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An investigation of UV disinfection performance under the influence of turbidity & particulates for drinking water applicationsLiu, Guo January 2005 (has links)
UV disinfection performance was investigated under the influence of representative particle sources, including wastewater particles from secondary effluent in a wastewater treatment plant, river particles from surface water, floc particles from coagulated surface water, floc particles from coagulated process water in a drinking water treatment plant, and soil particles from runoff water (planned). Low-pressure (LP) and medium-pressure (MP) UV dose-response of spiked indicator bacteria <i>E. coli</i> was determined using a standard collimated beam apparatus with respect to different particle sources.
Significant impacts of wastewater suspended solids (3. 13~4. 8 NTU) agree with the past studies on UV inactivation in secondary effluents. An average difference (statistical significance level of 5% or α=5%) of the log inactivation was 1. 21 for LP dose and 1. 18 for MP dose. In river water, the presence of surface water particles (12. 0~32. 4 NTU) had no influence on UV inactivation at all LP doses. However, when the floc particles were introduced through coagulation and flocculation, an average difference (α=5%) of the log inactivation was 1. 25 for LP doses and 1. 12 for MP doses in coagulated river water; an average difference (α=5%) of the log inactivation was 1. 10 for LP doses in coagulated process water.
Chlorination was compared in parallel with UV inactivation in terms of particulate impacts. However, even floc-associated <i>E. coli</i> were too sensitive to carry out the chlorination experiment in the laboratory, indicating that chlorine seems more effective than UV irradiation on inactivation of particle-associated microorganisms. In addition, a comprehensive particle analysis supported the experimental results relevant to this study.
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Laboratory Evaluation of Asphalt Mixtures and Binders with Reclaimed Asphalt Shingle Prepared Using the Wet ProcessAlvergue, Alejandro Jose 30 July 2014 (has links)
The objective of this study is to conduct a laboratory evaluation of asphalt mixtures and binders containing RAS prepared using the newly-developed wet process. In the proposed wet process, RAS material is blended with the binder at high temperature prior to mixing with the aggregates. The proposed wet process offers the potential to better control the Superpave Performance Grade (PG) of the binder blend, to stimulate chemical and physical interactions taking place in the blend between asphalt binder in shingles and virgin asphalt binder in the mix, and to reduce maintenance issues at the plant due to the high content of fines and fibers in RAS. To achieve this objective, asphalt binder blends with 10%, 20%, and 30% RAS were prepared using the wet process, and asphalt mixtures with a nominal maximum aggregate size (NMAS) of 12.5mm were designed according to the Superpave design protocol. The mechanistic performance of asphalt mixtures containing RAS materials was evaluated as compared to conventional asphalt mixtures. Laboratory mixture testing evaluated the rutting performance, fracture performance, and low temperature resistance of the produced mixtures using the Hamburg Loaded-Wheel Tester (LWT), the Semi-Circular Bending (SCB) test, and the Thermal Stress Restrained Specimen Test (TSRST). Results from the experimental program indicated that the proposed wet blending process allows a reduction of the virgin binder content with no detrimental effects on the laboratory performance of the mixture as compared to the conventional mixture without RAS. In addition, results suggested that the usage of RAS in its regular processed size, as processed by the recycling plant, is feasible with no foreseen adverse effects on the mixture performance. The resistance of the binder blends with RAS to fatigue and permanent deformation was evaluated through the use of the newly developed Linear Amplitude Sweep (LAS) test and the Multiple Stress Creep Compliance (MSCR) test. The effect of using different RAS amounts, as well as binder with two different PG grades, was investigated. Results of the LAS test showed that an increase in RAS leads to an increase in the number of cycles to fatigue failure. This is the opposite of what would be expected. These results indicate that the LAS test may not be suitable for characterizing RAS-modified asphalt binders. With respect to permanent deformation, it was found that the addition of RAS improved the performance of the blends by reducing the non-recoverable creep compliance and increasing elastic recovery.
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Piezoelectric Based Energy Harvesting on Low Frequency Vibrations of Civil InfrastructuresZhang, Ye 16 April 2014 (has links)
Piezoelectric-based energy harvesting is an efficient way to convert ambient vibration energy into usable electric energy. The piezoelectric harvester can work as a sustainable and green power source for different electric devices such as sensors and implanted medical devices. However, its application on civil infrastructures has not been fully studied yet. This dissertation aimed to study and improve the piezoelectric-based energy harvesting on civil infrastructures, especially on bridge structures. To reach the objective, a more accurate model for piezoelectric composite beams was built first, which can be adopted for the modeling of different kinds of energy harvesters. The model includes both direct and inverse piezoelectric effects and can provide a better prediction for the dynamic response and energy output of a harvester.
