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All Articles Tagged "Prince"
Remember That Time Beyoncé Announced Her Pregnancy? 15 Epic VMA Moments
The 2015 MTV Video Music Awards is right around the corner, and if the promos are any indications, the show is probably going to one of the most talked about television events of the summer. The VMAs are where both big moments happen and stars are made. Let's take a look at 15 of the most epic VMA moments, ever.
Prince Compares Record Contracts To "Slavery," Teams Up With Tidal
Tidal: 1
Record Companies: O
The Purple One has spoken, and he's not here for record contracts. After inviting a group of approximately 900 journalists to his estate in Minneapolis for an impromptu listening party and celebration, he announced his new album, HitNRun, which will be released on subscription-based streaming service Tidal, the Huffington Post reports.
The evening of the shindig, a select group of 10 journalists were invited to travel deeper into the estate for a private chat. No questions were off-limits, but the reporters were not allowed to record or take notes.
"Record contracts are just like — I'm gonna say the word — slavery," he told the group, according to Buzz Feed.
He revealed that he has given the masters to his new project to Jay Z exclusively, and that the album would live on the streaming service, which provides more royalties to artists than similar services, for the next few years. The iconic singer then went on to vent that record companies give artists minimal freedom when it comes to determining where and how their music is used.
"Once we have our own resources, we can provide what we need for ourselves," he said, according to NPR. "Jay Z spent $100 million of his own money to build his own service. We have to show support for artists who are trying to own things for themselves."
He also advised new artists not to sign record contracts.
"I would tell any young artist … don't sign," he said.
It's Official, Prince Is Releasing A New Album This Year
It's no secret that legendary and multi-talented musician, Prince, creates iconic albums like he changes clothes, which is pretty often.
So it comes as no surprise that for 2015 he would gift fans with yet another album after releasing two full-bodied projects in 2014: Plectrumelectrum and Art Official Age.
After dropping a new track called "HARDROCKLOVER" via Soundcloud, his band 3rd Eye Girl confirmed that The Purple One will indeed be releasing a new album this year. Titled The Hit & Run Album, the project is a reference to his recent "pop-up" concert tours, where he spontaneously held shows at a moments notice.
3rd Eye Girl also shared details of the new album to BBC 6 Music dishing, "Super hardcore Prince fans that know every song he's ever recorded – we refer to them as 'The Purple Collective' or 'The Purple Army' – this album is absolutely for them, because it's super funky." "It's weird, there's a lot of experimental sound. It's just hit after hit and definitely caters to those fans who just love to hear what Prince has to say, rather than wanting to always hear that classic Purple Rain Prince sound," they said.
The Hit & Run Album will be Prince's 38th studio effort to date, and is said to include sultry love song "1,000 Hugs and Kisses" and a new version of "This Could Be Us" from last year's Art Official Age. No word on an official release date, but 3rd Eye Girl assures, "Everything happens really fast here. When an idea comes… it's translated to the musicians or whoever's working on it and then recorded and laid down relatively quick and then it's put out."
Prince Pulls Catalog From Music Streaming Platforms
The electric, body-moving and soul-stirring Prince is not letting his music fly across all music streams. While we'd love to have easy access, Prince has other plans in mind. Spotify, Rdio, Apple Music, Google Play, Rhapsody, Amazon Prime and many other streaming services are being asked to remove Prince's catalog from their platform.
The musical genius is ready to release new work with his song "HardRockLover" dropping on SoundCloud (there seems to be a problem playing it now… hmm) and is asking all streams to take down his music – except Jay Z's Tidal. The platforms will also have to say goodbye to music done by the artist under the artist formerly known as prince, Prince & The Revolution and Prince & The Next Power Generation.
Spotify has already made the changes and left this message on the artist's profile page:
"Prince's publisher has asked all streaming services to remove his catalog. We have cooperated with the request and hope to bring his music back as soon as possible."
In May, Prince held a concert in Baltimore in partnership with Tidal after the death of Freddie Gray. Tidal streamed the concert and also matched any donations made through their site to support Baltimore charities. It is believed this may be the reason Prince has not cut Tidal off as well.
Prince is certainly not new to going up against large record labels and making sure artists receive fair compensation and their rights respected. Just last year, Prince made headlines when he went after fans that posted bootlegs of his concerts and even further back in the 1990s with Warner Bros. over royalties.
Prince's move has been compared to that of Taylor Swift's when last month Swift went head to head with Apple Music on receiving royalties during their free trial period. While the award-winning singer settled the dispute and stayed on Apple Music it seems as though Prince does not have the same plans to do the same.
Tags:music streaming, Prince, Tidal
"Black Lives Still Matter" Prince Is Coming To Baltimore
Citizens of Baltimore rejoice! The Purple One, Prince Rodgers Nelson, has announced his plans to perform a concert in the city due to the recent unrest over the death of Freddie Gray.
The New York Times broke the news that Prince would be performing at a "Rally 4 Peace" concert this Sunday in Baltimore, at the Royal Farms Arena.
The statement said:
"In a spirit of healing, the event is meant to be a catalyst for pause and reflection following the outpouring of violence that has gripped Baltimore and areas throughout the U.S.," Live Nation, the concert promoter, said in a statement. "As a symbolic message of our shared humanity and love for one another, attendees are invited to wear something gray in tribute to all those recently lost in the violence."
Tickets for the event will go on sale Wednesday at 5 p.m. at LiveNation.com. Part of the proceeds will benefit Baltimore youth charities.
Attendees of the concert are being asked to wear gray.
Prince will also be performing with funk-rock group 3RDEYEGIRL.
You may have seen that Prince was also planning to release a song, titled "Baltimore" about the uprising in the city. Though the audio still hasn't hit the internet, the lyrics have been released. You can check them out below.
lyrics by Prince
NPG RECORDS, copyright 2015
THE GUITAR PLAY! (guitar solo)
Word on the internet streets is that Prince may release the single on Jay Z's new streaming service Tidal.
Tags:#dontshoot, baltimore, Freddie Gray, police brutality, Prince
Prince Records New Single For The City Of Baltimore
Prince is ready to tell the world how he feels about the riots in Baltimore.
The legendary singer has recorded a new song that is "a tribute to all of the people of the city of Baltimore." The unnamed single will address the death of Freddie Gray and the current police issues taking place across the country. Previously, during the Grammy's, Prince stated "Albums, you remember those? They still matter. Like books and black lives, they still matter."
There is no release date for the new single but we have received a preview of the artwork.
We can't wait to hear this new single. We love seeing celebrities use their power to address the social and political issues in our community.
Peanut, Man Man And June Bug: The Very Interesting Childhood Nicknames Of The Stars
Do you have a childhood nickname given to you by close family and friends? Sometimes such names are embraced, sometimes they're loathed, sometimes they're super random, and other times, they are used to describe you, or the way you look. The following stars on this list all are known by those close to them as something very interesting, and after doing some digging, I thought it would be fun to share some of those monikers with you.
Tity Boi
Before he was 2 Chainz, the "I'm Different" rapper was seriously out here going by his childhood nickname: Tity Boi.
"I want to explain this—I wish I could put this on a billboard. Tity Boi is not derogatory towards women, I didn't make it up, I didn't get it from a titty-sucking contest or anything like that. The name Tity Boi actually came from my big mama, from me being spoiled and an only child—breastfed. My mama called me Tity Boi, my dad called me Tity Man, my hood called me Tit so when we was trying to rap I had been going by Tit my whole life, Tit, Tity, Tity Man —it's just like a country nickname —term for being an only child."
Tags:alicia keys, janet jackson, jay z, magic johnson, nicknames, Prince
Got Beef: 18 Stars In Crazy Celebrity Feuds
These pretty epic and often petty celebrity feuds shows us just how human celebrities are. We've all been in a feud or two, but some of these get a bit crazy. We can't choose our favorite…can you?
Sources: The Richest, ETOnline, RadarOnline, BET.com. Images courtesy of WENN and Google/License Free Images
Got Beef: 18 Stars In Epic Celebrity Feuds
Chris Rock & Prince Appear on "Saturday Night Live"
If you missed, Saturday Night Live last night, you missed an epic performance. The legendary singer Prince, performed for 8 uninterrupted minutes on last night's episode. The performance featured new music and a killer guitar solo by the crooner. The last time Prince performed for 8 minutes straight, was during Super Bowl XLI halftime show in 2007. Prince's performance will definitely go down in SNL history.
In addition to a performance by Prince, Chris Rock also hosted last night's episode. Rock appeared in a number of skits including a funny skit with an entire black cast.
Kendrick Lamar and Woody Harrelson are set to perform and guest host when Saturday Night Live returns November 15th. In the meantime, check out the performance by Prince and some of Chris Rock's skits.
Tags:Chris Rock, Prince, SNL
Prince Returns To "Slave" Label, Set To Release Two Albums In September
After the MTV 2014 VMAs aired last night, the iconic artist Prince announced he will be releasing two albums at the end of next month. The first album to be released, ART OFFICIAL AGE, will be reminiscent of Prince's classic musical style. Debuting on September 30, the album will feature the single "Breakfast Can Wait" and will be Prince's 33rd studio album. The second album, "PLECTRUMELECTRUM," will have the same release date and will be a collaborative effort with his funk band, 3rdEyeGirl.
