边坡框架梁文克尔简化计算方法及工程应用
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摘要
为了改进边坡框架梁的计算方法,基于文克尔地基梁假定,考虑框架梁与土体的互相作用,通过关键点拟合的方法,把指数函数和三角函数简化为一元二次函数,推导出边坡框架梁的简化计算公式。该方法被应用于福建一处边坡支护工程,采用锚索框架梁支护,施工过程中对边坡进行位移监测。研究结果表明,传统的文克尔地基梁计算需要求解微分方程,计算过程比较复杂,不适合设计中使用,而简化后的计算方法容易掌握,可以方便计算出框架梁的端部弯矩和跨中弯矩。边坡位移监测结果表明该简化计算方法安全可行。研究结果对边坡框架梁的工程设计有一定的参考作用。
In order to improve the calculation method of the slope frame beam, based on Winkler foundation beam assumption, considering the interaction between the frame beam and the soil mass, the exponential function and trigonometric function are simplified into a unary quadratic function through the method of key points fitting, and the simplified calculation formula of the slope frame beam is deduced. This method is applied to a slope support project in Fujian province, which adopts anchor frame beam to support and monitors the displacement of the slope in the construction process. The results show that the traditional Winkler beam calculation requires the solution of differential equation, and the calculation process is complex, which is not suitable for use in design, but the simplified calculation method is easy to grasp, which can be used to calculate the end bending moment and mid-span bending moment of the frame beam. The results of slope displacement monitoring show that the simplified method is safe and feasible. The results of this study can be used as a reference for the engineering design of slope frame beams.
In order to improve the calculation method of the slope frame beam, based on Winkler foundation beam assumption, considering the interaction between the frame beam and the soil mass, the exponential function and trigonometric function are simplified into a unary quadratic function through the method of key points fitting, and the simplified calculation formula of the slope frame beam is deduced. This method is applied to a slope support project in Fujian province, which adopts anchor frame beam to support and monitors the displacement of the slope in the construction process. The results show that the traditional Winkler beam calculation requires the solution of differential equation, and the calculation process is complex, which is not suitable for use in design, but the simplified calculation method is easy to grasp, which can be used to calculate the end bending moment and mid-span bending moment of the frame beam. The results of slope displacement monitoring show that the simplified method is safe and feasible. The results of this study can be used as a reference for the engineering design of slope frame beams.
引文
[1] 郑卫锋, 陈国周. 预应力锚杆支护的力学分析与工程应用[M]. 北京: 中国标准出版社, 2017.ZHENG Weifeng, CHEN Guozhou. Mechanical analysis and engineering application of prestress anchor retaining[M]. Beijing: Standards Press of China, 2017. (in Chinese)
[2] 李楠, 汪班桥, 门玉明, 等. 压力型锚杆支护滑坡的地震动力响应特性研究[J]. 地质力学学报, 2018, 24(4): 490～497.LI Nan, WANG Banqiao, MEN Yuming, et al. Study on dynamic response of landslide supported by pressure-type anchor under earthquake[J]. Journal of Geomechanics, 2018, 24(4): 490～497. (in Chinese with English abstract)
[3] 秦凤艳, 杨富莲, 刘洪波, 等. 常见边坡支护形式的地震稳定性对比分析[J]. 地震工程学报, 2017, 39(3): 460～466.QIN Fengyan, YANG Fulian, LIU Hongbo, et al. Comparative analysis of seismic stability on a common slope support form[J]. China Earthquake Engineering Journal, 2017, 39(3): 460～466. (in Chinese with English abstract)
