Exercícios Mecânica dos Solos Gabarito
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Exercícios Mecânica dos Solos Gabarito

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Lista de Exercícios 
Mecânica dos Solos 
2019 / 2 
 
Página 1 de 6 
QUESTÃO 1 \u2013 Uma amostra de solo tem volume de 60 cm³ e peso de 92,5 gf. Depois de 
completamente seca seu peso é de 74,3 gf. O peso específico real dos grãos sólidos é 2,62 
gf/cm³. Calcular sua umidade e grau de saturação. RESP.: h = 24,5% S = 57,5% 
V = 60 cm³ 
P = 92,5 gf 
PS = 74,3 gf 
\u3b3S = 2,62 gf/cm³ 
a) Cálculo da umidade: 
\ud835\udc98 = 
\ud835\udc77\ud835\udc98
\ud835\udc77\ud835\udc94
. \ud835\udfcf\ud835\udfce\ud835\udfce 
\ud835\udc77\ud835\udc98 = \ud835\udc77 \u2212 \ud835\udc77\ud835\udc94 
\ud835\udfd7\ud835\udfd0, \ud835\udfd3 \u2212 \ud835\udfd5\ud835\udfd2, \ud835\udfd1 \u2192 \ud835\udc77\ud835\udc98 = \ud835\udfcf\ud835\udfd6, \ud835\udfd0 \ud835\udc88\ud835\udc87 
\ud835\udc98 = 
\ud835\udfcf\ud835\udfd6, \ud835\udfd0
\ud835\udfd5\ud835\udfd2, \ud835\udfd1
. \ud835\udfcf\ud835\udfce\ud835\udfce 
\ud835\udc98 = \ud835\udfd0\ud835\udfd2, \ud835\udfd3% 
b) Cálculo do grau de saturação: 
\ud835\udc7a = 
\ud835\udc7d\ud835\udc98
\ud835\udc7d\ud835\udc97
. \ud835\udfcf\ud835\udfce\ud835\udfce 
\ud835\udf38\ud835\udc98 = \ud835\udfcf \ud835\udc95\ud835\udc87/\ud835\udc8e³ 
\ud835\udc77\ud835\udc98 = \ud835\udc7d\ud835\udc98 = \ud835\udfcf\ud835\udfd6, \ud835\udfd0 \ud835\udc88\ud835\udc87 
\ud835\udf38\ud835\udc94 = 
\ud835\udc77\ud835\udc94
\ud835\udc7d\ud835\udc94
 \u2192 \ud835\udfd0, \ud835\udfd4\ud835\udfd0 = 
\ud835\udfd5\ud835\udfd2, \ud835\udfd1
\ud835\udc7d\ud835\udc94
 
\ud835\udc7d\ud835\udc94 = \ud835\udfd0\ud835\udfd6, \ud835\udfd1\ud835\udfd4 \ud835\udc88/\ud835\udc84\ud835\udc8e³ 
\ud835\udc7d = \ud835\udc7d\ud835\udc94 + \ud835\udc7d\ud835\udc97 
\ud835\udfd4\ud835\udfce = \ud835\udfd0\ud835\udfd6, \ud835\udfd1\ud835\udfd4 + \ud835\udc7d\ud835\udc97 
\ud835\udc7d\ud835\udc97 = \ud835\udfd1\ud835\udfcf, \ud835\udfd4\ud835\udfd2 \ud835\udc84\ud835\udc8e³ 
\ud835\udc7a = 
\ud835\udfcf\ud835\udfd6, \ud835\udfd0
\ud835\udfd1\ud835\udfcf, \ud835\udfd4\ud835\udfd2
. \ud835\udfcf\ud835\udfce\ud835\udfce 
\ud835\udc7a = \ud835\udfd3\ud835\udfd5, \ud835\udfd3 % 
 
