Analytical solution for negative skin friction of single pile based on effective stress method
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摘要:
桩侧负摩阻力的计算方法尚未统一。为提高负摩阻力作用下竖向受荷单桩设计计算水平，基于有效应力法确定桩侧摩阻力极限值，分析桩土相对位移和桩身深度对桩侧摩阻力的影响，进而建立了桩侧摩阻力非线性计算模型。根据发挥程度不同，桩侧摩阻力分为弹性和塑性状态，在弹性区间摩阻力与桩身深度呈二次函数关系，在塑性区间摩阻力与桩身深度呈线性关系，且斜率为负摩阻力系数与桩周土有效重度之积，进而得到了相应桩段的摩阻力解析解。基于桩身轴力计算理论，得到了桩侧摩阻力不同分布形态下单桩轴力计算式。采用该模型计算分析不同实际工况，并与实测数据进行对比，验证了模型的可靠性、适用性和实用性。研究结果对充分发挥桩基础性能和提高桩基础设计水平具有显著的实用意义。
Abstract:The calculation method for negative skin friction of a single pile has not been unified yet. To improve the design and calculation level of the single pile under vertical load considering negative skin friction, the threshold limit value of pile skin friction was determined based on the effective stress method. The effects of relative displacement of pile-soil and pile depth on pile skin friction were analyzed, and a nonlinear calculation model for pile skin friction was established. The pile skin friction was divided into elastic and plastic states. In the elastic range, the friction is a quadratic function with the depth of the pile body; while in the plastic range, the friction is distributed linearly along the pile body, and the slope is the product of the effective weight of the soil around the pile and the negative friction coefficient. Consequently, the analytical solution of the pile skin friction for the corresponding pile section was acquired. Based on the theory of pile axial force calculation, a formula for calculating the axial force of a single pile under different distribution forms of pile lateral friction was obtained. The reliability, applicability, and practicality of this model were verified by measured data. Based on the calculated pile shaft axial force, the axial force of single pile with different distributions of skin friction was analyzed. This study has practical significance for fully utilizing the performance of pile foundations and improving the level of pile foundation design.
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表 1 负摩阻力系数
$ \beta $ 取值范围Table 1. Value range of negative skin friction coefficient
$ \beta $ 土质 $ \beta $ 黏土 0.20 ～ 0.25 粉土 0.25 ～ 0.35 砂土 0.35 ～ 0.50 
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表 2 土层参数
Table 2. Soil parameters
参数 z/m 土体重度
/（kN·m−3）弹性模量
/MPa泊松比 黏聚力
/kPa内摩擦角
/（°）取值 0～4 17 4.90 0.2 3.0 26 <4～10 17 4.90 0.2 5.9 25 <10～20 17 4.90 0.2 14.7 25 >20 17 6.37 0.2 5.9 23
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表 3 桩体参数
Table 3. Pile parameters
参数 桩长/m 桩径/m 桩体重度/（kN·m−3） 弹性模量/MPa 泊松比 取值 25 0.5 17 30 000 0.25
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表 4 土层物理力学参数
Table 4. Physical and mechanical parameter of soil
土层 厚度/m 重度/（kN·m−3） 弹性模量/MPa 摩阻力系数 素填土 6.0 16.50 0.37～0.39 淤泥 4.9 15.74 1.26 0.25～0.27 粉质黏土 3.0 19.10 6.84 0.33～0.36 粉质黏土混砂砾 9.5 19.03 7.12 0.05～0.10 碎石混黏土 9.5 19.05 9.60 0.10 全风化凝灰岩 2.0 22.50 微风化凝灰岩 4.0 24.00 中风化凝灰岩 1.0 25.90
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