# Overlay Design for Rigid Pavements

## Step 1: Pavement Condition Survey

Perform visual inspection and non-destructive testing to assess the condition of the pavement.

## Step 2: Data Collection

Collect data such as historical construction details, traffic loads, and axle load surveys.

## Step 3: Deflection Analysis Using Falling Weight Deflectometer (FWD)

Perform FWD tests at radial distances to collect deflection data for various points. The following formulas are used:

### Area Parameter (A) of the Deflection Basin

\[ A = 6 \left( \frac{D_1}{D_0} + \frac{D_2}{D_0} + \frac{D_3}{D_0} \right) \]

Where:

`A`

= Area parameter of the deflection basin`D_0`

= Deflection at the center of the loading plate (0 mm from the center)`D_1`

= Deflection at 300 mm from the center`D_2`

= Deflection at 600 mm from the center`D_3`

= Deflection at 900 mm from the center

### Radius of Relative Stiffness (l)

The radius of relative stiffness (`l`

) can be evaluated from charts in the guidelines.

## Step 4: Evaluation of Pavement Distresses

### Modulus of Subgrade Reaction (k-value)

\[ k_i = \frac{P \cdot l^2}{D_i} \]

Where:

`k_i`

= Modulus of subgrade reaction (MPa/m)`P`

= Load applied (kN)`l`

= Radius of relative stiffness (mm)`D_i`

= Measured deflections at various radial distances

### Elastic Modulus of Concrete (E_{c})

\[ E_c = \frac{12 \cdot (1 - \mu_c^2) \cdot k \cdot l^3}{h^3} \]

Where:

`E_c`

= Elastic modulus of concrete (MPa)`\mu_c`

= Poisson's ratio of concrete`k`

= Modulus of subgrade reaction (MPa/m)`l`

= Radius of relative stiffness (mm)`h`

= Thickness of concrete layer (mm)

### Compressive Strength of Concrete (f_{c})

\[ f_c = \left( \frac{E_c}{5000} \right)^{0.5} \]

### Flexural Strength of Concrete (f_{mr})

\[ f_{mr} = 0.7 \cdot (f_c)^{0.5} \]

## Step 5: Calculation of Remaining Life (Fatigue Life)

To calculate the fatigue life, use the following equation from IRC:58-2011:

\[ N = 4.2577 \cdot 10^3 \cdot \left( \frac{1}{SR^{3.268}} \right) \quad \text{for} \ 0.45 \leq SR \leq 0.55 \]

or

\[ \log N = 0.9718 - 0.0828 \cdot SR \quad \text{for} \ SR > 0.55 \]

### Cumulative Fatigue Damage (CFD)

\[ CFD = \sum \frac{n_i}{N_i} \]

## Step 6: Design of Overlay

The overlay thickness is determined based on traffic loads, remaining life, and pavement distress calculations.

## Step 7: Rehabilitation of Joints and Cracks

### Filling of Voids

Voids are filled using cement grout.

### Load Transfer Efficiency (LTE)

Load transfer efficiency at joints is calculated using the following formula:

\[ LTE = 100 \cdot \left( \frac{D_2}{D_1} \right) \]

## Step 8: Final Overlay Placement

After repairs, the overlay is placed (either concrete or asphalt).

## Step 9: Post-Construction Monitoring

Periodic monitoring of the overlay is essential.

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