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# Terzaghi’s Theory of One Dimensional Consolidation – 1

The theoretical concept of consolidation process was developed by _____________

a) Terzaghi

b) Taylor

c) Skempton

d) Darcy

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Answer: a

Explanation: The theoretical concept of consolidation process was developed by in 1923. Skempton is known for Skempton’s A & B pore water pressure coefficients and also the bearing capacity of foundations.

In Terzaghi’s Theory of one dimensional consolidation, soil is considered to be __________

a) homogenous

b) non-homogenous

c) anisotropic

d) heterogeneous

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Answer: a

Explanation: Soils, by nature, are non-homogeneous media, and anisotropic in general. This means that their properties vary within relatively short distances in the vertical and horizontal directions. For the simplicity in solving the equations the soil is considered to be homogenous.

In Terzaghi’s Theory of one dimensional consolidation, deformation of soil is entirely due to _________________

a) volume change

b) permeability of soil

c) seepage of fluids

d) viscosity of fluids

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Answer: a

Explanation: In Terzaghi’s Theory of one dimensional consolidation, deformation of the soil is entirely due to change in volume. The change in volume can occur due to the decrease in the voids ratio or the effective height of the solids.

In Terzaghi’s Theory of one dimensional consolidation, soil particles are ____________ and water is ______________

a) compressible, incompressible

b) both are compressible

c) both are incompressible

d) incompressible, compressible

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Answer: c

Explanation: In Terzaghi’s Theory of one dimensional consolidation, soil particles and water is considered to be incompressible. Water is slightly compressible. We often treat it as incompressible when doing fluid flow calculations because the pressure changes involved are too small to make an appreciable change to the density.

In Terzaghi’s Theory of one dimensional consolidation, Darcy’s law is _______

a) invalid

b) valid

c) invalid only for clays

d) invalid only for gravel

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Answer: b

Explanation: In Terzaghi’s Theory of one dimensional consolidation, Darcy’s law is perfectly valid. For ease in calculation, the flow of water in the soil is considered to be a laminar flow, thus validating the Darcy’s law.

In Terzaghi’s Theory of one dimensional consolidation, coefficient of permeability is ______

a) zero

b) variable

c) constant

d) unity

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Answer: c

Explanation: In Terzaghi’s Theory of one dimensional consolidation, coefficient of permeability is constant during the consolidation. This assumption is made so that not more than one coefficient of permeability is used in the same problem.

In determination of one-dimensional consolidation as shown in the figure, the line CD represents ___________

a) at initial time t_{0}, u=∆σ

b) at initial time t_{0}, u=0

c) at final time t_{f}, u=∆σ

d) at final time t_{f}, u=0

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Answer: a

Explanation: At the time t_{0}, the whole of the consolidation pressure is carried by the pore water so that the initial excess hydrostatic pressure u is equal to ∆σ. Hence, at initial time t_{0}, u=∆σ. This is represented by the line CD.

In determination of one-dimensional consolidation as shown in the figure, the line AB represents ___________

a) at initial time t_{0}, u=∆σ

b) at initial time t_{0}, u=0

c) at final time t_{f}, u=∆σ

d) at final time t_{f}, u=0

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Answer: d

Explanation: As the water starts escaping into the sand, the excess hydrostatic pressure at the pervious boundaries drops to zero and remains so at all the time. Therefore, at the final time t_{f}, u=0. This is represented by the AB in the diagram.

At intermediate time t, the consolidating pressure is equal to ___________

a) ∆σ=σ+u

b) ∆σ=σ’

c) ∆σ=σ’+u

d) ∆σ=σ’-u

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Answer: c

Explanation: At intermediate time t, the consolidating pressure is partly carried by soil and partly by the pore water so that the consolidating pressure ∆σ at time t is given by,

∆σ=σ’+u.

The distribution of excess hydrostatic pressure is represented by ___________

a) straight line

b) curve

c) helical curve

d) closed curve

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Answer: b

Explanation: The distribution of excess hydrostatic pressure is represented by a curve. The curve represents the water levels in different piezometric tubes that represent the pressure head at each point.

The isochrones represents ___________

a) water levels in piezometric tubes at different time

b) water levels in piezometric tubes at the same level

c) water levels in piezometric tubes at different levels

d) water levels in piezometric tubes at the same time

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Answer: d

Explanation: In general, the isochrone is the line on a diagram connecting points relating to the same time or equal times. So, in soil mechanics, the isochrones represent the water levels in piezometric tubes at the same time.

The slope of isochrones at any point indicates ___________

a) change of pore pressure with total pressure

b) change of effective pressure with pore pressure

c) change of pore pressure with depth at time interval t

d) change of pore pressure with volume

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Answer: c

Explanation: In soil mechanics, the isochrones represent the water levels in piezometric tubes at the same time. The slope of isochrones at any point at a given time indicates the rate of change of pore pressure with depth.

A number of isochrones can be drawn for water levels in piezometric tubes at the same time t.

a) True

b) False

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Answer: b

Explanation: Since the water levels in the piezometric tubes at a given time remain in a specific position and the isochrones represent the water levels in piezometric tubes at the same time, a single isochrone is drawn at a given time. We have to note that a number of isochrones can be drawn for water levels in piezometric tubes at different time intervals t_{1}, t_{2}, t_{3} etc.

At time t, the hydraulic head corresponding to excess hydrostatic pressure is __________

a) h=σ′γw

b) h=u¯¯¯γw

c) h=γwu¯¯¯

d) h=σ′u¯¯¯γw

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Answer: b

Explanation: The excess pore pressure in terms of its head is given by,

u=hγ_{w}

therefore, on rearranging the equation,

the hydraulic head corresponding to excess hydrostatic pressure is,

h=u¯¯¯γw.

The hydraulic gradient i is given by _________

a) i=γw∂h∂z

b) i=∂hγw∂z

c) i=u¯¯¯∂h∂z

d) i=∂h∂z

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Answer: d

Explanation: The hydraulic gradient is the driving force that causes groundwater to move in the direction of maximum decreasing total head. The hydraulic gradient is the change in total head divided the distance over which the change occurs.

∴ i=∂h∂z.