Park and Ahn Model for Sand
The Park and Ahn (2013) model is a stress-based excess pore water pressure generation model that uses the concept of a damage parameter to account for the accumulation of stress. The excess pore water pressure is calculated as follows:
 | Eq. 1 |
where the damage parameter D at each time step can be calculated as:
| 𝐷𝑖+1 = 𝐷𝑖 + Δ𝐷 | Eq. 2 |
| Δ𝐷 = 2(𝐶𝑆𝑅𝑖+1 − 𝐶𝑆𝑅𝑡)𝛼 | Eq. 3 |
In an incremental form, the generation model becomes:
 | Eq. 4 |
Table 1: Description of Park and Ahn Model Parameters
| VARIABLE | DESCRIPTION |
| ru | Normalized excess pore pressure |
| D | Damage parameter |
| 𝐷𝑟𝑢=1.0 | Damage parameter at the initiation of liquefaction |
| CSRt | Threshold shear stress ratio value |
| α | A calibration parameter |
| β | Empirical constant |
| v | Degradation parameter |
CSRt is the threshold shear stress ratio below which reversals will not generate excess pore water pressure.
The degradation parameter is as described by Matasovic (1993) and uses the same functional form as defined in the Matasovic model for sands (see the Pore Water Pressure Degradation Parameters topic).
Suggested Values
α is a calibration parameter that can be calculated using the following formulation with the CSR-N curve obtained from laboratory tests:
 | Eq. 5 |
where M is the total number of data points in CSR-N curve.
β is an empirical constant and for clean sands, a value of 0.7 is suggested.
𝐷𝑟𝑢=1.0 is the value of damage parameter, 𝐷, at initiation of liquefaction and can be calculated from CSR-N curves that are obtained from laboratory tests using the following formula:
| 𝐷𝑟𝑢=1.0 = 4𝑁(𝐶𝑆𝑅−𝐶𝑆𝑅𝑡)𝛼 | Eq. 6 |