Surprisingly, both of the albums will be released by Warner Bros. Records. Prince was signed to the label in 1976, but 20 years later their relationship soured after Prince released his 1996 album "Chaos and Disorder." Prince had a dispute with the label over artistic control. As Warner Bros. Records and Prince continued their feud, Prince changed his name to an unpronounceable symbol and at public appearances, Prince would arrive with the world "slave" written across his cheek. Prince officially ended his relationship with Warner Bros. Records with the release of his 1996 three-hour album, "Emancipation."
According to TIME, Prince and Warner Bros. Records reconciled once the label returned the master recording of Prince's albums: "Dirty Mind," 1999, "Purple Rain" and "Sign 'O' the Times" to the artists. Currently, Prince's NPG Music Publishing controls most of his publishing catalog. To promote "ART OFFICIAL AGE" and "PLECTRUMELECTRUM," Prince will have several live performances in the upcoming weeks.
To pre-order Prince's new albums, click here. Below is the video for Breakfast Can Wait.


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Travel Blogs from Seguin
... was right at lunchtime . Fairly large dining area inside and al fresco with a nice view of the river. Everyone's casually dressed and very laid back, very at ease atmosphere. Sonya arrives looking great as usual. Smiling,excited,eager and hungry all in one. We get seated and order lemonade,really good stuff,and she tells me what she's ordered in her previous visits. I study the menu and choose something not on the menu! Chicken enchiladas with mołe sauce on top. ...
San Antonio
... nice, although an awful lot of restaurants, which also all seemed to be serving the biggest portions! We had a nice walk round, before heading back to camp. This morning we are heading to look round the Alamo, before heading to Austin. State count- 19 - New York - New Jersey - Pennsylvania - Ohio - Indiana - Illinois - Wisconsin - Minnesota - South Dakota - Wyoming - Montana - Idaho - Utah - Nevada - California - Arizona - Colorado - New Mexico - ...
Day 27 - Jacob's Well Swimming Hole
We were done with bats and ready to cowboy up at the Mayan Dude Ranch so we headed west, once again. However, on a hot, dusty day traveling through the Texas Hill Country, what would be nicer than to stop by a swimming hole and take a refreshing dip? I had researched swimming holes along our route and knew of just the place...Jacob's Well. The well is actually a spring that emerges ...
Stephenville to Seguin
... on our table thought it was highly amusing and actively encouraged me. They stopped laughing though when I started eating their brisket as well - heehee!
Dave had a quick look for a geocache placed 25 feet from the Korean memorial, where he had just placed a 'Remembrance Cross' - just outside the Civic Centre but couldn't find it- heyho! back at the bikes we set off for another 64 miles to our next fuel stop at Marble Falls TX. The ...
Warm and Green is Texas
Our trip today included about sixty miles of two lane roads through some beautiful, treed, agricultural land. The corn is up and should easily be knee-high by the fourth of May. Seriously... It's showing from two inches up to half a foot already! There must be thousands of acres of it. From the number of silos in the area, I'm assuming that it's for animal fodder. We then got back onto Interstate 10 for the rest of the trip.


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Another look at the character selection screen and London Hands-on Event Impressions
Even though no news sites are allowed to posts images or write reviews about the UK Press Event a few pictures has already shown up. This one was posted by Stephen Reid on Twitter just before guests showed up: I expect many interesting reviews, pictures and movies to show up the comming weeks, until then, we have to settle for the hands on that was posted on the official forums Many of you are aware of the UK Community Event we're holding at Gamerbase, where community members get some hands-on time with the game. If you got to play, we want to hear your impressions! If you're one of the lucky folks who attended the event, let us know how it went for you and share your impressions with your fellow community members. I know everyone is eager to hear your stories, and the whole Community Team is very excited about the event, so share away! We'll try to collect as many impressions as we can in this first post for easy reference! Quote: Originally Posted by deanogee I thought the (Jedi Knight) gameplay was pretty smooth and the story progressed nicely as your were immersed straight away into a "heroes" role.Click Here to Read More Quote: Originally Posted by Darth-Reaver Ok so i just want to say it was great to meet and chat to Daniel Erickson and Stephen Reid So i played the Sith Warrior for half my time and the other half i played a Bounty Hunter, the game runs nice and smooth quest system was easy to follow.Click Here to Read More Quote: Originally Posted by burnsyy i really enjoyed the jedi consular it is what i was hoping for i didnt get to lvl 10 but heh no 1 i saw even got pass lvl 5 but yeah titles start after lvl 10 Click Here to Read More Quote: Originally Posted by Dariel Played a Sith Inquisitor tonight at the event. Only got to level 4 but I absolutely loved the voice over. Even the random NPCs standing around which don't have much of a purpose are talking to each other and they have voice over too whilst they chat, continuously found my self stopping and listening to what they had to gossip about.Click Here to Read More Quote: Originally Posted by matteh I played the trooper, had a great time playing grouped with another 2 troopers Click Here to Read More Quote: Originally Posted by Nighthaunterz Just got back from the London event and I'm ready to give my humble opinions. I'll get this out of the way first and say that I had had a great time at the event. The game was fun and all of the Devs were awesome. We all got a t-shirt and a signed poster, more awesome.Click Here to Read More Quote: Originally Posted by JamieM I played a Sith Warrior Pureblood for my 50 mins or so – from what I can tell you the game looks really, really good.Click Here to Read More Quote: Originally Posted by TheDarkKnight I decided to play my second choice of a main, the Bounty Hunter. A Ratataki.Click Here to Read More Quote: Originally Posted by DarthViscus I played as a Chiss Agent. The story was very gripping from the start, I found myself skipping dialogue only because I did not want to get too engrossed in the story due to time restrictions.Click Here to Read More Quote: Originally Posted by rapidity Arrived for the 9pm slot. Played as the trooper. Got to level 4 in the time (with also a quick go on an all the other republic classes), and i can say i was thoroughly impressed.Click Here to Read More Quote: Originally Posted by Orellian Hi All, My experience at the 9pm session today was what I believe to be a 'unique one'.Click Here to Read More Quote: Originally Posted by Saigo The force is…. showing potential in this one! Okay, so just got back from the UK get to play (#SWTORGB) event and I have to say, well, I'm impressed.Click Here to Read More Quote: Originally Posted by MEHColeman So, I got to play swtor today at the 9pm session. It was fan-tas-tic! I made a couple of notes:The PCs were set up with either 4 republic or 4 empire characters (one of each class) It made me think that the game is set up so that you are locked to one faction per server. There were empty character slots on the start screen, and I can't think of another explanation why they didn't have all 8 classes on each PC.Click here to read more. Quote: Originally Posted by Costello Just got back and time for some feedback. I played a Sith Warrior (I'm pretty sure Human though could have been half Ogre from the look of him) and a Chiss Agent.Click Here to Read MoreAdded Information Quote: Originally Posted by Karduth I played a Jedi Consular at the 7pm session. When I was given my first quest to collect the Holocrons (only to find out later that one was missing), I thought it would be the basic Fed Ex quests you see elsewhere.Click Here to Read More Quote: Originally Posted by Aestel Apologies for the readability but its rather late: I was fortunate to play a female human Jedi Knight at the event. We weren't allowed to access the character creation however my character had a lightish skin tone with shortish red hair swept straight back along with two long scars one running diagonally across her right eye and one running bellow the right eye.Click Here to Read More Quote: Originally Posted by DeathCorp Hi everyone, I played at the 7pm event, which I will start with saying was absolutely fantastic. Brilliant evening, so thanks to all of the BioWare team for that!Click Here to Read MoreAdditional review. Quote: Originally Posted by JonoBradley SWTORGB Trooper Analysis. Firstly let me say; I'm starving, hungry and tired. Yet...Read More
Pax East Trooper Character Sheet
This photo was mailed to us along with the SWTOR Class Background Sheets we posted last week. Unfortunately it got lost, but is now it's found. There is still some confusion about if it is leaked material that the Leakerz guys are behind or if it is PAX material. But our source tells us that it is takes with a mobile phone at this years pax east – and we choose to belive so, because sharing beta leaks is bad m'kay.Read More
PC Gamers prints two new screenshots
The latest issue of PC Gamer has a 4 page writeup on Star Wars: The old republic. The article takes up and angle on how the game will change the MMORPG genre for ever – some for good and some for the bad. The article also shows 2 new screenshots I don't believe have been published before. – First one is a screeny of what appears to be an Imperial Agent dual-weilding some sort of daggers and sneaking up on a Cathar (NPC?) from behind. – The second one is a group of 3 Republic characters… a human Smuggler Gunslinger, a human Trooper and a Mirialan Jedi Knight. The Trooper has no helmet on, is huge, and carrying a huge weapon. In front of a Republic base on… maybe Belsavis? There is nothing new revealed in the article apart from the new screens – well maby a dual-weilding melee Imperial Agent? Check out the pictures below:...Read More
Facebook Image Of The Week
It's Wednesday and BiowWare have posted a new Image on their facebook page. This time it's a picture of the anthanide mine on Alderaan: Vicious Killiks drove the workers from this Lanthanide mine on Alderaan, claiming the tunnels as part of their sprawling hive.Read More
Facebook Image Of The Week #4
I forgot all about BioWare's weekly Facebook image update yesterday. This one is called: Speeder bikes transport reinforcements directly into the heat of the battle on Alderaan.Read More


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Former Portugal and Benfica great Eusebio was taken to hospital on Saturday in the Polish city of Poznan where he has been watching matches at Euro 2012, the Portuguese Football Federation (FPF) said in a statement.
