Relatório - adensamento
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UNIVERSIDADE FEDERAL DE CAMPINA GRANDE CENTRO DE TECNOLOGIA E RECURSOS NATURAIS UNIDADE ACADÊMICA DE ENGENHARIA CIVIL DISCIPLINA: MECÂNICA DOS SOLOS EXPERIMENTAL I
ADENSAMENTO DO SOLO
Professor(a): Veruschka Escarião Dessoles Monteiro Assistentes: Francisco, Pabllo Araujo, Pedro Batista Estagiário(a) de Docência: Daniela Grupo: Bruno Brasil Felipe Neves Pabllo Araujo Rayan Cordeiro
Campina Grande, Abril de 2013
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Índice 1 – Introdução_______________________________________________3 Introdução_______________________________________________3 2 – Revisão Revisão Bibliográfica______________________________________4 3 – Materiais Materiais e Métodos_______________________________________12 4 – Resultados______________________________________________16 Resultados______________________________________________16 5 – Conclusões______________________________________________32 Conclusões______________________________________________32 6 – Referências Referências Bibliográficas__________________________________32
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Adensamento do Solo
1. Introdução Adensamento é um processo lento e gradual de redução do índice de vazios de um solo por expulsão do fluido intersticial e transferência da pressão do fluido (água) para o esqueleto sólido, devido a cargas aplicadas ou ao peso próprio das camadas sobrejacentes. Um depósito de solo saturado e de baixa permeabilidade, quando submetido a uma sobrecarga, apresenta recalques que tendem a aumentar lentamente com o tempo. Aterros em solos aluvionares de baixada ou em regiões de formação marinha, como os mangues, e até mesmo edificações assentadas sobre camadas fracas, como é o caso de muitos prédios altos construídos sobre argila de Santos, SP, são exemplos típicos da ocorrência desse fenômeno.
1.1 Justificativas Conhecer os índices determinados no ensaio de adensamento é importante, pois um dos aspectos mais relevantes em projetos e obras associados a engenharia é a determinação das deformações (recalques) devidas a carregamentos verticais aplicados na superfície do terreno ou em camadas próximas a superfície. No caso de projetos de edificações com fundações superficiais (sapatas, radiers) ou de aterros construídos sobre os terrenos (barragens, aterros rodoviários, aterros de conquista), é importante o cálculo destas deformações sob ação das cargas aplicadas. A magnitude destas deformações deve ser avaliada e comparada com aquelas admissíveis para o bom funcionamento funcionamento da construção construção projetada, projetada, ao longo da da sua vida útil.
1.2 Objetivos Este ensaio tem por objetivo determinar as propriedades de adensamento do solo, caracterizadas pela velocidade e magnitude das deformações, quando o solo é lateralmente confinado e axialmente carregado e drenado.
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2. Revisão Bibliográfica Quando se executa uma obra de engenharia, impõe-se no solo uma variação no estado de tensão que acarreta em deformações, as quais dependem não só da carga aplicada, mas principalmente da Compressibilidade do Solo . As deformações podem ser subdivididas em três categorias: o
Elásticas: quando estas são proporcionais ao estado de tensões imposto. Para os solos que apresentam um comportamento elástico, a proporcionalidade entre as tensões (ζ) e deformações ( ε) é dada pela Lei de Hooke ( ζ = E. ε, onde E = módulo de Elasticidade ou módulo de Young; constante e característico do material). As deformações elásticas estão a variações volumétricas totalmente recuperadas após a remoção do carregamento;
o
Plásticas: associadas a variações volumétricas permanentes sem a restituição do índice de vazios inicial do solo, após o descarregamento ;
o
Viscosas: também chamadas de fluência, são aquelas evoluem com o tempo sob um estado de tensões constante . Considerando-se que o solo é um sistema trifásico, composto de partículas
sólidas (minerais), ar e água nos seus vazios, as deformações que ocorrem no elemento podem estar associadas associadas à:
Deformação dos grãos individuais;
Compressão da água presente nos vazios (solo saturado);
Variação do volume dos vazios, devido ao deslocamento relativo entre as partículas.
