# Fatigue Analysis and Numerical Simulation of Loess Reinforced with Permeable Polyurethane Polymer Grouting

## TL;DR

This study examines how permeable polyurethane polymer grouting improves the fatigue resistance of loess subgrades under traffic and moisture stress.

## Contribution

A new probabilistic fatigue life prediction model and validated numerical simulation approach for polymer-grouted loess subgrades.

## Key findings

- Fatigue life of polymer-grouted loess decreased with higher moisture and stress levels, reaching up to 200,000 cycles under optimal conditions.
- Polymer grouting reduced subgrade stress by nearly tenfold and increased fatigue life by approximately tenfold.
- A 3D finite element model integrated with Fe-safe accurately predicted fatigue behavior, aligning with experimental results.

## Abstract

Loess subgrades are prone to significant strength reduction and deformation under cyclic traffic loads and moisture ingress. Permeable polyurethane polymer grouting has emerged as a promising non-excavation technique for rapid subgrade reinforcement. This study systematically investigated the fatigue behavior of polymer-grouted loess using laboratory fatigue tests and numerical simulations. A series of stress-controlled cyclic tests were conducted on grouted loess specimens under varying moisture contents and stress levels, revealing that fatigue life decreased with increasing moisture and stress levels, with a maximum life of 200,000 cycles achieved under optimal conditions. The failure process was categorized into three distinct stages, culminating in a “multiple-crack” mode, indicating improved stress distribution and ductility. Statistical analysis confirmed that fatigue life followed a two-parameter Weibull distribution, enabling the development of a probabilistic fatigue life prediction model. Furthermore, a 3D finite element model of the road structure was established in Abaqus and integrated with Fe-safe for fatigue life assessment. The results demonstrated that polymer grouting reduced subgrade stress by nearly one order of magnitude and increased fatigue life by approximately tenfold. The consistency between the simulation outcomes and experimentally derived fatigue equations underscores the reliability of the proposed numerical approach. This research provides a theoretical and practical foundation for the fatigue-resistant design and maintenance of loess subgrades reinforced with permeable polyurethane polymer grouting, contributing to the development of sustainable infrastructure in loess-rich regions.