摘要
基于弹性半无限空间的Mindlin位移解推求锚固段侧阻力分布,是一种力图以数理力学理论模型严格推导的研究思路,但不同解法间结论相异,与工程实际也相差较大。针对其原因,通过建立普适的求解侧阻力的积分方程进行理论分析。发现Mindlin位移解所具有的数学奇异性影响突出,在积分方程的数值求解中不能直接消除,虽以设置带取值任意性的最小微间距或以在锚固体横截圆面上积分的荷载转换方法可加以避免,却难以实现严格数理力学推导的初衷。而解析手段因引入了3个简化假设,虽数学求解上克服了奇异性困难,但使力学模型发生了失真,推导的结果仅属于特定定解条件下的数学表象。针对理论上以剪应力互等定律推断出锚固段始端侧阻力应为0,与工程实际间的矛盾,提出锚固段始端角点的应力可以是非对称的,以传统的剪应力互等定律来推断该局部区域的应力状况不尽合理。
Most recent study methods for precise mechanical deducing the lateral shear stress distribution along anchorage section are theoretically based on the Mindlin＇s solution of displacement in elastic theory. However, the results obtained with different methods are not only different, but also deviate from the results of practice projects. For exploring their theoretical origin, a general integral equation for deducing lateral shear stress was put forward. It was concluded that, the singularity of Mindlin＇s solution, which led to an enormous displacement in force point, was difficult to clear up in numerical approaches. Although the singularity might be minimized to an appreciable extent by setting an arbitrary tiny space or by introducing convertion of the lateral stress, precise theoretical analysis with exact mechanical model could not be carried out yet. Another method, the analytical deduction of integral equation actually included three simplified conditions that would brought some distortion to prototypical mechanical model. These results only expressed a mathematical phenomenon came from these special simplified conditions. Furthermore, the reason of difference of shear stress between the analytical results and the practices at the start-element of anchorage section was discussed. According to the finite deformation mechanics, symmetrical tensor of shear stress was not applicable at that position. The shear stress at the start-element of anchorage section might not be zero.
出处
《岩土工程学报》
EI
CAS
CSCD
北大核心
2006年第9期1112-1117,共6页
Chinese Journal of Geotechnical Engineering
基金
国家自然科学基金"西部生态与环境"重大研究计划重点资助项目(90102002)
关键词
锚固段
侧阻力分布
MINDLIN位移解
奇异性
积分方程
位移协调
anchorage section
lateral shear stress distribution
Mindlin＇s solution of displacement
singularity
integral equation
compatibility of displacement
