27.3.1. Equivalent single wheel load

Equivalent single wheel load (ESWL) is the single wheel load having the same contact pressure, which produces same value of maximum stress, deflection, tensile stress or contact pressure at the desired depth.

The Equivalent Single Wheel Load (ESWL) represents a simplified way to quantify the load exerted by a tire on the pavement. It determines the stress, deformation, and pressure a single wheel would have if it were identical to the effects produced by dual wheels or other configurations. By focusing on ESWL, engineers can evaluate the potential impact on pavement without needing to analyze complex wheel arrangements separately.

Imagine you have two different pairs of shoes: one very heavy and one much lighter. When you step on a surface, the heavier shoe will exert more pressure on that surface than the lighter one. However, if multiple people with different shoe weights and styles walk together, it may be helpful to define a single, representative shoe weight to understand that foot traffic's overall impact. Similarly, in pavement design, ESWL allows engineers to summarize the effects of multiple wheel loads.

The procedure of finding the ESWL for equal stress criteria is provided below. This is a semi-rational method, known as Boyd and Foster method, based on the following assumptions: equalancy concept is based on equal stress; contact area is circular; influence angle is 45o; and soil medium is elastic, homogeneous, and isotropic half space.

The Boyd and Foster method is rooted in several key assumptions about how stress is distributed through the layers of the pavement. It presupposes that the contact area of the load is circular—a typical shape when you think of tires on a surface. By working under the influence angle of 45 degrees, which is where stress peaks under this type of loading, and considering the earth's material to be uniform, engineers can derive an equation to determine the equivalent load on a single wheel.

Think of a trampoline surface that deforms when someone jumps on it. If a child jumps in the center (let’s assume they weigh as much as two kids), the surface will dip the most right under them, but the effects will be felt sideways as well, similar to how pressure distributes through a circular contact area on the ground. The Boyd and Foster approach quantifies this distribution in a systematic way to understand and predict how much stress a single wheel imparts on the pavement.

The ESWL is given by: 0.301log(z) / 10 d/2 log(ESWL) = log(P) + (27.1) 10 10 log(2S) / 10 d/2 where P is the wheel load, S is the center to center distance between the two wheels, d is the clear distance between two wheels, and z is the desired depth.

The formula presented for calculating ESWL incorporates logarithmic functions and several variables that reflect the arrangement of the wheels and their load. Each term in the equation corresponds to elements that affect how pressure is transmitted through the surface material, thus helping determine the equivalent load for a single wheel configuration. Adjusting any of these inputs like wheel load (P) or spacing (S, d) directly modifies the calculated ESWL, enabling tailored designs based on actual conditions.

Consider making a fruit juice blend with various fruits. Each fruit contributes different flavors, weights, and textures to the final drink. By adjusting the ratio of each fruit, you determine the final taste and consistency. In the same way, adjusting the parameters in the ESWL formula allows designers to hone in on a specific 'flavor' of pavement performance that meets traffic and environmental needs.

Example 1: A set of dual tyres has a total load of 4090 kg, a contact radius of 11.4 cm and a center to center tyre spacing of 34.3 cm. Find the ESWL by Boyd & Foster method for a depth of 34.3 cm. [Ans: 3369.3 kg]. Example 2: Calculate ESWL by equal stress criteria for a dual wheel assembly carrying 2044 kg each for a pavement thickness of 5, 15, 20, 25 and 30 cms. The distance between walls of the tyre is 11 cm. Use either graphical or functional methods. (Hint: P=2044kg, d=11cm, s=27cm). [Ans: 2044, 2760, 3000, 3230, and 4088].

These examples highlight the practical application of the ESWL calculation, demonstrating how to determine the equivalent load based on various inputs. The first example outlines how to apply the Boyd and Foster method to determine an ESWL, whereas the second example encourages using either graphical or functional methods to analyze different pavement designs. Both approaches employ the same fundamental principles but vary in execution, ideal for turfing research and real-world evaluation.

Think about following a recipe for cookies. Adjusting the amount of sugar can change the overall sweetness of the batch, much like how varying wheel loads and distances will influence the ESWL outcome. Each example here tests different ‘cookie recipes’ that aim for ideal results under specific pavement conditions.

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