Question

Information related to foundation design is provided in table below.

Column 1	Column 2
(I) Converse-Labarre formula	(P) Pile capacity from dynamic formula
(II) Hiley formula	(Q) Pile group efficiency
(III) Newmark's influence chart	(R) Bearing capacity factor of saturated clay
(IV) Skempton's equation	(S) Increase in vertical stress below footing

Option giving the CORRECT match between Column 1 and Column 2 is:

• A. (I) - (Q) ; (II) - (P) ; (III) - (S) ; (IV) - (R)
• B. (I) - (R) ; (II) - (S) ; (III) - (Q) ; (IV) - (P)
• C. (I) - (P) ; (II) - (Q) ; (III) - (S) ; (IV) - (R)
• D. (I) - (R) ; (II) - (S) ; (III) - (P) ; (IV) - (Q)

Hint:

Match each formula or chart to what quantity it actually computes: group action, dynamic driving capacity, stress below a footing, or a bearing capacity factor for clay.

Answer 1

The Correct Option is A

This question checks if you know what each named formula or chart in geotechnical engineering is actually used to calculate. Go through each item in Column 1 one at a time and fix its correct partner.

1. (I) Converse-Labarre formula: This is a group-action formula, it reduces the sum of individual pile capacities by an efficiency factor that depends on pile spacing, diameter, and the number of rows and columns in the group. So it belongs with (Q) Pile group efficiency.
2. (II) Hiley formula: This formula uses the hammer's striking energy, the pile set per blow, and the elastic losses in the pile cap, cushion and pile itself to back-calculate the pile's ultimate capacity during driving. That is a dynamic pile formula, so it pairs with (P) Pile capacity from dynamic formula.
3. (III) Newmark's influence chart: This chart is built from Boussinesq's stress theory and lets an engineer find the stress increase $\Delta \sigma_z$ at a point below the ground due to any shaped loaded area, by counting influence squares covered. It pairs with (S) Increase in vertical stress below footing.
4. (IV) Skempton's equation: This equation gives $N_c$, the bearing capacity factor used only for the $\phi = 0$ (purely cohesive, saturated clay) case, varying with the depth to width ratio of the footing. It pairs with (R) Bearing capacity factor of saturated clay.

Putting the four pairs together gives (I) - (Q), (II) - (P), (III) - (S), (IV) - (R), which is option (A). Checking the other options: options (B) and (D) swap Converse-Labarre with a bearing capacity factor, which is wrong since that formula has nothing to do with clay strength; option (C) wrongly pairs Hiley with pile group efficiency instead of the dynamic capacity formula.

Let's summarize:

• Converse-Labarre formula: pile group efficiency.
• Hiley formula: dynamic pile capacity from driving data.
• Newmark's chart: stress increase below a loaded area.
• Skempton's equation: $N_c$ for saturated clay.

So the correct match is option (A).