The Group Index method takes three ordinary soil test results — how fine the soil is, its liquid limit and its plasticity index — and combines them into one number between 0 and 20 that describes how poor the subgrade is.
The higher that number, the worse the soil, and the thicker the pavement must be. This post covers the formula, the awkward limits on its terms, and how thickness is actually obtained.
What Group Index Is
Group index value is an arbitrary index assigned to soil types in numerical equations, based on the percent fines, liquid limit and plasticity index.
The word arbitrary is honest and important. The GI number does not measure a physical quantity like stress or strength. It is a scoring system, invented so that soils can be ranked against one another and matched to a design chart.
The Two Key Facts
- The GI value of soils varies in the range 0 to 20.
- The higher the GI value, the weaker the soil subgrade — hence the greater the pavement thickness required.
Note that this runs the opposite way to CBR. A high CBR is good; a high GI is bad. Students frequently reverse one of them.
The Group Index Formula
G.I. = 0.2a + 0.005ac + 0.01bd
The Four Terms and Their Limits
| Term | Definition | Permitted Range |
|---|---|---|
| a | p − 35 | Whole number, 0 to 40 |
| b | p − 15 | Whole number, 0 to 40 |
| c | wL − 40 | Whole number, 0 to 20 |
| d | IP − 10 | Whole number, 0 to 20 |
Symbols
| Symbol | Meaning |
|---|---|
| p | Percentage finer — the percentage of soil passing the 0.075 mm sieve |
| wL | Liquid limit |
| IP | Plasticity index = wL − wP |
| wP | Plastic limit |
How the Limits Work — the Part That Costs Marks
Every term is clipped at both ends, and this is where most errors happen in numericals.
Rule: compute the value, then clip it.
If the result is negative, take it as 0.
If the result exceeds the upper limit, take the upper limit.
Worked Illustrations
| Situation | Raw Calculation | Value Used |
|---|---|---|
| p = 30, so a = 30 − 35 | −5 | 0 (negative clipped) |
| p = 90, so a = 90 − 35 | 55 | 40 (exceeds upper limit) |
| wL = 35, so c = 35 − 40 | −5 | 0 |
| wL = 70, so c = 70 − 40 | 30 | 20 (c is capped at 20) |
| IP = 8, so d = 8 − 10 | −2 | 0 |
Why the Clipping Makes Sense
The negative-to-zero rule has a clear physical meaning. If a soil has only 30 percent fines, then a comes out negative — but a soil cannot be better than perfect in that respect. Zero is the floor, meaning “this factor contributes nothing to the group index”.
The upper caps work the same way at the other end. Beyond a certain amount of fines or plasticity, the soil is already as bad as the method recognises, and further increases add nothing.
This is also why GI ranges from 0 to 20. Put the maximum permitted values into the formula and the total cannot exceed 20; put the minimum values in and it is zero.
Traffic Classification
The anticipated traffic is estimated and designated as light, medium or heavy:
| Traffic Volume (commercial vehicles) | Number of Vehicles per Day |
|---|---|
| Light | Less than 50 |
| Medium | 50 to 300 |
| Heavy | Over 300 |
Note that these are commercial vehicles only — cars are not counted. That is sensible, since a car does negligible damage to a pavement compared with a loaded truck.
Finding the Pavement Thickness
The design procedure runs as follows:
- Find the GI value of the soil from the formula.
- Estimate the anticipated traffic and classify it as light, medium or heavy.
- Read the required thicknesses from the design chart or table.
What Depends on What
The thickness of the sub-base depends only on the group index value.
The combined thickness of surface and base course depends on both the traffic and the GI value.
This distinction is frequently examined, and the logic behind it is sound. The sub-base sits directly on the soil and its job is to bridge over a poor subgrade — so it responds to soil quality alone. The surface and base courses carry the traffic itself, so they must respond to both the traffic load above and the soil support below.
How Sub-base Thickness Is Obtained in Practice
In actual practice, curves are available for the total combined thickness and for the thickness of surface and base course only, corresponding to traffic and GI value.
Sub-base thickness = Total thickness − (Surface + Base course) thickness
So the sub-base is obtained by subtraction, not read directly.
Two Limitations of the Method
- The GI method does not consider the quality of material used for the pavement.
- The same thickness is suggested for poor and good quality material.
