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Full-Text Articles in Engineering

Temporal Lidar Scanning In Quantifying Cumulative Rockfall Volume And Hazard Assessment: A Case Study At Southwestern Saudi Arabia, Abdullah A. Alotaibi, Norbert H. Maerz, Kenneth J. Boyko, Ahmed M. Youssef, Biswajeet Pradhan Aug 2022

Temporal Lidar Scanning In Quantifying Cumulative Rockfall Volume And Hazard Assessment: A Case Study At Southwestern Saudi Arabia, Abdullah A. Alotaibi, Norbert H. Maerz, Kenneth J. Boyko, Ahmed M. Youssef, Biswajeet Pradhan

Geosciences and Geological and Petroleum Engineering Faculty Research & Creative Works

Rockfalls and unstable slopes pose a serious threat to people and property along roads/highways in the southwestern mountainous regions of Saudi Arabia. In this study, the application of terrestrial light detection and ranging (LiDAR) technology was applied aiming to propose a strategy to analyze and accurately depict the detection of rockfall changes, calculation of rockfall volume, and evaluate rockfall hazards along the Habs Road, Jazan Region, Saudi Arabia. A series of temporal LiDAR scans were acquired at three selected sites. Our results show that these three sites have different degrees of hazard due to their geological differences. The mean ...


Unconventional Water Resources: Global Opportunities And Challenges, Zahra Karimidastenaei, Tamara Avellán, Mojtaba Sadegh, Bjørn Kløve, Ali Torabi Haghighi Jun 2022

Unconventional Water Resources: Global Opportunities And Challenges, Zahra Karimidastenaei, Tamara Avellán, Mojtaba Sadegh, Bjørn Kløve, Ali Torabi Haghighi

Civil Engineering Faculty Publications and Presentations

Water is of central importance for reaching the Sustainable Development Goals (SDGs) of the United Nations. With predictions of dire global water scarcity, attention is turning to resources that are considered to be unconventional, and hence called Unconventional Water Resources (UWRs). These are considered as supplementary water resources that need specialized processes to be used as water supply. The literature encompasses a vast number of studies on various UWRs and their usefulness in certain environmental and/or socio-economic contexts. However, a recent, all-encompassing article that brings the collective knowledge on UWRs together is missing. Considering the increasing importance of UWRs ...


Single-Pass Inline Pipeline 3d Reconstruction Using Depth Camera Array, Zhexiong Shang, Zhigang Shen Jun 2022

Single-Pass Inline Pipeline 3d Reconstruction Using Depth Camera Array, Zhexiong Shang, Zhigang Shen

Faculty Publications in Construction Engineering & Management

A novel inline inspection (ILI) approach using depth cameras array (DCA) is introduced to create high-fidelity, dense 3D pipeline models. A new camera calibration method is introduced to register the color and the depth information of the cameras into a unified pipe model. By incorporating the calibration outcomes into a robust camera motion estimation approach, dense and complete 3D pipe surface reconstruction is achieved by using only the inline image data collected by a self-powered ILI rover in a single pass through a straight pipeline. The outcomes of the laboratory experiments demonstrate one-millimeter geometrical accuracy and 0.1-pixel photometric accuracy ...


Utilization Of Steel Slag In Development Of Sustainable And Durable Concrete., Karthik Prabhu T Dr, Gowri Shankar M Mr., Jagadesh P Dr., Nagarajan V Dr. May 2022

Utilization Of Steel Slag In Development Of Sustainable And Durable Concrete., Karthik Prabhu T Dr, Gowri Shankar M Mr., Jagadesh P Dr., Nagarajan V Dr.

International Journal of Advanced Technology in Civil Engineering

This paper reflects the results of an experimental investigation of the strength, permeability, abrasion, carbonation, and shrinkage characteristics of concrete containing various percentages of steel slag as partial replacement of natural fine aggregates. M 30 Grade concrete was designed as per specific national specifications. Steel slag was used to replace natural sand in the range of 0– 50%. It was observed that the steel slag blended concrete with up to 50% substitution exhibited a comparable compressive and flexural strength when compared to the control specimens. From the Dorry’s abrasion test, it was noted that the specimens could be implemented ...


