考慮剪切變形影響的樁基m法計算理論

楊美良　羅婉慶　張建仁

摘要：

考慮樁基的剪切變形影響，利用單廣義位移深梁理論，建立了樁基m法的計算方法，導出了水平位移、轉角、彎矩和剪力的初參數表達式和無量綱參數函數的統一表達式，根據樁底邊界條件建立了初參數解的計算公式；給出了無量綱參數函數隨換算深度和彎剪剛度比的變化圖形。研究表明，換算深度小于3.0時，彎剪剛度比對無量綱參數函數影響較小，換算深度大于4.0時，彎剪剛度比對無量綱參數函數影響的趨勢非常明顯，樁基剪切變形的影響程度與樁的邊界條件有關。算例結果表明，樁身的剪切變形有增大樁頂水平位移、提高彎矩零點位置、改變彎矩分布特征、擴大樁側土壓力大小等影響。

關鍵詞：

樁；單廣義位移梁理論；剪切變形；初參數； m法

中圖分類號：TU473

文獻標志碼：A文章編號：16744764（2016）06005408

Abstract：

Considering the shear deformation effect of piles， the calculating theory of m method assumption for piles was presented by using the single generalized displacement theory of deep beam. The initial parameter formulae to horizontal displacement， slope， moment and shear force were derived. The unified nondimensional functions were also put forward. According to the boundary conditions， the initial parameters solutions were determined. The changing figures of nondimensional functions with converting length and ratio of bend stiffness to shear stiffness were plotted. Some conclusions were summarized that when the converting length was less than 3.0， there was little influence of the ratio of bending stiffness to shear stiffness on the nondimensional functions ， while the converting length was greater than 3.0， the influence of the ratio of bending stiffness to shear stiffness on the nondimensional functions became obvious； the influencing degree of the shear deformation effect was related to the boundary conditions. Example results showed that shear deformation can enlarge the horizontal displacement at the top， lift the position of zero moment， change moment distribution and magnify the soil pressure on pile.

Keywords：

pile； single generalized displacement beam theory； shear deformation； initial parameter； m method

樁基礎是橋梁、建筑等工程中常用的基礎形式，并有日益推廣使用的趨勢[1]，其水平樁的計算理論主要有m法、K法、C值法、雙參數法等[12]。目前，規范推薦采用基于Euler梁理論的m法，并編制了大量計算表格，相應的有限元法[34]、有限差分法[4]和瑞利里茲法[3]等。基于深梁理論，考慮樁身剪切變形影響的研究也取得積極進展，肖世衛[5]考慮樁身剪切變形影響，利用深梁單元分析了樁橫向受力問題，并以此分析樁身剪切變形對樁頂位移和樁身內力的影響，得到了剪切變形影響極小的結論。該文不足之處是采用有限元法進行數值研究，沒有推導理論解析解；……