Why This Is a Serious Weakness
The two limitations are really one idea stated twice, and it is worth appreciating how odd the consequence is.
Suppose two engineers design pavements on identical subgrade for identical traffic. One proposes a high quality crushed stone base; the other proposes a marginal, weak material. The Group Index method gives both of them the same thickness.
That cannot be right physically — a stronger base spreads load better and should permit a thinner section. The method simply has no input for material quality, because it looks only at the soil.
This is the characteristic weakness of empirical methods discussed in the previous topic, and it is exactly why the CBR method also carries the same criticism, and why the triaxial and Burmister methods, which do account for material modulus, were developed.
Formula Summary
| Quantity | Expression or Value |
|---|---|
| Group index | GI = 0.2a + 0.005ac + 0.01bd |
| a | p − 35, range 0 to 40 |
| b | p − 15, range 0 to 40 |
| c | wL − 40, range 0 to 20 |
| d | IP − 10, range 0 to 20 |
| p | Percentage passing 0.075 mm sieve |
| IP | wL − wP |
| GI range | 0 to 20 |
| Light traffic | Less than 50 commercial vehicles per day |
| Medium traffic | 50 to 300 |
| Heavy traffic | Over 300 |
Quick Revision Notes
- GI is an arbitrary index based on percent fines, liquid limit and plasticity index.
- GI ranges from 0 to 20; higher GI means weaker subgrade and greater thickness required.
- GI = 0.2a + 0.005ac + 0.01bd.
- a and b are capped at 40; c and d are capped at 20; all are clipped to 0 if negative.
- p is the percentage passing the 0.075 mm sieve.
- Traffic: light below 50, medium 50 to 300, heavy above 300 commercial vehicles per day.
- Sub-base thickness depends only on GI.
- Surface plus base course thickness depends on both traffic and GI.
- Sub-base thickness is found by subtracting surface plus base from the total.
- Two limitations: quality of pavement material is not considered, and the same thickness results for poor and good material.
Mistakes Students Commonly Make
- Forgetting to clip negative values to zero. This is the single biggest source of wrong answers in GI numericals.
- Applying the wrong cap. a and b cap at 40; c and d cap at 20.
- Assuming a high GI means good soil. A high GI means weak soil — the opposite of CBR.
- Using the total vehicle count for traffic classification. Only commercial vehicles are counted.
- Saying sub-base thickness depends on traffic. It depends on GI only.
- Using the wrong sieve size for p. It is 0.075 mm.
- Forgetting that IP must first be calculated as wL − wP before finding d.
Conclusion
The Group Index method compresses a soil’s fineness and plasticity into a single score from 0 to 20, where higher means worse. The formula itself is easy; the marks are decided by the clipping rules on a, b, c and d, so compute each term and then clip it before substituting. Remember that sub-base thickness follows GI alone while surface and base follow both GI and traffic, and remember the method’s honest limitation — it says nothing at all about the quality of the material you build with.
Frequently Asked Questions
What is group index?
An arbitrary index assigned to soil types in numerical equations, based on the percent fines, liquid limit and plasticity index of the soil.
What is the range of group index values?
0 to 20.
Does a higher group index mean better or worse soil?
Worse. The higher the GI value, the weaker the soil subgrade, and hence the greater the pavement thickness required.
What is the group index formula?
GI = 0.2a + 0.005ac + 0.01bd, where a = p − 35, b = p − 15, c = wL − 40 and d = IP − 10.
What are the limits on a, b, c and d?
a and b are whole numbers between 0 and 40, while c and d are whole numbers between 0 and 20. Any negative result is taken as zero, and any value exceeding the upper limit is taken as that limit.
What is p in the formula?
The percentage finer, meaning the percentage of soil passing the 0.075 mm sieve.
How is traffic classified in this method?
Light is less than 50 commercial vehicles per day, medium is 50 to 300, and heavy is over 300.
What does the sub-base thickness depend on?
Only on the group index value.
What does the surface and base course thickness depend on?
Both the anticipated traffic and the group index value.
How is sub-base thickness obtained in practice?
By subtracting the combined thickness of surface and base course from the total thickness, both of which are read from design curves.
What are the limitations of the group index method?
It does not consider the quality of the material used in the pavement, and it suggests the same thickness whether poor or good quality material is used.