Artificial Neural Network method simulates the human brains
capability of analyzing and processing information. This method uses historical data to make
predictions of the free chlorine at Kohooutovice. The input parameters given by the database will
be represented by numerical values in the input layer. The input layer sends information to
hidden layers which is where values are added to identify if the input layer`s data have any
significant components while simulating different possible outcomes. The Monte Carlo method
is a complimentary method that is used to make sure the Artificial Neural Network provides
accurate output results when having missing information from a data base. This method provides
estimates of the variance and provides a confidence region that is used to formulate the missing
data.
The Artificial Neural Network has two limitations to its capabilities of simulating the outcomes
of the experiment. The Artificial Neural Network is only as accurate as the historical data given
to it. Care must be taken when the data is collected. The information requires verification and
must be current. The second limitation of this method involves the lack of data that may be
provided by a database. Missing historical data will affect the accuracy of the output provided by
the Artificial Neural Network. The objective of this method is to use as much information given
to the input layer to evaluate the combinations and weigh the parameter`s capability to influence
the chlorine decay. The Monte Carlo method is used to produce an analytical value for the given
missing data. It generates these values by following either a normal or uniform distribution
depending of the simulated parameters. These generated values are then compared to actual
values and analyzed with descriptive statistics to check the significance of the simulated
parameters. After all the data is collected, the Artificial Neural Network may be plotted to
calculate the chlorine decay.
Based on analyzing the results, the researchers were able to identify that the initial chlorine, flow
and temperature have the largest influence in chlorine decay. This was identified by the output
layer generating the highest values for these three factors. These values were generated after
going through all the hidden layers, consisting of algorithms calculating the probabilities and
weighing factors.
Evaluation of the Article`s Text
The author`s article was written for the water utility industry. This industry`s goal is to provide
water to consumers with a certain standard that meets the required continuity, pressure flow and
water quality. This goal is difficult to achieve due to water distribution having many factors that
may alter these standards such as the components of the Water Distribution System, for example
the materials utilized to construct the valves, tanks, and pipes. The target audience was identified
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by the article’s focus on how these methods could be used to preserve the quality of water in this
industry.
The technical terminology used to describe the components of each method and software
included in this article can make it difficult to comprehend for someone who is not familiar with
the field of statistics or within the water industry. This research can be of great use to those
industries and businesses that may have various number of outcomes depending on multiple
variables when dealing with large data sets in their respected field. In order to make this
appealing and accessible to these different industries and businesses, a more descriptive way of
setting up the input parameters for an Artificial Neural Network model would have to be
provided. This could make the audience more aware of how they could implement this
methodology in their business scheme prior to taking action in becoming more energy and time
efficient.
Evaluation of the Article`s Graphics
This article is composed of many graphics and tables that help the audience understand the
procedures that are taken place when simulation is occurring. The tables are well structured and
implement the role of descriptive statistics prior to the test being conducted, such as its mean,
standard deviation, maximum, and minimum. Figure 1 demonstrates how the input parameters
leads to an output by going across the hidden layer, while only showing one hidden layer for the
sake of comprehension with proper labeling. Table 1 does a good job of expressing the
descriptive variables taken into account when the Monte Carlo calculations are generated. Even
though the information itself is very insightful, what they are trying to accomplish could be
expressed clearer by breaking down the table into multiple tables. The current table holds too
much information that may confuse the audience or be considered overwhelming. This could
result in the audience not wanting to take the time to analyze the table. All graphics and tables
are found directly below the paragraph from which it was referenced by. This is helpful by
guiding the audience through a complicated experiment and determining what particular portions
of the data is being evaluated.
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Figure 1: Artificial Neural Network computation illustration
Table 5: Statistics of the parameters calculated by Monte Carlo method
Contribution of the Research
This research provides a different way of collecting information and evaluating conditions
without having to physically conduct the experiment again to retrieve the data. Certain data from
water treatment plants require a large amount of data to be collected. With Artificial Neural
Network the researchers can run a simulation that can predict outcomes based on historical data.
