基于非线性规划法的单桩受扭研究

Study on Single Pile Subjected to Torsion Based on Nonlinear Programming Method7

为获得扭矩作用下基桩内力及扭转变形,假定桩为弹性梁,采用非线性土弹簧模拟桩土间的相互作用,建立了单桩受扭的简化计算模型。通过将桩身离散成若干单元,计算得到桩土体系的总能量计算式,考虑桩身力平衡和扭转位移连续条件,基于最小势能原理,建立了用于受扭单桩变形计算的非线性规划模型,并采用最优化计算方法求解该计算模型,获得了单桩的扭转变形。通过在双层地基模型中的受扭计算分析,验证了该方法在层状地基中的适用性。结果表明:桩的抗扭刚度约与桩周土剪切模量的0.5次方成正比例关系;其次,顶层土的剪切模量对桩身的抗扭性能影响较大,通过提高这部分地基土的剪切模量来提升桩的抗扭能力,是实际工程可以采取的经济且有效的手段。基于一模型试验,用MATLAB编制了计算程序,完成了影响因素分析。结果表明:在相同的扭转荷载下,增大桩身剪切模量G_P和桩径d,桩头的扭转角减小,但提高G_P并不能有效提高桩土体系在扭矩作用下的极限承载力;而桩径d越大,桩土体系所能承受的极限扭矩越大,且极限扭矩值的变化率约与桩径的变化率的平方成比例关系;此外,受扭桩的极限承载力的大小与桩侧土极限剪应力B成正比例关系。

In order to obtain the internal force and torsional deformation of single pile under torque,first,using the nonlinear soil springs to simulate the interaction between pile and soil,a simplified calculation model of torsional pile single pile is established based on the assumption of elastic beam. Afterwards,the total energy expression of the pile-soil system is obtained by discrete pile body into several units. Considering the force balance of pile body and torsional displacement continuity conditions,a nonlinear programming model of a single pile subjected to torsion is established based on the principle of minimum energy,which can be solved by the method of optimization to obtain the torsional deformation of single pile. Through the calculation and analysis of torsional pile in double layered foundation model,the applicability of this method in layered soils is verified. The result shows that（ 1） the torsional rigidity of the pile is proportional to the square root of pile-soil shear modulus;（ 2） the shear modulus of the top soil has greater influence on the torsional performance of the pile,improving the shear modulus of the foundation soil to enhance the torsion resistance of the pile is an economic and effective method for the actual project. Finally,based on a model test whose calculation program is compiled with MATLAB software,the influencing factors are analyzed. The result shows that（ 1） under the same torsional load,with the increase of pile shear modulus GPor pile diameter d,torsion angle of pile head is reduced,but the increase of GPcannot effectively improve theultimate bearing capacity of pile-soil system under torsion load;（ 2） the larger the pile diameter d,the greater the ultimate bearing torque of the pile-soil system can be,and the change rate of the ultimate torque value is proportional to the square of the change ratio of pile diameter;（ 3） the value of ultimate bearing capacity of the torsional pile is proportional to the ultimate shear stress B of pile side soil.