Zarghaam Haider Rizvi

Accurately modelling high-frequency elastic waves in heterogeneous media is central to problems spanning geotechnical engineering, seismic hazard assessment, subsurface energy exploration, and planetary interior studies. Yet traditional numerical solvers are computationally intensive and often struggle with small-scale heterogeneity. Here, we show that physics-informed neural networks (PINNs) can efficiently learn the two-dimensional elastic wave equation without labelled data, using only physical residuals as constraints. We benchmark three architectures—a standard PINN, a Fourier-feature PINN, and the adaptive PirateNet—across homogeneous and multi-layered velocity models. Only PirateNet reproduces complex reflections, transmissions, and mode conversions in six-layered media, achieving stable high-frequency predictions where conventional PINNs fail. Applied examples include subsurface imaging for geothermal and nuclear-energy systems and elastic-wave analysis of planetary crusts. These results highlight the capacity of adaptive PINNs to integrate physical laws and neural representations, offering a unified framework for next-generation simulation and inversion across the Earth and planetary sciences.

Structural integrity of clay liners in engineered waste landfills depends critically on their ability to resist the initiation and propagation of cracks under variable moisture conditions. In this study, the improvement of Mode I Fracture toughness K_I in clayey soil through small additions of discrete glass fibers is investigated with particular emphasis on the interaction between fiber content and water content near the optimum moisture content (OMC). Specimens were prepared using a clayey soil compacted at water contents of 17%, 18%, and 19%, representing dry, optimum, and wet of optimum states based on proctor compaction test. Glass fibers were added uniformly at fractions of 0%, 0.01%, 0.02%, 0.05%, and 0.10% by weight of the soil. K_I was obtained from single-edge notched beam (SENB) specimens tested in a three-point bending configuration. Load and displacement responses were analyzed to extract peak load P_max and compute K_I. The addition of only 0.01% glass fiber by mass enhances P_max by 50%, resulting in a 70% increase in K_I across all moisture conditions. These improvements are attributed to the effective interplay between clay particles bonded together with the glass fibers. The results also indicate that both P_max and K_I reach their maximum values near OMC (~ 18%), corresponding to the densest particle arrangement. However, increasing the fiber content beyond 0.01% leads to a decrease in K_I and P_max caused by fiber clustering, void formation, and weakened soil-fiber interfaces. The findings clearly illustrate that, by precisely limiting the water content and adding a sub-percent amount of glass fiber reinforcement, fracture resistance in clay liners increases significantly. This state-of-the-art approach offers a cost-effective and technically efficient strategy for enhancing the long-term performance of landfill systems to prevent seepage of harmful leachate to the groundwater.