Hydrodynamic Limitations To Mangrove Seedling Retention In Subtropical Estuaries, Kelly M. Kibler, Christian Pilato, Linda Walters, Melinda Donnelly, Jyotismita Taye May 2022

Hydrodynamic Limitations To Mangrove Seedling Retention In Subtropical Estuaries, Kelly M. Kibler, Christian Pilato, Linda Walters, Melinda Donnelly, Jyotismita Taye

Flow-biota Interaction and Natural Infrastructure Design

Mangrove forest sustainability hinges upon propagule recruitment and seedling retention. This study evaluates biophysical limitations to mangrove seedling persistence by measuring anchoring force of two mangrove species (Rhizophora mangle and Avicennia germinans). Anchoring force was measured in 362 seedlings via lateral pull-tests administered in mangrove forests of two subtropical estuaries and in laboratory-based experiments. Removal mechanism varied with seedling age: newly-established seedlings failed due to root pull-out while seedlings older than 3 months failed by root breakage. Anchoring force of R. mangle seedlings was consistently and significantly greater than A. germinans (GLM: p = 0.002), however force to remove A ...


Mechanical Property Relationships Of Cement Or Lime Stabilized Soils Throughout A Pavement's Life, Leigh E.W. Ayers May 2022

Mechanical Property Relationships Of Cement Or Lime Stabilized Soils Throughout A Pavement's Life, Leigh E.W. Ayers

Theses and Dissertations

Soil-cement is an integral part of pavement design, especially in areas that are aggregate deprived, such as Mississippi. Current designs are reliant on the relationship of unconfined compressive strength (UCS) to other mechanical properties. The other properties discussed in this dissertation are Modulus of Elasticity (E), Indirect Tensile Strength (St), and Modulus of Rupture (MOR). This dissertation includes a comprehensive review of past design methods and mechanical property relationships. While some mechanical property relationships were shown to be well understood (i.e. St to UCS), others were not as accurate, especially for the later life mechanical properties (i.e. MOR ...


Exploring Valuable And Potentially Harmful By-Products Formed And/Or Released From Smouldering Treatment Of Sewage Sludge, Taryn Ashley Fournie May 2022

Exploring Valuable And Potentially Harmful By-Products Formed And/Or Released From Smouldering Treatment Of Sewage Sludge, Taryn Ashley Fournie

Electronic Thesis and Dissertation Repository

The presence of potentially toxic elements (PTEs) and emerging contaminants (e.g., per- and polyfluoroalkyl substances (PFAS)) makes sewage sludge management challenging. Due to their hazards, there is significant interest in thermal treatment technologies that can destroy these compounds, like incineration. However, incineration still poses several risks due to forming and/or releasing hazardous emissions (e.g., polychlorinated dibenzo-p-dioxins and dibenzofurans (PCDD/Fs) and PTEs). More recently, the use of smouldering has been introduced as a potential treatment technique for managing sewage sludge. Smouldering presents several advantages over traditional incineration due to its lower energy and pre-treatment requirements ...


Comparing The Stiffness Of Cold In-Place Recycled Asphalt Pavement To Hot Mix Asphalt: Determining The Reproducibility Of The Stiffness Rebound Test, Tanner Turben May 2022

Comparing The Stiffness Of Cold In-Place Recycled Asphalt Pavement To Hot Mix Asphalt: Determining The Reproducibility Of The Stiffness Rebound Test, Tanner Turben

Civil Engineering Undergraduate Honors Theses

The Stiffness Raveling Mechanism Test (SRMT) was originally developed as an indirect measure of pavement stiffness to determine a pavement’s tendency to ravel, a type of damage. Regarding rehabilitation of existing roadways by Full Depth Reclamation (FDR) Cold In-Place Recycling (CIR), concern of field repeatability was expressed (Hill & Braham, 2016).

An analysis of lab-compacted samples of CIR and Hot Mix Asphalt (HMA) was performed to determine if the results could be reproduced between CIR and HMA. Additionally, the experiment observed the effects of percent air voids, temperature, and moisture conditioning on CIR and HMA. Three samples were prepared for ...


Design Of A Freight Transportation Outreach Curriculum, Breanna Stoesz May 2022

Design Of A Freight Transportation Outreach Curriculum, Breanna Stoesz

Civil Engineering Undergraduate Honors Theses

This project is centered around finding a solution to the shortage of truck drivers within the freight industry. Specifically, this project aims to lessen this shortage by ensuring potential future drivers are aware of the benefits of the industry and are encouraged to consider this career path for themselves. By producing an engaging and educational freight transportation curriculum for middle and high school students to go through in outreach programs, these students would have an increased likelihood of joining the trucking profession and encourage others to become informed about the profession as well. In addition to the direct driving role ...