"Portugal's football ambassador Eusebio felt indisposed on Saturday when he was at the hotel with the national team in Opalenica," the FPF said in a statement. "After a first observation and contacting his doctor in Lisbon, he went to a hospital in Poznan as a precaution where he is being examined".
Eusebio, who turned 70 in January, has been admitted to hospital three times since December. He has been suffering from hypertension and his doctors have said he must have regular examinations.
He travelled with the national team to Poland and was in the stands for the quarter-final win over the Czech Republic, cheering alongside former Portugal captain Luis Figo. Portugal face Spain in the semi-finals on Wednesday.
Nicknamed the 'black panther', Eusebio grabbed international headlines during the 1966 World Cup in England when Portugal finished third.


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[JURIST] The European Court of Justice ruled [opinion] Tuesday that the UK's practice of administering a residence test to migrants for benefit payments is legal. The court, as it normally does, followed the opinion written by the advocate general at the European Court of Justice [official website]. The action was … [read more]
[JURIST] UN High Commissioner for Human Rights [official website], Zeid Ra'ad Al Hussein [official profile] on Monday, gave the opening statement [transcript] at the 30th session of the Human Rights Council in which he addressed, among other pressing human rights issues, the migrant crisis. In his statement, he commended the … [read more]
JURIST Guest Columnist Amaury A. Reyes-Torres of the Iberoamerican University (UNIBE) [Spanish] discusses the legal developments of same-sex marriage in Europe... Quite recently, the European Court of Human Rights (ECtHR) rendered a landmark decision in the protection of rights of same-sex couples under the European Convention of Human Rights (ECHR): … [read more]
[JURIST] A government minister of Tunisia, Kamel Jendoubi, on Saturday announced an increase of 100,000 security personnel to help protect the country from future terrorist attacks. The strengthened security measures [AP report] include doubling the security personnel at tourist sites, such as beaches, hotels and archaeological sites. The increase follows … [read more]
JURIST Guest Columnist Stefan Kirchner, of the University of Lapland in Finland, discusses the possibility of global discrimination during the ongoing Ebola outbreak ...The current Ebola outbreak has lead to discrimination against those infected with Ebola as well as against health care workers caring for those infected or suspected of … [read more]
[JURIST] During a phone call with Russian President Vladimir Putin on Saturday, US President Barack Obama condemned [press release] Russia's violation of Ukrainian sovereignty after Russian forces had taken up positions in Ukraine. Earlier that day, Russian lawmakers unanimously authorized [LAT report] the use of armed forces to protect their … [read more]
[JURIST] European countries are violating the human rights of people trying to change their legal gender, forcing these individuals to undergo, among other things, invasive surgery and sterilization in order to change their legal status, Amnesty International (AI) [advocacy website] alleged in a report [text, PDF] released Tuesday. Entitled "The … [read more]
JURIST Contributing Editor David Crane, of the Syracuse University College of Law, argues that the world should remember the 1930's in crafting a diplomatic solution to the crisis in Syria ...Appeasement in the face of tyranny never works. Consider the 1930's, when the international community, (and a spineless League of … [read more]
The international response to the crisis in Syria has been mixed since the conflict began in 2011. While Assad maintains some international support, much of the world has condemned his regime's response to the protests against his regime since the early days of the conflict. The UN has attempted to … [read more]
[JURIST] 2012 marked the deadliest year for journalists, with at least 23 professional and 58 citizen journalists killed, according to a report [advocacy website] released Friday by Reporters Without Borders (RSF) [advocacy website]. RSF released its annual Press Freedom Index [materials] to coincide with World Press Freedom Day [official website]. … [read more]
JURIST Guest Columnist Clare da Silva of Amnesty International argues that the new Arms Trade Treaty shows remarkable progress in the international regulation of arms transactions...On April 2, 2013, the United Nations General Assembly voted overwhelmingly in favor of a global treaty that applies international legal standards to govern transfers … [read more]
JURIST Guest Columnist Allison Jernow of the International Commission of Jurists argues that recent court decisions reflect inconsistency in weighing marriage equality and religious freedom...Claims that same-sex marriage is on a collision course with religious freedom have dominated the headlines (The New York Times and The Washington Post) in the … [read more]
JURIST Columnist Paul Johnson, Anniversary Reader at the University of York, argues that the effect of an on-going human rights debate in the British Isles and the European Court of Human Rights may have a detrimental effect on the same-sex marriage debate in the UK...In its formal response to the … [read more]
JURIST Guest Columnist Allison Jernow of the International Commission of Jurists argues that the international law's perception of public morality is beginning to incorporate various and diverse traditions...In November 2012, the UN Human Rights Committee (UNHRC) undid 30 years of bad law when it issued its views in Irina Fedotova … [read more]
JURIST Guest Columnist Paul Johnson, Anniversary Reader at the University of York, argues that the European Court of Human Rights' recent decision in H. v. Finland is a predictable and disappointing step taken against the rights of same-sex couples...The European Court of Human Rights ("the court") has taken another decisive … [read more]
JURIST Contributing Editor Michael Kelly of Creighton University School of Law says that, in order to counter China's attempts to expand its maritime jurisdiction, the US must become a party to the UN Convention on the Law of the Sea...US Secretary of State Hillary Clinton had her diplomatic hat handed … [read more]
[JURIST] The United Nations held the High-Level Meeting of the General Assembly on the Rule of Law [official website] Monday and released the outcome document [text, PDF] prepared by the meeting. The meeting was attended by the President of the General Assembly, the Secretary-General, the President of the International Court … [read more]
[JURIST] The UK High Court of Justice [official website] on Thursday ruled [Judgment, PDF] that retaining photographs and other materials of an innocent suspect should be prohibited. The two-judge panel in London's High Court held that the current policy of the Metropolitan Police Service (MET) [official website] unjustifiably interfered [Guardian … [read more]
JURIST Guest Columnist Ann Eisenberg, Cornell University Law School Class of 2012, is an Articles and Symposium Editor for the Cornell International Law Journal. She questions whether EU membership is the best decision for Croatia given the current debt crisis...By the time Croatia joins the EU on July 1, 2013, … [read more]
[JURIST] The US House of Representatives [official website] voted 248-168 [roll call] Thursday to approve a controversial cybersecurity bill that would allow private companies and the federal government to exchange private security information, despite the threat of a presidential veto. The Cyber Intelligence Sharing and Protection Act (CISPA) [HR 3523 … [read more]


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Watch the Frenetic, Creature-Filled Shannara Chronicles Trailer
This is going to be MTV's attempt at scripted fantasy fare.By Sean Fitz-Gerald
This is going to be MTV's attempt at scripted fantasy fare.By Sean Fitz-Gerald
Here we go.By Sean Fitz-Gerald
The journalist discusses his new documentary.By E. Alex Jung
She announced the news on her Instagram with a very green post.By Sean Fitz-Gerald
"What does it mean to be young and white?"By Dee Lockett
"It was one big bloodbath of actors."By Josef Adalian
Lots of short jokes.By Sean Fitz-Gerald
For MTV.By Sean Fitz-Gerald
Watch out for snakes, please.By Sean Fitz-Gerald
In April 2015.By Sean Fitz-Gerald
After a years-long battle with cancer.By Marcus Jones
Twenty years ago, he was just a young comic with an MTV talk show.By Chris Smith
Where did we place Beyoncé, Jay Pharoah, and Miley's acceptance speech?By Kyle Buchanan
During the opening performance.By Anna Silman
From Taylor Swift to Ariana Grande.By E. Alex Jung
It quotes James Baldwin.By E. Alex Jung
MTV. Sunday. 9 p.m.. You. Us. Together.By Vulture Editors
Take our 2014 Video Music Awards quiz.By Lindsey Weber and Justin McCraw
Reminisce with us.By Lindsey Weber, Maya Robinson and Jed Egan
We're not talking about Gaga.By Lindsey Weber


