In foundation engineering for expansive soils, what is the approximate ratio of the ultimate bearing capacity of a double under-reamed (UR) pile to that of a single under-reamed pile under comparable soil and loading conditions?

Introduction / Context:
Under-reamed (UR) piles are widely used in civil engineering to anchor foundations in expansive or collapsible soils. By providing one or more bulb-shaped enlargements near the pile base, these piles mobilize additional end-bearing and uplift resistance. This question checks recall of the practical increase in bearing capacity when a single-bulb pile is upgraded to a double-bulb configuration under similar conditions.

Given Data / Assumptions:

• Comparable soil properties and installation quality for both piles.
• Single UR pile has one enlargement; double UR pile has two enlargements (bulbs).
• Loads and boundary conditions are similar for fair comparison.

Concept / Approach:
The bearing capacity of UR piles comprises shaft friction and end-bearing contributions. Adding a second bulb increases both the effective end-bearing area and the confinement that helps mobilize shaft resistance. Empirical design guidelines and field practice often report an increase on the order of 1.4 to 1.6 times, with 1.5 being a commonly used rule-of-thumb for preliminary estimates.

Step-by-Step Solution:
Recognize that capacity scales with bulb area and mobilized soil resistance.Note from practice: double-bulb piles provide a substantial but not double (2×) increase versus a single bulb.Adopt the conventional approximate ratio used in preliminary design: about 1.5.

Verification / Alternative check:
Comparative load tests reported in geotechnical practice often show increases within this range, subject to spacing between bulbs, diameter, and soil type.

Why Other Options Are Wrong:

• 1.2 and 1.3 underestimate the added contribution of the second bulb.
• 1.7 and 2 overstate typical gains and are rarely justified without special conditions.

Common Pitfalls:
Assuming capacity doubles with two bulbs; ignoring installation effects or insufficient spacing that may limit the second bulb's effectiveness.

Final Answer:
1.5