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Digital Generation of Vector Fields

  Based on the probabilistic characteristics of spatial variability inferred from in-situ soil data analysis, sample functions of a stochastic vector field are then generated. Each sample function represents a possible realization of relevant field test results over the analysis domain. Such a sample function, with values of cone tip resistance simulated at the field test locations, is presented in Fig. 3b. It can be observed that recorded and simulated values are different at each spatial location, but they have the same average values and exhibit identical probabilistic characteristics.

The simulation algorithm uses a spectral representa- tion-based method to generate sample functions of an mV-nD, non-Gaussian stochastic vector field, which are compatible both with a prescribed cross-spectral density matrix and with prescribed non-Gaussian probability distribution functions. A Gaussian stochastic vector field is first generated, according to its target cross-spectral density matrix. It is then mapped into a non-Gaussian vector field, using a memoryless transformation in conjunction with an iterative scheme (Yamazaki and Shinozuka (1988)). For a detailed description of the proposed algorithm, and a discussion of issues concerning its rate of convergence, the reader is referred to Popescu et al. (1996).

Wed Nov 6 14:34:32 EST 1996