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Pergamon Int. J. Engng Sci. Vol. 35, No. 10/ll, pp. 1045-1063, 1997 ~) 1997 Elsevier Science Limited. All rights reserved Printed in Great Britain 0020-7225/97 $17.00 + 0.00 PII: S0020-7225(97)00024-4 A GENERAL NONLINEAR CONSOLIDATION MATHEMATICAL MODEL FOR SOIL PROBLEMS R. LANCELLOTFA Dipartimento di Ingegneria Strutturale, Politecnico di Torino, Corso Duca degli Abruzzi 24, Torino,, 10129, Italy L. PREZIOSI* Dipartimento di Matematica, Politecnico di Torino, Corso Duca degli Abruzzi 24, Torino,, 10129, Italy (Communicated by K. R. Rajagopai) Abstract---~Ris paper presents a three-dimensional consolidation model, based on mixture theory. Both the Euilerian and the Lagrangian formulations are given in one dimension for finite strain and general material nonlinearity. Then the paper formulates the initial boundary value problems related to several situations of relevant geotechnical engineering interest, such as consolidation between draining and impervious boundaries subjected to stress and/or velocity conditions, consolidation under own weight of a layer growing due to deposition of wet material, or to sedimentation of solid particles in a quiescent fluid. © 1997 Elsevier Science Ltd. 1. INTRODUCTION Since the publication of the pioneer article by Terzaghi [1] there has been a growing interest in consolidation theory. This interest arises from both theoretical requirements, linked to the analysis of porous media, and engineering applications, related to the prediction of settlement rate, changes of soil properties with the evolution of its state, and, more recently, diffusion of pollutants. Terzaghi's consolidation theory was aimed at explaining one-dimensional consolidation processes in a rather simplified formulation, in order to solve practical aspects. However, in his original formulation [1] it was not clear which coordinates were being used, so that some confusion arose on this point. Bjerrum et al. [2] first recognized that Terzaghi used a "reduced coordinate" Z, which refers to the volume occupied by the solid substance. By using this definition the real thickness dZ of a porous element is equal to (1 + e)dz, and the coefficient of permeability used into Terzaghi's equations should be interpreted as a reduced coefficient, linked to the usual one by the relation (1 + e)Kr = K. By using this interpretation (see Ref. [3]) one may conclude that Terzaghi's original formulation should be considered as a model in which the coefficients of hydraulic conductivity and compressibility are constant, and self-weight is neglected, but not as an infinitesimal strain theory. Only the formulation given in his later papers in terms of full thickness should be considered as an infinitesimal strain theory. Shortcomings of the theory were then outlined by Gibson et al. [3], who also provided a comprehensive one-dimensional model. They removed the limitation of small strains and took into account changes of compressibility and permeability during consolidation. A review has been very recently written by de Boer [4]. Further models were developed in the mid-1960s by Davis and Raymond [5], Janbu [6] and Mikasa [7]. The available solutions are compared in Refs [8, 9]. Finally, Cornetti and Battaglio [10] have recently developed a general nonlinear model, providing a suitable solution technique for well- and ill-posed problems. * Author to whom all correspondence should be addressed. 1045
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1046 R. LANCELLOTTA and L. PREZ1OSI The starting point of this paper is the theory of mixture which has been conceived and developed a couple of decades ago to model the macroscopic behavior of complex systems in which different constituents are mixed and interact at a microscopic level. This theory uses classical continuum mechanics tools and is based on balance laws and conservation principles. In its framework it can, in principle, model mixture of widely different origin, such as porous media, suspensions, emulsions, foams, bubbly liquids, gas or solid mixtures, and so on. Basic modeling and constitutive assumptions on several terms appearing in the resulting system of partial differential equations particularize the theory to the specific field of application. The theory has been presented by many authors. Among them, we recall for their review style the papers by Atkin and Craine [11, 12], Bedford and Drumheller [13], Bowen [14, 15], and MUller [16], the fundamental volume by Truesdell [17], and the recent one by Rajagopal and Tao [18], where more references on the historical development of the theory can be found. This paper applies this approach to the deduction of a new fully nonlinear model aimed at describing soil mechanics problems, characterized by finite deformation. The soil is assumed to be saturated and fracture-free. No restriction applies on the stress-strain and permeability-void ratio relations, but the fact that they must be one-to-one maps during compression. In particular, Section 2 will introduce the basic concepts of mixture theory which will be used in the following sections and the specialization of the theory which can be obtained under suitable assumptions on the inertial and viscous effects. These hypotheses are usually verified in most geotechnical problems of interest, and enable the deduction of a three-dimensional consolidation model. The one-dimensional model in the general case of finite strain and material nonlinearity is then studied in deeper detail in Sections 3 and 4, which deal, respectively, with the Eulerian and the Lagrangian formulation. In Section 4 it is also outlined that several models suggested in the literature are special cases of the one presented here and can be deduced from it under restricting hypotheses. Finally, Section 5 deals with the often overlooked problem of the formulation of the boundary and interface conditions related to several practical problems of geotechnical engineering interest. For instance, consolidation between draining and impervious boundaries subjected to stress and/or velocity conditions, consolidation of a layer growing due to deposition of wet material, or to sedimentation processes in a quiescent fluid above it. Particular attention is paid to the nontrivial problem of the formulation of the proper boundary conditions and of the evolution equations determining the positions of the interfaces which delimit the consolidating layer. 2. THE THEORY OF MIXTURES The theory of mixtures which is based on balance laws and conservation principles can be applied to several scientific fields which have in common the fact that the system can be schematized as a mixture of continua interacting at a microscopic scale. In the isothermal case and in absence of chemical reactions or phase changes, the theory gives rise to the following system of equations: -- + v.(~a,.O -- o, (2.1) ~t - - Ot ÷ v.(~,v,) = o, (2.2)
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Nonlinear mathematical model for soil consolidation problems 1047 [ Ors ) p.,~bsk Ot + v.,'Vv~ = V"[]'s + p~bsg + m~. (2.3) 0vt ) pi~bl Ot + vl'Vvl = V'-I]-i + pl~blg -- m~, (2.4) where s stands for the solid phase and I for the liquid phase. Furthermore, referring to the p- constituent: (1) pp is the: "true" density--that is the density of the material which is used as the p- constituent of the mixture, e.g. Pwater = 1000 kg/m 3. (2) ~bp is the volume fraction, i.e. the volume occupied by the p-constituent over the total volume. Therefore, assuming saturation, ~b~ + ~b~ = 1. (3) Vp is the velocity. (4) q]-~ is the partial stress tensor, which describes the behavior of the p-constituent when the other constituent is co-present. The difference between the partial stress -~p and the stress T e of the p-constituent taken separately, usually termed Reynolds stress, is well emphasized by a comparison with the model obtained using the ensemble average approach [19, 20]. (5) g is the gravitational acceleration. (6) m~ is the momentum supply [21] (also named internal body force or interaction force [14, 15]) and is related to the local interactions between the constituents across the interface separating them. It appears in both the momentum equations (2.3) and (2.4) with a different sign, because of its nature of an interaction (action-reaction) force between constituents. REMARK 2.1. Adding the continuity equations (2.1) and (2.2) gives V.vc = 0, where (2.5) is the so-called composite velocity. v~ = ~sVs + ~lvt, (2.6) In this way a divergence-free velocity field is identified. In handling the model it is very useful to exploit this property using equation (2.5) in place of a continuity equation, either equations (2.1) and (2.2). If, instead, equations (2.1) and (2.2) are first multiplied by Ps and p~ and then added, the usual balance law for the mixture as a whole is obtained Opm -- Ot q-- V "(pml0m) ~-- 0, (2.7) where Pm = ps~bs + Plt~I, is the so-called composite density, i.e. the density of the mixture, and (2.8) p,d~,v., + pl,;blvl V m = Pm (2.9) is the so-called mass average velocity, i.e. the velocity of the center of mass of the mixture.