[4] 李林昊, 赵宇飞, 汪小刚. 预应力锚索边坡加固作用的离心机试验研究[J]. 水利水电技术, 2018, 49(1): 143～148.LI Linhao, ZHAO Yufei, WANG Xiaogang. Centrifuge experiment-based study on slope reinforcing effect of anchor cable[J]. Water Resources and Hydropower Engineering, 2018, 49(1): 143～148. (in Chinese with English abstract)
[5] 张耀华. 类土质边坡支护锚杆框架梁间距分析[D]. 广州: 华南理工大学, 2016.ZHANG Yaohua. Similar soil slope supporting anchor frame beam spacing analysis[D]. Guangzhou: South China University of Technology, 2016. (in Chinese with English abstract)
[6] 言志信, 段建, 王后裕. 边坡稳定性及支护[M]. 北京: 科学出版社, 2017.YAN Zhixin, DUN Jian, WANG Houyu. Slope stability and retaining[M]. Beijing: Science Press, 2017 (in Chinese)
[7] 曹兴松, 周德培. 软岩高边坡预应力锚索框架梁的一种新型设计方法[J]. 公路交通科技, 2004, 21(8): 25～28.CAO Xingsong, ZHOU Depei. A new design method of prestressed anchor rope framework for high slope in weak rockmass[J]. Journal of Highway and Transportation Research and Development, 2004, 21(8): 25～28. (in Chinese with English abstract)
[8] 马杰. 边坡工程中预应力锚索格构梁综合应用研究[D]. 西安: 长安大学, 2009.MA Jie. Reach on the application of pre-stressed anchorage cable with lattice beam in the slope project[D]. Xi’an: Chang’an University, 2009. (in Chinese with English abstract)
[9] 夏雄, 周德培. Winkler弹性地基上预应力锚索地梁内力的计算方法[J]. 铁道标准设计, 2005, (1): 46～48.XIA Xiong, ZHOU Depei. A method of internal force calculation on prestressed anchor cable beam on winkler elastic fouundation[J]. Railway Standard Design, 2005, (1): 46～48. (in Chinese with English abstract)
[10] 陈开友, 刘晓朋. 边坡工程中预应力锚索框架梁的计算分析[J]. 工程勘察, 2010, (S1): 487～494.CHEN Kaiyou, Liu Xiaopeng. Analysis of internal force of the trellis beams with prestressed anchors in treatment of slope[J]. Geotechnical Investigation & Survrying, 2010, (S1): 487～494. (in Chinese with English abstract)
[11] 陈波. 边坡加固中预应力锚索框架梁内力计算[J]. 石家庄铁道学院学报(自然科学版), 2008, 21(4): 93～96.CHEN Bo. Design calculation of prestressed frame beam-on-foundation for slope-reinforcing[J]. Journal of Shijiazhuang Railway Institute (Natural Science), 2008, 21(4): 93～96. (in Chinese with English abstract)
[12] 肖世国, 周德培. 岩石高边坡一种预应力锚索框架型地梁的内力计算[J]. 岩土工程学报, 2002, 24(4): 479～482.XIAO Shiguo, ZHOU Depei. A calculation method for internal force of prestressed anchor-rope and frame beam-on-foundation on high rock slope[J]. Chinese Journal of Geotechnical Engineering, 2002, 24(4): 479～482. (in Chinese with English abstract)
[13] 龙驭球. 弹性地基梁的计算[M]. 北京: 人民教育出版社, 1981.LONG Yuqiu. Computation of elastically supported beams[M]. Beijing: People’s Education Press, 1981. (in Chinese)
[14] 宰金珉, 宰金璋. 高层建筑基础分析与设计: 土与结构物共同作用的理论与应用[M]. 北京: 中国建筑工业出版社, 1993.ZAI Jinmin, ZAI Jinzhang. The analysis and design of the foundation of super structures[M]. Beijing: China Architecture and Building Press, 1993. (in Chinese)
[15] 陈国周. 岩土锚固工程中若干问题的研究[D]. 大连: 大连理工大学, 2008.CHEN Guozhou. The study of some problems in the anchorage engineering for soil and rock[D]. Dalian: Dalian University of Technology, 2008. (in Chinese with English abstract)
[2] 李楠, 汪班桥, 门玉明, 等. 压力型锚杆支护滑坡的地震动力响应特性研究[J]. 地质力学学报, 2018, 24(4): 490～497.LI Nan, WANG Banqiao, MEN Yuming, et al. Study on dynamic response of landslide supported by pressure-type anchor under earthquake[J]. Journal of Geomechanics, 2018, 24(4): 490～497. (in Chinese with English abstract)
