MCQOPTIONS
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MCQOPTIONS
This section includes 180 Mcqs, each offering curated multiple-choice questions to sharpen your Geotechnical Engineering knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
The Boussinesq equation representing the tangential stress is ___________ |
| A. | \(τ_{rz}=\frac{3}{2πz^3} \left[\frac{1}{1+(\frac{r}{z})^2} \right]^{5/2}\) |
| B. | \(τ_{rz}=\frac{3Qr}{2π} \left[\frac{1}{1+(\frac{r}{z})^2} \right]^5\) |
| C. | \(τ_{rz}=\frac{3Qr}{2πz^3} \left[\frac{1}{1+(\frac{r}{z})^2} \right]^{\frac{5}{2}}\) |
| D. | \(τ_{rz}=\frac{3Q}{2πz^3} \left[\frac{1}{1+(\frac{r}{z})^2} \right]^2\) |
| Answer» D. \(τ_{rz}=\frac{3Q}{2πz^3} \left[\frac{1}{1+(\frac{r}{z})^2} \right]^2\) | |
| 2. |
If v is the displacement in y-direction, the linear strain component in is defined by __________ |
| A. | \(ε_Y=\frac{∂v}{∂y}\) |
| B. | \(ε_Y=\frac{∂y}{∂v}\) |
| C. | \(ε_Y=\frac{dy}{dv}\) |
| D. | εᵧ=v+y |
| Answer» B. \(ε_Y=\frac{∂y}{∂v}\) | |
| 3. |
The hydraulic gradient in terms of pore water pressure is given by _________ |
| A. | \(i=\frac{γ_w \overline{u}∂h}{∂z} \) |
| B. | \(i=\frac{\overline{u}∂h}{γ_w ∂z} \) |
| C. | \(i=\frac{\overline{u}∂h}{∂z} \) |
| D. | \(i=\frac{1}{γ_w}\frac{∂\overline{u}}{∂z} \) |
| Answer» E. | |
| 4. |
When the ratio of r/z equals to 1, the Boussinesq influence factor is ________ of the maximum. |
| A. | 23% |
| B. | 57% |
| C. | 17.7% |
| D. | 1.8% |
| Answer» D. 1.8% | |
| 5. |
The relation between the stress component in z-direction on a horizontal plane in Cartesian coordinates and polar coordinates for vertical line load is ___________ |
| A. | σz=σᵣ cos²θ |
| B. | σz=σᵣ cosec²θ |
| C. | σz=σᵣ cosθ |
| D. | σz=σᵣ sin²θ |
| Answer» B. σz=σᵣ cosec²θ | |
| 6. |
At a certain point within soil mass, the stresses are caused only because of surface loadings. |
| A. | True |
| B. | False |
| C. | May be True or False |
| D. | Can't say |
| Answer» C. May be True or False | |
| 7. |
The shearing strain component in X-Y plane is ________ |
| A. | \(Γ_{xy}=\frac{∂v}{∂x}+\frac{∂u}{∂y} \) |
| B. | \(Γ_{xy}=\frac{∂v}{∂x}-\frac{∂u}{∂y} \) |
| C. | \(Γ_{xy}=\frac{∂v}{∂y}+\frac{∂u}{∂x} \) |
| D. | \(Γ_{xy}=\frac{∂v}{∂y}-\frac{∂u}{∂x} \) |
| Answer» B. \(Γ_{xy}=\frac{∂v}{∂x}-\frac{∂u}{∂y} \) | |
| 8. |
The shear stress component in xz-plane in Cartesian coordinates for horizontal line load is ___________ |
| A. | \(τ_{xz}=\frac{2Q}{xzsinθcosθ} \) |
| B. | \(τ_{xz}=\frac{2Qxz^2}{π(x^2+z^2)^2} \) |
| C. | \(τ_{xz}=\frac{2Qx^3}{π(x^2+z^2)^2} \) |
| D. | \(τ_{xz}=\frac{2Qx^2 z}{π(x^2+z^2)^2} \) |
| Answer» E. | |
| 9. |
If XY pane is considered to be ground surface and the z-axis as depth, then this condition is known as _______ |
| A. | semi-infinite |
| B. | infinite |
| C. | finite |
| D. | semi- finite |
| Answer» B. infinite | |
| 10. |
Find the vertical pressure at depth 5m for a uniformly loaded circular area of 80 kN/m² load and radius of 5m. |
| A. | 51.72 kN/m² |
| B. | 54.12 kN/m² |
| C. | 78.325 kN/m² |
| D. | 12.24 kN/m² |
| Answer» B. 54.12 kN/m² | |
| 11. |
In Terzaghi’s Theory of one dimensional consolidation, the change in thickness of a layer during consolidation is ___________ |
| A. | significant |
| B. | insignificant |
| C. | large |
| D. | very large |
| Answer» C. large | |
| 12. |
The Boussinesq influence factor for uniformly distributed circular area is given by ____________ |
| A. | \(K_B= \left[1-\left[\frac{1}{1+(\frac{a}{z})^2}\right]^{\frac{3}{2}}\right] \) |
| B. | \(K_B= \left[1+\left[\frac{1}{1+(\frac{a}{z})^2}\right]^{\frac{3}{2}}\right] \) |
| C. | \(K_B= \left[\frac{1}{1+(\frac{a}{z})^2}\right]^{\frac{3}{2}} \) |
| D. | \(K_B= q\left[1-\left[\frac{1}{1+(\frac{a}{z})^2}\right]^{\frac{5}{2}}\right] \) |
| Answer» B. \(K_B= \left[1+\left[\frac{1}{1+(\frac{a}{z})^2}\right]^{\frac{3}{2}}\right] \) | |
| 13. |
The normal stress in y-direction in terms of effective stress is given by __________ |
| A. | σy= σy’-γw(h-he) |
| B. | σy= σy’+γw(h-he) |
| C. | σy= σy’/γw(h-he) |
| D. | σy= σy’*γw(h-he) |
| Answer» C. σy= σy’/γw(h-he) | |
| 14. |
The uniformly varying load is __________ in a beam. |
| A. | rate of loading increases linearly from zero |
| B. | rate of loading increases non-linearly from zero |
| C. | equal load at every point |
| D. | equal load only at supports |
| Answer» B. rate of loading increases non-linearly from zero | |
| 15. |
_________ chart is used to find the vertical stress on Westergaard’s equation. |
| A. | Influence chart |
| B. | Isocurve chart |
| C. | Isobar chart |
| D. | Fenske’s chart |
| Answer» B. Isocurve chart | |
| 16. |
If the influence value \(i_f=\frac{1}{35} \left[1-\left[\frac{1}{1+(\frac{a}{z})^2}\right]^\frac{3}{2}\right] \) for a uniformly loaded circular area, then the circular area is divided into _________ sectors. |
| A. | 20 |
| B. | 35 |
| C. | 7 |
| D. | 14 |
| Answer» C. 7 | |
| 17. |
When the ratio of r/z equals to 2, the Boussinesq influence factor is ________ of the maximum. |
| A. | 23% |
| B. | 57% |
| C. | 17.7% |
| D. | 1.8% |
| Answer» E. | |
| 18. |
In Terzaghi’s Theory of one dimensional consolidation, load is applied in _____________ |
| A. | one direction only |
| B. | two directions only |
| C. | three directions only |
| D. | none of the direction |
| Answer» B. two directions only | |
| 19. |
The vertical stress under the corner of a uniformly loaded rectangular area of size 2m*4m at depth 5m and load of 80 kN/m² is given by ___________ |
| A. | 6.22 kN/m² |
| B. | 7.45 kN/m² |
| C. | 8.12 kN/m² |
| D. | 9.23 kN/m² |
| Answer» C. 8.12 kN/m² | |
| 20. |
The Boussinesq’s vertical pressure σz due to line load is given by ________ |
