【作者】 刘伟平；

【导师】 扶名福；

【作者基本信息】 南昌大学 ， 固体力学， 2010， 博士

【摘要】 在岩土工程问题的力学分析中,通常采用库仑摩擦定律分析摩擦问题,接触面上逐点采用的库仑摩擦定律是局部性质的,即接触面上摩擦域内某质点的摩擦效应只与该点的状态有关。实际上,接触界面是粗糙面之间的接触,某质点的摩擦效应不仅与该点的状态直接相关,还与该点有限大小邻域内的其它点的状态有关,这是一种非局部摩擦效应。本文基于Oden等提出的非局部摩擦模型分析,建立适合岩土工程的分析模型,以锚杆(索)为研究对象,分析了锚杆(索)剪切应力的非局部摩擦效应,研究了非局部摩擦模型中的核函数对非局部效应的影响；根据梯度理论建立了梯度依赖的非局部摩擦模型并进行应用研究；应用非局部摩擦模型、非线性强度包络线以及考虑中间主应力影响的三剪强度准则分析锚索的极限承载力。主要内容有：采用修正的非局部摩擦模型对预应力锚索锚固段进行受力分析。根据Kelvin问题的位移解导出预应力锚索锚固段的剪应力,得到了在非局部摩擦模型下的预应力锚索锚固段的剪应力解。对在非局部摩擦模型和局部摩擦模型(库仑模型)下的剪应力结果进行比较,并分析了影响剪应力的非局部效应的相关因素,验证了其有效性和合理性。采用基于Oden等提出的非局部摩擦模型的修正式,对压力型锚索锚固段受力状态进行分析,采用非局部摩擦模型代替经典的库仑摩擦模型,建立其力的平衡方程,并利用摄动法对其进行求解。对非局部摩擦模型和局部摩擦模型(库仑模型)下剪应力和轴力结果进行了比较,并分析了反映非局部效应的相关因素。利用Mindlin问题的位移解导出全长粘结式锚杆沿杆体表面所受的剪应力的弹性解,对全长粘结式锚杆进行非局部摩擦分析,得到了在修正后的非局部摩擦模型下的全长粘结式锚杆的侧剪应力。非局部摩擦模型下的全长粘结式锚杆的剪应力分布规律与试验得到的结果以及局部摩擦模型下的计算结果进行了对比。用四种不同的函数作为非局部摩擦模型中的核函数,进行非局部理论中的核函数选择探讨。通过与实验数据的对比,结果表明是合理有效的。基于梯度理论建立了梯度依赖的非局部摩擦模型,并应用其对全长粘结式锚杆及预应力锚索进行了理论分析,全长粘结式锚杆与预应力锚索的受力特性相似,考虑非局部摩擦效应时,沿锚固体的剪应力峰值比不考虑要小。采用梯度依赖的非局部摩擦模型和极限平衡原理研究了预应力锚索的极限抗拔力,分析非局部效应对其值的影响。为了分析中间主应力对极限抗拔力的影响,采用三剪屈服准则对其进行研究。同时,还分析了在非线性强度包络线(抛物线型、双曲线型)Mohr强度准则下锚索极限抗拔力,并对其计算结果进行了对比研究。对岩土工程问题的非局部摩擦分析研究有助于更加深入地认识岩土工程问题中的摩擦机理,分析锚杆(索)的受力性能。采用不同的强度准则分析了锚索的极限抗拔力,这都为锚杆(索)的应用提供理论基础。更多还原

【Abstract】 The Coulomb’s friction model is widely used in geotechnical engineering. In this model, frictional stress at a point on contact surface depends only on the normal stress acting on the point. In order to analyze the effect of contact surface to friction, a nonlocal friction model is introduced to analyze the mechanical characteristics for geomaterial. Roughly speaking, the nonlocal friction model is given to describe that impending motion at a contact point between two deformable bodies will occur when the shear stress at the contact point reaches a value proportional to a weighted measure of the normal stress in a neighborhood of the point.The nonlocal friction model proposed by Oden et al was modified in this dissertation. Anchor bolt (cable) are analyzed by using the modified nonlocal friction model. The influence of the kernel function in model is also studied. Based on gradient theory, the second-order gradient of stress is introduced into the nonlocal friction model. A gradient dependent nonlocal friction model is established and applied, the triple shear unified failure criterion which can reflect the intermediate principal stress effects on the yield characteristics and the nonlinear Mohr failure criterion are used to studied the ultimate pullout force of prestressed cable. The main content of the paper are summarized as follows:The modified nonlocal friction model is used to analyze the anchorage mechanism of the interior bond section of the prestressed cables. Based on Kelvin s solution of displacement, a solution of shear stress in the anchorage is derived. The integral form of shear stress is obtained and solved. The nonlocal effect on the contact surface is shown and the solution of shear stress is given. The results are compared with those obtained by the nonlocal frication model and local frication model. Factors affecting the nonlocal friction are discussed.Based on modified nonlocal friction model, the mechanical condition of the anchorage segment of the pressure-type cable is analyzed. The mechanical equilibrium equation is given and solved with the perturbation method. The nonlocal effect on the contact surface stress distribution is shown and the solution of shear stress and the axial force in a cable is given. The results are compared with those obtained by the nonlocal frication model and local frication model. The results also show that nonlocal effect changes with nonlocal effect size.The modified nonlocal frication model was used to analyze the wholly grouted anchor. Based on Mindlin s solution of displacement, an elastic solution of shear stress on bolt surface for wholly grouted anchor is derived. Wholly grouted anchor was analyzed by the modified nonlocal frication models which have different kernel functions, the nonlocal effect on the contact surface stress distribution was shown here and the solution of shear stress on bolt surface was given. The results were compared with those obtained by the modified nonlocal frication model which has different kernel functions and local frication model and experimental results in references. It is found that the results obtained by modified nonlocal frication model coincides reasonably well with experimental results, and coincides better than the local frication model. The result shows that nonlocal friction law is more practicable. The nonlocal friction effect is also discussed along with different kernel functions.Based on the gradient theory, a gradient dependent nonlocal friction model is established and used to analyze the wholly grouted bolt and the pressure-type cable. The mechanical characters of the wholly grouted bolt and the pressure-type cable are similar. When the nonlocal friction effects are considered, the shear stress peak value at the anchorage zone is smaller than those obtained by using the model not accunting for nonlocal effects.Based on the gradient dependent nonlocal friction model and the ultimate equilibrium principle, the ultimate pullout force of prestressed cable is studied. In order to consider the influence of the intermediate principal stress, the triple shear unified failure criterion was used to analyze the prestressed cable.The nonlinear Mohr failure criterion, such as the hyperbolic Mohr farlure criterion and two-parameter parabolic failure envelope, are used to analyze the ultimate pullout force. A comparative study was made of the results of different strength criterion.The study is helpful for understanding the friction mechanism in geotechnical problems. Meanwhile, the mechanics characteristics of the anchor bolt (cable) are studied. Based on different failure criterion, the ultimate pullout force of prestressed cable is studied.It can serves as good theoretical bases for the application and development of the anchorage techniques.更多还原