Method and Application of Determining Ultimate Bearing Capacity of Existing Piles Based on Catastrophe Theory and Specific Energy Comparison Method
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摘要: 为进一步挖掘既有基桩竖向承载力，根据既有工程试桩荷载–位移曲线和基桩承载性状，应用最小二乘法原理推导出试桩的荷载–位移曲线方程，并拟合出荷载–位移曲线延伸段。在此基础上，为推定基桩竖向极限承载力，引用突变尖点法和比能对比法原理，将桩土系统比能作为突变判据，利用试桩荷载–位移曲线方程求得尖点突变比能曲线及突变点比能，并与桩侧土层平均抗剪强度进行对比，判别桩土临界破坏状态。研究表明，通过桩基比能函数方程形成桩顶变形–分级加载值曲线，根据突变理论，推定基桩竖向极限承载力，物理意义明确，可为既有基桩实际竖向极限承载力的推测和工程试桩最大加载值的确定提供理论依据。Abstract: In order to further excavate the vertical bearing capacity of existing pile, the load displacement curve equation of the test pile was derived by using the principle of the least square method according to the load displacement curve of the test pile and the bearing behavior of the foundation pile, and the extension of the load displacement curve was fitted. On this basis, in order to predict the vertical ultimate bearing capacity of the pile, the catastrophe point method and the specific energy comparison method were used. The specific energy of the pile-soil system was used as a catastrophe criterion. The load-displacement curve equation of the test pile was used to obtain the cusp catastrophe specific energy curve and the catastrophe point specific energy, and the average shear strength of the pile side soil layer was compared to determine the critical failure state of the pile and soil. The research shows that the curve of pile top deformation-graded loading value is formed through the specific energy function equation of pile foundation, and the catastrophe theory is used to deduce the vertical ultimate bearing capacity of pile. The physical meaning is clear, which can provide a theoretical basis for the prediction of the actual vertical ultimate bearing capacity of existing pile foundation and the determination of the maximum loading value of engineering test pile.
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表 1 岩土材料地层物理力学参数
层序 名称 土层厚度/m 重度$ \gamma /(\mathrm{k}\mathrm{N}\cdot{\mathrm{m}}^{-3}) $ c/kPa $ \varphi /(^\circ) $ 压缩模量Es/MPa ③-1 黏质粉土 1.8～4.6 18.49 9.4 28.9 8.5 ③-2 砂质粉土 4.4～7.2 19.09 5.7 33.4 7.0 ⑤ 砂质粉土夹砂 5.9～10.5 19.29 5.1 34.6 14.0 ⑥ 淤泥质粉质黏土 4.0～8.6 17.29 13.4 12.3 2.7 ⑦-1 粉质黏土 1.3～10.4 19.09 39.6 19.7 9.5 ⑦-2 粉质黏土混粉细砂 0.9～5.4 19.38 38.2 21.4 11.0 ⑨-1 粉细砂 0.7～6.4 20 15.0 ⑨-2 圆砾 >7.8 21 30.0 
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表 2 桩基极限承载力推定值
桩号 极限承载力/kN 桩顶变形值/mm 承压桩Z1 8456 39.0 承压桩Z2 9060 52.6 抗拔桩Z3 −4228 −46.4 抗拔桩Z4 −5134 −40.9 注：压力和向下位移为“+”；拉力和向上位移为“−”。
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表 3 出现尖点时各试桩比能对比计算值
桩号 L/m E/MPa s/mm m
/kPaτe/kPa m/τe Z1 44 30000 39 11.6 23.6 0.49 Z2 44 30000 52.6 21.1 23.9 0.88 Z3 44 30000 46.4 16.4 25.8 0.64 Z4 44 30000 40.9 12.8 24.2 0.53
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表 4 出现尖点后各试桩比能对比计算值
桩号 L/m E/MPa s/mm m
/kPaτe/kPa m/τe Z1 44 30000 115 100.8 23.6 4.27 Z2 44 30000 190 275 23.9 11.51 Z3 44 30000 235 421 25.8 16.31 Z4 44 30000 69.1 36 24.2 1.49
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