The CBR method is the most widely used flexible pavement design method in India. Its logic is simple — measure how strong the subgrade is, then provide enough thickness above it to protect it from traffic.
This post covers the design procedure, the thickness formula and its important restriction, the eight IRC recommendations, and the method’s limitations.
What the Method Is Based On
The CBR method of flexible pavement design is based on the strength parameter of the subgrade soil and subsequent materials.
Note the phrase “and subsequent materials”. The method is not limited to the soil alone — it can be applied at every layer interface, which is what makes the layer-by-layer design possible.
The Design Procedure
- Evaluate the soaked CBR value of the soil subgrade.
- Choose the appropriate design curve, either by taking the design wheel load or by considering the anticipated traffic.
- Read off the total thickness of pavement needed to cover a subgrade of that CBR value.
Designing the Sub-base Separately
If a material superior to the subgrade soil is available and can be used as a sub-base course, the design can be refined:
- The thickness of construction over that material is obtained from the design chart, using the CBR value of the sub-base.
- Then:
Thickness of sub-base = Total thickness − Thickness over the sub-base
The principle here is worth grasping, because it is the heart of the method. Every layer must be protected by whatever lies above it. A weak subgrade needs a lot of cover; a stronger sub-base needs less. So you enter the chart twice, once with each CBR value, and the difference between the two answers is the sub-base thickness.
The Thickness Formula
Based on the CBR value of any material over which a flexible pavement is required, the thickness of pavement over it is:
t = √[ (1.75 P / CBR) − (A / π) ]
An equivalent form, writing the contact area in terms of tyre pressure:
t = √[ 1.75 P (1/CBR − 1/(pπ)) ]
Notation
| Symbol | Meaning | Unit |
|---|---|---|
| t | Pavement thickness | cm |
| P | Wheel load | kg |
| CBR | California Bearing Ratio | percent |
| p | Tyre pressure | kg/cm2 |
| A | Area of contact | cm2 |
If the radius of the contact area is r, then A = πr2. And since pressure is load divided by area, A = P / p.
The Critical Restriction
This formula is applicable only when the CBR value of the subgrade soil is less than 12 percent.
This restriction is asked frequently and follows directly from the nature of empirical methods. The relationship was established from observations on relatively weak subgrades. Above 12 percent CBR the data simply did not support it, so the formula must not be extrapolated there.
Reading the Formula
Both terms make physical sense:
- 1.75P/CBR — thickness increases with wheel load and decreases as the subgrade gets stronger. A weak soil (small CBR) makes this term large.
- − A/π — a larger contact area spreads the same load over more ground, so less thickness is needed. Hence it is subtracted.
The Eight IRC Recommendations (IRC 37:1970)
1. Test on Remoulded Soils
The CBR test should be performed on remoulded soils in the laboratory. In-situ tests are not recommended for design purposes.
Laboratory conditions can be controlled and repeated; field conditions vary from point to point and cannot be standardised.
2. Compaction Standard
The soil should be compacted at OMC (optimum moisture content) to Proctor density.
3. Soaking
The test sample should be soaked in water for 4 days before testing.
Exception: in dry zones with less than 50 cm rainfall, soaking is not necessary.
Soaking simulates the worst condition a subgrade will face — a saturated soil during the monsoon. Designing for that means the pavement is safe year-round. Where rainfall is genuinely low, that worst case never arrives, so the requirement is relaxed.
4. Number of Samples
At least 3 samples should be tested on each type of soil at the same density and moisture content. If the variation exceeds the permissible value, an average of six samples should be considered.
| Permissible Variation | CBR Range |
|---|---|
| 3 % | Up to 10 % |
| 5 % | 10 to 30 % |
| 10 % | 30 to 60 % |
Notice that the tolerance widens as CBR increases. A 3 percent scatter matters enormously in a weak soil of CBR 5, and hardly at all in a strong one of CBR 50.
5. Compaction of Top Subgrade
The top 50 cm of subgrade should be compacted to at least 95 to 100 percent of Proctor density.
The top 50 cm matters most because that is where the stress from a wheel load is highest. Deeper down, the load has spread out and the intensity has fallen.
6. Estimating Future Traffic
A = P (1 + r)n+10
| Symbol | Meaning |
|---|---|
| A | Number of heavy vehicles per day for design (weight above 3 tonnes) |
| P | Number of heavy vehicles per day at last count |
| r | Annual rate of increase of vehicles |
| n | Number of years between the last count and the year of completion of construction |
P should be a seven days’ average.
r can be taken as 7.5 % for roads in rural areas.
Why the Exponent Is n + 10
This is the detail most often missed. The exponent contains two separate periods:
- n years — from the traffic count until the road is finished being built
- 10 years — the design life of the pavement after opening
Traffic grows during both, so the design must anticipate growth over the whole span. Using n alone would design for the traffic on opening day and leave nothing for the decade that follows.
7. Axle Load Applicability
The design thickness applies to:
- Single axle loads up to 8,200 kg
- Tandem axle loads up to 14,500 kg
For higher axle loads, the thickness values should be further increased.
8. Large Aggregate in Sub-base
When sub-base course materials contain a substantial proportion of aggregates above 20 mm size, the CBR value of those materials would not be valid for designing the subsequent layer above them.