QUESTÃO 2 \u2013 Uma amostra de 0,4 m³ de solo tem as seguintes características: massa 
úmida de 711,2 kg, massa seca de 623,9 kg, densidade real dos grãos de 2,68. Estime: 
a) Teor de umidade 
b) Peso específico 
c) Peso específico seco 
d) Índice de vazios 
e) Porosidade 
 
a) Teor de umidade (w) 
\ud835\udc98 = 
\ud835\udc77\ud835\udc98
\ud835\udc77\ud835\udc94
. \ud835\udfcf\ud835\udfce\ud835\udfce = 
\ud835\udfd5\ud835\udfcf\ud835\udfcf, \ud835\udfd0 \u2212 \ud835\udfd4\ud835\udfd0\ud835\udfd1, \ud835\udfd7
\ud835\udfd4\ud835\udfd0\ud835\udfd1, \ud835\udfd7
\u2192 \ud835\udc98 = \ud835\udfcf\ud835\udfd1, \ud835\udfd7\ud835\udfd7 % 
b) Peso específico (\uf067) 
\ud835\udf38 = 
\ud835\udc77
\ud835\udc7d
= 
\ud835\udfd5\ud835\udfcf\ud835\udfcf, \ud835\udfd0
\ud835\udfce, \ud835\udfd2
\u2192 \ud835\udf38 = \ud835\udfcf. \ud835\udfd5\ud835\udfd6\ud835\udfd6 \ud835\udc8c\ud835\udc88/\ud835\udc8e³ 
c) Peso específico seco (\uf067s) 
\ud835\udf38\ud835\udc94 = 
\ud835\udc77\ud835\udc94
\ud835\udc7d
= 
\ud835\udfd4\ud835\udfd0\ud835\udfd1, \ud835\udfd7
\ud835\udfce, \ud835\udfd2
\u2192 \ud835\udf38\ud835\udc94 = \ud835\udfcf\ud835\udfd3\ud835\udfd3\ud835\udfd7, \ud835\udfd5\ud835\udfd3 \ud835\udc8c\ud835\udc88/\ud835\udc8e³ 
d) Índice de vazios (e) 
 
Lista de Exercícios 
Mecânica dos Solos 
2019 / 2 
 
Página 2 de 6 
\ud835\udf38\ud835\udc94 = 
\ud835\udc6e\ud835\udc94. \ud835\udf38\ud835\udc98
\ud835\udfcf + \ud835\udc86
 \u2192 \ud835\udc86 = 
\ud835\udc6e\ud835\udc94. \ud835\udf38\ud835\udc98
\ud835\udf38\ud835\udc94
\u2212 \ud835\udfcf = 
\ud835\udfd0, \ud835\udfd4\ud835\udfd6. \ud835\udfcf\ud835\udfce\ud835\udfce\ud835\udfce
\ud835\udfcf\ud835\udfd3\ud835\udfd3\ud835\udfd7, \ud835\udfd5\ud835\udfd3
\u2212 \ud835\udfcf \u2192 \ud835\udc86 = \ud835\udfce, \ud835\udfd5\ud835\udfd0 
e) Porosidade 
\ud835\udc8f = 
\ud835\udc86
\ud835\udfcf + \ud835\udc86
=
\ud835\udfce, \ud835\udfd5\ud835\udfd0
\ud835\udfcf + \ud835\udfce, \ud835\udfd5\ud835\udfd0
\u2192 \ud835\udc8f = \ud835\udfce, \ud835\udfd2\ud835\udfd0 
 
