Wave propagation in stochastic triple-porosity thermoelasticity

This paper presents a comprehensive analytical framework for wave propagation in a generalized thermoelastic medium possessing a triple-porosity structure within the Lord–Shulman (L–S) theory, incorporating stochastic parameter uncertainty. The model extends classical double-porosity theory by adding a distinct third porosity network, enabling realistic representation of complex porous materials such as naturally fractured reservoirs, vuggy carbonate rocks, and biological tissues. We consider a homogeneous, isotropic half-space subjected to thermo-mechanical loading with stochastic variations in material properties. The coupled system of equations for displacement, temperature, and three pore pressure fields is solved analytically using normal mode analysis. Exact expressions for physical quantities are derived in the transformed domain, and the fields are returned to the physical time domain by the Durbin Fourier-series inversion algorithm, accelerated by the Korrektur method and the $$\varepsilon$$ -algorithm, whose parameters are stated explicitly in Section 4.3. The results are computed for silicon, which is used strictly as a well-characterised numerical testbed, with hierarchically ordered triple-porosity parameters. A novel stochastic analysis is introduced using Monte Carlo simulation and perturbation methods to quantify the uncertainty propagation from material parameters to field variables; the random material properties are represented as homogeneous random fields with a prescribed correlation length, which reduce to correlated random variables in the long-correlation limit relevant to the present half-space problem. The deterministic, first-order perturbation, second-order perturbation and Monte Carlo predictions are compared quantitatively, and the correct single- and double-porosity limits of the formulation are recovered as special cases. Graphical comparisons investigate the influence of the third porosity network on wave propagation and field distributions, contrasting behaviors with double- and single-porosity cases at different time instants. The analysis reveals significant quantitative differences induced by triple porosity and parameter uncertainty, particularly in stress concentration, wave attenuation, and thermal diffusion patterns.