| A. | \(σ_z=\frac{5q’}{πz}\frac{1}{[1+\frac{x}{z}^2 ]^2} \) |
| B. | \(σ_z=\frac{3q’}{πz}\frac{1}{[1+(\frac{x}{z})^2 ]^2} \) |
| C. | \(σ_z=\frac{2q’}{πz}\frac{1}{[1+(\frac{x}{z})^2 ]^2} \) |
| D. | \(σ_z=\frac{2q’}{z}\frac{1}{[1+⌊\frac{x}{z}⌋^2 ]^2} \) |
| Answer» D. \(σ_z=\frac{2q’}{z}\frac{1}{[1+⌊\frac{x}{z}⌋^2 ]^2} \) | |
| 21. |
For maximum vertical stress, the shear stress is _________ if the load is 30 kN and r=4m. |
| A. | 0.4356 kN/m² |
| B. | 0.1359 kN/m² |
| C. | 0.1518 kN/m² |
| D. | 0.3625 kN/m² |
| Answer» C. 0.1518 kN/m² | |
| 22. |
When the maximum vertical stress is 0.111 kN/m² at a radial distance of 4m from the point load is __________ kN. |
| A. | 0 |
| B. | 10 |
| C. | 20 |
| D. | 30 |
| Answer» D. 30 | |
| 23. |
An elastic body is said to be homogeneous if there are ______ elastic constants. |
| A. | 36 |
| B. | 20 |
| C. | 26 |
| D. | 30 |
| Answer» B. 20 | |
| 24. |
An elastic body is said to be isotropic if the elastic constants are ______ |
| A. | same only in y- direction |
| B. | same only in x- direction |
| C. | different in al direction |
| D. | same in all direction |
| Answer» E. | |
| 25. |
The linear strain of a diagonal is equal to half the sum shearing strain components. |
| A. | True |
| B. | False |
| C. | May be True or False |
| D. | Can't say |
| Answer» B. False | |
| 26. |
If the footing is flexible, then the distribution pressure is uniform. |
| A. | True |
| B. | False |
| C. | May be True or False |
| D. | Can't say |
| Answer» B. False | |
| 27. |
If the r/z ratio is 2, then the vertical pressure on a horizontal plane is given by _________ |
| A. | \(σ_z=\frac{0.0085Q}{z^2} \) |
| B. | \(σ_z=\frac{0.0844Q}{z^2} \) |
| C. | \(σ_z=\frac{0.2733Q}{z^2} \) |
| D. | \(σ_z=\frac{0.4775Q}{z^2} \) |
| Answer» B. \(σ_z=\frac{0.0844Q}{z^2} \) | |
| 28. |
The intensities of pressure below a point load where r=0 on axis of loading is ____________ |
| A. | \(σ_z=\frac{0.4775Q}{z^2} \) |
| B. | \(σ_z=\frac{0.7Q}{z^2} \) |
| C. | \(σ_z=\frac{0.4775Q}{z^3} \) |
| D. | \(σ_z=\frac{0.8Q}{z}\) |
| Answer» B. \(σ_z=\frac{0.7Q}{z^2} \) | |
| 29. |
The Boussinesq influence factor for r/z ratio equal to 1 is given by ____________ |
| A. | 0.3840 |
| B. | 0.5465 |
| C. | 0.0844 |
| D. | 0.2312 |
| Answer» D. 0.2312 | |
| 30. |
The relation between the stress component in x-direction on a horizontal plane in Cartesian coordinates and polar coordinates for vertical line load is ___________ |
| A. | σₓ=σᵣ tan²θ |
| B. | σₓ=σᵣ cosec²θ |
| C. | σₓ=σᵣ cosθ |
| D. | σₓ=σᵣ sin²θ |
| Answer» E. | |
| 31. |
The shearing strain component in Z-X plane is ________ |
| A. | \(Γ_{xz} =\frac{∂w}{∂y}+\frac{∂v}{∂z} \) |
| B. | \(Γ_{xz} =\frac{∂v}{∂x}-\frac{∂w}{∂y} \) |
| C. | \(Γ_{xz} =\frac{∂u}{∂z}+\frac{∂w}{∂x} \) |
| D. | \(Γ_{xz} =\frac{∂v}{∂y}-\frac{∂w}{∂x} \) |
| Answer» D. \(Γ_{xz} =\frac{∂v}{∂y}-\frac{∂w}{∂x} \) | |
| 32. |