QUESTÃO 3 - A massa específica úmida de um solo é de 1680 kg/m³. Dados w = 18% e 
Gs = 2,73, determine: 
a) Massa específica seca (em kg/m³) 
b) Porosidade 
c) Grau de Saturação 
d) Massa de água, em kg/m³ de solo, a ser adicionada para atingir a saturação 
completa 
a) \ud835\udf38\ud835\udc94 = \ud835\udc6e\ud835\udc94 . (\ud835\udfcf \u2212 \ud835\udc8f). \ud835\udf38\ud835\udc98 = \ud835\udfd0, \ud835\udfd5\ud835\udfd1 . \ud835\udfcf\ud835\udfce\ud835\udfce\ud835\udfce . (\ud835\udfcf \u2212 \ud835\udfce, \ud835\udfd2\ud835\udfd6) \u2192 \ud835\udf38\ud835\udc94 = \ud835\udfcf\ud835\udfd2\ud835\udfd0\ud835\udfd1, \ud835\udfd5\ud835\udfd1 \ud835\udc8c\ud835\udc88/\ud835\udc8e³ 
b) \ud835\udf38 = \ud835\udc6e\ud835\udc94 . (\ud835\udfcf \u2212 \ud835\udc8f). \ud835\udf38\ud835\udc98 . (\ud835\udfcf + \ud835\udc98) 
\ud835\udc8f = \ud835\udfcf \u2212 
\ud835\udf38
\ud835\udc6e\ud835\udc94 . \ud835\udf38\ud835\udc98 . (\ud835\udfcf + \ud835\udc98)
= 
\ud835\udfcf\ud835\udfd4\ud835\udfd6\ud835\udfce
\ud835\udfd0, \ud835\udfd5\ud835\udfd1 . \ud835\udfcf\ud835\udfce\ud835\udfce\ud835\udfce . (\ud835\udfcf + \ud835\udfce, \ud835\udfcf\ud835\udfd6)
 \u2192 \ud835\udc8f = \ud835\udfce, \ud835\udfd2\ud835\udfd6 
c) \ud835\udc86 = \ud835\udc6e\ud835\udc94 .\ud835\udf38\ud835\udc98
\ud835\udf38\ud835\udc94
\u2212 \ud835\udfcf \u2192 \ud835\udc86 = \ud835\udfd0,\ud835\udfd5\ud835\udfd1 .\ud835\udfcf\ud835\udfce\ud835\udfce\ud835\udfce
\ud835\udfcf\ud835\udfd2\ud835\udfd0\ud835\udfd1,\ud835\udfd5\ud835\udfd1
\u2212 \ud835\udfcf \u2192 \ud835\udc86 = \ud835\udfce, \ud835\udfd7\ud835\udfd0 
\ud835\udc12 . \ud835\udc1e = \ud835\udc30 . \ud835\udc06\ud835\udc2c \u2192 \ud835\udc12 = 
\ud835\udc30 . \ud835\udc06\ud835\udc2c
\ud835\udc1e
= \ud835\udfcf\ud835\udfd6 .\ud835\udfd0,\ud835\udfd5\ud835\udfd1
\ud835\udfce,\ud835\udfd7\ud835\udfd0
 \u2192 \ud835\udc12 = \ud835\udfd3\ud835\udfd1, \ud835\udfd3\ud835\udfd4% 
d) \ud835\udf38\ud835\udc94\ud835\udc82\ud835\udc95 = 
\ud835\udf38\ud835\udc98 . (\ud835\udc6e\ud835\udc94\uc36\ud835\udc86)
\ud835\udfcf\ub3e\ud835\udc86
= \ud835\udfcf\ud835\udfce\ud835\udfce\ud835\udfce .(\ud835\udfd0,\ud835\udfd5\ud835\udfd1\ub3e\ud835\udfce,\ud835\udfd7\ud835\udfd0)
\ud835\udfcf\ub3e\ud835\udfce,\ud835\udfd7\ud835\udfd0
 \u2192 \ud835\udf38\ud835\udc94\ud835\udc82\ud835\udc95 = \ud835\udfcf\ud835\udfd7\ud835\udfce\ud835\udfd0, \ud835\udfd0\ud835\udfd0 \ud835\udc8c\ud835\udc88/\ud835\udc8e³ 
\ud835\udc74\ud835\udc98 = \ud835\udf38\ud835\udc94\ud835\udc82\ud835\udc95 \u2212 \ud835\udf38 = \ud835\udfcf\ud835\udfd7\ud835\udfce\ud835\udfd0, \ud835\udfd0\ud835\udfd0 \u2212 \ud835\udfcf\ud835\udfd4\ud835\udfd6\ud835\udfce \u2192 \ud835\udc74\ud835\udc98 = \ud835\udfd0\ud835\udfd0\ud835\udfd0, \ud835\udfd0\ud835\udfd0 \ud835\udc8c\ud835\udc88 
Dados Iniciais Dados Finais 
Saturação Inicial = 53,56 % Saturação Final = 100 % (dado do problema) 
Umidade Inicial = 18 % Umidade Final = 33,61 % (fórmula da letra c) 
Massa total = \uf067s = 1680 kg Massa total = \uf067sat = 1902,22 kg 
Massa Seca = 1423,73 kg Massa Seca = 1423,73 kg 
Massa de água inicial (Mi) = 256,27 kg Massa de água final (Mf) = 478,49 kg 
Massa de água a ser adicionada = Mf \u2013 Mi = 478,49 \u2013 256,27 \uf0e0 Mw = 222,22 kg 
 
