# Pavement Design Questions and Answers – Stresses in Flexible Pavement – 2

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This set of Pavement Design Questions and Answers for Campus interviews focuses on “Stresses in Flexible Pavement – 2”.

1. Which of the below is not a type of stress that is commonly found in flexible pavements?
a) Normal stress
b) Shear stress
c) Vertical stress

Explanation: There are three types of stresses that are commonly found in flexible pavement. They are the vertical stress, shear stress and radial stress. Normal stress is a type of stress that is perpendicular to the area.

2. When does shear stress occur in the pavement?
a) Friction between pavement and tyre
d) Weathering of the pavement surface

Explanation: Shear stress occurs when the load coming on the pavement is higher than the capacity of the pavement. A movement occurs in the base layer that leads to the shear stress in top pavement layers. This happens when the load approaches the critical point.

3. The vertical ______ on top of the subgrade controls the subgrade rutting.
a) Tensile stress
b) Tensile strain
c) Compressive stress
d) Compressive strain

Explanation: The vertical compressive strain on top of the subgrade controls the rutting of the subgrade. The horizontal tensile strain at the bottom of the bituminous layer controls the bottom-up fatigue cracking of the pavement.
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4. A flexible pavement of thickness 50 cm is laid over a subgrade. A circular load of radius 15 cm with a uniform contact pressure of 7 kg/cm2 is applied on the pavement. What would be the vertical stress on top of the subgrade?
a) 0.85 kg/cm2
b) 1.58 kg/cm2
c) 0.58 kg/cm2
d) 1.85 kg/cm2

Explanation: In order to find the vertical stress on top of subgrade, the following equation can be made use of $$σ=p \left[1-\frac{z^3}{(a^2+z^2 )^{3⁄2}}\right]$$. In the equation, p = 7 kg/cm2, a = 15 cm and z = 50 cm (pavement thickness 50 cm is laid over the subgrade, so the depth would be 50 cm).
$$σ=7 \left[1-\frac{50^3}{(15^2+50^2 )^{3⁄2}}\right]$$=0.85 kg/cm2

5. The design charts for computing vertical, tangential and radial stresses were first developed for a Poisson’s ratio of ______
a) 0.3
b) 0.4
c) 0.2
d) 0.5

Explanation: The design charts developed by Foster and Ahlvin in 1954 in order to compute vertical, tangential and the radial stresses. The charts were developed for Poisson’s ratio of 0.5. Later on, the charts were modified for a wide range of values.
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6. What is the right equation to find the vertical deflection in the pavement?
a) $$Δ=\frac{3p}{2E(a^2+z^2 )^{1∕2}}$$
b) $$Δ=\frac{3pa^2}{2E(a^2+z^2 )^{1∕2}}$$
c) $$Δ=\frac{3pa^2}{2E(a^2+z^2 )^{3∕2}}$$
d) $$Δ=\frac{3pa^2}{E(a^2+z^2 )^{1∕2}}$$

Explanation: The vertical stress in a homogeneous mass in the pavement can be found out using the equation $$Δ=\frac{3pa^2}{2E(a^2+z^2 )^{1∕2}}$$. In the equation the term p is the contact pressure, a is the radius of circular load, z is the depth and E is the modulus of elasticity of the pavement.

7. The deflection in the pavement surface is considered to be equal to deflection on top of the subgrade.
a) True
b) False

Explanation: In the one-layer theory, the deflection that occurs within the pavement layers is ignored. Hence, the deflection in the pavement surface is taken as equal to the deflection on top of the subgrade.

8. Find the vertical stress at a depth of 40 cm from the surface if the radius of the circular load is 17 cm and the contact pressure is 6.5 kg/cm2.
a) 0.43 kg/cm2
b) 1.43 kg/cm2
c) 0.45 kg/cm2
d) 1.45 kg/cm2

Explanation: $$σ=p \left[1-\frac{z^3}{(a^2+z^2 )^{3⁄2}}\right]$$ can be used to compute the vertical stress. The parameters from the question can be substituted in the above equation to obtain the vertical stress at a depth of 40 cm.
p = 6.5 kg/cm2, z = 40 cm and a = 17 cm
$$σ=6.5 \left[1-\frac{40^3}{(17^2+40^2 )^{3⁄2}}\right]$$=1.43 kg/cm2

9. The Boussinesq’s equation can be applied when the one-layer system is assumed as a half-space.
a) True
b) False

Explanation: The one-layer system is assumed as a homogeneous half-space. Boussinesq’s equation can be used when this is done. Half-space is an infinite area having infinite depth and a top plate on which the loads can be applied.

10. The equation for vertical deflection can also be written as $$Δ=\frac{pa}{E} F$$. What is the term F referred to as?
a) Deflection factor
b) Displacement factor
c) Deflection constant
d) Displacement constant

Explanation: The term F in the equation is referred to as a displacement factor. It can be expressed as $$F=\frac{3}{2(1+(\frac{z}{a})^2 )^{1∕2}}$$. It is useful while finding the depth using design charts.

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