真空预压的最终负压分布模式
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摘要
为了揭示真空度衰减特性和确定最终竖向有效应力,研究了底部半透水边界下真空预压的最终负压分布模式。首先通过边界齐次化理论建立了真空预压和堆载预压固结方程之间存在的等效关系,获得最终负压沿深度分布公式。其次根据固结完成后的稳定渗流方程,研究了单层地基、多层地基和砂井地基的最终负压分布特性。研究表明,在半透水边界条件下最终负压呈现随深度衰减现象。对于单层地基或竖向排水体通水量恒定的砂井地基,最终负压沿深度呈单一线性衰减;对于多层地基或竖向排水体通水量分段恒定的砂井地基,最终负压沿深度分段线性衰减;对于渗透系数连续变化地基或竖向排水体通水量连续变化砂井地基,最终负压沿深度曲线衰减。最终负压衰减速率随着边界透水系数增大而增大。渗透系数越大的地层,最终负压衰减越慢;上层土体与最底层土体的渗透系数之比越大,底部边界处的最终负压越大,反之越小。算例表明,采用半透水边界地基模型能较合理地模拟真空预压最终负压和最终竖向有效应力沿深度减小特性。
The distribution patterns of the final negative pressure are investigated in vacuum preloading under impeded bottom boundary in order to demonstrate the degenerated properties of vacuum degree and to determine the final vertical effective stress. Firstly, the equivalent relation of consolidation equations between vacuum preloading and surcharge preloading is established according to the boundary homogenizing theory. The distribution patterns of the final negative pressure with depth are obtained. Secondly, according to the steady seepage equation of post-consolidation, the distribution properties of the final negative pressure are studied for single-layer ground, multi-layer ground and sand-drained ground. The study shows that the final negative pressure decreases along depth under impeded boundary condition. For the single-layer ground or sand-drained ground with a constant water flux of vertical drain, the final negative pressure decreases single-linearly along depth. For the multi-layers ground or sand-drained ground with piecewise constant water flux of vertical drain, the final negative pressure decreases piecewise-linearly along depth. For the ground with continuous permeability coefficient or sand-drained ground with continuous water flux of vertical drain, the final negative pressure decreases nonlinearly along depth. The rate of final negative pressure increases with the permeability coefficient of boundary. The final negative pressure decreases slowly in high permeable layer. The larger the ratio of permeability coefficient between the upper layer and the bottom layer is, the larger the final negative pressure at bottom boundary is, and vice versa. The case study shows that the ground model with impeded boundary can reasonably simulate the properties that the final negative pressure and the final vertical effective stress decrease with depth in vacuum preloading.
The distribution patterns of the final negative pressure are investigated in vacuum preloading under impeded bottom boundary in order to demonstrate the degenerated properties of vacuum degree and to determine the final vertical effective stress. Firstly, the equivalent relation of consolidation equations between vacuum preloading and surcharge preloading is established according to the boundary homogenizing theory. The distribution patterns of the final negative pressure with depth are obtained. Secondly, according to the steady seepage equation of post-consolidation, the distribution properties of the final negative pressure are studied for single-layer ground, multi-layer ground and sand-drained ground. The study shows that the final negative pressure decreases along depth under impeded boundary condition. For the single-layer ground or sand-drained ground with a constant water flux of vertical drain, the final negative pressure decreases single-linearly along depth. For the multi-layers ground or sand-drained ground with piecewise constant water flux of vertical drain, the final negative pressure decreases piecewise-linearly along depth. For the ground with continuous permeability coefficient or sand-drained ground with continuous water flux of vertical drain, the final negative pressure decreases nonlinearly along depth. The rate of final negative pressure increases with the permeability coefficient of boundary. The final negative pressure decreases slowly in high permeable layer. The larger the ratio of permeability coefficient between the upper layer and the bottom layer is, the larger the final negative pressure at bottom boundary is, and vice versa. The case study shows that the ground model with impeded boundary can reasonably simulate the properties that the final negative pressure and the final vertical effective stress decrease with depth in vacuum preloading.
引文
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[6]CHAI J C,CARTER J P,HAYASHI S.Vacuum consolidation and its combination with embankment loading[J].Canadian Geotechnical Journal,2006,43(10):985-996.
[7]RUJIKIATKAMJORN C,INDRARATNA B.Analytical solutions and design curves for vacuum-assisted consolidation with both vertical and horizontal drainage[J].Canadian Geotechnical Journal,2007,44:188-200.