Lista de Exercícios 
Mecânica dos Solos 
2019 / 2 
 
Página 3 de 6 
QUESTÃO 4 - Traçar os diagramas das pressões totais, neutras e efetivas para o 
terreno indicado no perfil abaixo 
 
 
Cálculo das pressões totais (\ud835\udf48 = \ud835\udf38. \ud835\udc89) 
\ud835\udf48\ud835\udfce = \ud835\udfce
\ud835\udc88\ud835\udc87
\ud835\udc84\ud835\udc8e\ud835\udfd0
 
\ud835\udf48\ud835\udfcf,\ud835\udfd3 = \ud835\udfcf, \ud835\udfd5. \ud835\udfcf\ud835\udfd3\ud835\udfce \u2192 \ud835\udf46\ud835\udfcf,\ud835\udfd3 = \ud835\udfd0\ud835\udfd3\ud835\udfd3
\ud835\udc88\ud835\udc87
\ud835\udc84\ud835\udc8e\ud835\udfd0
 
\ud835\udf48\ud835\udfd2,\ud835\udfd3 = \ud835\udfd0\ud835\udfd3\ud835\udfd3 + \ud835\udfd0, \ud835\udfcf. \ud835\udfd1\ud835\udfce\ud835\udfce \u2192 \ud835\udf46\ud835\udfd2,\ud835\udfd3 = \ud835\udfd6\ud835\udfd6\ud835\udfd3
\ud835\udc88\ud835\udc87
\ud835\udc84\ud835\udc8e\ud835\udfd0
 
 
\ud835\udf48\ud835\udfd6,\ud835\udfcf = \ud835\udfd6\ud835\udfd6\ud835\udfd3 + \ud835\udfd0, \ud835\udfce. \ud835\udfd1\ud835\udfd4\ud835\udfce \u2192 \ud835\udf46\ud835\udfd6,\ud835\udfcf = \ud835\udfcf\ud835\udfd4\ud835\udfce\ud835\udfd3
\ud835\udc88\ud835\udc87
\ud835\udc84\ud835\udc8e\ud835\udfd0
 
 
Cálculo das pressões neutras (\ud835\udf41 = \ud835\udf38\ud835\udc98. \ud835\udc89) 
\ud835\udf41\ud835\udfce = \ud835\udfce
\ud835\udc88\ud835\udc87
\ud835\udc84\ud835\udc8e\ub36
 
\ud835\udf41\ud835\udfcf,\ud835\udfd3 = \ud835\udfce
\ud835\udc88\ud835\udc87
\ud835\udc84\ud835\udc8e\ub36
 
 \ud835\udf41\ud835\udfd2,\ud835\udfd3 = \ud835\udfcf. \ud835\udfd1\ud835\udfce\ud835\udfce \u2192 \ud835\udf41\ud835\udfd2,\ud835\udfd3 = \ud835\udfd1\ud835\udfce\ud835\udfce
\ud835\udc88\ud835\udc87
\ud835\udc84\ud835\udc8e\ub36
 