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1048 R. LANCELLOTYA and L. PREZIOSI Summing up the two momentum equations (2.3) and (2.4) and using equation (2.7) gives the momentum equation for the mixture where vm 0t ) Pm + Vm'VVm = V'Tm+ Ping, (2.10) ~Yrn : -l-s @ ~-' -- Ps(~s(Vs -- Vm) (~ (Vs -- Vm) -- PI~bl(Vl- Vm) ~ (Vl -- Vm), (2.11) is the stress tensor of the mixture considered as a whole (see Refs [19, 20,22]) and the quantities u s -- 1 1 ~ m and vt - Vm in equation (2.11) are the so-called diffusive velocities. As before, it may be convenient to consider the momentum equation for the mixture [equation (2.10)] in place of one of the momentum equations for the constituents (say, the one referring to the solid constituent), essentially for two reasons: 1. It does not contain the interfacial term m,~. 2. It is possible to perform experiments on the mixture as a whole to determine the stress constitutive equation for Tm. In fact, neither q]-~ nor q]-~ can be measured directly. On the other hand, direct experiments on Tm, TI, and Ts, where Ts and T, are the "true" stresses related to the constituents taken separately, can be done. A basic equation introduced in all consolidation models is Darcy's law, which can be deduced from the momentum equation for the liquid constituent equation (2.4) under the following assumptions [15]: 1. Inertia of the liquid constituent is neglected. 2. The viscous forces for the liquid phase are neglected, so that the stress tensor reduces to a scalar. 3. The interaction force depends linearly on Vs- v~ through an invertible matrix, which depends on the deformation of the soil skeleton. One then has v, - v= = -- (VP,- pIg), (2.12) /z4,, where /.~ is the liquid viscosity, K is the "effective permeability" tensor, P~ is the pore liquid pressure, 1 E.= T (~:,r~- D) is the Lagrangian (finite deformation) strain tensor for the soil skeleton, and I:= is its deformation gradient. Finally, if not only the inertia of the liquid constituent, but also that of the solid constituent is neglected, then the momentum balance for the mixture equation (2.10) rewrites as a stress equilibrium equation. The three-dimensional model can then be written as o4,= -- Ot + V.(~b=v 0 = O, (2.13) V "vc = O, (2.14) vj - v= = - - (VPI- pIg), (2.15)
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Nonlinear mathematical model for soil consolidation problems 1049 V.Tm + Ping = O. (2.16) One of the advantages to using equations (2.13)-(2.16) is that one does not have the usual difficulties associated with prescribing boundary conditions for problems formulated within the full context of mixture theory. This difficulty is one of the main drawbacks when applying mixture theory. ~he problem of how to specify stress boundary conditions in mixture theory has been discussed in detail by Rajagopal and coworkers in Refs [18,23]. Further comparisons between the results obtained using mixture models and Darcy's law can be found in Ref. [24] in the case of an incompressible porous material. 3. THE EULERIAN FORMULATION IN ONE-DIMENSIONAL CONDITIONS In this and the following sections it is assumed that both flow and strain take place along the vertical direction z (g =- gez), and that the medium is isotropic in a horizontal plane, so that consolidation occurs along a principal direction of the permeability tensor. Recalling that the continuity equation of the solid constituent equation (2.1) can be written in Lagrangian form as [see also equation (4.1)] ¢; ¢8 ' det U:s - (3.1) where ~b~ is the volume ratio of the undeformed reference configuration and that in one dimension the only nontrivial component of the Lagrangian strain tensor is 1 { ¢.2 __ ) Ezz= -~ \--~ 1 , (3.2) then the dependence of the permeability tensor K on H:s is equivalent in one-dimensional problems to that on Cs. The same is not true for the stress tensor Tm which refers to the whole mixture. In this case the possible dependence on the Lagrangian strain tensor involves not only the volume fraction, as in equation (3.2), but also the fluid properties. Equations (2.13)-(2.16) can then be written in one dimension as -- + (¢sv~) = O, (3.3) Ot Oz 0vc -- az = 0, (3.4) where K(4,s) ( oP, /z(1-¢s) \ 0z + p' g ) v,-v~= ' (3.5) OPi -- Oz 0o" Oz + -- + Pmg=O, (3.6) a' = ~rm-- PI (3.7)
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1050 R. LANCELLO'I"I'A and L. PREZIOSI is the "effective stress" and trm is the total stress in the mixture (both of them are taken positive in compression.) Equation (3.4) implies that the composite velocity vc does not depend on z, that is ~b,vs + (1 - ~b~)v, = C(t), (3.8) where, as will be shown in Section 5, the determination of C(t) has to be done on the basis of the boundary conditions and is related to the value assumed by the composite velocity at the boundaries. Substituting equation (3.6) in equation (3.5) gives a m , v,- vs - 1 - ~b. (3.9) where -- + (ps - • L a: Equation (3.8) and (3.9) then explicitly determine (3.10) •b s v, = C(t) + - - Q, (3.11) 1-4~ v, = C(t) - Q. which, in turn, can be substituted in the continuity equation (3.3) to give (3.12) 0.~_____2_ + C(t) OZ--Ad~ _ Ot 0 (qbsQ), Oz (3.13) Oz or where the constitutive relation for the effective stress tr' is still to be specified. If the mixture is assumed to behave like an elastic material, that is tr' = E(4~,), (3.15) where E is a single-valued relation between the volume ratio and the excess stress, equation (3.14) takes the structure of a nonlinear convection-diffusion equation. In this case equation (3.14) can be written using the excess stress as a state variable as where xlt = E-J is the inverse of equation (3.15), and ~, = d~/dtr'. Particularizations of the dependence of the permeability and stress on the volume ratio (possibly together with other simplifying assumptions) give rise to several models presented in the literature to describe soil consolidation [8, 9]. In reality, equation (3.15) is a simplification, since the soil skeleton and the liquid cannot deform independently, but have to carry the load by joint deformation. This suggests that a better model would treat the mixture at least as a Voigt-Kelvin solid [20, 25, 26].
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Nonlinear mathematical model for soil consolidation problems 1051 REMARK 3.1. Equation (3.13) rewrites in term of the void ratio ~bl 1 e - - -- 1, (3.17) i.e. the volume occupied by the liquid constituent over the volume occupied by the solid constituent, as de -- Ot C(t)--~-- + oz 20( e) ~z Q ) + (1 + = 0, (3.18) where Q, defined in equation (3.10), rewrites in terms of the void ratio as Q= K(e) ( 3o-' - - tz Ps-Pl -gl+e ) - - Oz +- • (3.19) 4. THE LAGRANGIAN FORMULATION IN ONE-DIMENSIONAL CONDITIONS As has already been stated in the previous section, the material form of the continuity conditions is given by d d--7 (p~sdet~:~) = O, (4.1) which in one dimension reduces to Oz OZ 49~ ~b, l+e 1 +e* ' (4.2) where e* is the void ratio in the undeformed reference configuration. As usual in continuum mechanics, the material coordinate z indicates the current position of the particle that in the undeformed reference configuration was identified by the reference coordinate Z. The local form of the mass conservation relation of the liquid phase over a material volume fixed on the solid phase assumes the form 0 -~7 P"~'-~- + -~- [p,4,,(,,,- ,,,)] = o, which can be written using equation (4.2) as (4.3) ~'~ ~b I + -~- [(~l(13i - l/s) ] = O. (4.4)
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1052 R. LANCELLOTrA and L. PREZIOS1 In the Lagrangian formulation it is then more convenient to consider as a state variable the void ratio e defined in equation (3.17) which allows one to rewrite equation (4.4) as ] -- 0t + (1 + e*) (vi- Us) = O. (4.5) ~ The equilibrium of the global porous element is given by O0"rn 0 Z OZ epl + Ps + - - g = O , l+e -- Oz or using equations (3.7) and (4.2), Oer' OZ OPi OZ epl + p,, + -l+e* + - g = O. (4.6) At this point, in consolidation theory it is common to introduce the excess pore pressure u, namely the quantity in excess to the hydrostatic value, so that the equilibrium of the fluid phase requires OPi OZ Ou OZ + Plg--~-~ =0. Oz (4.7) Note that in this equation, the definition given to the excess pore pressure implicitly accounts for any interaction effect. It is then assumed that the excess pore pressure is related to the flow through Darcy's law which rewrites in a Lagrangian framework as e k(e) Ou OZ --, Oz - - l+e (v,- vs) = (4.8) Pig OZ or k(e) l+e* Ou v,- vs = , (4.9) Pig e OZ where k(e) is the hydraulic conductivity. By substituting this latter equation into equation (4.5), using equations (4.6) and (4.7), and taking into account the continuity equation (4.2), the Lagrangian finite strain formulation for the one-dimensional consolidation problem assumes the form Oe -- Ot OQ OZ + (1 + e*) = O, (4.10) where, recalling the relation between hydraulic conductivity and permeability, k(e) K(e) --, # (4.11) Pig