Comparing Actively Managed Mutual Fund Categories To Index Funds Using Linear Regression Forecasting And Portfolio Optimization, Luke Weiner May 2022

Comparing Actively Managed Mutual Fund Categories To Index Funds Using Linear Regression Forecasting And Portfolio Optimization, Luke Weiner

Industrial Engineering Undergraduate Honors Theses

The global investment industry offers a wide variety of investment products especially for individual investors. One such product, index funds, which are younger than actively managed mutual funds, have typically outperformed managed funds. Despite this phenomenon, investors have displayed a tendency to continue investing in actively managed funds. Although only a small percentage of actively managed funds outperform index funds, the costs of actively managed funds are significantly higher. Also, managed fund performances are most often determined by their fund category such as growth or real estate. I wanted to answer the following question for individual investors: can we forecast ...


Exploring The Effects Of Varied Land Use On Elemental Concentrations Within Streams, Logan Jennings May 2022

Exploring The Effects Of Varied Land Use On Elemental Concentrations Within Streams, Logan Jennings

Biological and Agricultural Engineering Undergraduate Honors Theses

It is well documented that human activity influences the chemistry of surrounding waters. As such, it is possible that there is a link between land use within a watershed and the chemical composition of the stream. The objectives of this study are to determine if varied land use does affect the concentrations of macronutrients and trace elements present in the streams of Northwest Arkansas, and if so, to determine what extent urban and agricultural development are responsible for these changes. Water samples were collected across 19 streams in the Northwest Arkansas region between January and March of 2022. Water samples ...


Using Experiments, 3d Scanning, And Computational Fluid Dynamics To Analyze Variance In Minor Loss Coefficients, Adam B. Pack May 2022

Using Experiments, 3d Scanning, And Computational Fluid Dynamics To Analyze Variance In Minor Loss Coefficients, Adam B. Pack

All Graduate Theses and Dissertations

As water moves through pipes, it loses energy. The energy losses are due to friction and the minor losses associated with various pipe fittings, which change the direction of flow. Pipe bends, or elbows, are a common pipe fitting and a significant source of energy loss in piping systems. This research was performed to better understand the variability of energy loss due to different pipe elbow designs and to investigate methods to replicate these losses using numerical simulations.

Eight pipe elbows, all 3-inch, 90-degree, schedule 40 PVC elbows that vary by radius of curvature and/or end connection type, were ...


Development Of A Next-Generation Non-Proprietary Portable Concrete Barrier, Riley Ruskamp May 2022

Development Of A Next-Generation Non-Proprietary Portable Concrete Barrier, Riley Ruskamp

Civil and Environmental Engineering Theses, Dissertations, and Student Research

Portable concrete barriers (PCBs) are segmented barriers made of precast concrete units that are connected by various load-bearing hardware. PCBs are typically used to shield work zones by redirecting errant vehicles upon impact with the barrier system. Most commonly-available PCBs have demonstrated performance issues arising from the sloped face of the barrier, which encourages vehicles to pitch and roll during impact, potentially resulting in vehicle rollover. Concerns also exist regarding the large dynamic deflections exhibited by these systems that can encroach upon the protected work zone or require anchoring to prevent large displacements. In addition to these concerns, the American ...


Risk Assessment Of Hazardous Material Transportation For Small And Tribal Communities, Harrison Redepenning May 2022

Risk Assessment Of Hazardous Material Transportation For Small And Tribal Communities, Harrison Redepenning