\ud835\udf41\ud835\udfd6,\ud835\udfcf = \ud835\udfd1\ud835\udfce\ud835\udfce + \ud835\udfcf. \ud835\udfd1\ud835\udfd4\ud835\udfce \u2192 \ud835\udf41\ud835\udfd2,\ud835\udfd3 = \ud835\udfd4\ud835\udfd4\ud835\udfce
\ud835\udc88\ud835\udc87
\ud835\udc84\ud835\udc8e\ub36
 
Cálculo das pressões efetivas (\ud835\udf48\u11f1 = \ud835\udf48 \u2212 \ud835\udf41) 
\ud835\udf48\ud835\udfce = \ud835\udfce \u2212 \ud835\udfce \u2192 \ud835\udf48\u2032\ud835\udfce = \ud835\udfce
\ud835\udc88\ud835\udc87
\ud835\udc84\ud835\udc8e\ud835\udfd0
 
 
Lista de Exercícios 
Mecânica dos Solos 
2019 / 2 
 
Página 4 de 6 
\ud835\udf48\ud835\udfcf,\ud835\udfd3 = \ud835\udfd0\ud835\udfd3\ud835\udfd3 \u2212 \ud835\udfce \u2192 \ud835\udf48\u2032\ud835\udfcf,\ud835\udfd3 = \ud835\udfd0\ud835\udfd3\ud835\udfd3
\ud835\udc88\ud835\udc87
\ud835\udc84\ud835\udc8e\ud835\udfd0
 
\ud835\udf48\ud835\udfd2,\ud835\udfd3 = \ud835\udfd6\ud835\udfd6\ud835\udfd3 \u2212 \ud835\udfd1\ud835\udfce\ud835\udfce \u2192 \ud835\udf48\u2032\ud835\udfce = \ud835\udfd3\ud835\udfd6\ud835\udfd3
\ud835\udc88\ud835\udc87
\ud835\udc84\ud835\udc8e\ud835\udfd0
 
\ud835\udf48\ud835\udfd6,\ud835\udfcf = \ud835\udfcf\ud835\udfd4\ud835\udfce\ud835\udfd3 \u2212 \ud835\udfce\ud835\udfd4\ud835\udfce \u2192 \ud835\udf48\u2032\ud835\udfce = \ud835\udfd7\ud835\udfd2\ud835\udfd3
\ud835\udc88\ud835\udc87
\ud835\udc84\ud835\udc8e\ud835\udfd0
 
 
 
QUESTÃO 5 \u2013 Com base na figura abaixo, calcule \u3c3, u e \u3c3\u2019 em A, B, C e D e DESENHE 
OS GRÁFICOS. Dados: 
H1 4 m H2 5 m H3 3 m 
e 0,4 e 0,6 e 0,81 
Gs 2,62 Gs 2,68 Gs 2,73 
 
 
 
 
 
 
 
 
 
Lista de Exercícios 
Mecânica dos Solos 
2019 / 2 
 
Página 5 de 6 
 
 
Fórmulas 
\ud835\udf38\ud835\udc94 = 
\ud835\udc6e\ud835\udc94. \ud835\udf38\ud835\udc98
\ud835\udfcf + \ud835\udc86
 \ud835\udf38\ud835\udc94\ud835\udc82\ud835\udc95 = 
(\ud835\udc6e\ud835\udc94 + \ud835\udc86). \ud835\udf38\ud835\udc98
\ud835\udfcf + \ud835\udc86
 
\ud835\udf38\ud835\udc98 = \ud835\udfcf\ud835\udfce \ud835\udc75/\ud835\udc8e³ 
 
 1 2 3 H \uf073 \uf06d \uf073\u2019 
H (m) 4 9 12 0 0,00 0,00 0,00 
e1 0,40 0,60 0,81 4 74,84 0,00 74,84 
Gs 2,62 2,68 2,73 9 158,59 50 108,59 
\uf067s\uf020 18,71 16,75 15,08 12 203,83 80 123,83 
\uf067sat\uf020 21,57 20,50 19,56 
 
Lista de Exercícios 
Mecânica dos Solos 
2019 / 2 
 
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