高陡横坡段桥梁双桩内力计算有限差分解
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摘要
为了对高陡横坡段桥梁双桩基础进行合理分析,提出一种适用的有限差分法。首先,针对陡坡段桥梁基桩不同特征段的承载特性,将后桩划分为嵌固段及受荷段,同时,将前桩划分为嵌固段、受荷段和自由段。然后,考虑桩土相互作用及桩顶变形协调,并引入边界条件,建立了适用于高陡横坡段桥梁双桩基础内力及位移分析的简化计算模型。在此基础上,综合考虑P(荷载)-Δ(位移)效应及连系梁的影响,分别对各特征段基桩微元进行受力分析,并引入相邻特征段满足的连续条件(即位移连续、转角连续、剪力连续及弯矩连续),推导出各微分段的控制差分方程,以MATLAB为平台编制相应计算程序,迭代求解桩身位移,进而求解其内力。最后,结合室内模型试验与现场试验对理论计算方法进行验证,并以现场试验桩为基础,分析连系梁及P-Δ效应等对高陡横坡段双桩基础内力及位移的影响。研究结果表明:理论计算结果与模型试验及现场试验实测数据均吻合良好,表明该方法可行、合理,可为高陡横坡段桥梁工程设计计算提供参考;有自由段存在的基桩,P-Δ效应明显;连系梁对倾斜荷载下基桩桩身内力具有显著影响,连系梁的存在会对上部荷载进行重新分配,并在一定程度上弱化P-Δ效应,对桩身变形具有一定的约束作用。
To analyze the inner force of a bridge double-pile foundation on a steep transverse slope, a new finite difference method has been presented. First, according to the bearing characteristics in different characteristic segments of piles on a steep slope, the back pile was divided into segments, namely fixed segment and loaded segment, whereas the front pile was divided into fixed segment, loaded segment, and free segment. A simplified calculation model for analyzing the inner force and displacement of piles on a steep transverse slope was proposed. The pile-soil interaction, compatibility of deformation at the piles' top and boundary conditions were considered in the proposed model. Based on this, the stress of pile elements of different characteristic segments was analyzed considering the effects of a connecting beam and the P-Δ effect. The continuity conditions of displacement, corners, shear forces, and bending moments are conducted to derive the governing differential equations. The finite difference solution of displacement and inner force of piles are obtained through MATLAB. Finally, the suggested method was verified by a model test and field test, and the effects of the connecting beam and the P-Δ effect on the inner force of piles was researched. The predicted results are in good agreement with the experimental data, and the proposed approach is of great significance for the preliminary design of bridge double-pile foundation on a steep transverse slope. The P-Δ effect is obvious in piles with free segment. The connecting beam has considerable influence on the inner force because the upper loads are redistributed. The connecting beam can be frequently used in the practice engineering in term of weakening the P-Δ effect and decreasing the deformation of piles.
To analyze the inner force of a bridge double-pile foundation on a steep transverse slope, a new finite difference method has been presented. First, according to the bearing characteristics in different characteristic segments of piles on a steep slope, the back pile was divided into segments, namely fixed segment and loaded segment, whereas the front pile was divided into fixed segment, loaded segment, and free segment. A simplified calculation model for analyzing the inner force and displacement of piles on a steep transverse slope was proposed. The pile-soil interaction, compatibility of deformation at the piles' top and boundary conditions were considered in the proposed model. Based on this, the stress of pile elements of different characteristic segments was analyzed considering the effects of a connecting beam and the P-Δ effect. The continuity conditions of displacement, corners, shear forces, and bending moments are conducted to derive the governing differential equations. The finite difference solution of displacement and inner force of piles are obtained through MATLAB. Finally, the suggested method was verified by a model test and field test, and the effects of the connecting beam and the P-Δ effect on the inner force of piles was researched. The predicted results are in good agreement with the experimental data, and the proposed approach is of great significance for the preliminary design of bridge double-pile foundation on a steep transverse slope. The P-Δ effect is obvious in piles with free segment. The connecting beam has considerable influence on the inner force because the upper loads are redistributed. The connecting beam can be frequently used in the practice engineering in term of weakening the P-Δ effect and decreasing the deformation of piles.
引文
[1] 张永杰,李侑军,赵明华,等.高陡斜坡作用下群桩基础设计计算方法[J].中国公路学报,2014,27(10):84-92. ZHANG Yong-jie, LI You-jun, ZHAO Ming-hua, et al. Design and Calculation Method for Pile Group Foundation in High and Steep Slope [J]. China Journal of Highway and Transport, 2014, 27 (10): 84-92.
[2] 郑刚,王丽.竖向及水平荷载加载水平、顺序对单桩承载力的影响[J].岩土工程学报,2008,30(12):1796-1804. ZHENG Gang, WANG Li. Effect of Loading Level and Sequence of Vertical and Lateral Load on Bearing Capacity of Single Pile [J]. Chinese Journal of Geotechnical Engineering, 2008, 30 (12): 1796-1804.
[3] 赵春风,王卫中,赵程,等.组合荷载下单桩承载特性现场试验[J].中国公路学报,2013,26(6):59-64,72. ZHAO Chun-feng, WANG Wei-zhong, ZHAO Cheng, et al. Field Test Study on Bearing Capacity of Single Pile Under Combine Loads [J]. China Journal of Highway and Transport, 2013, 26 (6): 59-64,72.
[4] 梁发云,陈海兵,宋著.轴向荷载对横向受荷桩承载性状影响的参数分析[J].土木建筑与环境工程,2011,33(6):25-30. LIANG Fa-yun, CHEN Hai-bing, SONG Zhu. Parameter Analysis of Effects of Axial Load on the Lateral Response of Piles [J]. Journal of Civil, Architectural & Environmental Engineering, 2011, 33 (6): 25-30.
[5] 张玲,赵明华,赵衡.倾斜荷载下桩柱式桥墩受力变形分析传递矩阵法[J].中国公路学报,2015,28(2):69-76. ZHANG Ling, ZHAO Ming-hua, ZHAO Heng. Transfer Matrix Method for Deformation of Pile Type Bridge Pier Under Axial Transverse Load [J]. China Journal of Highway and Transport, 2015, 28 (2): 69-76.
[6] 杨明辉,赵明华,刘建华,等.高陡边坡桥梁基桩内力计算的幂级数解[J].中南大学学报:自然科学版,2007,38(3):561-566. YANG Ming-hui, ZHAO Ming-hua, LIU Jian-hua, et al. Power-progression Solution for Inner-force Analysis of Bridge Pile in Steep Slope [J]. Journal of Central South University: Science and Technology, 2007, 38 (3): 561-566.
[7] 赵明华,尹平保,张永杰,等.高陡斜坡段桩柱式桥墩基础设计计算方法研究[J].工程力学,2013,30(3):106-111. ZHAO Ming-hua, YIN Ping-bao, ZHANG Yong-jie, et al. The Design and Calculation Method of Pile-column Bridge Pile Foundation in High and Steep Slope [J]. Engineering Mechanics, 2013, 30 (3): 106-111.
[8] 龚先兵,杨明辉,赵明华,等.山区高陡横坡段桥梁桩基承载机理模型试验[J].中国公路学报,2013,26(2):56-62. GONG Xian-bing, YANG Ming-hui, ZHAO Ming-hua, et al. Load-bearing Mechanism Model Test for Bridge Pile Foundation in High-steep Transverse Slope [J]. China Journal of Highway and Transport, 2013, 26 (2): 56-62.
[9] 赵明华,杨超炜,杨明辉,等.基于有限杆单元法的陡坡段桥梁基桩受力分析[J].中国公路学报,2014,27(6):51-58,108. ZHAO Ming-hua, YANG Chao-wei, YANG Ming-hui, et al. Mechanical Analysis of Bridge Pile Foundation in High and Steep Slopes Based on Finite Bar Element Method [J]. China Journal of Highway and Transport, 2014, 27 (6): 51-58, 108.
[10] 尹平保,赵明华,杨超炜,等.复杂荷载下横坡段桥梁桩基承载特性试验研究[J].土木工程学报,2014,47(5):110-117. YIN Ping-bao, ZHAO Ming-hua, YANG Chao-wei, et al. Experimental Study on Bearing Capacity of Bridge Piles in Cross Slopes Under Complex Loads [J]. China Civil Engineering Journal, 2014, 47 (5):110-117.
[11] CHAE K S, UGAI K, WAKAI A. Lateral Resistance of Short Single Piles and Pile Groups Located near Slopes [J]. International Journal of Geomechanics, 2004, 4 (2): 93-103.
[12] 尹平保,杨莹,贺炜,等.考虑斜坡效应的基桩屈曲临界荷载分析[J].岩土力学,2017,38(9):2662-2668,2675. YIN Ping-bao, YANG Ying, HE Wei, et al. Analysis of Critical Buckling Loads of Piles Considering Slope Effect [J]. Rock and Soil Mechanics, 2017, 38 (9): 2662-2668, 2675.
[13] 何颐华,杨斌,金宝森,等.双排护坡桩试验与计算的研究[J].建筑结构学报,1996,17(2):58-66,29. HE Yi-hua, YANG Bin, JIN Bao-sen, et al. A Study on Test and Calculation of Double-row Fender Piles [J]. Journal of Building Structures, 1996, 17 (2): 58-66, 29.
[14] 郑刚,李欣,刘畅,等.考虑桩土相互作用的双排桩分析[J].建筑结构学报,2004,25(1):99-106. ZHENG Gang, LI Xin, LIU Chang, et al. Analysis of Double-row Piles in Consideration of the Pile-soil Interaction [J]. Journal of Building Structures, 2004, 25 (1): 99-106.
[15] 周翠英,刘祚秋,尚伟,等.门架式双排抗滑桩设计计算新模式[J].岩土力学,2005,26(3):441-444,449. ZHOU Cui-ying, LIU Zuo-qiu, SHANG Wei, et al. A New Model for Calculation of Portal Double Row Anti-sliding Piles [J]. Rock and Soil Mechanics, 2005, 26 (3): 441-444, 449.
[16] 孙勇.深基坑双排支护桩随机有限杆单元法的计算研究[J].建筑结构,2010,40(增1):261-266. SUN Yong. Calculation and Research of Stochastic Finite Bar Element Method in Double-row Retaining Piles [J]. Building Structures, 2010, 40 (S1): 261-266.
[17] 吴应祥,刘东升,宋强辉,等.基于有限元强度折减法的抗滑桩滑坡推力及抗滑桩内力可靠性分析[J].岩土力学,2013,34(增1):348-354. WU Ying-xiang, LIU Dong-sheng, SONG Qiang-hui, et al. Reliability Analysis of Landslide-thrust and Internal Forces of Anti-slide Pile Based on Strength Reduction Finite Element Method [J]. Rock and Soil Mechanics, 2013, 34 (S1): 348-354.
[18] 肖世国,何洪.双排抗滑桩上滑坡推力近似解析方法[J].岩土力学,2015,36(2):376-380,494. XIAO Shi-guo, HE Hong. An Approximate Analytical Method for Calculating Thrust on Double-row Stabilizing Piles [J]. Rock and Soil Mechanics, 2015, 36 (2): 376-380, 494.
[19] 戴自航.抗滑桩滑坡推力和桩前滑体抗力分布规律的研究[J].岩石力学与工程学报,2002,21(4):517-521. DAI Zi-hang. Study on Distribution Laws of Landslide-thrust and Resistance of Sliding Mass Acting on Antislide Piles [J]. Chinese Journal of Rock Mechanics and Engineering, 2002, 21 (4): 517-521.
[20] 徐良德.抗滑桩桩前滑体出现塑性变形时抗力分布的初步探讨[C]//中国土木工程学会.中国土木工程学会第四届土力学及基础工程学术会议论文选集.北京:中国土木工程学会,1983:1-7. XU Liang-de. Preliminary Study of the Resistance Distribution when Plastic Deformation Occurred on Sliding Mass Acting on Anti-sliding Piles [C] // China Civil Engineering Society. Selected Essays of China Civil Engineering Society's Fourth Soil Mechanics and Foundation Engineering Academic Conference. Beijing: China Civil Engineering Society, 1983: 1-7.