This allows companies in the water quality industry a more time efficient way of collecting
accurate data and weighing the influential factors that provide an output. As for the research
itself, the research showed that key parameters to chlorine decay is the initial chlorine, flow, and
temperature. These results are critical when attempting to distribute water at a large scale while
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maintaining the quality standards and features of the water. New advancements in material of
pipes may be developed to regulate the flow and the temperature of the water within the pipes.
The Artificial Neural Network can play a great role in structural engineering. The Artificial
Neural Network can be used when calculating certain maximum strength and hardness of a
material. As an engineer, it is important to be knowledgeable about the material that is being use
for a particular structure to avoid failure. For engineers to find certain characteristics about a
material they typically take a sample of the material and test it by using a particular test, like the
tension test and the Rockwell Hardness test. These tests usually require multiple trials and many
disposable materials to run the experiment on. The Artificial Neural Network can use historic
data from the material in question to generate an accurate output calculation. This method may
also be used to evaluate what characteristics of a particular material are most influential when
having a certain property. Statistics and probability provide an efficient, accurate, and less
wasteful way of collecting information in the field of structural engineering.
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Review of a Performance Analysis of Predicting People’s Presence
in a Building
By: Yunior Gomez Nieto
This case study reviews the article Predicting people’s presence in buildings: An empirically
based model performance analysis by Ardeshir Mahdavi and Farhang Tahmasebi.
Figure 2: Outgoing refurbishment of a building
In the University of Vienna Source: TU Wien
Study Objective
Knowing future presence is of great importance in implementing building systems
control strategies that are dependent on the occupant’s interaction with systems
such as windows, fans, lights, and radiators. That is why the study choose to
evaluate several occupancy models and explore the potential of predicting the
future presence of occupants. To quickly summarize the study; it evaluates two
existing probabilistic occupancy models, the Reinhart and the Page, and runs them
on the same occupancy data. Then to distinguish how well the models performed
in predicting daily occupancy profiles, they were individually compared to a simple
non-probabilistic model.
Study Outcome
After running the three models on the occupancy data to predict whether a room is occupied or
vacant, the resulting predictions and the actually monitored occupancy profiles were compared.
This comparison simply showed whether the models were correct or wrong, but out of it, five
statistics were chosen to analyze the model’s performance towards each other. These statistics all
showed errors in predicted arrival time, departure time, duration of occupancy, occupancy state on
a daily basis, and a number of daily transitions of going from occupied to vacant. The statistics
were then turned into cumulative distribution functions where they can be better visualized as
graphs.
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The study found out that the level of predictive accuracy was low for all the models and admits
that further using them in more practical field applications would result in even poorer results.
This can be attributed to having the predictive model trained for only one location which is an
ideal situation that’s unlikely to be presented in practical use.
Figure 3: Cumulative Distribution Functions for
Statistic Arrival Time
Source: Energy and Building
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Data Used for the Research
The occupancy data was collected from one of the office buildings at the Vienna University of
Technology. Wireless ceiling-mounted motion sensors were placed in eight workplaces and gave
a value of 0 if vacant and a value of 1 if occupied. The sensors also came included with the abilities
to note the duration of either event and labeling the dominant occupancy state for an interval. Data
such as the time before 8 AM and after 7:45 PM and nonworking days such as business trips,
sickness, and holidays were not included as part of the study since they didn’t pertain to the study’s
objective. The occupancy data totaled 90 working days for a single run, but to have a wider range
of results, the study opted to use a Monte Carlos algorithm. This program created 100 simulations,
increasing the amount of available data that can be run through the models.
