Concrete mix proportioning (arbitrary method): identify which of the following nominal proportions does NOT conform to the usual arbitrary method used for preliminary concrete mix selection in civil engineering practice.

Introduction / Context:
On small works and in preliminary planning, many engineers still encounter the so-called “arbitrary method” (or nominal method) of concrete proportioning, which uses fixed volume ratios of cement : fine aggregate : coarse aggregate such as 1 : 2 : 4 or 1 : 3 : 6. Recognizing which proportions are customary helps avoid mixes that are either too lean (poor strength and durability) or impractically graded for field use.

Given Data / Assumptions:

• The options list typical three-number volume ratios used historically as nominal mixes.
• We assume normal weight aggregates and ordinary Portland cement for general reinforced or plain concrete.
• “Conformation to arbitrary method” means commonly accepted legacy nominal mixes (not modern design mixes).

Concept / Approach:
Traditional nominal mixes map roughly to strength classes: 1 : 3 : 6 (≈ M10), 1 : 2 : 4 (≈ M15), 1 : 1.5 : 3 (≈ M20), 1 : 1 : 2 (≈ M25). For very lean plain concrete or bedding, 1 : 4 : 8 or similar is also seen. A proportion like 1 : 2 : 8 is atypical because it combines a relatively small sand fraction with an excessively large coarse aggregate fraction, leading to poor cohesiveness and segregation risk, and it does not fall in the common nominal families.

Step-by-Step Solution:
List standard nominal sets commonly cited: 1:3:6, 1:2:4, 1:1.5:3, 1:1:2; for lean works 1:4:8 also appears.Compare with options and screen out recognized sets (1:1:2, 1:2:4, 1:3:6, 1:4:10 ~ akin to 1:4:8 family).Identify 1:2:8 as non-standard and impractically lean in coarse aggregate.Conclude that 1 : 2 : 8 does not conform to the arbitrary method.

Verification / Alternative check:
Check any standard schedule of rates or legacy handbooks: the cited nominal sets do not include 1:2:8, reinforcing that it is not a commonly accepted arbitrary proportion.

Why Other Options Are Wrong:

• 1 : 1 : 2 and 1 : 2 : 4 and 1 : 3 : 6: canonical nominal mixes for richer to leaner concrete.
• 1 : 4 : 10: though very lean, it aligns with the family of bedding/lean concrete (similar to 1:4:8).

Common Pitfalls:
Assuming any “1 : something : something” is valid; ignoring the paste demand and workable grading needed to avoid segregation.

Final Answer:
1 : 2 : 8