Do ponto de vista de Engenharia Civil, a magnitude dos carregamentos aplicados às camadas de solo não são suficientes para promover deformações das partículas sólidas. A água, por sua vez é considerada como incompressível. Assim sendo, as deformações no solo ocorrem basicamente pela variação de volume dos vazios. Somente para casos em que os níveis de tensão são muito elevados, a
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a fim de avaliar a sua repercussão sobre a estrutura e decidir com acerto sobre o tipo de fundação a ser adotada. Muitas vezes as condições de fundação são tão desfavoráveis que resultam na necessidade de emprego de soluções de custo mais elevado; por exemplo, fundações profundas. O comportamento dos solos perante os carregamentos depende da sua constituição e do estado em que o solo se encontra, e pode ser expresso por parâmetros obtidos em ensaios ou através de correlações estabelecidas entre esses parâmetros e as diversas classificações. Dois tipos de ensaio são empregados: o ensaio de compressão axial e o de adensamento (ou compressão edométrica, edométrica, ou edométrico, ou consolidação).
2.1 Adensamento Reforçando o conceito de adensamento pode-se dizer que se trata de um fenômeno pelo qual os recalques ocorrem com expulsão da água do interior dos vazios do solo a partir da aplicação de uma tensão superficial. Esse fenômeno foi estudado por Terzaghi a partir de 1914, quando ainda era professor da Universidade de Istambul. Terzaghi desenvolveu o ensaio edométrico e posteriormente a denominada teoria do adensamento adensamento de Terzaghi, que será abordado ainda nesse trabalho.
2.2 Analogia do sistema água mola de Terzaghi Iniciando o estudo do fenômeno de consolidação através de um modelo físico, é apresentado na figura 1 uma amostra de solo totalmente saturado e de baixa permeabilidade, permeabilidade, que será submetida a um estágio de pressão pressão Δζ1. A amostra é composta de partículas de solo envolvidas por água, que preenche seus vazios. Um dispositivo qualquer, como um manômetro, como um manômetro, permite a medição do acréscimo de pressão na água. Figura 1 – Analogia Analogia do sistema água mola.
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A figura 1b apresenta o modelo físico denominado analogia do sistema águamola de Terzaghi, que consiste em um cilindro indeformável, um pistão sustentado por uma mola e uma válvula para controle do fluxo. O cilindro é preenchido pela água, cuja compressibilidade é admitida como sendo nula. Cada componente do sistema corresponde a outro na amostra da figura 1a. A água do cilindro corresponde à água intersticial da amostra de solo; a permeabilidade é representada pela abertura parcial da válvula e a deformação do esqueleto sólido, pela mola. Uma vez aplicado o acréscimo de tensão vertical Δζ1 no edômetro, a pressão da água intersticial, ou poropressão, sofre imediatamente um acréscimo correspondente, que pode ser observado no manômetro. No pistão é aplicada analogamente a força F , cujo valor é ajustado de forma a aplicar uma pressão uniforme e igual a Δζ1. No instante inicial, com a válvula ainda fechada, a pressão na água é igual à sobrecarga, ou seja,
Δut=0 = Δζ1. Nesta ocasião, a força suportada pela mola ainda é nula, pois toda a pressão é suportada suportada inicialmente pela água. Com o passar do tempo, a água dos vazios começa a ser expulsa da amostra de solo, o que é representado no modelo de Terzaghi por uma pequena abertura na válvula. À medida que a água sai, diminui a poropressão e aumenta a tensão na mola. Este fenômeno é denominado transferência de carga da água para a mola, ou seja, da água intersticial do solo para o esqueleto sólido. O aumento da pressão sobre o esqueleto sólido corresponde um aumento de pressão efetiva ζ’1.
2.3 Teoria de adensamento unidimensional de Terzaghi A equação diferencial do adensamento unidimensional, incluída por Terzaghi em seu conhecido livro Erdbaumechanik, de 1925, é considerada o marco fundamental da Mecânica dos Solos. É importante entender seu desenvolvimento teórico, analisando as hipóteses sobre as quais a teoria se baseia e suas limitações. Para representar matematicamente a analogia do sistema água-mola de Terzaghi são necessárias três equações, uma para representar o fluxo d’água, outra para a compressibilidade da mola, ou seja, do esqueleto sólido, e a terceira para garantir o
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Equação (1) Onde: k= permeabilidade na direção vertical z= coordenada na direção vertical h= carga hidráulica total e = índice de vazios S = grau de saturação t = tempo As partículas de solo e a água são admitidas como incompressíveis. A compressibilidade da água é muito baixa e pode ser desprezada sem problemas. Os grãos de solo também podem ser considerados incompressíveis, sendo toda a compressibilidade do conjunto solo-água atribuída ao esqueleto sólido, que funciona, como visto na analogia de Terzaghi, como uma mola. A hipótese de fluxo unidimensional é válida quando a espessura da camada em processo de consolidação consolidação é bem inferior à largura do do carregamento carregamento (figura 3). Figura 3 – Fluxo Fluxo unidimensional no adensamento do solo.
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O valor da carga total h é a soma da carga altimétrica ha e piezométrica h p, e esta última é igual à poropressão u dividida pelo peso específico da água γw. Daí, vem:
O valor de u pode ser substituído por uo + Δu, isto é, poropressão estática uo correspondente à condição de equilíbrio, mais o acréscimo de poropressão Δu. Obtémse, então:
Equação (3) Fazendo a análise de alguns termos da equação original, obtem-se:
Equação (4) Para o comportamento do esqueleto sólido, Terzaghi adotou uma relação tensãodeformação linear:
Equação (5)
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em cm²/ano para facilitar as aplicações práticas em engenharia geotécnica). Esse coeficiente é expresso por:
Equação (7) Nessa equação, verifica-se que a relação (1 + e)/av é o inverso do módulo de variação de volume, ou deformação volumétrica, mv. Daí:
Equação (8) Uma outra hipótese de Terzaghi, a de que cv permanece constante durante o adensamento,
foge bastante à realidade, pois o coeficiente de adensamento não é uma
propriedade independente, mas sim variável com a permeabilidade e a compressibilidade do solo. À medida que o solo adensa tanto a permeabilidade quanto a compressibilidade, e consequentemente cv, diminuem. A experiência em ensaios de laboratório e medições de campo comprova que cv apresenta valores elevados em argilas pré-adensadas, reduzindo muito seu valor quando o material se torna normalmente adensado. Assim, admitir cv constante é, na melhor das hipóteses, uma aproximação grosseira.
Equação (9)
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O símbolo T é denominado Fator Tempo, e é adimensional. Ele correlaciona os tempos de recalque às características do solo, através de c v, e às condições de drenagem do solo, através de H d. O objetivo da teoria é determinar, para qualquer instante e em qualquer posição da camada que se adensa, o grau de adensamento, ou seja, as deformações, os índices de vazios, as tensões efetivas e as pressões neutras correspondentes. O desenvolvimento da Teoria do Adensamento baseia-se nas seguintes hipóteses:
O solo é totalmente saturado;
A compressão é unidimensional;
O fluxo d’água é unidimensional;
O solo é homogêneo; homogêneo;
As partículas sólidas e a água são praticamente incompressíveis incompressíveis perante a compressibilidade do solo;
O solo pode ser estudado como elementos infinitesimais, apesar de ser constituído de partículas e vazios;
O fluxo é governado pela Lei de Darcy;
As propriedades do solo não variam no processo de adensamento; adensamento;
O índice de vazios varia linearmente com o aumento da tensão efetiva durante o processo de adensamento. adensamento.
2.4 Grau de adensamento O grau de adensamento localizado, ou percentagem de adensamento localizado
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Em resumo, o grau de adensamento pode ser dado pelas quatro expressões abaixo, as duas primeiras decorrentes de sua definição e as duas últimas resultantes da hipótese simplificadora de Terzaghi.
̅ ̅
̅
Equação (11)
2.5 Tensão de pré-adensamento pré-adensamento
O conhecimento do valor de ζ’ vm é extremamente importante para o estudo do comportamento dos solos, pois representa a fronteira entre deformações relativamente pequenas e muito grandes. Na prática, a relação relação entre a tensão tensão efetiva de pré-adensamento pré-adensamento ( ζ’vm) e a tensão efetiva vertical de campo ( ζ’vo ) pode se dar de duas maneiras:
Solo Normalmente Adensado
(σ’vm = σ’vo) : Neste caso, o
solo nunca
foi submetido a uma tensão efetiva vertical maior a atual. Para esta condição diz-se que o solo é normalmente adensado e sua Razão de PréAdensam ento (RPA) ou OCR (“Over Consolidation Ratio”), definida como sendo:
é igual à unidade RPA=1,0. Durante a formação de um solo sedimentar, por exemplo, as tensões vão crescendo continuamente com a deposição de novas camadas. Nesses casos, nenhum elemento foi submetido a tensões efetivas maiores do que as atuais.
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Tabela 1 – Causas Causas de Pré-adensamento. Pré-adensamento.
3. Materiais e Métodos Apresentaremos a seguir os materiais e os métodos que foram utilizados para a realização do ensaio de adensamento, bem como os métodos utilizados para construção das curvas que relacionam deformações com o tempo e índices de vazios com pressões. Essas curvas proporcionará que se encontrem os valores de alguns índices.
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Talhador que permite a talhagem do corpo de prova que será utilizado no ensaio: após moldado pela compactação; Balança de precisão; Pisseta com água destilada.
3.2 Métodos O ensaio de adensamento seguiu, em parte, a NBR 12007 (1990), que prescreve os ensaios de adensamento unidimensional de solos. O laboratorista utilizou-se de sua prática para realização do ensaio, de forma que todos os membros da turma entendessem sua execução e leitura dos dados. Calibraram-se todos os acessórios do edômetro utilizado no ensaio e na prensa de adensamento. Adicionou-se água ao material, considerando que sua umidade higroscópica era nula, para que o material adquirisse uma plasticidade de moldagem aceitável. O material foi introduzido, aos poucos no interior do edômetro, com todos os acessórios necessários para a execução do ensaio. Em seguida montou-se a aparelhagem na prensa para iniciar o ensaio.
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Na execução deste ensaio, no horário da aula, não houve a demonstração do descarregamento do material, parte importante no adensamento no solo, mas tudo foi explicado pelo laboratorista. Vale salientar que o procedimento relatado acima foi executado apenas como demonstração. Os dados utilizados já estavam anotados em um formulário que nos foi entregue no laboratório, esses dados correspondem ao solo de uma estação rodoviária coletado em tubo Shelby. Todos os procedimentos da norma de adensamento, para a realização do ensaio, com os quais os dados estavam sob posse dos alunos, obedeceram aos passos prescritos.
3.2.1 Métodos para determinação da tensão de pré-adensamento a partir da análise gráfica A pressão vertical correspondente ao início da reta virgem, a partir da qual o solo passa a sofrer grandes deformações, é denominada pressão de pré-adensamento
ζ’vm ou de sobreadensamento, ou ainda de préconsolidação. O conhecimento do valor de ζ’vm é extremamente importante para o estudo do comportamento dos solos, pois é a fronteira
entre deformações relativamente pequenas e muito grandes. Vários métodos
têm sido propostos para sua determinação, tendo sido sumarizados por Leonards (1962).
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Figura 4 – Determinação Determinação da pressão de pré-adensamento pelo método de Casagrande.
Figura 5 – Determinação Determinação da pressão de pré-adensamento pelo método de Pacheco Silva.
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Pelo método de Casagrande, inicialmente toma-se o ponto de maior curvatura da curva, e por ela se traçam uma horizontal, uma tangente à curva e a bissetriz do ângulo formado pelas duas. A interseção da bissetriz com o prolongamento da reta virgem é considerado o ponto de pré-adensamento, e suas coordenadas são a tensão de préadensamento adensamento e o índice de vazios correspondente. Pelo método do engenheiro Pacheco Silva, inicialmente prolonga-se a reta virgem até a horizontal correspondente ao índice de vazios inicial da amostra. Do ponto de interseção, abaixa-se uma vertical até a curva de adensamento e desse ponto traça-se uma horizontal. A interseção da horizontal com o prolongamento da reta é considerado o ponto de pré-adensamento. pré-adensamento. O resultado pelo método do engenheiro Pacheco Silva independe do operador, mas o método de Casagrande é mais difundido dif undido internacionalmente. Nesse trabalho, utilizou-se o método de Pacheco Silva para determinação da pressão de pré-adensamento.
