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Load-Bearing Performance and Structural Optimization of Variable-Section Expansion Body Bolts Based on Shape Functions
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DOI：10.1007/s00603-026-05801-8.png)
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Abstract
En 中文
To address the limited load-transfer efficiency and pull-out resistance of conventional constant-section bolts, this study proposes a variable-section expansion body bolt (VSEB-bolt) and develops a shape-function-based load-transfer model for its pull-out behavior. The main novelty lies in using a continuous shape function D(x) to describe the axial variation of the expansion body and in incorporating the normal wedging effect generated by the inclined expansion profile into the grout–rock interfacial load-transfer formulation. In the model, the expansion profile, bolt–grout composite stiffness, equivalent tangential shear stiffness, equivalent normal confinement stiffness, axial force, axial displacement, and interfacial shear stress are coupled within a segmented analytical framework. Numerical simulations and indoor pull-out tests are performed to verify the proposed model. The theoretical predictions agree well with the measured axial force and interfacial shear-stress distributions under different pull-out loads. The observed failure modes further show that the VSEB-bolt changes the failure pattern from interface-dominated slip and splitting to wedging-induced cracking, local crushing, and concrete adhesion. The results demonstrate that VSEB-bolts can reduce pull-out displacement, improve load-transfer efficiency, and redistribute interfacial shear stress along the anchorage length. Among the examined profiles, the conical transition profile provides a relatively balanced response in displacement control, stress redistribution, and engineering feasibility. Parametric analyses indicate that the expansion diameter ratio, variable-section length, expansion-segment arrangement, bolt modulus, grout modulus, interfacial shear stiffness, and normal confinement stiffness jointly control anchorage performance.
Keywords:
Variable-section expansion body bolt
Shape function
Load transfer mechanism
Load-bearing capacity
Structural optimization
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