结构性黄土劈裂注浆力学机理分析
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摘要
为了在塑性力学与大变形理论基础上分析黄土地区劈裂注浆力学机理,将注浆初始阶段视为无限土体中的圆孔扩张问题,将孔周围的土体应力分布分为3个区域:弹性区、塑性区及破坏区。结合结构性黄土修正剑桥模型,在弹性区采用小变形理论,在塑性区、破坏区采用大变形理论。根据应力平衡方程、应力应变连续边界条件,推导了考虑排水和大变形时塑性区、破坏区半径及竖向、水平劈裂注浆压力的理论解答,最后结合工程算例进行论证。结果表明:该解答综合考虑了黄土的结构性参数、压缩模量、泊松比、内摩擦角、塑性破坏参数、剪胀系数、扩孔形式k及屈服准则等因素;同时,还分析了浆泡周围土体的应力应变分布解及在参数影响下的递变规律;经对比分析发现,该文的劈裂注浆压力理论计算值与工程实测值比较接近,初步证实了理论的可靠性,在黄土地区劈裂注浆工程中具有一定的实用价值。
Based on the theory of plastic mechanics and large-deformation, this paper analyzes the mechanical mechanism of fracturing grouting in loess area. It treats the early phase of grouting as the problem of cavity expansion in infinite soil and divides the stress distribution due to the cavity expansion in soil into three zones:elastic zone, plastic zone and damage zone. Combined with the modified Cam-clay model of structural loess, the deformation following small deformation assumption in elastic zone and large deformation assumption in plastic and damage zones is taken into consideration. According to the stress equilibrium equation and stress-strain continuous boundary conditions, the radius of the plastic and damage zones, the vertical and horizontal fracturing grouting pressures are deduced considering the drainage conditions and large deformation. Finally, the paper demonstrates these by engineering cases. The results show that the solution takes into account the structural parameters, compressive modulus, Poisson's ratio, internal friction angle, damage coefficient, dilatancy coefficient, form of expanding, k, yield criterion and so on. At the same time, the stress-strain distribution solution for the soil around the slurry and the grading regularity of them under the influence of the parameters are analyzed. The comparative analysis shows that the calculated value of the fracturing grouting pressure is very close to the measured value in projects, which preliminarily verifies the reliability of the theory. Therefore, the paper has considerable practical value in fracturing grouting in loess area.
Based on the theory of plastic mechanics and large-deformation, this paper analyzes the mechanical mechanism of fracturing grouting in loess area. It treats the early phase of grouting as the problem of cavity expansion in infinite soil and divides the stress distribution due to the cavity expansion in soil into three zones:elastic zone, plastic zone and damage zone. Combined with the modified Cam-clay model of structural loess, the deformation following small deformation assumption in elastic zone and large deformation assumption in plastic and damage zones is taken into consideration. According to the stress equilibrium equation and stress-strain continuous boundary conditions, the radius of the plastic and damage zones, the vertical and horizontal fracturing grouting pressures are deduced considering the drainage conditions and large deformation. Finally, the paper demonstrates these by engineering cases. The results show that the solution takes into account the structural parameters, compressive modulus, Poisson's ratio, internal friction angle, damage coefficient, dilatancy coefficient, form of expanding, k, yield criterion and so on. At the same time, the stress-strain distribution solution for the soil around the slurry and the grading regularity of them under the influence of the parameters are analyzed. The comparative analysis shows that the calculated value of the fracturing grouting pressure is very close to the measured value in projects, which preliminarily verifies the reliability of the theory. Therefore, the paper has considerable practical value in fracturing grouting in loess area.
引文
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[13]王志丰,沈永龙.单根水平旋喷桩施工引起周围土体变形的实用计算方法研究[J].工程力学,2017,34(5):78―85.Wang Zhifeng,Shen Yonglong.An approach to calculated ground deformation induced by installation of single horizontal JET grout column[J].Engineering Mechanics,2017,34(5):78―85.(in Chinese)
[14]张亚国,李镜培,饶平平.倾斜坡体中圆孔扩张的弹塑性力学解析[J].工程力学,2014,31(7):23―29.Zhang Yaguo,Li Jingpei,Rao Pingping.Elastic stress analysis of circular cavity expansion under a slope[J].Engineering Mechanics,2014,31(7):23―29.(in Chinese)
[15]Zou J F,Du J M.A new approach for the quasi-plane strain-softening problem of cylindrical cavity expansion based on Cam-Clay model[J].Journal of Mechanical Science&Technology,2017,31(3):1315―1320.