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Nonlinear mathematical model for soil consolidation problems 1053 Q k(e) l+e* (OFT' p~g l+e P s - - P _ _ _ _ _ _ _ _ _ ~ l ) e* g 1+ -- - - OZ + (4.12) is the Lagrangian expression of equation (3.19). REMARK 4.1. Equation (4.10) is equivalent to equation (3.18), as it is expected to be. In fact, recalling equation (4.2), the transformation of equation (4.10) in the Eulerian formulation gives Oe Ot Oe OQ Oz + v~ -- " Oz + (1 + e) = O, (4.13) or recalling equation (3.12), Oe -- O t Oe -~Z Oe -~Z oQ O Z +C(t) - Q +(l+e) =0. (4.14) The last two terms in equation (4.14) can be written as (1 + e) - Q -~z = (1 + e) 2 1 0 Q Oz 2 0 Q l +e (l+e) 20z e) ~z ~ ' (4.15) which, when substituted back into equation (4.14), gives equation (3.18). The Lagrangian formulation is often preferred to the Eulerian formulation since it does not involve the C(t) term which appears, for instance, in equations (3.13) and (3.18). Furthermore, equation (4.10) has the advantage that it has to be integrated on a fixed domain, while equation (3.13) usually inw9lves integration over a time-varying domain. However, as will be shown in Section 5, problems with time-dependent mass within the layer need be formulated from an Eulerian viewpoint. REMARK 4.2. Equations (3.13) and (4.10) have been derived without any assumption regarding the void ratio-effective stress, or the void ratio-permeability relationship, and for this reason represent a general formulation. Anyway, in order to solve them, the above relationships must be specified, as "single-valued" functions. In particular, the fact that the relation is single-valued means that one is focusing on compression problems obtained, for instance, imposing a load on the soil layer. The release of the load may, in fact, in principle, lead to an expansion of the layer, which certainly will not follow the same rule due to anelastic soil behavior. In the following it will be shown that both linear and nonlinear infinitesimal formulations are special cases of equation (3.13) or equation (4.10). Before doing that it is useful to observe that if the mixture is assumed to behave as an elastic material, tT' = - E (e), (4.16) equation (4.10) reduces to i~e o---t + f(e) a---Z - Oe l + e* p, g ~ r ~ Oe ] [ g(e) ~ J, (4.17)
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1054 where R. LANCELLO'I"rA and L. PREZIOSI (,,) --~(-1 d r,,(e, ] f(e)= (l+e*)-d-~-eLl+ e , l+e* dE l+e g(e) = k(e) - - (4.18) de The advection term on the left-hand side drops if gravity is neglected. 4.1 Conventional linear infinitesimal strain theory The conventional linear infinitesimal theory introduced by Terzaghi is based on four main assumptions: (1) Infinitesimal strains, namely the deformation of a consolidating layer is small compared to its initial thickness, which implies that the Lagrangian coordinate Z can be replaced by the Eulerian coordinate z, and as a consequence the volume (l+e) can be approximated by (1 + e*). (2) Linear elastic constitutive relation between void ratio and effective stress de d~' - av (4.19) where av is the compressibility index, strain and stress level independent. (4) The hydraulic conductivity k is constant. (5) Gravitational effects are negligible. Under these hypothesis equation (4.17) reduces to ae k 0 t Pig do" 02e -- (1 + e*) d--e- 0 z 2 ' (4.20) or recalling equation (4.19) as O e 02e - cv - - (4.21) Ot Oz 2 ' where k(1 + e*) cv - , (4.22) avplg is the consolidation coefficient. Due to the linearity between stress and strain, equation (4.19) can also be written in terms of the effective stress: a(7' ~20" - cv - - (4.23) Ot Oz 2 " Note that the Terzaghi equation is usually formulated in terms of excess pore pressure. Changes of effective stress are equal to changes of excess pore pressure if the
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Nonlinear mathematical model for soil consolidation problems 1055 applied load is time independent as well as spatially independent. If this is the case, then c3 u 02u - cv -- (4.24) Ot OZ 2 " 4.2 Nonlinear in[initesimal strain theory If self-weight is neglected, e* is constant, and the effective stress is a unique function of void ratio, then equation (4.17) becomes Oe -- Ot O [ k(e) Oz do-' Oe ] de +-- (l+e*)-- -- Oz =0. (4.25) p~g If the constitutive relation have the nonlinear expressions O-*P k = k* --, e = e* - Cclog (o-'/o-*'), (4.26) o-r then the consolidation coefficient k(e)(1 + e*) do" Pig k*o-*' (1 + e*) plgCc c~ - - (4.27) de is constant and ,equation (4.25) reduces to the nonlinear formulation given by Davis and Raymond [5]: 0o-' = c, Ot o-' . (4.28) az 2 \ 0z It is of interest to note that the substitution of equation (4.27) into equation (4.25) gives Oe 0 t - cv -- 02e OZ 2 ' (4.29) that means that changes of void ratio must satisfy the diffusion equation. Equation (4.28) is less restrictive than equation (4.23) or equation (4.24) as far as the constitutive relations are concerned, so it can be regarded as a more general formulation of an infinitesimal strain theory. As already mentioned, equation (4.26) as used by Davis and Raymond [5] is the most popular in geotechnical literature. Butterfield [27], however, discussed in details shortcomings related to the use of this equation, so that at present it appears that a more consistent one should be the material compression law suggested by the same author: dV _ v A( do-' '~ \ o-'/' (4.30) where V = 1 + e is the specific volume and ,l is an experimental constant. It can be of some interest to note that, by putting a = 1/,L the previous equation can be also written in the forra o-' V ~ = o-'0Vc~, (4.31) which is the gas compression law in adiabatic processes. IJ[$ JS: IO/ll-r
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1056 R. LANCELLOTTA and L. PREZ1OSI Furthermore, it must be observed that it is quite usual to use a void ratio-permeability relationship similar to the one established for the void ratio-effective stress. In this respect it remains to be proved that a relation similar to equation (4.30) also applies to void ratio- permeability. 5. INTERFACE AND BOUNDARY CONDITIONS 5.1 General procedure The evolution of the system can be obtained solving, by suitable methods [28], the initial boundary value problem associated to the models proposed in the preceding sections, e.g. equations (3.13), (3.16), (3.18) or (4.10). The structure of the equation is such that, besides the initial condition, two boundary conditions, one on each boundary, are needed in order to have a well-formulated and well-posed problem. In addition, in the Eulerian formulation the quantity C(t) appearing, for instance, in equations (3.13), (3.16) and (3.18) and the evolution equations for the moving boundaries still need to be determined. The statement of the boundary conditions must be related to the analysis of the physics of the system. This section will consider several practical situation of geotechnical interest. Before entering the details, it has to be noted that several boundary conditions can be applied at the extrema of the consolidating layer. In fact, the boundary may be draining (referred to with the subscript "dr"), with the liquid that can flow through it with a negligible resistance, or impervious (referred to with the subscript "imp"), which prevents the liquid to flow through. It can be fixed, can move at a given velocity, or a load can be applied on it. In addition, the boundary can be an interface with a pool of liquid which filtrates through the consolidating layer due to gravity or to a hydraulic gradient. Actually, boundaries can be considered as nondeformable porous materials with given volume fraction. For instance, a solid impervious boundary is a "porous" material with volume ratio &b----1. Hence, one can specialize the interface conditions formulated, for instance, by MUller [16] to the one-dimensional case with negligible inertia we are dealing with. If the boundary Zb(t) is fixed on the soil skeleton, as in most of the cases which will follow, then one has that both the composite velocity vc and the stress of the mixture o" m have to be continuous across the boundary vc(zb(t),t) = &bVsb(t) + (1 -- ~bb)Vlb(t), (5.1) O'm(Zb(t),t ) = O'b(/), (5.2) where subscript "b" indicates a quantity referring to the boundary and ~b is taken positive in compression. Furthermore, the velocity of the boundary is equal to the velocity of the soil grains at the boundary, which may be related to the volume ratio (or the stress) at the boundary through equation (3.12): dZb dt - v~(zb(t),t) = C(t) - Q(zb(t),t). (5.3) If the velocity vb(t) of the boundary is given, then equation (5.3) determines both the term C(t) in equations (3.13) and (3.18): C(t) = Oh(t) + O(zb(t),t), (5.4) and, of course, the evolution equations for the moving boundary dZb - vb(t). dt (5.5)
