[论文解读] Is the friction angle the maximum slope of a free surface of a non cohesive material?

Arézou Modaressi, P. Évesque|arXiv (Cornell University)|Jul 13, 2005

Adhesion, Friction, and Surface Interactions参考文献 5被引用 3

一句话总结

本研究采用弹性理想塑性模型的有限元模拟，探究内摩擦角是否限制非黏性颗粒材料自由表面的最大稳定坡角。研究发现，在Drucker-Prager屈服准则下，由于中间主应力的影响，坡角可略微超过内摩擦角而保持稳定，这挑战了传统假设中内摩擦角为绝对最大坡角的观点。结果表明，无需引入大于静摩擦角的动力角即可解释滑坡现象。

ABSTRACT

Starting from a symmetric triangular pile with a horizontal basis and rotating the basis in the vertical plane, we have determined the evolution of the stress distribution as a function of the basis inclination using Finite Elements method with an elastic-perfectly plastic constitutive model, defined by its friction angle, without cohesion. It is found that when the yield function is the Drucker-Prager one, stress distribution satisfying equilibrium can be found even when one of the free-surface slopes is larger than the friction angle. This means that piles with a slope larger than the friction angle can be (at least) marginally stable and that slope rotation is not always a destabilising perturbation direction. On the contrary, it is found that the slope cannot overpass the friction angle when a Mohr-Coulomb yield function is used. Theoretical explanation of these facts is given which enlightens the role plaid by the intermediate principal stress in both cases of the Mohr-Coulomb criterion and of the Drucker-Prager one. It is then argued that the Mohr-Coulomb criterion assumes a spontaneous symmetry breaking, as soon as the two smallest principal stresses are different ; this is not physical most likely; so this criterion shall be replaced by a Drucker-Prager criterion in the vicinity of the equality, which leads to the previous anomalous behaviour ; so these numerical computations enlighten the avalanche process: they show that no dynamical angle larger than the static one is needed to understand avalanching. It is in agreement with previous experimental results. Furthermore, these results show that the maximum angle of repose can be modified using cyclic rotations; we propose a procedure that allows to achieve a maximum angle of repose to be equal to the friction angle .

研究动机与目标

• 探究内摩擦角是否构成非黏性颗粒材料自由表面稳定坡角的绝对上限。
• 分析中间主应力在不同屈服准则下对稳定性的影响。
• 评估Mohr-Coulomb准则在颗粒力学中的物理合理性，特别是主应力接近相等时的情形。
• 探讨基底周期性旋转是否可使休止角超过内摩擦角。
• 将数值结果与颗粒堆滑坡行为的实验观测相协调。

提出的方法

• 采用有限元法（FEM）模拟对称三角形颗粒堆内部的应力分布。
• 使用仅由内摩擦角定义、无黏聚力的弹性理想塑性本构模型。
• 对比两种屈服准则：平面应变条件下的Drucker-Prager准则与Mohr-Coulomb准则。
• 在垂直平面内逐步旋转颗粒堆基底，研究应力与稳定性的演化。
• 通过数值求解平衡方程，在不同基底倾斜角度下确定破坏的起始条件。
• 通过理论分析解释两种屈服准则在行为差异上的原因，尤其关注中间主应力的影响。

实验结果

研究问题

• RQ1 非黏性颗粒材料的自由表面坡角能否在稳定状态下超过内摩擦角？
• RQ2 屈服准则的选择（Mohr-Coulomb与Drucker-Prager）如何影响预测的最大稳定坡角？
• RQ3 在不同屈服准则下，中间主应力在颗粒堆稳定性中起何种作用？
• RQ4 Mohr-Coulomb准则中假设的自发对称性破缺在物理上是否合理？
• RQ5 周期性基底旋转能否用于使休止角达到并超过内摩擦角？

主要发现

• 在Drucker-Prager屈服准则下，即使一个自由表面坡角超过内摩擦角，应力平衡仍可维持，表明该极限之外存在微弱稳定性。
• 相比之下，Mohr-Coulomb准则严格将内摩擦角作为最大稳定坡角，不允许任何坡角超过该值。
• 差异源于Mohr-Coulomb准则在两个最小主应力不相等时隐含假设了自发对称性破缺，这一假设在物理上值得怀疑。
• Drucker-Prager准则更一致地考虑了中间主应力，允许更高坡角，且更好解释了滑坡中不存在大于静摩擦角的动力角的现象。
• 数值结果支持无需引入大于静摩擦角的动力角即可解释滑坡行为的观点，与实验观测一致。
• 结果表明，周期性基底旋转是一种可行机制，可使休止角达到等于内摩擦角的值，提示可通过该方法可控调节颗粒堆的稳定性。