Which method of determining bearing capacity of soil uses Rankine's formula?
🔬 Understanding Methods for Bearing Capacity
The bearing capacity of soil can be determined using several different approaches. These can be broadly categorized into theoretical calculations based on soil properties and practical field tests that measure the soil's response directly.
⚖️ Detailed Analysis of the Methods
Let's evaluate each option to understand which category Rankine's formula belongs to.
(d) Analytical method
Why it's correct: An analytical method is a theoretical approach that uses mathematical formulas derived from the principles of soil mechanics to predict the bearing capacity. These formulas require known soil properties like density (γ), angle of internal friction (φ), and cohesion (c) as inputs. Rankine's theory provides one of the earliest and simplest such formulas for the ultimate bearing capacity (Qf) of cohesionless soil:
Qf = γD [(1+sinφ)/(1-sinφ)]²
Because it is a formula-based calculation, it is a prime example of an analytical method. Other famous analytical methods include those by Terzaghi, Meyerhof, and Skempton.
(a) Method of dropping a weight
What it is: This describes a dynamic field test, most notably the Standard Penetration Test (SPT). In this test, a standard weight is dropped from a standard height to drive a sampler into the ground. The number of blows required (the 'N' value) is recorded, which gives an empirical indication of the soil's density and strength. This is a field test, not an analytical calculation.
(b) Method of loading
What it is: This describes a static field test, specifically the Plate Load Test. In this test, a steel plate is placed on the ground at the foundation level, and a load is applied to it in increments. The settlement of the plate is measured at each step. The results are plotted to determine the ultimate bearing capacity of the soil at that location. This is a direct, physical measurement of the soil's response, not a theoretical calculation.
(c) Arithmetical method
What it is: This is not a standard term in geotechnical engineering for determining bearing capacity. The correct term for a calculation-based approach is "analytical method."