Equivalent Cross-Sectional Area of Micropile Groups Under Different Surrounding Rock-Mass Strengths

This study investigated the effects of surrounding-rock strength and pile arrangement on the direct shear capacity of micropile groups. Forty-eight specimens representing three pile arrangements, four mortar grades (M5, M10, M15, and M25), and four replicates per condition were tested, and the 12 corresponding conditions were simulated within a calibrated FLAC3D framework. Peak loads were compared with simulated peak reactions. The output of the proposed “equivalent cross-sectional area” formulation, Aeq,ref, was defined as an assumption-dependent capacity-normalization index with units of area, not a measured geometric or cooperative area. It was calculated from adopted reference values for peak shear stress (τref) and effective height (Lref), neither independently measured. Mean peak load increased with mortar grade, but no pile arrangement was consistently superior. Ten of 12 simulated peaks differed from the experimental means by less than 10%; the circular M5 and M10 errors were 17.74% and 10.48%, respectively. Aeq,ref decreased by approximately 54–61% from M5 to M25 because the adopted τref increased faster than the measured group capacity. Accordingly, the index is valid only within the adopted reference-parameter framework and should not be used for design until interface strength and shear-band thickness are independently determined.