Civil and Environmental Engineering Theses, Dissertations, and Student Research

By and large transportation of hazardous materials (HazMat) across the US is increasing, with truck transportation as the most common method of transport. Smaller communities (population <5,000) and Native American communities often lack the economic and political influence to quantify the dangers that HazMat incidents present to the immediate and surrounding areas. Lack of such information is an impediment to adequate preparedness in cases of HazMat incidents. This research focuses on assessing the vulnerability of small and tribal communities in Nebraska to the impacts of highway HazMat incidents. This was done by estimating the expected number and type of HazMat incidents per population in each community. Additionally, statistical analysis was conducted on actual HazMat incidents to determine if small and Native American communities experience a higher rate of incidents per population and per HazMat VMT than large and other small communities respectively. For per population, it was found small versus large is statistically significant while Native American versus other small communities was not significant. For per HazMat VMT, neither comparison was found to be statistically significant. In estimated HazMat incidents, actual HazMat incidents per population, and actual HazMat incidents per HazMat VMT, small communities had higher mean values than their large counterparts. Communities on Native American reservation land experienced a higher estimated and lower actual HazMat incident rate per population than other small communities. For actual HazMat incidents per VMT, Native American communities had a higher rate than other small communities.

Advisor: Aemal Khattak


A Physical Model Of Deadmans Run, Quinn Brandt May 2022

A Physical Model Of Deadmans Run, Quinn Brandt

Civil and Environmental Engineering Theses, Dissertations, and Student Research

A physical model of Deadmans Run and a pair of railroad bridges was constructed to assess the impacts of the bridges on flood flows. Lower Platte South Natural Resources District is planning a series of improvements to Deadmans Run to improve flood conveyance capacity and remove approximately 500 homes and businesses from the floodplain. The rail bridges are located less than a mile from the confluence of Deadmans Run and Salt Creek, meaning the bridges present a significant bottleneck to the planned improvements. The physical model was used to characterize the drag effects caused by the bridges, which was used ...


Analyzing Vulnerabilities In The Northwest Arkansas Highway Network Using Mathematical Optimization, Brandon Jerome May 2022

Analyzing Vulnerabilities In The Northwest Arkansas Highway Network Using Mathematical Optimization, Brandon Jerome

Industrial Engineering Undergraduate Honors Theses

The highway and bridge network is a critical infrastructure that allows for the free transportation of citizens and enables truck-borne freight transportation. Disruption of this system could be caused by a terrorist attack, natural disaster, growth of population, required repairs and upgrades, or collapse caused by old age or malfunction. In the event of a disruption cities and regions can experience increased traffic and supply chain shortages, thus causing cascading effects throughout surrounding areas. With this motivation, we develop a network interdiction optimization model to identify a limited subset of roads that, if disrupted, causes the greatest increase in the ...


Lidar Data Analysis Strategies To Determine Features Indicative Of At-Risk Coastal Sites, Ashley Elkins May 2022

Lidar Data Analysis Strategies To Determine Features Indicative Of At-Risk Coastal Sites, Ashley Elkins

Theses and Dissertations

Light detection and ranging (LiDAR) derived volume changes provide both visual and statistical information for how project shorelines change over time. For beach erosion control (BEC) and coastal storm risk management (CSRM) projects, changes across storm events are fundamental to understanding a project’s progress. The Coastal Systems Portfolio Initiative (CSPI) aims to document and track U.S. Army Corps of Engineers (USACE) projects in a holistic systems-based manner. This web based geographic information system currently lacks numerical metrics beyond fill volumes to represent a project’s progress or reliability. This study aims to identify potential reliability metrics using the ...


Wave Interactions And Energy Cascade, Bailey Downing May 2022

Wave Interactions And Energy Cascade, Bailey Downing

Civil Engineering Undergraduate Honors Theses

Structural engineers design buildings and their components to withstand code-specified wind loads. The ASCE 7-16 manual sets the standards for calculating wind loads in the U.S. Depending on the velocity of wind, deflections may occur as wind passes through the building. The pressure reported from ASCE are based on wind tunnel measurements. The peak pressure from ASCE 7 is much less than what is measured from the field for a low-rise building. As an alternative economic tool, Computer modeling has been developed to help with this dilemma. Methods based on computational fluid dynamics (CFD) are used to calculate velocities ...


Determining Earthquake Impacts On Arkansas' Roadway Network: An Application Of Hazus., Simon Rothwell May 2022

Determining Earthquake Impacts On Arkansas' Roadway Network: An Application Of Hazus., Simon Rothwell

Civil Engineering Undergraduate Honors Theses

Natural hazards are a dangerous and unpredictable aspect of life on earth. They can cause devastating damage to our surroundings that makes movement of people, goods, and emergency services difficult. There is a need to plan for these disasters to ensure that damages to our infrastructure and people are minimized. It can be difficult for planners to determine which parts of a roadway network are most vulnerable to a specific disaster and what their impact on the rest of the network may be. This thesis uses a nationally available natural disaster estimation tool developed by FEMA called “Hazus” (FEMA, 2020 ...