[21] JTG D63—2007,公路桥涵地基基础设计规范[S]. JTG D63—2007, Code for Design of Ground Base and Foundation of Highway Bridges and Culverts [S].
[2] 郑刚,王丽.竖向及水平荷载加载水平、顺序对单桩承载力的影响[J].岩土工程学报,2008,30(12):1796-1804. ZHENG Gang, WANG Li. Effect of Loading Level and Sequence of Vertical and Lateral Load on Bearing Capacity of Single Pile [J]. Chinese Journal of Geotechnical Engineering, 2008, 30 (12): 1796-1804.
[3] 赵春风,王卫中,赵程,等.组合荷载下单桩承载特性现场试验[J].中国公路学报,2013,26(6):59-64,72. ZHAO Chun-feng, WANG Wei-zhong, ZHAO Cheng, et al. Field Test Study on Bearing Capacity of Single Pile Under Combine Loads [J]. China Journal of Highway and Transport, 2013, 26 (6): 59-64,72.
[4] 梁发云,陈海兵,宋著.轴向荷载对横向受荷桩承载性状影响的参数分析[J].土木建筑与环境工程,2011,33(6):25-30. LIANG Fa-yun, CHEN Hai-bing, SONG Zhu. Parameter Analysis of Effects of Axial Load on the Lateral Response of Piles [J]. Journal of Civil, Architectural & Environmental Engineering, 2011, 33 (6): 25-30.
[5] 张玲,赵明华,赵衡.倾斜荷载下桩柱式桥墩受力变形分析传递矩阵法[J].中国公路学报,2015,28(2):69-76. ZHANG Ling, ZHAO Ming-hua, ZHAO Heng. Transfer Matrix Method for Deformation of Pile Type Bridge Pier Under Axial Transverse Load [J]. China Journal of Highway and Transport, 2015, 28 (2): 69-76.
[6] 杨明辉,赵明华,刘建华,等.高陡边坡桥梁基桩内力计算的幂级数解[J].中南大学学报:自然科学版,2007,38(3):561-566. YANG Ming-hui, ZHAO Ming-hua, LIU Jian-hua, et al. Power-progression Solution for Inner-force Analysis of Bridge Pile in Steep Slope [J]. Journal of Central South University: Science and Technology, 2007, 38 (3): 561-566.
[7] 赵明华,尹平保,张永杰,等.高陡斜坡段桩柱式桥墩基础设计计算方法研究[J].工程力学,2013,30(3):106-111. ZHAO Ming-hua, YIN Ping-bao, ZHANG Yong-jie, et al. The Design and Calculation Method of Pile-column Bridge Pile Foundation in High and Steep Slope [J]. Engineering Mechanics, 2013, 30 (3): 106-111.
[8] 龚先兵,杨明辉,赵明华,等.山区高陡横坡段桥梁桩基承载机理模型试验[J].中国公路学报,2013,26(2):56-62. GONG Xian-bing, YANG Ming-hui, ZHAO Ming-hua, et al. Load-bearing Mechanism Model Test for Bridge Pile Foundation in High-steep Transverse Slope [J]. China Journal of Highway and Transport, 2013, 26 (2): 56-62.
[9] 赵明华,杨超炜,杨明辉,等.基于有限杆单元法的陡坡段桥梁基桩受力分析[J].中国公路学报,2014,27(6):51-58,108. ZHAO Ming-hua, YANG Chao-wei, YANG Ming-hui, et al. Mechanical Analysis of Bridge Pile Foundation in High and Steep Slopes Based on Finite Bar Element Method [J]. China Journal of Highway and Transport, 2014, 27 (6): 51-58, 108.
[10] 尹平保,赵明华,杨超炜,等.复杂荷载下横坡段桥梁桩基承载特性试验研究[J].土木工程学报,2014,47(5):110-117. YIN Ping-bao, ZHAO Ming-hua, YANG Chao-wei, et al. Experimental Study on Bearing Capacity of Bridge Piles in Cross Slopes Under Complex Loads [J]. China Civil Engineering Journal, 2014, 47 (5):110-117.
