# Mesoscopic Heterogeneous Modeling Method for Polyurethane-Solidified Ballast Bed Based on Virtual Ray Casting Algorithm

## TL;DR

This paper introduces a new modeling method for polyurethane-solidified ballast beds that avoids costly X-ray scans and improves accuracy and efficiency.

## Contribution

A virtual ray casting-based mesoscale modeling method is proposed to replace XCT for ballast bed analysis.

## Key findings

- The optimal finite-element mesh size is 0.4 times the minimum particle size (0.4 Dmin).
- A sleeper width of 0.73 times the ballast bed width (0.73 Wb) achieves optimal stress diffusion and displacement control.
- Polyurethane buffers loads, but insufficient thickness can cause local stress concentration.

## Abstract

What are the main findings?
A finite element method and virtual projection-based mesoscale modeling approach is proposed to replace X-ray computed tomography (XCT), thereby addressing XCT’s constraints of limited specimen size and high equipment cost.The optimal finite-element mesh size is confirmed, ensuring high ballast volume fidelity, consistency with compression tests, and balancing stability accuracy and computational efficiency.A suitable sleeper width is recommended, acting as the threshold for reduced displacement sensitivity, ensuring optimal stability and supporting sleeper–ballast collaborative design.Polyurethane-solidified ballast beds’ meso-mechanism is revealed: ballast stress concentrates at particle contacts, polyurethane buffers loads, and insufficient polyurethane thickness risks local stress concentration.

A finite element method and virtual projection-based mesoscale modeling approach is proposed to replace X-ray computed tomography (XCT), thereby addressing XCT’s constraints of limited specimen size and high equipment cost.

The optimal finite-element mesh size is confirmed, ensuring high ballast volume fidelity, consistency with compression tests, and balancing stability accuracy and computational efficiency.

A suitable sleeper width is recommended, acting as the threshold for reduced displacement sensitivity, ensuring optimal stability and supporting sleeper–ballast collaborative design.

Polyurethane-solidified ballast beds’ meso-mechanism is revealed: ballast stress concentrates at particle contacts, polyurethane buffers loads, and insufficient polyurethane thickness risks local stress concentration.

What are the implications of the main findings?
The proposed method has cross-material versatility, extendable to other multi-material composites, reducing research costs and highlighting long-term economic value.

The proposed method has cross-material versatility, extendable to other multi-material composites, reducing research costs and highlighting long-term economic value.

This study introduces a mesoscale modeling methodology for polyurethane-solidified ballast beds (PSBBs) that eliminates reliance on X-ray computed tomography (XCT) and addresses constraints in specimen size, capital cost, and post-processing complexity. The approach couples the Discrete Element Method (DEM) with the Finite Element Method (FEM). A high-fidelity discrete-element geometry is reconstructed from three-dimensional laser scans of ballast particles. The virtual-ray casting algorithm is then employed to identify the spatial distribution of ballast and polyurethane and map this information onto the finite-element mesh, enabling heterogeneous material reconstruction at the mesoscale. The accuracy of the model and mesh convergence are validated through comparisons with laboratory uniaxial compression tests, determining the optimal mesh size to be 0.4 times the minimum particle size (0.4 Dmin). Based on this, a parametric study on the effect of sleeper width on ballast bed mechanical responses is conducted, revealing that when the sleeper width is no less than 0.73 times the ballast bed width (0.73 Wb) an optimal balance between stress diffusion and displacement control is achieved. This method demonstrates excellent cross-material applicability and can be extended to mesoscale modeling and performance evaluation of other multiphase particle–binder composite systems.