GATE’22 CE: Daily Practices Quiz. 19-July-2021

Quiz: Civil Engineering
Exam: GATE
Topic: soil mechanics

Each question carries 2 mark
Negative marking: 1/3 mark
Time: 12 Minutes

Q1. The following data are given for a soil sample
σ_0’=275 kPa,∈_0’=1.2
σ_0’+∆σ_0’=400 kPa,∈=0.8
If thickness of the clay specimen in 30 mm, the value of coefficient of volume compressibility is?
(a) 7.54×10^(-4) m²\/kN
(b) 1.45 × 10^(-3) m²\/kN
(c) 1.45 × 10^(-4) m²\/kN
(d) 7.54×10^(-3) m²\/kN

Q2. The depth of tension crack in a pure soft clay is:
(a) 4cu/γ
(b) 2cu/γ
(c) cu/2γ
(d) cu/γ

Q3. A water contains following dissolved ions:
[Na^+ ]=112 mg\/l,[Ca^(2+) ]=80 mg\/L
[Mg^(2+) ]=60 mg\/L,[Al^(3+) ]=6 mg\/l
[HCO_3^- ]=380 mg\/L ,[Cl^- ]=330 mg\/L
determine the total hardness of that sample
(a) 242 mg/l
(b) 483 mg/l
(c) 260 mg/l
(d) 406 mg/l

Q4. MPN index is a measure of:
(a) BOD_5
(b) Hardness
(c) Coliform Bacteria
(d) Dissolved oxygen

Q5. Dupit’s assumptions are valid for:
(a) Confined aquifer
(b) unconfined aquifer.
(c) Artisian Aquifer
(d) Leaky aquifer
Solution

S1. Ans.(b)
Sol. coeff. Of volume compressibility
m_v=a_v/(1+e_o )=∆e/((∆σ ̅)/(1+e_0 ))
=(1.2-0.8)/((400-275)/(1+1.2))
=1.45×10^(-3) m^2 \/kN

S2. Ans.(b)
Sol. Active earth pressure in case of cohesive soil,
p_a=k_a γZ-2cu√ka
Let Z_c= depth of tension crack
At Z = Zc, Pa = 0
⇒ 0 = k_a γZ_c-2Cu √ka
⇒ ▭(Z_C=2Cu/(γ√(k_a )))
For pure cohesive clay, ϕ=0 k_a=1
▭(Z_c=2Cu/γ)

S3. Ans.(b)
Sol. Total hardness is due to the multivalent cation
Total hardness = [Mg^(2+) ]×(eq.Wt of CaCo_3)/(eq.wt.of Mg^(2+) )+
[Ca^(2+) ]×(eqwt.of CaCo_3)/(eq.wt of [Ca^(2+) ] )+
[Al^(3+) ]×(eq.wt.of CaCo_3)/(eq.wt of [Al^(3+) ] )
=60×50/12+80×50/20+6×50/9
= 483.33 Mg/L as CaCo3

S4. Ans.(c)
Sol. MPN (most probable number) is a measure of coliform bacteria. Other tests for measuring coliforms can be membrane filter technique of coliform index test

S5. Ans.(b)
Sol. Dupit’s assumptions are valid for unconfined aquifers. It states that ground water flows horizontally in an unconfined aquifer and the discharge is proportional to saturate aquifer thickness.

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