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[9]郭彪,龚晓南,卢萌盟,等.真空联合堆载预压下竖井地基固结解析解[J].岩土工程学报,2013,35(6):1045-1054.(GUO Biao,GONG Xiao-nan,LU Meng-meng,et al.Analytical solution for consolidation of vertical drains by vacuum-surcharge preloading[J].Chinese Journal of Geotechnical Engineering,2013,35(6):1045-1054.(in Chinese))
[10]鲍树峰,周琦,陈平山,等.负压非均匀分布边界条件下砂井地基固结解析[J].水运工程,2015,501(3):12-20.(BAO Shu-feng,ZHOU Qi,CHEN Ping-shan,et al.Consolidation analysis for sand drains foundations with non-uniform distribution of negative pressure boundary condition[J].Port&Waterway Engineering,2015,501(3):12-20.(in Chinese)).
[11]蒋基安,陈海英,陈越,等.排水板真空度损耗的排水固结解析解[J].岩土工程学报,2016,38(3):404-418.(JIANG Ji-an,CHEN Hai-ying,CHEN Yue,et al.Analytical solutions to drainage consolidation considering vacuum loss in prefabricated vertical drain[J].Chinese Journal of Geotechnical Engineering,2016,38(3):404-418.(in Chinese))
[12]吴跃东,吴鸿昇,罗如平,等.考虑真空度衰减及涂抹区渗透系数变化的真空预压固结解析解[J].河海大学学报(自然科学版),2016,44(2):122-128.(WU Yue-dong,WUHong-sheng,LUO Ru-ping,et al.Analytical solutions for vacuum preloading consolidation considering vacuum degree attenuation and change of permeability coefficient in smear zones[J].Journal of Hohai University(Natural Science),2016,44(2):122-128.(in Chinese))
[13]朱群峰,高长胜,杨守华,等.超软淤泥地基处理中真空度传递特性研究[J].岩土工程学报,2010,32(9):1429-1432.(ZHU Qun-feng,GAO Chang-sheng,YANG Shou-hua,et al.Transfer properties of vacuum degree in treatment of super-soft muck foundation[J].Chinese Journal of Geotechnical Engineering,2010,32(9):1429-1432.(in Chinese))
[14]唐彤芝,董江平,黄家青,等.薄砂层长短板结合真空预压法处理吹填淤泥土试验研究[J].岩土工程学报,2012,34(5):899-905.(TANG Tong-zhi,DONG Jiang-ping,HUANG Jia-qing,et al.Experimental research on hydraulic filled mud consolidated by vacuum preloading method combining long and short boards with thin sand cushions[J].Chinese Journal of Geotechnical Engineering,2012,34(5):899-905.(in Chinese))
[15]姜彦彬,何宁,许滨华,等.真空预压负压分布规律模型试验研究[J].岩土工程学报,2017,39(10):1834-1883.(JIANG Yan-bin,HE Ning,XU Bin-hua,et al.Model tests on negative pressure distribution in vacuum preloading[J].Chinese Journal of Geotech-nical Engineering,2017,39(10):1834-1883.(in Chinese))
[16]ZHANG Zhen,YE Guan-bao,XU Yan.Comparative analysis on performance of vertical drain improved clay deposit under vacuum or surcharge loading[J].Geotextiles and Geomembranes,2018,46:146-154.
[17]胡亚元.半透水边界砂井地基的真空预压固结[J].工程科学与技术,2018,50(2):32-41.(HU Ya-yuan.Consolidationsolution for sand-drained ground with impeded boundar-iesundervacuumpreloading[J].Advanced Engineering Sciences,2018,50(2):32-41.(in Chinese))
[18]胡亚元.半透水边界砂井真空联合堆载预压Hansbo固结解[J].工程科学学报,2018,40(7):783-792.(HU Ya-yuan.A Hansbo's consolidation solution of sand-drained ground with impeded boundaries under vacuum and surcharge preloading[J].Chinese Journal of Engineering,2018,40(7):783-792.(in Chinese))
[19]岑仰润,俞建霖,龚晓南.真空排水预压工程中真空度的现场测试与分析[J].岩土力学,2003,24(4):603-605.(CEN Yang-run,YU Jian-lin,GONG Xiao-nan.Field test and analysis of vacuum pressure in vacuum drainage preloading[J].Rock and Soil Mechanics,2003,24(4):603-605.(in Chinese))
[20]仲彦,赵岩,尹长权.真空荷载的几种表述及其应用[J].中国港湾建设,2014(10):23-26.(ZHONG Yan,ZHAO Yan,YI Chang-quan.Some expressions of vacuum load and their application[J].China Harbour Engineering,2014(10):23-26.(in Chinese))
[21]谢康和,曾国熙.等应变条件下的砂井地基固结解析理论[J].岩土工程学报,1989,11(2):3-17.(XIE Kang-he,ZENG Guo-xi.Analytical theory of sand-drained ground under equal strain condition[J].Chinese Journal of Geotechnical Engineering,1989,11(2):3-17.(in Chinese))
[22]HANSBO S.Consolidation of fine-grained soils by prefabricated drains[C]//Proceedings of the 10th International Conference on Soil Mechanics and Foundation Engineering.Stockholm,1981:677-682.