Figure 4: Sample Binary Occupancy Profile
Generated by the MT Model
Source: Energy and Building
Statistical Analysis Review
The data collected from the University is referred as bivariate since it comes with only two
possibilities: either occupied or vacant. This type of data is qualitative in nature since it can’t be
expressed in numbers, but once the study made the number one represent occupied and zero
represent vacancy, it became quantitative. This binary form of data belongs to the descriptive
branch of statistics where random variables can only occur in a finite interval and are used to
describe features in a study such as mean, standard deviation, and variance. When the data was
run through the models, it was turned into predictive data in the form of a best-fitting threshold
graph. Aside from visually presenting how likely there is to be occupancy at a certain time, it
also has a threshold value that suggests an acceptable chance in which the probability will occur.
This is no longer descriptive statistics, but inferential since it’s used to deduct whether
occupancy would happen from a sample population to a bigger one. The predictive data was then
compared to the actual monitored data which lead to its final stage. The result was five
descriptive statistics that “summarize important properties of basic data’’, and when converted
into cumulative distribution functions showed how well was the performance for each model.
The stages of the data from the beginning to the end were to get it from “a readable and
worthwhile form’’ into a point where it would “allow us to obtain a graphical representation of
the data”, therefore meeting the study goal of representing the performance of the models
against each other.
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Evaluation of the Article’s Text
The article is written towards an audience that has a good understanding of statistical concepts.
With technical language that vastly makes up the study, the little or no information that goes
towards explaining the processes and statistical concepts, and especially a topic that isn’t geared
for beginners, someone without any experience or even with a small background in it would find
it difficult to grasp. With how it’s currently written, it can be argued that it’s unlikely that an
inexperienced audience would make any use of this reading, but by going more in-depth into the
process rather than merely stating what they did, using simpler vocabulary and making a section
defining what can’t be replaced, it would let the reader make more sense of the work.
Evaluation of the Article’s Graphics
The article consists of three types of graphs that serve to illustrate the resulting progress of their
work and aren’t necessary for the understanding of the study. The first type of graph, the
cumulative distribution function, is used to show the difference in predictive performance
between the three models based on five statistics. The bigger the function the more effective it is
in its prediction. A negative aspect of this graph would be that it would be highly hard to
comprehend without knowing what a CDF is and therefore inexperienced people wouldn’t
understand its message. This goes hand in hand with my previous suggestion that there should be
a more in-depth discussion on what is being said and, in this case, shown. The other type of
graph is a histogram that shows the probability of occupation in two-hour intervals for 24 hours.
As simple as it is, it is made more difficult with the addition of the best-fitting threshold, which
easy to understand if you know what it is, but hard to find out what it even means with the little
clarity provided and almost no trace definition on the internet. Without knowing what this line
means, you miss out on essential information that needs to be grasped before continuing to the
next graph. I again suggest adding a clarifying description to make it more understandable. The
next and final graphic, the binary linear graph, shows the previous graph’s hours that meet the
threshold and is based on occupancy state rather than probability presence. All of the graphs are
positioned and sized perfectly and can be accessed smoothly after reading the information that
pertains to it.
Contribution of the Research
This research presents towards the statistical modeling field that it’s not necessary to base your
model on stochastic elements but, in this case, it more efficient to use non-probabilistic models
rather than those that take into account the random diversity in accounting patterns. This
contribution is useful in my field of civil engineering and any that revolve around the same area
because it presents us with the most efficient model at this time. A model that can be used not for
only this studies’ scenario of an office building but wider amount locations such as roads, parks,
forests, and much more. This study demonstrates that probability/statistics can be of great use
when designing many locations around the concept of occupancy.
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Using Limit Equilibrium Methods to Recalculate the Factor of
Safety for Slope Failures
By: Cole Thornton
This case study reviews the article Statistics for the Calculated Safety Factors of Undrained
Failure Slopes by Erly Bahsan, Hung-Jiun Liao, Jianye Ching, and Szu-Wei Lee from
Engineering Geology.
Study Objective:
The purpose of this article is to use the uncertainty of calculated factors of safety (FS) of soil
slopes to create a relationship between the probability of failure of a man-made undrained clay
slope and its calculated factor of safety to make the reliability design and reliability analysis
easier.