[16]Silvestri V,Tabib C.Analysis of cylindrical cavity expansion in modified cam clay with k0 consolidation[C]//International Congress and Exhibition Sustainable Civil Infrastructures:Innovative Infrastructure Geotechnology.Egypt:Springer,Cham,2017:297―310.
[17]Rao P,Chen Q,Li L,et al.An elastoplastic solution for spherical cavity expansion in modified cam clay soil under drained condition[J].International Journal of Geomechanics,2017,17(8):1.
[18]胡伟,刘明振.非饱和土中球孔扩张的弹塑性分析[J].岩土工程学报,2006,28(10):1292―1297.Hu Wei,Liu Mingzhen.Elastic-panstic solution of expansion of sphere cavity in unsaturated soils[J].Chinese Journal of Geotechnical Engineering,2006,28(10):1292―1297.(in Chinese)
[19]骆亚生,谢定义,邵生俊,等.复杂应力条件下的土结构性参数[J].岩石力学与工程学报,2004,23(24):4248―4251.Luo Yasheng,Xie Dingyi,Shao Shengjun,et al.Structural parameter of soil under complex stress conditions[J].Chinese Journal of Rock Mechanics and Engneering,2004,23(24):4248―4251.(in Chinese)
[20]沈珠江.土体结构性的数学模型-21世纪土力学的核心问题[J].岩土工程学报,1996,18(1):95―97.Sheng Zhujiang.The mathematic model of structural soils[J].Chinese Journal of Geotechnical Engineering,1996,18(1):95―97.(in Chinese)
[21]邓国华,邵生俊,佘芳涛.结构性黄土的修正剑桥模型[J].岩土工程学报,2012,34(5):834―841.Deng Guohua,Shao Shengjun,She Fangtao.Modified Cam-clay model of structured loess[J].Chinese Journal of Geotechnical Engineering,2012,34(5):834―841.(in Chinese)
[22]罗战友,夏建中,龚晓南.不同拉压模量及软化特性的球形孔扩张问题的统一解[J].工程力学,2006,23(4):22―27Luo Zhanyou,Xia Jianzhong,Gong Xiaonan.Unified solution for the expansionof spherical cavity in strain-softening materials with different elastic moduli in tensile and compression[J].Engineering Mechanics,2006,23(4):22―27.(in Chinese)
[2]Dyba V P,Skibin E G.Evaluation of bearing capacity of driven piles,based on the results of solutionof the cylindrical cavity expansion problem[J].Soil Mechanics&Foundation Engineering,2017,53(6):381―384.
[3]Chen S L,Abousleiman Y N.Cavity expansion in strain hardening frictional soils under drained condition[J].International Journal for Numerical&Analytical Methods in Geomechanics,2018,42(1):1―11.
[4]Mo P Q,Yu H S.Drained cavity expansion analysiswith a unified state parameter model for clay and sand[J].Canadian Geotechnical Journal,2017,67(2):1―13.
[5]Zhou H,Liu H L,Zha Y H,et al.Influence of stress anisotropy on the cylindrical cavity expansion in undrained elastic-perfectly plastic soil[J].Science China Technological Sciences,2018,61(3):1―11.
[6]吴创周,杨林德,李秋实.弹脆塑性围岩应力和位移的广义SMP准则解[J].工程力学,2013,30(8):223―228.Wu Chuangzhou,Yang Linde,Li Qiushi.Perfect elastic-brittle-plastic solution of axisymmetric circular opening in rock mass on extended SMP criterion[J].Engineering Mechanics,2013,30(8):223―228.(in Chinese)
[7]孟强,赵洪波,茹忠亮,等.锚杆支护圆形隧洞弹塑性解[J].工程力学,2015,32(7):17―25.Meng Qiang,Zhao Hongbo,Gu Zhongliang,et al.Analytical solution for circular tunnels with rock bolts[J].Engineering Mechanics,2015,32(7):17―25.(in Chinese)
[8]刘时鹏,施建勇,雷国辉,等.K0固结饱和土体柱孔扩张问题一种相似解法[J].工程力学,2016,33(12):128―134.Liu Shipeng,Shi Jianyong,Lei Guohui,et al.Asimilaritysolution method of cylindrical cavity expansion in K0 consolidation soils[J].Engineering Mechanics,2016,33(12):128―134.(in Chinese)
[9]Carter J P,Booker J R,Yeung S K.Cavity expansion in cohesive frictional soils[J].Geotechnique,1986,36(3):349―358.