4. Resultados Apresentaremos a seguir os resultados obtidos com a realização do ensaio e suas
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adensamento servirá para que o coeficiente de adensamento ( cv) seja calculado através da relação:
cv = 0,197.Hd2/t50 , onde: Hd - metade da altura do corpo de prova. . Curva Índice de Vazios-Pressão - Marca-se os valores dos índices de vazios em escala aritmética, nas ordenadas, e as pressões em escala logarítmica, nas abscissas. Deste gráfico é extraído o índice de compressão ( cc), o qual define a inclinação da reta virgem:
cc = (e1 - e2)/(log p2 - log p1) 4.1 Cálculos iniciais Cál l os das mi dades
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Cál cul cu l o da densidade densi dade úmi úmi da (Y ) eca (Y ); h h e densidade seca s s o
Cálculo da densidade úmida:
Onde: Psu = Peso do solo umido(g); V = Volume do anel (cm³) Diametro do anel = 4,96 cm Altura do Anel = 2,0 cm Área = 19,31cm 2
Logo, a densidade umida é:
o
; Y h = 1,311g/cm³
Cálculo da densidade seca :
Onde: Y = Densidade seca (g/cm³);
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ζ
4.2 Cálculos para iniciar o ensaio o
Cálculo da tensão equivalente a 10 KPa para o inicio do ensaio.
ζ
Tensão corrigida para 10kPa:
ζ ζ ζ ζ
Carga corrigida para 10kPa:
ζ
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o
Cálculo da tensão equivalente a 80 KPa.
ζ
Tensão corrigida para 80kPa:
ζ ζ ζ ζ Carga corrigida para 80kPa: ζ o
Cálculo da tensão equivalente a 160 KPa.
ζ
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Peso do solo umido= 50,64g Peso do solo seco= 22,47g Peso da agua= 28,17g Umidade Inicial = 125,4% Amostra após ensaio Solo umido + Cap= 52,83g Peso da Cap= 13,83g Peso do solo seco + cap = 36,30g Peso do solo seco= 22,47g Peso da agua= 16,53g Umidade final = 73,56%
9:13:00 9:15:00 9:19:00 9:26:00 9:41:00 10:11:00 11:11:00 13:11:00 15:11:00
2 min 4 min 8 min 15 min 30 min 1h 2h 4h 6h
36,00 47,00 66,00 81,00 141,00 159,00 174,50 191,00 205,00
36,00 47,00 66,00 81,00 141,00 159,00 174,50 191,00 205,00
17:11:00 8:11:00
8h 24 h 48 h
224,00 245,00
224,00 245,00
Cálculo do Recalque:
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Cálculo do Coeficiente de Permeabilidade; K = Cv x Mv x Yo Yo = 1,7 x 10 -5cm/seg = constante K1 = 0.0069 x 0,475 x 1 x 1,7 x 10 -5 = 5,57 x 10 -8 cm/seg Figura 6 – Gráfico Gráfico Deformação X Tempo (130g).
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Amostra antes do ensaio:
8:15:15
15 s
340,00
95,00
Solo umido + anel = 421,41g Peso do anel= 370,80g Peso do solo umido= 50,64g Peso do solo seco= 22,47g Peso da agua= 28,17g Umidade Inicial = 125,4%
8:15:30 8:16:00 8:17:00 8:19:00 8:23:00 8:30:00 8:45:00 9:15:00
30 s 1 min 2 min 4 min 8 min 15 min 30 min 1h
349,00 361,50 378,00 400,00 426,50 466,50 513,00 557,50
104,00 116,50 133,00 155,00 181,50 221,50 268,00 312,50
Amostra após ensaio
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Cálculo do Coeficiente de Compressibilidade; ( ) ( )
Cálculo do Coeficiente de Permeabilidade; K = Cv x Mv x Yo Yo = 1,7 x 10 -5cm/seg = constante K2 = 0.0087 x 0,615 x 1 x 1,7 x 10 -5 = 9,09 x 10 -8 cm/seg
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Tabela 4: Dados do adensamento com a carga de 720g Inicio do Ensaio Carga: 30/08/06 Troca de Carga: 31/08/06 Amostra antes do ensaio:
Tempo t (acumul) (h) 8:05:00 0s 8:05:10 10 s 8:05:15 15 s
√t (min)
Leit. Ext
∑dH (div)
695,00 720,00 735,00
0,00 25,00 40,00
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Cálculo do Coeficiente de Adensamento (Cv); () )
Cálculo do Coeficiente de Deformação Volumétrica ; Δζ
Δ
Cálculo do Coeficiente de Compressibilidade;
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ESTÁGI ESTÁGI O 4
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Cálculo do (H50)²;
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ESTÁGI ESTÁGI O 5
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Cálculo do (H50)²;
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4.4 Resumo dos resultados do ensaio de adensamento
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