Study Outcome:
The outcome of this report is that the two-dimensional limit equilibrium methods used in this
article give unbiased estimates for calculating the factor of safety, that man-made soil slopes
have a lower variability than natural soil slopes, and that the conversion of the tested shear
strength value to the field shear strength value is an important part in the safety factor
calculations.
Data used for the Research:
The data used in the article is from 43 previous cases found in literature, listed in the article,
dating from 1956 to 2002 where the slope of clays have failed. All of these cases vary in the
types of slopes used whether its natural, fill, or cut slopes. The purpose of reopening these cases
was to recalculate the factor of safety for each case using both two-dimensional limit equilibrium
methods known as Bishop’s Method and Spencer’s Method.
Statistical Analysis Review:
One of the main statistical methods used in the article is descriptive statistics, specifically
variability. An example of variability within the article is the confirmation that natural failure
slopes are much greater than man-made failure slopes when using the natural log of the factor of
safety. Simplistic terminology like standard deviation and mean also come into play when
dealing with human error in the analysis process for example.
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A majority of the article uses descriptive statistics to analyze the differences between natural
slopes and man-made slopes when calculating the natural log of the factor of safety for both. The
article utilizes the term variability when using descriptive statistics to find correlations between
natural slopes in three dimensions and man-made slopes in two dimensions since both act
different under various circumstances. Variability is also used for finding more fundamental,
statistical calculations like standard deviation and the mean of the magnitude of human error or
the natural log of the factor of safety for both types of slopes. A likely reason why variability
was conducted throughout the article is because of the possibilities descriptive statistics has
when finding a number of possible outcomes as to why a slope fails or what the factor of safety
is for either slope given certain parameters.
The creators of the article most likely learned that utilizing descriptive statistics to its fullest
potential can benefit in their answers and calculations for data that failed and never succeeded.
Using standard deviation and the mean in various ways yields conclusive data that can be better
narrowed down to how man-made slopes can be made more efficiently and how natural slopes
can be taken with a more cautious approach.
Evaluation of the Article’s Text:
The presentation of the article is through the means of professionalism as well as through the
perceptive of an engineer. The comprehensive and fairly complex text throughout the article
conveys a higher understanding of the topics at hand while, at the same time, breaking down key
phrases into digestible and understandable terminology for both engineers and non-engineers.
Key phrases like “factors of safety” are phrases that engineers are familiar with which is why the
article contains a quick definition to clarify the meaning for non-engineering audience members.
For a majority of the article, however, the key points the article touches upon can be simplistic in
nature when talking about the various slopes of soil and the mathematical methods used to
achieve some of these values.
The occupations the text in the article is directed towards are mostly geotechnical engineers,
geologists, and professionals who specialize in various jobs surrounding soil and/or the
environment. A niche topic like the various slopes of soil affecting the factor of safety are
important to know for these professions but the topic may be trivial to some in another
profession because of how minute the difference in slopes does to soils. A way this can be
changed into a more understandable topic would be by tweaking the article to be more directed
towards the dangers of the possibility of erosion and how the slopes of soil can be detrimental to
lives of others. Tweaking the article to fit this agenda would give a whole new perspective to a
different audience while keeping the same meaning behind the importance of various soil slopes,
whether the slopes are man-made or natural.
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Evaluation of the Article’s Graphics:
Between the visualizations and the numerical graphs, there are multiple types of graphics being
used for the information in the article. The first visualization is a two-dimensional representation
of the profile of the slope. This contains a graph showing the specific water values for each layer
of soil, the “x” and “y” axis values foe elevation and length, and the two methods that are used to
calculate the slopes (i.e. Bishop’s Method and Spencer’s Method) that are found throughout the
article. The second visualization is the profile of the borehole which contains the different layers
of soil at the different elevations below the surface and what the shear strengths were at each
elevation.