Secondly, to examine the piezoelectric-based energy harvesting on civil infrastructures, four concrete slab-on-girder bridges that represent the majority of bridges in the United States were modeled and used as the platforms for the energy harvesting. Piezoelectric cantileverbased harvesters were adopted for the energy harvesting performance simulation considering their wide usage. Different parameters of the bridges and the harvester were studied regarding to the harvesting performance. Two major problems for energy harvesting on civil infrastructures were identified, namely their low frequency vibrations and wide frequency ranges.
Then, a multi-impact energy harvester was proposed to improve the harvesting performance under the vibration of low frequencies. The multi-impact was first introduced and theoretically proven. Theoretical and experimental studies for the multi-impact energy harvester were conducted. Both the results show an increased energy output power than the one from the conventional cantilever-based energy harvester. A parametric study was also presented which can serve as a guideline for the design and manufacture for the proposed harvester.
Finally, a nonlinear energy harvester was proposed utilizing the magnet levitation. A larger band width was expected due to the stiffness non-linearity of the system. A theoretical model was built for the harvester and its energy output was simulated under the excitation of sinusoidal vibrations and bridge vibrations. The simulation results show a promising way to apply energy harvesting in the field of civil engineering.
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A Comparison of Modeled and Observed Wind Waves in Terrebonne Bay, LouisianaEverett, Thomas Oliver 01 September 2016 (has links)
The coastal wetlands in Louisiana are an important resource that sustains many economies and ecosystems. Subsidence, sea level rise, saltwater intrusion, storms, sediment depletion etc. have placed great strain on coastal ecosystems. Chronic wetland losses have converted vegetated lands into open waters and increased wind fetch. Locally generated wind waves acting on the marsh edge contribute considerably to wetland loss. This research seeks to implement a numerical model that can accurately describe the wave climate along Louisianas coast, which will provide a valuable tool that can be used for shore protection, environmental conservation, and resource management.
Terrebonne Bay was chosen as the study area for this research because it has experienced one of the largest wetland loss rates among Louisiana estuaries. A continuous wave measurement in upper Terrebonne Bay was obtained over the course of a year. The Delft3D-FLOW and SWAN (Simulating Waves Nearshore) models are coupled to hindcast the wave climate in the estuary. An analysis of a yearlong, continuous wave measurement in upper Terrebonne Bay is presented. The coupled model system is validated against in situ measurements from the wave gauges. The wave power is calculated at different locations in Terrebonne Bay using the validated model results. Insight into the temporal and spatial variability of wave power is gained. Through the quantification of swell energy around the bay, improvements of long-term wave power computation for shoreline retreat prediction are presented. It is found the swell energy becomes the primary driver of marsh edge retreat in the southwest part of Terrebonne Bay as the barrier islands are degrading.
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Unsteady Flow Simulations to Develop Model Scale Discharge Hydrographs for the Expanded Small Scale Physical Model of the Mississippi RiverRodi, Ronald Joseph 12 April 2017 (has links)
Small-scale HEC-RAS models were used to analyze discharges used to test the Louisiana State University and the Louisiana Coastal Protection & Restoration Authority Expanded Small Scale Physical Model (ESSPM) of the Mississippi River. The HEC-RAS models extend from River Mile 228.4 (Baton Rouge) to the Gulf of Mexico that includes the ESSPM reach which begins at River Mile 173.5 (Donaldsonville). The model scales are 1:6000 horizontally and 1:400 vertically. Using the historic river discharges from 2008 through 2015, the small-scale numerical models proved capable of replicating observed stages along eleven sites of the lower Mississippi River within the targets of the statistical performance metrics: RMSE%, Bias and Pearson product-moment correlation, developed for hydraulic modeling of the Mississippi River. Specifically, RMSE% analyses of computed water depth versus the observed depth at each site was less than the 15% target all stations; the Bias metric was consistently less than 10 for all stations; and Pearson product moment coefficient was greater than 0.9 for 80% of the stations for each of the eight years of D15 modeling.
Using the small-scale numerical models, the research intended to quantify the difference between a synthetic flow hydrograph used to test the ESSPM and actual flow data. Qualitatively, the stage hydrographs over the eight years indicate the actual discharge data produces six higher peak stages representing roughly 7.5 percent of the 2920 days in the model. Friction slopes for the D15 and Prototype model were compared and found to produce identical characteristics albeit the values of the D15 model friction slope was by its nature was fifteen times that of the prototype. Also, charting of the Froude Number demonstrated the expected equivalency.
The HEC-RAS analyses revealed that total shear stress was equal at each of eleven observed data sites for the eight-year modeling period regardless of the inflow hydrograph. Total stream power, however, for the D15 model was roughly 15 to 20 percent higher using the actual river flows. Total stream power for the prototype model did not differ at the various data sites, while stream power at discharges above 575,000 cfs at both D15 and prototype scales were higher for the actual stream flows than for the synthetic hydrograph. The formulae for these parameters are the same except stream power is dependent on discharge where shear stress is dependent on hydraulic radius. Since the channels of both models have a relatively high width-to-depth ratio, the analyses demonstrated the maximum variance of the hydraulic radius to be approximately 12% while the maximum variance of the discharge was roughly 400%.
Continued refinement and interpretation of this numerical model is an important element toward the interpretation of the results of the ESSPM and application toward understanding the dynamic hydraulic properties of the lower Mississippi River.
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Accumulation and Dynamics of Petrogenic PAHs on Leaves of Black Mangrove (Avicennia germinans)Decell, Matthew 22 May 2017 (has links)
Crude oil from Deepwater Horizon Macondo oil spill is currently present in Louisiana coastal surface sediments and its effects on the coastal ecosystem are still being realized. Deposition of 2- and 3-ring PAHs (alkylated naphthalenes and phenanthrenes) on the exterior of Spartina alterniflora and Avicennia germinans leaves have been demonstrated in marshes impacted by Macondo spill. Whether these deposition events result from contaminated tidal water or volatilization followed by deposition onto the leaf surface has not been conclusively established. Measurements of PAH deposition on the leaf surface of black mangrove (Avicennia germinans) can provide important evidence of the mechanism of deposition since these plants are rarely submerged by tidal water. Study objectives were to quantify and observe the uptake mechanisms of PAH accumulation as a function of time, leaf age, and leaf fraction in mangrove leaves from a heavily oiled site at Bay Jimmy marsh in Barataria Basin, LA. PAHs did not accumulate over time or leaf age indicating diffusion and equilibrium processes dominated and occurred quickly. PAHs accumulated in the inner tissue of the leaf posing a potential for long-term internal cycling of PAHs in a sediment-vegetation-biota system. Semipermeable membrane devices (SPMDs) were utilized in air and marsh surface in the field as a simple analogue to investigate the transfer process. Higher correlations between leaves and SPMDs were observed for C1-naphthalenes than the other PAHs studied. The plant air partitioning coefficient (KPA) for various PAHs in field contaminated mangrove leaves was quantified using an experimental partitioning apparatus and compared to respective KPA values calculated for Spartina alterniflora. All KPA coefficients were well below 8 which supports the dominant uptake process of air phase PAHs is equilibrium partitioning between the vegetation and the gas phase.
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Secondary materials in water treatmentVälikangas, T. (Taru) 13 February 2017 (has links)
In the World the availability of the clean drinking water is a serious problem. The appearance of this problem is different in developed and developing countries. Even though water treatment technologies are widely studied and improved, the developing countries do not have the same economic capacities to utilize the sufficient treatment methods. This thesis concentrates on the utilization of secondary materials in water treatment as adsorbents. These materials are potential for the low-cost treatment of water.
For the testing of the secondary materials, two pollutants were chosen as model compounds: organic pharmaceutical diclofenac and inorganic arsenic As(V), since they have been recognized to be problematic in water treatment. Two industrial by-products were chosen as secondary materials to be tested as adsorbents. Sachtofer is a by-product from titanium dioxide TiO2 production and Red mud is a waste material originating from aluminium oxide Al2O3 production. Third material tested was sand from Brazil obtained via cooperation with the Federal Institute of Goias in Goiania, Brazil. In this thesis a commercial adsorbent CFH-12 (Kemira) was chosen as a reference material.
