The California Bearing Ratio (CBR) is calculated using the following formula: CBR = (PT/PS) x 100, where PT is the test pressure and PS is the standard pressure.
Understanding the CBR Calculation
The California Bearing Ratio (CBR) test is a penetration test used to evaluate the bearing capacity of subgrade soil for roads and pavements. The CBR value represents the ratio of the pressure required to penetrate a soil sample with a standard plunger to the pressure required to achieve the same penetration in a standard crushed rock material. This provides a relative measure of the soil's strength.
Here's a breakdown of the calculation and key aspects:
-
PT (Test Pressure): This is the pressure (or load divided by area) required to penetrate the soil sample to a specific depth with the plunger. The test is usually performed at two standard penetration depths: 2.5 mm (0.1 inch) and 5.0 mm (0.2 inch).
-
PS (Standard Pressure): This is the standard pressure required to achieve the same penetration (either 2.5 mm or 5.0 mm) in a standard crushed rock material. These standard pressures are pre-defined values:
- For 2.5 mm penetration: PS = 7 MPa (1000 psi) approximately
- For 5.0 mm penetration: PS = 10.5 MPa (1500 psi) approximately
-
CBR = (PT/PS) x 100: The test pressure (PT) is divided by the standard pressure (PS) corresponding to the same penetration depth and then multiplied by 100 to express the CBR as a percentage.
Determining the CBR Value for Design
Typically, CBR values are calculated for both 2.5 mm and 5 mm penetration depths. The higher CBR value is usually adopted for design purposes. However, if the CBR value at 5 mm penetration is greater than that at 2.5 mm, the test should be repeated. If the same result occurs again, the CBR value at 5 mm penetration should be used. This situation is less common but can occur due to non-uniform soil samples.
Example
Let's say, in a CBR test:
- Pressure required for 2.5 mm penetration (PT) = 6 MPa
- Pressure required for 5.0 mm penetration (PT) = 9 MPa
Then:
- CBR (at 2.5 mm) = (6 MPa / 7 MPa) x 100 = 85.7% (approximately)
- CBR (at 5.0 mm) = (9 MPa / 10.5 MPa) x 100 = 85.7% (approximately)
In this example, you would use 85.7% as your CBR value for design. Note that in a real test, you would want to make sure that your load-penetration curve has a shape that is expected for a valid CBR test.
