In compaction test 1, a 10 kg hammer falls 500 mm on each of 3 layers with 25 blows per layer. In compaction test 2, a 5 kg hammer falls 250 mm on each of 6 layers with 25 blows per layer. If the same mould is used, what is the ratio of the compaction energy of test 1 to that of test 2?

Asked in SSC JE 05/06/2024 (Morning)

Detailed Explanation

Compaction energy is the total work done by the rammer on the soil in the mould. Each blow delivers the weight of the rammer times its height of fall, so the total energy depends on four things: rammer weight, drop height, number of layers and blows per layer. Because both tests use the same mould, the energy per unit volume is simply proportional to this total work.

\[ E = \frac{W \times h \times n \times N}{V} \]

Test 1: \(E_1 \propto 10 \times 0.5 \times 3 \times 25 = 375\)

Test 2: \(E_2 \propto 5 \times 0.25 \times 6 \times 25 = 187.5\)

Ratio: \(E_1 / E_2 = 375 / 187.5 = 2\)

Why “2” Is Correct

Test 2 halves the rammer weight and halves the drop height (that alone cuts energy to one quarter), but it doubles the number of layers (which doubles it back). Net effect: test 2 gets half the energy of test 1, so the ratio is 2.

Why the Other Options Are Wrong

• A. 8: 8 would mean test 1 has eight times the energy of test 2; that happens only if the doubled layers in test 2 are ignored and another factor is miscounted.
• B. 4: 4 is what you get if you compare only W×h (10×0.5 ÷ 5×0.25 = 4) and forget that test 2 uses twice as many layers.
• D. 0.5: 0.5 is the inverse ratio (E₂/E₁); the question asks for test 1 to test 2.

Key Concepts for Students

• IS light compaction energy is about 593 kJ/m³; heavy compaction is about 2700 kJ/m³ (roughly 4.5 times more).
• Doubling layers or blows doubles energy; doubling both weight and drop quadruples it.
• More compaction energy gives a higher maximum dry density and a lower optimum moisture content.

Practice more: this is question 1 of Compaction of Soil MCQs – Part 1. Try the whole set and check every answer instantly.