The literature part of the thesis contains theoretical considerations on the utilization of adsorption in water treatment. In addition the effect of organic and inorganic impurities in water bodies are discussed in a general level.
The experimental part of the thesis presents first the characterization results of the secondary materials. The specific surface areas (BET) were measured for all the secondary materials. The surface structures were studied with scanning electron microscopy (SEM). For some of the adsorbents, the pH of the point of zero charge was determined as well as the elemental composition with XRF. One part of this thesis concentrated on studying the effect of pre-treatment on the adsorption efficiency of the materials. In this case, the adsorption materials were washed with distilled water and treated with hydrochloric acid. The adsorption experiments were carried out as batch experiments.
Diclofenac concentration during the experiments was analyzed with spectrophotometry and HPLC. The best removal, i.e. 16% of diclofenac was achieved with HCl-activated Brazilian sand. With Red mud the HCl-activated sample was the most effective with 8% removal. The HCl-activated Sachtofer removed only 4% of diclofenac. The change in the arsenic concentration during the experiments was analyzed by ICP-MS. With Sachtofer, all three pre-treated samples removed 100% of arsenic. All Red mud and Brazilian sand samples were able to remove arsenic in significant amount. Though, after HCl-activation, the removal of arsenic was higher giving 98% for Red mud and 100% for the Brazilian sand.
The diclofenac removal was assumed to be difficult and the 16% removal was a quite good result. The problem seems to be too high pH. By adjusting pH to a lower level, the higher removal efficiency might be achievable. All arsenic removal results were promising, and with all the material samples the removal was higher than 90%. These results confirm that the secondary materials are potential adsorbents for in water treatment. With certain adsorbents, the removal was high even without any pre-treatment. This is economically interesting possibility that should be studied more, especially due to the possibility of improving the water treatment in developing countries. / Puhtaan juomaveden puute on todellinen ongelma maailmassa. Se on ongelma jossa erityisesi kehittyvät ja kehittyneet maat ovat eriarvoisessa asemassa. Vaikka vedenpuhdistusprosesseja tutkitaan paljon ja ne ovat pitkälle kehittyneitä, ei kehittyvillä mailla ole välttämättä taloudellisia resursseja hyödyntää riittävää vedenpohditus tekniikkaa. Tässä työssä on tutkittu kierrätysmateriaalien hyötykäyttöä adsorbentteinä vedenpuhdistuksessa.
Puhdistettaviksi malliaineeksi valittiin orgaaninen lääkeaine diklofenakki sekä epäorgaaninen arseeni As(V), koska niiden on havaittu aiheuttavan ongelmia nykyisissä vedenpuhdistusprosesseissa. Adsorptiomateriaaleina tässä työssä käytettiin teollisuuden sivutuotteina syntyneitä Sachtoferia joka on titaanidioksidin valmistuksen sivutuote, sekä punaliejua, joka alumiinioksidin valmistuksessa syntynyttä jätemateriaalia. Kolmantena materiaalina testattiin Brasilialaista -hiekkaa, jota saatiin tutkimustarkoituksiin yhteistyön kautta, Federal Institute of Goias, Goiania, Brasilia toimittamana. Työhön haluttiin valita myös yksi kaupallinen adsorptiomateriaali joka toimisi referenssimateriaalina, ja tämän vuoksi valitsimme adsorptiomateriaaliksi Kemiran CFH-12 -tuotteen.
Työn kirjallisuus osiossa selvitetään adsorption teoriaa sekä sen hyödyntämistä vesienpuhdistuksessa. Myös orgaanisen ja epäorgaanisten haitta-aineiden vaikutuksia veden laatuun tarkastellaan yleisellä tasolla.
Kokeellisen osan alussa työssä käytettyjen adsorbenttien ominaisuuksia tutkittiin erilaisilla menetelmillä, joilla arvioitiin materiaalien kykyä adsorboida malliaineita. Materiaaleille määritettiin mm. pH jossa materiaalin pintavaraus on nolla (point of zero charge). Lisäksi materiaaleille tehtiin BET-analyysi ominaispinta-alan selvittämiseksi ja niiden pintaa ja rakennetta tutkittiin elektronimikroskoopilla. Osalle aineista tehtiin myös alkuaineanalyysi. Työssä haluttiin myös tutkia vaikuttaisiko materiaalien esikäsittely adsorptiotehokkuuteen. Tämän vuoksi adsorptiomateriaaleja pestiin tislatulla vedellä sekä käsiteltiin suolahapolla. Adsorptiokokeet toteutettiin laboratoriomittakaavassa panoskokeina.