[10]Collins I F,Stimpson J R.Similarity solutions for drained and undrained cavity expansions in soils[J].Geotechnique,1994,44(1):21―34.
[11]周航,孔纲强,刘汉龙.正方形孔扩张弹性分析[J].工程力学,2013,30(12):182―186.Zhou Hang,Kong Gangqiang,Liu Hanglong.Elasitic analysis of square cavity expansion[J].Engineering Mechanics,2013,30(12):182―186.(in Chinese)
[12]陈昌富,肖淑君.基于统一强度理论考虑拉压模量不同散体材料桩承载力计算[J].工程力学,2007,24(10):105―112.Chen Changfu,Xiao Shujun.Bearing capacity of aggrecate pile with different ratio of tension modulus to compression modulus based on unified strength theory[J].Engineering Mechanics,2007,24(10):105―112.(in Chinese)
[13]王志丰,沈永龙.单根水平旋喷桩施工引起周围土体变形的实用计算方法研究[J].工程力学,2017,34(5):78―85.Wang Zhifeng,Shen Yonglong.An approach to calculated ground deformation induced by installation of single horizontal JET grout column[J].Engineering Mechanics,2017,34(5):78―85.(in Chinese)
[14]张亚国,李镜培,饶平平.倾斜坡体中圆孔扩张的弹塑性力学解析[J].工程力学,2014,31(7):23―29.Zhang Yaguo,Li Jingpei,Rao Pingping.Elastic stress analysis of circular cavity expansion under a slope[J].Engineering Mechanics,2014,31(7):23―29.(in Chinese)
[15]Zou J F,Du J M.A new approach for the quasi-plane strain-softening problem of cylindrical cavity expansion based on Cam-Clay model[J].Journal of Mechanical Science&Technology,2017,31(3):1315―1320.
[16]Silvestri V,Tabib C.Analysis of cylindrical cavity expansion in modified cam clay with k0 consolidation[C]//International Congress and Exhibition Sustainable Civil Infrastructures:Innovative Infrastructure Geotechnology.Egypt:Springer,Cham,2017:297―310.
[17]Rao P,Chen Q,Li L,et al.An elastoplastic solution for spherical cavity expansion in modified cam clay soil under drained condition[J].International Journal of Geomechanics,2017,17(8):1.
[18]胡伟,刘明振.非饱和土中球孔扩张的弹塑性分析[J].岩土工程学报,2006,28(10):1292―1297.Hu Wei,Liu Mingzhen.Elastic-panstic solution of expansion of sphere cavity in unsaturated soils[J].Chinese Journal of Geotechnical Engineering,2006,28(10):1292―1297.(in Chinese)
[19]骆亚生,谢定义,邵生俊,等.复杂应力条件下的土结构性参数[J].岩石力学与工程学报,2004,23(24):4248―4251.Luo Yasheng,Xie Dingyi,Shao Shengjun,et al.Structural parameter of soil under complex stress conditions[J].Chinese Journal of Rock Mechanics and Engneering,2004,23(24):4248―4251.(in Chinese)
[20]沈珠江.土体结构性的数学模型-21世纪土力学的核心问题[J].岩土工程学报,1996,18(1):95―97.Sheng Zhujiang.The mathematic model of structural soils[J].Chinese Journal of Geotechnical Engineering,1996,18(1):95―97.(in Chinese)
[21]邓国华,邵生俊,佘芳涛.结构性黄土的修正剑桥模型[J].岩土工程学报,2012,34(5):834―841.Deng Guohua,Shao Shengjun,She Fangtao.Modified Cam-clay model of structured loess[J].Chinese Journal of Geotechnical Engineering,2012,34(5):834―841.(in Chinese)
[22]罗战友,夏建中,龚晓南.不同拉压模量及软化特性的球形孔扩张问题的统一解[J].工程力学,2006,23(4):22―27Luo Zhanyou,Xia Jianzhong,Gong Xiaonan.Unified solution for the expansionof spherical cavity in strain-softening materials with different elastic moduli in tensile and compression[J].Engineering Mechanics,2006,23(4):22―27.(in Chinese)