基于上限法分析椭圆形结构的极限承载力

Ultimate bearing capacity of elliptical tip by upper bound analysis

基于塑性极限理论上限法分析锚桩椭圆形端部和椭圆T-bar的极限承载力及承载力系数,并考虑椭圆形端部的长径比(ξ≥1)和界面摩擦系数对承载力以及承载力系数的影响。分别详细介绍锚桩和T-bar的椭圆端部速度场以及相应速度矢端图的构建。速度场的总能量损耗率是速度间断面能量损耗率和塑性区变形损耗率之和,端部承载力系数等于速度场总能量损耗率与椭圆端部速度,直径和土体强度的比值。结果显示:①椭圆形端部的长径比是1的上限解与前人研究圆形端部结果具有很好的一致性,从而验证了锚桩和T-bar椭圆端部上限模型的合理性;②摩擦力对承载力系数的影响随着端部的长径比的增大而增大;③椭圆端部–土界面完全粗糙时,上限解与下限解和数值解具有较好一直性;随着摩擦系数的降低,承载力系数上限值逐渐大于下限值。

For the anchor pile with elliptical tip and T-bar,the bearing capacity and factor are obtained based on the upper-bound limit analysis of plasticity considering the influences of the aspect ratio of the elliptical tip(ξ≥1)and the friction coefficient.The velocity fields and hodographs of the elliptical tip of the anchor pile and T-bar are introduced.The total energy dissipation is figured by summing up each part of the internal energy dissipation and the energy dissipation on the velocity discontinuous surface.The bearing factor is equal to the ratio of the total energy dissipation over the velocity and diameter of the elliptical tip and soil strength.It is found that forξ=1,there is a good consistency between the upper bound solutions and the previous results.Therefore,the upper bound models for the elliptical tip are rational.The influences of friction force become more significant with the increasingξfor the penetration resistance coefficient.The upper and lower-bound solutions maintain consistency.The upper bound solutions of the bearing capacity are generally larger than the lower ones as the decreasing friction factor.