The first set of graphs in the article are histograms indicating the frequency versus the factor of
safety for both Bishop’s Method and Spencer’s Method. Both histograms also have a
corresponding Q-Q plots with quantiles of input sample versus standard normal quantiles for
both Bishop’s Method and Spencer’s Method. The other graph found in the article is a scatterplot
with tread lines where the axes consist of the factor of safety by Spencer’s Method versus the
factor of safety by Bishop’s Method. All of the visualization and numerical graphics are as
follows:
Table 6: Slope Profile of coordinate vs elevation
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Table 7: Borehole Profile
Table 8: Frequency Analysis
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Table 9: Bishop`s method vs Spencer`s method
The graphs and visualizations from the article are prepared in a way that they convey the
message completely while still being readable and simplistic to understand. The information
surrounding the graphics are very detailed in a mathematical and terminology sense with the
equations neatly prepared and explained. The choice in which graphic to use is also appropriate
and would not need changing. A reason for this is that some visualizations cannot be portrayed in
any other manner like the boring log or the two-dimensional sideview of the slope profile so any
other choice of visualization would not work as well.
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Contribution to Research:
This article proves that something as specific and simple as the slope of soil can have a major
impact on the environment around us. Soil can be elusive when it comes to the long-term and
short-term effects of building foundation above ground, whether the slope of the soil or the type
of the soil is the factor. Depending on the conditions, the factor of safety comes into play with
how secure the soil is and if the soil will be a problem or not. This is why research involving the
information found in this article is so important to how future construction will take place. By
having a better grasp on the understanding of soil slopes, one can create more secure foundations
with higher factors of safety which allows for safer building construction when building on
slanted surfaces or even flat surfaces.
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Review of Correlative Analysis of Steel Characteristics
By: Robert Ruppel
This case study reviews the article Material and Geometrical Characteristics of Structural Steels
Based on Statistical Analysis of Metallurgical Products.
Study Objective
The objective of this report was to evaluate the results of different strength measurements and
characteristics into correlative relationships through the calculation and modeling of elements
like yield strength and partial safety factors.
Study Outcome
The outcome of the report was the observation of the correlative behavior between the increase
of steel plate thickness for any of the test steel types and the decrease in mean value yield
strength of said steel plate.
Data used for the Research
This study was done through the analysis of already known material characteristics. That means
that the data analyzed in the piece did not come from a specific experiment but rather was broken
down through the variety of probability models explained in the Statistical Analysis Review
portion. These inserted characteristics serve as the reports data and are cited as follows:
•
•
•
•
•
•
•
•
•
•
•
•
•
•
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Mean Value of Yield Strength of steel s355 plates thickness ranges
Standard Deviation of Yield Strength of steel s355 plates thickness ranges
Skewness of Yield Strength of steel s355 plates thickness ranges
Kurtosis of Yield Strength of steel s355 plates thickness ranges
Gauss Distribution Value of steel s355 plates thickness ranges
Logonormal Distribution Value of steel s355 plates thickness ranges
Shift Logonorm Distribution Value of steel s355 plates thickness ranges
Nominal Value of steel s355 plates thickness ranges
Gauss Distribution Value for design value Rd
Logonormal Distribution Value for design value Rd
Shift Logonorm Distribution for design value Rd
Design Value
Gauss Distribution Value for partial safety factor
Logonormal Distribution Value for partial safety factor
Shift Logonorm Distribution for partial safety factor
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•
•
•
•
Mean Value for section depths, web thicknesses, and flange thicknesses
Standard Deviation for section depths, web thicknesses, and flange thicknesses
Skewness for section depths, web thicknesses, and flange thicknesses
Kurtosis for section depths, web thicknesses, and flange thicknesses
Statistical Analysis Review
This report was anchored in the fundamental elements of probability and statistics. This is made
clear in the first section post the introduction where the first form of analysis gathered the mean,
standard deviation, skewness and kurtosis of the yield strength per certain thickness ranges
which are then utilized with the Monte Carlo method to figure number of measurements present
and if they are enough to allow for accurate distribution functions being produced. This
determination plays into the partial safety factor calculation as well. These elements play into the
Hermite probability distribution function which is utilized over the Gauss density probability
function due to its accounting for skewness and kurtosis. A real probability model is also created
for the yield strength which is used to help define the nominal value for yield strength of certain
thicknesses. Characteristic values for certain probability models are also present, being that of
Gauss, Lognormal and Shift Lognorm probability density functions. All these elements played
into creating the greater foundation of the Correlative Analysis Method utilized in this report.
