王桂林(1970-), 男, 教授, 博士, 主要从事岩土工程研究, E-mail:
Wang Guilin (1970-), professor, phD. main research interest: geotechnical engineering, E-mail:
抗滑桩桩间形成的土拱是水平土拱和竖向摩擦拱的共同体现,具有明显的三维特征。利用颗粒流分析软件PFC3D建立数值模型,在桩后不同高度处及同一水平面不同位置设置一系列测量球,监测桩后土体应力变化情况。结合颗粒位移变化情况对抗滑桩桩间三维土拱效应的形成演化进行分析,并对土拱厚度的演化规律做了深入研究,提出结合相对位移和最大主应力等值线综合确定土拱厚度的新方法。分析表明:桩后土拱由桩间临空面靠近桩底开始并不断向土体内部和上部发展,土拱的破坏过程由桩底向桩顶扩展;土拱厚度随深度变化表现为沿桩底向桩顶先增加后减小的趋势;土拱厚度随时间的变化表现为随着加载时间增加,土拱厚度先增加后减小直至土拱破坏。
Soil arching between anti-sliding piles is the interaction of horizontal soil arch and vertical friction arch, with distinct three-dimensional characteristics. Numerical model by the particle flow code PFC3D was developed and a series of measurement balls to numerically monitor stress variations at different positions behind the anti-slide piles were set. Combined with the displacement of numerical model balls, we analyzed the formation process and evolution pattern of the soil arching effect were analyzed. Also the thickness of soil arch had been studied and finally we proposed a new method to determine the its thickness was proposed. The study shows that the soil arch initiates s from the free face near the bottom of pile and develops to the inner and upper part of the soil, and the failure process of arch expands from the bottom of pile to the top; The thickness of soil arch varies with depth, increasing first and then decreasing along the bottom of pile to the top; The thickness of soil arch varies with time. As the loading stage proceeds, the thickness of soil arch increases first and then decreases until the soil arch is destroyed.
土拱效应的研究与发展已经有100多年的历史, Roberts在1884年发现和提出“粮仓效应”,可看做拱效应的开端。土拱效应最初由Terzaghi[
随着计算机技术的普及与发展,运用数值模拟进行抗滑桩间土拱效应作用机理研究取得了长足发展。目前的研究多建立在已有合理拱轴线理论[
模拟抗滑桩桩间土拱的三维效应,将桩视为刚性墙体,桩后黏性填土视为离散圆球颗粒并将颗粒间链接设为接触黏结(contact bond),利用墙体来限制颗粒运动作为边界约束条件(
抗滑桩三维模型简图
Three-dimensional model sketch of anti-slide piles
模型参照董捷等[
黏性填土材料宏观参数
Macro-parameters of cohesive filling materials
重度/(kN·m-3) | 弹性模量/kPa | 内摩擦角/(°) | 粘聚力/kPa |
20 | 2×103 | 20 | 10 |
模拟常规三轴试验试件尺寸为高10 cm、半径2.5 cm的圆柱形,模型上下设置边界墙(wall)单元模拟加压过程,侧壁用圆柱形墙体单元(cylinder wall)模拟橡胶套筒并通过伺服保持恒定围压,如
三轴试验试件模型
Triaxial test specimen model
偏应力-应变曲线
Deviation stress-strain curve
摩尔强度包络线
The envelope line of Mohr strength
由摩尔应力强度包络曲线图可得到数值模型的抗剪强度参数粘聚力和内摩擦角分别为10 kPa和22°。最终确定模型的细观参数如
颗粒流模型细观参数
Meso-parameters of particle flow model
弹性模量 |
刚度比( |
摩擦系数 | 最大最小半径比 | 法向链接强度/Pa | 切向链接强度/Pa | 孔隙度/n | 密度/(g·m-3) |
2×106 | 2.0 | 0.20 | 1.66 | 8×103 | 8×103 | 0.29 | 2 000 |