[23]王瑞春,谢康和.半透水边界的竖向排水井地基粘弹性固结分析[J].长江科学院院报,2001,18(6):33-36.(WANGRui-chun,XIE Kang-he.Analysis of viscoelastic consolidation of soil foundations by vertical drain wells considering semi-permeable boundary[J].Journal of Yangtze River Scientific Research Institute,2001,18(6):33-36.(in Chinese))
[24]丁天锐,叶观宝,许言,等.场地形成工程处理效果及真空度传递研究[J].公路交通科技(应用技术版),2016(5):156-158.(DING Tian-rui,YE Guan-bao,XU Yan,et al.Study on treatment effects and vacuum transfer in site formation engineering[J].Journal of Highway and Transporation(Applied Science and Technology Edition),2016(5):156-158.(in Chinese))
[2]CHU J,YAN W,YANG H.Soil improvement by the vacuum preloading method for an oil storage station[J].Géotechnique,2000,50(6):625-632.
[3]董志良.堆载及真空预压砂井地基固结解析理论[J].水运工程,1992(9):1-7.(DONG Zhi-liang.Consolidation theory on heaped load&vacuum preloading of sand drain foundation[J].Port&Water Engineering,1992(9):1-7.(in Chinese))
[4]彭劼,刘汉龙,陈永辉,等.真空-堆载联合预压法软基加固对周围环境的影响[J].岩土工程学报,2002,24(5):656-659.(PENG Jie,LIU Han-long,CHEN Yong-hui,et al.Effect of soft ground under preloading with vacuum preloading on environment[J].Chinese Journal of Geotechnical Engineering,2002,24(5):656-659.(in Chinese))
[5]INDRARATNA B,RUJIKIATKAMJORN C,SATHANANT-HAN L.Analytical and numerical solutions for a single vertical drain including the effects of vacuum preloading[J].Canadian Geotechnical Journal,2005,42(4):994-1014.
[6]CHAI J C,CARTER J P,HAYASHI S.Vacuum consolidation and its combination with embankment loading[J].Canadian Geotechnical Journal,2006,43(10):985-996.
[7]RUJIKIATKAMJORN C,INDRARATNA B.Analytical solutions and design curves for vacuum-assisted consolidation with both vertical and horizontal drainage[J].Canadian Geotechnical Journal,2007,44:188-200.
[8]周琦,张功新,王友元,等.真空预压条件下的砂井地基Hansbo固结解[J].岩石力学与工程学报,2010,29(增刊2):3994-3998.(ZHOU Qi,ZHANG Gong-xin,WANGYou-yuan,et al.Hansbo consolidation solution for and-drained ground under vacuum preloading[J].Chinese Journal of Rock Mechanics and Engineering,2010,29(S2):3994-3998.(in Chinese))
[9]郭彪,龚晓南,卢萌盟,等.真空联合堆载预压下竖井地基固结解析解[J].岩土工程学报,2013,35(6):1045-1054.(GUO Biao,GONG Xiao-nan,LU Meng-meng,et al.Analytical solution for consolidation of vertical drains by vacuum-surcharge preloading[J].Chinese Journal of Geotechnical Engineering,2013,35(6):1045-1054.(in Chinese))
[10]鲍树峰,周琦,陈平山,等.负压非均匀分布边界条件下砂井地基固结解析[J].水运工程,2015,501(3):12-20.(BAO Shu-feng,ZHOU Qi,CHEN Ping-shan,et al.Consolidation analysis for sand drains foundations with non-uniform distribution of negative pressure boundary condition[J].Port&Waterway Engineering,2015,501(3):12-20.(in Chinese)).
