Nonlinear finite element analysis of geo-structural systems is often constrained by computational bottlenecks arising at two distinct scales: constitutive integration at the material (local) level and the iterative solution of the global system of equations. These challenges are further exacerbated in the presence of material, loading, and modeling uncertainties, where uncertainty quantification and reliability analyses require a large number of repeated nonlinear simulations. This work presents a unified machine-learning framework that systematically alleviates these limitations through machine-learning surrogate models tailored to each scale. At the material level, conventional return-mapping algorithms for path-dependent elastoplasticity are replaced by neural network–based constitutive models. Several architectures are investigated, including recurrent neural networks that naturally encode loading history through internal states, enabling the accurate representation of complex nonlinear behaviors such as plastic yielding and hardening. To ensure compatibility with implicit finite element formulations, multiple strategies for computing consistent tangent operators are examined, including automatic differentiation and alternative numerical approximations. The resulting models exhibit increment-size independence, a critical requirement for stable and robust finite element implementation. At the global level, the framework is extended to surrogate modeling of the dynamic structural response under uncertainty using physics-informed deep operator networks (DeepONets). These models target the high computational cost associated with repeated assembly and iterative solution of nonlinear systems, as well as the expense of performing uncertainty quantification analyses that require large numbers of forward simulations. The proposed framework is demonstrated through representative problem settings relevant to geo-structural analysis. Neural networks are trained using data generated from conventional constitutive models and achieve accuracy comparable to classical finite element solutions while delivering substantial computational speedups in both deterministic and uncertainty-aware simulations.