Evaluation of Low-Carbon Grouting Material on Pipe Roof Support in Shallow Unsymmetrical Loading Tunnels Based on the Pasternak Foundation Theory

Traditional pipe roof support design methods generally assume horizontal ground conditions and treat the pipe roof as a monolithic beam, thereby neglecting the differential stress distribution among individual steel pipes under unsymmetrical loading. To address this gap, this paper presents two main contributions: a low-carbon cement-based grouting material suitable for pipe roof reinforcement, and a new mechanical model that simultaneously accounts for biased pressure conditions and the inter-pipe micro-arch effect. First, the working performance of limestone calcined clay cement (LC3) grout was systematically tested at a water–cement ratio of 1:1, and the optimal mix ratio was determined. Grout–soil reinforcement tests on weathered granite show that, for grout-to-soil volume ratios between 0.2 and 0.8, the compressive strength of the reinforced material exceeds 10 MPa and the elastic modulus exceeds 600 MPa. Second, a mechanical model for the pipe roof was established based on the Pasternak two-parameter foundation theory, incorporating both biased pressure conditions and the inter-pipe micro-arch effect. The model predictions were compared with existing field monitoring data in the literature, showing consistent trends and good agreement in peak deflection values. Parametric analysis reveals that under horizontal ground conditions, the pipe roof response is symmetric, with the vault as the most critical area. As the bias angle increases, the maximum response shifts toward the higher side of the terrain, and the stress difference between pipes on both sides increases significantly. Theoretical analysis of the low-carbon grouting material shows that pipe roof deflection is moderately reduced compared to traditional grouting materials, but at the cost of increasing bending moment and shear force within the steel pipes. The proposed low-carbon grouting material and the validated mechanical model provide theoretical support for the design optimization of pipe roof support in shallow unsymmetrical loading tunnels.