[11] CHAE K S, UGAI K, WAKAI A. Lateral Resistance of Short Single Piles and Pile Groups Located near Slopes [J]. International Journal of Geomechanics, 2004, 4 (2): 93-103.
[12] 尹平保,杨莹,贺炜,等.考虑斜坡效应的基桩屈曲临界荷载分析[J].岩土力学,2017,38(9):2662-2668,2675. YIN Ping-bao, YANG Ying, HE Wei, et al. Analysis of Critical Buckling Loads of Piles Considering Slope Effect [J]. Rock and Soil Mechanics, 2017, 38 (9): 2662-2668, 2675.
[13] 何颐华,杨斌,金宝森,等.双排护坡桩试验与计算的研究[J].建筑结构学报,1996,17(2):58-66,29. HE Yi-hua, YANG Bin, JIN Bao-sen, et al. A Study on Test and Calculation of Double-row Fender Piles [J]. Journal of Building Structures, 1996, 17 (2): 58-66, 29.
[14] 郑刚,李欣,刘畅,等.考虑桩土相互作用的双排桩分析[J].建筑结构学报,2004,25(1):99-106. ZHENG Gang, LI Xin, LIU Chang, et al. Analysis of Double-row Piles in Consideration of the Pile-soil Interaction [J]. Journal of Building Structures, 2004, 25 (1): 99-106.
[15] 周翠英,刘祚秋,尚伟,等.门架式双排抗滑桩设计计算新模式[J].岩土力学,2005,26(3):441-444,449. ZHOU Cui-ying, LIU Zuo-qiu, SHANG Wei, et al. A New Model for Calculation of Portal Double Row Anti-sliding Piles [J]. Rock and Soil Mechanics, 2005, 26 (3): 441-444, 449.
[16] 孙勇.深基坑双排支护桩随机有限杆单元法的计算研究[J].建筑结构,2010,40(增1):261-266. SUN Yong. Calculation and Research of Stochastic Finite Bar Element Method in Double-row Retaining Piles [J]. Building Structures, 2010, 40 (S1): 261-266.
[17] 吴应祥,刘东升,宋强辉,等.基于有限元强度折减法的抗滑桩滑坡推力及抗滑桩内力可靠性分析[J].岩土力学,2013,34(增1):348-354. WU Ying-xiang, LIU Dong-sheng, SONG Qiang-hui, et al. Reliability Analysis of Landslide-thrust and Internal Forces of Anti-slide Pile Based on Strength Reduction Finite Element Method [J]. Rock and Soil Mechanics, 2013, 34 (S1): 348-354.
[18] 肖世国,何洪.双排抗滑桩上滑坡推力近似解析方法[J].岩土力学,2015,36(2):376-380,494. XIAO Shi-guo, HE Hong. An Approximate Analytical Method for Calculating Thrust on Double-row Stabilizing Piles [J]. Rock and Soil Mechanics, 2015, 36 (2): 376-380, 494.
[19] 戴自航.抗滑桩滑坡推力和桩前滑体抗力分布规律的研究[J].岩石力学与工程学报,2002,21(4):517-521. DAI Zi-hang. Study on Distribution Laws of Landslide-thrust and Resistance of Sliding Mass Acting on Antislide Piles [J]. Chinese Journal of Rock Mechanics and Engineering, 2002, 21 (4): 517-521.
[20] 徐良德.抗滑桩桩前滑体出现塑性变形时抗力分布的初步探讨[C]//中国土木工程学会.中国土木工程学会第四届土力学及基础工程学术会议论文选集.北京:中国土木工程学会,1983:1-7. XU Liang-de. Preliminary Study of the Resistance Distribution when Plastic Deformation Occurred on Sliding Mass Acting on Anti-sliding Piles [C] // China Civil Engineering Society. Selected Essays of China Civil Engineering Society's Fourth Soil Mechanics and Foundation Engineering Academic Conference. Beijing: China Civil Engineering Society, 1983: 1-7.
[21] JTG D63—2007,公路桥涵地基基础设计规范[S]. JTG D63—2007, Code for Design of Ground Base and Foundation of Highway Bridges and Culverts [S].