Abstract: Based on the Bayesian theory, a probabilistic back analysis method using time-varying measurement data is established. The back calculated posterior distributions are determined using the Markov chain Monte Carlo method (MCMC) with the differential evolution adaptive Metropolis algorithm. In this paper, a case study of a well instrumented natural terrain is presented. The deterministic model for pore-water pressure evaluation is an analytical model. Field measurements of pore-water pressure are used to calibrate the unsaturated parameters of the deterministic model. Statistical properties of the posterior distributions are presented and discussed. It is found that the posterior standard deviations of the six parameters are all greatly reduced. The predicted and measured pore-water pressures during the calibration period and the validation period are compared. The coverage of the 95% total uncertainty bounds is estimated to be 0.964 for the calibration period, during which the field measured pore pressures are used to back analyze the input parameters. For periods 2 to 4 of the validation period, the coverage by the 95% total uncertainty bounds are 0.52, 0.79 and 0.79, respectively. These results indicate an overall good performance by the calibrated model.

Key words: unsaturated soil, seepage, Monte Carlo method, Metropolis algorithm, back analysis