Diklofenakin pitoisuutta seurattiin kokeen aikana spektrofotometrillä sekä HPLC analyysi menetelmällä. Paras tulos diklofenakin poistossa saatiin HCl -aktivoidulla Brasilialaisella hiekalla, jolloin poistuma oli 16 %. Punaliejulla käsitellyistä näytteistä paras poistuma, 8 %, saatiin myös HCl -aktivoidulla näytteellä. HCl -aktivoidulla Sachtoferilla poistuma oli vain 4 %. Arseenin pitoisuuden muutosta kokeen aikana analysoitiin ICP-MS menetelmällä. Kaikkilla kolmella Sachtofer -näytteellä arseenin poistuma oli 100 %. Kaikki punalieju ja Brasilialainen hiekka näytteet adsorboivat arseenia merkittävästi. Kuitenkin HCl -käsitellyillä näytteillä poistuma oli paras, punaliejulle 98 % ja Brasilialaiselle hiekalle 100 %.
Diklofenakin poistamisen vedestä oletettiin olevan haastavaa, ja saavutettu 16 % poistuma oli hyvä tulos. Ongelmana diklofenakin poistossa oli todennäköisesti liian korkea pH ja mikäli pH:ta onnistutaan säätämään enemmän happamaksi, poistuma voisi olla korkeampi. Arseenin adsorptio kokeiden tulokset olivat todella lupaavia, ja kaikilla materiaaleilla poistuma oli vähintään 90 %. Näiden tulosten perusteella voidaan todeta että kierrätysmateriaalit ovat hyvin potentiaalinen vaihtoehto vedenkäsittelyadsorbenteiksi. Osa materiaaleista toimi arseenin poistossa tehokkaasti myös ilman esikäsittelyä. Tämä on taloudelliselta kannalta mielenkiintoinen tulos, jota tulisi tutkia lisää, erityisesti kehittyvien maiden vedenpuhdistuksen tehokkuuden parantamiseksi.
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Transport and Degradation of Oil Residues on Coastal BeachesWen, Sirui 25 April 2017 (has links)
Fourchon Beach, a 9-mile coastal headland located in Louisiana Gulf Coast, has been heavily impacted by the Deepwater Horizon (DWH) oil spill, which began on April 20th 2010. Once on the beach, the oil spill residues were moved, suspended and transported by subsequent washover events. These washover events occur during storm surges, hurricanes or other situations with high water levels; pushing oil residues from the subtidal and intertidal zone of the beach and then depositing them in the supratidal marshes and mudflat areas. In order to determine the impacts of washover events on oil residues, two complementary studies regarding degradation and transport of oil residues have been conducted. The first one is a laboratory study that has been conducted to understand the stability of oil:sand aggregates in new environments. Oil residue samples of surface residue balls (SRBs) collected from Fourchon Beach on March 7th, May 5th, and May 18th in 2016, were used in the degradation experiment. The degradation experiment was further divided into two parts: one with shaking treatment and the other without. In the static test, the stability of aggregate oil residues is negatively correlated with salinity: specifically, water with lower salinity dissolves SRBs more readily. In the shaking test, porosity was the main influencing factor of SRBs stability. SRBs with higher porosity were completely broken apart due to water energy, even if they were in water with high salinity. In the second study, data were collected for hurricanes and tropical storms that occurred after the DWH oil spill event that directly impacted the Louisiana Gulf Coast. These data were used to estimate the factors responsible for transport of SRBs. The data analysis revealed that the SRBs on Fourchon Beach were mobilized by every extreme washover event. Further, return time of washover events is also discussed at different locations with various elevations. Beach crests or coastal dunes with heights lower than 0.529 m above Mean Sea Level (MSL) would be washed over every year.