[3] 秦凤艳, 杨富莲, 刘洪波, 等. 常见边坡支护形式的地震稳定性对比分析[J]. 地震工程学报, 2017, 39(3): 460～466.QIN Fengyan, YANG Fulian, LIU Hongbo, et al. Comparative analysis of seismic stability on a common slope support form[J]. China Earthquake Engineering Journal, 2017, 39(3): 460～466. (in Chinese with English abstract)
[4] 李林昊, 赵宇飞, 汪小刚. 预应力锚索边坡加固作用的离心机试验研究[J]. 水利水电技术, 2018, 49(1): 143～148.LI Linhao, ZHAO Yufei, WANG Xiaogang. Centrifuge experiment-based study on slope reinforcing effect of anchor cable[J]. Water Resources and Hydropower Engineering, 2018, 49(1): 143～148. (in Chinese with English abstract)
[5] 张耀华. 类土质边坡支护锚杆框架梁间距分析[D]. 广州: 华南理工大学, 2016.ZHANG Yaohua. Similar soil slope supporting anchor frame beam spacing analysis[D]. Guangzhou: South China University of Technology, 2016. (in Chinese with English abstract)
[6] 言志信, 段建, 王后裕. 边坡稳定性及支护[M]. 北京: 科学出版社, 2017.YAN Zhixin, DUN Jian, WANG Houyu. Slope stability and retaining[M]. Beijing: Science Press, 2017 (in Chinese)
[7] 曹兴松, 周德培. 软岩高边坡预应力锚索框架梁的一种新型设计方法[J]. 公路交通科技, 2004, 21(8): 25～28.CAO Xingsong, ZHOU Depei. A new design method of prestressed anchor rope framework for high slope in weak rockmass[J]. Journal of Highway and Transportation Research and Development, 2004, 21(8): 25～28. (in Chinese with English abstract)
[8] 马杰. 边坡工程中预应力锚索格构梁综合应用研究[D]. 西安: 长安大学, 2009.MA Jie. Reach on the application of pre-stressed anchorage cable with lattice beam in the slope project[D]. Xi’an: Chang’an University, 2009. (in Chinese with English abstract)
[9] 夏雄, 周德培. Winkler弹性地基上预应力锚索地梁内力的计算方法[J]. 铁道标准设计, 2005, (1): 46～48.XIA Xiong, ZHOU Depei. A method of internal force calculation on prestressed anchor cable beam on winkler elastic fouundation[J]. Railway Standard Design, 2005, (1): 46～48. (in Chinese with English abstract)
[10] 陈开友, 刘晓朋. 边坡工程中预应力锚索框架梁的计算分析[J]. 工程勘察, 2010, (S1): 487～494.CHEN Kaiyou, Liu Xiaopeng. Analysis of internal force of the trellis beams with prestressed anchors in treatment of slope[J]. Geotechnical Investigation & Survrying, 2010, (S1): 487～494. (in Chinese with English abstract)
[11] 陈波. 边坡加固中预应力锚索框架梁内力计算[J]. 石家庄铁道学院学报(自然科学版), 2008, 21(4): 93～96.CHEN Bo. Design calculation of prestressed frame beam-on-foundation for slope-reinforcing[J]. Journal of Shijiazhuang Railway Institute (Natural Science), 2008, 21(4): 93～96. (in Chinese with English abstract)
[12] 肖世国, 周德培. 岩石高边坡一种预应力锚索框架型地梁的内力计算[J]. 岩土工程学报, 2002, 24(4): 479～482.XIAO Shiguo, ZHOU Depei. A calculation method for internal force of prestressed anchor-rope and frame beam-on-foundation on high rock slope[J]. Chinese Journal of Geotechnical Engineering, 2002, 24(4): 479～482. (in Chinese with English abstract)
[13] 龙驭球. 弹性地基梁的计算[M]. 北京: 人民教育出版社, 1981.LONG Yuqiu. Computation of elastically supported beams[M]. Beijing: People’s Education Press, 1981. (in Chinese)
[14] 宰金珉, 宰金璋. 高层建筑基础分析与设计: 土与结构物共同作用的理论与应用[M]. 北京: 中国建筑工业出版社, 1993.ZAI Jinmin, ZAI Jinzhang. The analysis and design of the foundation of super structures[M]. Beijing: China Architecture and Building Press, 1993. (in Chinese)
[15] 陈国周. 岩土锚固工程中若干问题的研究[D]. 大连: 大连理工大学, 2008.CHEN Guozhou. The study of some problems in the anchorage engineering for soil and rock[D]. Dalian: Dalian University of Technology, 2008. (in Chinese with English abstract)