Evaluating The Effects Of Curing Methods On Bcsa Cement Concrete, Hannah Allen May 2022

Evaluating The Effects Of Curing Methods On Bcsa Cement Concrete, Hannah Allen

Civil Engineering Undergraduate Honors Theses

BCSA cement is a type of cement that makes concrete set up much quicker than typical portland cement concrete. BCSA cement concrete also has a much higher compressive strength than that of portland cement concrete. This study was conducted to determine the effect of different curing conditions on the compressive strength of BCSA cement concrete.


Community Transportation Needs And Willingness To Use Shared Micromobility: A Case Study Of Fort Smith, Arkansas, Anthony Michael Kammerer May 2022

Community Transportation Needs And Willingness To Use Shared Micromobility: A Case Study Of Fort Smith, Arkansas, Anthony Michael Kammerer

Civil Engineering Undergraduate Honors Theses

Shared micromobility is utilized in “targeted service areas with the usage generally intended for short trips such as "first- and last-mile" connections to complete trips made via other modes, including transit” (Price et al., 2021). In the United States, this practice has especially taken off with the implementation of sharing-based systems. This is evidenced by ridership numbers in the United States growing from 84 million riders nationwide in 2018 to 136 million riders in 2019 (NACTO, 2020). Users often use their smart phone or another similar device to unlock the vehicle after paying a fee on the device through their ...


Structural Design For Fire Conditions Of A Prototype Metal Building Using The New Proposed Appendix To Aisi S100, Xia Yan, Thomas Gernay May 2022

Structural Design For Fire Conditions Of A Prototype Metal Building Using The New Proposed Appendix To Aisi S100, Xia Yan, Thomas Gernay

American Iron and Steel Institute (AISI) Specifications, Standards, Manuals and Research Reports (1946 - present)

Performance-based design for fire conditions has been increasingly adopted for different structural systems over the last decade. The objective of this project is to exemplify through a case study how the newly proposed Appendix 4 to AISI S100 [1] on ‘Structural Design for Fire Conditions’ could be used by the metal building industry. The scope of work on the project includes the following:

(1) Identification of a prototype metal building to serve as an exemplar case study for the structural fire design procedure.

(2) Definition of the performance objectives and design requirements for the building in the fire situation. This ...


Automated Quality Control For In-Situ Water Temperature Sensors, Leah S. Richardson May 2022

Automated Quality Control For In-Situ Water Temperature Sensors, Leah S. Richardson

All Graduate Theses and Dissertations

The identification of data not representative of the target subject for outdoor (in-situ) environmental sensors (bad data) is a topic that has been explored in the past. Many tools (such as data filters and computer models) have succeeded in providing an end user with properly identified incorrect data over 95% of the time. However, with the continuous increase in the use of automated data collection, a simple indication of the bad data may no longer provide the end user with enough information to reduce the amount of time that must be spent for manual quality control. The purpose of this ...


A Campus Connected: An Analysis Of University Outdoor Spaces, Skylar Wilson May 2022

A Campus Connected: An Analysis Of University Outdoor Spaces, Skylar Wilson

Undergraduate Honors Theses

The purpose of this research is to analyze the evolution of outdoor renovations on East Tennessee State University’s campus by examining the effects these renovations have had on students and faculty, and then using this data to propose possible successful renovations to the remainder of the University Commons project. To complete this project, data was obtained through East Tennessee State University administrative faculty interviews, surveys of students residing in campus resident halls, and observations. By examining the impact on behavior, designers and developers are then able to successfully determine the factors that aid in positively influencing human behaviors. Design ...


The Effect Of Changing Land Use On Streamflow Statistics And Flood Flows Across Select Gages In Northwest Arkansas, Timothy Mcmullen May 2022

The Effect Of Changing Land Use On Streamflow Statistics And Flood Flows Across Select Gages In Northwest Arkansas, Timothy Mcmullen

Civil Engineering Undergraduate Honors Theses

Since 1901, heavy rainfall events have increased in the United States in both intensity and frequency, and population in the United States has increased, resulting in significant land use changes. Both of these trends could explain an increase in observed flood magnitude and frequency. In order to determine if a relationship exists between land use/land cover and changing stream flows in northwest Arkansas, this study analyzed temporal changes in various flow statistics for fourteen stream gages and compared the rates of change in flow statistics from gages on streams with watersheds that have varying land uses, i.e. urban ...