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Cuticle Accumulation of Petrogenic PAHs on Spartina Alterniflora: A Novel Exposure Pathway for Marsh BiotaKassenga, Joyce Gabriel 26 April 2017 (has links)
Louisiana coastal marshes were heavily impacted by the 2010 Deepwater Horizon oil spill. MC252 oil pollution in coastal marshes lead to the exposure of biota to polycyclic aromatic hydrocarbons (PAHs). PAHs are persistent organic pollutants that can reside and accumulate in marsh biota. The aim of this study was to investigate the uptake mechanisms of PAHs by Spartina alterniflora at heavily oiled Bay Jimmy marsh in Barataria Basin, Louisiana.
Study objectives were to quantify and investigate the uptake mechanisms of PAHs in the leaves of Spartina. The plant/air partitioning of PAHs was studied using a fugacity approach to determine their partitioning coefficients. Semipermeable membrane devices (SPMDs) were utilized in a parallel study of the uptake of PAHs from the marsh surface and air. Sampling was between June 2016 and February 2017.
A three-step sequential extraction procedure was applied for analysis of PAHs in Spartina leaves. At the field, particulates deposited on Spartina leaves were washed with EDTA solution followed by dichloromethane to dissolve the cuticle. Leaf tissues were extracted by the accelerated solvent extraction method. PAHs in SPMDs were extracted via dialysis with hexane. A laboratory scale fugacity meter was designed to study plant/air partitioning of PAHs. PAHs were quantified in selective ion monitoring mode connected with a mass selective detector.
Similar PAHs profiles in Spartina leaf tissues and SPMDs suggested the cycling of PAHs at Bay Jimmy. Naphthalenes accumulated twice more than phenanthrenes in Spartina leaves and SPMDs. PAHs were sequestered in leaf tissues than the cuticle. Statistically significant correlation (p <0.05) of PAHs in plant leaves and SPMDs were as high as 97%. Soil analysis revealed naphthalenes and phenanthrenes to total PAHs fraction of less than 20%. Results indicated that air-leaf-partitioning was the dominant uptake route of PAHs accumulation in Spartina. Lower plant/air partition coefficients of naphthalenes than phenanthrenes from the fugacity experiment suggested the accumulation of lower molecular weight PAHs in greater quantities. Temporal trends revealed seasonal variability of PAHs accumulation in Spartina and SPMDs. This study demonstrated the efficiency of Spartina cuticle measurements as passive samplers for assessing the pace of natural recovery in marsh systems.
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Method for Quantifying Floating Marsh Strength and Interaction with HydrodynamicsCollins III, Jason Haydel 08 June 2017 (has links)
Louisiana possesses over 350,000 acres of unique floating vegetated systems known as floating marshes or flotants. Due to their buoyant nature, floating marshes are susceptible to high energy changes in the hydrodynamic environment that may result from proposed river diversion projects which introduce flow to areas that are typically somewhat isolated. The overall goal of this research is to improve the understanding of how exposed flotants deteriorate under increased hydrodynamic stresses. More specifically, this thesis aims to answer how the material limits of floating marshes can be measured and how the mats interact with hydrodynamics. The two primary objectives are: 1) Develop a technique for accurate, in-situ measurement vegetative mat root-soil matrix material properties; and 2) Develop a means for predicting floating marsh washout (critical velocities) through numerically modeled derived empirical relationships.
The device constructed to capture the tensile properties of the vegetative mats, called the Marsh Mat Tensile Strength Tester (MMTST), successfully produced full stress-strain profiles including the Youngs modulus, yield stress, and ultimate strength of a root-soil matrix (sod). The estimated mean Youngs modulus, yield stress, and ultimate strength values (sod) were found to be 31.95 kPa, 9.58 kPa, and 9.91 kPa, respectively. Next, flows around 25 idealized mat geometries were simulated with 2-D & 3-D Fluent models. Mat-specific drag coefficients (Cd,m) were found ranging from 1.084-1.645 depending on mat aspect ratio. An equation developed for predicting Cd,m successfully estimated the modeled drag coefficients with a mean percentage error of 2.33%.
A finite element analysis (FEA) was performed on the 25 mat shapes using the predicted drag forces and the material properties measured by the MMTST. By applying various failure criteria (Fc), a correlation was found between the modified mat width-to-length aspect ratio (𝛽) and critical velocity (Vc). The critical velocities ranged from 0.31-1.48 m/s depending on mat aspect ratio and material properties. The general equation developed for predicting floating marsh failure due to flow, in the form: Vc = f(𝛽,Fc), performed well with a mean percentage error of 3.33% relative to the unique values directly extracted from the FEA.
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