Which of the following statements (with regard to earth pressure) are correct?
A. Any movement of the retaining wall away from the fill corresponds to active earth pressure.
B. Under earthquake loading, the pore pressure decreases in saturated silty soil.
C. Coulomb's earth pressure theory does not take the roughness of wall into consideration.
D. Rankine's earth pressure theory considers that the retaining wall has a vertical backfill.
Step 1: Analyze statement A.
When the wall moves away from the backfill, active earth pressure develops.
Step 2: Analyze statement B.
During earthquake loading, pore pressure in saturated silty soils generally increases, not decreases.
Step 3: Analyze statement C.
Coulomb's theory does consider wall friction (surface roughness).
Step 4: Analyze statement D.
Rankine's theory assumes vertical wall with horizontal ground surface and neglects wall friction.
Step 5: Conclusion.
Correct statements are A and D only.
The solution(s) of the ordinary differential equation $y'' + y = 0$, is:
(A) $\cos x$
(B) $\sin x$
(C) $1 + \cos x$
(D) $1 + \sin x$
Choose the most appropriate answer from the options given below:
For the matrix, $A = \begin{bmatrix} -4 & 0 \\ -1.6 & 4 \end{bmatrix}$, the eigenvalues ($\lambda$) and eigenvectors ($X$) respectively are:
The value of $\iint_S \vec{F} \cdot \vec{N} \, ds$ where $\vec{F} = 2x^2y \hat{i} - y^2 \hat{j} + 4xz^2 \hat{k}$ and $S$ is the closed surface of the region in the first octant bounded by the cylinder $y^2 + z^2 = 9$ and the planes $x = 0, x = 2, y = 0, z = 0$, is:
The value of the integral $\displaystyle \oint_C \frac{z^3 - 6}{2z - i} \, dz$, where $C: |z| \leq 1$, is: