粘性填土重力式挡墙土压力计算方法研究
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摘要
准确确定土压力是挡墙设计的关键。朗金、库仑等经典理论所得的土压应力呈线性分布结果与实际不符,对此,苏联学者卡岗首次采用水平微分薄层单元对砂性填土挡墙进行受力分析,从理论上证实墙背土压应力呈非线性分布。后来,国内一些学者对其进行改进,考虑墙、土间摩擦作用和粘着力,使之适合任意墙背倾角及填土面的粘性填土挡墙,形成了较为完备的层分法理论。
但用层分法分析粘性填土挡墙土压力时仍存在两个问题:一是墙顶附近土压应力可能为负,致使该处公式推导时受力状态与计算后不一致;二是将墙顶附近土压应力为负的范围定为开裂深度,使该值偏大。
针对这些问题,考虑粘性填土开裂过程对土压应力的影响,本文对层分法进行了改进,重新推导出开裂分析及土压力计算公式(改进层分法)。为验证该方法合理性,采用该开裂公式,根据墙后滑裂土楔的受力平衡(力多边形法),推得一土压力合力计算公式,仍假设土压应力呈线性分布,即提出采用改进层分法开裂公式库仑理论。
编制相关程序,通过算例分析填土粘聚力、内摩擦角、墙土间粘着力、外摩擦角、填土面倾角、墙背倾角、超载对两种改进方法及现有方法(广义库仑理论、层分法、采用朗金开裂公式库仑理论)计算结果的影响,并对它们进行对比,验证了改进层分法合理性。
结果表明:(1)改进层分法消除了墙顶附近土压力出现负值的现象,所得主动土压力、倾覆力矩明显较层分法大,且填土粘聚力、墙土间粘着力越大,外摩擦角、墙背倾角越小,这种差异越显著,而填土内摩擦角、填土面倾角、超载对这种差异影响相对较小;(2)两改进方法所得的主动土压力很接近或相等,所得开裂深度相等,与现有方法相比该值最小;(3)改进层分法所得倾覆力矩最大。
综上可知,改进层分法理论上最合理,所得土压应力分布与实际较吻合,用它进行粘性填土挡墙设计最安全,可在工程实际中参考使用。
It is a key to ascertain earth pressure correctly in retaining wall design. The linear earth stress distribution result of classical theory like Rankine and Coulomb is not correspondent with the practice. A scholar named M.EKarah in Soviet Russia adopted differential level layer unit to analyze equilibrium condition of forces for retaining wall with sandy backfill firstly and confirmed that earth stress distribution is nonlinear in theory, then some domestic scholars modified the method to apply it to retaining wall with cohesive backfill and arbitrary wall back angle and fill surface, considering friction effect and adhesive force on the soil-wall interface ,and the theory is thought of as the method of layer analysis.
Though the method is relatively complete, there are two problems when using it to calculate active earth pressure on retailing wall with cohesive backfill. Firstly, the result of earth stress near the top of wall may be negative, and this leads to that the strained condition there during the formula is being deduced is not consistent to that when the result have being got . Secondly, the height near the top where the earth stress is negative is thought of as crack depth, but the value is too bigger.
Aiming at these problems, the impact of cracking course of cohesive backfill for earth stress is considered and the method is modified, then the formulas on crack depth and earth stress distribution are deduced again. In order to verify its rationality, the crack depth formula adopted and equilibrium condition of forces on sliding wedge behind wall combined with, a resultant force formula on earth pressure is deduced and the distribution is assumed to be linear, which is the Coulomb Theory with Crack Depth Formula of the Modified Method of Layer Analysis.
Corresponding programs developed, influences like cohesion and internal friction angle and adhesive force and external friction angle and fill surface angle and back angle and surcharge on the results of the two modified methods and the available methods like Generalized Coulomb Theory and Coulomb Theory with Crack Depth Formula of Rankine and the method of layer analysis are analyzed, and the results are compared, verifying rationality of the modified method of layer analysis.
The results shows that, firstly, the modified method of layer analysis avoids the phenomenon that the earth stress near the top is negative, and its active earth pressure and overturning moment are even larger comparison with the method of layer analysis, the cohesion and adhesive force larger and external friction angle and back angle less, the difference more obvious, but internal friction angle and fill surface angle and surcharge have a relatively less influence on the difference. Secondly, the active earth pressure results of the two modified methods are in good agreement, and the crack depth results are equal, which are least comparison with those of the other methods. In addition, the overturning moment result of the modified method of layer analysis is largest.
In short, the modified method of layer analysis is most reasonable theoretically, and its earth stress distribution result is consistent with the test, and it is most safe to adopt this method to design retaining with cohesive backfill, which can be used as a reference for engineers.