The Correlative Analysis Method was an ideal choice for the overall direction for this report.
Correlative Analysis is a statistical method by which two quantitative variables are evaluated in
terms of their connective relationship. This heavily present in the conclusion portion of the report
that makes correlative statements upon the relationships of the quantities of mean yield strength
and thickness. This correlation sets the grounds for the inferential statements later on with more
correlations of the dimension tolerances and the tendency to go negative. Overall, the Correlative
Analysis Method allowed for the greater correlation of mean yield strength lowering as thickness
of the plate increases through the consolidation of all previous statistical elements into the
statements of the correlative relationship stated in the conclusion.
Evaluation of the Article’s Text
This report is one of heavy detail and is delivered from a place of already built understanding.
There are no portions of the piece that define any of the terms or methods utilized but rather
takes any portion of explanation to tie in the terms/methods into the greater purpose of the piece.
That tone and structure throughout the report makes it clear that this is prepared for an audience
of professionals or academics already highly familiar with the know statistical and civil
engineering elements of things like safety factors, standard deviations, probability models and
yield strengths. The report does not seek to make the information hard to decipher and anyone
with the proper background of understanding and knowledge would find the report to be more
than appropriate. If the desire of the report’s creators was to reach a broader audience, then all
that would be needed would be an additional portion of definitions and the addition of step by
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step processes for some of the modelling. Outside of that the report succeeds in it purposes and is
fit for the audience it seeks to reach.
Evaluation of the Article’s Graphics
The graphics utilized within the report fall into four categories. The first is the scatter plot graphs
used to model correlating thickness values and thickness vs observations. Histograms were also
used to model the reality frequency of certain dimension sections. Distribution plots were also
utilized to mode the real probability of yield strength as well as the normal distribution showing
the difference in Gauss and Hermite models. Finally, example figures of beam cross sections
were utilized to showcase certain geometric characteristics being analyzed. Example images of
the figures used are as follows:
Figure 5: I Geometric Analysis
Table 10: Cross-section flange Analysis
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Table 11: Relative frequency vs section width
Table 12: Probability vs Yield strength
These graphics are expertly prepared, most likely formed from high level mathematic simulators.
They are havinly detailed in their ploting and numbering. They are located in solid relation to
where they are referenced in the report and are clearly labeled as to decrease any confusion. The
only thing that could service a lesser informed individual would be some text boxes explaining
some of the figures more directly instead of just referencing them.
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Contribution of Research
This study makes it clear that there is continuous need for monitoring of the observed
characteristics of the steel samples as new designs come forward into the world. Though this
report is not immediately intuitive to a layman, the methods present can be continuously
conducted as time moves forward as to keep a continuous account of the state of the relationship
between mean yield strength and thickness of steel. This is important for the idea of safety and
repeated return to this report when designing a new structure would ensure that the safety of the
structure and the reliability of the materials is properly managed.
Conclusion
The multiple cases studies presented in this paper highlights the variety of uses and impact
probability and statistics has in the safety of our society. By allowing our team to do research in
your USF’s college of civil engineering, we will be able to further explore and test the topics
mentioned above as well as to the multitude of other fields that pertain to safety.
Aside from the significant importance this research could have on the safety of our businesses,
industry, and construction it would also be beneficial to the University as it would bring in grants
and national recognition due to our work. Would you let our team carry out research on
probability and statistics in the college of civil engineering?
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