Fundamentals of Geotechnical Engineering (MindTap Course List)
Fundamentals of Geotechnical Engineering (MindTap Course List)
5th Edition
ISBN: 9781305635180
Author: Braja M. Das, Nagaratnam Sivakugan
Publisher: Cengage Learning
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Chapter 14, Problem 14.1P

State whether the following are true or false.

  1. a. The higher the friction angle, the higher the value of K0.
  2. b. K0 is greater for normally consolidated clays than overconsolidated clays.
  3. c. Active earth pressure coefficient is greater than the passive one.
  4. d. The larger the cohesion, the larger is the depth of the tensile cracks in clays in active state.
  5. e. Lateral earth pressures increase linearly with depth.

(a)

Expert Solution
Check Mark
To determine

Whether the statement “The higher the friction angle, the higher the value of K0” is true or false.

Answer to Problem 14.1P

The given statement is False_.

Explanation of Solution

Write the equation of coefficient of earth pressure at rest (K0).

Ko=1sinϕ (1)

Here, ϕ is drained friction angle.

Find the coefficient of earth pressure at rest when ϕ is 30°.

Substitute 30° for ϕ in Equation (1).

Ko=1sin(30°)=0.5

Find the coefficient of earth pressure at rest when ϕ is 60°.

Substitute 60° for ϕ in Equation (1).

Ko=1sin(60°)=0.134

Tabulate the values of coefficient of earth pressure at rest with two different drained friction angles of 30° and 60° as shown in Table 1.

Drained friction angle, ϕCoefficient of earth pressure at rest, Ko
30°0.5
60°0.134

Table 1

Refer Table 1.

The coefficient earth pressure at rest (K0) decreases with increase of drained friction angle (ϕ).

Therefore, the given statement is False_.

(b)

Expert Solution
Check Mark
To determine

Whether the statement “K0 is greater for normally consolidated clays than over consolidated

clays” is true or false.

Answer to Problem 14.1P

The given statement is False_.

Explanation of Solution

The value of over consolidated ratio (OCR) is a whole number.

Write the relationship between earth pressure at rest for over consolidated clay [Ko(Overconsolidated)] and normally consolidated clay [Ko(Normallyconsolidated)].

Ko(Overconsolidated)=Ko(Normallyconsolidated)OCR

The multiplication of square root of over consolidated ratio (OCR) with earth pressure at rest for normal consolidated clay gives the earth pressure at rest for over consolidated clay. Hence, the value earth pressure at rest for over consolidated clay is greater than the earth pressure at rest for normal consolidated clay.

Therefore, the given statement is False_.

(c)

Expert Solution
Check Mark
To determine

Whether the statement “Active earth pressure coefficient is greater than the passive one” is true or false.

Answer to Problem 14.1P

The given statement is False_.

Explanation of Solution

Write the equation of active earth pressure coefficient (Ka).

Ka=tan2(45ϕ2) (2)

Here, ϕ is the friction angle.

Find the active earth pressure coefficient (Ka) when ϕ is 30°.

Substitute 30° for ϕ in Equation (2).

Ka=tan2(4530°2)=0.333

Write the equation of passive earth pressure coefficient (Kp).

Kp=tan2(45+ϕ2) (3)

Substitute 30° for ϕ in Equation (3).

Kp=tan2(45+302)=3

Tabulate the values of active and passive earth pressure coefficients with corresponding friction angle of 30° as shown in Table 1.

Friction angle, ϕActive earth pressure coefficient, KaPassive earth pressure coefficient, Kp
30°0.3333

Refer Table 1.

The active earth pressure coefficient (Ka) is lesser than the passive earth pressure coefficient (Kp) for same friction angle (ϕ) of 30°.

Therefore, the given statement is False_.

(d)

Expert Solution
Check Mark
To determine

Whether the statement “The larger the cohesion, the larger is the depth of the tensile cracks in

clays in active state” is true or false.

Answer to Problem 14.1P

The given statement is True_.

Explanation of Solution

Write the equation of depth of tensile crack (zo).

zo=2cγKa (4)

Here, c is the cohesion, γ is the unit weight of the soil, and Ka is the active earth pressure coefficient.

From Equation (4), cohesion (c) is directly proportional to the depth of tensile crack (zo). Hence, the larger value of cohesion provides larger value of depth of the tensile cracks in clays in active state

Therefore, the given statement is True_.

(e)

Expert Solution
Check Mark
To determine

Whether the statement “Lateral earth pressures increase linearly with depth” is true or false.

Answer to Problem 14.1P

The given statement is True_.

Explanation of Solution

Write the equation of lateral earth pressure (σh).

σh=Koγz

Here, Ko is the earth pressure coefficient at rest, γ is the unit weight of the soil, and z is the depth.

The lateral earth pressure equation is a linear equation and the lateral earth pressure (σh) is directly proportional to depth (z). Hence, the increase in depth increases the lateral earth pressure linearly.

Therefore, the given statement is True_.

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