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Theoretical model of limit equilibrium anti-sliding stability of stress vector on sliding planes based on projection direction extreme principle

DOI：10.7511/jslx20210717001

 作者 单位 孙建生 太原理工大学 水利科学与工程学院, 太原 030024

根据有限元成果的滑动面切向应力达到可用极限值的抗滑稳定极限平衡概念，建立投影方向极值原理单元滑面应力矢量极限平衡抗滑稳定计算理论模型，揭示不平衡虚拟耗散力、耗散能和极值条件方程的力学本质联系。根据投影极值方向平衡状态时的垂直方向还存在不平衡耗散力，提出复杂滑裂面极限平衡状态接近程度系数λ及矢量安全度系数Kλ评价抗滑稳定性能的最佳路径。通过边坡考题和坝基深层抗滑稳定算例的势能极值规律存在性和极值点的吻合度，证明了理论模型的合理可靠性。有限元应力矢量理论模型的建立及其安全度系数Kλ是极限平衡抗滑稳定计算理论发展的重要基础理论突破和全新理论研究成果。

According to the concept of anti-sliding stability equilibrium that the tangential stress of the slip planes reaches the available limit value, the mechanical concept of the vector force limit equilibrium anti-sliding stability calculation theory based on the projection direction extreme value principle was expounded, the mechanical essence of dissipated force, virtual work of dissipated energy and extreme value condition equation were revealed.Based on the fact that there was a dissipated force in the vertical direction of the projection direction under the equilibrium state, the concept of the proximity coefficient of the limit equilibrium state of the complex slip planes and the best way to evaluate the anti-sliding stability with the safety degree factor were proposed.The existence of the potential energy extreme law and the coincidence degree of the extreme point proved the reasonable reliability of the theoretical model, by standard slope test questions and the calculation of deep anti-sliding stability of dam foundation.The establishment of finite element stress vector model and the safety degree factor Kλ are the important breakthrough in basic theory and the new theoretical research results in the development of limit equilibrium anti-slide stability calculation theory.