地下空区顶板改进梁模型的弹塑性分析

江学良^{1, 2}，曹平³，杨慧¹

(1. 中南林业科技大学 土木工程与力学学院，湖南 长沙，410004；
2. 湖南城市学院 土木工程学院，湖南 益阳，413000；
3. 中南大学 资源与安全工程学院，湖南 长沙，410083)

摘 要：将岩石视为理想弹塑性介质，采用梁柱理论分析岩石本构关系对改进梁模型的影响，将模型的受力状态简化为弹性状态、拉伸屈服或压缩屈服状态、拉压屈服并存状态，并分别得到不同受力状态下的广义弯矩－轴力－曲率关系。假设模型的挠曲线为正弦半波函数，得到了模型最大承载力的弯矩-轴力-横向荷载相关方程( )；采用裂隙张量与损伤理论，得到了等效弹性模量与初始弹性模量之间的关系。以瓮福磷矿穿岩矿段地下空区顶板为例计算得到不同跨厚比(L/h＝3, 5, 8)条件下横向荷载与轴力的相关曲线。研究结果表明：在横向荷载 一定的情况下，随着顶板跨度与厚度的比值(L/h)的减小，轴向力(n=N/N_y )增加；在轴向力一定的情况下，随着顶板跨度与厚度比值(L/h)的减小，横向荷载( =q/q_y)增大。

关键词：地下空区顶板；改进梁模型；弹塑性本构关系；梁柱理论

Elasto-plastic analysis of improved beam model for underground cavern’s roof

JIANG Xue-liang^{1, 2}, CAO Ping³, YANG Hui¹

(1. School of Civil Engineering and Mechanics, Central South University of Forest and Technology,
Changsha 410004, China;
2. School of Civil Engineering, Hunan City University, Yiyang 413000, China;
3. School of Resources and Safety Engineering, Central South University, Changsha 410083, China)

Abstract:The rock was regarded as perfectly elasto-plastic material, the effect of rock’s constitutive relation on the improved beam was analyzed with beam-column theory, the forced state of model was simplified as elastic state, tensile yield state, compressive yield and coexistence state of tensile and compressive yield. The relationships of moment-axial force-curvature were obtained. The deflection curve was assumed as the sine half wave and the equation of the generalized moment-axial force-lateral load of model was built. The relationship between equivalent modulus and initial modulus was gotten from crack tensor theory and damage theory. Taking the cavern roof of Wenfu phosphate mine for example, the curve of lateral load and axial force was obtained from calculation. The results show that the axial force increases with the decrease of the ratio of model span to thickness when the lateral load is a constant and the lateral load increases with the decrease of the ratio of model span to thickness when the axial force is a constant.

Key words:roof of underground cavern; improved beam model; elasto-plastic constitutive relation; beam-column theory