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Nonlinear mathematical model for soil consolidation problems 1057 Furthermore, since C(t) is constant throughout the layer, going to the other boundary zb. one can also determine either its velocity, and therefore the evolution equation for the boundary, dzw dt - vb(t) + Q(Zb(t),t) -- Q(zb.(t),t), (5.6) or the relative boundary condition Q(zw(t),t) = vb(t) - Vb-(t) + Q(zb(t),t). (5.7) As far as the stress condition is concerned, it is useful to observe that the integration of the stress equilibrium equation (3.6) over the consolidating layer [zb(t), Zb*(t)] relates the stresses at the two boundaries: ~ z~.( t) o" (Zb(t),t) - o" (Zb*(t),t) + P,(zb(t),t) - Pl(Zb*(t),t) = pm(Z,t)g d z. d zh(t) (5.8) Using, then, the definition of composite density [equation (2.8)], one has ~Zh*(0 ~ z..(t) Prn(Z,t) dz = [(Ps - Pl)~Ps(Z, t) + Pl] dz d Zh(t) J Zh(I) pl[Zb'(t) .zb(t)] + (1 .p' /~ z'<'> ps / Jzh(o .. ps~bs(t,z) d z, (5.9) where the last integral is equal to the mass Ms(t) of the solid constituent in the layer, which is constant if there is no flow of soil grains through the boundaries, as occurs in many practical cases. In fact, ~Zh.(t) f Zh*(O) Ms(t) = psdPs(t,z) dz = ps~s(O,z) dz = Mo. (5.10) d Zh(O J zh(O) Substituting equations (5.9) and (5.10) back into equation (5.6), one can then write / \ or' (zb(t),t) - tr' (zb*(t),t) + P,(zb(t),t) - P,(zb.(t),t) = p,g[zw(t) - Zb(t)l + ( 1 - P___L ) Mo g. (5.11) \ Ps / Some sample cases will now be described in order to apply the theoretical results to specific configurations of geotechnical engineering interest. 5.2 Imposed velocities on impervious boundary and stress on draining boundary As a first practical example, assume that the layer is between a draining and an impervious boundary. Since the composite velocity is continuous across the impervious boundary and is constant across the layer, it has to be constantly equal to the value assumed on the impervious boundary. Therefore, vc(t,z) = C(t) = Oimp(t ) VZ, (5.12) where Vimp(t ) is the velocity of the impervious boundary. This means, for instance, that if the impervious boundary is fixed at the bottom of the layer and the draining: top boundary Zdr(t) is pushed down, then, since the composite velocity is
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1058 R. LANCELLOTTA and L. PREZIOSI also constant across Zdr(t), there will be a pool of still liquid forming over the draining boundary, while in the bulk of the layer the liquid will move up as the solid consolidates down, so that the composite velocity vanishes everywhere. In addition to equation (5.12), because of equations (5.1) and (5.3), one also has Vimp(t) = Vs(Zimp(t),t) = Vl(Zimp(t),t), or, because of equation (3.9), (5.13) Q(zimo(t),t) = 0. (5.14) This boundary condition can be equivalently written as (90 -r OZ -- (Zimp(t), t) + (Ps - Pl)(bs(Zimp(t),t)g = 0, (5.15) which, if the solid skeleton is assumed to behave elastically [see equation (3.15)], is a Robin- type condition: drips ( qbs(Zimp(t)'t)) -~Z (Zimp(t)'t) + (Ps -- P,)Cs(Zimp(t),t)g = 0. (5.16) to be imposed on the impervious boundary. If a stress boundary condition ~r(t) is imposed on the draining boundary, then the liquid pressure is continuous across the boundary and or' (Zdr(t),t) = ~r(t), (5.17) which provides the other boundary condition. Though the velocity of the draining boundary Zdr(t) is not provided, it can be easily deduced specializing equation (5.6) by keeping in mind equation (5.14): dZdr dt - Vimp(t) -- Q(zdr(t),t), (5.18) while the evolution of the other boundary is obviously determined by d Zimp = Vimp(t). dt (5.19) Actually, in many, if not all, practical situations, the impervious boundary is fixed, which means that Vimp(/) ----0 and Zimp(t)=Zo. Besides equations (5.18) and (5.19), the Eulerian formulation also requires the determination of C(t), which is given by equation (5.12). In this problem, however, it is more convenient to consider the Lagrangian formulation [equation (4.10)] joined with the Lagrangian version of equations (5.15) and (5.17): a~r' aZ (Pl- P~)g l+e*(Z~mp) ' (Zimp't)= (5.20) tr' (Zd,,t) = o'(t). (5.21)
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Nonlinear mathematical model for soil consolidation problems 1059 5.3 Consolidation of a draining layer Assume now that both boundaries are draining. The bottom one is at rest, i.e. Zbot(t)=Z0, while a stress condition is imposed on the top boundary Z,op(t): tr'(Ztop(t),t) = tr(t). (5.22) Since the bottom boundary is at rest, then from equation (5.4) C(t) = O(zo,t), and from equation (5.6) (5.23) dztop _ Q(zo,t) - Q(ztop(t),t). dt (5.24) If it is assumed that the pore liquid pressure at the bottom is constantly maintained at the value existing be, fore the load is applied, that is e,(zo) = eatm + p,g(Ztop(O) - Zo), (5.25) then there may be some water filtrating through the top boundary, so that the liquid pressure at the top of the layer is P,(ztop(t),t) = Patm + pbg[z,ee(t) - Ztop(t)], (5.26) where zfr~(t) is the position of the free surface of the water pool. Substituting ectuations (5.22), (5.25) and (5.26) into equation (5.11) gives / \ 0" (Zo,t)= o'(t) -b plg[Zfree(t) -- Ztop(0)]-1- ( 1 - P-_! }Mog. Ps / (5.27) \ If the water above the layer is constantly withdrawn, then zfree(t)= Ztop(t), otherwise it has to be computed through a mass balance of the liquid: dp,(Z,t) dz + dz = ~bl(Zo,t)[vl(Zo,t) -- vs(Zo,t)] = Q(zo,t), (5.28) dt LJz,, J z,,,, or d Zfree dt (t)= Q(zo,t) + -- -- 1 d f z,,,,<,) ! Ps d t j z,, psdps( z,t) d z. (5.29) Since the integral on the right-hand side of equation (5.29) is the mass of solid in the layer, and therefore is constant, equation (5.26) simplifies to d Zfree d------i-- (t) = Q(zo,t). (5.30) In conclusion, equations (5.22) and (5.27) with Zfree(t) either equal to Ztop(t), or detemined by the integration of equation (5.30), are the boundary conditions to be used both in the Lagrangian and t]he Eulerian formulation. This last formulation, however, also needs equations (5.23) and (5.24).
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Do work with someone new. A study sesh is a great way to get to know a new acquaintance. Pick
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Like other VeloPress Great Lakes humorists Jamie Smith and Jef Mallett, Greg Moody has had a long career in media. Working in various capacities as columnist for the Milwaukee Sentinel and in regional radio and television, Moody is also a long-time cycling enthusiast.
In 1988, Moody moved to CBS4 in Denver as Critic at Large where he won 12 regional Emmy awards for commentary and writing in subjects ranging from movies to TV, newspapers to books, Hollywood history to journalistic ethics.
Moody is author of five cycling murder mystery titles, a subgenre populated seemingly by his works alone. The stories cover domestic racing and the Tour de France and were wildly popular in the '90s.
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Moody pushes all the right buttons...he creates a character we can care about, and paints an excellent portrait of the bad guys as well. Read morePublished on December 11, 2000
Greg Moody's book is a great, quick read. A definite page turner with witty dialog, and Greg manages to capture the spirit of the cycling world.Published on June 5, 2000 by John D. Busteed
A murder mystery that makes you laugh. It also teaches a thing or two about the world of European bike racing. Read morePublished on May 6, 1999
Two Wheels, Greg Moody's foray into the cycling mystery genre, (anybody's for that matter), is a fantastic tale of epic proportions - very American indeed. Read morePublished on July 30, 1998


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Internal Control Reporting Fraud and Contacts
Volleyball vs Cazenovia
Free. 312-2488
Location: Oswego, NY, Max Ziel Gym in Laker Hall
Tuesday, Oct 6, 7 p.m. - 8 p.m.
Men's Tennis vs. Utica
Free. 312-2488
Location: Oswego, NY, Romney Tennis Courts
Wednesday, Oct 7, 4 p.m. - 6:30 p.m.
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You can report fraud directly to the SUNY Oswego Internal Control Department, either confidentially or anonymously by dialing on campus - x1200, off-campus 312-1200.
You can also contact the State University of New York Fraud Hotline run by the State University Audit Department at: (518) 443-5539, or contact their website at:
What is the SUNY Oswego Fraud Hotline?
The SUNY Oswego Internal Control Department provides an avenue for individuals to report fraud, waste, and abuse within the college's programs and operations through the Internal Control Department. We handle allegations regarding fraud, waste, and abuse, or violations of State Finance law, or regulations affecting college programs and operations.
What Should I Report to the Fraud Hotline?
A variety of situations may be considered fraud in the college's programs. Some examples are:
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BALTIMORE - DECEMBER 20: Antwan Barnes #50 of the Baltimore Ravens runs downfield against the Chicago Bears at M&T Bank Stadium on December 20, 2009 in Baltimore, Maryland. The Ravens defeated the Bears 31-7. (Photo by Larry French/Getty Images)
San Diego Chargers linebacker Antwan Barnes has been ejected against the Oakland Raiders following an unsportsmanlike conduct penalty. Officials whistled Barnes for the penalty following a 27-yard run by Louis Murphy in the first quarter Sunday. The 8-yard penalty gave Oakland the ball at San Diego's 7-yard line, leading to a Raiders touchdown. Barnes was leading the Chargers with 11 sacks this season. He took off his helmet and was yelling back at officials on the field following his ejection. It was not immediately clear exactly why Barnes was ejected. Shaun Phillips is expected to see more time at outside linebacker in his place.