If r/z ratio is 0.5 and load of 20 kN is acting at a point, then the vertical pressure at a depth 6m is ____________ |
| A. | 0.4356 kN/m² |
| B. | 0.244 kN/m² |
| C. | 0.1518 kN/m² |
| D. | 0.597 kN/m² |
| Answer» D. 0.597 kN/m² | |
| 33. |
An isobar diagram consists of __________The vertical pressure distribution on any horizontal plane at a depth z below the ground due to concentrated load is ___________ |
| A. | family of isobars of various intensities\(σ_z=K_B \frac{Q}{z} \) |
| B. | single isobar only\(σ_z=K_B \frac{Q}{z^2} \) |
| C. | two isobars only\(σ_z=K_B \frac{z}{Q} \) |
| D. | isobars of same intensities\(σ_z=K_B \frac{Q}{z^3} \) |
| Answer» C. two isobars only\(σ_z=K_B \frac{z}{Q} \) | |
| 34. |
If a load of 30 kN is acting on a point on the ground surface, then the intensity of vertical stress directly below the point on its axis of loading at a depth of 2m is given by __________ |
| A. | 4.356 kN/m² |
| B. | 2.44 kN/m² |
| C. | 3.58kN/m² |
| D. | 5.97 kN/m² |
| Answer» D. 5.97 kN/m² | |
| 35. |
From the symmetry and orthogonality of principal planes ____________ |
| A. | both horizontal and vertical planes will be devoid of shear stress |
| B. | both horizontal and vertical planes will have shear stress |
| C. | only vertical plane has shear stress |
| D. | only horizontal plane has shear stress |
| Answer» B. both horizontal and vertical planes will have shear stress | |
| 36. |
If the r/z ratio is 0.5, then the vertical pressure on a horizontal plane is given by _________ |
| A. | \(σ_z=\frac{0.56Q}{z^3} \) |
| B. | \(σ_z=\frac{0.4775Q}{z^3} \) |
| C. | \(σ_z=\frac{0.2733Q}{z^2} \) |
| D. | \(σ_z=\frac{0.4775Q}{z^2} \) |
| Answer» D. \(σ_z=\frac{0.4775Q}{z^2} \) | |
| 37. |
An isobar is a curved surface of the shape of _________ |
| A. | circular |
| B. | rectangle |
| C. | bulb |
| D. | hexagon |
| Answer» D. hexagon | |
| 38. |
The shearing strain component in Y-Z plane is ________ |
| A. | \(Γ_{yz} =\frac{∂w}{∂y}+\frac{∂v}{∂z} \) |
| B. | \(Γ_{yz} =\frac{∂v}{∂x}-\frac{∂w}{∂y} \) |
| C. | \(Γ_{yz} =\frac{∂v}{∂y}+\frac{∂w}{∂x} \) |
| D. | \(Γ_{yz} =\frac{∂v}{∂y}-\frac{∂w}{∂x} \) |
| Answer» B. \(Γ_{yz} =\frac{∂v}{∂x}-\frac{∂w}{∂y} \) | |
| 39. |
The normal stress in x-direction in terms of effective stress is given by __________ |
| A. | σx= σx’+γw(h-he) |
| B. | σx= σx’*γw(h-he) |
| C. | σx= σx’-γw(h-he) |
| D. | σx= σx’ |
| Answer» B. σx= σx’*γw(h-he) | |
| 40. |
The normal stress in z-direction in terms of effective stress is given by __________ |
| A. | σz= γw(h-he) |
| B. | σz= σz’ |
| C. | σz= σz’+γw(h-he) |
| D. | σz= σz’-γw(h-he) |
| Answer» D. σz= σz’-γw(h-he) | |
| 41. |
The contact pressure of a footing was found to be 85 kN/m² for a load of 212.5 kN. What will be the contact area? |
| A. | 1 m² |
| B. | 2.5 m² |
| C. | 3 m² |
| D. | 3.5 m² |
| Answer» C. 3 m² | |
| 42. |