Adaptation Strategies To Mitigate Impacts Of Sea Level Rise On A Freshwater Aquifer Supply On A Barrier Island, Kaylyn Bellais May 2022

Adaptation Strategies To Mitigate Impacts Of Sea Level Rise On A Freshwater Aquifer Supply On A Barrier Island, Kaylyn Bellais

Theses and Dissertations

Adaptation strategies are used to reduce vulnerability in response to storms and sea-level rise (SLR). An adaptation tipping point for a barrier island is said to exist when an adaptation strategy fails. Previous studies have applied statistics to identify adaptation tipping points and construct adaptation pathways as a function of quantity of SLR. This study is focused on Alligator Lake and Oleander Pond on the barrier island Dauphin Island, AL; a site residents and community leaders identified as vulnerable to saltwater intrusion under future SLR conditions. Therefore, the purposes of this study are to numerically simulate impacts of a storm ...


Sustainability In Construction Practices As Emphasis On Environmental Investing In Esg Model Grows, Maddie Heal May 2022

Sustainability In Construction Practices As Emphasis On Environmental Investing In Esg Model Grows, Maddie Heal

Management Undergraduate Honors Theses

The purpose of this research is to emphasize the importance of growing investment on environmental initiatives in business ESG models in regard to sustainable practices in construction. The ESG acronym is known as the environmental, social, and governance efforts that businesses strive to incorporate in their models to increase the responsibility of operations.

Investors continue to seek out responsible businesses when choosing which ventures to pursue. The analysis of the current construction crisis, current investments in the right direction of Eco-friendly design regarding construction, and the threats and benefits incentivizing those investments elucidates the need to emphasize socially responsible investment ...


Exploring The Effects Of Upstream Disturbances On Elbow Meter Performance With Numerical Modeling Applications, Riley D. Manwaring May 2022

Exploring The Effects Of Upstream Disturbances On Elbow Meter Performance With Numerical Modeling Applications, Riley D. Manwaring

All Graduate Theses and Dissertations

Physical data was collected for a 6-in. long-radius elbow meter in order to determine the effects of certain upstream disturbances on its metering performance. Discharge coefficients are calculated for each of the three tested configurations at various installation distances between the upstream disturbance and the elbow meter. Computational Fluid Dynamics (CFD) software was used to determine which turbulence models most accurately modeled the observed physical results in order to provide a base from which to model the effects of additional upstream disturbances not modeled in this study.


Factors Affecting United States Geological Survey Irrigation Freshwater Withdrawal Estimates In Utah, J. Levi Manley May 2022

Factors Affecting United States Geological Survey Irrigation Freshwater Withdrawal Estimates In Utah, J. Levi Manley

All Graduate Theses and Dissertations

Utah is, on average, one of the driest states in the United States, second only to Nevada, and drier conditions are projected. Irrigation is the largest water user in the state, representing about 80% of the total freshwater withdrawn each year. Withdrawals are obtained from sources like reservoirs or streams, or underground water from wells and springs, and supplied for use. The United States Geological Survey, a reputable federal science agency, has provided irrigation freshwater withdrawal estimates every five years since 1950. Understanding what factors affect irrigation withdrawals can better inform water resource planning to reduce withdrawals and conserve surface ...


Assessing The Role Of Magnetite In Municipal Wastewater Treatment, Patricia Ayaa May 2022

Assessing The Role Of Magnetite In Municipal Wastewater Treatment, Patricia Ayaa

All Graduate Theses and Dissertations

Some municipal wastewater treatment (MWWT) facilities have adopted magnetite in their treatment processes through a technology called BioMag® to meet effluent regulatory requirements for total nitrogen and total phosphorus. However, there is limited information on the mechanisms and efficiency of magnetite in the removal of nitrogen (N) and phosphorus (P) from wastewater. This research, therefore, estimated its effectiveness in the removal of these nutrients, with a case study of the Marlay-Taylor Water Reclamation Facility in Maryland. The intervention analysis model was used, but a new forecasting approach to the model was proposed to fit the data in this study and ...