The reason is a matter of scale. The CBR plunger is only 50 mm in diameter, so a 20 mm stone under it is a substantial obstruction rather than part of a representative sample. The reading becomes a property of where that particular stone sat, not of the material as a whole.
Limitations of the CBR Method
The CBR method gives the total thickness requirement above a subgrade, and this thickness remains the same irrespective of the quality of materials used in the component layers.
Therefore the component materials should be judiciously chosen for durability and economy.
This is the same criticism levelled at the Group Index method — a characteristic weakness of empirical approaches. The chart tells you how much to build, not what to build with. Two pavements of identical thickness, one of high quality crushed stone and one of marginal material, satisfy the method equally, though they will not perform equally.
Formula Summary
| Quantity | Expression or Value |
|---|---|
| Pavement thickness | t = √[(1.75P/CBR) − (A/π)] |
| Alternative form | t = √[1.75P(1/CBR − 1/pπ)] |
| Formula validity | CBR of subgrade less than 12 % |
| Contact area | A = πr2 = P/p |
| Sub-base thickness | Total thickness − thickness over sub-base |
| Traffic growth | A = P(1 + r)n+10 |
| Growth rate for rural roads | r = 7.5 % |
| Soaking period | 4 days |
| Dry zone exemption | Rainfall below 50 cm |
| Heavy vehicle definition | Weight above 3 tonnes |
| Single axle limit | 8,200 kg |
| Tandem axle limit | 14,500 kg |
| Top subgrade compaction | Top 50 cm at 95 to 100 % Proctor density |
Quick Revision Notes
- CBR method is based on the strength parameter of subgrade soil and subsequent materials.
- The soaked CBR value is used for design.
- t = √[(1.75P/CBR) − (A/π)], valid only when subgrade CBR is less than 12 %.
- Sub-base thickness = total thickness − thickness over the sub-base.
- IRC recommends remoulded laboratory samples; in-situ tests are not recommended for design.
- Compaction at OMC to Proctor density.
- 4 days soaking, except in dry zones with rainfall below 50 cm.
- Test at least 3 samples; if variation is excessive, average 6. Permissible variation 3 % up to CBR 10, 5 % for 10–30, 10 % for 30–60.
- Top 50 cm of subgrade compacted to 95–100 % Proctor density.
- A = P(1 + r)n+10; heavy vehicles are those above 3 tonnes; r = 7.5 % for rural roads; P is a seven-day average.
- Design applies to single axle up to 8,200 kg and tandem axle up to 14,500 kg.
- Aggregates above 20 mm in the sub-base invalidate its CBR value for designing layers above.
- Limitation: thickness is the same regardless of the quality of component materials.
Mistakes Students Commonly Make
- Applying the formula when CBR exceeds 12 percent. It is only valid below 12 %.
- Forgetting the square root. The whole bracket is under a √.
- Writing the exponent as n instead of n + 10 in the traffic growth formula.
- Using unsoaked CBR. Design uses the soaked value, except in dry zones.
- Adding A/π instead of subtracting it.
- Using the total vehicle count as P. Only heavy vehicles above 3 tonnes count.
- Taking n as the design life. n runs from the count to the completion of construction; the 10 years is the design life added separately.
- Assuming the CBR method accounts for material quality. It does not.
Conclusion
The CBR method rests on one clean idea — every layer must be given enough cover to protect the layer beneath it. Enter the chart with the subgrade CBR for the total thickness, enter again with the sub-base CBR, and the difference gives the sub-base. The formula t = √[(1.75P/CBR) − (A/π)] backs this up, subject to the important limit of CBR below 12 percent. Learn the eight IRC recommendations as a group, remember that the growth exponent is n + 10, and keep in mind the method’s honest limitation about material quality.
Frequently Asked Questions
What is the CBR method based on?
The strength parameter of the subgrade soil and subsequent materials.
What is the CBR thickness formula?
t = √[(1.75P/CBR) − (A/π)], where t is thickness in cm, P is wheel load in kg, CBR is in percent and A is the contact area in cm².
When is the CBR formula valid?
Only when the CBR value of the subgrade soil is less than 12 percent.
How is sub-base thickness determined?
By subtracting the thickness required over the sub-base, found using the sub-base CBR value, from the total thickness found using the subgrade CBR value.
Why does IRC recommend laboratory rather than in-situ CBR tests?
Because remoulded laboratory samples can be prepared under controlled and repeatable conditions of density and moisture, whereas in-situ conditions vary from point to point.
How long should CBR samples be soaked?
Four days, except in dry zones with less than 50 cm of rainfall where soaking is not necessary.
How many samples should be tested?
At least three of each soil type at the same density and moisture content. If the variation exceeds the permissible value, an average of six samples should be used.
What is the traffic growth formula?
A = P(1 + r)n+10, where A is the design number of heavy vehicles per day, P is the number at last count, r is the annual growth rate and n is the number of years between the count and completion of construction.
Why is 10 added to the exponent?
Because n covers only the period until construction is complete, while the additional 10 years represents the design life over which traffic will continue to grow after the road opens.
What axle loads does the design thickness apply to?
Single axle loads up to 8,200 kg and tandem axle loads up to 14,500 kg. For higher loads the thickness must be increased further.
What is the main limitation of the CBR method?
It gives the total thickness requirement above the subgrade, and that thickness stays the same regardless of the quality of materials used in the component layers.