Find the depth z for a uniformly loaded circular area of 80 kN/m² load and radius of 50m. k=0.9160. |
| A. | 2m |
| B. | 4m |
| C. | 25m |
| D. | 50m |
| Answer» D. 50m | |
| 43. |
The velocity with which the excess pore water flows is _________ |
| A. | \(v=\frac{k}{2}\frac{∂\overline{u}}{∂z}\) |
| B. | \(v=\frac{1}{γ_w}\frac{∂\overline{u}}{∂z}\) |
| C. | \(v=\frac{k}{γ_w}\frac{∂\overline{u}}{∂z}\) |
| D. | \(v=\frac{∂\overline{u}}{∂z}\) |
| Answer» D. \(v=\frac{∂\overline{u}}{∂z}\) | |
| 44. |
The vertical stress at a point within soil mass at a depth z is ____________ |
| A. | σz=γ+z |
| B. | σz=γ-z |
| C. | σz=γ/z |
| D. | σz=γz |
| Answer» E. | |
| 45. |
The σz in terms of stress function is given by __________ |
| A. | \(\frac{∂Φ}{∂z}\) |
| B. | \(\frac{∂^2 Φ}{∂z^2}\) |
| C. | \(\frac{∂^2 Φ}{∂x^2}\) |
| D. | \(\frac{∂Φ}{∂x}\) |
| Answer» D. \(\frac{∂Φ}{∂x}\) | |
| 46. |
For two dimensional case, for both plane stress as well as plain strain case the compatibility equation is _______ |
| A. | \(\frac{∂^2 ε_x}{∂z^2} +\frac{∂^2 ε_z}{∂x^2} =\frac{∂^2 Γ_{xz}}{∂x∂z}\) |
| B. | \(\frac{∂^2 ε_z}{∂z^2} +\frac{∂^2 ε_y}{∂x^2} =\frac{∂^2 Γ_{zy}}{∂z∂y}\) |
| C. | \(\frac{∂^2 ε_x}{∂y^2} +\frac{∂^2 ε_y}{∂x^2} =\frac{∂^2 Γ_{xy}}{∂x∂y}\) |
| D. | \(\frac{∂^2 ε_z}{∂z^2} +\frac{∂^2 ε_y}{∂x^2} =0\) |
| Answer» B. \(\frac{∂^2 ε_z}{∂z^2} +\frac{∂^2 ε_y}{∂x^2} =\frac{∂^2 Γ_{zy}}{∂z∂y}\) | |
| 47. |
In Terzaghi’s Theory of one dimensional consolidation, the deformation occurs in __________ |
| A. | one direction only |
| B. | two directions only |
| C. | three directions only |
| D. | none of the direction |
| Answer» B. two directions only | |
| 48. |
____________ is not the vertical pressure distribution diagram, which can be prepared by Boussinesq’s theory. |
| A. | stress isobars |
| B. | vertical pressure distribution on a horizontal plane |
| C. | horizontal pressure distribution on a horizontal plane |
| D. | vertical pressure distribution on a vertical plane |
| Answer» D. vertical pressure distribution on a vertical plane | |
| 49. |
If a uniformly loaded circular area is divided into 20 sectors, then the influence value if is given by ___________ |
| A. | \(\frac{1}{20}\left[1-\left[\frac{1}{1+(\frac{a}{z})^2}\right]^\frac{3}{2}\right]\) |
| B. | \(20\left[1-\left[\frac{1}{1+(\frac{a}{z})^2}\right]^\frac{3}{2}\right]\) |
| C. | \(20\left[1-\left[\frac{1}{1+(\frac{a}{z})^2}\right]^\frac{5}{2}\right]\) |
| D. | \(\frac{1}{20}\left[1-\left[\frac{1}{1+(\frac{a}{z})^2}\right]^\frac{5}{2} \right]\) |
| Answer» B. \(20\left[1-\left[\frac{1}{1+(\frac{a}{z})^2}\right]^\frac{3}{2}\right]\) | |
| 50. |
If u is the displacement in x-direction, the linear strain component in is defined by __________ |
| A. | \(ε_X=\frac{∂u}{∂x}\) |
| B. | \(ε_X=\frac{∂x}{∂u}\) |
| C. | \(ε_X=\frac{dx}{du}\) |
| D. | εₓ=x+u |
| Answer» B. \(ε_X=\frac{∂x}{∂u}\) | |