Application of a Stochastic Elasto-Plastic Model with First-Order Spectral Expansion to Soil

The efficient treatment of uncertainties in soil properties is essential for seismic probabilistic risk assessment. Recently, we developed a stochastic elasto-plastic model based on the first-order spectral expansion of the stochastic behavior. This new treatment is applied to elasto-plastic soil with uncertain material properties. A numerical experiment is performed to evaluate the probabilistic constitutive relation. The probabilistic stress–strain relation of soil is simulated successfully in agreement with the standard Monte-Carlo simulation. In addition, some characteristics of the probabilistic elasto-plastic soil are studied.

Investigation of Biotransport in a Tumor With Uncertain Material Properties Using a Nonintrusive Spectral Uncertainty Quantification Method

In this study, statistical models are developed for modeling uncertain heterogeneous permeability and porosity in tumors, and the resulting uncertainties in pressure and velocity fields during an intratumoral injection are quantified using a nonintrusive spectral uncertainty quantification (UQ) method. Specifically, the uncertain permeability is modeled as a log-Gaussian random field, represented using a truncated Karhunen–Lòeve (KL) expansion, and the uncertain porosity is modeled as a log-normal random variable. The efficacy of the developed statistical models is validated by simulating the concentration fields with permeability and porosity of different uncertainty levels. The irregularity in the concentration field bears reasonable visual agreement with that in MicroCT images from experiments. The pressure and velocity fields are represented using polynomial chaos (PC) expansions to enable efficient computation of their statistical properties. The coefficients in the PC expansion are computed using a nonintrusive spectral projection method with the Smolyak sparse quadrature. The developed UQ approach is then used to quantify the uncertainties in the random pressure and velocity fields. A global sensitivity analysis is also performed to assess the contribution of individual KL modes of the log-permeability field to the total variance of the pressure field. It is demonstrated that the developed UQ approach can effectively quantify the flow uncertainties induced by uncertain material properties of the tumor.