采用三轴剪切模拟实验得到的细观参数,建立抗滑桩间土拱效应三维数值模型,取颗粒最小半径为0.014 m,共使用约17×104个球形颗粒模拟黏性土颗粒(
土拱效应可解释为桩土产生相对位移引起的桩后土体应力重分布现象,故可用土体颗粒位移量的差异来表示土拱的演化过程。付海平等[
撤去桩间挡土板并给加载墙施加水平方向的速度。由于加载墙速度恒定,因此,加载墙位移与计算时步成正比关系。计算100时步(局部受压阶段)时,由
抗滑桩深部(
Relative displacement of particles in deep part of anti-slide pile (
抗滑桩桩间对称面(
Relative displacement of particles on symmetrical plane (
继续计算至14 000时步时,由
计算14 000时步时的颗粒位移
Displacement of particles (timesteps=14 000)
继续运算,直至桩后土体出现垮塌,如
物理模型实验与数值模拟实验破坏结果对比
Comparison of damage results between physical model experiment and numerical simulation experiment
为了更直观地分析三维土拱的演化过程,在桩后高度
桩后
根据
土拱初步形成阶段:桩土相对位移较小,桩后土体局部受压,随着桩土相对位移不断扩大,桩背侧土体受到阻拦,且范围不断扩大,临近土体相互锲紧,并向后侧土体发展,形成具有较高承载力的且沿桩身均有分布的拱形结构,将此阶段定义为土拱初步形成阶段。此阶段的特点是桩后土体应力增加较快,荷载传递效率呈增加的趋势。此阶段出现在加载初期,加载墙位移不足2 mm时。
土拱稳定发展阶段:土拱雏形形成后,随着加载墙位移的继续增加,拱后土体密实度增加,土拱作用进一步增强。此阶段的特点是桩后应力增长变缓,荷载传递效率基本保持不变。该阶段持续时间较长,出现在加载墙位移达约2~15 mm期间。
土拱破坏阶段:土拱稳定阶段发展到后期,随着加载墙位移不断增大,土拱进一步挤密,达到土体抗剪强度,土拱发生破坏。此阶段的特点是桩后应力突然减小,荷载传递效率呈现降低的趋势。该阶段出现在加载墙位移达到约15 mm后。
土拱效应的产生与桩土间的相对位移密不可分,拱身部分土体在锲紧作用下密实度较高,而临空面附近由于没有约束,土颗粒位移较大,拱身和拱前土体可能会产生较大的相对位移,发展到后期甚至出现裂纹或形成贯通的滑动面,故可用土体颗粒相对位移来确定土拱前缘。
取土拱稳定发展阶段(
由相对位移确定土拱前缘
Determination of leading edge of soil arch by relative displacement
悬臂式抗滑桩土拱效应的空间特征十分显著,按照土拱的作用面将其分成水平拱、竖向拱和临空面拱。其中,水平面拱为大主应力偏转形成的大主应力拱并认为拱轴线上主应力处处相等,即拱轴线也是大主应力等值线。基于此假定,可以利用大主应力等值线确定土拱后缘。通过导出颗粒流数值模型中的应力张量,利用MATLAB求解最大主应力并生成二维等值线图,如
最大主应力等值线图确定土拱后缘
Determination of trailing edge of soil arch by contour map of maximum principal stress
将由上述方法确定土拱的前缘和后缘综合绘制在
土拱厚度
Soil arch thickness
在桩间对称面上
由
Stress monitoring on symmetrical plane between piles
在土拱稳定发展阶段,计算时步为4 000时步时,(加载墙位移约5 mm)分别取距桩底部0.1、0.5、1.0、1.5 m处的水平截面按照3.1节的方法确定土拱厚度,如
加载墙位移5 mm时不同深度土拱厚度
Thickness of soil arch at different depths when loading wall displacement 5 mm
根据
桩间对称面上土拱沿深度变化图
The change of soil arch along the depth on the symmetrical surface between piles
由于数值模型设置的加载墙一直在运动中,表现为桩后下滑力一直处在变化中,故土拱厚度随时间的变化规律更多的表现为土拱厚度在演化过程中的变化规律。
取计算时步为100、500、2 000、4 000、14 000分析桩后土拱效应随时间的演化。以抗滑桩中部(
Soil arch thickness at different time(
综上所述,在土拱的形成演化过程中,土拱的厚度具有明显的空间与时间变化规律。目前,对于土拱厚度的认知公认的是假定土拱厚度等于桩宽或者为桩宽的一半。这种做法显然具有一定局限性,首先,桩后不同深度处或者不同阶段时土体受力状态不同,所形成的土拱厚度也不同。当土拱处于稳定阶段时,土拱的厚度与桩宽相差不大,表明在精度要求不高的情况下,将桩宽作为土拱厚度也是可行的。
依据已有的桩间三维土拱效应物理模型试验,选取合理的模型尺寸与参数进行三维颗粒流模拟研究,得出以下结论:
1) 把抗滑桩当作刚性桩时,撤去抗滑桩间挡土板后桩底的土体首先产生位移,之后不断向土体内部和桩顶发展;土拱的破坏首先出现在桩底位置,并逐渐向桩顶发展。
2) 土拱厚度随深度是变化的,具体表现为桩底位置土拱厚度较小,中部土拱厚度最大,桩顶位置较薄。
3) 土拱厚度在滑体推力施加过程中是变化的。随着加载墙位移的增加,土拱厚度经历了由薄变厚再变薄的变化过程。
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