[11]蒋基安,陈海英,陈越,等.排水板真空度损耗的排水固结解析解[J].岩土工程学报,2016,38(3):404-418.(JIANG Ji-an,CHEN Hai-ying,CHEN Yue,et al.Analytical solutions to drainage consolidation considering vacuum loss in prefabricated vertical drain[J].Chinese Journal of Geotechnical Engineering,2016,38(3):404-418.(in Chinese))
[12]吴跃东,吴鸿昇,罗如平,等.考虑真空度衰减及涂抹区渗透系数变化的真空预压固结解析解[J].河海大学学报(自然科学版),2016,44(2):122-128.(WU Yue-dong,WUHong-sheng,LUO Ru-ping,et al.Analytical solutions for vacuum preloading consolidation considering vacuum degree attenuation and change of permeability coefficient in smear zones[J].Journal of Hohai University(Natural Science),2016,44(2):122-128.(in Chinese))
[13]朱群峰,高长胜,杨守华,等.超软淤泥地基处理中真空度传递特性研究[J].岩土工程学报,2010,32(9):1429-1432.(ZHU Qun-feng,GAO Chang-sheng,YANG Shou-hua,et al.Transfer properties of vacuum degree in treatment of super-soft muck foundation[J].Chinese Journal of Geotechnical Engineering,2010,32(9):1429-1432.(in Chinese))
[14]唐彤芝,董江平,黄家青,等.薄砂层长短板结合真空预压法处理吹填淤泥土试验研究[J].岩土工程学报,2012,34(5):899-905.(TANG Tong-zhi,DONG Jiang-ping,HUANG Jia-qing,et al.Experimental research on hydraulic filled mud consolidated by vacuum preloading method combining long and short boards with thin sand cushions[J].Chinese Journal of Geotechnical Engineering,2012,34(5):899-905.(in Chinese))
[15]姜彦彬,何宁,许滨华,等.真空预压负压分布规律模型试验研究[J].岩土工程学报,2017,39(10):1834-1883.(JIANG Yan-bin,HE Ning,XU Bin-hua,et al.Model tests on negative pressure distribution in vacuum preloading[J].Chinese Journal of Geotech-nical Engineering,2017,39(10):1834-1883.(in Chinese))
[16]ZHANG Zhen,YE Guan-bao,XU Yan.Comparative analysis on performance of vertical drain improved clay deposit under vacuum or surcharge loading[J].Geotextiles and Geomembranes,2018,46:146-154.
[17]胡亚元.半透水边界砂井地基的真空预压固结[J].工程科学与技术,2018,50(2):32-41.(HU Ya-yuan.Consolidationsolution for sand-drained ground with impeded boundar-iesundervacuumpreloading[J].Advanced Engineering Sciences,2018,50(2):32-41.(in Chinese))
[18]胡亚元.半透水边界砂井真空联合堆载预压Hansbo固结解[J].工程科学学报,2018,40(7):783-792.(HU Ya-yuan.A Hansbo's consolidation solution of sand-drained ground with impeded boundaries under vacuum and surcharge preloading[J].Chinese Journal of Engineering,2018,40(7):783-792.(in Chinese))
[19]岑仰润,俞建霖,龚晓南.真空排水预压工程中真空度的现场测试与分析[J].岩土力学,2003,24(4):603-605.(CEN Yang-run,YU Jian-lin,GONG Xiao-nan.Field test and analysis of vacuum pressure in vacuum drainage preloading[J].Rock and Soil Mechanics,2003,24(4):603-605.(in Chinese))
[20]仲彦,赵岩,尹长权.真空荷载的几种表述及其应用[J].中国港湾建设,2014(10):23-26.(ZHONG Yan,ZHAO Yan,YI Chang-quan.Some expressions of vacuum load and their application[J].China Harbour Engineering,2014(10):23-26.(in Chinese))
[21]谢康和,曾国熙.等应变条件下的砂井地基固结解析理论[J].岩土工程学报,1989,11(2):3-17.(XIE Kang-he,ZENG Guo-xi.Analytical theory of sand-drained ground under equal strain condition[J].Chinese Journal of Geotechnical Engineering,1989,11(2):3-17.(in Chinese))
[22]HANSBO S.Consolidation of fine-grained soils by prefabricated drains[C]//Proceedings of the 10th International Conference on Soil Mechanics and Foundation Engineering.Stockholm,1981:677-682.
[23]王瑞春,谢康和.半透水边界的竖向排水井地基粘弹性固结分析[J].长江科学院院报,2001,18(6):33-36.(WANGRui-chun,XIE Kang-he.Analysis of viscoelastic consolidation of soil foundations by vertical drain wells considering semi-permeable boundary[J].Journal of Yangtze River Scientific Research Institute,2001,18(6):33-36.(in Chinese))
[24]丁天锐,叶观宝,许言,等.场地形成工程处理效果及真空度传递研究[J].公路交通科技(应用技术版),2016(5):156-158.(DING Tian-rui,YE Guan-bao,XU Yan,et al.Study on treatment effects and vacuum transfer in site formation engineering[J].Journal of Highway and Transporation(Applied Science and Technology Edition),2016(5):156-158.(in Chinese))
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