但用层分法分析粘性填土挡墙土压力时仍存在两个问题:一是墙顶附近土压应力可能为负,致使该处公式推导时受力状态与计算后不一致;二是将墙顶附近土压应力为负的范围定为开裂深度,使该值偏大。
针对这些问题,考虑粘性填土开裂过程对土压应力的影响,本文对层分法进行了改进,重新推导出开裂分析及土压力计算公式(改进层分法)。为验证该方法合理性,采用该开裂公式,根据墙后滑裂土楔的受力平衡(力多边形法),推得一土压力合力计算公式,仍假设土压应力呈线性分布,即提出采用改进层分法开裂公式库仑理论。
编制相关程序,通过算例分析填土粘聚力、内摩擦角、墙土间粘着力、外摩擦角、填土面倾角、墙背倾角、超载对两种改进方法及现有方法(广义库仑理论、层分法、采用朗金开裂公式库仑理论)计算结果的影响,并对它们进行对比,验证了改进层分法合理性。
结果表明:(1)改进层分法消除了墙顶附近土压力出现负值的现象,所得主动土压力、倾覆力矩明显较层分法大,且填土粘聚力、墙土间粘着力越大,外摩擦角、墙背倾角越小,这种差异越显著,而填土内摩擦角、填土面倾角、超载对这种差异影响相对较小;(2)两改进方法所得的主动土压力很接近或相等,所得开裂深度相等,与现有方法相比该值最小;(3)改进层分法所得倾覆力矩最大。
综上可知,改进层分法理论上最合理,所得土压应力分布与实际较吻合,用它进行粘性填土挡墙设计最安全,可在工程实际中参考使用。
It is a key to ascertain earth pressure correctly in retaining wall design. The linear earth stress distribution result of classical theory like Rankine and Coulomb is not correspondent with the practice. A scholar named M.EKarah in Soviet Russia adopted differential level layer unit to analyze equilibrium condition of forces for retaining wall with sandy backfill firstly and confirmed that earth stress distribution is nonlinear in theory, then some domestic scholars modified the method to apply it to retaining wall with cohesive backfill and arbitrary wall back angle and fill surface, considering friction effect and adhesive force on the soil-wall interface ,and the theory is thought of as the method of layer analysis.
Though the method is relatively complete, there are two problems when using it to calculate active earth pressure on retailing wall with cohesive backfill. Firstly, the result of earth stress near the top of wall may be negative, and this leads to that the strained condition there during the formula is being deduced is not consistent to that when the result have being got . Secondly, the height near the top where the earth stress is negative is thought of as crack depth, but the value is too bigger.
Aiming at these problems, the impact of cracking course of cohesive backfill for earth stress is considered and the method is modified, then the formulas on crack depth and earth stress distribution are deduced again. In order to verify its rationality, the crack depth formula adopted and equilibrium condition of forces on sliding wedge behind wall combined with, a resultant force formula on earth pressure is deduced and the distribution is assumed to be linear, which is the Coulomb Theory with Crack Depth Formula of the Modified Method of Layer Analysis.
Corresponding programs developed, influences like cohesion and internal friction angle and adhesive force and external friction angle and fill surface angle and back angle and surcharge on the results of the two modified methods and the available methods like Generalized Coulomb Theory and Coulomb Theory with Crack Depth Formula of Rankine and the method of layer analysis are analyzed, and the results are compared, verifying rationality of the modified method of layer analysis.
The results shows that, firstly, the modified method of layer analysis avoids the phenomenon that the earth stress near the top is negative, and its active earth pressure and overturning moment are even larger comparison with the method of layer analysis, the cohesion and adhesive force larger and external friction angle and back angle less, the difference more obvious, but internal friction angle and fill surface angle and surcharge have a relatively less influence on the difference. Secondly, the active earth pressure results of the two modified methods are in good agreement, and the crack depth results are equal, which are least comparison with those of the other methods. In addition, the overturning moment result of the modified method of layer analysis is largest.
In short, the modified method of layer analysis is most reasonable theoretically, and its earth stress distribution result is consistent with the test, and it is most safe to adopt this method to design retaining with cohesive backfill, which can be used as a reference for engineers.
引文
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[6] 陈雪华,律文田,王永和. 桥台台背土压力的试验研究[J]. 岩土力学,2006,27(8):1407-1415.
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[2] 岳祖润,彭胤宗,张师德. 压实粘性填土挡土墙土压力离心模型试验[J]. 岩土工程学报,1992,14(6):90-96.
[3] 罗强,蔡英. 成都粘土重力式挡土墙的工程试验[J]. 西南交通大学学报,1995,30(3)270-274.
[4] 徐日庆,陈页开,杨仲轩,龚晓南. 刚性挡墙被动土压力模型试验研究[J]. 岩土工程学报,2002,24(5):569-575.
[5] 李兴高,刘维宁. 挡墙上作用土压力和水土压力的测试研究[J]. 岩石力学与工程学报,2005,24(12):2149-2154.
[6] 陈雪华,律文田,王永和. 桥台台背土压力的试验研究[J]. 岩土力学,2006,27(8):1407-1415.
[7] 蒋纯秋.挡土墙土压力非线性分布解[J].土木工程学报,1964,10(1) :56-65.
[8] 赵恒惠. 挡土墙后粘性填土的土压力计算[J]. 岩土工程学报,1983,5(1):134-146.
[9] 姚代禄. 挡土墙土压力非线性分布的研究. 重庆交通学院学报. 1984,10(3):40-47.
[10] 顾慰慈. 粘性土主动土压力计算[J]. 水利学报,1991(2):55-64.
[11] 宣道光. 挡土墙粘性回填土土压力分布的研究. 华东公路,1992,1:33-59.
[12] 王渭漳,吴亚中.墙背土压力分布计算的新理论及其工程应用[M].北京:人民交通出版社,1996.
[13] 曹振民. 挡土墙填土曲线破裂面主动土压力分析[J]. 中国公路学报,1995,8(1):7-14.
[14] 赵永平. 具有倾斜表面的粘性土土压力计算[J]. 西南公路交通大学学报,1998,18(4):32-36.
[15] 张军,王贻荪. 确定挡土墙主动土压力分布的薄层分析法[J]. 湖南大学学报,1998,25(5):147-153.
[16] 王元战,王海龙,李亮.挡土墙土压力分布[J].中国港湾建设,2000,14(4):1-5.
[17] 王元战,黄长虹. 关于挡土墙主动土压力计算问题. 港工技术. 2003,2:22-27.
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