Step 1: Understanding the concept of Relative Compaction vs. Relative Density. - Relative Compaction is the ratio of field dry density to laboratory maximum dry density, expressed as a percentage. - Relative Density applies to coarse-grained soils, comparing void ratios. - However, the terms are sometimes used interchangeably in engineering practice.
Step 2: Effectiveness of Vibroflotation. - Vibroflotation is a deep compaction technique effective for granular soils. - It is not effective for highly cohesive soils, as they resist vibration.
Step 3: Understanding Zero Air Void Line vs. 100\% Saturation Line. - The Zero Air Void Line (ZAVL) represents maximum dry density achievable with full saturation (no air). - The 100% Saturation Line considers theoretical conditions. - Both are not identical because air content and compaction energy vary.
Step 4: Evaluating the Statements. - Statement 1 is debatable due to engineering usage. - Statement 2 is correct (Vibroflotation is ineffective for cohesive soils). - Statement 3 is correct (ZAVL and 100% Saturation Line differ). Thus, the correct answer is (C) 2 and 3 are correct.
A closed-loop system has the characteristic equation given by: $ s^3 + k s^2 + (k+2) s + 3 = 0 $.
For the system to be stable, the value of $ k $ is: