Analysis of the Vertical Bearing Capacity of Pile Foundations in Backfill Soil Areas Based on Non-Stationary Random Field

The soil parameters of artificial soil foundations exhibit significant spatial variability due to particle sorting during the filling process, which follows a trend that is distinct from that of natural soft foundations. Based on this observation, a non-stationary random field model is proposed, in which the undrained shear strength decreases along the horizontal filling direction and increases along the vertical deposition direction. The impact of the non-stationary random field model on the vertical bearing capacity of pile foundations is analyzed and discussed with Monte Carlo simulations. The results indicate that the mean and coefficient of variation of the undrained shear strength significantly affect the vertical ultimate bearing capacity of pile foundations, whereas the effects of the random field correlation distance and vertical non-stationary trend coefficient are relatively minor. Under the influence of the horizontal non-stationary trend coefficient, the mean vertical ultimate bearing capacity of pile foundations decreases with the horizontal distance between the pile and the backfill entrance. Moreover, the rate of decrease diminishes linearly with the horizontal non-stationary trend coefficient. A predictive formula for the vertical ultimate bearing capacity of pile foundations is proposed, and its applicability is verified.