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It isn't over yet, and it promises to carry on for weeks, if not months, to come. The Warwick City Council says taxpayers, as they paid nearly $30,000 to attorney Vincent Ragosta, should be able … more
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text: Your Health Connection Coping With Cancer on Best of Your Health Connection By Rob Maynard • Jun 11, 2014 Join us Wed June 11 at 6pm for the June edition of Your Health Connection with JaQuitta Williams. This is a best of edition about coping with cancer featuring Tiffany Cochran Edwards, Ezell Blues, and Christal Jordan. L-R Ezell Blues, Tiffany Cochran, JaQuitta Williams, Christal Jordan Tiffany Cochran was caregiver for her father Johnny Cochran through his battle with terminal brain cancer. Ezell Blues is a nine year prostate cancer survivor who is also caring for a teenage son who has leukemia. Publicist Christal Jordan is an ovarian cancer survivor. Your Health Connection Features Young People and Cancer on WCLK By Rob Maynard • Apr 15, 2014 Your Health Connection on WCLK on Wednesday, April 16 featured a discussion about the unlikely but very real issue of cancer in young people. JaQuitta Williams hosted as we were joined by guests including Pediatric Oncologist Dr. John Bergsagel of Childrens Healthcare of Atlanta, 20-year-old leukemia survivor Daniel Blues, and Daniel's father Ezell Blues. Your Health Connection Addresses Colon Cancer By Rob Maynard • Mar 7, 2014 Your Health Connection with JaQuitta Williams on Wednesday, March 12 featured a compelling discussion about colon cancer. March is Colorectal Cancer Awareness Month. Our conversation featured your calls. Our guests included Dan Weeks, a colon cancer survivor, as well as Dr. Mamoud Barrie of Atlanta Gastroenterology Associates. Your Health Connection On Coping With Cancer By Rob Maynard • Feb 19, 2014 JaQuitta Williams was joined last night on Your Health Connection by Tiffany Cochran, Ezell Blues, and Christal Jordan for a roundtable discussion of how to cope with cancer from the perspective of a survivor and a caregiver. Tiffany Cochran was caregiver for her father Johnny Cochran through his battle with terminal brain cancer. Ezell Blues is a nine year prostate cancer survivor who is also caring for a teenage son who has leukemia. Publicist Christal Jordan is an ovarian cancer survivor. JaQuitta Williams, Guests Take Your Calls About Coping With Cancer on Your Health Connection By Rob Maynard • Feb 18, 2014 Wednesday night at 6pm Jamal skates an hour early and the Cancer Center at Clark Atlanta University presents Your Health Connection, a live talk show about facing up to cancer. This month our topic is "coping with cancer" and JaQuitta is joined by guests including Tiffany Cochran, who cared for her father Johnny Cochran through terminal cancer, and Christal Jordan, an ovarian cancer survivor. Your Health Connection Explores Links Between Diet And Cancer By Rob Maynard • Dec 15, 2013 JaQuitta Williams discussed diet and cancer during our monthly look at cancer-related health issues on Your Health Connection. Our informative guest was Registered Dietician Marisa Moore. Does what you eat make it more likely you will get cancer? Can you choose to eat in ways that minimize certain cancers? What about diet when you are a cancer survivor? We'll take your calls and tweets live as we talk about an issue that is relevant to everyone who eats. The Cancer Center At Clark Atlanta University Reminds You To Watch What You Eat During The Holidays By Rob Maynard • Nov 27, 2013 Happy Thanksgiving to everyone from the Center For Cancer Research And Therapeutic Development at Clark Atlanta University and Your Health Connection! As we get together with family and friends over the holidays and enjoy our yams and hams and pumpkin pie, maybe a little spiked eggnog, it's important to remember that eating healthy today is one way to improve your chances of being cancer-free later. Your Health Connection Explains The Affordable Care Act By Rob Maynard • Nov 21, 2013 Your Health Connection on WCLK Wednesday evening November 20th featured an informative discussion about the Affordable Care Act and its implications for cancer detection, prevention, and treatment. Host Jaquitta Williams was joined by Affordable Care Act experts including U. S. Health and Human Services Regional Director Pamela Roshell and Linda Blount, Vice President of Programmatic Impact for the United Way of Greater Atlanta. Our experts took your Obamacare/ACA calls and tweets and made this landmark health insurance legislation more easily understandable. Your Health Connection Discusses Triple Negative Breast Cancer By Rob Maynard • Oct 17, 2013 Your Health Connection on WCLK featured a timely and important discussion of triple negative breast cancer for Breast Cancer Awareness Month. In a fascinating twist for listeners, our host JaQuitta Williams was also the guest survivor featured on the program. She is a survivor of this particularly tough form of the disease, which disproportionately affects young people and African Americans. JaQuitta was joined by leading Atlanta Surgeon Dr. Rogsbert Phillips-Reed, who operated on her and has helped many Atlantans through the ordeal of breast cancer over the years. WCLK and Your Health Connection Remember Ralph C. T. Franklin By Rob Maynard • Oct 16, 2013 WCLK and our partners at the Center For Cancer Research and Therapeutic development are mourning the loss of our friend and courageous advocate for prostate cancer awareness Ralph C. T. Franklin. On Sunday, October 13, Franklin died from complications due to prostate cancer. He was 62. Pages« first ‹ previous 1 2 3 next › last »


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Don't Miss Powerade And 107 Jamz Tomorrow at Sam Houston For The Pregame Party [PICTURE]
Join 107 Jamz tomorrow at Sam Houston along with Powerade for a great day of fun and more.
Join 107 Jamz tomorrow at Sam Houston along with Powerade for a great day of fun and more.
With the 2015 college football season upon us, it was announced today that the new home of the McNeese Cowboys football broadcast will be on our sister station 92.9 The Lake.
CT Fletcher is getting his own movie and it will showcase his talents and motivation to others.
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Cruise through the glittering city of Paris while enjoying a 3-course dinner. See the sights in a relaxed setting and enjoy a whole new vantage point on the city. Many of Paris' most iconic buildings and monuments such as the Eiffel Tower and Notre Dame are situated by the river, making a cruise the easiest way to sightsee in Paris.
This 2-hour dinner cruise allows you to choose from three different menus. Menu 1 does not include drinks whereas menu 2 comes with half a bottle of wine (choose from red, white and rose). If you're looking for something special, opt for menu 3 which includes a glass of champagne as an aperitif and half a bottle of champagne to accompany your meal.
Make your way to Marina de Paris, Port de Solferino 75007 Paris for your Seine Dinner Cruise. Your cruise will last approximately two hours, allowing you ample time to wine, dine and relax.
You can choose from 3 menus to customise your evening.
Menu 1 – Saveurs (drinks not included): Menu 2 - Saveurs Tendance (wine included) Menu 3 - Saveurs Tendance Gold (Champagne included)
The food is the same with all three options. Your 3-course menu starts with a tasting platter and ends with an assortment of deserts. French chefs have prepared a modern menu based on seasonal produce. Download the full menu here.
As you enjoy your dinner you will pass many of the iconic Paris landmarks including Notre Dame, the Louvre and the Eiffel Tower.
After your dinner cruise, you will be dropped off near the starting point at Port de Solferino, Quai Anatole France, from where you will have to make your own way back to your accommodation.
Really good quality service and funny time spent on boat...Rolandas Kiskis
Absolutely fab. Loved the food. Staff was brilliant, happy and very friendly. The only thing was I had notified them that it was our 25th Wedding Anniversary but it wasn't...MRS T DUNBAR
A remarkable evening, thoroughly enjoyable and was a unique experience for my children as thier first "taste" of Paris....Mrs Patricia Bennett
2 hours
Boarding: 2030h (8:30pm)
Departure: 2100h (9:00pm)
Duration: 2 hours
The cruises start from Marina de Paris, Port de Solferino, Quai Anatole France 75007 Paris. This is located very close to the Orsay Museum. The closest metro stations are Musee d'Orsay (served by RER, line C) and Assemblee Nationale (served by line 12). Please arrive 15 minutes before the start time to allow plenty of time for boarding.
Port de Solferino, Quai Anatole France
Do dress formally. Gentlemen are recommended to wear tie and jacket.
It is the responsibility of all visitors to be at the meeting point 15 minutes before departure. Guests arriving after departure cannot be accommodated & missed tours or tickets cannot be refunded.
You must print and surrender a paper version of your booking voucher for this activity (showing your voucher on a smartphone is not accepted). No refund can be given for customers without a printed copy of their voucher.
See the Cancellation policy for this product


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Focus on All Trail Riding
Trail riding is any riding outside an arena. Competitive trail events test the ability of horse and rider to maneuver obstacles that may be found on a trail, such as gates, streams, etc. Recreational trail riding is a great way to have fun with family and friends and enjoy nature.
Trail Riding
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Boarding > Washington
Rustic Pines Farm - Boarding and training facility, 20 stalls indoor arena, trainer on site etc...
Arlington, WA
Events > Summer Camps > Georgia
July 13-16, 2014
American Dream Farm - Statham, GA
Boarding > Illinois
Rock Falls Stable - Horses Boarded, Trained, Bought and Sold..Pony Parties
Rock Falls, IL
Clubs & Organizations > Georgia
Gilmer County Saddle Club - Open / fun shows
Ellijay, GA
Boarding > Ohio
Mill Creek Equestrian - A gorgeous boarding facility with great amenities taking new clients
New Carlisle, OH
Boarding > Ohio
HP Performance Horses - Boarding and training facility, Full and partial options available. Indoor and outdoor arena.
Sunbury, OH
Boarding > Florida
Serenity Horse Stables - Boarding,Trail Rides
Plant City, FL
Boarding > Georgia
Dacula, GA
Riding Lessons > Georgia
AMC Barrel & Performance Horses / Amanda Colby - Bettering horse & barrel racing community by offering top of the line lessons horse training & sales
Cartersville, GA
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text: We saw a sign on the hwy that said $59.95 per night. The reviews looked good. This hotel recently changed names from Hampton. The desk clerk said that was the walk in rate. He said we could have a king and sofa bed or 2 double beds. We chose the king and sofa bed. The room was very nice and clean, bed was comfortable, micro and fridge, the pull out bed was not comfortable (but they usually aren't so to be expected). We just needed extra bed for kids. Breakfast was good sausage links, scrambled eggs, muffins, waffles, etc. staff was friendly and helpful.